The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Federal
Reserve Bank of
New \brk
Quarterly Review
Summer 1988
Volume 13 No. 2
Studies on Equities Markets
1
Introduction and Summary
4
Evidence on Stock Market Speculative Bubbles:
Japan, the United States, and Great Britain
17
The International Transmission of Stock Price
Disruption in October 1987
34
International Linkages among Equities Markets
and the October 1987 Market Break
47
Margin Requirements on Equity Instruments
61
Consistent Margin Requirements: Are They
Feasible?
80
Margin Requirements and Stock Market Volatility
90
Treasury and Federal Reserve
Foreign Exchange Operations
This Quarterly Review is published
by the Research and Statistics Group
of the Federal Reserve Bank of New
York. An introduction to this
collection of studies on equities
markets begins on page 1. Among
the members of the staff who
contributed to this issue are GIKAS
HARDOUVELIS (on evidence on
stock market speculative bubbles:
Japan, the United States, and Great
Britain, page 4; and on margin
requirements and stock market
volatility, page 80); PAUL BENNETT
and JEANETTE KELLEHER (on the
international transmission of stock
price disruption in October 1987,
page 17); ROBERT ADERHOLD,
CHRISTINE CUMMING, and ALISON
HARWOOD (on international linkages
among equities markets and the
October 1987 market break, page
34); GEORGE SOFIANOS (on margin
requirements on equity instruments,
page 47); and ARTURO ESTRELLA
(on consistent margin requirements:
are they feasible? page 61).
A quarterly report on Treasury and
Federal Reserve foreign exchange
operations for the period May through
July 1988 begins on page 90.
Introduction and Summary
Since October 1987, a number of careful investigations
of the stock market crash have been prepared, and
each has added to our understanding of what did— and
what did not— occur. Studies have explored the rea
sons for the crash and have made recommendations
for preventing another such episode. The collection of
articles in this Quarterly Review represents an effort to
achieve a still better understanding of certain signifi
cant technical issues related to equity market perfor
mance. Many of the questions examined here have
been debated by economists and others for many
years and will no doubt be debated for years to come.
Looked at in that light, the results presented in these
papers are offered not as definitive answers to these
questions, but rather as contributions to the ongoing
discussion of the workings of equity markets here and
abroad.
The first three articles discuss the international char
acter of the crash. One is an econometric test of the
proposition that a particular form of speculative price
development, called “rational speculative bubbles” by
economists, preceded the crash in the United States,
the United Kingdom, and Japan. The next two pieces
analyze the worldwide transmission of the disruption
from one national stock market to another. The last
three articles examine the role of equity-related margin
requirements in the United States. One summarizes
the diverse margin rules in the various markets.
Another discusses the analytical and conceptual issues
surrounding the question of making margins “consis
tent” across markets. And the last piece introduces
some new evidence into the debate about how margin
requirements may affect stock market activity.
The stock market crash was a thoroughly interna
tional event, and its worldwide nature needs to be bet
ter understood. In the first article in this issue, Gikas
Hardouvelis examines the notion that the October
crash was preceded by the buildup of speculative price
movement in major world stock markets. Noting that it
is difficult to make an empirical distinction between
bubble-type price movements and movements based
on changes in fundam ental values, Hardouvelis
chooses to test a specific theoretical model of specula
tive behavior, rational price bubbles. With this
approach, he finds that the data are consistent with the
existence of such a speculative bubble in the United
States in the period before the crash. He finds similar
evidence in Japan, but concludes that the case for a
pre-October bubble in the United Kingdom is weaker.
Hardouvelis’ findings square with the widespread
opinion that in the months leading up to the crash,
stock prices in various centers had an upward bias that
was not related in obvious ways to economic funda
mentals. A somewhat loose but probably fair interpreta
tion of the statistical work is that the October fall in
stock prices was preceded by speculative trading activ
ity that pushed prices above their fundamentals; and,
once the correction was underway, it took on special
dynamics of its own.
In the second article, Paul Bennett and Jeanette
Kelleher focus on the dynamic interactions among
stock price movements in different countries during the
crash. Were the interactions characteristic of the
behavior of major stock markets during prior, less dra
matic periods of volatility? In what respects were the
worldwide relationships in October unique? Did recent
FRBNY Quarterly Review/Summer 1988 1
trends in cross-border trading and investments in
stocks influence these relationships?
Bennett and Kelleher estimate statistical equations
describing how major markets had interacted during
previous periods of stress. They find patterns that in
certain key respects suggest that the international
character of the downwaird break in stock prices in
October should not be regarded as especially surpris
ing. In the pre-October data, unusually high daily price
volatility in one market tended to coincide with aboveaverage volatility in other markets as well. Moreover,
when prices became especially volatile in episodes
prior to October 1987, the alignment of up and down
movements among markets became unusually close—
that is, foreign and domestic stock price movements
tended to become more closely correlated.
The growing internationalization of stock trading and
investment activities may have changed the patterns of
interaction among national stock markets in recent
years. Bennett and Kelleher find that price indexes in
major markets have in fact moved more closely
together in the 1980s than in earlier years, both on a
day-to-day and a month-to-month basis. They also
show that a given rise in daily volatility has, on aver
age, been associated with a greater increase in cor
relation between markets in the 1980s than in the
1970s. However, the propensity of high volatility in one
market to be associated with high volatility in others
was about the same in the two decades.
To relate their findings to the crash, the authors
examine how well their estimated relationships charac
terize the October interactions among major markets.
In October 1987, correlations of day-to-day price move
ments among key markets increased approximately as
they had in previous periods of high volatility. At the
same time, however, the spillover of volatility from one
market to another far exceeded even the substantial
extent of transmission predicted by the precrash rela
tionships. This aspect of the crash was unusual, partic
ularly because— as noted above— little evidence
existed in the precrash data to suggest that the pro
pensity of volatility to spill over from market to market
had risen in the 1980s.
Bennett and Kelleher’s findings support the view that
extreme price disruption in a major stock market is
systematically associated with disruption in other mar
kets. Thus, to the extent that the likelihood of exces
sive volatility can be reduced in any one major market,
other markets stand to benefit as well.
In the next article, Aderhold, Cumming, and Harwood
examine the possible roles of cross-border investment
flows and of stock trading in centers outside the home
market in promoting October’s simultaneous downturns
in major world stock markets. This analysis focuses on
2 FRBNY Quarterly Review/Summer 1988
the patterns of international stock trading flows and
price movements in the days surrounding the crash.
Although the methodology of this article differs signifi
cantly from that of the preceding piece, the two sets of
findings reinforce one another.
Aderhold, Cumming, and Harwood show that direct
international linkages—cross-border investments and
24-hour trading— played at most a limited role in the
simultaneous declines in major markets. Only in Japan
did cross-border selling by nonresidents appear to
exacerbate the crash significantly. Twenty-four-hour
trading seems to have been an important factor only
with regard to U.K. equities traded in the United States
in the form of American depositary receipts (ADRs);
price declines on these ADRs were transmitted into
U.K. share prices. Overall, however, the direct interna
tional linkages among the largest markets were not
developed enough to account for a dominant share of
total activity in those markets during the crash period.
Nevertheless, information links among major markets
are now extraordinarily good, and direct trading and
clearing linkages are in the early stages of develop
ment and likely to evolve further. The authors suggest
that the surge in foreign stock turnover in London dur
ing the crash hints at the broader potential for stream
lined international trading links to transmit price
reactions across markets in the future. Thus, while
direct trading and investment linkages were not the
principal cause of market interactions in the crash, the
trend toward worldwide integration is continuing, and it
may further increase the sensitivity of the major stock
markets to one another.
The last three articles in this issue take up topics
related to margin requirements on various equity
instruments. In “Margin Requirements on Equity Instru
ments,” George Sofianos outlines the structure of mar
gin requirements for stocks, stock options, and stock
index futures and options, not only for retail transac
tions but for professional trading as well. In the pro
cess of describing the margin rules, Sofianos’ piece
conveys the complex variety of approaches taken at
the various exchanges. The differences in rules reflect
not only differences in regulatory structures and in the
roles assigned to margin requirements, but also the
c u rre n t d iv e rs ity of c le a rin g and s e ttle m e n t
arrangements.
In the following article, Arturo Estrella provides some
conceptual guidance for assessing the adequacy and
consistency of equity-related margins among the
numerous classes of instruments, participants, and
trading arenas. He notes that whether margin levels
are adequate or whether a sufficient degree of consis
tency exists across markets depends on the purposes
assigned to margin requirements. Moreover, even when
the role of margins is reasonably well defined, consis
tency can be hard to define and evaluate.
Estrella illustrates this point by outlining an approach
to evaluating the relative adequacies of stock and stock
index futures margins, using protection of market integ
rity as the criterion. Briefly, his approach is to simulate
a variety of price outcomes and to compare how well
different systems of margins perform. The simulations
take into account the risk diversification in index
futures, the different amounts of time currently allowed
for margin payments in the various markets, and the
different levels and configurations of margin require
ments. On the one hand, the results indicate that the
cash market margins and the much lower initial futures
margins provide a similar degree of protection against
the possibility that price movements will exceed margin
buffers. On the other hand, the likelihood of large mar
gin calls is much greater in the futures market. Large
margin calls arguably carry the potential to accelerate
price movements or to raise concerns about the integ
rity of market participants and clearing mechanisms.
Thus the assertion that margins are effectively similar
in the two markets must be qualified to the extent that
the higher-leveraged futures margining system
depends on the ability to meet these sizable calls.
The need to assess the consistency of margins
across markets in light of the objectives sought in
imposing these requirements stands out especially
clearly with respect to equity-related options. Options
by nature can provide purchasers with greater leverage
than other instruments. Nevertheless, option buyers
stand to lose no more than their original premium pay
ment, whereas option sellers face potentially unlimited
risks due to price changes. If the goal of margin
requirements is narrowly defined as protection against
failed contract performance by writers of options, mar
gins on stock-related options can be set so that the
probability of losses exceeding margin buffers can be
made as small as for stocks. On the other hand, mar
gins set at levels consistent with an acceptably small
probability of contract failure by option writers might
also be consistent with a very high degree of implicit
leverage, that is, very high gearing of risk by option
purchasers. This high leverage in turn might conflict
with other purposes of margin requirements.
Estrella explains that the diversity of clearing and
settlement arrangements, which creates important dif
ferences among instruments in the timing of margin
payment flows, is another obstacle to achieving consis
tent margin requirements for different equity-related
instruments. More margin is needed to protect against
losses when it takes several days to collect additional
margin calls than when it takes only a few hours.
Estrella concludes that determining proper degrees of
consistency and adequacy for margin requirements
must involve a large measure of good judgment in
addition to technical analysis.
The link between the purpose of margins and their
adequacy and consistency highlights another important
issue: How much can margin requirements realistically
be expected to accomplish? However important any
one goal for margin requirements might appear, the
question remains whether the tool can help with the
job. In the final article in this issue, Gikas Hardouvelis
examines the argument that margin requirements help
protect the stock market by reducing excessive price
volatility.
Hardouvelis investigates how the volatility of stock
price movements since the 1930s has changed as Fed
eral Reserve initial margin requirements have changed
over the same period. His statistical results are consis
tent with the notion that higher margin requirements
can help to reduce volatility. However, volatility of stock
prices is not necessarily undesirable if it reflects
changes in underlying determinants of values. There
fore, he extends his statistical formulation to control for
volatility of fundamental influences on stock prices. He
also adjusts for the historical propensity of the Federal
Reserve to react to volatility in setting margin require
ments. The simple relationship between stock price
volatility and margin requirements could be a distorted
indicator of the effect of margins on volatility, since
margin requirement levels traditionally have been
adjusted partly in response to erratic price changes.
A fter s tatistically controlling for these factors,
Hardouvelis finds that the original inverse relationship
between margins and volatility holds up.
As noted earlier, the purpose of these articles is not
to suggest that they— individually or collectively—are
the final word on the various technical aspects of
equity market behavior addressed in this issue. How
ever, taken as a whole, they should provide insights
and suggest new lines of inquiry as observers,
analysts, and policymakers seek a better understand
ing of the complex forces at work in equity markets in
the United States and elsewhere.
FRBNY Quarterly Review/Summer 1988 3
Evidence on Stock Market
Speculative Bubbles: Japan, the
United States, and Great Britain
The sudden worldwide collapse of stock prices in Octo
ber 1987 has puzzled observers of financial market
developments. President Reagan commented that the
fall had nothing to do with the economy. Market
analysts described the event as “absurd” or as “mind
less herd movement.” Indeed, it is hard to justify such
a large drop in stock prices. Economists typically
attribute large swings in stock prices to the impact of
important economic news on financial markets. New
information can cause investors to make drastic reas
sessments of the size of future cash flows or the future
discount rates at which these cash flows are cap
italized. But the adverse economic news that preceded
the fall in stock prices on Monday, October 19, 1987
does not appear dramatic enough to have caused the
unusual drop of 23 percent.1
The view that the stock price collapse cannot be
explained by economic fundamentals leads to the
question, Did the collapse represent an abrupt down
ward correction of an overvalued market or did the
market become grossly undervalued after prices fell?
This article focuses specifically on the possibility of
overvaluation before the October crash in the three
major national stock markets of the United States,
Japan, and Great Britain. It proposes a new method of
detecting market overvaluation and finds evidence con
sistent with this phenomenon.
’The adverse news included the disappointing U.S. trade deficit
figures announced the previous Friday and reports of a possible tax
law that would negatively affect mergers and acquisitions.
4
FRBNY Quarterly Review/Summer 1988
Overview
Persistent market overvaluation followed by market col
lapse is often referred to as a speculative bubble. Such
bubbles may be triggered by an extraneous event that
is unrelated to fundamental economic conditions; one
group of investors buys with the expectation of a large
capital gain, and others follow suit, without paying
proper attention to economic factors such as future div
idends or interest rates. If such behavior persists, it
may feed on itself as consecutive waves of buying
increase prices. Speculative bubbles may subsequently
burst very suddenly; an overvalued market is fragile
and a relatively unimportant piece of “bad” news may
easily create pessimism and set off a selling wave.2
The traditional method of searching for market over
valuation or speculative bubbles counts the number of
unusually high returns during the suspected bubble
period and assesses the likelihood that the total
number of these high returns could have arisen from
chance.3 An unusually high return (or a positive “abnor
mal” return) is a return higher than the risk-free rate
plus the usual risk premium necessary to compensate
2Note that although the general description of a speculative bubble
assumes some sort of collective market irrationality, irrationality is not
a necessary characteristic of a speculative bubble. In a special case
described later, agents know the market is overvalued but they
remain in the market because they expect to be compensated for
staying in an overvalued market.
3Olivier J. Blanchard and Mark W. Watson, "Bubbles, Rational
Expectations, and Financial Markets,” in Paul Wachtel, ed., C rises in
the Econom ic an d Financial S tructure (Lexington, Massachusetts:
Lexington Books, 1982), chap. 11, pp. 295-315.
risk-averse stockholders for the uncertainty associated
with their security returns. In the absence of a specula
tive bubble, a very large number of unusually high
returns would normally occur by chance only with a
small probability. Hence a large number of unusually
high returns constitutes evidence consistent with the
presence of speculative bubbles. Unfortunately,
although simple, the traditional test has low statistical
power to detect speculative bubbles: Stock prices are
very volatile and their swings generate both large posi
tive and large negative returns. The latter tend to mask
any existing bubble evidence.
In order to construct a more powerful test for bub
bles, it is necessary to formulate a more precise eco
nomic account of the development of the bubble. One
can imagine many different scenarios of market over
valuation, but this analysis restricts the possible sce
narios to those in which investors know that the market
is overvalued yet show no special desire to liquidate
their positions and continue to buy or sell as they
would in the absence of bubbles. This is a realistic
working assumption for the period before October
1987. Robert Shiller provides survey evidence indicat
ing that before October 1987, 71.7 percent of individual
investors and 84.3 percent of institutional investors
thought that the market was overvalued at the time.4
Explaining why investors did not get out of an over
valued market is more difficult. One could argue that
the presence of highly liquid futures markets and asso
ciated trading strategies such as portfolio insurance
led investors to the false belief that they could enjoy
large positive returns in an upward market yet still
avoid suffering a large loss if the market took a big
plunge.5 This article, however, pursues an explanation
that does not depend on some sort of collective irra
tionality. Academic economists call it the “rational
speculative bubble” hypothesis.
♦The survey results are described in Robert J. Shiller, “Investor
Behavior in the October 1987 Stock Market Crash," National Bureau
of Economic Research, Working Paper no. 2446, November 1987. The
survey was conducted after the crash, so there is reason to suspect
that the respondents’ answers were influenced by the crash. Shiller
also reports consistent answers to a similar question: only 36.1
percent of individual investors and 22.2 percent of institutional
investors described themselves as bullish and optimistic relative to
other investors before October 1987.
*The expression portfolio insurance is a misnomer for a dynamic
portfolio allocation strategy designed to guarantee a specified
minimum return. The strategy assumes a liquid market where one
can sell stocks whenever the need arises. Portfolio insurance can
work well when the number of insurers is small and they cannot
influence the market. But when the same technique is employed by
many insurers, liquidity in the market is destroyed. This is particularly
true when noninsurers act in anticipation of what portfolio insurers
will do. Thus portfolio insurers who assume the presence of a liquid
market suffer from irrationality. The October 1987 stock market
collapse provided an example of portfolio insurance failure exactly at
the time the insurance was needed most.
In the case of a rational speculative bubble, investors
know that the bubble may crash and that they will not
be able to get out once the crash starts, but they
remain in the market because they believe—for what
ever reason—there is good probability that the bubble
will continue to grow, bringing them large positive
returns. These returns are expected to be higher than
the risk-free rate plus the usual risk premium in the
absence of bubbles, and large enough to compensate
them exactly for the probability of a bubble crash and a
large onetime negative return. Hence it is rational for
investors to stay in the market. The expected extra
return when no bubble crash occurs can be called the
“bubble premium.” The theory implies that the bubble
premium is not only positive, but also increases during
the lifetime of the bubble. The time trend in the bubble
premium derives from the explosive nature of the bub
ble component of the stock price. As time goes on, the
bubble component of the stock price grows larger and
larger relative to the fundamental component. This
growth implies that with the passage of time, the
expected drop in the stock price in the case of a bub
ble crash grows larger too, necessitating a larger and
larger bubble premium.
The evidence points to a positive and rising bubble
premium for approximately a year and a half before
October 1987 in the national stock markets of the
United States and Japan. A positive and rising bubble
premium is also present in the national stock market of
Great Britain, but it appears much later, in mid-1987.
Overall, the evidence is consistent with the hypothesis
of rational speculative bubbles.
The nature of rational speculative bubbles
This section provides an intuitive description of a ratio
nal speculative bubble. A more detailed mathematical
example is presented in the accompanying Box. Recall
that a rational speculative bubble is a special case of a
speculative bubble. The characteristic that makes a
speculative bubble rational is the particular size of its
expected rate of growth. The expected rate of growth
of a rational speculative bubble is such that investors
have no incentive to get out of the market, although
they know the market is overvalued.
Rational bubbles and investor behavior
To understand how a rational speculative bubble works,
let us consider a concrete example: Suppose that
investors require a rate of return of 10 percent in order
to invest in the stock market. This required rate of
return of 10 percent equals the risk-free rate that they
could get by investing, say, in Treasury bills or eurodol
lars, plus an extra return that represents a compensa
tion for the risk they assume when investing in stocks,
FRBNY Quarterly Review/Summer 1988 5
Box: An Example of a Rational Speculative Bubble
For expositional simplicity, assume that the sum of the
risk-free rate and the risk premium is constant over time
and equals r. The presence of a time-varying risk-free
rate or risk premium does not affect the main point of
the example. Rationality of behavior and of expecta
tions, together with market clearing, implies that the
expected rate of return on a stock equals the required
rate r:
The following example, advanced by Blanchard,
realistic scenario of a bubble that grows for some
but eventually bursts:^
(B6)
bt+1 = (1/q) (1 + r) b, + vt+1
with probability
vt+1 with probability
with E,vt+1 = 0.
(B1)
In each period the bubble continues with probability q
or crashes with probability 1-q. It is straightforward to
check that the bubble process B6 satisfies the condition
E,bt+1 = (1 + r) b„ that is, the bubble is expected to grow
at the rate r. However, on the condition that the bubble
does not crash, the bubble is expected to grow at a rate
higher than r: Etbt+1|NC = (1/q)(1 + r)bt. This implies that
conditional on the event of no bubble crash, markets
expect to receive a rate of return higher than r. This
extra expected return is the bubble premium.§
The bubble premium is positive and increasing with
time. To clarify these two properties of the bubble pre
mium, let us continue the example by assuming that
expected dividend payments are constant:
(B7) dt+i = d + ut+i, with E,+I_1ut+I = 0, i = 1, 2, ...
EtRt+1 = r,
Rt+1 = (pl+i - pt + dt+1) / pt,
where p denotes the stock price, d the dividend, and E,
the expectations operator at time t. Rearranging the
expected arbitrage condition, B1, yields:
(B2)
pt = (1/(1+ r)) E,pt+, + (1/(1+ r)) Etdt+,-
Substituting for pt+1 in equation B2 and continuing
recursively, one can derive the familiar present value
model, which states that the price equals the infinite
sum of expected future dividends discounted at the
required rate of return r :f
(B3)
p*t = f [1/(1 + r tf E,dt+i.
i= 1
Here p*t is the “ market fundamental value” of the stock.
Note, however, that p*t is not the only solution to B2.
Any p, of the following form is a solution as well:
(B4)
p, = p*t + b„
with Etbt+1 = (1 + r) bt.
To see that equation B4 is a solution, observe that
according to B4, pt+1 = p*,+1 + b,+1. Then, substitute p,
and pt+1 in B2 and check that B2 is satisfied. Equation
B4 says that the market price can deviate from the mar
ket fundamental value by b„ a bubble component, with
out violating the expected arbitrage condition B2 or B1.
The intuitive reason why a bubble component can exist
is straightforward: arbitrage conditions in financial mar
kets are expressed in terms of rates of return, not in
terms of price levels. Therefore, even if an asset is, say,
overvalued by an amount b„ it is still "rational” for an
investor to buy it, if the degree of overvaluation is
expected to grow every period at the rate r.
Observe that the characteristic that makes a bubble
rational is its expected rate of growth and not neces
sarily its actual rate of growth. Therefore, theory cannot
determine with precision the actual form of the bubble
process. A multiplicity of bubble processes may exist.
An obvious candidate is the following:
(B5)
bt+1 = (1 + r) bt + vt+1,
is a
time
q
1-q
In this case the fundamental component p*, is constant
over time and equals d/r, and the realized abnormal rate
of return during the lifetime of the bubble is:
(B8) Rt+1 - r = [(1 + r)((1-q)/q) b, + ut+1 + vt+1] / pt.
The expected abnormal rate of return conditional on no
bubble crash taking place, that is, the bubble premium,
is:
(B9) E,(Rt+1 - r | NC) = [(1 + r)(1-q)/q] bt/pt.
Equation B9 shows that the bubble premium is positive
and increasing with time. The term b,/pt is an increasing
function of bt. Since b, is itself rising as the bubble
unfolds, E,(Rt+1-r | NC) is increasing with time. Our test
exploits these two properties of the bubble premium. In
contrast, the Blanchard-Watson test exploits the fact
that the realized abnormal return in equation B8 is on
average positive. One of the reasons the BlanchardWatson test has low statistical power is the presence of
the noise terms ul+1 and vt+1, which are absent from the
bubble premium of equation B9.
E,vl+1 = 0.
The bubble process B5 satisfies the condition Etbt+1 =
(1 + r) bt but explodes to infinity with the passage of
time. Since the stock price cannot be infinite, the bub
ble process B5 is not realistic.
f i t is assum ed that the transversality condition holds, that is,
Et[1/(1 + r)']Pl+i = 0.
Digitized forFRBNY
FRASER Quarterly Review/Summer 1988
^O livier J. Blanchard, “ S peculative Bubbles, Crashes and
Rational E xpectations,” E conom ics Letters, vol. 3 (1979),
pp. 387-89.
§ln “ Rational Inflationary B ubb le s,” Journal o f M onetary
Economics, vol. 21 (January 1988), pp. 35-46, Behzad T. Diba
and Herschel I. Grossman argue that once a rational bubble
bursts, it cannot restart. However, they also show that a
rational bu bble can p e rio d ica lly shrink to a very small positive
number. For the purposes of this article, the distinction
between shrinking and bursting bu bbles does not matter.
the risk premium. Suppose also that investors expect
to receive a constant dividend equal to $5.0 each year.
Then, according to the present value model of stock
prices, the fundamental or bubble-free price of the
stock is $5.0/0.10 = $50.0. The price will stay at $50.0
as long as the required rate of return (the discount
rate) and the expected dividend remain constant. The
investors’ expected rate of return over their holding
period equals the expected dividend of $5.0 plus the
zero expected capital appreciation or depreciation,
divided by $50.0. Thus the expected rate of return is 10
percent, the same as the required rate of return, and
investors are satisfied.
Now suppose there is a bubble component on the
stock price equal to $4.0, so that the market price is
$54.0.6 For simplicity, let the holding period horizon of
investors be one year and assume that the probability
that the bubble will crash to zero during the year is,
say, 1/10, and the probability that it will continue after
the end of the year is 9/10. Normally, if investors know
the stock price is overvalued by $4.0, they will attempt
to sell the stock, driving its price down to the funda
mental level of $50.0. In the case of a general specula
tive bubble, investors stay in the market because they
do not pay sufficient attention to fundamentals and do
not know that the market is overvalued. However, in the
case of a rational bubble, investors know the market is
overvalued but have no incentive to sell because they
expect that the bubble component will grow and com
pensate them appropriately.7 Specifically, suppose that
if the bubble continues, it will reach the level of $4.89
at the end of the year. Then the expected level of the
bubble at the end of the holding period equals the
probability of a bubble crash times the value of zero8
plus the probability of no bubble crash times $4.89,
that is, 1/10 $0.00 + 9/10 $4.89 = $4.40. The expected
bubble level of $4.40 is exactly 10 percent higher than
the original level of $4.0 and implies an expected capi
tal gain of $0.40. It also implies that the expected rate
of return from the stock is $(5.0 + 0.4)/$54.0 =
10 percent, which is the rate of return required to sat
isfy investors. Thus, when the expected value of the
•For a discussion of how a bubble can start, see Diba and Grossman,
“Rational Inflationary Bubbles."
7lt is perhaps difficult to understand why investors expect the bubble
to grow in the state of no crash. However, the point of the example is
not to explain how such expectations are formed, but to show that
once these expectations are formed, they can be consistent with an
equilibrium in which the required rate of return is 10 percent.
■The bubble value of zero, that is, a return of the stock price to the
fundamental value of $50.0, is assumed only for purposes of
simplicity. It is possible that when a bubble crashes, the stock price
overshoots or undershoots its fundamental value. The example in the
Box allows for such possibilities by adding an error term to the
bubble component.
bubble at the end of the year is 10 percent above its
level at the beginning of the year, investors have no
incentive to get out of the market.
Positive bubble premium
Next, let us see how an unfolding rational bubble is
consistent with the presence of a positive bubble pre
mium. Recall that a bubble premium is the extra com
pensation that investors expect to receive while the
bubble continues to grow. In the previous example, the
rate of return investors expect to receive if the bubble
does not crash is $(5.0 + 4.89)/$54.0 = 10.91 percent,
and thus the bubble premium is 0.91 percent. The bub
ble premium is positive because it compensates inves
tors for the negative excess return in case the bubble
crashes. In the previous example, the expected return
in case of a bubble crash is $(5.0 - 4.0)/$54.0 = 1.85
percent, which implies a negative expected excess
return of -8 .1 5 percent. Observe that 9/10 (0.91 per
cent) + 1/10 (-8 .1 5 percent) = 0. This is the sense in
which the bubble premium exactly compensates inves
tors for the probability of a bubble crash and a nega
tive onetime excess return.9
Increasing bubble premium
The bubble premium is not only positive but also grows
progressively larger as long as the bubble continues.
This growth occurs because the bubble component
gets larger and larger relative to the fundamental com
ponent of the stock price. A higher bubble component
implies a larger loss in case of a bubble crash, an out
come which necessitates a larger bubble premium. To
clarify this point, let us continue the previous example.
Assume that at the end of the year the bubble reaches
the level of $4.89, which implies a new stock price of
$54.89. If the bubble crashes at the end of the second
year, investors expect to make a return of $(5.0 4.89)/$54.89 = 0.20 percent, which implies a negative
excess return of - 9 .8 0 percent. This expected loss,
larger in absolute terms than the corresponding excess
return of -8 .1 5 percent of the first year, necessitates a
larger bubble premium. The new bubble premium
•Clearly, the greater the probability of a bubble crash, the larger the
bubble premium. To understand this point, let the probability of a
bubble crash be 1/3 instead of 1/10. If investors are to stay in the
market, they must expect that so long as no crash occurs, the bubble
will grow from $4.0 to $6.6, or that the stock price will increase from
$54.0 to $56.6. The overall expected bubble level is (2/3) $6.6 +
(1/3) $0.0 = $4.4, which is 10 percent larger than the current bubble
of $4.0, as is the case in the example of the text. As in the text, the
expected rate of return from the stock (which equals the sum of the
dividend of $5.0 plus the expected capital gain of $0.4, divided by
the current price of $54.0) is 10 percent; thus, investors have no
incentive to get out of the market. However, the bubble premium is
larger. The bubble premium can be found from the expected rate of
return in the state of no crash, which is equal to $(5.0 + 2.6)/$54.0
= 14.07 percent. Thus the bubble premium is 4.07 percent and is
larger than the bubble premium of 0.91 percent in the text.
FRBNY Quarterly Review/Summer 1988 7
should be such that 9/10 times the bubble premium, bp,
equals 1/10 times 9.80 percent, that is, (9/10) bp =
(1/10) 9.80 percent. This equality implies a bubble pre
mium of (10/9)(1/10) 9.80 percent = 1.09 percent,
which is larger than the previous bubble premium of
0.91 percent.
To see the rising bubble premium in an alternative
way, recall that investors will have no incentive to liqui
date their positions if during the second period they
expect to receive their required rate of return of 10 per
cent. Since the stock price at the beginning of the sec
ond year is $54.89, investors are satisfied if in addition
to the $5.0 in dividends, they also expect the price on
the average to rise by $0.49 to $55.38, so that the
expected rate of return is ($5.0 + $0.49)/$54.89 = 10
percent. Now recall that the example assumes two
possible states, one with a bubble crash and one with
out. In the state of a bubble crash, the bubble compo
nent, currently at $4.89, will drop to zero, causing the
price to drop to $50.0. If investors are satisfied with an
overall expected price level of $55.38, they must
expect that in the state of no bubble crash, the price
will rise by $1.09 to the level of $55.98, so that the
expected price is (9/10) $55.98 + (1/10) $50.0 =
$55.38. Put differently, investors expect that in the
absence of a bubble crash they will make a return of
($5.0 + $1.09)/$54.89 = 11.09 percent. Thus the bub
ble premium is 1.09 percent and is higher than the bub
ble premium of the first year.
Realized abnormal return versus bubble premium
If at the end of the second year the bubble does not
crash, the example suggests that the price will rise to
$55.98 and investors will receive exactly their bubble
premium of 1.09 percent. In the example, the realized
abnormal return at the end of a year does not differ
from the bubble premium, a subjective expected abnor
mal return at the beginning of the year; thus, realized
abnormal returns are also positive and growing over
time. In practice, however, realized abnormal returns
are positive and growing over time only in an average
sense. For example, if the bubble does not crash, there
is no guarantee that at the end of the second year the
stock price will be $55.98. Many unforeseen events
occur that may affect the stock price, driving it either
above or below the level of $55.98. Thus, during the
lifetime of the bubble, realized abnormal returns will
fluctuate considerably, and this volatility may mask
their upward trend. Empirically, this volatility is partic
ularly problematic when the lifetime of the bubble is
short. In contrast, the bubble premium is not affected
directly by the volatility of the stock market. For this
reason, the empirical methodology focuses on the bub
ble premium.
8 FRBNY Quarterly Review/Summer 1988
The example discussed in this section has made a
number of simplifying assumptions. These include a
constant risk-free rate, a constant risk premium, and a
constant probability that the bubble will collapse even
as the bubble grows. These assumptions were made
for expository purposes only. They are not required for
the empirical analysis that follows.
Measurement of the bubble premium
The previous section showed that in the presence of
rational speculative bubbles, investors expect to
receive a positive bubble premium that increases over
time as the bubble unfolds. This section describes the
empirical measurement of the bubble premium. Recall
that the bubble premium is an extra return investors
expect to receive over their required rate of return, as
long as the bubble does not burst.
Methodology
Let R denote the realized rate of return of a stock,
which consists of the dividend payment during the
period plus the realized capital gain or loss at the end
of the period. During the lifetime of the bubble, R can
be decomposed into the following four components:
(1)
R = rf + rp + bp + e,
where rf denotes the risk-free rate, say, the eurodollar
deposit rate, an observable variable at the beginning of
the period; rp and bp denote the risk premium and the
bubble premium respectively, variables known subjec
tively to market participants at the beginning of the
period but not directly observable; and e denotes an
unanticipated random disturbance arising from unfore
seen events. The sum of the risk-free rate and the risk
premium represents the required rate of return, or the
discount rate. The sum bp + e is the realized abnor
mal return during the bubble period. The bubble pre
mium, bp, is zero during periods with no bubbles.
The sum of the bubble premium and risk premium,
bp + rp, represents the excess return over the risk
free rate that market participants expect to receive
provided that the bubble does not crash. The realized
excess return at the end of the period, R - rf, is what
market participants actually receive. The difference
between the actual and the expected excess return is
the disturbance e. If investors’ expectations are ratio
nal, then the disturbance e cannot be predicted at the
beginning of the period and has an expected value of
zero. Put differently, the assumption of rational expec
tations implies that the investors’ expected compensa
tion for assuming risk and investing in a bubble period,
rp + bp, is on the average equal to the actual compen
sation, R - rf. Thus the observable R - rf can be
spreads within or across countries. Volatility measures
are obvious empirical proxies for the risk premium, but
interest rate spreads are also good proxies for risk and
bubble premia. To understand this point, recall that
financial variables are the aggregate outcomes of
investors’ actions in financial markets. These actions
are motivated not only by investors’ expectations of
future profits but also by their willingness to assume
risk and their knowledge of a possible underlying bub
ble. Thus, in equilibrium, financial variables provide
information about the risk premium and the bubble pre
mium. For example, the spread between the Japanese
10-year government and industrial bond yields repre
sents a proxy for corporate risk; the spread between
the 12-month and 3-month eurodollar deposit rates rep
resents a proxy for the risk of a change in interest
rates 3 months hence.10
The holding period over which returns are calculated
is assumed to be either 3 or 12 months. Shorter hold
ing periods are perhaps more representative of the
horizons of active investors but are less useful for
used in conjunction with the assumption of rational
expectations in order to estim ate the unobservable
sum of the risk premium and bubble premium.
The sum of the risk premium and bubble premium
can be estimated by regressing R - rf on variables
known to market participants at the beginning of the
period. The regression equation decomposes R - rf
into a predictable component— an estimate of bp +
rp— and an unpredictable random component repre
senting news that develops after the beginning of the
holding period. The regression equation is as follows:
(2)
R -
rf = [a + b, x, + ... + bj x j + e,
where x1f
^ are variables known to market partici
pants at the beginning of the period. When this regres
sion is run over the sample period before the crash,
the regression fit—the estimated item in the brackets—
represents the excess return expected if no bubble
crash takes place and is a proxy for the sum of the risk
premium and bubble premium.
The inform ation variables x1( ..., Xj of the above
regression equation were chosen to maximize explana
tory power over the entire sample period (September
1977 through December 1987). They are financial vari
ables such as vo la tility measures and interest rate
10For more inform ation on the regression variables and the statistical
techniques that were em ployed, see the tech nical version of this
paper, entitled: “ Evidence on Stock Market S peculative Bubbles:
Japan, United States, and Great B ritain,” Federal Reserve Bank of
New York, Research Paper no. 8810, February 1988.
Table 1
Realized Excess Stock Returns
(Percent Return in Domestic Currency)
Three-M onth Holding Period
D ecem ber 1977 to March 1985
Mean
Standard deviation
Correlation with
Japan
United States
United Kingdom
April 1985 to D ecem ber 1987
Japan
United States
United Kingdom
Japan
United States
United Kingdom
10.1
25.0
3.1
29.7
8.4
31.4
22.6
44.9
9.7
44.0
7.6
49.7
1.00
0.24
0.39
1.00
0.52
1.00
1.00
0.58
0.64
1.00
0.88
1.00
Twelve-Month Holding Period
A pril 1985 to D ecem ber 1987
Septem ber 1978 to March 1985
Mean
S tandard deviation
Correlation with
Japan
United States
United Kingdom
Japan
United States
United Kingdom
Japan
United States
United Kingdom
9.8
11.6
2.9
15.7
9.8
12.2
33.1
20.6
17.1
10.3
19.3
12.6
1.00
0.30
0.32
1.00
0.61
1.00
1.00
0.37
0.29
1.00
0.75
1.00
Note: Excess stock returns are realized total returns, including dividends, minus the 3-month (12-month) eu rode posit rate of 3 (12) months
earlier. They correspond to R-rf of equation 2 in the text. All returns are annualized. Note that in the period M arch-A pril 1985, the
do lla r began a downw ard slide.
FRBNY Quarterly Review/Summer 1988
9
uncovering speculative bubbles because returns over
short periods have a large variance and are not easily
predictable.11 The large swings in stock prices over
short horizons would mask any evidence of a positive
and rising bubble premium.12 Note, however, that the
holding period assumption is only a practical tool and
11This technique of searching for bu bbles depends c ritic a lly on the
p re d ic ta b ility of stock returns because it utilizes the bubble premium,
w hich is an expected as op posed to a realized abnorm al return.
Financial econom ists have recently shown that contrary to the
tra ditiona l random walk hypothesis of stock prices, stock returns are
indeed predictab le, but over longer horizons. See Eugene F. Fama
and Kenneth R. French, "Perm anent and Temporary C om ponents of
S tock P rices," Journal o f P olitical Economy, vol. 96 (April 1988),
pp. 246-73; and Gikas A. H ardouvelis, “ M argin Requirements,
Volatility, and the Transitory Com ponent of Stock P rices," Federal
Reserve Bank of New York, Research Paper no. 8818, July 1988.
12S tock price volatility is more pronounced at the daily level. Thus it is
not surprising that Santoni was unable to find evidence consistent
with the presence of speculative bubbles when he examined daily
stock returns in the U.S. stock m arket before O ctober 1987. See Gary
S. Santoni, "The Great Bull Markets 1924-29 and 1982-87: S peculative
B ubbles or Econom ic Fundam entals?” Federal Reserve Bank of St.
Louis Review, Novem ber 1987, pp. 16-30.
does not affect the conclusions regarding the presence
of speculative bubbles.
Preliminary data analysis
Before turning to the estimation of the bubble premium
and the risk premium, it is instructive to perform a pre
liminary data analysis. Table 1 presents summary sta
tistics of the realized excess rate of return R - rf.
Consistent with the previous discussion, excess rates
of return are less volatile in the 12-month horizon than
in the 3-month horizon. Also note that after March
1985, excess rates of return increased, a necessary
development if bubbles are to be found.13
Table 2 presents summary information from prelimi13Data on eu rode posit rates represent London m idm orning rates (after
O ctober 1986 they are closing rates) during the last tra ding day of
the month and were provided by DRI. S tock returns are based on
national stock market indexes on the last tra ding day of the month.
For Japan and Great Britain, the data com e from the Morgan Stanley
C apital International Indices data bank. For the United States, the
data reflect the S&P 500 and com e from the C itibase data bank and
the Wall Street Journal.
Table 2
The Predictability of Excess Stock Returns
R -
rf = a + b, x, + . . . + b, x, + e
Sample: D ecem ber 1977 to D ecem ber 1987, 121 observations
________________________ Significance Level
Chow Tests
Periods
1 vs. (2 + 3)
Periods
1 vs. 2
Periods
2 vs. 3
Three-M onth Holding Period
R2
SEE
Test of
b, = . .. = b(= 0
Japan
United States
United Kingdom
.07
.13
.10
30.9 percent
31.9
35.1
.060
.000
.001
.002
.880
.260
.190
.020
.000
.001
.044
.007
.47
.16
.32
13.3 percent
14.3
10.5
.000
.427
.000
.000
.000
.000
.041
.001
.000
.000
.000
.003
TWelve-Month Holding Period
Japan
United States
United Kingdom
Notes: R2 is the coefficient of determ ination adjusted for degrees of freedom ; SEE is the regression standard error. S ignificance levels
lower than .050 constitute evidence for rejecting the null hypothesis. R is the annualized total gross return, and rf is the risk-free rate, that
is, the 3- or 12-month eurodeposit rate for each country and holding period. The estim ation uses ail overlapping observations with the
necessary adjustm ents; see Lars P. Hansen, “ Large Sample Properties of G eneralized M ethods of Moments E stim ators,” Econom etrica,
vol. 50 (July 1982), pp. 1029-54. Period 1 runs from D ecem ber 1977 through July 1982, period 2 from A ugust 1982 through March 1985,
and period 3 from April 1985 through Decem ber 1987. In the 12-month horizon of Japan, the sam ple begins in Septem ber 1978. The
inform ation variables x( are as follows: (1) for Japan, in the 3-month horizon: spread betw een 10*year Japanese governm ent bond yield and
3-month euroyen rate, spread between 3-month and 1-month euroyen rates, spread between 3-month and 1-month eurodollar rates, spread
betw een 10-year Japanese governm ent and industrial bond yields, and spread between 3-month eurodollar and euroyen rates; in the
12-month horizon: spread between Japanese governm ent 10-year bond yield and 12-month euroyen rate, spread between 12-month and
3-month eurodollar rates, spread between 12-month eurodollar and euroyen rates, and yen/dollar exchange rate volatility; (2) for the United
States, in the 3-month horizon: spread between 3-month and 1-month eurodollar rates, and spread between 3-month eurodollar and
eufoyen rates; in the 12-month horizon: lagged dependent variable, spread between 12-month eurodollar and europound rates, spread
between 12-month and 3-month eurodollar rates, and spread between 30-year and 5-year U.S. governm ent yields; (3) for the United
Kingdom , in the 3-month horizon: lagg ed dependent variable, spread between 12-month eurodollar and europound rates, and volatility of
U.K. stock prices; in the 12-month horizon: lagged dependent variable, europound rate, and spread between the 20-year and 5-year
British governm ent bond yields.
10
FRBNY Quarterly Review/Summer 1988
nary regressions utilizing the whole sample, including
postcrash data. Observe that the explanatory power of
the information variables, measured by the R2 statistic,
is much higher in the 12-month holding period. This
result is consistent with the finding of Fama and French
and others that stock returns are more predictable over
longer horizons. The table shows the results of testing
the hypothesis that all slope coefficents b,....... bj are
jointly zero: b, = ... = b, = 0. Zero slope coefficients
would imply that the sum of the risk premium and bub
ble premium is constant over time. In five of the six
cases the hypothesis is, however, rejected, an outcome
that shows that excess stock returns are partially pre
dictable and that, in the absence of bubbles, risk pre
mia are time-varying.
Table 2 also presents tests of structural change of
the param eters a, b,, ..., bj( with the break points
occurring in July 1982, the time when a bull market
began around the globe, and in March 1985, the time
when the dollar began a downward slide. Although
coefficient instability can be caused by the inability of
the information variables x,.......x; to capture the vari
ability in the risk premium adequately, it can also be
caused by the presence of speculative bubbles. The
tests reveal considerable instability, particularly at the
March 1985 break point, indicating that speculative
bubbles could be present after March 1985.14
Estimation
Let us turn now to the actual estimation of the risk pre
mium and the bubble premium. Regression equation 2
can be used to estimate the sum of the risk premium
14The presence of bubbles can cause instability, but the reverse is not
true: the presence of insta bility does not necessarily im ply the
presence of speculative bubbles. C oefficient insta bility can be
caused by many other factors.
C h a rt 1
Japanese Stock Returns
P e rc e n t*
8 0 ------------
I
I
12-month holding period
E x c e s s re turn R -rf
B ubble prem ium
'p lu s ris k prem ium
mium
-2 0
- 3 0 Ll l Ll i I n I i
1978
i
1979
1980
1981
1982
1983
1984
1985
1986
1987
*A n n u a liz e d ra tes o f re turn .
FRBNY Quarterly Review/Summer 1988
11
C hart 3
U.K. Stock Returns
P erce nt *
5 0 ------------------- 1------------------- 1-----12-m onth holding period
4 0 ----------------------------------------------
E xcess re turn R -rf
B ubble premium plus
3 0 ------------------------------------------- n
—20
1978
1979
1980
* A n n u a liz e d ra te s o f return.
12
FRBNY Quarterly Review/Summer 1988
1982
1983
1984
1985
1986
M
/JL
|U |
1987
and bubble premium. In order to partition the estimated
sum into its two separate components, it is necessary
to make two reasonable assum ptions: firs t, it is
assumed that during the earlier part of the sample
there were no speculative bubbles. This assumption
makes it possible to use the data of the earlier period,
specifically from September 1977 through March 1985,
in order to estimate the parameters a, b,, ..., bf of
equation 2 that characterize the evolution of the risk
premium.15 Second, it is assumed that the parameters
a, b,...... bj that characterize the risk premium over the
subperiod from September 1977 through March 1985
remain the same during the subperiod from A pril
1sThe assum ption that no bubbles were present before A pril 1985
sim plifies the exposition but does not invalidate the conclusion on the
presence of a bu bble after A pril 1985. If a bubble were present
during the earlier part of the sam ple, then the results of the article
would sim ply be interpreted as evidence that the bubble becam e
stronger after A pril 1985.
1985 through September 1987 and that any observed
changes are caused by the presence of a bubble.
These assumptions make it straightforward to esti
mate the risk premium over the period from April 1985
through September 1987. One simply utilizes the esti
mated parameters a, b,....... bf from the September
1977-March 1985 sample together with the information
variables of the April 1985-September 1987 sample.
Constructing the bubble premium involves estimating
a new set of parameters, a', b /, b2', ..., bj', over the
period from April 1985 through September 1987. The
bubble premium is calculated using the difference
between the new estimates a', b /, ..., bj' and the old
estimates a, b1t ..., bj, together with the information
variables of the later period. Specifically, the estimation
method allows for possible instability in the regression
coefficients throughout the April 1985 to September
1987 sample period through the use of a rolling regres
sion: beginning in April 1985, the coefficients of equa
tion 2 are reestimated every month, with a new month
added to the sample each time.16 Thus every month in
the post-March 1985 sample has an associated set of
regression coefficients. These coefficients, together
with the information variables of each month, provide
an empirical proxy for the sum of the risk premium plus
the bubble premium. Since the risk premium is already
estimated, one can promptly deduce the size of the
bubble premium by simple subtraction.17
Empirical evidence on rational speculative bubbles
Charts 1, 2, and 3 present plots of the realized excess
return R - rf (dashed black line), the risk premium
(solid colored line), and the post-March 1985 sum of
the risk premium and the bubble premium (solid black
line) for the national stock markets of Japan, the
United States, and Great Britain. A 12-month holding
period horizon is assumed in each case. Observe that
16A single regression over the A pril 1985 to S eptem ber 1987 period
allows for a more ab rupt change in the estim ated coe fficients from
the earlier period but does not allow the coe fficients to vary during
the A pril 1985 to S eptem ber 1987 period itself. It turns out that the
resulting bu bble prem ium from a single regression ig very sim ilar to
the one from the rolling regression.
17As noted earlier, one of the assum ptions underlying the m ethodology
is that the param eters of the reduced form equation 2 that de scribe
the time varia bility of the risk prem ium do not change during the
post-M arch 1985 suspected bu bble period. However, the mere
presence of bubbles should increase the riskiness of holding stocks.
In a rational bubble, investors expect the volatility of stocks to
increase as the bu bble unfolds because the size of the potential loss
(and gain) increases with time. Thus the con structe d bu bble premium
is the sum of two com ponents: the expected abnorm al return
conditional on no crash taking place plus the extra risk prem ium due
to the presence of bubbles. The presence of this extra risk premium
does not affect the interpretation of the results, however, because it
cannot exist w ithout the presence of rational bubbles; if it exists, it
indicates the presence of a bubble.
FRBNY Quarterly Review/Summer 1988
13
after 1985, realized excess returns are positive in all
three countries. Indeed, during the last three years
investors received higher rates of return in the stock
markets than in the eurocurrency markets, a finding
that suggests but does not constitute firm evidence
that speculative bubbles are present. Evidence for the
presence of speculative bubbles would be a positive
and rising bubble premium. Recall that the bubble pre
mium is an expected excess return over and above the
risk-free rate plus the risk premium and is present only
during the lifetime of the bubble. In Charts 1, 2, and 3
the bubble premium is the gap between the two solid
lines after March 1985; for clarity, it is plotted sep
arately in Chart 4.
Chart 4 shows that, indeed, the bubble premia are
positive and increasing with time. Japan and the United
States show the strongest bubble evidence, and in both
countries the evidence is stronger when a 12-month
holding period is utilized. In Great Britain the evidence
is mixed because in the 3-month holding period the
bubble premium becomes positive only after mid-1987.
To confirm the upward trend of the bubble premium,
one can regress the bubble premium, bp, on a linear
time trend:
(3)
bp = c + d TIME + u,
and test the hypothesis that the slope coefficent, d, is
positive. Table 3 presents the regression results. In all
six cases the slope coefficients are positive and signifi
cantly different from zero and thus confirm the positive
evidence of the charts on the existence of rational
speculative bubbles.
Table 3 also presents results from regressions in
which the dependent variable is the realized abnormal
return, bp + e, instead of the expected abnormal
return, bp. These results offer similar evidence of an
upward trend, but the evidence is relatively weak. As
noted earlier, the noise term e creates excessive vol
atility and tends to mask the upward trend.18
This method of detecting speculative bubbles differs
significantly from the traditional method of counting the
number of abnormal positive returns, bp + e. The
traditional test requires independent observations and
thus, if an adequate number of observations is to
1®The sam ple in Table 3 begins in January 1986 because earlier
estim ates of the bubble prem ia tend to be negative and thus result in
an overestim ate of the upward trend in the bu bble premia.
Table 3
Is There a Time Trend in the Bubble Premium?
Sample: January 1986 to S eptem ber 1987, 21 observations
bp = c + d TIME + u
bp + e = c' + d' TIME + v
c
d
R2
SEE
c'
d'
R2
SEE
Three-m onth holding period
Japan
-6 .8 8
(5.57)
.77*
(.24)
.43
5.4
5 6 .1 4 t
(31.21)
- 1 .3 2
(1 5 8 )
- .0 1
38.8
U nited States
- 0 .4 3
(1.14)
.13*
(.05)
.36
1.0
10.30
(19.28)
.21
(.83)
-.0 5
26.3
-1 4 .3 4 *
(5.45)
.39*
(.19)
.21
4.2
-9 2 .7 1 *
(46.23)
3.17*
(1.35)
.23
33.2
Japan
- 7 .3 9 *
(1.09)
.63*
(0 5 )
.91
1.2
12.74
(14.26)
1.72*
(.74)
.29
15.8
U nited States
-4 .8 1 *
(.56)
.52*
(.03)
.89
1.1
7.21
(4.48)
.92*
(.22)
.47
5.9
United Kingdom
-2 .6 4 *
(0.39)
.10*
(.01)
.70
0.4
-1 5 .1 0
(13.75)
.81 f
(-43)
.18
9 7
U nited Kingdom
Twelve-m onth holding period
‘ S ignificant at the 5 percent level.
•[Significant at the 10 pe rcent level.
Note: bp is the bu bble premium , the expected abnorm al return conditional on no bu bble crash taking place, and bp + e is the realized
abnorm al return (see equation 1 of the text). R2 is the coe fficient of determ ination adjusted for degrees of freedom . SEE is the
regression standard error. Numbers in parentheses are corrected OLS standard errors; the correction is due to the overlapping
intervals.
14
FRBNY Quarterly Review/Summer 1988
be obtained, can only be performed using the 3-month
holding period. There is only a maximum of two non
overlapping observations in the case of a 12-month
holding period. Table 4 tabulates the realized abnormal
returns, bp + e, for the 3-month holding period. Take,
for instance, the subperiod January 1986 to September
1987, which contains seven nonoverlapping observa
tions. In Japan, the holding period sequence JanuaryApril-July-October shows four positive and three nega
tive abnormal returns, while the other two holding
period sequences, February-M ay-August-Novem ber
and March-June-September-December, show five posi
tive and two negative abnormal returns. Clearly, one
cannot reject the null hypothesis that these abnormal
returns were generated by chance. For example, the
case of five positive abnormal returns out of seven
Table 4
Realized Abnormal Returns*
A pril 1985 to S eptem ber 1987
Three-Month H olding Period
(In Percent)
Date
Japan
United States
United Kingdom
1985
April
May
June
July
August
S eptem ber
O cto ber
November
D ecem ber
- 4 .8 0
- 2 .3 0
- 7 .6 0
11.78
- 1 7 .9 6
- 2 6 .2 7
- 4 .9 9
- 2 6 .2 8
-1 0 .2 2
- 1 6 .3 9
- 4 .5 5
6.87
4.86
-1 9 .4 0
-3 8 .8 6
- 2 1 .1 3
11.87
44.54
- 6 .7 6
2.88
-3 5 .2 7
- 3 5 .1 2
-1 6 .6 4
-2 2 .9 4
- 2 .2 8
- 7 .8 4
7.43
1986
January
February
March
A pril
May
June
July
August
Septem ber
O cto ber
November
Decem ber
- 1 5 .9 8
13.51
74.07
71.29
67.69
- 2 .2 5
39.98
68.83
62.10
- 4 .8 3
-2 2 .0 0
- 8 .2 0
18.91
28.45
37.17
34.27
22.02
8.00
- 1 1 .8 0
- 4 .4 2
- 4 1 .0 2
- 1 .4 7
- 1 9 .0 3
2.34
-1 3 .1 1
- 3 .2 7
42.27
18.24
- 2 4 .0 2
- 1 4 .0 0
-3 8 .0 4
- 1 7 .1 7
- 6 5 .8 3
- 2 8 .5 2
- 3 5 .0 7
- 1 1 .7 0
1987
January
February
M arch
A pril
May
June
July
August
S eptem ber
77.58
58.64
60.56
57.92
62.49
9.90
-3 6 .4 5
- 1 5 .9 9
5.36
33.46
46.00
73.17
5.74
- 5 .1 5
2.32
25.23
41.02
8.59
19.01
46.66
54.20
37.19
53.31
68.84
63.63
10.61
19.20
•Realized abnorm al returns refer to bp + e of equation 1 in the
text. They are annualized.
returns can arise from chance with probability 0.227.19
In the United States, the number of positive abnormal
returns is five for the first holding period sequence,
four for the second, and six for the third. In Great Bri
tain, the evidence against the likelihood that the results
could be due to chance is the weakest: four positive
abnormal returns in the first sequence, three in the
second, and four in the third. Overall, these findings
show that the traditional runs test is unable to reject
the null hypothesis of no bubbles. The procedure of
relying on bubble premia clearly has more power.
Finally, it should be noted that the hypothesis of
rational bubbles cannot predict how much a market
would collapse once a bubble bursts. Although the
example presented in the Box assumes that the market
returns to its fundam ental value afte r the bubble
bursts, the market could, in reality, overshoot or under
shoot its fundamental value. For example, in October
1987 the U.K. market that had earlier shown weak bub
ble evidence fell by about as much as the U.S. market,
a lth o u g h th e la tte r had show n s tro n g b u b b le
evidence.20
Conclusion
Despite the difficulty of uncovering speculative bubbles
from the data, this article isolated evidence consistent
with the hypothesis of rational bubbles in the national
stock markets of Japan and the United States before
the October crash. In Great Britain the evidence is
somewhat weaker. Evidence for the presence of ratio
nal bubbles is a p o s itiv e and in cre a sin g bubble
premium, which market participants require in order to
invest during a bubble period. During the lifetime of a
rational speculative bubble, market participants expect
to receive positive abnormal returns (bubble premia) as
compensation for the probability of a bubble crash and
19This is the pro b a b ility of obtaining two or less negative tickets (five
or more positive tickets) when draw ing seven tim es with replacem ent
from a box that contains two tickets, one positive and one negative.
There are 128 possible sequences of positives and negatives, out of
which 1 sequence contains exactly zero negatives (seven positives),
7 sequences contain exactly one negative (six positives), and 21
sequences contain exactly two negatives (five positives).
Thus (1 + 7 + 21) / 128 = 0.227.
“ Those who question the rational bubbles hypothesis as a general
cha racte ristic of stock m arket fluctuations ty p ic a lly argue that any
evidence interpreted as a rational bubble can also be interpreted as
arising from the econom etrician's ignorance about un observable
market fundam entals. For a review of such arguments, see James D.
Hamilton, "On Testing for Self-Fulfilling S peculative B ubb le s,”
International Econom ic Review, vol. 27 (O ctober 1986), pp. 545-52.
Although this criticism of speculative bubbles is plausible in general,
it cannot be easily a p plied to the specific evidence in the text. It is
very hard to con struct a story based on fundam entals that can
explain both the sudden collap se of stock prices in O cto ber 1987
and the previous upward trend. This d ifficu lty becom es im m ediately
evident once one tries to use H am ilton’s examples.
FRBNY Quarterly Review/Summer 1988
15
a large onetime loss. The size of the bubble premium
grows over time as the bubble unfolds because the
degree of market overvaluation rises. As the magnitude
of the potential loss during a crash increases, investors
require progressively larger compensation. Indeed, the
data show a positive and rising bubble premium for one
16 FRBNY Quarterly Review/Summer 1988
and a half years before October 1987 in the national
stock markets of Japan and the United States, and for
half a year before October 1987 in the national stock
market of Great Britain.
Gikas A. Hardouvelis
The International Transmission
of Stock Price Disruption in
October 1987
One of the most striking features of the October 1987
collapse of equities prices was its worldwide scope.
During the month of October, prices in many countries
dropped even more than in the United States (Table 1),
and day-to-day volatility reached extraordinary levels in
many markets. Thus an adequate understanding of the
event must include some grasp of why the disruptions
so quickly circled the globe.
Were the spillovers of huge, correlated price move
ments typical of how world stock markets tend to inter
act under stress? Or, alternatively, were the market
interactions of October 1987 unprecedented? Is it likely
that future price disruptions would spread worldwide?
This article presents evidence that the interactions
among international stock price movements during the
October crash were in certain respects similar to the
reactions of major markets to volatility in the past. Our
principal findings are as follows:
• The statistical evidence from before October 1987
clearly shows that when one major market experi
ences particularly large price changes, other coun
tries’ stock prices will typically be subject to higher
volatility also.
• Nevertheless, in last year’s crash, the spread of high
volatility from one major market to another was con
siderably greater than the earlier statistical relation
ships would have predicted.
• The pre-October 1987 evidence also indicates clearly
that, when volatility is high, the price swings in major
markets tend to become more highly correlated. That
is, even well before the crash, when price swings in
major markets became enlarged, they also became
increasingly likely to go in the same direction.
• During the crash period, these correlations between
up and down price movements generally increased,
in accordance with the earlier, precrash pattern.
• Viewed from a longer time perspective, stock price
movements in major markets have become increas
ingly similar in the 1980s, compared to the 1970s and
before. This development appears generally consis
tent with the ongoing strengthening of cross-border
trading, listings, and investment activities. The
increased similarity of price moves has been com
paratively small, however, and does not appear to
have decisively influenced how markets interacted in
October 1987.
In short, while the crash was qualitatively similar to
prior episodes in that the volatility spread from market
to market and correlations among some markets
strengthened, the particular degree to which volatility
spread was unusual. Indeed, in this respect, the Octo
ber pattern of market interactions was unique, yet not
easily attributable in a direct sense to the trend toward
integrated world equities markets.
Market volatilities and correlations
The interaction among stock markets can be charac
terized by assessing the volatilities of prices in differ
ent markets and the degree to which day-to-day price
movements are correlated with one another. Volatility is
a statistical characteristic of price behavior in a single
market. In this article, volatility is measured as the
FRBNY Quarterly Review/Summer 1988 17
standard deviation of daily percent price movements.1
Correlation is a statistical attribute of a pair of markets.
Here, correlation is measured as the correlation coeffi
cient between percent changes in price indexes for
pairs of markets.2
Note that a high correlation between price move
ments in two markets does not necessarily imply that
they experience similar volatilities. It may be, for exam
ple, that even though two markets tend to move up and
down at the same time, the size of the movements in
one market (its volatility) is much greater than in the
other.
To begin, let us review how volatilities and correla
tions behaved during the October 1987 crash. Chart 1
shows the volatility of daily price changes during 30day periods in four equities markets. It is evident that
1A “ standard de via tion” is a statistica l measure of the amount of
dispersion in a p a rticular series of numbers. For example, if daily
price changes have a standard deviation of, say, 1 percent, then it is
typ ica l for prices on a given day to rise or fall 1 percent above or
below the average underlying trend.
*The “ correlation co e ffic ie n t” is a statistic that varies between minus
one and plus one. A value near zero means that da ily percent
m ovements in two markets bear essentially no relationship to each
other during the period. A positive value means that when one
m arket rises at more than its trend rate, the other on average rises
above its trend rate as well. A positive value close to one means that
when-one m arket's rise equals one standard deviation above its
trend, then the other market can on average be expected to rise at
close to one standard deviation above its trend as well.
Table 1
October 1987 Changes in World Stock Prices*
Country
A ustralia
Hong Kong
Singapore Malaysia
M exico
Norway
United Kingdom
Spain
S w itzerland
Belgium
West Germany
N etherlands
France
C anada
U nited States
Sweden
Italy
A ustria
Japan
D enm ark
Percent
S tock
Price
Change
- 5 8 .3
- 5 6 .3
-4 0 .1
- 3 8 .7
- 2 9 .8
-2 6 .1
-2 5 .5
- 2 3 .4
-2 3 .2
-2 2 .9
- 2 2 .6
- 2 2 .0
- 2 1 .8
- 2 1 .5
- 2 0 .7
- 1 5 .5
- 1 4 .9
-1 2 .6
-1 2 .6
‘ Percent changes betw een S eptem ber 30 and O ctober 31,
1987, local currency indexes; data from Morgan Stanley C api
tal International.
18
FRBNY Quarterly Review/Summer 1988
the volatilities of daily price movements rose sharply
and virtually simultaneously in major markets around
the time of the crash. Chart 2 shows the correlation,
coefficients of daily price movements, also during 30day periods, in three pairs of stock markets. The chart
reveals that the October 1987 correlation between U.S.
and Japanese stock price changes was higher than
average. Between the United States and the United
Kingdom, correlation was moderately above average,
but the correlation of daily price movements in the U.S.
and German markets was slightly below average.
How should this October pattern of volatilities and
correlations be interpreted? Unfortunately, pure eco
nomic theory does not provide simple rules on how
stock prices in different countries should interact,
either routinely or under stress. Economic forces that
benefit companies listed in one country could either
help or hinder companies listed elsewhere. Changes in
exchange rates, for example, could conceivably make
one stock market go up and another go down. On the
other hand, it is possible that a jolt in oil prices might
affect a number of major markets similarly.
It is also the case that some stock traders may react
not only to relevant news and announcements but also
to foreign stock price movements themselves. As Chart
2 shows, economic events and trading patterns have
most often caused stock prices in different major mar
kets to be positively correlated. To some extent this
positive correlation might become self-reinforcing if it
prom pts dom estic traders to adopt a condition ed
response to foreign price change even when they do
not fully understand its source. Indeed, in the face of
particularly large price swings abroad, such responses
by domestic traders could dominate domestic price
movements as well. Thus it seems plausible that, within
short time horizons, high price volatility in one market
could lead to increased volatility in a second market,
with unusually high correlation between the price
movements.
The October 1987 collapse may have been a partic
ularly important example of traders’ quick responses to
foreign price changes not easily explained by adverse
news or economic fundamentals. Large price swings in
one market may thus have led directly to similar large
swings in another.
This article explores the extent to which the October
1987 pattern of responses was typical. In the sections
that follow, we seek to determine whether earlier epi
sodes of high volatility were associated with increased
volatility in other major markets. We also investigate
whether correlations among price movements rose dur
ing previous periods of high volatility. Clearly, the rela
tive importance and qualitative nature of identifiable
world events affecting markets will vary from one his-
C hart 1
Daily Stock Price V o latility
P ercent
P ercent
6 --------U.S. vo latility
Japan ese volatility
C rash pe riod
C rash period
0 L J ..I
1972
I
74
l
I
76
I
I
78
I
I .I
80
I .1. I .1... ± - J - J
82
84
86
88
P ercent
P ercent
6 --------
6 --------
U.K. volatility
German volatility
C rash p e rio d ^
qL_L.-1.-1...1
1972
74
76
I I I I I I I I I I I I I
78
80
82
84
86
88
S tandard deviations of d a ily p e rc e n t changes, com puted fo r n o n o ve rla p p in g 3 0 -tra d in g -d a y periods.
^ T h e cra s h p e rio d is the 3 0 -tra d in g -d a y p e rio d beginnin g on O c to b e r 16, 1987 and ending in the U nited S tates and Japan on
D ecem ber 1, 1987 and in the U nited K ingdom and G erm any on N ovem ber 27, 1987.
Sources: M organ S tanle y C apital International and F e deral R eserve Bank of New York.
FRBNY Quarterly Review/Summer 1988
19
C hart 2
Daily Stock Price C o rrelatio n s*
C orrelatio n c o e ffic ie n t
C orrelation betw een U nited States
C rash period t
0 5 I__ I__ I__ I__ I__ I__ I__ 1__ I__ I__ I__ I__ I__ I__ I__ I__ I__ I
1972
74
76
78
80
82
84
86
88
C o rre la tio n c o e ffic ie n t
1.0 -------------------------------------------------------------------------------------------C orrelation betw een United S tates and
United Kingdom
Crash
p erio d'
1972
74
76
78
80
82
84
86
88
C o rre la tio n c o e ffic ie n t
1.0 --------------------------------------------------------------C o rrelation between United S tates and G erm any
* C o rre la tio n c o e ffic ie n ts betw een daily p e rc e n t changes
in stock p ric e indexes, com puted fo r no noverlapping
3 0 -tra d in g -d a y pe rio d s .
+ The crash period is the 3 0 -tra d in g -d a y period beginning
on O c to b e r 16, 1987 and ending in the United S tates and
Japan on D ecem ber 1, 1987 and in the United Kingdom
and G erm any on N ovem ber 27, 1987.
S ources: Morgan S tanley C apital International and the
F e deral R eserve Bank of New Y ork.
20
FRBNY Quarterly Review/Summer 1988
torical period of volatility to the next. Sorting out the
driving factors behind each episode is beyond the
scope of this article. Rather, our approach will be to
see whether identifiable patterns of spreading volatility
and steady or rising correlations characterized market
interactions in previous periods of uncertainty. If they
did, one might have to be prepared for similar patterns
should the markets once again enter a stressful period.
Spreading volatility
Regression analysis was used to test the assertion that
higher day-to-day volatility in one major market tends
to be accompanied by higher expected v o la tility in
other markets. The regression model posits that a
h igher sta n d a rd d e v ia tio n of d a ily p e rce n t p rice
changes in one market during a 30-day period will be
associated with a higher standard deviation in a sec
ond market during that same period, when daily price
changes in the second market occur after daily price
changes in the first.
Since stock trading takes place virtually around the
clock in the various stock markets of the world, it is
necessary in implementing the analysis to establish
some particular market as the starting point of the 24hour “ days” used as the units of observation. How
ever, since this choice of a starting point is essentially
arbitrary, we repeat the analysis, shifting the start of
the day to other major markets. For example, we can
define the 24-hour day as starting in the New York mar
ket and measure the standard deviation of 30 daily
stock price movements in that market. Then, a corre
sponding standard deviation can be computed for the
subsequent price changes occurring in Japanese mar
kets within the same set of 24-hour days. Alternatively,
we can start the day in Japan, in which case the corre
sponding volatility calculations for the New York market
are shifted forward by one calendar day.
The next step is to estimate a regression equation
that uses volatility in the starting market to predict
the level of volatility in another market trading within
the same day. For example, in the equation assuming
that the day starts in the United States, a positive
regression coefficient indicates that the volatility of
daily Japanese price movements tends to be high in
those 30-day periods in which U.S. daily stock price
v o la tility is high. Conversely, a zero or negative
regression coefficient would be inconsistent with this
assertion.
Table 2 summarizes the regression results. Equations
were estimated over 30-trading-day periods from 1980
to September 1987, and also from 1972 through 1979.
As hypothesized, increased volatility in the starting
market is associated with higher volatility in the other
markets. The results are qualitatively similar whether
the equations are estimated for 24-hour days beginning
in the United States, Japan, or the United Kingdom.
(See also Appendix A.)
Association between volatility and correlation
The second hypothesis to be tested is that higher vol
atility in one market will lead to increased correlation
between daily price movements in that market and
daily price movements in other markets. We computed
30-day correlation coefficients between the daily price
changes in pairs of markets within the same 24-hour
days. Again, different sets of 30-day correlations were
calculated using varying assumptions about where the
24-hour days start.
The regression equation hypothesis was that the
higher the volatility in the first market trading in the
day, the closer the correlation between daily price
movements in that market and price movements in a
second market. These estimated effects of volatility on
co rre la tio n c o e ffic ie n ts for the period from 1980
through Septem ber 1987 and the period from 1972
to 1979 are summarized in Table 3. All are positive;
that is, the higher the 30-day level of volatility in the
first market trading in the day, the higher the 30-day
correlation between daily price movements in that first
market and price movements in another. Not only are
all the regression coefficients positive in each estima
tio n p e rio d , but in m any c a se s th e y are also
statistically significant (Appendix A, Table A1). These
findings support the hypothesis that even prior to Octo
ber 1987, high volatility tended to be associated with
higher correlations in the price movements of different
markets.3
Evidence on the strengthening of linkages over time
Casual empirical support abounds for the notion that
world stock markets have become more closely linked
in recent years. According to one survey, the number of
stocks traded globally (that is, on a daily basis in at
least one center outside the home market) rose from
236 in 1984 to 493 in 1987.4 In addition, the amount of
3These results were not affected by one notable com plication in the
data. No S aturday tra ding data were used for Japan even though
Saturday tra ding may have occu rred . This om ission cou ld interfere
with the estim ated relationships when the 24-hour day starts in the
United States or the United Kingdom on Fridays and is im plicitly
assumed to continue on Monday in Japan. Nevertheless, when we ran
the regressions again, throw ing out such Friday-M onday
com binations, the results were little changed.
*Euromoney, May 1987, pp. 187-222.
Table 2
Effects of High Stock Price Volatility
on Stock Price Volatility in Other Markets
Standard Deviations of Day-to-Day Percent Changes in Stock Price Indexes
1980 to September 1987 Estimates
Normal
Stock Price
Volatility*
Change in Volatility
Associated with High
Volatility in Market
Where Day Begins§
1972 to 1979 Estimates
Normal
Stock Price
Volatility*
Change in Volatility
Associated with High
Volatility in Market
Where Day Begins§
Day begins in the United States
Japan volatility
United Kindom volatility
West Germany volatility
.74
.88
.81
+.17*
+ .2 2 f
+.05
.64
1.19
.68
+ .3 2 t
+ .41 f
+ .20 f
Day begins in Japan
United Kingdom volatility
West Germany volatility
United States volatility
.88
.82
.85
+ .14*
+ .00
+.10
1.16
.69
.80
+ .2 9 t
+ .26 f
+ .2 2 f
Day begins in the United Kingdom
West Germany volatility
United States volatility
Japan volatility
.86
.90
.79
+ .2 7 f
+ .28 f
+ .2 8 f
.63
.76
.60
+ .1 7 f
+ .1 7 f
+.16*
^Predicted volatility from estimated equation relating volatility in the indicated market to volatility where the day starts, based on the average
1972 to September 1987 level of volatility in the day-starting market.
§Change in predicted volatility when day-starting volatility rises from 1972 to September 1987 mean value to two standard deviations above
that mean.
‘ Effect of day-starting volatility on volatility in indicated market is statistically positive at the 95 percent level.
fE ffect of day-starting volatility on volatility in indicated market is statistically positive at the 99 percent level.
FRBNY Quarterly Review/Summer 1988
21
Table 3
Effects of High Stock Price Volatility
on Correlations between Stock Price Movements
C orrelations betw een D aily Percent C hanges in Stock Price Indexes
1980 to September 1987 Estimates
Average
Correlation
Coefficients
1972 to 1979 Estimates
Change in Correlation
Associated with High
Volatility in Market
Where Day Begins§
Average
Correlation
Coefficient:):
Change in Correlation
Associated with High
Volatility in Market
Where Day Begins§
Day begins in the United States
Japan-U.S. correlation
U.K.-U.S. correlation
West Germany-U.S. correlation
.26
.29
.36
+ .2 1 f
+.16
+ .1 3 f
.16
.19
.22
+ .03
+.02
+.10*
Day begins in Japan
U.K.-Japan correlation
West Germany-Japan correlation
U.S.-Japan correlation
.14
.22
.08
+ .08*
+ .06
+.03
.04
.12
.05
+.00
+ .1 0 t
+ .05
Day begins in the United Kingdom
West Germany-U.K. correlation
U.S.-U.K. correlation
Japan-U.K. correlation
.27
.24
.18
+ .29f
+.20*
+.20*
.06
.10
.02
+ .02
+.03
+ .04
^Correlation coefficient predicted from estimated equation relating correlation between the indicated markets to volatility where the day starts,
where starting-market volatility is set to its 1972 to September 1987 average level.
§Rise in predicted correlation coefficient when day-starting volatility is raised from its 1972 to September 1987 mean to two standard
deviations above that mean.
•Effect of day-starting volatility on correlation in indicated market is statistically positive at the 95 percent level.
•{Effect of day-starting volatility on correlation in indicated market is statistically positive at the 99 percent level.
cross-border buying and selling of stocks in many mar
kets has risen d ra m a tica lly since 1980 (Table 4).
Exchanges have been establishing a variety of interna
tional trading links for equities and derivative products.5
These improving connections and increasing crossborder activities imply that participants’ awareness of,
and responsiveness to, daily foreign stock market
developments have been growing as well. Greater
cross-border investments have increased the need for
participants to stay informed about securities price per
formances. Changes in communications and trading
technology have made it easier to track and respond to
overseas developments, including price developments.
In addition, unifying trends in the world economy such
as increased trade and wider international operations
by business corporations may have made stock prices
in different centers sensitive to an increasingly similar
set of underlying influences.
It is at least possible that these stronger linkages
between stock markets may have influenced the mar
ket interactions of October 1987. The following sections
address this possibility in more detail.
*For a list of some recently established eq uity trading links between
U.S. and foreign exchanges, see Securities Week, July 6, 1987, p. 1.
22for FRASER
FRBNY Quarterly Review/Summer 1988
Digitized
Table 4
Cross-Border Stock Transactions
Gross Purchases and Sales of Domestic Stocks by Nonresidents
(In Billions of U.S. Dollars)
1980
1981
1982
1983
1984
1985
1986
1987
United States*
Japanf
Germany^
Canada§
75.2
75.5
79.9
134.1
122.6
159.0
277.5
481.9
26.2
43.7
34.6
71.5
78.3
81.9
201.6
374.7
6.8
6.9
6.3
13.4
12.4
36.9
77.9
76.8
12.4
9.2
5.2
8.4
8.8
11.9
20.2
45.7
*U.S. Treasury International Capital data.
fJapanese Ministry of Finance.
^Deutsche Bundesbank, Balance of Payments Statistics, Statistical
Supplements to the Monthly Reports of the Deutsche Bundes
bank, Series 3.
§Statistics Canada, Security Transactions with Non-Residents and
Quarterly Estimates of the Canadian Balance of International
Payments.
Stronger connections among volatilities
and correlations?
A possible consequence of the increased awareness of
foreign developments could be a stronger propensity
for high price volatility in one market to be associated
with a rise in price volatility abroad and with higher
price correlations between markets. In effect, a given
rise in foreign volatility may spark a bigger domestic
response now that participants are watching other mar
kets more closely.
With respect to the link between volatility and cor
relation, there is strong statistical evidence that the
relationship has strengthened over time. We performed
formal statistical tests on each of the equations linking
price co rre la tio n s to price vo la tility. These tests
showed that between the 1970s and the 1980s most of
the regression coefficients relating volatility to correla
tion increased by statistically significant amounts. The
size and significance of the measured increases were
very similar whether the relationship was allowed to
change in 1980 or 1983 (Appendix A, Table A3).
However, with respect to the linkage between vol
atility in one market and volatility in others, no persua
sive evidence was found that the relationship had
strengthened. Formal tests yielded little or no support
for the assertion that the regression coefficients linking
volatilities in different markets had increased between
the 1970s and the 1980s (Appendix A, Table A3).
Closer percentage changes?
A related, but slightly different way of characterizing
how stock markets interact is to ask how large a per
cent change in one country’s stock price index should
be expected when another country’s index changes by
a given percentage. For example, if the U.S. market
rises by one percent, how much would the Japanese
market be likely to rise subsequently? For want of a
better name, this statistic can be referred to as a
“ beta” coefficient between the two markets. A beta as
high as one would mean that, on average, percentage
changes in the two markets tend to be of the same
size and sign.6
8Betas can be com puted by d ire ctly regressing percent price
changes on one another, or, alternatively, com bining the correlation
and volatility figures for 30-day periods using the form ula, beta = r
times (s2 / s1), where r is the correlation coefficient, s1 is volatility in
the first market, and s2 is volatility in the second market. Table 5
applies the latter ap proach with one further adjustm ent: Since r and
s2 have been shown in the first part of the a rticle to vary
system atically through tim e with changes in s1, the betas in Table 5
have been adjusted to elim inate differences between 1970s and
1980s values a ttributa ble to variations in s1 between the decades.
A lternative m ethods of calcu la tin g betas, however, give sim ilar results
(A ppendix A, Table A4).
Table 5
“Betas” between Stock Markets
E xpected Percent C hange in Stock Prices A ssociated with a
One Percent Price C hange in Market Where Day Begins*
1980 to S eptem ber 1987 Estim ates
1972 to 1979 Estim ates
E ffect with
Normal Volatility
Where Day
Begins
Effect with
High Volatility
Where Day
Begins
Effect with
Normal Volatility
Where Day
Begins
Effect with
H igh Volatility
Where Day
Begins
.22
.30
.34
.30
.34
.29
.12
.26
.17
.13
.23
.20
.17
.25
.09
.16
.16
.07
.06
.11
.05
.05
.20
.10
.22
.20
.13
.31
.26
.20
.04
.06
.01
.03
.06
.02
Day begins in the United States
Price change in:
Japan
United Kingdom
West Germany
Day begins in Japan
Price change in:
United Kingdom
West Germany
United States
Day begins in the United Kingdom
Price change in:
West Germany
United States
Japan
•Effects com puted using the form ula for a sim ple regression “ b e ta ,” rs/s*, where r is the correlation coe fficient between pe rcent price
changes in the starting m arket and in another market, s* is the standard deviation of percent p rice changes in the starting market, and s
is the standard deviation of percent price changes in the other market. Values of r and s for normal and high values of s* are com puted
using the mean 1972 to S eptem ber 1987 value of s* and a value of two standard deviations above that mean, in conjunction with esti
m ated regression equations relating r and s to s*.
FRBNY Quarterly Review/Summer 1988
23
As Table 5 shows, betas for the 1980s period are uni
formly higher than for the 1970s, a finding which is
again consistent with growing intermarket awareness
and trading. Estimates of betas using other methods
confirm that these associations between pairs of per
cent changes have become closer in recent years
(Appendix A, Table A4).
Monthly interactions
As a further check on how the pattern of market inter
actions had been evolving prior to October, monthly
average price movements were examined. Monthly
movements of course abstract from day-to-day swings.
Thus, the m onthly averages focus on the broader
downward shift in stock price levels from before to
after the crash, instead of daily movements. Was it nor
mal for monthly market movements in different markets
to behave as sim ilarly as they did around October
1987? Had monthly average movements of prices in
different markets become significantly more similar in
the 1980s?
To answer these questions, we estimated regression
equations e xplainin g m onthly average stock price
indexes in four countries on the basis of domestic eco
nomic variables and foreign stock prices. Including
econom ic variables (inflation, industrial production,
unemployment, and short- and long-term interest rates)
sharpens the focus on stock market dynamics by hold
ing constant other more fundamental determinants of
stock prices. Thus, the estimated regression equations
can be used to see how movements in foreign stock
prices norm ally affect dom estic stock prices. (See
Appendix B for a fuller explanation.)
Table 6 summarizes the regression estimates show
ing how stro n g ly m onthly average dom estic stock
prices in four countries are influenced by foreign stock
price changes when economic influences are held con
stant. For example, if the average level of stock prices
in each of six major foreign countries fell by 1 percent
in a given month, then the equation predicts that U.S.
stock prices would be 0.83 percent lower as a result,
even if no U.S. economic variables changed.
By letting the size of the regression coefficients link
ing foreign and domestic stock prices change after
1981, the equation allows for a possible strengthening
of the relationship. Before 1981, a 1 percent drop in for
eign stock prices would have lowered U.S. prices by
only 0.72 percent. Of the four countries, three show an
increased sensitivity to foreign stock price movements
after 1981. Although none of these increases in sensi
tivity achieves statistical significance, the increases are
generally consistent with the modest increases in dayto-day betas found above (Table 5 and Appendix A,
Table A4). The m onthly equations were also reestimated, allowing the coefficients to shift at other
dates, and the results are qualitatively similar to those
obtained when the 1981 change is allowed (Appendix
B, Table B2).
The monthly equations were estimated starting in
1950 or the early 1960s, depending on data availability
for each country, with the estimation periods ending in
September 1987. Thus the monthly results provide
additional evidence that even well before the crash,
world stock prices were significantly linked. As the dayto-day movements also demonstrated, the closeness of
monthly percent price movements in different markets
appears to have increased moderately in recent years.
The October crash
We have yet to determine how well the pre-October
day-to-day and m onthly-average estim ated relation
ships fit the pattern of events during the crash. Was the
degree of volatility spillover in line with what earlier
estimates would have indicated? Were the pre-October
Table 6
Tests of Changing Sensitivity of National Stock Price Indexes to Monthly Movements in Foreign Stock
Markets*
Estimated Percent Change in Monthly Average Domestic Stock Price Index Corresponding to One Percent Change in Each of Six Monthly Average
Foreign Stock Price Indexes, Controlling for Domestic Real Output, Price Level, Unemployment, and Short- and Long-Term Interest Rates.
West
Germany
United
States
Japan
United
Kingdom
Sensitivity before December 1981
.72
.37
.82
.45
Sensitivity after January 1982
.83
.57
.54
.58
+ .11
+ .20
-.2 8
+.13
C hangef
*See Appendix B for details.
■fMone of these estimated increases in sensitivity to foreign stock prices is statistically greater than zero, using a one-tailed test at a 95 percent level
of significance.
24
FRBNY Quarterly Review/Summer 1988
Table 7
Explaining the October 1987 Spillovers
A ctual and Predicted Measures of Spillovers of Market D isruptions during the O cto ber 1987 S tock Market Crash
Correlation C oefficient
V olatility
O cto ber
Prediction)!
O cto
ber
Actual
4.2*
4 .1 1
4 .2 f
.22
.30
.34
.30
.23
.21
.62
.38
.29
1.1
1.0
1.3
4 .2 f
4 .2 t
5 .3 f
.17
.25
.09
.13
.05
.16
.67
.60
.22
2.0
1.8
2.0
4.2*
5 .2 t
4.2
.22
.20
.13
.44
.33
.35
.75
.78
.30
O cto ber
Prediction||
Day begins in the United
States
Japan
United Kingdom
West Germany
.26
.29
.36
.97
.70
.91
.77
.49
.29*
0.7
0.9
0.8
1.6
1.6
1.2
Day begins in Japan
U nited Kingdom
West Germany
United States
.14
.22
.08
.50
.52
.22
.68
.59
.18
0.9
0.8
0.9
Day begins in the United
Kingdom
West Germany
United States
Japan
.27
.24
.18
.88
.74
.70
.72
.59
.29
0.9
0.9
0.8
§Predictions using equations estim ated from January
deviation of starting-m arket percent price changes,
P re d ic tio n s using equations estim ated from January
deviation of starting-m arket percent price changes,
H y p o th e s is that O cto ber observation was generated
percent level.
tH ypo thesis that O cto ber observation was generated
pe rcent level.
Normal
Value§
O cto ber
Prediction||
O cto
ber
Actual
1980 through S eptem ber 1987, setting the independent variable, the standard
to its mean value for 1972 through S eptem ber 1987.
1980 through S eptem ber 1987, setting the independent variable, the standard
to its actual O cto ber 1987 period value.
by the statistical model estim ated through S eptem ber 1987 is rejected at the 95
by the statistica l model estim ated through S eptem ber 1987 is rejected at the 99
relationships between volatility and correlation on tar
get in the crash? Were percent movements— day-today and month-to-month— in line with what the earlier
equations would have predicted?
To answer these questions, actual October 1987 daily
volatility in each major market was used to predict vol
atility in other markets, correlations among markets,
and betas between markets, based on the estimated
pre-October statistical relationships. In addition, analo
gous simulations of the crash were run using the preOctober monthly equations.
The results based on the daily movements (Table 7)
indicate some notable qualitative similarities between
the crash and earlier episodes. The pre-October rela
tionship predicted that the correlations in daily price
movements between pairs of major markets would
increase su bstan tia lly. Indeed, most c o rrelatio ns
showed a clear rise (see also Chart 2). The one excep
tion was the U.S.-German correlation, which actually
fell in October, contrary to the earlier pattern that
would have predicted a correlation increase.
A more striking difference between the October and
earlier patterns was observable in the extent to which
volatility spread. For example, given the U.S. volatility
spike, volatilities in Japan and the U.K. would “ typ-
Beta
Normal
Value§
Normal
Value§
October
Actual
Table 8
Actual and Predicted
Monthly Stock Price Changes
S eptem ber to N ovem ber 1987
S&P 500
Tokyo index
West German index
U.K. index
Actual
Price
C hange*
(In Percent)
Predicted
Price
Changef
(In Percent)
- 2 6 .3
- 1 1 .9
-3 4.34 :
- 2 6 .3 *
-2 6 .5
- 1 8 .0
-1 3 .9
- 9.8
‘ Percent change, S eptem ber 1987 average to Novem ber 1987
average.
tE ach country's index is pre d icte d using a regression equation,
based on dom estic econom ic variables and foreign stock
price indexes, estim ated through S eptem ber 1987. See
A ppendix B for details.
^H ypothesis that Novem ber observation was generated by the
statistical m odel estim ated through S eptem ber 1987 is
rejected at the 99 pe rcent level.
ically” have doubled, and German volatility would have
risen noticeably as well. In fact, as Table 7 shows,
these volatilities increased by factors of four to six
times above normal levels. A similar pattern of sur
FRBNY Quarterly Review/Summer 1988
25
prisingly large volatility spillover shows up when the
day is started outside the United States.
With the unusual spread in volatilities, the betas
relating percent changes in major markets to one
another jumped as well. While betas would have been
expected to rise only slightly or even decline, most
rose substantially. The one exception was again the
U.S.-Germany beta, whose value during the crash
period was slightly lower than during more normal
times.
These results are consistent with the common view
that a wave of panicky selling circled the globe, with
traders paying an unusually large amount of attention
to price developments in foreign markets in the
absence of fundamental news sufficient to account for
the disruption. The panic among participants probably
explains the unanticipated extent of volatility spillover.
Monthly interactions around October 1987
The actual monthly average price changes in the crash
were neither consistently larger nor consistently
smaller than the predicted changes from the regression
equations (Table 8).
The U.S. price index fell about as much as expected,
given the drops everywhere else. The Japanese index
fell less than the equation predicted. (It is tempting to
attribute this result to the circuit-breaker system
installed in Japan following the stock market debacle in
the 1960s.) Both the U.K. and German indexes fell sub
stantially more than the equations indicated. While the
equations did not predict accurately in three of the four
cases, the prediction errors were dispersed around the
actual outcomes. This suggests that the basic degree
of linkage among monthly average prices in different
stock markets during the crash was neither clearly
stronger nor weaker than it had been prior to October.7
It does not appear that the prediction errors can be
systematically linked to the strengthening relationships
between stock markets identified in the monthly
regression equations: The U.K. and German equations
showed the least persuasive evidence that domestic
7Since the predicted price changes for each of the four markets take
actual foreign price changes in the period as given, if there were in
fact consistent under- or over-prediction in Table 8, then the true
error would be greater for the system of equations as a whole. This
does not appear to be a problem, however, since the errors are
dispersed.
26
FRBNY Quarterly Review/Summer 1988
stock prices were becoming more responsive to foreign
stock prices, while the actual October drops in those
two countries substantially exceeded the predicted
drops. The Japan regression equation showed a fairly
distinct strengthening of the linkage, but the actual
Japanese price drop was far less than the forecast.
(See Appendix B, Table B2.)
Conclusion
Although a panic is a unique event, the crash experi
ence conformed to the pre-October pattern in impor
tant respects. The coincidence of volatility surges in
major stock markets was qualitatively similar to earlier
patterns found in the data, as were the increases in
correlations between price movements in most mar
kets. At a monthly-average level, the large downward
shift in prices worldwide—while unprecedented in mag
nitude—was qualitatively similar to earlier relationships
among stock markets as well.
Although the crash interactions were a clear demon
stration of the preexisting interdependencies among
major stock markets, the October events differed from
earlier patterns in the extent of the volatility spillover
from one market to another. Since there is no evidence
that the propensity of volatility shocks to spread had
strengthened before the crash, it seems unlikely that
the unexpected degree of October spillover can be
accounted for by a tightening of relationships among
markets during the 1980s.
It seems fair to conclude that if huge price move
ments were again to occur in one of the world’s major
stock markets, the disruptions would be likely to spread
worldwide. This assessment suggests that measures to
prevent excessive volatility in one market, such as “cir
cuit breakers” or deeper margin buffers, if successful,
could have international benefits. One caveat to our
conclusion derives from the modest signs in the 1980s
data that world stock prices in different countries have
been tending to move more similarly than before. If this
trend continues, some increased degree of interna
tional regulatory coordination would become neces
sary to augment the effectiveness of domestic
measures in lessening the chances of another market
collapse.
Paul Bennett
Jeanette Kelleher
Appendix A: Estimating Relationships among Stock Market Volatilities and Correlations
be periods of high price correlations among stock
markets. Implicit in our approach is the notion that
high volatility is leading to high correlations, perhaps
because participants in a second market only react to
changes in a first market when those changes are
large. Volatility in stock index a, sf, within a 30-trad
ing day period, t, is measured as the standard devia
tion of daily percent changes. Analogously, r f is the
correlation coefficient between stock markets a and b
within period t. The regression equation estimated
across periods t is:
This appendix describes four sets of statistical com
putations used in the text. The first section outlines the
tests used to determine whether the level of stock price
v o la tility in a m arket in flu e n c e s the c o rre la tio n s
between stock price movements in that market and in
other markets. The second section describes analogous
procedures for testing how stock price volatility in a
market is related to volatility in other stock markets.
The third section presents formal tests for identifying
changes over time in the statistical relationships among
volatilities and correlations. The fourth section outlines
calculations of coefficients linking percent changes in
one stock market to percent changes in another; these
coefficients are referred to as “ betas” in the text,
although this terminology is somewhat different from the
standard usage in financial economics. The accompany
ing tables (A1 through A4) provide the statistical results.
In ((1 + 0
/ ( 1 - 0 ) = A + Bsf + e„
where A is a constant and et is the regression error.
The transformation of rf* on the left-hand side of the
equation creates an asymptotically normal dependent
va ria b le : this tra n sfo rm a tio n is needed since r f
ranges only between plus and minus one.*
1. Tests of the link between volatility and correlation.
The first hypothesis to be tested states that periods
of high price volatility in stock markets also tend to
*T.W. A nderson, An Introduction to M ultivariate S tatistical
A nalysis (New York: John Wiley & Sons, 1958), p. 78.
Table A1
Impact of Volatility on Correlation of Stock Prices^
Regression Coefficients
Jan. 1, 1972
to Dec. 31, 1979
A
Jan. 1, 1980
to Oct. 15, 1987
B
A
B
Day starts in the United States:
Japan
0.24*
West Germany
0.14
United Kingdom
0.30*
Japan
0.21*
G ermany
0.14
0.35*
United Kingdom
10.49
36.05*
9.26
13.04
35.97
4.06
- 0 .1 8
0.30
0.36*
- 0 .2 9
0.05
0.38*
8 4 .0 3 t
53.52*
26.21
9 5 .7 0 t
7 9 .8 5 f
24.91
Day starts in Japan:
West Germany
U nited Kingdom
U nited States
West Germany
United Kingdom
United States
3 0 .5 5 f
0.81
17.45
27.39+
5.98
9.40
0.29*
0.11
0.09
0.29*
0.12
0.08
20.28
23.82*
8.56
20.71
22.09
9.57
4.89
7.13
9.93
4.20
5.63
10.37
-.2 4
-.0 2
- .1 1
-.2 6
-.0 4
.01
7 4 .1 4 f
47.38*
45.06*
77.79*
40.64
32.20
0.03
0.07
- 0 .0 4
0.05
0.03
0.02
Day starts in United Kingdom:
West Germany
0.07
United States
0.12
Japan
- 0 .0 8
West Germany
- 0 .0 8
United States
0.15
Japan
- 0 .0 9
A utocorrelation Rho
Jan. 1, 1972
to Dec. 31, 1979
—
Jan. 1, 1980
to Oct. 15, 1987
—
—
—
- 0 .1 0
0.24*
0.15
0.24*
0.26*
- 0 .0 5
—
—
—
—
—
—
-0 .2 2 *
0.19
- 0 .2 0
—
0.21
- 0 .5 7
0.01
—
—
—
0.01
0.13
0.05
0.02
0.12
0.22*
R -squared
1972-79
1980-87
0.01
0.05
0.00
0.02
0.11
0.02
0.15
0.08
0.03
0.19
0.14
0.03
0.08
0.00
0.02
0.12
0.03
0.05
0.03
0.04
0.01
0.06
0.04
0.01
0.00
0.01
0.02
0.00
0.03
0.02
0.13
0.05
0.06
0.14
0.06
0.10
^E stim ated equation is In ((1 + r ) /( 1 - r ) ) = A + Bs + e.
’ C oefficient estim ate is sta tis tic a lly significant at the 95 percent level, one-tailed test.
tC o e ffic ie n t estim ate is sta tis tic a lly significant at the 99 percent level, one-tailed test.
FRBNY Quarterly Review/Summer 1988
Appendix A: Estimating Relationships among Stock Market Volatilities and Correlations (continued)
the importance of this problem, prelim inary regres
sions were run using an alternative data set in which
days beginning during calendar Fridays and ending
during calendar Mondays were dropped. The regres
sion estimates were very similar to those obtained
when these days were included. Thus, the problem
appeared to be minor, and the fuller data were used
in the final estimates. (Note that since initial price vol
atility in Japan is computed as the percent change
between Friday and Monday closes' in Japan, the
analogous problem does not exist for 24-hour days
starting in Japan.) Those 24-hour days in which at
least one of a given pair of markets was closed were
deleted before construction of the 30-day-time-period
series for the regressions relevant to that particular
pair of markets.
Since the standard deviation and correlation coeffi
cient variables are constructed using daily data on
market prices in various parts of the world, the start
ing point for the 24-hour day must be selected. Which
market, a or b, will be used to measure the standard
deviation for period t must also be decided. It is
assumed that market a is the first market open in the
24-hour day. The regression is estimated over non
overlapping 30-day periods in the 1970s and 1980s;
each period makes up one observation with its own
correlation and volatility.
The results are shown in Table A1, with and without
autocorrelation corrections. The U.S. data are daily
closing figures for the S&P 500 index. Data for the
other three countries are daily stock indexes from
Morgan Stanley Capital International.
Weekends presented a problem in defining a 24hour day. It was assumed that days that begin during
a calendar Friday are interrupted over the weekend
and completed during the first part of calendar Mon
day. But difficulties arose with those periods in which
the days were assumed to begin in the United States
(or the United Kingdom) and to end in Japan. Stocks
trade in Japan on some but not all Saturdays; conse
quently, it is possible that the relevant correlation
should be between price movements on calendar Fri
days and Saturdays when trading occurs. To assess
2. Tests for spreading volatility. Analogous regressions
were estimated using volatility as the dependent vari
able, measured as the standard deviation of daily
percent price changes within 30-day periods (Table
A2).
3. Tests for structural breaks. Combining the samples
from the 1970s and 1980s, we allowed a dummy vari
able to interact with the slope coefficient for each of
the co rre la tio n -vo la tility and the vo la tility -v o la tility
equations (Table A3). The shift coefficients (B2) were
Table A2
Impact of Volatility on Other Market Volatility^
Regression Coefficients
Jan. 1, 1972
to Dec. 31, 1979
Jan. 1, 1980
to Oct. 15, 1987
A utocorrelation Rho
R -squared
B
A
B
Jan. 1, 1972
to Dec. 31, 1979
Day starts in the United States:
Japan
-1 .9 5 *
West Germany
-3 .0 0 t
U nited Kingdom
-2 .1 2 f
0.64+
0.41 +
0.48+
-3 .3 1 +
-4 .3 2 +
-2 .9 6 +
0.33*
0.10
0.37+
0.46+
0.56+
0.72+
0.58+
0.64+
0.31 +
0.35
0.47
0.66
0.37
0.41
0.29
Day starts in Japan:
West Germany
United Kingdom
United States
- 3 .0 9 +
—3.14 f
-3 .3 9 +
0.38+
0.26+
0.29+
-4 .8 1 +
-3 .8 9 +
-4 .1 0 +
0.00
0.17*
0.13
0.46+
0.76*
0.71 +
0.63+
0.32+
0.46+
0.55
0.60
0.60
0.39
0.12
0.23
Day starts in United Kingdom:
West Germ any
-3 .5 5 f
-3 .5 3 +
United States
Japan
-3 .6 1 +
0.33+
0.29+
0.33*
-3 .0 0 +
-2 .9 5 +
-2 .8 5 +
0.38+
0.38+
0.43*
0.57+
0.71 +
0.50+
0.74+
0.38+
0.63+
0.41
0.66
0.31
0.51
0.33
0.42
A
Jan. 1, 1980
to Oct. 15, 1987
1972-79
1980-87
^E stim ated equation is In ( S 0Th e r ) = A + B (In S STARTin g ) + e, where S is a standard deviation of pe rcent d a ily price changes.
‘ C oefficient estim ate is s tatistica lly significant at the 95 percent level, one-tailed test.
tC o e ffic ie n t estim ate is s ta tistica lly significant at the 99 pe rcent level, one-tailed test.
FRBNY Quarterly Review/Summer 1988
Appendix A: Estimating Relationships among Stock Market Volatilities and Correlations (continued)
Table A3
Dummy Variable Tests for Strengthening Relationships
Shift in 1980
Regression Coefficients
A
B,
B2
B1+ B2
A utoco rrelation
Rho
R-squared
Relationship betw een C orrelation and V o la tility *
Day starts in the United States:
Japan
0.10
West Germany
0.19
United Kingdom
0 .3 2*
25.08*
30.62*
6.86
29 .40*
34 .96*
24 .19*
5 4 .4 8 *
6 5 .58*
3 1 .15*
—
—
—
0.14
0.17
0.09
Day starts in Japan:
West Germany
United Kingdom
United States
15.38
- 1 .3 5
10.51
19.47*
27 .4 7 *
5.40
3 4 .8 5 *
2 6 .1 2 *
15.92
—
—
—
0.09
0.09
0.02
9.39
9.23
10.45
40 .3 8 *
2 6 .89*
31 .7 9 *
4 9 .7 7 *
3 6 .12*
4 2 .2 4 *
—
—
—
0.16
0.08
0.12
0.15*
0.09
0.02
Day starts in United Kingdom:
West Germany
0.00
0.09
United States
Japan
- 0 .0 8
Relationship betw een O ther Market Volatility and S tarting Market V o la tility !
Day starts in the United States:
-2 .5 7 *
Japan
West Germany
-3 .6 6 *
-2 .5 7 *
United Kingdom
0 .5 1 *
0 .2 8*
0.4 0*
-0 .0 1
-0 .0 4 *
0.05*
0 .5 0 *
0.24*
0 .4 5 *
0 .5 3 *
0 .6 1 *
0 .6 2 *
0.37
0.47
0.59
Day starts in Japan:
West Germany
United Kingdom
United States
-4 .0 9 *
-3 .3 9 *
-3 .7 4 *
0 .1 8 *
0 .2 2*
0.2 2*
-0 .0 4 *
0.05*
- 0 .0 2
0.14*
0.2 7 *
0 .2 0*
0 .5 8 *
0 .6 5 *
0 .6 3 *
0.47
0.51
0.47
Day starts in United Kingdom:
West Germany
-3 .3 5 *
United States
-3 .3 6 *
Japan
-3 .3 3 *
0 .3 7*
0 .3 3*
0 .3 8 *
- 0 .0 6 *
- 0 .0 3 *
- 0 .0 4
0.3 1 *
0 .3 0 *
0 .3 4 *
0 .6 7 *
0 .6 0 *
0 .5 6 *
0.50
0.54
0.37
S h if t in 1 9 8 3
R elationship betw een C orrelation and V o la tility *
Day starts in the United States:
Japan
0.04
West Germany
0.13
0.29
United Kingdom
38 .3 7 *
46 .6 0 *
18.27
2 9 .51*
29 .09*
15.46*
6 7 .8 8 *
75.69*
33.73*
—
—
—
0.12
0.13
0.04
Day starts in Japan:
West Germany
United Kingdom
United States
29 .07*
11.17
4.68
- 0 .5 6
9.98
15.47
2 8 .51*
21.15*
20.15*
—
—
—
0.06
0.03
0.03
32.15*
19.99*
21.60*
4 0 .0 8 *
27.96*
29.30*
—
—
0.07
0.03
0.04
0.13
0.08
0.05
Day starts in United Kingdom:
West Germany
0.12
0.18
United States
0.04
Japan
^E stim ated equation is In ((1 + r)/(1 - r)) =
§Estim ated equation is In ( S 0 Th e r ) = A +
'S ig n ific a n t at 95 percent level, one-tailed
-(-Significant at 99 percent level, one-tailed
7.93
7.97
7.70
—
A + (E^ + E^D) s + e.
(B, + B2D) (In ( S STAr t i n g ) ) + e.
test.
test.
FRBNY Quarterly Review/Summer 1988
29
Appendix A: Estimating Relationships among Stock Market Volatilities and Correlations (continued)
Table A3
Dummy Variable Tests for Strengthening Relationships (continued)
Shift in 1983
Regression C oefficients
A
B,
B2
B, + B2
A utocorrelation
Rho
R-squared
Relationship betw een O ther Market Volatility and Starting Market V o la tility !
Day starts In the United States:
Japan
-2 .5 3 f
West Germany
- 3 .4 9 +
United Kingdom
- 2 .6 8 +
0.53+
0.32+
0 .3 8 f
- 0 .0 6 *
-0 .0 7 +
0.05*
0.47+
0.25+
0.43+
0.50+
0.52+
0.64+
0.39
0.49
0.59
Day starts in Japan:
West Germany
United Kingdom
United States
—4.14+
- 3 .3 3 *
- 3 .7 0 +
0.17+
0 .2 4 f
0 .2 1 f
—0.06+
0 .0 6 f
0.01
0.11
0 .3 0 f
0.22+
0.52+
0.62+
0.63+
0.49
0.51
0.47
Day starts in United Kingdom:
West Germany
-*-3.301- 3 .4 2 +
United States
Japan
- 3 . 201-
0.38+
0.30+
0.42+
-0 .0 9 +
-0 .0 1
-0 .0 8 f
0 .2 9 f
0.29+
0.34+
0.58+
0.64+
0.52+
0.52
0.53
0.39
^E stim ated equation is In ((1 + r ) /( 1 - r ) ) =
§Estim ated equation is In ( S 0 THe r ) = A +
'S ig n ific a n t at 95 percent level, one-tailed
tS ig n ific a n t at 99 percent level, one-tailed
A + (B, + B2D) s + e.
(B, + B2D) (In ( S STAr t i n g ) ) +
test.
test.
generally significantly positive for the correlation
equations and not significant for the volatility equa
tions. When the shift was allowed in 1983 instead of
1980, quite similar results concerning the size, sign,
and significance of shifts were found.
4. Calculation of betas. Beta coefficients, b, are defined
by the regression equation on logarithm changes,
D(ln p2) = a + b D(ln p1) + e,
where
b = r (S2/S1).
Here r is the correlation coefficient between percent
changes in p1 and p2, S1 and S2 are the corres
ponding standard deviations, and D indicates first
differences.
FRBNY Quarterly Review/Summer 1988
e.
Table A4 shows three different measures of b, for
two time intervals each. The first measure is the aver
age of betas for 30-day periods, calculated with 30day values of r, S1, and S2. The second measure is
the same, except the values of r and S2 are predicted
values from regression equations that estimate r and
S2 as dependent on S1 (see above); average values
of S1 over 1972 through September 1987 are used.
Thus this second measure is net of the effects of
changes through time in market volatility. The third
measure is directly estimated with daily data. A sig
nificant statistic for the third measure reflects a t-test
on the difference in coefficient values, where t is cal
culated assuming two independent samples with dif
ferent variances.
Appendix A: Estimating Relationships among Stock Market Volatilities and Correlations (continued)
Table A4
Beta Coefficient Estimates
R elating Percent Changes in Daily Stock Price Indexes
Average Betas from
30-Day P erio d sf
Average Betas
A djusted fo r
V olatility Changes^
Average Betas,
D irectly Estim ated§
1980 to
Sept. 1987
1972-79
1980 to
Sept. 1987
1972-79
1980 to
Sept. 1987
1972-79
Oay starts in the U nited States:
Japan
United Kingdom
West Germany
.23
.31
.36
.14
.27
.20
.22
.30
.34
.12
.26
.17
.24*
.31
.33*
.15
.29
.20
Oay starts in Japan:
United Kingdom
West Germany
United States
.19
.25
.09
.08
.13
.03
.17
.25
.09
.06
.11
,05
.18
.20*
.08
.11
.14
.04
Oay starts in United Kingdom:
West Germany
United States
Japan
.19
.20
.12
.04
.07
.00
.22
.20
.13
.04
.06
.01
.19*
.20*
.12*
.05
.06
.02
fB e ta s were com puted for each 30-day period as rS l/S 2, where r is the correlation coe fficient and S1 and S2 are the standard
deviations for each period. Averages for 30-day periods during 1972-79 and the 1980s are shown.
^P redicted values were calc u la te d for r and S1 from equations relating them to S2, setting S2 to its 1972 to S eptem ber 1987
average and using separately estim ated equations for the 1970s and 1980s.
§Estim ated using sim ple da ily regressions of percent changes in pairs of markets.
‘ D irectly estim ated beta for the 1980s is significa ntly greater than for the 1970s at the 95 pe rcent level.
Appendix B: Monthly Regression Model Relating Foreign and Domestic Stock Price Indexes and
Controlling for Economic Variables
An econometric model was estimated to measure the
effects of foreign stock prices on domestic stock prices
while controlling for key economic variables. An equa
tion was estimated for each of four countries. In each
equation the dependent variable was a monthly-average
domestic stock price index, and the explanatory vari
ables included short- and long-term interest rates,
industrial production, the CPI, and the unemployment
rate. Each of these economic variables was included as
an explanatory regression variable contemporaneously
and w ith five m onths of lagged values. C o n te m
poraneous monthly-average values of stock indexes for
six major countries were also included as explanatory
variables. In addition, error autocorrelation coefficients
(rho (-1) and rho (-2)) were estimated and found to be
statistically significant.
The regression results for the United States, Japan,
the United Kingdom, and West Germany are shown in
Table B1. Explicit allowance was made for the coeffi
cients on foreign stock price indexes to change starting
in January 1985. (The variable transformations made to
allow such coefficient changes are explained in a foot
note to Table B1.)
As the R2 for each equation shows, the explanatory
variables account for between 40 and 80 percent of the
monthly variation of the dependent variable. The auto
correlation terms account for virtually all remaining vari
ation (since the Rz that includes the explanatory power
of the rho coefficients is nearly unity in each case).
The foreign stock index coefficients are almost all
positive (or are quite small), with sizable and statis
tically significant positive coefficients on several foreign
stock indexes in each equation. This finding is consis
tent with the hypothesis that foreign and domestic stock
prices are positively correlated, even after economic
trends have been taken into account. It should be
noted, however, that since stock price indexes tend to
be quite correlated through time, the size of one foreign
FRBNY Quarterly Review/Summer 1988
31
Appendix B: Monthly Regression Model Relating Foreign and Domestic Stock Price Indexes and
Controlling for Economic Variables (continued)
Table B1
Regression Coefficients for the United States, Japan, the United Kingdom, and West Germany
S ensitivity of National S tock Markets to Movements in Dom estic Economic Variables and Foreign S tock Prices
(M onthly D a ta ;t All Variables in Log Form)
Dependent Stock Price Index
S&P 500
Independent
Variables : f
C onstant term
Through
D e c . 1984
Jan. 1985
S hift*
+ .24*
+ .02
+ .00
+ .02
+ .01
-.1 0
UK lndex§
Through
Dec. 1984
Jan. 1985
S h ift*
- 3 .2 6
.11
+ .71*
.09
.14*
.00
.02
.02
-.1 3
- .0 1
+ .03
-.4 9 *
+ .06
West German Index
Through
D e c . 1984
.41*
.10
- .0 1
-.2 2
.12
-.0 4
.04
.13*
-.0 4
+ .07
+ .33
-.1 7
.09
.14
.09*
+ .32
-.1 8
-.1 9
.11*
- .0 1
.10*
- .0 7
-.1 5
+ .15
.01
.04
-.0 9 *
-.0 3
- .0 1
-.0 7
-.0 8 *
-.0 3
.01
-.0 3
-.0 5
-.0 6
-.0 3
.00
- .0 1
-.0 3
-.0 4
- .0 1
-.2 5 *
.02
-.0 6
.02
.01
.00
.21*
- .0 1
.01
.03
-.0 6
-.0 1
- .2 4 *
-.2 5 *
-.0 8
-.0 7
.01
.08
- .2 5 *
.17
-.0 5
-.0 6
.11
-.0 9
.15
.30*
-.0 4
.08
.18
.04
.02
.02
.06
.03
.02
.04
.41*
.26
.09
.07
.10
- .0 1
.35
- .6 1
-.4 9
.03
.20
.16
-.0 1
.05
-.2 1
.05
.93*
.26
.15
.45*
.52*
.09
-.1 7
-.1 0
- 1 .4 2
.26
-.1 7
-.0 9
.95
-.1 0
-.0 0
.02*
.00
.01
.01
.01
.01
- .0 1
.02
.01
.03*
.01
.58
.92*
-1 .0 0 *
.11
.04
.04
.01
.01
.01
.02
- .0 1
.01
1.34*
1.22*
.96*
-0 .3 5 *
-.2 8 *
- .1 5 *
.809
.437
.714
.804
999
999
997
.991
.91*
.03
R2
Jan. 1985
S hift*
3.14*
.04*
- .0 4 *
.01
.02
-.0 2
.00
rho (-2)
R2 (error based at
nrininal levels
Tokyo Index
Through
Dec. 1984
-.6 4
-.3 8
Foreign stock price indexes:
United States
Japan
.03
.14*
United Kingdom
West Germany
.10*
France
.03
.37*
C anada
.04
Italy
Dom estic variables:
Short-term rate
(-1)
-2)
(-3
-4
(-5)
Long-term rate
(-1)
(-2)
(-3)
(-4)
(-5)
Industrial production
(-1)
-2
(-3)
(-4)
(-5)
C onsum er p rice index
(-1)
(-2)
-3
(-4
(-5)
Unem ploym ent
(-1)
-2
(-3
(-4
(-5)
rho (-1)
Jan. 1985
S hift*
*t-sta tistic s ignifica nt at the 95 percent level for a one-tailed test (critica l value = 1.645).
tF o r S&P 500 equation, data are for August 1950 through S eptem ber 1987. For Tokyo index equation, data are for August 1963
through S eptem ber 1987. For U.K. index equation, data are for August 1961 through S eptem ber 1987. For West German index
equation, data are for A ugust 1967 to S eptem ber 1987.
^C oefficie nt on the shift variable corresponding to the independent variable X, and con structe d acco rd in g to the form ula: shift
variable = D8485 * (X, - X , ^ ) , where D8485 equals zero through D ecem ber 1984 and one thereafter, and where X12m4 equals the
D ecem ber 1984 value of the independent variable X,.
U n e m p lo y m e n t rates for the U nited Kingdom were not available on a consistent basis for the sam ple period.
FRBNY Quarterly Review/Summer 1988
Appendix B: Monthly Regression Model Relating Foreign and Domestic Stock Price Indexes and
Controlling for Economic Variables (continued)
to the Table B2 sums (lower left-hand corner), prior to
1985 this increase would have been associated on aver
age with a 7.1 percent change in the S&P 500, assum
ing there were no associated change in underlying U.S.
economic variables. Had the foreign stock price rise
occurred after January 1985, however, the associated
rise in the S&P 500 index would have been 9.7 percent
when other variables were held constant.
Table B2 also summarizes the results of reestimating
the statistical equations when the foreign stock price
coefficient shifts were allowed to occur at earlier dates.
stock index’s influence relative to the size of another’s
is estimated with a high degree of uncertainty. By con
trast, a more consistent story emerges from the sums of
these coefficients in each equation. Similarly, the indi
vidual shift coefficients are hard to interpret, with siz
able shifts in positive or negative directions.
Table B2 imposes some order by comparing the totals
of the coefficients on foreign stock indexes with the
totals of these coefficients plus the sum of the shift
coefficients. These latter totals are the new, postshift
coefficient sums. Suppose, for example, that all foreign
stock prices were to rise by 10 percent. Then, according
Table B2
Changing Sensitivity of National Stock Markets to Movements in Foreign Stock Markets*
Japan
United States
Date of
Hypothesized
Structural Shift
Jan.
Jan.
Jan.
Jan.
S ensitivity
before
Shift
1971
1979
1982
1985
.80
.74
.72
.71
Sensitivity
after
Shift
.74
.82
.83
.97+
United Kingdom
W est Germ any
Sensitivity
before
Shift
S ensitivity
after
Shift
S ensitivity
before
Shift
S ensitivity
after
Shift
S ensitivity
before
Shift
Sensitivity
after
Shift
.35
.33
.37
.38
.44
.56
.57
.55
.54
.86
.82
.76
.78
.55
.54
.71
.74
.45
.45
.52
.51
.44
.58
.40
*See Table B1 for 1985-shift regressions. The statistics shown here equal the sums of estim ated foreign stock p rice coefficients, with
and without the shift coefficients, for each of the four equations. The stock price indexes used were the S&P 500 for the United
States and broad indexes available from C itibase for Japan, the United Kingdom , West Germany, C anada, France, and Italy,
t S ensitivity after shift is larger, at a 95 percent level of statistica l significa nce (one-tailed test).
FRBNY Quarterly Review/Summer 1988
International Linkages among
Equities Markets and the
October 1987 Market Break
Equities markets around the world lost, in total, about
$1.2 trillion in market capitalization during the October
1987 crash. Half of the losses took place on stock mar
kets outside the United States. The speed, size, and
simultaneity of the price declines in such a wide vari
ety of markets stunned participants and observers
alike and prompted a search for explanations.
In the United States, structural features such as the
market-making mechanism and the interaction of the
stock market with equity-related futures and options
markets have received considerable attention. But
these features differ across national boundaries and
hence do not easily explain the similar downturns
around the globe.
This article considers the role of direct international
linkages across markets in promoting October’s simul
taneous downturns. These linkages take two principal
forms: cross-border equity investment and stock trad
ing in centers outside the home market. A review of the
October experience suggests the following:
• Direct international linkages cannot explain the
worldwide decline in equities markets in mid-October. In the three largest equities markets— New
York, Tokyo, and London—cross-border selling of
equities played a significant role only in Tokyo, and
trading of stocks outside the home market mainly
affected U.K. equities traded in the form of Ameri
can depositary receipts.
• The limited role of direct international linkages in
the crash in these markets reflected the small
scale of international equity investment and 24hour trading relative to activity in the large markets
34
FRBNY Quarterly Review/Summer 1988
and the absence of heavy selling by cross-border
investors based in some large countries.
• Thus, the primary international linkage was indi
rect. In the charged atmosphere of October 19 and
20, market participants read steep price declines
overseas as signals of the price direction in their
own market.
• In the weeks after the crash, international inves
tors liquidated large amounts of equities and
slowed other financial investment overseas. But
the slowdown fell short of the widespread with
drawal and repatriation of funds feared in the
immediate wake of the crash. It appears that many
sellers resided outside the G-10 countries and had
few investment opportunities at home.
The surge in international activity in equities
Cross-border investment
Equities achieved unusual prominence in international
investment after 1984. Investors participated in over
seas equities markets by building a portfolio of foreign
stocks, investing in mutual funds specializing in global
equities, and purchasing derivative equity instruments
such as convertible bonds and equity warrants. An
impression of the growth of cross-border investment
can be gained by looking at five major domestic mar
kets for which timely, though imperfect, data are avail
able:1 Canada, Germany, Japan, the United Kingdom,
and the United States.
'D ata measuring international flows in equities are, like most capital
flow data, subject to a number of shortcomings. The problems
include confusion between residence and nationality, gaps in
coverage, difficulties in recording conversions of convertible bonds
C ro s s -b o rd e r in ve s tm e n t in e q u itie s picked up
sharply from 1985 until the beginning of the fourth
quarter of 1987. In 1986 in particular, net equity pur
chases by nonresidents more than tripled in the United
States and Germany and rose by more than one half
in the United Kingdom (Table 1). Generally, stock mar
kets throughout Europe and the Far East appeared to
benefit from strong international purchases.
Japan, however, was a notable exception, as interna
tional investors sold Japanese shares out of concern
that the market was overvalued. These international
investors, mainly U.S. and U.K. institutional accounts
such as trust and pension funds, had been net pur
chasers of Japanese shares until 1984.2 Ironically, the
selling developed just before the yen began to rise and
sizable dollar returns on yen investments emerged.
The buying in the North American and U.K. markets
Footnote 1 continued
and equity w arrants into shares, and reporting errors. The definition
of equities varies from country to country: some include preferred
stock w hile others do not. An investment position may be classified
as a dire ct investm ent or a portfolio investment depending on the
share of outstanding equity held by a single investor. Finally, in this
article, cro ss-b o rd e r equity flows for the United Kingdom are
measured by proxies.
*The net sales position of nonresidents in Japan may som etimes be
overstated. N onresidents can acquire Japanese shares by exercising
eq uity options on eurobonds, usually in the form of equity warrants.
These acquisitions are not included as nonresident purchases in
some statistics, such as those produced by the Tokyo Stock
Exchange (TSE), w hile sales of such shares are included as
nonresident sales. The Bank of Japan’s capital flow statistics in
Table 1 include a measure of equity acquired through exercising
options and still report very large net sales.
and the selling in Japan increased in the first nine
months of 1987. Net nonresident purchases in the first
three quarters in Canada, the United Kingdom, and the
United States exceeded the amounts purchased in
these markets in the full year 1986, while net sales in
Japan picked up as rapidly increasing prices drove
Japanese price-to-earnings ratios to 60 or more, com
pared with 15 to 30 in other major markets.
Who were the major buyers in the surge in crossborder investment? The nationality of the end-investors
is often difficult to determine because many investors
make their overseas investments through international
financial centers. A large portion of investment activ
ities in the United Kingdom are conducted on behalf of
investors located outside the country, such as U.S.
pension funds and other international institutional
accounts. Substantial amounts of equities are pur
chased through Switzerland and some offshore cen
ters, w hich serve in te rn a tio n a l clients from both
industrial and developing countries.
Nevertheless, it appears that in 1986 participation in
cross-border equity investm ent was geographically
broad-based, with investors in all five major countries
in Table 1 increasing their net cross-border purchases.
U.K. and Japanese residents expanded their buying
most sharply. Large flows through international centers
such as the United Kingdom and Switzerland suggest
that at least a portion of cross-border equity invest
ment came from outside the G-10 countries.
In the first nine months of 1987, however, Japanese
residents alone appeared to fuel the continued expan
sion of cross-border equity investment; their buying
Table 1
The Expansion of Cross-Border Equity Flows before the Break
In Billions of Dollars
N onresident Net Purchases*
1985
Net Purchases of Foreign E quities*
1986
Of dom estic equities in
C anada
Germany
Japan
United K in g d o m f
U nited States
0.8
2.1
-0 .7
6.0
4.9
0.5
6.8
—15 8
9.6
18.7
1987
1985
Jan.-Sept.
By residents of
4.2
2.9
- 2 1 .9
11.2
23.3
C anada
Germany
Japan
United Kingdom }:
United States
1986
1987
Jan.-Sept.
0.4
1.6
1.0
5.6
1.9
1.6
2.4
7.0
10.5
2.4
0.3
-0 .6
13.5
5.3
1.6
* ( - ) = net sales.
tT ransa ctions by overseas residents in U.K. com pany securities; believed to be largely equities.
^N et purchases of ordinary shares of overseas com panies by nonbank financial institutions.
Sources: S tatistics Canada, Security Transactions with Nonresidents, Table 3; S tatistics Canada, Q uarterly Estim ates o f the C anadian
B alance of International Payments, Table 1; D eutsche Bundesbank, B alance o f Payments S tatistics, S tatistical Supplements to the
Monthly Reports o f the D eutsche Bundesbank, Series 3, Table 5d; Bank of Japan, Foreign D epartm ent, B alance o f Payments
Monthly, “ Long-Term C a p ita l” ; Central S tatistical O ffice (United Kingdom ), Financial S tatistics, Tables 7.1 and 8.7; U.S.
D epartm ent of Comm erce, Survey o f C urrent Business, Tables 2, 6, and 9; Board of G overnors of the Federal Reserve System,
Federal Reserve Bulletin, Table 3.24.
FRBNY Quarterly Review/Summer 1988
35
accounted for two-thirds of the net equity purchases by
residents of the five countries cited in Table 1. From
January to September, Japanese residents purchased
$13.5 billion net— an amount that, when annualized,
was more than double the previous year’s purchases.
Much of those funds flowed to the United States.
According to U.S. Treasury data, Japanese purchases
of U.S. equities came to $9.5 billion in the first nine
months of 1987.
Despite the growth in cross-border equity invest
ment, the share of foreign ownership remained low in
the largest markets. The foreign-held share of equities
outstanding was lowest in Japan and the United States
at around 5 percent, and somewhat higher in the
United Kingdom at 10 percent. In contrast, foreign own
ership ranged from 25 percent to 35 percent in some
other European markets.
Cross-border trading
Cross-border investors not only increased their net pur
chases in 1986 and 1987, but also traded their portfo
lios more actively. The value of their gross transactions
soared over 1986 and 1987 (Table 2). Viewed across
market centers, the rise was geographically broadbased in 1986, but became somewhat more concen
trated in 1987, because of the continued rapid growth
of cross-border transactions in the Japanese and U.S.
equities markets.3
Viewed by country of investor residence, transactions
by residents of Japan and the United States accounted
for most of the growth of cross-border transactions in
1986 and 1987. The high value of transactions reflected
the im p o rta n c e of in s titu tio n a l in ve sto rs, in c lu d
3Transactions data are not available for the United Kingdom.
ing m utual funds, in the tw o c o u n trie s and the
emphasis placed on active management of in stitu
tional investm ent portfolios. Japan’s equity transac
tions more than doubled in the first nine months of
1987 compared with the previous year. Cross-border
equity trading by residents of the four countries cited
in Table 2 accounted fo r roughly half of the total
transactions volum e by nonresidents recorded in
those same four countries. Available bilateral flow
data suggest that U.K. residents accounted for a
large part of the remainder.
Growth in transactions by nonresidents, however,
coincided with strong growth in home market transac
tions by domestic residents, so that in many larger
markets, the foreign share of transactions remained
low. In Japan, for example, nonresidents churned their
stock portfolios to realize gains from rising prices in
the overall market. In value terms, their gross transac
tions during the first nine months of 1987 more than
tripled on an annual basis compared to 1984 (Table 3).
This increase was less, however, than the rise for any
other investor group in the Japanese market. Foreign
transactions represented just over 10 percent of the
turnover on the major stock exchanges in the United
States and Japan, around 20 percent in the United
Kingdom (where a large proportion of all nonresident
transactions in London involved foreign stocks listed on
the International Stock Exchange), and nearly 25 per
cent in Canada and Germany.
In summary, by September 1987, the activities of
cross-border investors had grown considerably in most
major equity markets, but the foreign share of total
s to c k s o u ts ta n d in g and of tra n s a c tio n s vo lu m e
remained fairly low in the largest markets. Thus, quite
concentrated selling by nonresidents would have been
Table 2
The Expansion of Cross-Border Equity Transactions Value before the Break
Sum of Gross Purchases and Sales in Billions of Dollars
Transactions in Foreign E quities
N onresident Transactions
1985
1986
Jan.-Sept.
In dom estic equities in
C anada
Germany
Japan
United States
1987
11.3
38.3
81.3
159.0
18.9
77.1
189.6
277.5
33.7
59.3
278.0
359.7
1985
1986
C anada
Germany
Japan
United States
1987
Jan.-Sept.
By residents of
18.8
20.6
10.0
45.7
32.8
43.1
34.8
100.2
37.5
48.1
88.6
142.0
Sources: S tatistics Canada, S ecurity Transactions with Nonresidents, Table 3; S tatistics Canada, Q uarterly Estim ates o f the C anadian
B alance o f International Payments, Table 11; D eutsche Bundesbank, B alance of Payments S tatistics, S tatistical Supplem ents to the
Monthly Reports o f the D eutsche Bundesbank, Series 3, Table 5d; Bank of Japan, Foreign D epartm ent, Balance of Payments
Monthly, “ Long-Term C a p ita l” ; U.S. Departm ent of Com m erce, Survey o f C urrent Business, Tables 2, 6, and 9; Board of
Governors of the Federal Reserve System, Federal Reserve Bulletin, Table 3.24.
36
FRBNY Quarterly Review/Summer 1988
necessary to make a profound impact on stock prices
in New York, London, and Tokyo.
Twenty-four-hour trading
Trading of stocks on exchanges outside the home
country was the other principal channel for increased
international equities trading and investment. Markets
for foreign stocks had developed chiefly in New York
and London. Those markets remained confined to par
ticular segments of the global equities market, notably
U.K. stocks in New York and Continental European
s to c k s 'in London. Only a small market for foreign
stocks existed in Tokyo.
In New York, the principal instrument for trading in
overseas shares is the American depositary receipt
(ADR). ADRs are certificates that represent a given
number of shares of a foreign firm and are traded like
the public shares of U.S. companies. U.S. commercial
banks hold the underlying foreign shares in custodial
accounts in their London branch offices. The most
actively traded ADR issues, with few exceptions, are
the “ sponsored” programs of U.K. companies.4
Agent banks estimate that the ADR investor base is
largely institutional; about 10 percent to 20 percent is
retail. Institutional ADR investors are often newcomers
to the international share markets. Some have bylaws
that prevent them from purchasing securities not regis
tered in the United States while others may be able to
hold shares directly but prefer to keep some holdings
4U nder a sponsored ADR program , a foreign com pany designates a
U.S. com m ercial bank as custodian for the ADR program .
Table 3
Gross Transactions of Nonresidents
on the Tokyo Stock Exchange
1984
1985
1986
1987: Jan.-Sept.
Percent of Total
Transactions*
Value of
T ra n s a c tio n s 'f
Turnover
Ration
15.1
13.3
11.5
10.3
15.2
16.0
30.2
39.5
116
100
165
284
*By calen dar year,
f i n trillions of yen.
£The turnover ratio was ca lcu la te d by d ividin g the value of
nonresidents' gross transactions for an entire calendar year by
the value of their shareholdings as of March of the following
year. For exam ple, the turnover ratio for 1985 is based on
gross transactions for calendar year 1985 divide d by equity
holdings as of M arch 1986. For 1987, however, the ratio was
ca lcu la te d by d ividin g gross transactions through Septem ber
by equity holdings at the end of that month.
Source: Tokyo Stock Exchange.
in ADR form for liquidity reasons (essentially because
New York’s five-day settlement period is often short
compared to other markets).
The International Stock Exchange (ISE) in London
has the most extensive market in foreign equities.
Before the market break in October, about 800 foreign
equities were quoted on the ISE’s automated quotation
system (SEAQ In te rn a tio n a l); roughly 200 were
actively traded. The London foreign share market pri
marily consisted of European equities, with French and
German shares accounting for about a third of the
value of securities traded daily in. September 1987.
Trading in U.S. shares, in contrast, amounted to only
5 percent of daily transactions value or about $50 mil
lion per day. Trading in Japanese stocks was somewhat
greater, amounting to around 10 percent of daily trans
actions value or roughly $100 million a day.5
From Big Bang—the liberalization of the U.K. domes
tic securities markets in October 1986—to September
1987, foreign share trading on the ISE grew 70 per
cent, reaching £525 million ($850 million) a day. Before
the October 1987 market break, it constituted almost
o n e -th ird of to ta l e q u ity tu rn o v e r v a lu e on the
exchange. Foreign equities were also widely traded in
London off the ISE; the ISE estimated the off-exchange
volume to be roughly equal to that on the exchange.
Institutional investors dom inated trading rn foreign
equities, as reflected in an average transaction size of
£140,000, roughly five times that of the domestic sec
to r; and o ver h a lf of th e tra d in g was done by
nonresidents.
The fo re ig n sto ck se ctio n of the Tokyo Stock
Exchange (TSE) grew rapidly from a very low base but
remained relatively unimportant. Trading value in the
first nine months of 1987 tripled from the previous year
but still amounted to only 1.5 percent of TSE trading
value. Listings rose from 11 companies at the end of
1984 to 67 in September 1987. Most of the listings
were intended prim arily to improve name recognition
with Japanese investors as a means of attracting funds
in other markets rather than to promote significant trad
ing of the company’s shares on the TSE. The number
of foreign com panies whose shares were actively
traded in Tokyo was small.
Thus, compared to cross-border investment, 24-hour
trading represented a more limited and specialized
channel for the transmission of disturbances from one
equities market to another. As a general phenomenon,
it had not developed to the point where it could easily
spread a stock market decline around the globe.
5The ISE points out that trading volum es in foreign shares are volatile.
For the first six months of 1987, German and French shares
accounted for 26 percent of tra ding value; U.S. shares, 8 percent;
and Japanese shares, 21 percent.
FRBNY Quarterly Review/Summer 1988
37
The role of linkages in the crash
Stock markets turned down sharply in mid-October in
New York, Tokyo, and London, but the precise timing of
the events differed among the cities in two important
respects (Chart 1). First, while New York’s fall began
on October 14, London and Tokyo did not experience
large declines until the following week. The ISE began
falling slowly with New York on October 14, but a storm
on Friday the 16th prevented people from getting to
work, virtually closing the market. London’s first large
decline occurred on October 19. Tokyo did not fall
sharply until October 20. Second, although a severe
decline occurred in all markets on October 19 or 20,
New York and Tokyo recovered somewhat while Lon
don continued to fall over the next three weeks, reach
ing its low on November 9. The London pattern was far
more common both on the European continent and in
most of the Far East outside Japan.
For the three largest equities markets, a discernible
role for cross-border investment and overseas trading
in equities during the market break was confined to two
instances: heavy sales by nonresidents in Tokyo on
October 20 and price declines in U.K. ADRs traded in
New York around October 19. Thus, direct linkages
C hart 1
Dow, FT-SE 100, and N ikkei 2 2 5 Indexes
P e rce n t c ha nge
Aug
Sep
O ct
1987
1" N ikkei 225 data fo r S a tu rd a y tra d in g tw ic e a month are
not in clud ed.
38
FRBNY Quarterly Review/Summer 1988
U.S. equities
Most accounts of the New York market break focus on
the actions of U.S. residents and do not attribute a
major role to nonresident investors. The Brady Com
mission report made no mention of nonresident selling
in New York on October 19 or 20. The SEC staff report
recorded rum ors th a t in te rn a tio n a l investors were
“ dumping” U.S. stocks but concluded that the volume
of selling was not heavy. U.S. Treasury data also sug
gest that nonresident selling could not have been
heavy since, on balance, nonresidents purchased U.S.
stocks in October.6
Sales of U.S. stocks in London on October 19 by U.S.
institutional investors may have played a small role by
providing early indications of the strength of selling
pressures to come that day. According to the SEC staff
report, much of the London trading in U.S. stocks on
October 19 and 20 apparently was arranged in New
York and executed in London. The report attributed
much of the transactions volume to U.S. prenegotiated
trades crossed in London and to U.S. futures-related
and other special purpose trades.
The volume of trading of U.S. equities in London,
however, remained relatively small. For U.S. stocks
included in the Dow Jones Industrial Average, the
number of shares traded probably never exceeded 3
percent of New York share volume on any day between
October 14 and October 21. In the week of October 19,
the value of turnover in U.S. stocks was about normal;
however, the number of deals rose sharply. From the
resulting lower average transactions value, the ISE
inferred that retail business assumed more importance.
One explanation consistent with both the U.S. and Lon
don reports is that U.S. institutions traded in London
on October 19 and 20 and withdrew for the balance of
the week.7
The liquidity available in U.S. stocks in London
apparently declined after October 19, making transac
tions d iffic u lt. The In te rn a tio n a l Stock Exchange
reported that U.S.-affiliated market makers, on orders
from their head offices, did not always quote prices in
the week beginning October 19. The loss of liquidity in
U.S. shares was common to other foreign equities
traded in London. The spread between best bid and
Nov
* H olida y.
were not alone responsible for the rapid spread of the
break to virtually all of the world’s equities markets.
•See The Report o f the P residential Task Force on M arket
M echanism s, January 1988, and U.S. S ecurities and Exchange
Comm ission, Division of Market Regulation, The O cto ber 1987 Market
Break, February 1988, chap. 11.
7The ISE report on the crash appeared in the E xchange’s publication,
The Q uality o f Markets Quarterly, W inter 1987-88.
best offer (the “ touch” ) widened. For the 200 most
active foreign shares (accounting for 60 percent of for
eign share volume), the touch rose from about 0.8 per
cent precrash, a spread about equal to that for the
most liquid U.K. shares, to 1.2 percent postcrash.
Some linkage of price movements in London and
New York can be observed around October 19 in two
major stocks that trade 24 hours a day, IBM and Exxon.
(The shares of relatively few U.S. companies traded
actively around the clock at the time.) However, the
overlap in trading days and the difficulties in placing or
executing orders that emerged in both markets make
the extent of a New York-London price cycle virtually
impossible to identify. Both stocks opened roughly 1
percent to 2 percent lower in London than they had
closed in Tokyo on October 14, October 15, and Octo
ber 19, all days of large price declines in U.S. stocks
(Charts 2 and 3). Using London opening prices under
states London’s effect, since trading continues for five
hours before the New York market opens.
The size of London’s price decline on October 19 is
probably particularly understated by using opening
C h a rt 3
C hart 2
Global Trading in Exxon Shares
Global Trading in IBM Shares
M a rk e t-to -M a rk e t P ric e C hanges
M a rk e t-to -M a rk e t P rice C hanges
P erce nt change
30 —
New Y o rk c lo s e to
□
T o kyo c lo s e
P e rce n t c ha nge
3 0 ---------------------------------------------------------------------I----- 1 New Y o rk clo se to
I----- 1 T o k y o c lo s e
20
prices. London prices for IBM and Exxon opened down,
but the London market dropped throughout the day.
New York opened roughly 10 percent below the pre
vious day’s close in both stocks; a good part of the
drop may already have occurred in London. The fall in
London could conceivably have accounted for as much
as one-third of the total decline in the prices of these
two stocks on O ctober 19. S im ilarly, both stocks
opened much higher in London on October 20, as they
did a few hours later in New York.
In contrast, price movements in Tokyo bore little rela
tionship to price movements later in London and New
York. Trading volume in foreign shares in Tokyo, never
large, declined sharply after October 19 to less than
half the September average. Trading of U.S. shares in
Tokyo was clearly too small to have had a significant
effect on prices of U.S. stocks in London or New York.
Indeed, prices of both IBM and Exxon rose most days
between October 13 and October 23 in the Tokyo mar
ket, including October 19. A similar lack of correlation
between Tokyo and domestic price movements can be
found for other U.S. and U.K. stocks.
I----- 1 T o kyo c lo s e to
■----- ' Lo ndon open
20-
—
|
□
London open to
New Y o rk c lo s e
| London open to
New Y o rk c lo s e
2 4 -h o u r p ric e change
(N.Y. c lo s e to N.Y. c lo s e )
10
■ J l
T o k y o clo se to
London open
I
%
2 4 -h o u r p ric e change
(N.Y. c lo s e to N.Y. clo s e )
10-
a
Ji
i=f:t r r
% ~ T I
-1 0
-2 0
-3 0
13
14
15
16
19
O c to b e r
1987
20
21
22
23
13
14
15
16
19
20
21
22
23
O c to b e r
1987
FRBNY Quarterly Review/Summer 1988
39
Japanese equities
Although nonresidents owned only about 5 percent of
the Japanese market and accounted for about 10 per
cent of trading value, they were able to influence the
October 20 downturn strongly. The October 19 declines
on the New York and London exchanges heightened
the fear of an impending major correction in Tokyo.
That fear may have been exacerbated by the antici
pated supply overhang stemming from the huge Nippon
Telegraph and Telephone offering scheduled for
November. These worries may have led to some priceinsensitive selling by investors outside Japan.
Nonresidents placed orders to sell Japanese stock in
Tokyo early on the morning of October 20. Most of
these orders were “market” orders. That is, the saitori
member who matches buy and sell orders on the
exchange was instructed to sell the stock at the current
price.8 According to TSE rules, if a buyer cannot be
found at the current price, the saitori member drops the
price a notch at about 10 minute intervals until a buyer
is found. However, prices are only allowed to fall on
average about 15 percent from the previous day’s
close. On October 20, buyers proved difficult to find
and th6 price floors on many stocks were reached.9
Over the rest of the week, however, Japanese resi
dents absorbed large amounts of shares from nonresi
dents who were liquidating their holdings. According to
Tokyo Stock Exchange data, nonresidents sold over
¥1 trillion ($7 billion) of stock from October 19 to Octo
ber 24. Continued heavy sales the following week are
reflected in Japanese balance of payments data that
show nonresident sales of over $12 billion for all of
October.
The TSE bore most of the nonresident selling pres
sure on October 20. Few Japanese companies traded
in the United States in ADR form. Trading of Japanese
stocks in London was also small, although international
investors made heavier use of the London market for
Japanese stocks in the week of the crash. Measured in
value term s, transactions in Japanese shares
expanded five times. The surge occurred even though
Japanese dealers were not obliged to quote prices in
Japanese stocks on SEAQ on October 20, according to
the ISE.
•Unlike a specialist on the New York Stock Exchange, the saitori
member does not take positions in stocks.
•Price limits did not halt trading in foreign stocks, since the limits
operate differently for domestic and foreign stocks. For domestic
stocks, price limits for the current trading day are calculated from
the previous day’s close. For foreign stocks, the TSE uses the closing
price in the home or another major overseas market as its
benchmark. In practice, this means that a foreign stock can drop
more than 15 percent in the home market and then still drop an
additional 15 percent in Tokyo. SmithKline Beckman, for example, fell
30 percent from October 19 to October 20 in Japan.
40
FRBNY Quarterly Review/Summer 1988
U.K. equities
While some market analysts have argued that direct
sales of U.K. shares in London by nonresidents, partic
ularly European investors, may have influenced the
London crash, the behavior of domestic residents was
the driving force in the decline. Some U.K. institutional
investors sold heavily, while other U.K. institutions were
reluctant to buy, a reflection of the unusually large
equity positions they had taken on. Added to this was
the overhang from the British Petroleum (BP) under
writing and from commitments to take up shares from
previously scheduled U.K. company “rights” offerings.
These factors prevented institutional investors from
supporting ihe market with buying—a degree of which
might have been expected otherwise—and led them to
reduce heavy equity positions to make room for the
new issuance coming onto their books.10
The more important international influence on U.K.
stock prices was trading of top U.K. company shares in
the form of ADRs. Large net sales of U.K. ADRs in the
United States would have been reflected in a sharp
contraction in ADRs outstanding and a net flowback of
underlying registered shares into the London market.
The analysis below of the 10 largest sponsored U.K.
ADR programs during October and November shows
that a significant withdrawal from U.K. shares in ADR
form in fact occurred.
The development of a deep market for leading U.K.
shares in New York, backed by the increased liquidity
of the domestic U.K. equity market after Big Bang,
made U.K. shares more accessible and attractive to
international investors. From May to September 1987,
the share turnover (adjusted for the number of ordinary
shares per ADR) of the top 18 U.K. ADR programs was
roughly 4 percent to 5 percent of total U.K. customer
share turnover in London. The top 18 represent the
bulk of U.K. ADR trading volume in New York. The top
10 U.K. ADR programs analyzed here had adjusted
share trading volumes that ranged between 12 percent
and 70 percent of their combined London and New
York turnover in August and September 1987 (Table 4).
Differences in U.S. and U.K. investor attitudes toward
U.K. shares should, at the margin, be reflected in U.K.
“ Most major U.K. institutional investors were members of the
subunderwriting group in the record £3.7 billion BP privatization. The
subscription period ended on October 24. As in previous
privatizations, the BP indenture included a “clawback" provision
designed to assure maximum retail investor participation. Whenever
retail subscriptions exceeded the shares set aside for those investors,
shares allocated to institutions could be “clawed back" to meet retail
demand. The institutions, therefore, would typically oversubscribe—
sometimes by a factor of 10— to have a better chance of being
allotted the number of shares desired. Consequently, in the BP
offering, when retail investors failed to materialize once the sell-off in
London began, institutions revised their expectations and anticipated
receiving shares far in excess of the amount desired.
ADR creation or liquidation because of arbitrage bet
ween markets. Differences in attitude can reflect differ
ing expectatio n s about exchange rates and other
variables influencing investment returns. When such
differences lead to selling pressure from international
investors, we would expect to find that U.K. ADRs had
been broken down into their constituent shares and
sold into the U.K. stock market. ADRs outstanding for
individual issues, in fact, tend to ebb and flow signifi
cantly from month to month, within a range of 7 per
cent in either direction, according to ADR banks.
In October, the 10 ADRs studied showed large flowback on balance, follow ed by fu rth e r flow back in
November. Outstandings of 4 of the 10 U.K. ADRs fell
by more than 7 percent, and those of 2 more fell bet
ween 5 percent and 7 percent in October. The variation
ranged from an increase of 0.2 percent to a 14 percent
contraction. Outstandings of the 10 ADRs declined by
6 percent on average when weighted by the value of
A D R s o u t s t a n d in g
at th e e n d o f J u ly
(Table 4). In November, which may have been as impor
tant as October because of the five-day settlement
period for New York exchanges and the extended
decline of the U.K. market, all 10 ADRs experienced
flowback. Although only 1 program contracted more
than 7 percent, another 4 had flow back between
Table 4
Ten Leading U.K. ADR Programs:
Volume and Flowback Data*
1987
Aug.
Percent of total tra ding volum e*
Low
12.3
High
70.4
42.4
M edian
W eighted-average*
47.5
C reation/flow back ( + / - ):§
Low
-8 .4
High
37.0
M edian
-2 .0
4.2
W eighted-average*
Sept.
Oct.
Nov.
21.0
66.0
43.3
45.5
10.5
64.1
29.3
35.2
8.1
61.5
29.9
31.5
-5 .2
20.7
1.5
1.8
-1 4 .3
0.2
-6 .5
-5 .9
-8 .9
-0 .8
- 4 .5
-3 .8
*Top ten sponsored U.K. ADR program s: Hanson, Glaxo,
Jaguar, BP, Beecham, Saatchi, ICI, Reuters, Shell Transport,
and British Gas.
fAD R ordinary share equivalent volume as a percentage of the
sum of U.K. share volume and ADR ordinary share equivalent
volume.
^W eighted by the value of ADR ce rtifica te s outstanding at the
end of July.
§Percentage change in ADRs outstanding over the period.
Flowback is defined as a de clin e in outstandings over the
period.
Sources: S&P’s S ecurity Owner's Stock Guide, ADR agent
banks.
4.5 percent and 7 percent. The weighted average level
of flowback declined to about 4 percent, with the range
spanning 0.8 percent to 9 percent. Other U.K. ADR
programs showed mixed trading results over the two
months, with heavy flowback reported for some and
ADR creation for others.
The size of the flowback does not alter the earlier
conclusion that domestic, not foreign, selling was the
major trigger in the U.K. decline. In comparison with
London trading volume in the days following October
19, the number of U.K. shares represented by this level
of flowback was not overwhelming. Net sales of ADRs
in New York, however, did bid down prices in New York,
a development that may have had an important nega
tive psychological effect in London.
To see how trading in New York may have influenced
price behavior in London, changes in closing ADR
prices in New York from the London close earlier that
day were compared with closing price changes in Lon
don the following day. The period considered was the
week before and after October 19. The results of this
analysis were averaged across 10 leading U.K. com
panies with ADR programs and are summarized in
Chart 4.
Around October 19, changes in the London prices of
the 10 shares tended to reflect changes in their ADR
prices in New York after London’s close on the previous
business day. On October 20, for example, those
shares declined 14 percent in London after the ADR
prices had fallen 11 percent on October 19. The price
declines in New York on October 16 may have been
related in part to a storm in London that brought trad
ing there to a virtual halt, although the market was still
technically open. Together, the size of flowback in
October and the pattern of price changes around Octo
ber 19 suggest that some significant selling pressure
on U.K. stocks emanated from the ADR market in New
York.11
Implications for other market centers
Elsewhere in Europe and the Far East, where the for
eign share of ownership and transactions was greater
than in the largest markets, the effect of nonresident
selling was probably more pronounced. Relatively
heavy selling in some smaller markets can be seen in
the bilateral flow data from some large countries. For
example, U.S. residents sold substantial amounts in
"N evertheless, ADR flow back and price declines for individual shares
were not closely tied in October, underscoring the point that overseas
investors were not the drivin g force in the U.K. stock m arket decline.
Reuters, for instance, registered a 44 pe rcent price decline in
O ctober but showed below average flow back of 2'lz percent. Shell
Transport, by contrast, showed a below average price decline of 20
percent over the same period but showed heavy flow back of close to
14 percent.
FRBNY Quarterly Review/Summer 1988
41
some European countries and in some Asian countries
(including Japan) in October.
It seems likely that the ability to trade European
stocks in London somewhat accelerated the spread of
the worldwide decline to other European markets, an
effect that did not seem to hold for U.S. and Japanese
shares. Trading of foreign equities on the ISE rose
sharply during the week of the crash. In some cases—
the ISE report on the October market break mentions
French equities— selling pressures in London were
transmitted directly to the domestic market as market
makers sold in the home market the shares they had
absorbed from investors in London.
Even though the direct linkages were stronger in
markets other than the three largest equities markets,
cross-border investment and 24-hour trading of equi
ties probably did not create connections strong enough
to explain the synchrony in the world’s equities mar
kets. Thus, the principal linkage was most likely an
indirect one. In the panicky environment surrounding
C hart 4
Influence of New York Trading in U.K.
Shares on D ay-to-Day Price Changes
in London *
P erce nt change
1987
* A ve ra g e s fo r 10 leading U.K. e q u itie s tra d e d in ADR
form in New Y ork.
1" C hange in p ric e s from the London c lo s e to the
New Y ork close.
^ C hange in London c lo s in g p ric e s from the p re v io u s day.
42
FRBNY Quarterly Review/Summer 1988
the crash, market participants interpreted steep price
declines in overseas markets as signals of impending
declines in their own markets.
International linkages after the October break
Although cro ss-b o rd e r selling of equities cannot
explain the global spread of the crash, substantial
cross-border net sales did occur in the weeks after the
market break (Table 5). These sales no doubt contrib
uted to the weak tone in worldwide stockmarkets in the
last quarter of 1987. Indeed, heavy cross-border selling
created fears that international investors, shaken by
the October crash, were liquidating investments of all
types in the major markets and repatriating funds to
their home markets, a view that became known as the
“ homing” hypothesis.
The available data suggests, however, that the pat
tern of cross-border transactions in the weeks after the
break more closely resembled the development of
flows in the U.S. securities markets than the flows envi
sioned by the homing hypothesis. Some investor seg
m e n ts c le a rly d e c id e d to re d u c e th e ir e q u ity
investments, but others m aintained their holdings.
Cross-border demand for government securities picked
up shortly after the crash, but a sharp temporary slow
ing of corporate debt issuance in the eurom arkets
lasted into early 1988. As a result, the banking sys
tem—and the central banks—played an increased role
in international financial intermediation.
Cross-border trading after the crash
Sales by cross-border investors in the major equities
markets in the weeks after the crash were substantial.
After liquidating $12 billion in Japan in October (primar
ily in the second half of the month), nonresidents sold
another $9 billion in November. In the United States,
nonresidents, who were on balance net buyers in Octo
ber, sold nearly $7 billion in November. In Germany
and, to a lesser extent, in Canada, nonresident selling
continued to be heavy relative to m arket size in
November. In total, cross-border sales amounted to
$30 billion in four markets—Canada, Germany, Japan,
and the United States— in October and November.12
Another sign of cross-border investor withdrawal was
a drop in total transactions value after October, sug
gesting that nonresidents not only sold stocks but
traded their portfolios less actively. The value of non
residents’ gross transactions was unusually high in
October in four major countries (Table 6), well above
the average in the first nine months of 1987. However,
the value as a share of total turnover on the major
12Available statistics do not indicate the scale of net sales of foreign
equities in London.
stock markets did not rise above levels seen earlier in
1987. Transactions value dropped sharply in November
to levels well below the monthly average for the first
nine months in all markets. This broad-based slowdown
in activity was accompanied by reduced trading of for
eign stocks in domestic markets. Trading of foreign
stocks declined sharply on the Tokyo Stock Exchange,
and after a surge in October, fell close to its lows for
the year in London.
The identity of the heavy sellers in the fourth quarter
of 1987 is a mystery. U.K. residents accounted for as
much as a third, or around $10 billion, of the outflows in
the major markets. The United Kingdom’s importance
as a seller is borne out in bilateral flow data for the
major markets. But the United Kingdom channels funds
from many U.S. and other foreign institutional and large
investors who run their international portfolios out of
London.
Residents of the other four major countries for which
data are available do not account for much of the
sales. Of this group, U.S. residents were the only sub
stantial net sellers, but the sales were less than $3 bil
lion for October and November combined. A large part
of that sum appears attributable to sales by U.S.-based
Table 5
Cross-Border Equity Flows before and after the Market Break
In Billions of Dollars
N onresident Net Purchases*
1987MI
Net Purchases of Foreign E quities*
1987IV
1988I
1987
Oct.
1987
Nov.
-0 .3
-2 .0
- 1 2 .4
N.A.
2.5
-0 .5
-1 .4
-8 .5
N.A.
-6 .7
Of dom estic equity in
C anada
G ermany
Japan
United K in g d o m !
United States
1987MI
1987IV
1988I
1987
O ct.
1987
Nov.
-0 .3
0.6
2.4
N.A.
- 2 .1
0.1
-0 .3
0.8
N.A.
-0 .7
By residents of
1.3
0.8
-8 .0
5.4
5.0
-1 .0
-4 .2
- 2 1 .5
3.9
-7 .8
-0 .6
-0 .9
6.6
-0 .2
-0 .2
C anada
Germany
Japan
United Kingdom }:
United States
- 0 .1
0.4
3.5
1.2
0.4
0.4
0.6
3.3
-9 .6
-3 .9
0.1
1.9
-0 .6
-1 .0
0.7
* ( - ) = net sales.
fT ransa ctions by overseas residents in U.K. com pany securities; believed to be largely equities.
tN e t purchases of ordinary shares of overseas com panies by nonbank financial institutions.
Sources: S tatistics Canada, S ecurity Transactions with Nonresidents, Table 3; S tatistics Canada, Q uarterly Estim ates o f the Canadian
B alance o f International Payments, Table 1; D eutsche Bundesbank, Balance o f Payments S tatistics, S tatistical Supplements to the
Monthly Reports o f the D eutsche Bundesbank, Series 3, Table 5d; Bank of Japan, Foreign D epartm ent, B alance o f Payments
Monthly, “ Long-Term C ap ita l” ; Central S tatistical O ffice (United Kingdom ), Financial S tatistics, Tables 7.1 and 8.7;
U.S. D epartm ent of Com m erce, Survey o f C urrent Business, Tables 2, 6, and 9; Board of G overnors of the Federal Reserve
System, Federal Reserve Bulletin, Table 3.24.
Table 6
Cross-Border Equity Transactions Value before and after the Market Break
Sum of Gross Purchases and Sales in Billions of Dollars
N onresident Transactions
1987IM
Transactions in Foreign Equities
1987IV
1988I
1987
Oct.
1987
Nov.
6.8
13.7
74.3
95.4
4.3
8.4
41.2
58.0
2.6
5.2
20.8
34.0
In dom estic equities in
C anada
Germ any
Japan
United States
1987MI
1987IV
1988I
1987
Oct.
1987
Nov.
13.4
17.9
40.3
52.1
13.4
11.6
36.4
47.3
8.9
11.6
38.4
35.7
5.7
5.7
14.4
23.9
4.4
3.1
10.8
14.5
By residents of
11.2
22.5
85.9
136.8
9.4
17.0
76.5
122.2
C anada
Germany
Japan
U nited States
Sources: S tatistics Canada, S ecurity Transactions with Nonresidents, Table 3; S tatistics Canada, Q uarterly Estim ates o f the C anadian
B alance o f International Payments, Table 11; Deutsche Bundesbank, B alance o f Payments S tatistics, S tatistical Supplements to the
Monthly Reports o f the D eutsche Bundesbank, Series 3, Table 5d; Bank of Japan, Foreign Departm ent, Balance o f Payments
Monthly, “ Long-Term C ap ita l” ; U.S. D epartm ent of Comm erce, Survey o f C urrent Business, Tables 2, 6, and 9; Board of Governors
of the Federal Reserve System, Federal Reserve Bulletin, Table 3.24.
FRBNY Quarterly Review/Summer 1988
43
mutual funds investing in foreign stocks. They sold
$2.4 billion of stocks in October and November to meet
redemptions and switches out of international funds—
roughly 15 percent of the assets of all international
mutual funds at the end of 1986.
Indeed, residents of Japan, Germany, and Canada
were net buyers of overseas equities in the fourth quar
ter of 1987. Japanese net purchases, a major force in
the expansion of cross-border investment, slowed in
November and December after substantial net pur
chases in October.
A large part of the $20 billion balance of net sales
appears to be from countries that, like the United King
dom, traditionally channel investment from industrial
and nonindustrial countries. Estimated sales from
Switzerland accounted for roughly $3 billion; from
Asian centers, about $7 billion; and from other Euro
pean countries, around $3 billion. It seems likely, then,
that a significant portion of the disinvestment came
from outside the G-10 countries. In Germany, for exam
ple, selling by residents of Switzerland, offshore cen
ters, and LDCs came to roughly 40 percent of fourth
quarter 1987 net sales by all nonresidents.
Investment behavior of international investors
The apparent concentration of selling from interna
tional centers calls into question the homing hypoth
esis that circulated in the weeks following the crash. As
noted earlier, the homing hypothesis posited that inter
national investors, alarmed by the October crash, liqui
dated investments of all types in the major markets
and repatriated the funds to their home markets.
Two observations seem inconsistent with the homing
hypothesis. First, investors in the wealthiest coun
tries—Japan, Germany, and the United States—did not
flee the international equities markets, although Japa
nese and German residents slowed their external
investments after October and U.S. residents sold a
relatively small portion of holdings. Residents of these
countries had played an important role in the surge in
cross-border equity investment, accounting for a $26
billion increase in net cross-border equity investments
from the end of 1985 to September 1987.
These investors could have most easily repatriated
any proceeds from sales of their overseas assets. In
contrast, residents outside the G-10 countries who sold
equities would have had more limited domestic invest
ment opportunities and are more likely to have rein
vested their funds with international banks or in the
international markets.
Second, the pattern of cross-border investments in
the fourth quarter of 1987 resembles the flows in U.S.
domestic markets more than the withdrawal and
repatriation of funds posited by the homing hypothesis.
44
FRBNY Quarterly Review/Summer 1988
In the international as in the U.S. securities markets,
investors responded to the October break with caution.
Some investors sharply reduced their equity portfolios.
Many investors sought out the relative safety of the
government bond markets. Cross-border investment in
the major domestic bond markets— chiefly in govern
ment bonds— recovered sharply in November after net
sales in October, when rapidly rising interest rates pro
moted a shift to shorter-term investments. On balance,
nonresident bond purchases outweighed sales in the
fourth quarter in the five major countries examined
(Table 7). Issuance of eurobonds by Japanese and U.S.
borrowers—mainly corporations—slowed abruptly after
the crash, however, as did corporate bond issuance in
the United States, which in November and December
fell by more than a third from its monthly average in
1987.
The international banking system therefore inter
mediated a larger share of cross-border financial flows
than it had in recent quarters. The net eurocurrency
liabilities of BIS reporting banks, a group that includes
most banks in industrial countries and many offshore
centers, grew $28 billion in the fourth quarter of 1987,
net of exchange rate changes, compared to $6 billion
in the fourth quarter of 1986 (Table 7). In the balance of
payments accounts, bank inflows were initially the
major offset to the large outflows resulting from non
resident sales of equities recorded in Japan and Ger
many. The banking sector was also a heavy net crossborder lender to nonbanks in the fourth quarter, lending
$23 billion net, twice as much as in any other quarter
in the last two years. No doubt, the higher lending
reflected the slowdown in the international securities
markets.13
C apital flows were sufficiently disrupted and
exchange rate expectations sufficiently changed in the
weeks after the crash that central bank reserve flows
also became an important channel for international
capital flows. These reserve flows assisted directly—
and indirectly through the banking system—in financing
the U.S. current account deficit in the fourth quarter of
1987.
Cross-border portfolio investment by residents of the
large industrial countries picked up strongly in early
1988, and even investments in equities began to
improve late in the first quarter. Indeed, international
investors on balance bought $7 billion in Japanese
equities in the first quarter of 1988, the first net pur
chases in two years. Japanese and U.K. residents,
however, did not participate in the resumption of cross«u.S.
bank lending to nonfinancial corporate borrowers also increased
in the fourth quarter but was not out of line with the experience in the
fourth quarter of previous years, when financial flows were greatly
affected by tax law changes.
border equity purchases in the first quarter. And trading
of stocks outside the home market recovered even less
in the first months of 1988. The value of foreign equi
ties trading in London recovered to its year-earlier level
b u t re m a in e d w e ll b e lo w the m id -1 9 8 7 p e a k.
Table 7
Selected Flows from the Balance of
Payments*
Billions of Dollars Not Seasonally Adjusted; ( - ) = Outflow
1987-111
1987-IV
1988-1
N onresident p o rtfo lio Investm ent
Bonds
C anada
2.0
Germany
-0 .3
Japan
6.2
3.9
United K in g d o m }
-2 .4
United States
Eurobonds
Japan
14.0
6.3
United States
0.7
0.4
2.3
0.9
1.1
2.7
1.4
-1 .2
0.6
6.2
5.6
3.3
8.1
2.6
R esident p o rtfolio investm ent abroad
Bonds
- 0 .2
C anada
Germany
4.7
17.1
Japan}:
United Kingdom
- 2 .0
1.4
United States
0.4
0.5
7.3
-5 .8
5.7
-0 .4
8.0
13.2
5.7
3.8
Net bank flows§
C anada
Germany
Japan
United Kingdom
United States
BIS reporting area
1.6
3.4
24.0
-3 .3
13.1
27.9
1.5
2.2
2.9
10.0
-6 .7
7.4
Foreign currency reserves; ( - ) = increase
- 1 .1
-0 .6
C anada
Germany
-1 .5
- 1 5 .6
Japan
-2 .8
-8 .9
- 1 2 .7
-0 .5
U nited Kingdom
U nited States
- 0 .1
0.9
-4 .4
5.8
-3 .2
0.3
2.6
0.3
3.9
- 1 2 .2
- 6 .1
22.7
15.9
*For the United States, transactions with foreign official
institutions are excluded.
fG o vernm ent bonds only.
^E xcluding bonds issued by nonresidents in Japan.
§A djusted for exchange rates.
Sources: S tatistics Canada, Q uarterly Estimates of the
C anadian B alance of International Payments, Table 1;
Deutsche Bundesbank, Balance o f Payments
S tatistics, S tatistical Supplements to the Monthly
R eports o f the D eutsche Bundesbank, Series 3, Table
5d; Bank of Japan, Econom ic S tatistics Monthly,
"Foreign and O verseas Investments in S ecurities";
C entral S tatistical O ffice (United Kingdom ), Financial
S tatistics, Tables 3.5, 7.1, and 8.7; U.S. Departm ent
of C om m erce, Survey o f Current Business, Tables 2,
6, and 9; Board of Governors of the Federal Reserve
System, Federal Reserve Bulletin, Table 3.24; Bank
for International Settlem ents, International Banking
a n d Financial M arket Developments, August 1988;
International Monetary Fund, International Financial
Statistics.
Trading of leading U.K. ADRs in New York and of for
eign stocks in Tokyo was still at half the year-earlier
levels.
Conclusion
Cross-border investment and 24-hour trading cannot
explain the rapid worldwide spread of the stock market
break in October 1987. Direct linkages among the three
largest equities markets— New York, Tokyo, and Lon
don— played a role in two instances. Selling by inves
tors outside Japan in response to the declines in
London and New York appears to have helped precipi
tate the Tokyo decline. New York’s drop and recovery
were transmitted fairly quickly into the prices of leading
U.K. shares traded in ADR form in New York, although
the principal downward push in London came from
domestic investors.
The international linkages among the three largest
equities markets were not sufficiently developed to pro
duce the simultaneous and severe downturn in stock
prices worldwide, and many large international inves
tors, p a rtic u la rly those in Japan, did not sell off.
Domestic investors shaped the decline in the largest
m arkets. Thus, the prin cip a l in te rn a tio n a l linkage
between national stock markets appears to be the
unobservable and indirect one created when sharp
price declines in overseas markets contribute to a pan
icky market psychology.
The significance and the potential force of the inter
national transmission of disturbances are likely to grow.
Even after the nonresident liquidations in October and
November, the stock of cross-border equity holdings is
substantia l. Inform ation links among m arkets are
already extraordinarily good and, in the area of direct
trading and clearing linkages, the connections are now
in the early stages of development. At present, trading
lin ks e xist betw een C anadian and re g io n a l U.S.
exchanges. Although clearing links do not yet exist with
Tokyo, they are being developed between London and
New York. In time, the completion of these links and a
streamlining of the international clearing and settle
ment mechanism for internationally-traded equities
could allow price discovery to occur outside the home
market time zone and thus accelerate the reaction of
domestic equities prices to foreign disturbances. A hint
of this potential can be seen in the large increase in
the trading volume of foreign equities in London—
i n c l u d i n g J a p a n e s e and E u r o p e a n s h a r es
—during the break. The shifting of European equities
trading to London with clearing through Euroclear or
Cedel represents the type of mechanism that could
strengthen those international linkages.
The still relatively underdeveloped state of interna
tional equities trading reflects the many practical diffi
FRBNY Quarterly Review/Summer 1988
45
culties to be overcome in establishing trading and
clearing links among markets. The presence of practi
cal problems suggests that implementation of proposed
measures to reduce the chance of another U.S. market
break would not quickly and easily drive U.S. equities
trading to offshore markets. And in an international
context, reducing the chance of a market crash in the
large U.S. market—or any other large market—would
46
FRBNY Quarterly Review/Summer 1988
work to prevent the cycle of round-the-globe panic sell
ing seen last October.
Robert Aderhold
Christine Cumming
Alison Harwood
Margin Requirements on Equity
Instruments'
The stock market crash of October 1987 focused con
siderable attention on the adequacy and consistency of
margin requirements on U.S. equity-related products.
The analysis of these issues is difficult because of the
complexity of U.S. margin rules. To help clarify the dis
cussion, this article outlines the margin rules in the
markets for stocks, stock index futures, stock options,
stock index options, and stock index futures options.2
The general principle behind margin requirements is
simple. Margin requirements oblige investors who
undertake contractual obligations to deposit and main
tain a minimum amount of cash or securities with their
counterparties. Margin requirements in different mar
kets serve several different goals,3 but in all cases mar
gin deposits reduce counterparty losses whenever
contractual obligations are not fulfilled: if the investor
defaults, the counterparty at the very least retains the
margin deposit.
This principle applies in all markets, even though the
underlying contractual obligations that create the need
for margin requirements may differ. These contractual
obligations are outlined in Table 1. In practice, margin
'This article is intended only to provide a brief overview of margin
regulations and related topics. It is not designed to be used, and
should not be used, as a substitute for the appropriate regulations
and published interpretations thereof. Questions concerning margin
regulations should be addressed to your legal counsel.
2A more detailed description of margin requirements can be found in
George Sofianos, "Description of Margin Requirements,” Federal
Reserve Bank of New York, Unpublished research paper, September
1988.
*See the discussion in Arturo Estrella, "Consistent Margin
Requirements: Are They Feasible?” in this issue of the Q uarterly
Review.
requirements modify these obligations, since investors
must satisfy the margin rules on a continuous basis.
As described in the table, the contractual obligations
of short and long positions in the stock index futures
market are to receive or make payments sometime in
the future. Both long and short positions are required
to put up and maintain minimum margin deposits with
their counterparties. In options markets, the basic con
tractual obligation of the short position is to purchase
or deliver the underlying security if and when the long
position exercises the option. The short position is
required to put up and maintain a minimum margin
deposit with the counterparty. Finally, in the stock mar
ket, contractual obligations arise in two distinct trans
actions: buying stock on margin and selling stock
short. Investors buying stock on margin take out a loan
and use the proceeds together with their own funds to
buy stock. The stock is then deposited as collateral
with the lender. The basic contractual obligation of
each investor is to repay the loan. Margin requirements
oblige investors to deposit and maintain stock collat
eral at a specified minimum level above the face value
of the loan. In short sales, investors sell borrowed
stock, so their basic contractual obligation is to return
the stock to the lender. Each short seller is required to
put up a minimum deposit with the stock lender.
Describing the margin rules governing transactions in
the U.S. financial markets is a difficult task. Different
margin systems have developed for different markets
and, even within individual markets, the rules may vary
depending on the type of investor and transaction. The
purpose of this article is to identify the appropriate
margin-setting authorities, to sort out the rules apply-
FRBNY Quarterly Review/Summer 1988 47
Table 1
Summ ary of Basic Contractual Obligations*
Stocks
B uying s to c k on m a rgin: Investors b u yin g stock on m argin
take out a loan and use the proceeds together with their own
funds to buy stock. The stock then serves as collateral for the
loan. Such loans are known as margin loans. The basic co n tra c
tual ob lig ation of each investor is to repay the margin loan plus
interest. In general, m argin loans carry no stated maturity. The
cou nterparty is the provider of the margin loan.
Selling sto ck short: In short selling, investors sell borrowed
stock. The basic con tractu al obligation of each short seller is to
return the s to c k to the co u n te rp a rty, the stock lender. S tock
lending agreem ents are usually of indefinite duration, but they
are su b je ct to call by the lender.
Stock Index futures
Long po sitio n s: The con tractu al ob lig ation of the long position
is to receive on settlem ent date a m ultiple (usually $500) times
the underlying stock index minus the futures price. (Negative
receivables denote a paym ent.)
Short po sitio ns: The con tractu al obligation of the short po si
tion is to make a paym ent on settlem ent date equal to the m ulti
ple tim es the un derlying stock index minus the futures price.
(N egative paym ents denote receivables.)
Because all positions must be marked to market and losses
and gains realized daily, the settlem ent date differs from other
days only in that positions are marked to market for the last
tim e and then closed.
The ultim ate cou nterparty for both short and long positions is
the clearinghouse associated w ith each exchange.
Stock options
Long po sitio ns: The long position in an option con tract has
the right to exercise the option some time in the future and pur
chase (call option) or sell (put option) the underlying stock at
the strike p rice fixed when the position is opened. Because the
long position has a right but not an obligation, once the option
prem ium is fully paid, no contractual obligations remain.
Short po sitio ns: The contractual obligation of the short p o si
tion is to sell (call option) or buy (put option) the underlying
stock at the strike price if the long position exercises the option.
The ultim ate cou nterparty in all stock option transactions is
the Options C learing C orporation (OCC).
Stock index options
The con tractu al ob lig ation s are the same as for stock options
e x c e p t th a t the u n d e rly in g " s e c u r ity " is a m u ltip le (u s u a lly
$500) tim es a s to c k index. The ultim ate c o u n te rp a rty is the
OCC.
Stock index futures options
The con tractu al o b lig ation s are the same as for stock options
except that underlying a stock index futures option is a stock
index futures contract. The ultim ate counterparty is the clear
inghouse associated w ith each exchange.
‘ This table sum m arizes the b a sic contractual obligations in the
a b s e n c e of m a rg in re q u ire m e n ts . The p re s e n c e of m a rg in
requirem ents changes the contractual obligations of investors
because the m argin requirem ents must be satisfied on an ongo
ing basis. For exa m ple, w hen investors buy sto ck on m argin
from broker-dealers, they are required by the margin rules to
maintain a spe cifie d level of eq uity in the margin account at all
times.
48
FRBNY Quarterly Review/Summer 1988
ing to particular parties in particular situations, and to
outline each set of rules briefly.
In describing the rules, the article focuses on five
features that together determine the amount of protec
tion provided to counterparties:
• Initial margin requirements set the minimum mar
gin deposit with which a position can be opened.
• M aintenance m argin requirem ents set a flo o r
below which margin is not allowed to fall as long as the
position remains open.
• Variation margin refers to the flow of payments
from losers to gainers that results from the daily or
intraday reevaluation of positions in futures markets.
• Posting period is the amount of time an investor is
given to satisfy the initial, maintenance, and variation
margin requirements. If the investor fails to satisfy the
requirements within the allowable time, the counter
party can close the undermargined position. The length
of the posting period is im p o rta n t because as it
increases, counterparty losses may cumulate. In prac
tice, posting periods range from as many as 15 days to
a few hours.
• Allowable form of m argin refers to the type of
securities other than cash that can be used as margin.
In some cases only cash is allowed as margin; in other
cases securities and letters of credit can also be used.
The form of margin influences the cost of maintaining a
margined position and determines how easily the mar
gin deposit can be converted into cash if needed.
The following sections examine the margin require
ments in each market. Table 2 lists the markets that will
be discussed, the main contracts, and the various mar
gin-setting bodies. The table also identifies the clear
inghouses that play an im portant role in the margin
process for futures and option transactions.
Throughout, the a rtic le focuses on the m argin
requirements imposed by the regulatory bodies cited in
the table. It is important to remember that these are
minimum requirements. Counterparties, such as brokerdealers, often impose more stringent requirements.
Stocks
The Federal Reserve Board divides stocks into margin
and nonmargin groups. Margin stocks consist of all
U.S. exchange-traded stocks and some but not all overth e -co u n te r (OTC) stocks. B roker-dealers are not
allowed to use nonmargin stock as collateral in making
loans. By contrast, banks and other lenders can lend
any amount they like on nonmargin stock. Both margin
and nonmargin stocks can be sold short.4 The following
sections describe the rules established by the Board
and the New York Stock Exchange (NYSE) for buying
margin stock using a margin loan and for short selling.5
♦It is likely that some thinly tra ded nonmargin stocks are not sold
short because no stock is available to borrow, but the Board does
not p rohibit such a sale.
sThe margin rules of the various exchanges and the National
Association of Securities Dealers (NASD) are similar. This is partly
the result of a 1975 am endm ent of the Securities Exchange Act
Buying stock on m argin
Margin requirements for buying margin stock using a
margin loan differ depending on the source of the loan.
Margin loan so u rce s—the lenders— fa ll into three
groups: broker-dealers, banks, and other lenders. Reg
ulation T of the Federal Reserve Board determines the
Footnote 5 continued
of 1934, w hich prohibits the use of m argin rules to get a com petitive
advantage. The rules of the various exchanges and the NASD apply
to each organization’s members.
Table 2
Instrum ents, Markets, Clearing, and Margin Setting*
Stocks
Markets
M argin-setting Bodies
New York S tock Exchange
Over-the-Counter Market
Am erican Stock Exchange
M idw est Stock Exchange
Pacific S tock Exchange
P hiladelphia Stock Exchange
Boston Stock Exchange
C incinnati S tock Exchange
Federal Reserve Board, Regulations T, U, G, X (initial m a rg in s f)
Exchanges and the National Association of S ecurities Dealers (NASD) (m aintenance m argins)
The Securities and Exchange Comm ission (SEC) must approve exchange and NASD m argins
Stock Index Futures
Main C ontracts
S&P500
NYSE C om posite
Major Market
Value Line
M argin-setting Bodies
Clearing
Markets
C hicago M ercantile Exchange (CME)
New York Futures Exchange (NYFE)
C hicago Board of Trade (CBOT)
Kansas C ity Board of Trade (KCBOT)
CME Clearinghouse
Interm arket C learing C o rp 4
CBOT Clearing Corp.
KCBOT Clearing Corp.
Exchanges and clearinghouses
The C om m odities Futures Trading
Com m ission (CFTC) can im pose
em ergency m argins§
Stock Options
C learing
Main Markets
C hicago Board O ptions Exchange
Am erican Stock Exchange
P hiladelphia Stock Exchange
Pacific Stock Exchange
New York Stock Exchange
M argin-setting B odies
Options C learing Corp. (OCC)
Federal Reserve Board||
Exchanges and the OCC
SEC must approve exchange and OCC m argins
Stock Index Options
Main C ontracts
S&P 100
Value Line
Major Market
S&P 500
NYSE C om posite
Markets
C learing
M argin-setting Bodies
C hicago Board Options Exchange
P hiladelphia Stock Exchange
Am erican Stock Exchange
C hicago Board Options Exchange
New York Stock Exchange
Options C learing Corp.
Same as for stock options
Stock Index Futures Options
Main C ontracts
S&P500
NYSE C om posite
Markets
C hicago M ercantile Exchange
New York Futures Exchange
Clearing
M argin-setting Bodies
CME C learinghouse
Interm arket C learing Corp.
Same as for stock index futures
*For each instrum ent, markets are ranked according to average da ily share or con tract volume in March 1988 (greatest volume first).
fA lth o u g h the Board has the authority to set m aintenance margins, it has chosen not to exercise it.
tT h e Interm arket C learing C orporation is a wholly owned s ub sid iary of the Options C learing Corporation.
§The exchanges and clearinghouses do not have to get CFTC approval for changes in the level of m argin requirem ents. Major changes in
margin system s, however, must be approved by the CFTC.
IJSince S eptem ber 1985, the Board has allowed the exchanges to set their own m argins. Nevertheless, the Board prohibits banks from
m aking margin loans using options as collateral; only m argin loans to specialists are exem pted from this rule.
FRBNY Quarterly Review/Summer 1988
49
initial margin requirements on margin loans provided
by broker-dealers, and the NYSE determines the main
tenance margin requirements on loans provided by its
members. Margin loans from banks and other lenders
are regulated e xclusively by the Federal Reserve
Board through Regulations U, G, and X.6
Margin requirements also differ depending on the
destination of the loan. Margin loan destinations—the
borrowers—fall into three groups: public customers,
market makers, and broker-dealers other than market
makers.7 Diagram 1 shows the nine resulting combina
tions of lenders and borrowers. Because the rules are
the same for some com binations, only six distinct
cases are discussed.
Margin loans from broker-dealers to public customers.
A public customer wishing to borrow from a brokerdealer to buy m argin stock must open a margin
account with the broker-dealer. The account is debited
with the face value of the margin loan and credited with
the market value of the stock. The market value of the
stock minus the face value of the loan is the net equity
in the account. The initial margin requirement sets the
minimum acceptable net equity level at the beginning
of the transaction at 50 percent of the stock value.8
Equivalently, the investor cannot borrow more than 50
percent of the market value of the stock; that is, the
loan value of the stock is 50 percent.9 To satisfy this
requirement, the investor can make a cash down pay
ment equal to 50 percent of the market value of the
stock. For example, to buy a stock worth $100, the
investor can put up $50 in cash and borrow $50. The
margin account will be credited with $100 worth of
stock and debited with the $50 margin loan.10 Regula-
Diagram 1
Sources and D estinations of Margin Loans
*B a n ks include member banks o f the F ederal R eserve System
and no nm em ber ba nks tha t have signe d a s p e c ia l a g re e m e n t
w ith the Federal R eserve Board.
^O ther le n d e rs in c lu d e savings and loan a s s o c ia tio n s , c re d it
u nions, finance co m panie s, in s u ra n c e com panies, and
fo re ig n s o u rc e s o f m argin loans.
^M a rk e t m akers c o n s is t of s p e c ia lis ts , o d d -lo t de alers, OTC
m arket m akers, th ird m arket m akers, and b lo c k p o s itio n e rs .
^P ublic c u s to m e rs include all in v e s to rs e x c e p t m arket
m akers and b ro k e r-d e a le rs .
Distinct Cases for Margin Requirements
The Board regulations cover only those loans that are (a) extended
for the purpose of purchasing, carrying, or maintaining margin stock
(“ purpose c re d it” ) and (b) secured by margin stock. A purpose loan
secured with a bond or with a m ortgage on the borrower's home is
not covered. Also, a loan secured by margin stock that is used to
buy a bond or a house ("n onp urp ose c re d it” ) is not covered.
6
7There are no m argin requirem ents on loans to non-U.S. borrowers
outside the United States. In many cases, however, U.S. citizens are
covered by the margin regulations even if they borrow offshore.
(i) Loans from broker-dealers to p u blic custom ers
(arrow 6 ).
(ii) Loans from banks and other lenders to p u blic
custom ers (arrows 3 and 7).
(iii) Loans from banks and broker-dealers to m arket makers
(arrows 2 and 5).
(iv) Loans from banks to broker-dealers (arrow 1 ).
(v) Loans from broker-dealers to other broker-dealers
(arrow 4).
(vi) Loans from other lenders to broker-dealers and market
m akers (arrows 8 and 9).
•NYSE rules also require that a minimum net equity of $2,000 be
maintained in the account at all times.
®ln general, the loan value of a secu rity equals one minus the margin
requirem ent. For example, Treasury bills are subject to a 1 percent
NYSE-determ ined initial m argin requirem ent and consequently have a
loan value of 99 percent. Nonm argin OTC stock has zero loan value
at broker-dealers.
^A lternatively, the investor can deposit in the m argin account a fully
owned security, borrow an amount equal to the loan value of the
security, and use this amount as the cash down payment. For
exam ple, the investor can de posit $100 in Treasury bills, borrow $99,
50
FRBNY Quarterly Review/Summer 1988
Footnote 10 continued
and use this dollar am ount as the cash down paym ent together with
a $99 margin loan to buy $198 worth of stock. The margin account
will have $298 in assets (b ills and stock) and $198 in liabilities.
Because the account also includ es Treasury bills, net eq uity is less
than 50 percent.
tion T gives investors up to seven business days to
make this down payment.11
The initial margin requirement also determines the
amount an investor can withdraw from the account. As
the price of the margin stock increases, the maximum
allowable margin loan (50 percent of the stock value)
also increases. The difference between the outstanding
margin loan and the maximum allowable loan is an
unused credit line that the investor can draw down. In
the example, if the stock rises to $ 120 , the maximum
allowable margin loan is $60, so with a $50 margin
loan outstanding, the investor can withdraw $ 10.12
To satisfy the maintenance margin requirements, the
equity in the account must not fall below 25 percent of
the market value of the margin stock.13 If equity falls
below 25 percent, the broker must make a margin call
asking the investor to restore the account to at least
the maintenance level. Margin calls must be met “as
promptly as possible and in any event within 15 busi
ness days.”14 If the margin call is not met, the broker
must sell enough stock to restore the account to the
maintenance level.
Margin loans from banks and other lenders to public
customers. Loans in this category cannot exceed the
maximum loan value of the margin stock securing the
loan. This maximum loan value is set at 50 percent of
the market value of the stock; consequently, it is equiv
alent to the initial margin requirements for brokerdealer loans. There is no explicit maintenance margin
requirement. Margin loans to customers outside the
United States, to other domestic and foreign banks,
and to qualified employee stock ownership plans may
be made on a good faith basis. The phrase “on a good
faith basis” means that banks and other lenders, “exer
cising sound banking judgement,” can lend any amount
they like against margin stock.15
Margin loans from banks and broker-dealers to market
makers. The Board allows banks and broker-dealers to
make margin loans to market makers on a good faith
basis. These loans can be made to registered
exchange specialists, odd-lot dealers, and dealers cer
tifying that they are qualified OTC-market makers, qual
ified third-market makers, or qualified block positioners
as defined by the rules of the Securities and Exchange
Commission (SEC ).16 Market makers must certify that
the loans will be used solely for financing their marketmaking activities.
Margin loans from banks to broker-dealers other than
market makers.'7 Loans in this category may be used
for financing proprietary margin buying or for financing
broker-dealer margin loans to customers. Regulation U
treats bank loans to broker-dealers for financing propri
etary margin buying the same way as bank loans to pub
lic customers: such loans cannot exceed the 50 percent
loan value of margin stock. Several “special purpose
loans,” however, are exempted and can be made on a
good faith basis. Special purpose loans include arbitrage
loans, intraday loans, loans for securities in transit or
transfer, temporary advances in payment-against-delivery transactions, and distribution loans.18
When bank loans are used to finance broker-dealer
margin loans to customers, the broker-dealer acts as
an intermediary between the banks providing the funds
and the margin customers .19 Regulation U allows
broker-dealers to borrow from banks up to the total
indebtedness of their customers on a good faith basis,
pledging customers’ securities. For example, a brokerdealer that provided $1 million in margin loans to its
customers to buy $2 million worth of stock could use
this stock as collateral to borrow at most $1 million on
a good faith basis.20
Margin loans from one broker-dealer to another. The
"Broker-dealers often give investors less time to make the down
payment.
“ In general, if on day one the initial margin requirement is just
satisfied and on day two the stock price increases, the investor can
withdraw half of the increase.
“ All exchanges and the NASD impose the same 25 percent
maintenance margin requirement. Broker-dealers can impose higher
maintenance margins on their customers, just as they can impose
higher initial margins.
14NYSE Rule 431(f)(6). Broker-dealers usually allow only one to two
days for a call to be met. The Securities and Exchange Commission’s
capital rules require that broker-dealers take capital charges for any
maintenance margin deficiencies (less than 25 percent equity) that
persist for more than five days. Margin calls can be met by
depositing cash or securities.
1sThe quotation is from Regulation U. The good faith loan should not
exceed 100 percent of the value of the collateral.
“ Only banks may provide good faith margin loans to block positioners.
^Margin loans to broker-dealers are not the only loans made by banks
to securities firms; only margin loans, however, are subject to the
Board's margin requirements. Banks regularly provide securities firms
with other types of loans, including unsecured loans and loans for
financing activities unrelated to the broker-dealer function.
"For a loan to qualify as a special purpose loan, the borrower must
state in writing the purpose of the loan.
“ The broker-dealer is not a mere pass-through between the bank and
the margin customers. If a customer defaults, the broker-dealer must
use its own capital to repay the lending bank.
“ Loans to broker-dealers secured by customer securities are called
hypothecation loans. Written certification of their purpose is required.
SEC rules stipulate that a broker-dealer cannot pledge more than its
aggregate customer indebtedness but can pledge up to 140 percent
of the debit balance in an individual margin account.
FRBNY Quarterly Review/Summer 1988 51
Board does not allow margin loans from one brokerdealer to another for financing proprietary buying of
stock. Certain other loans between broker-dealers can
be made on a good faith basis. These include loans for
the purchase of securities for customer accounts21 and
loans by a broker-dealer to any of its partners or stock
holders for the purchase of its own stock, the stock of
an affiliated corporation, or the stock of another brokerdealer.
Margin loans from other lenders to broker-dealers. The
Board does not allow margin loans from other lenders
to broker-dealers, including market makers.22 The only
exceptions are emergency and capital contribution
loans. Unsecured loans to broker-dealers are theo
retically possible.23
Selling stock short
In general, a short sale consists of two distinct transac
tions, each subject to different requirements. One
transaction is between a customer and the customer’s
broker-dealer. In this transaction the broker-dealer pro
vides the stock that the customer sells short. The stock
comes from the broker-dealer’s own inventory, from
other customers of the broker-dealer, from other brokerdealers, or from other institutions.24 If the stock does
not come from the broker-dealer’s own inventory, then
there is a second transaction— in this case, between
the broker-dealer and the stock lender.
Consider first the transaction between broker-dealer
and stock lender. According to Regulation T, the
broker-dealer must deposit with the stock lender cash
or other acceptable collateral equal to 100 percent of
the stock’s current market value.25 The broker must
adjust or mark to market the amount of collateral daily
so that it is at all times equal to 100 percent of the
stock value at the close of the preceding business day.
For example, if the stock closes $10 higher than the
"These loans are subject to the same rules as bank loans to brokerdealers used to purchase securities for customer accounts.
®Non-broker-dealer affiliates of securities firms are also not allowed to
make margin loans to broker-dealers.
"Nevertheless, because virtually all of a broker-dealer’s assets are
securities, it is difficult to argue that any loan to a broker-dealer is
not secured directly, or indirectly, by securities and hence exempt
from the Board's lending restriction. One example of a permitted
unsecured loan is subordinated debt that complies with SEC rules.
previous closing, the broker must deposit $10 with the
stock lender by the next day’s opening.
Consider next the transaction between customer and
broker-dealer. The short sale must take place through a
margin account. The value of the stock sold short
appears as a debit in the account. The proceeds from
the short sale are retained by the broker-dealer and
credited to the customer’s margin account. According
to Regulation T, the customer then has seven business
days to deposit in the account an additional amount
equal to 50 percent of the value of the stock. This addi
tional deposit need not be in cash; securities can be
used instead. Once this deposit is made, the account
will show a credit equal to 150 percent of the stock
value, a debit equal to the market value of the bor
rowed stock, and net equity equal to 50 percent of the
stock value.
The account is marked to market daily so that a
change in the value of the stock will lead to an equal
and opposite change in the account’s equity position,
all else equal. For example, a $10 increase in stock
value will reduce the equity in the account by $10. The
customer need not deposit additional funds unless the
account drops below the maintenance level. The NYSE
requires customers to maintain net equity at a level
equal to at least 30 percent of the market value of the
borrowed stock.26 The customer must restore an undermargined account to the required level promptly, and in
no more than 15 days—the same requirement that
applies to customers who buy stock on margin.
Finally, two special cases must be mentioned. First,
for market-maker short sales that are related to market
making, only good faith margin is required. Second,
because proprietary broker-dealer short sales involve a
single transaction—that between the broker-dealer and
the stock lender—the broker-dealer is only subject to
the requirements for this transaction: 100 percent col
lateral marked to market daily.27
Stock index futures
In the stock index futures market, a clearinghouse
interposes between customers with long and short
positions. The clearinghouse is the ultimate counter
party in all trades and guarantees all transactions.
Customer transactions entail an additional layer of
intermediation: a clearing member comes between the
customer and the clearinghouse. A clearing member is
an exchange member firm that is also a member of the
"To borrow stock from a customer, a broker-dealer must have the
customer’s written consent. The broker-dealer cannot borrow more
than the debit in a customer's margin account.
"Maintenance margins for low-priced stocks are slightly higher.
“ As usual, this is a minimum requirement; in practice more collateral
may be put up. Acceptable collateral includes Treasury securities,
negotiable bank certificates of deposit, banker acceptances, and
irrevocable letters of credit.
" If the proprietary short sale has to be done through an account with
another broker-dealer (because the short selling broker-dealer is not
self-clearing), then it is subject to the 50 percent initial and 30
percent maintenance margin requirements.
52
FRBNY Quarterly Review/Summer 1988
clearinghouse. C learing m embers accept fina ncial
responsibility for the performance of their customers.28
C ustom ers include public custom ers, nonclearing
broker-dealers, and the floor traders or “ locals.” Only
proprietary trades of clearing members clear directly
through the clearinghouse.29
Customers deposit margin at clearing members, and
clearing members deposit margin at the clearinghouse.
Each clearing member maintains two separately mar
gined accounts with the clearing h o use : a house
account for proprietary trades and a customer account
for the trades of its customers. The exchanges deter
mine the custom er margin rules, and the cle aring
houses determine the rules for the deposit of margin
by the clearing members in their house and customer
accounts.30
For both customers and clearing members, there are
two distinct sets of margin flows: those associated with
the deposit of initial and maintenance margin and
those associated with the payment of variation margin.
The payment of variation margin is important because
once such a payment has been made, future counter
party losses depend on the change in the value of the
futures position till the next variation margin payment is
due on the following day. As a result, margin deposits
are required to protect counterparties against the pos
sible one-day loss in the value of futures positions.
The next two sections examine the requirements for
both types of margin flows, focusing on the rules of
the Chicago Mercantile Exchange (CME) and its clear
inghouse. The most popular futures contract, the S&P
500, trades on this exchange.
lar figures translate to 15.6 percent and 7.8 percent,
respectively, of the value of the contract on August 22,
1988. The maintenance margin is $10,000 per contract
for both speculators and hedgers. To be classified as
hedgers, customers must convince clearing members
that they have a need to hedge. For example, cus
tomers will qualify as hedgers if they hold diversified
baskets of stock and take short futures positions (socalled bona fide hedging). Customers may also qualify
as hedgers if they anticipate future capital flows and
want to lock in prices (anticipatory hedging). In prac
tice, the criteria used in making the classification vary
from clearing member to clearing member; the majority
of customers put up hedger margins. Table 3 lists the
current margin requirements for the main stock index
futures contracts.
The clearinghouse requires clearing members to
pass the maintenance portion of customer initial mar
gin on to their customer accounts with the clearing
house. For example, a speculator opening a single
position will deposit at least $20,000 with the clearing
member. The clearing m em ber w ill then forw ard
$10,000 to the clearinghouse and retain the balance.
For a hedger, the required initial and maintenance mar
gins are the same, so unless the clearing member asks
Footnote 31 continued
op posite positions in con tracts on the same index but w ith different
settlem ent days; interm arket spreade rs take op posite positions in
contracts based on different stock indexes. Intram arket spreaders
have margin requirem ents as low as $ 2 0 0 per contract.
Table 3
Initial and maintenance margin requirements. Initial
and maintenance margin requirements are specified in
fixed dollar amounts to be deposited per contract. As
of August 22, 1988, customers are required to deposit
with clearing members $20,000 per S&P 500 contract if
they are classified as speculators, and $10,000 per
contract if they are classified as hedgers.31 These dol“ For example, if a custom er defaults, then the clearing m em ber must
use its own cap ital to honor the de faulte r’s obligations to the
clearinghouse.
» ln practice, the structure of the market is more com plicated . Public
custom ers and nonclearing broker-dealers (but not the locals) must
trade through a futures com m ission m erchant (FCM). Some FCMs are
clearing m embers and some are not. Moreover, not all clearing
m em bers are FCMs. N onclearing FCMs must clear both custom er and
p roprietary trades through a clearing m em ber— a requirement that
adds an extra step in the whole process. This extra step is ignored
here. For more details, see Sofianos, “ D escription of Margin
Requirem ents.”
“ The CME clearinghouse sim ply determ ines what portion of the initial
margin de posit required by the exchange should be forw arded to the
clearinghouse and when this must be done.
Margin Requirements for Stock Index Futures
(As of August 22, 1988)
Initial
In
In
Dollars
Percent
M aintenance
In
In
Dollars
Percent
C hicago M ercantile Exchange (S&P 500)
Speculators
2 0 ,0 0 0
15.6
10,000
Hedgers
10 ,0 0 0
7.8
10 ,0 0 0
C hicago Board of Trade (Major Market)
Speculators
15,000
15.5
10 ,0 0 0
Hedgers
10 ,0 0 0
10 ,0 0 0
10.3
New York Futures Exchange (NYSE C om posite)
Speculators
6,0 0 0
8 .2
4,000
Hedgers
4,000
5.5
4,000
Kansas City Board of Trade (Value Line)
Speculators
6.4
7,500
H edgers
5,000
4.3
7,500
5,000
7.8
7.8
10.3
10.3
5.5
5.5
6.4
4.3
The percent requirem ents are the do lla r requirem ents as a
fraction of the ap p ro p ria te m ultiple tim es the A ugust 22, 1988
value of each index (500 x 257.0 for the S&P 500, 500 x
145.9 for the NYSE C om posite, 500 x 234.1 for the Value
Line, and 250 x 387.4 for the Major Market).
^T here are two other classifications: intram arket spreaders take
FRBNY Quarterly Review/Summer 1988
53
for more than the required $ 10 ,000 , the whole of the
deposit must be forwarded to the clearinghouse. The
total margin each clearing member must have on
deposit in its customer account at the clearinghouse
equals the total number of open positions it carries
times the maintenance margin per position. The CME
clearinghouse requires clearing members to make this
deposit based on the gross positions of their cus
tomers. For example, a clearing member whose cus
tomers are long 100 positions and short 99 positions in
the same S&P 500 contract must have at least
$ 1 ,9 9 0 ,0 0 0 in its c u s to m e r a c c o u n t at th e
clearinghouse.32
For proprietary positions, clearing members are sub
ject only to the $ 10,000 maintenance margin because
they clear directly through the clearinghouse.33 Clear
ing members must deposit this amount in their house
account at the clearinghouse. Because the mainte
nance level is the same for hedgers and speculators,
this distinction is irrelevant for clearing member propri
etary positions.
The exchange requires clearing members to collect
initial margin from customers in advance of opening a
position. The clearinghouse has the following timetable
for collecting margin from clearing members: every
day, after trading stops, it calculates the number of
open positions in each clearing member's accounts,
and early every morning it notifies members of their
total margin requirements. If a clearing member has on
deposit with the clearinghouse more margin than is
required, it can withdraw the excess.34 If the margin on
deposit is not sufficient, then the system generates a
cash margin call. For example, if open positions
increase from 199 to 200 and only $1,990,000 is on
deposit, the clearing member will get a call for an extra
$10,000. By 7:00 a.m. a bank acting on behalf of the
clearing member must confirm that it will meet the call
within the same day.35 In emergencies the clearing
house may call for additional margin to be deposited,
possibly within an hour.
*The example assumes that the maintenance margin is $10,000 for
each of the 199 positions. The other three clearinghouses (see Table
2) require clearing members to forward maintenance margin based
on the net positions of their customers. The netting is done not only
for each customer (opposite positions in the same contract cancel
each other out) but also across customers. In the example, clearing
members would forward the maintenance margin on only one
position.
*»The required margin is lower for intermarket or intramarket spreads.
*An excess will occur if the clearing member experienced a net
closing of positions.
“ Even though the bank makes a commitment at 7:00 a.m. to meet the
margin call, the clearing member need not put up the cash till some
time later in the day.
Digitized
FRASER Quarterly Review/Summer 1988
54forFRBNY
Clearing members can accept as margin from cus
tomers cash, U.S. Treasury securities, letters of credit,
and listed securities.36 The clearinghouse, however, is
more restrictive in what it accepts as margin from
clearing members. The first $25,000 of margin assets
per member account must be in cash, after which Trea
sury securities are acceptable 37 Letters of credit can
be used after $50,000 in cash and Treasury securities
have been deposited. The letters of credit must be irre
vocable and callable within 60 minutes. The clearing
house does not accept listed securities.
Variation margin. After the end of the trading day, the
clearinghouse marks to market each position in a
member’s house and customer accounts.38 It then for
wards this information to the clearing members ahead
of the next day’s opening. Variation margin flows
between customers and clearing members and
between clearing members and the clearinghouse.
Consider first the flows between customers and
clearing members. Each clearing member typically has
some customers that lose and some that gain on their
S&P 500 futures positions. Using the information pro
vided by the clearinghouse, each member credits the
accounts of the gainers with the gain in their positions
and debits the accounts of the losers with the loss.
Customers whose accounts have been credited can
withdraw any gains in excess of the initial margin. Cus
tomers whose accounts have been debited will get a
margin call if the loss pushed the account balance
below the maintenance level.39 An investor who gets a
margin call has to replenish the account, restoring it to
the initial margin level. Consider the speculator who
originally deposited $ 2 0 ,000 — $ 10,000 with the clear
inghouse and a $ 10,000 buffer with a clearing member.
A $7,000 loss in the position may be met out of the
buffer. No margin call has to be made, but the buffer
will be reduced to $3,000. A further loss of $4,000 will
leave the account undermargined by $ 1,000 and will
lead to a margin call for $ 11,000 to restore the account
to the initial level. Clearing members determine the
time allowed customers to meet a margin call. Accord
ing to the CME rules, “if within a reasonable time the
customer fails to comply with such demand (the clear
ing member may deem one hour to be a reasonable
“ The securities must be listed on the NYSE or American Exchange
and are accepted at 70 percent of market value.
"Treasury notes and bonds are subject to at least a 5 percent haircut.
»ln marking to market, the clearinghouse uses closing settlement
prices.
“ In practice investors whose accounts have been debited may get a
margin call even if the account is above the maintenance level.
time), the clearing member may close out the cus
tomer’s trades or sufficient contracts thereof to restore
the customer’s account to required margin status.” 40
The clearinghouse calculates variation margin sep
arately for each clearing member’s customer account
and house account. Customer account variation margin
depends on the net gains or losses of each clearing
m em ber’s customers. A member whose customers
experienced more losses than gains will make a cash
payment to its customer account at the clearinghouse
equal to the net loss. For example, a member with 10
customers losing $4,000 each and 5 customers gaining
$4,000 each must pay the clearinghouse $20,000. A
member that experienced net losses on its proprietary
positions will have to make a payment to its house
account at the clearinghouse. The clearinghouse will
forward these payments to clearing members whose
accounts are experiencing net gains.
Banks acting on behalf of clearing members must
confirm by 7:00 a.m. that the variation margin will be
posted with the clearinghouse sometime later the same
day. Table 4 summarizes the timing of margin flows
between clearing members and the clearinghouse. In
times of extreme price volatility, the clearinghouse may
ask clearing members to make intraday payments of
variation margin, usually within an hour. The CME
clearinghouse recently introduced a regular 2:00 p.m.
intraday variation margin call.41
Stock options
The institutional arrangements for stock options are
similar to those for futures. The ultimate counterparty
in all stock option transactions is the Options Clearing
Corporation (OCC). For customer transactions, a clear
ing member always interposes between the customer
and the OCC. Only proprietary trades of clearing mem
bers clear directly through the OCC. Public customers,
nonclearing broker-dealers, and market makers must
clear through a clearing member.
The option exchanges determine the minimum mar
gin to be deposited by customers to clearing members,
and the OCC determines the minimum margin to be
deposited by clearing members to the OCC.42 The OCC
uses a margining system that differs from the one used
by the exchanges. The next two sections describe the
NYSE rules for the deposit of margin by customers to
clearing members43 and the OCC rules for the deposit
of margin by clearing members.
Deposit of margin by customers to clearing members.44
Option buyers—that is, the long positions—must pay
the full premium in cash; they are not allowed to buy
options on margin.45 Once the premium is paid, the
^T h e margin rules of the option exchanges are very similar. This
sim ilarity enabled the NYSE to spe cify a uniform set of option rules
for all its members, irrespective of where options are listed. The
NYSE rules cover most of the m arket participants.
^ O p tio n transactions usually, but not necessarily, take place through a
margin account. Options may be both held and w ritten in a cash
account. This section de scrib e s the requirem ents for margin account
option transactions. W riting options through a cash account is subject
to a variety of restrictions: most im portant, the account must hold
either (a) the underlying stock in the case of a call option, or (b)
cash or money m arket instrum ents in the amount of the exercise
price in the case of a put option.
^E quivalently, the loan value of options is zero. This restriction applies
only to borrowing for the purpose of buying options (or stock). It is
possible to use the value of long option positions as collateral to
borrow for other purposes.
Table 4
Timing of Margin Flows between Clearing
Members and Clearinghouse (Chicago
Mercantile Exchange, S&P 500 Futures
Contract)
C hicago Time
3:15 p.m.
Trading ends.
9:00 p.m.
The cle a rin g h o u se be g in s fina l tra d e re con
cilia tio n . A fte r it is c o m p le te d , the c le a rin g
house calcula tes two sets of margin flows:
(a.) the am ount of m a rg in ea ch m e m ber
should d e posit or can w ithdraw to keep total
m argin in its custom er and house accounts at
the required level (num ber of open positions
tim es m aintenance margin);
(b ) the am ount of v a ria tio n m a rg in each
m em ber should pay or receive (the net loss or
gain in each account).
Early
morning
The clearinghouse informs clearing members
of the two sets of margin flows.
7:00 a.m.
The clearinghouse receives irrevocable com
m itm ents from banks acting on behalf of the
c le a rin g m em bers that both sets of m argin
paym ents w ill be m ade w ithin the day. The
tim ing of the actual cash flows betw een clear
ing m em bers and th e ir banks and betw een
the banks and the clearinghouse varies from
case to case.
8:30 a.m.
T ra d in g in th e S&P 50 0 fu tu re s c o n tra c t
begins.
«°CME rulebook, chap. 8 , section 827(D). The clearing m em ber may
also lend the required margin to the customer.
41The CBOT C learing C orporation has had a regular 2:00 p.m. intraday
variation margin call since before the O ctober 19 stock market crash.
^T h e Board has the authority to set option m argin requirements. Since
Septem ber 1985 the Board has allowed individual exchanges to
determ ine the margin requirem ents on the options that they list.
Nevertheless, the B oard’s Regulation U prohibits banks from making
m argin loans against options.
Source: C hicago M ercantile Exchange, Clearing Division,
“ C learing House Banking Interfa ce,” White Paper Series,
D ecem ber 1987.
FRBNY Quarterly Review/Summer 1988
55
option buyer has no remaining contractual obligations
and so is not required to put up and maintain a margin
deposit.
Margin requirements on option issuers—the short
positions— consist of a set of basic requirements for
naked (uncovered) positions. These requirements are
reduced for covered positions. Table 5 summarizes the
requirements.46 For a naked position, the issuer must
deposit as margin all the proceeds from the sale of the
option. If the option is in the money, the issuer must
also deposit extra margin equal to 20 percent of the
underlying stock price. If the option is out of the money,
the extra margin required is 20 percent of the stock
price minus the out-of-the-money amount but no less
than 10 percent of the stock price.
There are three types of covered short positions:
hedges, spreads, and combinations. To hedge a short
call (put), the issuer has to be long (short) in the
underlying s to c k .47 No margin is required for the
hedged short option.48 Spreads combine short with
long positions in a given call or put option. The posi
tions can have different expiration dates, different exer
cise prices, or both. Combinations consist of short puts
and short calls on the same underlying stock, possibly
with different expiration and exercise prices. The rules
for spreads and combinations are summarized in Table 5.
Maintenance margin requirements on short options
are the initial requirements marked to market daily. If
stock and option prices move favorably, funds will be
freed to support other investments. For unfavorable
moves, additional funds will be required to support
option positions. For example, if the underlying stock
price increases by $5 and the premium of an in-themoney naked short call option increases by $1, the
margin requirement will increase by $2.
With options, as with stock margin transactions, ini
tial margin must be deposited within seven business
days from the trade date, and margin calls must be met
promptly.49 Margin stock and U.S. government securi
ties, valued at their loan value, can be used to satisfy
««Table 5 shows the minimum amounts that must be in de posit at
clearing m em bers for each custom er short position. In all cases the
out-of-pocket paym ent of an option issuer is the required deposit
minus the proceed s from issuing the option.
option margin requirements.
The only groups exempted from the customer margin
rules are stock specialists, option specialists,50 and
other registered market makers. The NYSE allows its
members to carry long and short option positions of
these groups on “ a margin basis satisfactory to the
concerned parties.” 51 In the case of option market
makers, this special treatment applies only to positions
in the options in which they are making markets. In the
case of stock market makers, the special treatment
applies only to positions in options overlying the stock
in which they are making markets. When market-maker
positions in other options are allowed, they are subject
win addition to the option specialists, com petitive option tra ders who
qualify as sp e cia lists under SEC rules are also exem pted.
51NYSE Rule 431 (f)(2)(J). Moreover, the B oard’s Regulation U allows
banks to lend against long option positions to stock and option
specialists on a good faith basis. Such loans must be used to
finance narrowly defined “ perm itted offset positions.”
Table 5
Customer Margin Requirements on Stock
Options
(As of July 11, 1988)
Long options:
Premium must be paid in full
Naked short options
In-the-money:
Out-of-the-money:
i 7 + (0 .2 0 xS )
it + M A X [(0.20xS ) -
Hedges
Short call, long stock:
0
Short put, short stock:
Spreads
Long expires
before short:
Long does not
expire before short
Call spreads:
Put spreads:
Short com binations:
47For example, issuers of IBM calls must hold the underlying IBM stock
so that their ab ility to de live r the stock, whenever the calls are
exercised, is assured.
« lf the stock hedging a short call is not owned outright, it is subject
to the usual stock initial and m aintenance m argin requirements. The
same applies for stock sold short to hedge a put.
49As in the case of stocks, the NYSE perm its members to give
custom ers as many as 15 business days to meet a call. In practice,
broker-dealers usually give much less time.
56
FRBNY Quarterly Review/Summer 1988
T, 0.10X S ]
for call
0 .5 0 x S for stock
0 for put
1.5 0 x S for stock
Premium must be paid in
full for long
Short treated as naked
Premium must be paid
long
M A X [E (lo n g )-E (sh o rt),
Premium must be paid
long
M A X [E (sh o rt)-E (lo n g ),
in full for
0] for short
in full for
0] for short
The greater of the naked short put
or the naked short call requirem ent
plus it for the option with the lower
requirem ent
Explanations:
Option prem ium
S
Value of underlying stock
E
Exercise p rice of option
T
O ut-of-the-m oney amount = M A X [E -S ,0 ] for a call
= M A X [S —E,0] for a put
tt
to the customer margin rules.52
Proprietary positions of broker-dealers that are nei
ther market makers nor clearing members of the OCC
are treated like those of any other customer. The pro
prietary positions of OCC clearing members are only
subject to the OCC requirements.
The deposit o f margin by clearing members to the
OCC. Each clearing member must maintain separate
customer, house, and market-maker accounts with the
OCC. These accounts are margined separately. Total
margin for the customer account is calculated differ
ently from total margin for the house and market-maker
accounts.
The rules for the house and market-maker accounts
are examined first. Within each account, the OCC pairs
all long positions in an option class with short positions
in the same option class.53 Each option class now con
sists of some paired long and some paired short posi
tions, and in most cases, either some unpaired long or
some unpaired short positions.54 Concentrating on the
paired positions, the OCC subtracts the aggregate
value of the paired long options from the aggregate
value of the paired short options.55 A positive balance
is called excess short value and a negative balance is
called excess long value. There are now four possi
bilities for each option class:
• Excess short value, unpaired short positions. Total
margin is 130 percent of the excess short value plus
130 percent of the value of the unpaired short
positions.56
• Excess short value, unpaired long positions. Total
“ Market makers’ allowable option transactions are narrowly defined.
Stock specialists can only hold options overlying their specialty
stock, any option position established must be on the opposite side
of the market from the stock position, and the range of permissible
hedge ratios is limited.
“ An option class consists of either puts or calls on the same stock,
possibly with different expiration dates and strike prices. The pairing
is done as follows: positions in the same option series are paired
first, then the highest priced longs are matched with the highest
priced shorts, and so on till either the long or the short positions run
out.
“ For example, if an option class consists of two long and three short
positions, there will be two paired long, two paired short, and one
unpaired short position.
“ Values are based on the option premium at the close of trading.
“ Consider an option class consisting of two long options—one $5 and
the other $6—and three short options—one $5, one $7, and one $8.
The $5 long will be paired with the $5 short (same option series) and
the $6 long will be paired with the $8 short, leaving the $7 short
unpaired. Subtracting the paired longs from the paired shorts will
give $2 excess short value (($5+ $8)-($5+ $6)). Total margin will be
$2.60 (130 percent of the excess short value) plus $9.10 (130 percent
of the unpaired short).
margin is 130 percent of the excess short value minus
70 percent of the value of the unpaired long positions.
• Excess long value, unpaired short positions. Total
margin is minus 70 percent of the excess long value
plus 130 percent of the value of the unpaired short
positions.
• Excess long value, unpaired long positions. Total
margin is minus 70 percent of the excess long value
minus 70 percent of the value of the unpaired long
positions.
If an option class ends with a margin credit, 50 per
cent of this credit can be applied against the margin
required in other option classes within the same
account.
Margin for the customer account is calculated more
conservatively. All long positions in an option class are
classified as unsegregated or segregated. Unsegre
gated positions form the long leg of an identified
spread in the account of an individual customer. The
OCC then follows the same procedure used for the
house account, but with two differences: only the
unsegregated long positions are paired with short posi
tions,57 and segregated long positions and excess long
values are set to zero.58 The end result is that clearing
members must deposit 130 percent of the aggregate
value of customer short positions, with some short
positions offset by the value of unsegregated longs.
Option classes never end with a margin credit in the
customer’s account.
The calculations described above are repeated every
day after trading stops. By 7:00 a.m. every morning,
clearing members get a report stating the aggregate
required margin on short positions that must be in
deposit with the OCC by 9:00 a.m. Margin must be
deposited in the form of cash, U.S. government securi
ties, bank letters of credit, or margin stock at 50 per
cent of market value. For short calls, the clearing
member can deposit the underlying security rather
than deposit the margin. The OCC has the authority to
change margin requirements at short notice if market
conditions make this necessary.
Stock index options
The same institutional arrangements are used for stock
index options as for stock options: the OCC is the ultitfMoreover, unsegregated longs cannot be paired with shorts with
longer expirations.
“ Segregated long positions are set to zero because if one customer
defaults, the OCC cannot seize the long positions of another
customer. The customer account of a clearing member at the OCC
consists of the positions of the clearing member’s many customers.
Even though the clearing member has a lien on the positions of each
of its customers, the OCC does not have an indiscriminate lien on all
the positions in the customer account.
FRBNY Quarterly Review/Summer 1988 57
mate counterparty but clearing members interpose
between customers and the OCC. The rules for the
deposit of margin by customers to clearing members
are almost identical to the corresponding rules for
stock options: long options cannot be bought on mar
gin, and the margin deposit on naked short positions is
calculated in the same way. For naked short positions
in broad-based index options, however, the investor is
required to deposit extra margin equal to 15 percent—
instead of 20 p erce nt— of the underlying ind ex.59
Spreads and combinations are given the same treat
ment as in stock options, but hedged index option posi
tions are treated the same as naked positions. Posting
periods are the same as for stock options.
The rules governing the deposit of margin by clear
ing members in their customer, house, and marketmaker accounts at the OCC are different from the cor
responding stock option rules.60 The most interesting
feature of these rules is the use of an option-pricing
model to estimate the net cost (or value) of liquidating
all positions in an account that belong to the same
option group.61 For each option group, the OCC has
specified a range, known as the margin interval, that
“ B road-based index options include those on the S&P 500, S&P 100,
Major Market, Value Line, and NYSE C om posite indexes.
“ The OCC m argins all nonequity options (for example, options on
governm ent secu rities or foreign currencies) in the same way as
index options.
^ A n option group consists of all positions (long or short, put or call, at
any strike price and any expiration date) on the same underlying
index. Long positions give rise to liquidation value w hile short
positions represent a liquidation cost.
Table
6
OCC Stock Index Option Margin Intervals
(As of July 11, 1988)
Option
S&P 100
S&P 500
AMEX Major Market
NYSE C om posite
AMEX Institutional
PSE FNN C om posite
PHLX National OTC
Value Line Com posite
AMEX C om puter Tech.
PHLX Gold and Silver
AMEX Oil
PHLX U tility Index
In
Points
M argin Interval
In
Dollars
16.00
1,600
1,600
2,400
800
1,600
10 .0 0
1,0 0 0
15.00
1,500
12.0 0
1,2 0 0
16.00
16.00
24.00
8 .0 0
6 .0 0
600
11.0 0
1,10 0
8 .0 0
800
700
7.00
Percent
of Index
6.19
5.91
5.86
5.23
5.99
5.34
5.77
4.89
5.16
10.48
4.54
3.80
Source: OCC Inform ation Memo, A pril 11, 1988, updated. Index
percentages are based on the closing values of the underlying
indexes on July 11, 1988.
58
FRBNY Quarterly Review/Summer 1988
reflects the likely one-day change in the underlying
index. Table 6 lists the current margin intervals for all
stock index options. For example, the margin interval
for the S&P 100 index is 16 points. Every day, after
trading stops, the OCC calculates the current liquida
tion cost using the closing option premia and estimates
the liquidation cost under the assumption that the cur
rent closing index value increases and decreases by
the full margin interval. If the closing value of the S&P
100 is 250, the OCC will estimate the liquidation cost at
234 and 266.62 The required margin is equal to the
maximum of the estim ated and current liquidation
costs.63 With stock index options, as with stock options,
the OCC calculates margin for custom er accounts
more conservatively than for house accounts. The main
difference is that the OCC assigns zero value to segre
gated long positions in a customer account. Posting
pe rio d s fo r house, m arket-m aker, and cu stom er
accounts are the same as for stock options.
Stock index futures options
Stock index futures options trade on futures exchanges
and clear in the same way as futures. The most popu
lar contract is the S&P 500 futures option. Like its
underlying futures contract, this option contract trades
on the CME and clears through the CME clearing
house.64 This section describes the rules of the CME
and its clearinghouse.
The rules for the deposit of margin by customers to
clearing members are sim ilar to the corresponding
stock option rules: both sets of rules are strategybased. A set of basic requirements applies to naked
short positions; these requirements are reduced for
hedges, spreads, and combinations. To calculate mar
gin, clearing members use the margin requirements for
stock index futures, so the classification of customers
as speculators or hedgers carries over to stock index
futures options. Table 7 lists customer margin require
ments for a sample of positions in the S&P 500 futures
option. For example, a customer with a naked long
position must pay the premium in full. A customer with
a naked in-the-money short position must deposit the
premium plus the margin for the underlying futures
contract (either $20,000 or $10,000). If the position is
“ The OCC also estim ates the liquid ation cost at all strike prices
between these two extremes.
“ This is a sim plified representation of the rules. For more details, see
Sofianos, "D escription of M argin R equ irem ents” A nother interesting
feature of these rules is tha t options based on broad-based indexes
form a single “ product g ro u p ” and are m argined as an integrated
portfolio.
MOne advantage of this arrangem ent is that it facilitates the crossm argining of S&P 500 futures option positions and S&P 500 futures
positions.
out of the money, less margin is required. Customers
can deposit securities and letters of credit as margin
instead of cash—the same alternatives open to futures
customers. Positions are marked to market daily. Cus
tom ers must pay any additional required margin in
cash, daily, and no later than 10 minutes before the
market opens.
The clearinghouse uses a delta-based margin sys
tem to calculate the margin to be deposited by clear
ing members. Everyday it estimates the delta for each
option position.65 The daily margin requirement for each
“ The option delta is the rate at w hich the option prem ium changes as
the underlying futures price changes. Deltas range from - 1 to + 1.
Table 7
Customer Margin Requirements on S&P 500
Futures Options
(S elected Positions; As of S eptem ber
1
, 1988)
Long options:
Premium must be paid in full
Naked short options
In-the-money:
Out-of-the-money:
it + M
ir + M A X [M -(0 .5 x T ), 2,250]
O ption-futures spreads (hedges)
Short call/lon g futures
|
ir + M A X [m -(0 .5 x N ), 2,250]
j
on com bined position
Short put/short futures
Long call/short futures
Long put/long futures
O ption-option spreads
Horizontal*
Long expires
before short:
1
j
M A X fm -iT , 0] for futures
Premium must be paid in full
for long options
H. + M AX[tt ( s h o r t) - it (long),
] for short
Premium must be paid in full
for long
0
Short expires
before long:
Short com binations
S tra d d le s f:
for short
Premium must be paid in full
for long
0
ir(p u t) + -rr (call) + m
Explanations:
ir
Option prem ium
M
M argin on S&P 500 futures con tract (20,000 or 10,000)
m
H edge m argin on S&P 500 futures contract (10,000)
MS pread m argin on S&P 500 futures contract (400)
S
Value of underlying index
E
Exercise p rice of option
T
Out-of-the-m oney am ount = M A X [E -S ,0 ] for a call
= M A X [S -E ,0 ] for a put
N
In-the-money am ount = M A X [S -E ,0 ] for a call
= M A X [E -S ,0 ] for a put
*H orizontal spreads: one short plus one long, call or put, same
exercise price, diffe ren t expiration date.
fS h o rt straddles: one short put plus one short call, same
exercise price, same expiration date.
short position is the current option premium plus the
$10,000 m aintenance m argin requirem ent for the
underlying S&P 500 futures contract multiplied by the
relevant delta. There is a minimum margin charge of
$475 per naked short option. As in the case of futures
positions, clearing members can deposit Treasury
securities and letters of credit as margin. Because both
the option premium and the delta can vary from day to
day, the total margin that must be on deposit with the
clearinghouse will change daily even if the number of
open positions does not change.66 The clearinghouse
uses the same timetable for calculating and collecting
margin on options that it uses for futures.
The CME is currently replacing both its strategybased and its delta-based margin systems with a new
system called Dollars-at-Risk.67 It will use the new sys
tem to calculate the margin that must be deposited
both by customers to clearing members and by clear
ing members to the clearinghouse. The new system is
sim ilar to the OCC margin system for stock index
options. Under the new system, the CME will be using
an option-pricing model to obtain daily estimates of the
liquidation cost of a portfolio of positions on the S&P
500 index under a variety of assumptions about the
underlying futures price and its volatility. It will set mar
gin to cover the maximum estimated liquidation cost.
The portfolio may consist of positions on S&P 500
futures and options on these futures, so that estimated
gains (losses) on the futures can offset (augment) esti
mated losses on the options. The CME will impose
additional margin charges for spread positions with dif
ferent settlement dates, and there will be a minimum
margin charge for short options.68
Summary
The differences in margin requirements examined in
this article can be sum m arized briefly. The margin
rules on U.S. equity-related products differ depending
on the product and the identity of the parties in the
transaction. Often, for a given product and investor, the
requirements will also depend on the investor’s combi
nation of positions. Differences in margin requirements
go beyond simple variations in margin levels; there are
differences in the way margin is calculated, the length
of the posting period, and the form margin can take.
Investors buying stock on m argin face diffe re n t
“ For stock index futures contracts, the total margin that must be on
de posit with the clearinghouse changes only if the num ber of open
positions changes.
^T h e new system will be used for S&P 500 futures options and all
other CME options on futures.
« A more de tailed d e scription of the new D ollars-at-R isk system can be
found in Sofianos, “ D escription of Margin Requirem ents.”
FRBNY Quarterly Review/Summer 1988
59
requirements depending on whether the source of the
margin loan is a broker-dealer, a bank, or some other
lender. The requirements also depend on whether the
margin borrower is a public customer, a market maker,
or a broker-dealer. For short sales, the identity of the
short seller is important: the short seller may be a pub
lic customer, a market maker, or a broker-dealer, and
the requirements vary in each case.
In the stock index futures market, one set of rules
governs the deposit of initial, maintenance, and varia
tion margin by customers to clearing members. Initial
margin is higher if the customer is classified as a spec
ulator rather than a hedger. Another set of rules gov
erns the deposit of margin by clearing members to the
clearinghouse. Each clearing member maintains one
customer account and one house account with the
clearinghouse, and the two accounts are margined
separately.
60 FRBNY Quarterly Review/Summer 1988
For options, there are again two sets of rules: one for
the deposit of margin by customers to clearing mem
bers and another for the deposit of margin by clearing
members to the clearinghouse. For stock options, stock
index options, and stock index futures options, cus
tomer margins are strategy-based: in all cases margins
vary depending on whether short positions are naked,
or whether they are hedges, spreads, or part of some
other combination. For each of these three types of
options, a completely different margining system is
used to calculate clearing member margins. In all
cases, clearing members maintain separate customer
and house accounts with the clearinghouse. The two
accounts are margined separately using different rules.
George Sofianos
Consistent Margin
Requirements: Are They
Feasible?
With the development of a wide variety of markets in
equity-related financial instruments, investors have at
their disposal numerous ways of investing in stock
“exposure.” That is, they may invest in various instru
ments whose returns are determined primarily by the
returns on individual stocks or portfolios of stocks. For
every position in each of these equity-related instru
ments, there are minimum margin requirements that
compel the investor to maintain a specified level of
equity in a margin account. This article examines the
issues surrounding the consistency of margin require
ments across e q u ity-rela te d m arkets, suggests
methods for reducing inconsistencies, and identifies
the inherent problems.
The equity-related instruments currently available are
summarized in Table 1. There are three basic con
structs through which new instruments are created:
indexes, futures contracts, and options contracts. In
addition, these techniques may be combined to pro
duce other derivative securities, such as index futures
or options on index futures. The available combinations
allow investors to obtain equivalent returns in various
markets and to choose the market that is most suitable
for their particular needs (as regards transaction costs
and the timing of the transactions, for example). The
derivative markets also permit reallocations of riskbearing among investors over time with a flexibility that
would be difficult to achieve with the underlying instru
ments alone.
Because of the relationship between the returns on
derivative assets and those of the corresponding
stocks, each derivative instrument is priced in a way
that is closely related to that of the underlying equity
position. Otherwise, arbitrage profits would be avail
able on an almost riskless basis to investors who
assume positions in pairs of instruments that are mis
priced according to the basic implicit relationships.
Two questions are examined here. First, should mar
gin requirements be made consistent across all equityrelated markets? Margin requirements serve more than
one objective, and they are set by numerous institu
tions with different backgrounds in different markets, so
they exhibit little apparent consistency across markets.1
Second, if it is deemed advisable to make margin
requirements more consistent, how does one go about
this task? The analysis that follows concludes that it is
desirable to have a degree of consistency across mar
kets, but not necessarily identical requirements. On the
other hand, the opportunities for fine tuning are limited
by the uncertainty that prevails as to the exact results
of applying margin requirements. The lesson is that a
healthy dose of good judgment is essential in the set
ting of margin requirements.
Why impose margin requirements?
Before proceeding to the questions regarding the con
sistency of margin requirements, it is necessary to con
sider the ultimate objectives of such requirements.
Only in that context will the appropriate criteria for con
sistency become clear.
At no point in time has there been a clear consensus
about the rationale for imposing margin requirements.
’George Sofianos, "Margin Requirements on Equity Instruments,” this
issue of the Quarterly Review, provides a detailed summary of the
margin requirements on equity-related instruments for various investor
categories.
FRBNY Quarterly Review/Summer 1988 61
As expertise has developed in this area, some of the
proposed motivations have lost most of their support.
For example, the argument has been advanced that
margin requirem ents reduce the diversion of funds
from productive uses (such as physical investment) to
speculative uses. Real resources, however, are not in
general used up by margin loans, which represent the
insertion of an additional instrument in the chain of
financial intermediation channeling savings into invest
ment. It is possible, however, that margin requirements
could be used to deal with market imperfections.
A n o th e r fo rm e rly p o p u la r claim is th a t m argin
requirements protect unwise small investors from them
selves by limiting the amount of risk they can incur.
Margin requirements apply to broad classes of inves
tors and thus are, at best, a blunt instrument for weed
ing out these problem cases. In addition, they only
restrict the credit that may be obtained directly by
using the securities purchased as collateral and take
Table 1
Menu of Available Equity Instruments
Instrum ent
Individual stocks
Futures on stocks
O ptions on stocks
O ptions on futures
Indexes
Index futures
Index options
O ptions on index
futures
Key:
AMEX
CBOE
CBT
CME
KC
NYFE
NYSE
NASDAQ
PSE
PHLX
NA
62
R epresentative
Exchanges
NYSE, AMEX,
NASDAQ
NA
CBOE, AMEX,
PHLX, PSE,
NYSE
NA
NA (proposed for
AMEX, NYSE,
PHLX)
CME
NYFE
CBT
KC
CBOE
AMEX
NYSE
PHLX
Underlying S ecurity
_
—
Individual Stocks
—
—
NASDAQ
S&P 500
NYSE Com posite
Major Market Index
Value Line
S&P 100, S&P 500
Major Market Index
NYSE Com posite
Value Line, OTC
Com posite
NASDAQ 100
CME
NYFE
S&P 500
NYSE C om posite
Am erican Stock Exchange
C hicago Board Options Exchange
C hicago Board of Trade
C hicago M ercantile Exchange
Kansas C ity Board of Trade
New York Futures Exchange
New York S tock Exchange
National Association of Securities Dealers
Autom ated Quotation System
Pacific Stock Exchange
P hiladelphia Stock Exchange
Not available
FRBNY Quarterly Review/Summer 1988
no account of the investor’s overall leverage.
Only two motivations seem to have withstood the test
of time, although the issue of their validity is by no
means completely settled. The first of these is the pro
tection of the integrity of the markets. In practice, this
involves limiting the degree of credit risk to which mar
ket participants are exposed so that, in a period of
adverse events, defaults do not cumulate to cause a
breakdown in the market as whole. In the absence of
dictated m argin requirem ents, cre d ito rs would be
expected to protect their own interests by requiring
prudent margin levels. But they would focus on their
own perception of their own risks— not the risks to the
system — and they might be subject to com petitive
pressures. Thus, the proxim ate objective of margin
requirements may be to protect the creditors from the
risk of default, but this objective serves the ultimate
goal of protecting the system.
The other side of the tradeoff in setting margin levels
under this criterion involves the liquidity of the market.
It is generally possible to reduce credit risk to arbi
trarily low levels by imposing very strict margin require
ments. A side effect of this strategy, however, is to
exclude from the market certain investors who, given
sufficient potential for borrowing, would take positions
that would enhance the liquidity of the market. With
extreme margin requirements, the whole market might
be stifled.
Initial margins are usually emphasized in considering
the effects of high margin requirements on liquidity.
Large margin calls, however, which might result from
strict maintenance or variation margin requirements,
could be just as disruptive to the markets as strict ini
tial requirements. A significant cushion between initial
and maintenance margins, such as exists for individual
stocks, allows for the possibility of major price changes
without an accompanying unexpected strain on the
demand for short-term liquidity.
A second m otivation behind the establishm ent of
margin requirements may be the control of excessively
speculative activity, which could exacerbate the devia
tions of actual stock prices from the values implicit in
the fundamental information on the corporations issu
ing the securities. These deviations may be in the form
of increased volatility in stock price movements or they
may involve persistent discrepancies between the
actual and fundamental stock prices, as in the phenom
ena known as “ bubbles” and “ fads.” 2 Once again, the
drawback in setting higher margin requirements is the
possible loss of liquidity.
2See Gikas Hardouvelis, "M argin Requirem ents and Stock Market
Volatility,” in this issue of the Q uarterly Review. Earlier em pirical work
had not found persuasive evidence that m argin requirem ents curb
speculative activity. Using diffe ren t statistica l methods, H ardouvelis
This second motivation for margin requirements is
not altogether distinct from the first. If margin require
ments are effective in reducing excessive price vol
atility by controlling speculation, some of the price
uncertainty that contributes to credit risk will be elimi
nated. Indeed, experience has shown that the most
significant threats of credit disturbances to the stock
markets occur during episodes of excessive volatility.
Thus, reducing the likelihood of such volatility may be
an important channel through which margin require
ments protect the integrity of the markets.
Running parallel to the two basic motivations for
imposing margin requirements is the notion that the
stock market is special in that it involves the trading of
claims in the ownership of the productive resources of
the economy. In a market-oriented democracy, broad
involvement in such activities on the part of individual
investors is usually considered a desirable objective.
Any development that would tend to chase these inves
tors away from the market (such as unwarranted vol
atility, systemic risk, or manipulation) should, in this
view, be vigorously avoided.
Perhaps because few instances of severely desta
bilizing volatility have been experienced in the U.S.
stock markets, the empirical evidence supporting the
use of margin requirements either for protecting market
integrity or for curbing excessive speculation is techni
cally not very strong. Conversely, the results of the
technical studies have not rejected the usefulness of
margin requirements as an instrument for protecting
the markets or guarding against excessive speculation.
General considerations in the setting of margin
requirements
The general principles to be followed in setting margin
requirements, as well as the final results, will differ
according to the particular goals pursued by regulators.
In this section, a basic course of action is laid out for
each of the two major objectives identified earlier. Most
of the issues raised here are examined in greater detail
in subsequent sections.
In the case of the market integrity motivation, there
are three questions to investigate in trying to determine
what level of margin requirements would provide a
given level of systemic protection. The first concerns
the accuracy of knowledge about the probability distri
bution of future price movements in the underlying
security. Simply looking at the past or making some
theoretical assumption may not be sufficient to obtain a
Footnote 2 continued
presents evidence that when margin requirements are higher, stock
price volatility is lower. For an examination of the possibility of
“bubbles” in stock prices, see Hardouvelis, "Evidence on Stock
Market Speculative Bubbles: Japan, United States, and Great
Britain," in this issue of the Quarterly Review.
precise representation of future price movements. This
is particularly true for worst case scenarios, which may
not seem plausible or even conceivable until after the
fact.
The second question concerns the relationship
between the movements in the prices of the underlying
equity security and the price of a particular derivative
instrument. Important strides have been made in the
last two decades in working out the mathematics of the
appropriate pricing of derivative securities, such as
options and futures, under given conditions. The pric
ing relationships developed, however, apply only to
some types of instruments, involve substantial compli
cations, and may produce results that differ consis
tently from observed prices. The difficulties vary from
instrument to instrument but are most severe in the
case of options.
The third question is probably the hardest. Once the
credit risk in an individual transaction or position has
been analyzed, what are the implications for the mar
ket as a whole? A liquid market may be able to absorb
a number of delinquencies, but how many defaults
would cause a serious market failure? Are several
small defaults worse than a large one? What is the
interaction among different market participants in the
event of defaults? Does this interaction tend to acceler
ate the collapse of a market, and by how much? In
view of these uncertainties, the setting of margin
requirements to protect the integrity of the markets can
hardly be approached as a simple academic exercise
in measuring the credit risk associated with a range of
potential price movements.
The use of margins to control speculation raises
equally daunting questions. One must ask whether it is
desirable to control speculation at all, and whether
margin requirements are an adequate means of achiev
ing that objective. Even if they do contain speculation
in one market, high margin requirements may drive
speculators to other markets. The empirical evidence
in this respect is far from clear cut, but there are rea
sons to believe that the control of some types of spec
ulative activity is a valid concern of regulators and that
margins may be useful for that purpose.3
Finally, the consistency of the two regulatory objec
tives poses a potential problem. If the objectives of
protecting financial integrity and limiting speculation
have different implications for the level of margin
requirements, what relative weight should be assigned
to each objective? All of the foregoing difficulties are
encountered for each individual instrument even before
considerations of consistency across different instru
ments are entertained.
®For a discussion and some evidence, see Hardouvelis, “Margin
Requirements."
FRBNY Quarterly Review/Summer 1988 63
Margin requirements and the integrity of the
markets
This section outlines the analytical process by which
margin requirements may be used to control credit risk
as a means of protecting the integrity of the markets.
The process is described separately for stocks,
futures, and options.4 The same kind of analysis is per
formed in the next section for the alternative objective
of controlling speculative activity.
In general, the procedure involves determining the
probability of an exposure to credit loss that is associ
ated with each margin level, and choosing the level
that produces an acceptable amount of risk for the
creditor. The first step is to identify the potential credit
risks. In the case of stocks bought on margin, a loan to
the investor is collateralized by the stocks purchased.
The danger to the creditor is that the value of the secu
rity may fall to levels that would be insufficient to cover
the amount of the loan. Even though the debtor would
still have a legal obligation to repay the loan in full, the
practical likelihood of a default is clearly greater if
some or all of the loan is unsecured by the assets in
the margin account.
Suppose a margin of 25 percent is required on the
purchase. Equivalently, the amount of the loan may not
exceed 75 percent of the initial value of the security. If
no further margin calls are made, the stock price may
fall by as much as 25 percent before the lender is
exposed to any actual credit risk.
Given a set of precise— though probabilistic—
assumptions about the future behavior of the price of
the stock, the probability of developing an exposure to
credit risk during the period allowed for the posting of
margin may be computed. The same may be done for
other proposed margin levels from zero to 100 percent.
The level selected would then be the lowest that would
keep the probability of credit exposure within accept
able limits. It should be noted, however, that there is no
objective way of selecting the acceptable level of risk,
so that ultimately judgment is the only available guide.
The foregoing example applies to a long position in
stocks. Similar principles apply to the short sale of
stocks, but with short sales, the risk is related to a rise,
as opposed to a decline, in the price of the securities.
In the case of futures contracts, credit risk exists
whenever the futures price, which is determined at the
outset of the contract, differs from the value of the
underlying stock portfolio at maturity. Either side may
show a deficiency at that time, depending on who is
long and short and on the realized price of the secu
rity. Thus, each side is a potential credit risk and mar
gin must be required from both sides. In general, the
4The technical analysis that underlies the procedures described in
this section is illustrated in Appendix B.
64for FRASER
FRBNY Quarterly Review/Summer 1988
Digitized
long side profits from upward movements in the stock
price and loses if the price declines, while the opposite
is true for the short side of the contract. The relevant
probability is that of the event that the amount at risk
over the margin-posting period—the current shortfall
for a given party, if any—exceeds the total margin that
has been collected from that party, either as initial or
variation margin.
Once the probability is calculated for each set of
margin requirements ,5 one proceeds as before to
choose a combination of margin requirements that
keeps the probability within acceptable bounds.
With options contracts, the fundamental asymmetry
of returns relative to those of the underlying asset
means that the level of credit risk is dramatically differ
ent for the buyer and the writer. The buyer of an
option— be it a put or a call—obtains exposure to each
share of the underlying stock for a premium that is
generally considerably less than the stock’s price per
share. Unlike a futures contract, the long side of an
option poses no credit risk once the premium is paid in
full, since no further payments are ever required from
that party. If the option expires (or is exercised) in the
money, a credit accrues to the long side. If on the other
hand the option expires out of the money, there is no
obligation to exercise it and, hence, no further loss. For
this reason, there is no need to require margin from the
buyer beyond the premium itself.
For the writer, quite the opposite is true. The writer
makes no initial payment other than the posting of mar
gin and is subject to adverse changes in the price of
the underlying security that may cause the option to
move far into the money. Traditionally, margins on writ
ten options have implicitly included components reflect
ing expected movements in stock prices as well as the
volatility or uncertainty of future price movements. In
the margin formulas, these parameters are represented
by proxies—for example, the amount by which an
option is in or out of the money, or a percentage of the
current market price of the underlying asset. The
requirements are marked to market daily, and addi
tio n al m argin calls or w ith d raw als are made
accordingly.
As with futures, the margin regulator starts with a
given structure of margin requirements and, using a
model of stock price movements, calculates the proba
bility of any remaining credit risk. This is then done for
other conceivable levels of margin requirements,
whereupon a structure with an acceptable probability
level is selected.
^Margins in the futures markets have traditionally included variation
margin as well as initial margin. The variation margin requirement for
stock index futures is 100 percent, but there is no conceptual
difficulty in having a variation rate other than zero or 100 percent.
Traditionally, margin requirements have been applied
separately to the positions held by an investor with dif
ferent brokers, in different markets, or through different
clearing corporations. With cooperation and coordina
tion among brokers, exchanges, and clearing houses, it
would be possible to apply margin requirements to an
individual’s consolidated overall position. Such “cross
margining” currently exists to a limited degree, and fur
ther initiatives are in progress among several
exchanges and clearing corporations.
For each instrument or combination of instruments
considered above, the setting of margin requirements
to control credit risk requires precise knowledge about
the instruments, the markets, and the probability distri
butions of price movements. The structure of the mar
ket is taken as given, and it is assumed that changes in
margin requirements do not affect the fundamental
pricing of the underlying securities.
Margin requirements and speculative activity
A widely accepted principle of financial theory states
that stock prices should reflect all the available and rel
evant information about the issuing firm’s fundamen
tals. This is not a statement of the “efficient markets
hypothesis,”6 but a prescriptive statement to the effect
that an investor should be able to determine and pay a
fair price for a share in the ownership of a corporation.
Most would agree that the stock market should be
used by corporations to raise capital, but not by spec
ulators to place uninformed bets that could drive prices
away from their fundamental values.
If making stock prices conform to fundamentals is
the ultimate objective, why use margin requirements,
which control the degree of leverage available to inves
tors? One argument might be that speculators tend to
be risk-takers and find leveraged positions, which
involve greater risk than their unleveraged counter
parts, attractive. In addition, leverage allows an inves
tor to control a greater amount of shares with a given
dollar amount of initial capital. To the extent that long
term fundamental investors are not heavily leveraged,
the relative influence of speculators may increase as
the maximum permitted leverage increases.
As an illustration, consider a speculator who tends to
overreact to news. With $100,000 of capital and a 100
percent margin requirement, he would be able to pur
chase only $100,000 worth of stocks. If the required
margin were only 10 percent, however, he would be
able to buy $ 1,0 0 0 ,0 0 0 of stocks, a purchase that
would have a much greater effect on stock prices.
•One form of the efficient markets hypothesis states that security
prices reflect all available information. This is a (perhaps) testable
empirical proposition, as opposed to a normative statement such as
the one in the text.
Other investors with longer-term objectives would be
subject to excessive price volatility resulting from the
g re a te r purchasing power of the overreacting
speculator.
The statistical relationships between margin require
ments, speculation, and volatility are not well estab
lished. Hence, there is no precise way of determining
the degree of allowable leverage that would reduce the
volatility associated with speculation to acceptable pro
portions, just as there is some fuzziness in the rela
tionship between individual credit risk and the integrity
of the market. In this case, it is necessary to identify
the parties whose activities should be controlled and to
understand the nature and magnitude of their opera
tions. Because many important market participants
(such as pension funds) typically want to hold long
unleveraged positions on balance, they need not be
significantly affected by stricter margin requirements.
How could margin requirements be used to limit
leverage in the futures market? A futures position in
stocks is economically equivalent to a fully leveraged
position in the underlying securities over the term of
the futures contract. In both cases, there is no initial
cash outflow. At the futures maturity date, the long
party in the futures has the value of the stock minus
the initial futures price, while the long leveraged posi
tion has the stock minus the amount owed on the loan.
The similarity of these positions causes the market to
set the futures price at inception to the amount owed
on the loan, including interest, at the futures maturity
date. Otherwise, arbitrageurs could obtain riskless
profits by shorting the position with the higher price
(futures or loan price) and buying the other. The differ
ence between the spot and futures prices thus tends to
be the interest cost of the loan.7
Thus, in terms of the amount of leverage permitted, a
zero initial margin requirement on the futures would be
equivalent to a zero initial margin requirement on the
underlying stock in the cash market. Similarly, an initial
margin requirement on the futures of any magnitude
between zero and 100 percent is equivalent in terms of
leverage to an initial margin requirement of the same
magnitude on the underlying stocks.
The implicit leverage in an options position is more
difficult to determine because of the complexity of
options pricing. For options on relatively simple assets,
fairly accurate pricing formulas have been developed.8
*The futures prices predicted by these arbitrage relationships do not
in general coincide with observed prices, in large measure due to
institutional factors. These factors include transactions costs,
dividend payments, different settlement practices in the spot and
futures markets, and the fact that the futures apply to an index,
whereas only individual stocks are traded in the spot market.
•As in the case of a non-dividend-paying stock studied by Fischer
Black and Myron Scholes in "The Pricing of Options and Corporate
FRBNY Quarterly Review/Summer 1988 65
In these cases, it is possible to construct a “ hedge
portfolio” that consists of time-varying proportions of
cash and the underlying stocks and that replicates the
option returns. The resulting hedge portfolio for a call
option normally consists of a long position in the stock
and a short cash position (a loan), so that an implicit
leverage ratio may be easily computed from the pricing
formula. This implicit leverage is the ratio of the value
of the loan to the value of the stocks in the hedge
portfolio.
Table 2 presents the implicit leverage ratios for long
positions in various call options, as calculated using
the Black-Scholes option pricing formula. The implicit
leverage is quite substantial, particularly for options
that are around the money or out of the money. The
additional margin that would be necessary to bring the
leverage down to 50 percent, as required for stocks in
the spot market, is also shown in Table 2. This amount
may be several times the option premium. A similar
Footnote 8 continued
L ia b ilitie s," Journal of P olitical Economy, May-June 1973.
Table 2
Implicit Leverage for a Long Call Option
Volatility
Exercise
(Percent
Price
Per Annum ) (In Dollars)
Additional
Im plicit
Call
Margin
Premium
Leverage
(Percent)* (In D o lla rs )t (In D ollars)^
32.42
7.43
0.36
17.47
23.81
2.75
64
79
85
33.28
3.76
13.54
17.37
8.93
59
70
76
35.72
18.29
8.78
7.88
12.51
9.87
20
70
68
20
100
88
20
130
94
40
40
40
70
60
60
60
100
130
70
100
130
12.8 6
A ssum ptions:
U nderlying stock p rice = $100
M aturity = 6 months
Interest rate = 7 percent per annum
*Black and Scholes (see footnote 8 in text) have shown that a
call option may be re plicated with a continuously rebalanced
portfolio consisting of a long stock position and a short cash
position (a loan). At time t, the values of these two positions
should be:
A, = stocks = StN(ht),
L, = loan = e ,T K N(h,-aT),
where S, is the value and a is the volatility of the underlying
stocks, K is the exercise price, T is the time to m aturity of the
option, r is the risk-free interest rate, N ( ) is the standard
Gaussian cum ulative distrib ution function, and
h, = [log(S,/K) + (r + .5 or)T)]/<rT.
The im p lic it leverage is L,/A,.
fT h e Black-Scholes prem ium is A,-L,.
^M argin required to bring im plicit equity proportion to 50
percent, that is, max[0, Lt-.5 A,].
66
FRBNY Quarterly Review/Summer 1988
exercise may be performed for a short call or a put
option, with similar results.
It should be clear from the foregoing discussion that
using margin requirem ents to control the leverage
obtained with options is a d ifficu lt task. The rules
based on implicit leverage are complex, even in the
basic Black-Scholes case discussed above. For some
options, there are no explicit pricing formulas on which
to rely.
Another complication that arises in the context of
margins on options is the wide discrepancy that may
result from applying the two objectives for margin
requirements. It has been previously argued that if
credit risk is the major concern, there is no need for
margin beyond the option premium for a long call,
since the credit risk posed by the long side is then
zero. A glance at Table 2, however, shows that implicit
leverage in excess of 80 or 90 percent is possible with
option positions even if they involve no credit risk. A
speculator who prefers the return patterns arising from
a highly leveraged stock position could bypass the
requirements of the spot market by investing in an
option position with very high implicit leverage. Under
most circum stances, this strategy would produce
essentially the same investment results as investing in
the corresponding leveraged position in the spot mar
ket. Through arbitrage, such activities would ultimately
affect pricing in the spot market.
Why make margins consistent?
The question whether margins should be consistent
across markets must be considered within the context
of the basic objectives for margin requirements. It is
not clear a priori that the two objectives would produce
the same results. In some cases, sim ila r margin
requirements may be used to satisfy both goals at
once. For some instruments, notably options, the solu
tion is dramatically different depending on which of the
two objectives is given priority.
Furthermore, the structure of each of the various
equity-related markets is so unique in ways that are
fundamental to the problem at hand that, in addition to
the margin rates, a whole series of other parameters
must be considered in the context of margin require
ments. Before going into the consistency question in
detail, it is useful to list the parameters that are poten
tially under the regulators’ control. Not all of the follow
ing have been explicitly utilized in all markets.
Initial margin. Initial margin requirements for individ
ual stocks are set by the Federal Reserve Board (they
are currently 50 percent). The Board also controls ini
tial margins on stock options and stock index options
but has left the details to the appropriate exchanges
subject to the approval of the Securities and Exchange
Commission. For stock index futures and options on
index futures, initial margins are set by the exchanges
and by the self-regulatory organizations.
M aintenance margin. Some form of m aintenance
margin requirement is found in virtually all markets. In
the markets for individual stocks, there is a large gap
between the initial (50 percent) and the maintenance
(25 percent) requirements, and there is no obligation to
issue margin calls before the maintenance level is hit.
However, whenever the equity in a margin account falls
below the maintenance level, new cash or securities
must be deposited to bring it back up to that level (or
to the initial level, as in the index futures market). The
level of the re q u ire m e n t is g e n e ra lly set by the
exchange. With options, maintenance margins are
based on current market premiums and are used as a
means of marking positions to market.
Variation margin. The concept of variation margin is
used primarily in the futures markets. Investors are
required to mark their positions to market (on a daily or
intraday basis for stock index futures) and to post an
amount corresponding to any adverse change in the
futures price. While variation margin has traditionally
been set at 100 percent in the futures markets and not
required in the cash markets, it is conceptually possi
ble to set this requirement at fractional values of the
change resulting from marking to market.
Posting period. The length of the period allowed for
the posting of margin calls is of the utmost importance
for the credit risk control objective. Risk and uncer
tainty are clearly greater if investors are allowed up to
15 business days to post margin (as in the spot market,
in principle) than if they are allowed no more than one
day (as in the index futures market). The length of the
posting period bears a direct relationship to the clear
ing and settlement practices of the individual markets.
Form of margin. The types of securities accepted to
cover margin requirements differ from market to mar
ket. In the various markets, these may include cash,
Treasury securities, and nonpublic instruments, includ
ing credit lines.
Explicit exemptions. Different types of investors have
different margin requirements in each market. A brokerdealer, for example, will generally have more flexibility
than a customer. The same applies with greater force
to a market maker in the security. In some cases, cus
tomers are classified as hedgers or speculators for the
purpose of applying different margin requirements.
Degree of discretion. In some cases, the regulatory
authority may grant specific exemptions to investors on
a discretionary basis. For example, the Options Clear
ing Corporation may reduce overall margin require-
Table 3
Margin Sim ulation Statistics for Spot and Futures Markets over One Year
Stocks
(Five-Day Periods)
V olatility
(Percent Per Annum)
Equity
Average
P robability of negative equity
Margin Calls
Minimum
Maximum
Average positive call
P robability of:
positive call
call of at least $ 1
Futures
(One-Day Periods)
60
40
40.2 percent
percent
42.1 percent
0 percent
0 .0 0 2
-$ 5 3 .4 4
$40.76
$ 0.26
8.4 percent
6.4 percent
-$ 2 3 .0 4
$11.69
$ 0.08
40
20
15.2 percent
percent
14.7 percent
0 percent
0 .0 1
-$ 2 8 .3 1
$28.35
$ 1.05
3.9 percent
2 . 6 percent
49.7 pe rcent
34.1 pe rcent
- $ 7 .6 0
$7.51
$0.51
49.2 percent
21.4 percent
Assum ptions:
Initial value of secu rity = $100
Instantaneous expected return = 7 percent per annum
M argins on stocks:
Initial m argin = 50 percent
Maintenance margin = 25 percent
Posting period = 5 days
M argins on futures:
Initial margin = $15
Variation m argin = 100 percent
Posting period = 1 day
N um ber of iterations = 2000
FRBNY Quarterly Review/Summer 1988
67
merits for its members on a discretionary basis when
options held long by the members are substantially in
the money.
The implications— in terms of the likelihood of nega
tive equity and of margin calls—of recent choices as to
margin parameters in the stock market and in the stock
index futures market are illustrated by the simulation
statistics presented in Table 3. The basic assumptions
for the simulations are intended to be generally repre
s e n ta tiv e of c o n d itio n s in the New York S to ck
Exchange for the stock market and in the Chicago Mer
cantile Exchange for the futures market. Price move
ments are represented by a mathematical formulation
(the Wiener process) widely used in the context of
stock prices and derivative instruments.
Two different volatility assumptions are examined in
each market. In general, a diversified po rtfo lio of
stocks will experience lower price volatility than an
individual issue. Since index values correspond to the
prices of such a diversified portfolio, a relatively low
volatility is assumed for index futures (20 percent). For
the stock market, higher values are used (40 and 60
percent). The case of index futures with a volatility of
40 percent is included for the purpose of comparison
with the stock market.
The results in Table 3 indicate that the requirements
in the spot and futures markets are roughly equivalent
in terms of the probability of exposure to credit risk
(probability of negative equity). A range of volatilities
has to be considered for the spot market, but the prob
abilities tend to be quite low for most reasonable
values, as they are for the index futures. Nevertheless,
other statistics vary markedly across markets.
In the stock market, initial margins are relatively
high, and there is a built-in buffer against margin calls
provided by the difference between initial and mainte
nance margins. In the futures market, initial margins
are lower, but additional margin is required any time
prices change. The effects are noticeable in the rela
tionship between equity levels and margin calls.
Equity in the spot market is on average between two
and three times higher than in the futures market. A
large portion of this difference is attributable to the
buffer against calls. As a result, both the incidence and
magnitude of positive margin calls (in contrast to nega
tive calls, or allowable margin withdrawals) are much
lower in the stock market. The chances of a margin call
are about even in the futures market, and a call of 1
percent or more of the original stock price occurs
about one-fifth of the time. The dollar value of the aver
age call in the futures market is about twice that corre
sponding to a stock whose volatility (60 percent) is
three times that of the index. These figures provide a
clear illustration of the tradeoff between high initial
68 for
FRBNY
Quarterly Review/Summer 1988
Digitized
FRASER
margins and frequent large margin calls.9
Consistent margins and the integrity of the markets
All of the parameters identified in the previous section
affect the expectations and probability distributions
associated with credit risk for each of the equityrelated instruments. A simple rule of thumb to make
margins consistent is to set the parameters so that the
probability of an equity deficiency in an investor’s posi
tion is the same for all instruments. This ignores the
distinct possibility that the relationship between individ
ual default and the overall integrity of the market may
vary from one market to another. A system with many
essentially independent intermediaries is more resilient
than one in which intermediation takes place in several
steps with the potential of a chain reaction of defaults.
Alternatively, the netting out of positions may be differ
ent from market to market. A large volume of open
positions on either side is not necessarily risky if the
holdings of individual investors are hedged for the
most part. In any case, the rule of thumb described
above is a useful first step.
More specifically, the regulator would proceed with
the analysis described earlier for controlling credit risk
in each p a rtic u la r instrum ent. C onsistency would
require that the acceptable probability level selected be
the same for each instrument.
Conceptually, the application of this method is not
•Note that the figures reported in Table 3 are based on a
m athem atical sim ulation and not on historical data. The m athem atical
techniques have been used elsewhere to calcu la te the p ro b a b ility of
negative equity during a single posting period, starting from the
m aintenance level (for exam ple, Interim Report o f the Working Group
on Financial Markets, W ashington, D.C., May 1988). The sim ulation in
Table 3 is more general in tha t it covers all the events that may
develop over the course of a year, incorporating initial, m aintenance,
and variation margin requirem ents, as well as an e xp licit posting
period.
Table 4
S&P Composite Index:
Frequency of Extreme Monthly Returns
(Percent of O bservations w ithin Period)
Period
1930-39
1940-49
1950-59
1960-69
1970-79
1978-87
1926-87
Loss of More Than
8.5 Percent
Gain of More Than
8.2 Percent
18.3
2.5
15.8
0 .8
0 .0
1.7
0 .8
0 .8
4.2
4.2
5.0
4.2
5.0
5.0
Source: Ibbotson A ssociates, SBBI/PC da ta base.
difficult in the context of the spot and futures markets
where, because of arbitrage pricing, the relevant
events are essentially the same.10 A simple way to
impose consistent margins would be to make them uni
formly equivalent, that is, to set every parameter—ini
tial, maintenance, and variation rates; posting period;
exemptions; and so forth—at the same level in each
market. While theoretically attractive, this requires very
fundamental changes in the way these markets pres
ently operate. Virtually every one of the parameters
described above varies significantly from market to
market. Since some of these differences—such as the
margin posting period—arise from operational features
of the markets, regulators contemplating a change
must consider the potential disruption.11
Another less disruptive way to deal with the problem
is to make the requirements dynam ically equivalent,
that is, to allow for the possibility of setting the param
eters at different levels in the spot and futures markets,
but in such a way that the resulting probabilities of
equity deficiencies are the same across markets. For
example, if the initial margin requirement were lowered
in the spot market, the probability of deficiencies would
increase. To lower the probability to the original level,
some fractional variation margin requirement might be
imposed. Alternatively, the posting period might be
shortened, and so on.
While the calculation of these tradeoffs is theo
retically feasible, it is by no means an easy task in
practice. It requires detailed knowledge of the proba
bility distribution of movements in the price of the
underlying security, as well as a clear representation of
the relationship between the pricing of futures and the
pricing of the underlying security.
To illustrate the problems, Table 4 presents the fre
quency of unusually large positive or negative price
movements in the S&P Composite index for the period
from 1926 to 1987 and for a series of 10-year periods
within those years. The results indicate that the
assumption that future volatility will resemble past vol
atility is highly suspect, even though some stability is
imposed by the substantial length of the periods
considered.
Option returns bear a complicated relationship to
those of the underlying asset, and the problems they
»Margin requirements in the spot and futures markets are analyzed
graphically in Appendix A.
"As markets evolve in response to generally available technical
advances, their operational features may converge and thus simplify
the establishment of cross-market consistency.. For example, the New
York Stock Exchange and the American Stock Exchange are currently
moving towards a one-day clearing system for all listed equity trades.
This development would facilitate the use of shorter margin-posting
periods (closer to those in the futures markets), if such a move
seems desirable.
create in the context of consistent margins are even
greater. The use of uniform equivalence is out of the
question. It is still possible to impose dynamic equiva
lence, though the complexity of the pricing relationship
makes this even harder than in the case of futures.
In general, theoretical analysis along these lines may
provide regulators with some guidelines for the estab
lishment of consistent margin requirements. It is clearly
not an exact science, however, and substantial judg
ment is required.
Consistent margins and speculation
Initial margin is the most important parameter in the
setting of margin requirements if the control of spec
ulation qua leverage is the objective. The goal is to
make it harder for pure speculators to borrow a large
proportion of the amount that they invest in equity
securities, and thus lower their chances of affecting
trading volume and market prices.
Once again, the equivalence between spot and
futures markets is not conceptually difficult because of
the close relationship between their returns. The practi
cal problem is that in each market, initial margin has
been set in conjunction with all the other parameters. If
the markets have dynamically consistent margin
requirements (that is, if the exposure to credit risk is
the same in each market), it may be inadvisable to
change the initial margin requirement without making
offsetting changes in at least some of the other
parameters.
Options again present a greater challenge, since an
implicit leverage level must be computed as in Table 2,
and it is quite difficult to come up with precise values,
especially if no theoretical representation exists for the
price of a particular option.
The natural tendency is that speculators will shift to
markets where initial margin requirements are effec
tively lower. That is, they will move to markets where a
position with a large degree of actual or implicit
leverage is permitted. Because of strong interconnec
tions among markets, however, those markets with high
margin requirements are not immune to the actions of
speculators in other derivative markets. Excessive vol
atility, as well as nonfundamental pricing, may be
transmitted from one market to another. Thus, if spec
ulation is a real issue, the consistency of initial margins
should be seriously considered.
Conclusion
The results of this article are perforce not a neat set of
rules, but a series of guidelines to be considered by
regulators. Making margins consistent across markets
demands some serious thought about why there are
margin requirements at all; it also confronts regulators
FRBNY Quarterly Review/Summer 1988 69
with difficult technical problems. Since the mathemati
cal accuracy of the available methods is limited, it is
necessary for those regulators to exercise a great deal
of judgment in the process.
Even if the technical problems are adequately han
dled, there are still significant difficulties in bringing
together markets that have developed operationally in
dramatically different ways. Massive changes would be
necessary to equalize each parameter across all mar
kets, even if that were mechanically feasible.
Nevertheless, the concerns about the integrity of the
70
FRBNY Quarterly Review/Summer 1988
markets and about the dangers of destabilizing spec
ulation are genuine. Dealing with them in only some
markets, or in a piecemeal fashion, does not ade
quately confront the issue. In seeking to adjust margin
requirements to meet these objectives, regulators can
look to technical studies for guidance but must rely on
their good judgment as the ultimate tool.
Arturo Estrella
Appendix A: Graphical Analysis of the Spot and Futures Markets*
The basic diagram
The elements of margin requirements may be compared
graphically across markets in the cases of individual
stocks and index futures. Because of the simplicity of
the arbitrage pricing relationship between spot and
futures markets, margin requirements apply in much the
same way in the two markets. As argued in the text,
options present a greater challenge in terms of compar
ative analysis and do not easily lend themselves to this
type of graphical exposition.
Chart 1 illustrates the three basic types of margin
requirements in a single diagram. The investor's equity
in a stock position is graphed on the vertical axis
against the price of the stock on the horizontal axis.
The 45-degree line, OG, shows the equity that would
exist in an unmargined account, namely, 100 percent of
the stock value. If the initial price of the shares is S0,
then the unm argined investor has in itia l equity of
exactly S0. In the absence of margin calls, account
equity increases or decreases by a dollar for every dol
lar change in the price of the stock.
If the stock is subject to an initial margin requirement
of m„ then account equity must at least equal m,S0 at
the time the stock is purchased (point A). The line OB,
which has slope m„ demonstrates this constraint. By
choosing to borrow less than the maximum allowable
am ount, the in ve sto r could in itia lly lie anyw here
between A and G.
A maintenance margin requirement of mM restricts the
position equity to be at all times in excess of mMS„ or
above the line OD, whose slope is mM. As long as the
maintenance margin is less than the initial margin, the
line OD will lie everywhere beneath OB.
If the variation margin requirement is mv, the one-forone change in the account equity given a change in the
stock price is offset by the amount mv. Thus, equity will
change by 1 - mv for each dollar change in the price of
the stock. Consequently, a line such as AF, passing
through point A with slope 1 - mv, demonstrates this
type of margin requirement. In contrast to the lines
demonstrating the other two types of margin require
ment, the variation margin line may shift as the stock
price moves if the upper and lower bounds for required
margin are binding. This phenomenon is illustrated
below in the discussion of spot market requirements.
Two extreme cases help to illustrate the effects of
variation margin. If there is a 100 percent variation mar
gin, the variation margin line will be horizontal. In other
words, account equity is restricted to remain c o n s ta n teach dollar change in the underlying price will be fully
passed through to the investor. By contrast, if the varia
tion margin is zero, the slope of the line will be unity
because account equity changes dollar-for-dollar with
every change in the underlying price.
An interesting case arises if the sum of the initial and
variation margin requirements is exactly 100 percent.
This is equivalent to setting the margin requirement to
be at all times a constant proportion of the current
stock value. Under these circumstances, the line AF in
Chart 1 coincides with AB. They intersect the schedule
AD of maintenance requirements only at the origin, so
that the concept of maintenance margin is essentially
irrelevant.
Both the stock and futures markets in the United
States have, in some form, initial, maintenance, and
variation margins, although variation margin is some
what disguised in the stock market and prominent in the
futures market.
Current institutional framework: a stylized summary
The stock market (New York Stock Exchange). To pur
chase stock on margin at the New York Stock Exchange
(NYSE), a retail investor must put down cash for at
least 50 percent of the value of the stock at the time of
the purchase.! This minimum initial margin requirement
f i n addition, a margin account must be opened with at least
$ 2 ,00 0 .
C h a rt 1
Initial, M aintenance, and Variation Margins
Equity (E)
‘ Stephen R. King m ade valuable contributions to the w riting of
this appendix.
FRBNY Quarterly Review/Summer 1988
71
Appendix A: Graphical Analysis of the Spot and Futures Markets (continued)
is set by the Federal Reserve Board’s Regulation T. In
addition, the NYSE requires that a retail customer’s
equity must at all times exceed 25 percent of the cur
rent value of the stock (the so-called 25 percent main
tenance margin)4 The equity in the stock position may
only be reduced from 50 to 25 percent as a result of
declines in the stock price, not by additional borrowing.
On the other hand, if the price of the stock were to rise,
the investor would be entitled to increase the size of the
margin loan to 50 percent of the current stock price.§
The margin requirements in the stock market are
illustrated diagrammatically in Chart 2, which follows
the same basic construction as Chart 1. Once again,
the investor starts at point A, which represents a margin
of m,S0 on a position worth S0. In this case, equity must
exceed the line OGAB, where the slopes of the line
segments OG, GA, and AB are 0.25, 1, and 0.5, respec
tively. The segment OG is simply the maintenance mar
gin requirement. GA is determined by a variation margin
requirement of zero— position losses can be fully sub
tracted from account equity. Although AB is defined by
the initial margin requirement, it also performs the role
of a variation margin applied at the initial rate, because
it specifies that the investor can withdraw 50 cents for
each dollar by which the stock price rises above its ini
tial value.
As a numerical example, consider a customer who
buys 100 shares for $1 each, financing the purchase by
borrowing $50 from a broker, if the price of the shares
rises to $1.50, the customer’s equity rises to $100, or
two-thirds of the current value of the investment. The
margin requirements would allow borrowing of up to $75
(50 percent of the current share value), so the customer
would be entitled to withdraw $25 from the broker. Note
that this is also 50 percent of the rise in value.
If, instead of rising, the price had fallen from its initial
$1.00 to $0.50, the customer’s equity would have evapo
rated (the value of the stock would exactly equal the
$50.00 debt to the broker). The NYSE maintenance
requirements demand that the customer’s equity be at
least 25 percent of the current value of the stock
($12.50, in this case), so the customer would have to
post this amount to avoid being sold out.
Since margin may be removed from the account if it
exceeds 50 percent, and since there are margin calls
whenever equity drops below 25 percent, the line seg
ment AG in Chart 2 may shift as stock prices move
through time. For example, if the stock price rises to S1f
then the investor will be faced with a new variation martT h e same regulations do not necessarily a p ply to specialists
or some other professional organizations. Cf. The Report o f the
P residential Task Force on M arket Mechanisms, January 1988,
p. VI-15.
§ln other words, to w ithdraw equity from the account.
FRBNY Quarterly Review/Summer 1988
gin line, A'G ', showing the allowable decline in account
equity should the stock price subsequently decline.
Similarly, if equity drops to the line segment OG follow
ing a price decline, any subsequent increases would be
along a line parallel to AG, but not necessarily along
AG itself.
This shifting makes it difficult to anticipate the exact
relationship between the uncertain stock prices and the
minimum required equity. Point G', for instance, which
represents a level of equity lower than the initial amount
at A, is attainable only if prices and equity first move up
to point A'. In general, knowing the value of the stock at
the end of a given period (or equivalently, the average
return over the period) is insufficient to determine the
required equity at that time because the whole path of
sto ck p ric e s over the p e rio d m ust be taken into
consideration.
This phenomenon may be illustrated using the numer
ical examples given earlier. Suppose that the stock
price goes from $1.00 to $1.50, and then back to $1.00.
As shown above, the margin requirement after the first
price movement is $75. After the price drops back to
$1.00, the value of the portfolio is $100 once more, but
equity is allowed to fall by the full price drop of $50 to
the maintenance level of $25.
Alternatively, suppose that the price first falls to 50
C hart 2
Stock M arket
E q u ity (E)
Appendix A: Graphical Analysis of the Spot and Futures Markets (continued)
cents and then rebounds to $1.00. The maintenance
margin requirement, as calculated above, would be
binding at $12.50 after the initial drop. When the price
rises again to $1.00, equity increases to $62.50, but the
excess over 50 percent may be withdrawn so that the
required level is $50. Thus, we have two situations in
which the value of the portfolio starts and ends at $100,
but the margin requirement at the end of the period is
either at the minimum or at the maximum rate (25 and
50 percent, respectively).
Another complication arises from the length of the
period allowed for the posting of margin calls. In the
stock market, margin calls may be satisfied by a deposit
of cash into an investor’s margin account, typically
within five days. In the intervening time, the stock price
might move adversely, lowering the customer’s equity.
Partly as a response to the delayed payment, brokers
g enerally make m argin calls before the custom er
reaches the margin limit. Diagrammatically, this would
imply that the path OGA would contain some curvature.
If price moves are gradual, then a curve such as OHA
might capture the effective requirement. However, if
prices were to drop very sharply, OHA could actually dip
below OGA before margin payments were made.
The Futures Market (Chicago Mercantile Exchange).
C ustom er m argins in the futures m arkets perform
essentially the same function as margins in the cash
market, but they do differ in some important institutional
respects. As in the spot market, futures market cus
tomers are constrained by both initial and maintenance
margins. At the end of 1987, initial margins for a spec
ulator on an S&P 500 futures contract were $20,000, or
about 16 percent of the price of the contract. Mainte
nance margins were $15,000, or 12 percent.|| For a
hedger, margins are considerably lower. In contrast to
the spot market, variation margins are 100 percent of
price movements. They must be posted by the begin
ning of the following trading day, and in some instances
there may be intraday margin calls.
Futures margins are diagramed in Chart 3.11 This for
mulation is particularly simple if the futures price rises.
In this case, the 100 percent variation margin allows the
investor to withdraw all equity in excess of the initial
margin. If the price falls, then the equity in the account
may be reduced by that amount to pay for the variation
call, unless the balance in the equity falls below the
maintenance level. If that occurs, then equity must be
raised to its initial level. Consequently, the constraint on
the investor may exhibit a sawtooth shape to the left of
the initial price. In practice, additional margin may be
required from the customer at the broker’s discretion so
that the actual minimum equity may be closer to the
horizontal line BA.
For comparison with the numerical example in the
previous section, we can consider the situation of an
investor purchasing a hypothetical $100 futures contract
with initial margin of $16 and maintenance margin of
$12. Before undertaking the transaction, the investor
will be required to have $16 in a margin account. At no
stage is credit actually extended in a futures transac
tion, but the investor’s initial equity is the $16 down pay
ment. If the contract rises in value to $150, the investor
will have an equity of $66 (the initial $16 plus the
increase of $50 in the value of the contract). Because
the contracts are marked to market each business day,
the investor would receive the increase in the value of
the contract ($50) at that time and could withdraw the
full amount of this increase in value as cash. However,
the investor can never withdraw an amount that would
reduce the position’s equity beneath its initial margin
amount.
C hart 3
Futures M arket
Equity (E)
||AII institutional details on futures in this appendix relate to
con tracts on the S&P 500 on the C hicago M ercantile
Exchange. These con tracts are for $500 m ultiplied by the
value of the S&P 500 index, or about $125,000 per contract at
year-end 1987 prices. Initial m argins have been reduced
som ewhat since that time, to $15,000.
fN o distinctio n between spot and futures prices is m ade here
or in A ppe ndix B. It is assum ed that the futures price is
adjusted for interest costs (w hich are known con tem p ora
neously) and divid e n d payouts (w hich are highly predictable).
FRBNY Quarterly Review/Summer 1988
73
Appendix A: Graphical Analysis of the Spot and Futures Markets (continued)
If, instead of rising, the value of the contract had
fallen to $50, the investor’s equity would drop from $16
to - $ 3 4 (a capital loss of $50 on the contract). The
exchange requires that if the margin account drops
below its maintenance value ($12), it must be increased
by the start of the next day’s trading to the full initial
amount. Consequently, the investor would be required
to put $50 into the account.
Had the price decline been less severe—for example
from $100 to $97—the situation would be somewhat dif
ferent. In this case, account equity would have shrunk
from $16 to $13. Since the margin account would still
exceed the minimum maintenance amount ($12), the
broker would not be required to demand a margin pay
ment from the customer. Instead, the broker could sim
ply forward the $3 of variation margin to the clearing
house, debiting the customer’s margin account by the
same amount.
Differences between the two markets. Chart 4 com
bines the analysis from Charts 2 and 3 to show the
relationship between margins in the stock and futures
markets in a single figure. For clarity, it is assumed that
customers in the futures market are required to keep
their equity at the minimum maintenance level.** The
**As they would be perm itted to do in principle if they kept their
C hart 4
Com parison of Stock
and Futures Markets
Equity (E )
diagram im m ediately reveals the high initial burden
placed on an investor purchasing an instrument on the
cash market rather than the futures market. However, it
also reveals that in a severe market decline, when
prices fall by more than one-half of their initial levels,
the minimum equity in the futures market would exceed
that in the cash market. The reason for this difference
is that the futures margins are specified in absolute dol
lar terms, whereas cash market maintenance margin is
stated as a percentage of the current stock price. As
prices decline, the required margin rate on the futures
market investor increases, unless the requirements are
modified on an ad hoc b a s is .tt
The same information can be displayed in terms of
marginal and average margin requirements in the cash
and futures markets, as in Charts 5 and 6. The marginal
rate (Chart 5) is simplest in the futures market since it
is constant at 100 percent—the investor’s margin calls
increase dollar-for-dollar with a decline in the price of
Footnote ** continued
balance one cent above the minimum m aintenance level.
W hile in p ractice the minimum may be clo se r to the initial
d o lla r level, the m aintenance requirem ent represents the
lowest po ssib le— if not ty p ic a l— level.
t tT h e futures exchanges can and do adjust m argin levels on
current and existing con tracts in response to cha nged market
conditions, p rin cipally to variations in volatility. If p rice s move
downw ards sharply, w ith an apparent increase in volatility,
then the exchanges would likely increase m argin
requirements. If they fell gra d u a lly w ithout an increase in
volatility, then it is uncertain w hether m argin levels w ould be
reduced.
C hart 5
M arginal M argins
M argin call rate
Futures m arket
C ash m arket
2 /3
74
FRBNY Quarterly Review/Summer 1988
S q
S q
S tock p ric e (S)
Appendix A: Graphical Analysis of the Spot and Futures Markets (continued)
the contract.
There are three different marginal margin rates in the
cash market, depending on the relationship between
the initial price and the current price of the stocks. If
the price of the stock rises from its initial value, the
C hart
6
Average M argins
E qu ity/S
investor may withdraw 50 cents for each dollar of price
change. If the price falls from its initial value, no addi
tional equity need be added until the 25 percent main
tenance level is hit. In this range, th erefore, the
marginal margin is zero. Once the maintenance level is
hit, however, the investor must deposit 75 cents for
each dollar by which the price falls. As indicated earlier,
the position of the middle range over which there are no
margin calls may change if the initial or maintenance
margin rates become binding. This corresponds to the
shifting of line segment AG in Chart 2.
The average margin rate is computed by dividing total
required equity by the price of the underlying invest
ment. The average rates for the cash and futures mar
kets are plotted in Chart 6. In the cash market, the
average rate is 50 percent above the initial price and 25
percent once the maintenance level is hit. The futures
margin rate is always decreasing because the require
ment is fixed in dollar terms. As the contract price rises,
the average margin drops towards zero, and as the
price falls, the average margin increases indefinitely. If
the value of the contract falls beneath the initial margin,
the average margin rate can exceed 100 percent.
An important difference between the spot and futures
C h a rt
C hart 7
8
Sample R ealization (Bear M arket)
Sample R ealization (B ull M arket)
Equity
70 --------------------------------------------------------------------------------50% /
E quity
60 -------------------------------------------------------------
5 0 ----------------------------------------------
-----------
-
a S pot
4 0 -------------------------------------- £■
Futures
Q l-----------------1----------------- 1-----------------1----------------- 1-----------------1----------------- 1
40
60
80
100
S tock value
120
140
160
40
60
80
100
S to ck value
120
140
160
_ _ _ _ _ _ ------------------------------------------
FRBNY Quarterly Review/Summer 1988
75
Appendix A: Graphical Analysis of the Spot and Futures Markets (continued)
markets concerns the length of time that customers
have to post margin calls with their brokers. This is
technically 15 days in the spot market, as compared
with at most one trading day in the futures market.
These numbers overstate the actual difference, how
ever, since brokers in the spot market have the right to
be more demanding, and usually are.
Simulation analysis
To provide a more specific illustration of how required
margins in the spot and futures markets vary over time
in relation to the value of the underlying stocks, Charts
7 and 8 present the results of a simulation of margin
requirem ents for a stock or futures portfolio over a
period of a year. The underlying stock prices are drawn
randomly from a distribution with a mean return of 15
percent and a volatility (standard deviation) of 40 per
c e n t.^ For the spot market, the requirements are those
described earlier, with initial margin of 50 percent and
maintenance margin of 25 percent. For the futures mar
ket, it is assumed that required margin is always 15 per
cent of the original value of the stocks.
The value of each point on the vertical axis repre
sents the dollar value of equity in a customer’s margin
account just before a margin call is posted, with the cort t T h e S&P 500 index, w hich corresponds to a w ell-diversified
stock portfolio, has a historical volatility of about 15 to 20
percent. Volatilities for individual stocks vary substantially,
but most would be greater than that of the index as a
whole, some significa ntly so.
responding value of the stocks on the horizontal axis.
Because of the different periods allowed for posting
margin calls in the two markets, it is assumed that the
time between two consecutive observations is one trad
ing day in the futures market and five trading days in
the spot market. Hence, there are 250 and 50 points,
respectively, for the futures and spot markets.
Each chart starts with a stock value of $100 and pre
sents a particular realization (series of randomly gener
ated values) of the stock value process over the course
of a year. The same realization is used in each chart for
both the spot and futures markets. In Chart 7, daily
returns were generally positive over the course of the
year and a wide discrepancy developed between the
margin levels in the two markets. Some equity was
removed from the spot market account when the level
exceeded 50 percent, but the maintenance level was
not tested. The realization of Chart 8 is essentially a
bear market, and the margin levels are much more
comparable across markets, especially when stock
prices fell to 60 percent or less of their original levels.
Broadly speaking, margin requirements in both mar
kets perform a similar role, restricting the investor’s
exposure in the instrum ents and the cre d ito r’s risk.
Because of the daily and intraday marking to market for
futures positions, futures exchanges set their initial and
maintenance margin requirements considerably lower
than those set in the cash market. This represents a
rational response to the lower risk exposure that results
from frequent marking to market.
Appendix B: Calculation of Credit Risk for Equity-Related Instruments
This appendix provides specific illustrations of the pro
cedures described heuristically in the text for calculat
ing the likelihood of an equity deficiency in a margin
account. A model of margin requirements and position
equity is developed along the lines of the graphical
analysis of Appendix A. For stocks, options, and index
futures, the events that correspond to negative equity
positions within a margin-posting period are identified.
Numerical examples are also provided, based on a the
oretical Wiener process distribution for stock price
movements.
The model
The following basic definitions (consistent with those
of Appendix A) are used in the subsequent discussion:
S,
= value of the underlying stocks at time t,
xt
= log(St/SD) = return from time 0 to time t,
E[ = required equity at time t,
FRBNY Quarterly Review/Summer 1988
Digitized76
for FRASER
m, = initial margin requirement (proportion),
mM = maintenance requirement (proportion).
For long stocks, the initial required equity is given by
E,r = m,S0.
Thereafter, equity is allowed to change by any move
ment in stock prices,
Et — E,., + S, ~ SM,
except that E,r is constrained above and below by:
mMSt*sE,r
m,St.
Thus,
Etr = min [maxJEI., + S, - SMl mMSt], m,S,].
Appendix B: Calculation of Credit Risk for Equity-Related Instruments (continued)
In the NYSE, the current requirements are m, = .5
and mM = .25. The maximum period for posting margin
calls is officially 15 business days, but in practice bro
kers rarely allow more than 5 days, usually just 1 or 2
days.* Since position equity must in principle always be
above mM, the key question from a credit risk point of
view is whether, starting from mM, equity will become
negative at any time during the posting period. This
event may be represented as:
T ssT ^ T + H
mwST + S, - S t < 0,
where H is the length of the posting period. This condi
tion may be restated in terms of returns (using the ear
lier definition for x,) as:
Tss^ t'ssT+ H
xt )< Io 9(^
—mM)
If the distribution of price movements is stationary, as is
the case for a Wiener process, the last condition is
equivalent to:
(1)
o^
posting period if
T^Hf'ssT-t- H PD + S, - St < 0.
In terms of returns, this is
T s s ^ '^ T + H ^x*—xt )< I°9(1 —pD/Sj)
or, if stationarity holds,
<2 >
0 s
‘ D etails about the rules and practices regarding m argin
posting periods in the stock m arket are found in: New York
Stock Exchange Guide, Rule 431, Paragraph (6 ); Robert P.
R ittereiser and John P. Geelan, Margin Regulations and
Practices, 2d ed. (New York Institute of Finance, 1983); and
R ichard J. Teweles and Edward S. Bradley, The Stock Market,
5th ed. (Wiley, 1987).
fA s explained in A ppe ndix A, no distinction is m ade between
spot and futures prices.
^M argins on index futures are discusse d in John L. Maginn and
Donald L. Tuttle, eds., M anaging Investment Portfolios:
A D ynam ic Process, 1985-1986 U pdate, chap. 16.
x '< l o 9 < 1
- P D / S ')-
Ey = irT + max [.15 ST - m a x[K -S r,0 ], .05 Sr],
where irT is the current call premium and K is the exer
cise price. This formula applies to both initial and main
tenance requirements with the -rrx and ST marked to
market daily.§
Here, negative equity results within the posting period
(the buyer of the call is exposed to credit risk) if the
intrinsic value of the option exceeds the margin, that is,
if
max
o _ k > Er
T=s t ssT+ H
*
tT
T I h X4<log(1_mM)'
In the market for index futures, initial margin is stated
in dollar terms, so in proportional terms m, varies in
versely with the level of the index:
F0 = D,
m, = D/SOI
where D is the required dollar amount.f There is a vari
ation margin requirement of 100 percent of movements
in the futures price, that is, positions must be marked to
market. Any additional margin must be posted within 1
business day, but when large sudden price movements
occur, there may be intraday margin calls. Thus, at the
start of every business day, the position equity should
equal D. A further com plication is that brokers are
allowed to let their clients’ equity positions fall to a
maintenance level that is about 75 percent of the initial
requirement. In practice, however, the effective require
ment is probably closer to D 4 Thus,
mM = pD/S„
where .75 =£ p =£ 1. Negative equity is observed within the
r t " i H
For a written call option on an individual stock, the
NYSE margin requirement is
Based on returns, this expression becomes
(x,-xT)>log((E;+ K)/Sr)
or, if stationary,
(3)
max Y
0*s t
> log((Ej + K)/Sr).
An illustrative probability distribution:
the Wiener process
Once the types of events that concern creditors and
regulators are identified, the likelihood of those events
can be evaluated. In this section, a Wiener process is
used to represent the distribution of future price move
ments, as is the case in much of the theoretical stock
market lite ra tu re . The param eters of the process
(instantaneous mean and variance) are chosen on the
basis of empirical evidence, but the shape of the proba
bility distribution is constrained to a Gaussian or normal
form. An alternative is to use actual empirical distribu
tions from the past. Such distributions, however, vary
substantially over time and do not lend themselves to
accurate measurement and prediction.|| The Wiener for
mulation, while certainly imperfect, is roughly represen
tative of actual movements and is useful for sensitivity
analysis.
The basic definition of a W iener process for log
arithmic changes in stock prices, that is, for
§See Sofianos, “ Margin R equirem ents.”
||See Table 4 in the text, as well as the discussion there.
FRBNY Quarterly Review/Summer 1988
Appendix B: Calculation of Credit Risk for Equity-Related Instruments (continued)
x, = log(St/S0),
is given by the stochastic differential equation:
dx = (xdt + adz,
where dz represents driftless unit-variance Brownian
motion. Given this process, it may be calculated that
P[xH<a]
has the same value as (4) above.1I Also,
P[max x > a]
= P[min - x < - a],
which leads to expression (4) with the signs reversed
for the arguments of the function N (since p. becomes
-p . and a becomes - a in equation (4)).
The right hand side of equation (4) is a function of
four parameters:
= NfeVFT
where N(«) is the standard Gaussian distribution, and,
more importantly for present purposes,
a, H, p,, a.
<4)
Only the first two of these parameters depend on the
particular type of instrument, the last two being deter
mined by the characteristics of the underlying asset. In
order to apply expression (4) to the events defined in
’’ ios'tsH *•<»)
= n<SVh-
+
U^ H )Since the Wiener process is stationary,
IF o r a discussion of W iener processes, includ ing the calcula tion
of these expressions, see D.R. Cox and H.D. Miller, The Theory
o f S tochastic Processes (Chapm an and Hall, 1980), chap. 5.
^ h ^ tssT + H (x»- x T)< a ]
Probability of Negative Equity within Posting Period
Instrum ent
Stocks
h-
E xercise Price
Value (Percent)
___
Maintenance
Margin (Percent)
Posting Period
(Days)
25
2
20 Percent
—
3
5
15
O ptions
70
(18.3, 20.7)
2
___
3
5
15
100
(27.9, 33.3)
2
—
3
5
15
130
(38.8, 43.8)
2
—
3
5
15
Index futures
___
7.5
1
0
6 .0
1
.000 001
4.5
1
.000237
7.5
2
.0 0 0 0 10
6 .0
2
4.5
2
.000450
.008747
Volatility
40 Percent
60 Percent
0
0
0
.0 0 0 0 11
0
.002672
.000634
.045657
.000003
.000142
.003367
.097719
.000485
.004475
.028321
.213326
0
0
0
.000016
.014426
.000013
.000776
.055525
0
0
0
0
0
.000 021
.001045
.015167
___
___
Notes:
(1) It is assum ed that the underlying stocks follow a W iener process with an expected return of 12 pe rcent per annum and a
v olatility as in dica ted in the table. There are 250 tra ding days per year.
(2) An entry of “ 0 ” denotes a p robab ility of less than .0000005.
(3) For stocks and options, some param eter values are based on NYSE rules and praxis; for index futures, on the CME.
Further values are included to illustrate the sensitivity of the results to these param eters and to aid in interm arket
com parisons.
(4) O ptions are p ric e d using the Black-Scholes form ula w ith no divide nds and a riskless interest rate of 7 pe rcent per
annum. The m aintenance m argins given are based on the NYSE rules for options on individual stocks and correspond to
volatilities of 40 and 60 percent, respectively.
FRBNY Quarterly Review/Summer 1988
Appendix B: Calculation of Credit Risk for Equity-Related Instruments (continued)
(1)-(3) of the preceding section, values of n, cr, and H
must be determined, and the specific form of parameter
a must be obtained from the appropriate expression in
(1)-(3). The parameter a is
lo g (1 -m M)
for stocks,
log(1 - pD/Sr)
for futures, and
log((E/ + K)/St)
in the case of options.
Numerical examples based on the Wiener process
The accompanying table provides numerical estimates
of the probability of negative equity based on the
Wiener process. These figures illustrate the range of
pro b a b ilitie s th at correspond to param eter values
roughly representative of those currently observed in
the markets. Stocks and options are assumed to corre
spond to individual securities, while index futures are
based on a broad index such as the S&P Composite.
For this reason, the volatility of the latter is taken to be
lower than those of the individual instruments.
Almost all the probabilities based on realistic parame
ters are less than 1 percent, in most cases significantly
so. An exception is the in-the-money option (K =70) on
a stock with a volatility of 60 percent, for which the
probability of an equity deficiency within five days is 2.8
percent. Creditors would presumably be aware of the
reduced margin protection on options that are well into
the money and would accordingly reduce the posting
period for margin calls. The probabilities in the table
seem in general to be quite low. Any such appraisal,
however, is of necessity subjective.
FRBNY Quarterly Review/Summer 1988
79
Margin Requirements and
Stock Market Volatility
Margin requirements in the stock market restrict the
amount of credit that brokers and dealers can extend
to their customers for the purpose of buying stocks.
The current initial margin requirement of 50 percent
implies that at least 50 percent of the value of a new
stock purchase should come from investors’ own capi
tal. If the stock price rises after the initial purchase,
investors can withdraw the differential from their mar
gin account or can use it to buy additional stock on 50
percent margin. If the price declines after the initial
purchase, investors are not required to add funds to
their margin account unless their equity position falls
below the so-called maintenance margin, which is cur
rently 25 percent.1
Federal regulation of securities margins was manda
ted by Congress in the Securities Exchange Act of
1934. The stock market experience of the late 1920s
led Congress to conclude that credit-financed specula
tion in the stock market might create excessive market
volatility: In the absence of adequate margin require
ments, optimistic investors with relatively low degrees
of risk aversion might borrow large amounts of funds to
buy stocks, causing a price rise that could not be justi
fied by economic fundamentals. The price rise might
then feed on itself; the speculators could use their
increased wealth to borrow more funds and purchase
more stock, thus driving prices even higher. This pyra
miding effect could in turn be followed by a market col
lapse if less optimistic investors began to sell in the
belief that the market had been overbought. As the
’ Note that brokers themselves set maintenance margins higher than
25 percent and vary them across customers and across time.
FRBNY Quarterly Review/Summer 1988
Digitized80
for FRASER
price declined, brokers and other creditors would ask
for more collateral on their loans to speculators. If
some speculators could not provide the additional col
lateral, creditors would sell the stocks they kept as col
lateral, forcing prices still lower. This outcome would
generate further calls for collateral, more liquidations,
and additional price declines. Congress reasoned that
the imposition of margin requirements could prevent
the excessive volatility caused by this process of pyra
miding and depyramiding and gave the Federal
Reserve jurisdiction over the level of initial margin
requirements.2
Do initial margin requirements curb speculative
excesses in the stock market and reduce stock price
volatility? This question has gained new importance
among regulators and students of financial market
developments following the sudden collapse of stock
prices in October 1987.3 Clearly, theory alone cannot
provide a definite answer. Those who believe that
speculation is stabilizing because it deepens the mar
ket and increases liquidity are likely to view margin
requirements as harmful. Those who believe that an
2For a review of the pyramiding-depyramiding process, see Kenneth
D. Garbade, "Federal Reserve Margin Requirements: A Regulatory
Initiative to Inhibit Speculative Bubbles,” in Paul Wachtel, ed., Crises
in the Economic and Financial Structure (Lexington, Massachusetts:
Lexington Books, 1982). Garbade also discusses Congress' related
objectives in imposing margin requirements, such as protecting small
investors and inhibiting the diversion of credit to unproductive
speculative activities.
3See, for example, the "Interim Report of the Working Group on
Financial Markets," submitted to the President of the United States,
May 1988. See also Arturo Estrella, “Consistent Margin Requirements:
Are They Feasible?” in this issue of the Quarterly Review.
unchecked market is often subject to destabilizing
speculation are likely to think that margin requirements
could prevent speculative excesses. The question can
only be resolved empirically.
This a rtic le exam ines the em pirical re la tion ship
between initial margin requirements and the volatility of
stock prices in the cash market. Since 1934, the Fed
eral Reserve has changed the initial margin require
ment in stocks 23 times (Table 1). The different levels
of initial margin requirements during the last 50 years
make it possible to analyze the presence or absence of
an association between initial margin requirements and
volatility. Certainly, stock market volatility can also vary
over time for reasons unrelated to margin requirements
and the unrestrained behavior of speculators. For
example, in an environment with more volatile interest
rates or cash flows, one expects to find more volatile
stock prices. Thus the present study also takes into
consideration econom ic factors that may influence
stock price volatility.
The empirical evidence reveals an economically and
statistically significant negative relationship between
initial margin requirements and stock market volatility.
Higher initial margin requirements are associated with
a reduction in both actual stock market volatility and
excess stock market volatility, that is, volatility which is
over and above the volatility caused by the variability
of the economic environment.
Margin requirements and destabilizing speculation:
the theoretical connection
The proposition that margin requirements help curb
de sta b ilizin g sp eculatio n is based on two im plicit
claims. The first claim is that speculation by some
groups of investors can be destabilizing. The second
claim is that margin requirements can impose an effec
tive constraint on the market activities of speculators.
The first claim is plausible but is not accepted by all
economists. For example, Milton Friedman argues that
speculation is destabilizing only if speculators on the
average lose money by selling when assets are low in
price and buying when assets are high.5 Although
Friedman’s position is shared by many economists,
increasing numbers of market professionals and aca
demic econom ists believe that the high daily and
monthly volatility of stock prices may be the result of
asset churning by speculators who have very short
term investment horizons. Furtherm ore, econom ists
have constructed theoretical models of destabilizing
speculation featuring speculators who do not lose
money. These models show that speculation can desta
bilize prices in an efficient market, but they do not
claim to show that speculation will necessarily destabi
lize prices. The effect of speculation on price volatility
is an empirical question.6
The claim that margin requirements can impose a
binding constraint on the behavior of destabilizing
speculators is also plausible. Finance theory predicts
that the less risk-averse investors, that is, the potential
speculators, hold more stocks and less cash in their
portfolios and are therefore more likely to be con
strained by margin requirements than the more riskaverse and conservative investors.7
Although there is a theoretical connection between
margin requirements and destabilizing speculation, the
connection would be uninteresting if its quantitative
magnitude were trivial or nonexistent. Thus at the
Table 1
Initial Margin Requirements
5Milton Friedman, “ The Case for Flexible E xchange Rates," in Essays
in Positive Econom ics (C hicago, Illinois: U niversity of C hicago Press,
1953).
(In Percent)
Effective
Date
10/15/34
02/01/36
11/01/37
02/05/45
07/05/45
01/21/46
02/01/47
03/30/49
01/17/51
02/20/53
01/04/55
04/23/55
Rate
45
55
40
50
75
100
75
50
75
50
60
70
Effective
Date
Rate
01/16/58
08/05/58
10/16/58
07/28/60
07/10/62
11/06/63
06/08/68
05/06/70
12/06/71
11/24/72
01/03/74
50
70
90
70
50
70
80
65
55
65
50
Sources: New York Stock Exchange Fact Book, 1987, p. 54;
and Board of Governors of the Federal Reserve System,
Annual Report, various issues.
6See Oliver D. Hart and David M. Kreps, “ Price D estabilizing
S pecu la tion,” Journal o f P olitical Economy, vol. 94 (O ctober 1986),
pp. 927-52. A step tow ards m odeling d e stabilizing speculation is
also taken by B radford J. DeLong, Andrei Shleifer,
Lawrence H. Summers, and Robert J. Waldman, "The Economic
C onsequences of Noise Traders,” National Bureau of Economic
Research, Working Paper no. 2395, O cto ber 1987.
7Dudley G. Luckett, “ On the E ffectiveness of the Federal Reserve’s
M argin Requirem ents,” Jou rnal of Finance, vol. 37 (June 1982),
pp. 783-95, utilizes data on investors’ equity positions in margin
accounts and finds that margin requirem ents constrain investment in
the stock market. Another piece of evidence consistent with the
claim that margin requirem ents constrain investment in the stock
m arket is the fact that total m argin borrowings as a fraction of the
value of the New York S tock Exchange stocks decrease after an
increase in m argin requirem ents; see Gikas A. Hardouvelis, "M argin
Requirements, Volatility, and the Transitory C om ponent of Stock
P rices,” Federal Reserve Bank of New York, Research Paper no. 8818,
July 1988.
FRBNY Quarterly Review/Summer 1988
81
present stage, the key research question is empirical in
nature.
The Federal Reserve’s reaction function
One factor complicating the empirical analysis of mar
gin requirements and their effects on market volatility
is the behavior of the Federal Reserve as a regulator
of margins. Thus before we turn to the effects of mar
gin requirements on stock price volatility, a rough char
acterization of the Fed’s behavior is in order. Recall
that the Federal Reserve has changed the initial mar
gin requirements 23 times since 1934. Increases in
margin requirements were presumably initiated during
periods when stock prices were perceived to be influ
enced by excessive speculation, while decreases in
m argin requirem ents were initia te d during calm er
times, perhaps in order to enhance participation in the
market and increase liquidity.8
•The follow ing excerpt from the 1951 Annual Report of the Board of
Governors is representative of the Fed’s explanations of m argin
requirem ent changes: “Although the total amount of cre d it in use in
the stock market had not assumed heavy proportions, there had
been some increase during the precedin g months, together with
increases in the volume of tra ding and in prices of securities. The
expanding business and econom ic situation appeared to be
encouraging stock market a ctivity and speculation, and the Board of
G overnors believed that in the existing circum stances a further
substantial price advance supported by a rapid expansion of stock
market cre d it was a d istinct possibility. The increase in margin
requirem ents was effected as a preventive measure” (p. 81). Also
Table 2
The Federal Reserve’s Reaction Function
M, = -0 .0 0 1 + 0 .9 56’ M,., + 0.024* (P,.,/P)
(.008)
(.014)
(.007)
-
0.274 MCREDIT,., + u,
(.251)
R2 = 0.95, SEE = .034, M = 0.59
Sample: Novem ber 1934 to D ecem ber 1987
*Statistically significa nt at the 5 percent level.
M,
= O fficial margin requirement (in decim als).
MCREDIT,., = Ratio of broker margin credit to the total value
of the New York Stock Exchange stocks at the
_
end of month t- 1 .
PM/P
= S&P C om posite index (including d ivide nds) at
the end of month t - 1 divide d by the average
S&P C om posite of the previous five years.
R2
= C oefficient of determ ination adjusted for
de grees of freedom.
SEE
= Regression standard error.
M
= Sam ple average of Mt.
Note: Num bers in parentheses are standard errors adjusted
for conditional heteroskedasticity. When the sam ple period
ends in 1974, the regression results are similar. When an
index of sm all stocks is sub stituted for the S&P C om posite,
the results are also similar.
82
FRBNY Quarterly Review/Summer 1988
Two indicators of speculative excesses are the level
of stock prices relative to trend and the amount of mar
gin credit. Both variables are prominent in the explana
tio n s given by the Fed a fte r changes in m argin
requirements. A regression of the level of margin
requirements on lagged values of these indicators may
provide a characterization of the Fed’s regulatory
response to speculative excesses. Table 2 presents the
regression results. Observe that the Fed’s setting of
margin requirem ents is not very se n sitive to the
amount of broker and dealer credit, but it is sensitive to
the level of stock prices relative to trend.9 When stock
prices rise above trend, indicating that excessive buy
ing may be present, the margin requirement tends to
increase.
The tendency of the Federal Reserve to raise margin
requirements when stock prices are high relative to
trend and lower them when stock prices are low rela
tive to trend may create a spurious negative correlation
between margin requirements and stock market vol
atility. This spurious relationship should be taken into
account if the true relation between margin require
ments and volatility is to be assessed correctly. The
spurious relation arises as follows: Finance economists
have found a negative relationship between stock
prices and stock price volatility. During periods of high
stock prices, the debt-to-equity ratio of firms that are
publicly traded is low and, consequently, stock price
volatility is low.10 Since high stock prices cause both an
increase in margin requirements and a decrease in
stock price volatility, they may result in a negative cor
relation between margin requirements and stock price
volatility. This correlation could be falsely interpreted
as evidence that higher margin requirements cause a
decrease in volatility. The empirical work of the follow
ing section avoids such a false interpretation by includ
ing s to c k p ric e s re la tiv e to tre n d as an e x tra
explanatory variable in the regressions.
Margin requirements and volatility
There is an extensive empirical literature on the effects
Footnote 8 continued
cha racte ristic is the B o a rd ’s explanation after a de crease in m argin
requirem ents in 1962: “ In m aking this change, the Board noted that
there had been a sharp reduction in stock m arket cre d it in recent
weeks, with an abatem ent in speculative p sych o lo g y” (Annual Report,
1962, p. 113).
®More involved “ G ranger ca u sa lity” tests show that m argin
requirem ents G ranger cause (are tem porally prior to) margin
borrowings, but margin borrow ings do not G ranger cause margin
requirements.
10This phenomenon is the ore tically plausible and is ob served in
practice. See Andrew A. C hristie, “ The S tochastic Behavior of
Common Stock Variances: Value, Leverage and Interest Rate E ffects,”
Journal o f Financial Econom ics, vol. 10 (D ecem ber 1982), pp. 407-32.
of margin requirements but, surprisingly, empirical work
on the influence of margin requirements on stock mar
ket volatility is scarce. Thomas Moore contends that
margin requirements are an ineffective tool for control
ling volatility because the volatility of stock prices has
remained relatively stable despite several changes in
margin requirements since 1934.11 James O’Brien takes
a similar position, arguing that short-term speculative
excesses have not been a characteristic of the
post-1929 period.12 A detailed study by the Board of
Governors of the Federal Reserve System is more cau
tious, concluding only that the evidence is insufficient
for a definite answer on the effectiveness of margin
requirements.13 The studies by O’Brien and the Board
of Governors are very careful and quite extensive, but
they focus on the relationship between margin require
ments and the level or the rate of change of stock
prices rather than the volatility of stock prices. Moore
does not provide any regression evidence whatsoever.
Nevertheless, the relationship between margin require
ments and stock price volatility was studied by George
Douglas and by R. R. Officer, and both authors found a
negative association between the two variables. This
section complements their work and seeks to sharpen
their empirical analysis by using more available data
and running a more complete set of regressions with
variables that these authors excluded from their
analyses.14
Because theory does not provide any guidance on
the use of real or nominal stock prices, both measures
are used. Specifically, monthly realized real rates of
return and realized excess nominal rates of return are
used to calculate the volatility measures. Real rates of
return are constructed from a nominal stock price
index that includes dividends, deflated by the consumer
price index (CPI). Excess nominal rates of return are
nominal returns minus the known one-month Treasury
bill rate at the beginning of the one-month holding
period.15 It turns out that the volatility measures based
"Thomas G. Moore, “Stock Market Margin Requirements,” Journal of
Political Economy, vol. 74 (April 1966), pp. 158-67.
“ James M. O’Brien, "Speculative Bubbles in Stock Prices and the
Need for Margin Regulation,” Unpublished Working Paper, Board of
Governors of the Federal Reserve System, December 1984.
“ Board of Governors of the Federal Reserve System, A Review and
Evaluation of Margin Requirements, Staff Study, December 1984.
MSee George W. Douglas, “Risk in the Equity Markets: An Appraisal of
Market Efficiency," Yale Economic Essays, Spring 1969, pp. 3-45; and
R. R. Officer, The Variability of the Market Factor of the New York
Stock Exchange,” Journal of Business, vol. 46 (July 1973),
pp. 434-53.
“ The purpose of subtracting the one-month Treasury bill rate from
realized nominal stock returns is to construct a measure of stock
on real rates of return are very similar to the volatility
measures based on excess nominal rates of return.
The reason for the similarity is that the monthly vol
atility of stock prices overwhelms the volatilities of the
CPI and the Treasury bill rate.
The volatility measure used in this study is the stan
dard deviation of monthly returns calculated over 12
consecutive months. This appears to be the best
measure for capturing the possible presence of a pyra
miding and depyramiding process in stock prices, a
process likely to last more than a few months. Further
more, this volatility measure focuses the analysis on
longer-run volatility.16
The empirical analysis utilizes both large and small
stocks. Large stocks are represented by the Standard
and Poor (S&P) Composite index, and small stocks are
represented by an index that consists of the ninth and
tenth deciles of the New York Stock Exchange when its
stocks are ranked by their capitalized values. For each
month in the sample, a standard deviation is con
structed from the data of that month and the previous
11 months. Chart 1 plots the standard deviations of the
S&P Composite and of small stocks together with the
official margin requirement. Observe that small stocks
are more volatile than the large stocks in the S&P
Composite and that the early 1930s are characterized
by unusually high volatility.17
Chart 1 brings out a crucial point: the monthly sam
ple from the early 1930s to the present is long but, for
the purposes of this analysis, it is effectively very small
because margin requirements did not change often.
The small effective sample size requires more refined
statistical techniques and more caution in interpreting
all empirical results. A casual examination of the data
would not be informative. For example, if investigators
simply scanned the chart, they might falsely conclude
that no relationship existed between margin require
ments and volatility after 1934 and, for this reason,
forgo a more detailed analysis of the data. Thus the
Footnote 15 continued
return volatility that is over and above the normal volatility of monthly
interest rates. Note that if inflationary expectations are incorporated
into the one-month Treasury bill rate, then excess nominal returns are
similar to real rates of return and have an advantage: the data series
on both stock prices and Treasury bill rates refer to the last trading
day of the month and are, therefore, matched exactly. In contrast,
data on the consumer price index refer to days within the month and
are announced much later.
“ Thus the empirical evidence in this study complements the evidence
provided by the studies of O’Brien and the Board of Governors
because that evidence could be interpreted as referring to short-run
volatility.
17The standard deviations in Chart 1 are based on real rates of return.
When excess nominal rates of return are used to construct volatility
measures, the new chart is very similar.
FRBNY Quarterly Review/Summer 1988 83
limitations of the sample may explain why previous
studies have neglected to undertake a rigorous exam
ination of the correlation between margin requirements
and volatility.
The regression analysis uses all the available
monthly observations from the late 1920s through 1987.
As noted earlier, for every month in the sample, a stan
dard deviation is calculated using the returns of that
month and the previous 11 months. This standard devi
ation is matched with an average official margin calcu
lated over the same 12 months. The use of overlapping
data provides more statistical power but also creates
some technical difficulties.18
18The use of rolling 12-month periods generates a moving average
process of order 11 in the error term. In this case, OLS standard
errors are biased estim ates of the true standard errors and lead to
incorrect inferences. Thus a m odification of the OLS variancecovariance m atrix is used, providing asym ptotically consistent
standard errors. See Lars P. Hansen, "Large Sample Properties of
G eneralized Methods of Moments E stim ators,” Econom etrica, vol. 50
(July 1982), pp. 1029-54. An alternative setup would be a
nonoverlapping annual sam ple with both stock return volatility and
Digitized 84
for FRASER
FRBNY Quarterly Review/Summer 1988
Tables 3 and 4 present the regression results. Table
3 refers to real rates of return and Table 4 refers to
excess nominal rates of return. Two types of regres
sions are run: the first includes the official margin
requirement as the only explanatory variable, and the
second includes additional explanatory variables that
characterize the changing economic environment. Let
us examine the simple set of regressions first. Observe
that there is a statistically significant negative associa
tion between the official margin requirement and stock
market volatility. This is true for both large and small
stocks and for volatility measures based on either real
or excess nominal stock returns. The negative associa
tion is present over the entire sample period and over
the sample period that begins in November 1934, after
the imposition of official margin requirements.
The magnitude of the effect of margin requirements
on volatility is economically significant. For example,
Footnote 18 continued
the average margin ca lcu la te d from January to Decem ber.
margin requirements, however, are those set by brokers
and dealers who may add a spread over the official
margin for certain customers and during certain time
periods. The official margin requirement thus equals
the unknown effective margin plus an error. This error
causes a bias in the estimated coefficients.19 Observe
now that before October 1934 the official margin is
zero, which is a more severe underestimate of the true
effective margin of the pre-1934 period than the official
margin of later dates. R ecall also that the same
pre-1934 period is characterized by unusually high vol
atility. Thus the com bination of a downward-biased
proxy of the true margin and an unusually high vol-
the estimated coefficient -0.110 in Table 3 shows that
over the entire sample an increase in the margin
requirement by 10 percentage points from, say, 50 per
cent to 60 percent decreases the monthly volatility of
large stocks by 1.10 percentage points. The effect of
margin requirements on small stocks is even greater
(1.91 percentage points). To put these numbers in per
spective, observe that the average monthly volatility of
large stocks, a, is 4.8 percentage points and of small
stocks, 7.4 percentage points. Thus a 10 percentage
point increase in margin requirements decreases vol
atility by approximately one-quarter its average value.
The results from the entire sample could overesti
mate the effect of margin requirements on volatility.
Recall that our measure of margin requirements is the
official measure, tabulated in Table 1. The effective
19See the discussion in G. S. M addala, Econom etrics (New York:
M cGraw-Hill Book Company, 1977), pp. 292-94.
Table 3
Margin Requirements and the Volatility of Monthly Real Stock Returns
R egression Equation: a, = p0 + Pi cr,.t2 + p2 cr(yt) + p3 a(rtCB) + p4 (P,/P) + p5 m, + e,
Estim ated R egression C oefficients
Sample
Po
P,
p2
P3
P4
Ps
R2
SEE
- .110*
(.025)
- .0 5 7 *
(0 1 7 )
.43
.024
.63
.019
- .0 4 3 *
(.016)
- .0 2 7 *
( 011)
.10
.017
.40
.014
.47
.039
- .0 1 5 *
(.005)
- .1 9 1 *
(.032)
- .0 7 9 *
(.025)
.6 8
.030
.18
.033
- .009 f
(.005)
- .1 1 4 *
(0 3 1 )
- .0 4 8 *
(.019)
.57
.024
a
N
.048
673
.042
627
.074
673
.064
627
S&P index:}:
D ecem ber 1931 to
D ecem ber 1987
O cto ber 1935 to
D ecem ber 1987
.1 1 0 *
(0 1 5 )
.091*
(.0 2 2 )
.067*
(.0 1 0 )
.050*
(. 0 1 2 )
-.0 2 0
(1 2 5 )
.183*
(.074)
1.003*
(.186)
.897*
(.267)
- .0 2 4 *
(. 0 1 0 )
.358*
(1 2 5 )
.266*
(.092)
- . 0 1 1 1
(.007)
Small Stocks^
D ecem ber 1931 to
D ecem ber 1987
O cto ber 1935 to
D ecem ber 1987
.179*
(.019)
.095*
(. 0 2 2 )
.131*
(. 0 2 0 )
.055*
(.015)
.234*
(.119)
.470*
(.092)
1.427*
(.290)
1.393*
(.378)
.361 *
(.173)
,2 4 2 f
(1 3 4 )
'S ta tis tic a lly significa nt at the 5 percent level.
tS ta tis tic a lly significa nt at the 10 percent level.
^In sid e the parentheses are standard errors corrected for conditional heteroskedasticity and the MA-11 process of the error term,
a,
= Standard deviation of the m onthly real rate of return of stocks (nom inal rate of return in clud ing divid e n d s minus the CPI inflation
rate), ca lcu la te d from t - 1 1 to t (in decim als).
a(y,)
= S tandard deviation of the m onthly percentage change in the industrial production index from t-1 1 to t (in decim als).
a(rp8)
= Standard deviation of the m onthly real rate of return on corporate bonds from t-11 to t (in decim als).
P,/P
= Average stock p rice from t-11 through t, d iv id e d by the average stock price from t-71 through t-1 2.
m,
= Average official margin requirem ent from t-11 to t (in decim als).
R2
= C oefficient of determ ination adjusted for degrees of freedom.
SEE
= Regression standard error (in decim als).
a
= Sam ple average of <x, (in decim als).
N
= Total num ber of overlapping observations.
FRBNY Quarterly Review/Summer 1988
85
atility during the pre-1934 period causes the estimated
coefficient to be more negative than the true parame
ter. For this reason, Tables 3 and 4 rerun the regres
sions starting in November 1934. Of course, now the
new and less negative coefficient estimate is biased in
the p o s itiv e d ire c tio n because a zero w eig ht is
assigned to the low m argin/high vo latility pre-1934
sample period. Clearly, the coefficient that captures the
influence of effective margins on volatility lies between
the two estim ates from the two d iffe re n t sam ple
periods. It is reassuring that the post-1934 set of esti
mates are qualitatively similar. The estimated coeffi
cient drops in m agnitude but rem ains s ta tis tic a lly
significant. Actual stock return volatility also drops in
magnitude. Thus an increase in margin requirements
by 10 percentage points during the later sam ple
decreases volatility by approximately 10 to 18 percent
its average value.
Charts 2 and 3 present scatterplots of the relation
ship between volatility and margin requirements for the
post-1934 period. Unlike Chart 1, the scatterplots show
a clear negative relationship between volatility and
margin requirements for both the S&P Composite and
small stocks. The line through the cloud of data points
is the regression line. The regression line has a nega
tive slope and is steeper for small stocks, characteris
tics that are consistent with the results of the tables.
Observe that in the case of the S&P Composite, the
negative slope is primarily driven by observations that
belong to the 1930s and 1940s. In the case of small
Table 4
Margin Requirements and the Volatility of Monthly Excess Nominal Stock Returns
R egression Equation: a, =
30
+ p, <rM2 + 3 2 cr(yt) + p 3 ^(ip8 ) + 3 4 (P,/P) + P5 m, + e,
Estim ated Regression Coefficients
Sample
3o
Pi
Pa
Ps
R2
SEE
.44
.024
- .0 2 3 *
(. 0 1 0 )
- .112*
(.024)
- .0 6 0 *
(.017)
.63
.020
.12
.017
—. 0 1 1 f
(0 0 7 )
- .0 4 6 *
(0 1 5 )
- .0 2 9 *
(011)
.40
.014
.47
.039
- .0 1 5 *
(.005)
- .1 9 2 *
(.031)
- .0 8 1 *
(.025)
.68
.030
.18
.034
-.0 0 9 f
(.005)
-.1 1 8 *
(.031)
- .0 5 1 *
(.019)
.57
.025
<T
N
.048
673
.042
627
.074
673
.064
627
S&P In dext
D ecem ber 1931 to
D ecem ber 1987
O cto ber 1935 to
D ecem ber 1987
.1 1 2 *
(0 1 5 )
.094*
(. 0 2 2 )
.069*
0 10 )
.051*
(.013)
-.0 3 6
(.127)
1.013*
(1 9 1 )
.331*
(. 1 2 0 )
(
.186*
( 078)
.890*
(.274)
.244*
(.090)
Smalt Stocks^
D ecem ber 1931 to
D ecem ber 1987
O cto ber 1935 to
D ecem ber 1987
.180*
(0 1 9 )
.097*
(. 0 2 2 )
.134*
(. 0 2 0 )
.058*
(0 1 6 )
229t
(. 1 2 0 )
.463*
(.099)
1.432*
(.291)
1.389*
(.387)
300t
(1 6 3 )
.205
(1 3 3 )
‘ S tatistically significa nt at the 5 percent level.
fS ta tis tic a lly significa nt at the 10 percent level.
tln s id e the parentheses are standard errors corrected for conditional heteroskedasticity and the MA-11 process of the error term,
86
cr,
= S tandard deviation of the monthly excess nominal rate of return of stocks (nominal rate of return minus the one-m onth T-bill rate at
the end of the previous month), calcula ted from t - 1 1 to t (in decim als).
<r(y,)
= Standard deviation of the monthly pe rcentage change in the industrial production index from t-11 to t (in decim als).
tr( ifB)
= S tandard deviation of the monthly nominal rate of return on corporate bonds from t-1 1 to t (in decim als).
P,/P
= Average stock p rice from t-11 through t, d ivid e d by the average stock price from t-71 through t-1 2.
m,
= Average official margin requirement from t-11 to t (in decim als).
R2
= C oefficient of determ ination adjusted for degrees of freedom.
SEE
= Regression standard error (in decimals),
a
= Sample average of a, (in decim als).
N
= Total num ber of overlapping observations.
FRBNY Quarterly Review/Summer 1988
stocks, the negative slope is a characteristic of the
entire sample period.20
Let us turn now to the more complicated regressions
that include additional explanatory variables. The addi
tional variables are lagged volatility, the standard devi
ation of the monthly growth rate of the industrial
production index, the standard deviation of the monthly
rate of return of a five-year corporate bond, and stock
prices relative to trend. A standard deviation is again
computed from variables over the current and previous
11 months. The price relative to trend is the average
price of the stock over the current and previous 11
months divided by the average price over an earlier 60month period. The volatility of the industrial production
index serves as a proxy for the volatility of dividends,
and the volatility of the corporate bond return as a
proxy for the volatility of discount rates. The price rela
tive to trend is included in order to disentangle the
“ The scatterplo ts also reveal con sid era ble heteroskedasticity. The
estim ation procedure autom atically corrects for an unknown form of
heteroskedasticity, as in H arbert White, “A H eteroscedasticityC onsistent Covariance Matrix Estim ator and a Direct Test for
H ete rosced asticity," Econom etrica, vol. 48 (May 1980), pp. 817-38.
direct effect of margin requirements on volatility from
the possible spurious correlation arising from the
effects of stock prices on both margin requirements
and stock volatility. Finally, lagged volatility is included
in order to capture other variables that may affect
stock market volatility with a delay.
The inclusion of additional explanatory variables
does not affect the qualitative results from the earlier
simple regressions. Margin requirements continue to
have a negative and statistically significant effect on
stock market volatility. For example, Table 4 shows that
over the post-1934 sample period, when other vari
ables are kept constant, an increase in margin require
ments by 10 percentage points decreases the volatility
of large stocks by 0.29 percentage points and the vol
atility of small stocks by 0.51 percentage points, or by
7 to 8 percent of their average sample values. The
effect of margin requirements may appear economi
cally small, but note that since volatility is positively
related to lagged volatility, the long-run effect of margin
C hart 3
Sm all Stock V olatility Regressed on
O fficial Margin Requirement
C hart 2
S e p te m b e r 1935-D ecem ber 1987
S&P Composite V o latility Regressed on
Official Margin Requirement
P e rce n t
S e p te m b e r 1935-D ecem ber 1987
P ercent
22
20
18
16
14
oo°
12
10
6
4
2
0
30
40
50
60
70
80
O ffic ia l margin re quire m en t
90
100
N otes: S to c k v o la tility is the sta n d a rd d e v ia tio n of
m onthly e x c e s s nom inal ra te s o f re tu rn du rin g th e last
12 m onths. O ffic ia l m argin re q u ire m e n t is th e a v e ra g e
o ffic ia l m argin re q u ire m e n t o v e r th e same 1 2 -m onth pe rio d .
30
40
50
60
70
80
O ffic ia l m a rgin re quire m en t
90
100
N otes: S to ck v o la tility is th e sta n d a rd d e via tio n of
m onthly e x c e s s no m inal ra te s o f re tu rn du ring the la st
12 m onths. O ffic ia l m argin re q u ire m e n t is th e a ve ra g e
o ffic ia l m argin re q u ire m e n t over the sam e 1 2 -m onth p e rio d .
FRBNY Quarterly Review/Summer 1988
87
requirements is larger.21
The estimated coefficients of the additional explana
tory variables in Tables 3 and 4 confirm intuition and
our earlier discussion. Stock prices are more volatile
when economic output is more volatile, when interest
rates are more volatile, and, as finance economists
have found, when stock prices are relatively low.22
Finally, note that a negative correlation between mar
gin requirements and volatility does not necessarily
imply causation from margin requirements to volatility.
A third, unknown variable may have caused both vol
atility and margin requirements to move in opposite
directions. However, the regression equations of Tables
3 and 4 take most plausible third variables into
account. First, the regression controlled for the vari
able that entered significantly in the Fed’s reaction
function, namely, the level of stock prices relative to
trend. Second, the regression controlled for lagged vol
atility and thus for possible delayed responses by the
Federal Reserve to volatility changes. Third, although
there is no presumption that the Fed responded to vol
atility, if it had, it probably would have raised rather
than lowered margin requirements following an
increase in volatility. Thus the Fed’s possible contem
poraneous response to stock market volatility itself (as
opposed to those other indicators of speculative
excesses already taken into account) could only gener
ate a positive correlation between margin requirements
and volatility and work against the finding of a negative
correlation.
Margin requirements and excess volatility
The previous section showed that an increase in mar
gin requirements tends to mitigate stock market vol
atility. However, volatility in itself is not a direct
measure of speculative excess. A more direct measure
of speculative excess is excess volatility, or volatility
that cannot be explained by the variation of current and
expected future dividends and discount rates. This sec
tion treats the relation between margin requirements
and excess volatility.
One could interpret the expanded regression results
in Tables 3 and 4 as evidence of the effect of margin
requirements on excess volatility. The reason is simple:
the regression equations include measures of the vol
atility of the fundamental determinants of stock prices
such as dividends and discount rates, and thus the
estimated effects of margin requirements on volatility
are not effects that work their way through the included
measures of the volatility of the fundamental determi
nants of stock prices. The estimated coefficients reflect
the effect of margin requirements on the unexplainable
component of volatility. The unexplainable component
of volatility is a rough proxy of excess volatility.23 How
ever, unexplainable volatility is only a proxy of excess
volatility because the regressions do not control per
fectly for the variability of fundamental factors, partic
ularly expected future dividends and discount rates.
Furthermore, the regression equations do not take into
consideration the precise theoretical relation of divi
dends and discount rates to stock prices, that is, the
present value model.
Further analysis of the effects of margin require
ments on excess volatility is beyond the scope of this
article. A more technical research paper that served as
the basis of this article develops a precise measure of
excess volatility and examines alternative evidence of
excessive speculation in the form of long-run devia
tions of stock prices from their fundamental values.24
One of the major findings of that paper is that during
periods of low or decreasing margin requirements,
excess volatility of stock prices is higher than during
periods of high or increasing margin requirements.
Another finding is that “fads,” that is, long-term devia
tions of stock prices from their fundamental values, are
more prevalent during periods of low or decreasing
margin requirements than in periods of high or increas
ing margin requirements. Again, this evidence is con
sistent with the hypothesis that margin requirements
help curb speculative excesses.25
»The slope coefficient of lagged volatility is .186 for the S&P
Composite and .463 for small stocks. Thus the effects of margin
requirements cumulate as time goes on and, in the long run, they are
1.23 to 1.86 times larger than the short-run effects. The multiplicative
factors of 1.23 and 1.86 can be derived by iterative forward
substitution. They are equal to 1/(1 —0.186) and 1/(1-0.463),
respectively.
»ln “The Persistence of Volatility,” Poterba and Summers argue that
volatility is well approximated by an AR(1) process. In this article’s
specification, volatility is calculated over a one-year interval, and thus
the lagged volatility of 12 months earlier is similar to an AR(1) term.
The inclusion of a lagged volatility measure in addition to the other
contemporaneous variables sharpens the claim that the unexplainable
volatility is a proxy of excess volatility.
“ The size and statistical significance of lagged volatility conflict with
an assertion made recently by James M. Poterba and Lawrence H.
Summers in "The Persistence of Volatility and Stock Market
Fluctuations,” American Economic Review, vol. 76 (December 1986),
pp. 1142-51, that shocks to volatility dissipate quickly. Poterba and
Summers use a slightly different volatility measure based on daily
observations of the S&P Composite. They also run simple
autoregressive models with no additional explanatory variables.
MSee Gikas A. Hardouvelis, “Margin Requirements, Volatility, and the
Transitory Component of Stock Prices.”
88
FRBNY Quarterly Review/Summer 1988
»For an exposition of the fads hypothesis, see Lawrence H. Summers,
“Does the Stock Market Rationally Reflect Fundamental Values?”
Journal of Finance, vol. 41 (July 1986, Papers and Proceedings of the
44th Annual Meeting of the American Finance Association),
pp. 591-600.
Conclusion
Higher initial margin requirements in the cash market
are statistically associated with a reduction in both
actual and excess stock price volatility. The evidence
should be interpreted with caution, however, because it
is based on a small number of effective observations.
Margin requirements have changed only 23 times since
1934. Furthermore, the last change in margin require
ments occurred almost 15 years ago, in January 1974.
Since that time, financial markets have changed dras
tically, especially with the introduction of derivative
markets and the globalization of capital flows. Thus
one can not use this article’s findings to support spe
cific policy changes in the cash market in full confi
dence that the a rtic le ’s predicted effe cts w ill be
realized with great precision. But the results do sup
port the contention that increases in margin require
ments reduce market volatility. At a minimum, the
evidence shows that the presence of margins contrib
utes to a more stable market.
Since the stock market crash of October 1987, the
role of derivative markets in index-based contracts has
become a major topic in the public policy debate.
Futures and options m arkets in stock indexes are
praised for providing liquidity and hedging capabilities
to large institutional investors, but the same markets
are also accused of contributing excessive volatility
that spills over to the cash market. To date, the primary
aim of margins in derivative equity markets has been
to reduce the probability of contractual defaults and the
risk of a d e riva tive m arket breakdown, under the
assumption that the volatility of stock prices is a given
exogenous factor.26 The results of this article suggest,
however, that margins may play an additional role by
affecting market volatility itself. The evidence from the
cash market experience with different margin require
ments over the last 50 years should be taken into
account in assessing the adequacy of margins in deriv
ative equity instruments.
Gikas A. Hardouvelis
“ Another aim is the harm onization of m argins in derivative markets
with the m argins in the cash market. The fea sib ility of such
harm onization is examined by A rturo Estrella in “ C onsistent Margin
Requirem ents,” in this issue of the Q uarterly Review.
Appendix: Data and Sources
The primary data source is the 1988 yearbook of the
Ibbotson Associates, which contains end-of-month data
from 1926 through 1987. Two aggregate stock price
indexes are used. The first is the Standard and Poor’s
C om p osite index. C urre n tly, the S&P C om posite
includes 500 of the largest stocks, but before March
1957 it consisted of 90 of the largest stocks. The sec
ond index covers small capitalization stocks. It is com
posed of stocks making up the ninth and tenth smallest
deciles of the New York Stock Exchange. The data on
the one-month Treasury bill rate and the five-year cor
porate bond yield also come from Ibbotson Associates.
Data on the consumer price index were taken from
Ibbotson Associates, and on the industrial production
index, from the following sources: (i) for the period
1926-46, from Industrial Production, Board of Gover
nors of the Federal Reserve System, 1986; (ii) for the
period 1947-October 1987, from Citibase data banks;
(Hi) for November and December 1987, from Interna
tional Financial Statistics, April 1988.
Data on broker and dealer margin credit come from:
(i) the series entitled "Customer Net Debit Balances,”
which appears in Banking and M onetary S tatistics,
Board of Governors of the Federal Reserve System,
1943, Table 143; and Banking and Monetary Statistics:
1941-1970, 1976, Table 12.23; and (ii) the series entitled
“ Credit Extended to Margin Customers,” which appears
in various issues of the Federal Reserve Bulletin under
the “ Stock Market Credit” table. The first series runs
from November 1931 through June 1970; the second
series, from March 1967 through December 1987. The
two series are not identical. To avoid an abrupt jump in
July 1970, the second series was multiplied by the fac
tor of 1.43, which is the average ratio of the first to the
second series during the overlapping interval from
March 1967 through June 1970. Data on the value of all
New York Stock Exchange Stocks are end-of-month and
come from New York Stock Exchange publications.
FRBNY Quarterly Review/Summer 1988
89
Treasury and Federal Reserve
Foreign Exchange Operations
May-July 1988
Market sentiment toward the dollar turned strongly pos
itive during the three months ending in July, and the
dollar moved higher for most of the period. On balance,
the dollar rose 9 V2 percent in terms of the other Group
of Ten currencies on a trade-weighted basis (Federal
Reserve Board of Governors staff index). But the
increase against individual currencies varied consid
erably. The dollar rose approximately 12 percent
against the German mark and most Continental curren
cies, returning close to its level against the German mark
of a year ago. It advanced a more modest 6 V2 percent
and 93/4 percent, respectively, against the Japanese
yen and British pound, remaining well below its levels
of a year ago. Against the Canadian dollar, the dollar
declined IV2 percent.
In keeping with the Group of Seven (G-7) under
standings about fostering exchange rate stability—
most recently reiterated in the June Toronto Summit
Economic Declaration—the U.S. authorities entered the
market at times to counter the dollar’s rise, operating in
coordination with other central banks. Market sales of
dollars by the U.S. authorities between late June and
the end of July totaled $2.9 billion, all against German
marks.
Throughout the period, the dollar was buoyed by any
new signs of strength in the U.S. economy, which were
thought likely to lead to a tighter monetary policy and
higher interest rates. With statistics measuring U.S.
economic growth continuing to point to greater gains
A report presented by Sam Y. Cross, Executive Vice President in
charge of the Foreign Group at the Federal Reserve Bank of New
York and Manager of Foreign Operations for the System Open Market
Account. H. Randi DeWitty was primarily responsible for preparation
of the report.
90FRASER
FRBNY Quarterly Review/Summer 1988
Digitized for
than had previously been expected, market partici
pants recognized that the focus of policy attention had
shifted from concerns about recession to concerns
about inflation. Statements by several Federal Reserve
officials had conveyed uneasiness about the potential
risks for inflation of relatively tight labor markets and
capacity constraints in some industries. As it was,
short-term interest rates in the United States had
already firmed somewhat between mid-March and the
beginning of May, maintaining and in some cases
increasing interest differentials favoring investment in
dollar-denominated assets.
Until mid-June, the factors supporting a higher dollar
were partially counterbalanced by uncertainty about
the sustainability of external adjustment and about offi
cial reactions to any rise in dollar exchange rates.
Thus, the dollar’s rise early in the period was relatively
modest. The dollar strengthened more decisively after
mid-June with market participants increasingly perceiv
ing that international adjustment was indeed proceed
ing and that major industrial nations might tolerate
some further increase in the dollar.
For the period as a whole, the dollar’s upward move
ment against the mark was especially pronounced.
There were questions about the longer-term prospects
for investment in the German economy, in part stem
ming from labor costs, and continued concern over the
government’s intended imposition of withholding taxes
on foreign investments in Germany. In these circum
stances, there were heavy flows of capital out of Ger
many, amounting in the first half of 1988 to a record
DM 50.6 billion.
The dollar’s relative stability against the yen in part
reflected favorable assessments of the outlook for the
Japanese economy. In particular, market participants
were impressed with the extent to which the Japanese
economy appeared to be adjusting to its external
im balances and experiencing vigorous increases in
domestic demand.
May to mid-June
The dollar rose gradually against the mark from May
u n til the m id d le of June. From its o p e n in g of
D M 1.6775, it m oved irre g u la rly higher, brea kin g
through the DM1.70 level by mid-May and reaching
DM1.7224 by mid-June. It showed little increase on
balance against the yen, however.
The dollar’s rise partly reflected a widening percep
tion that U.S. economic growth continued to be buoy
ant and that the Federal Reserve’s policy stance might
C h a rt
1
After trading within a relatively narrow
range against most major foreign
currencies throughout the spring, . . .
be tightened if pressures on capacity became trouble
some. The report, in early May, of a decline in U.S.
civilian unemployment to its lowest level in 14 years
and of strong gains in m anufacturing employment,
together with a larger-than-expected upward revision in
first-quarter GNP figures later that month, provided fur
ther evidence that economic activity was expanding
rapidly. The fact that the country’s export sector and
manufacturing industries were contributing strongly to
the economy’s improved performance provided reas
surance that adjustment was well underway. Moreover,
market participants detected that the Federal Reserve
had adopted a firmer policy stance. With financial mar
kets generally reassured by the authorities’ concern
about inflation, U.S. long-term interest rates eased
somewhat, and long-term interest rate differentials
favoring the dollar generally narrowed, though they
remained strongly positive. But as U.S. short-term
interest rates rose, short-term differentials favoring the
dollar widened between the beginning of May and midJune, especially against the European currencies.
In addition, confidence in the efforts of G-7 authori
ties to foster exchange rate stability had increased as
P e rce n t
C hart 2
Short-term interest rate differentials
favoring the dollar widened from May
through mid-June, especially against the
European currencies.
P erce ntag e p o in ts
6 -----------------------------------------------------------------------------------E urom ark
1987
1988
the dollar rose by varying amounts against
several major currencies, especially in the
second half of the May-July 1988 period.
The c h a rt show s the p e rc e n t c ha nge of w eekly ave rage
ra te s fo r the d o lla r from July 3, 1987. A ll fig u re s are
ca lcu la te d fro m New Y o rk noon qu otatio ns.
—4
L
L .l I
Feb
I
I
I I
Mar
I
I I
- L J . 1 - 1 . . 1 J 1 1 I 1 1. 1...L1—1
A pr
May
Jun
Jul
1988
I
The chart sho w s w e e k ly ave rage in te re s t ra te d iffe re n tia ls
betw een th re e -m o n th E u ro d o lla r ra tes and th re e -m o n th
E uro m arke t d e posit ra tes fo r G erm an m arks, Japanese yen,
and B ritis h pounds.
FRBNY Quarterly Review/Summer 1988
91
the dollar traded in a relatively narrow range through
out the spring and U.S. export performance improved.
As a consequence, concerns about exchange rate risk
dim inished, and investors became more confident
about investing in dollar-denominated assets to take
advantage of the relatively high yields on fixed-income
securities available in the United States.
M oreover, re p o rts c irc u la te d in the m arket of
increased demand for dollars by banks’ customers.
Many firm s had previously established short-dollar
positions in the expectation that the dollar’s three-andone-half-year decline would continue well into 1988.
Table 1
Federal Reserve Reciprocal Currency
Arangements
In M illions of Dollars
Amount of Facility
Institution
July 31, 1988
A ustrian National Bank
National Bank of Belgium
Bank of C anada
National Bank of Denm ark
Bank of England
Bank of France
German Federal Bank
Bank of Italy
Bank of Japan
Bank of M exico
N etherlands Bank
Bank of Norway
Bank of Sweden
Swiss National Bank
Bank for International Settlem ents:
Dollars against Swiss francs
Dollars against other
authorized European currencies
250
1,0 0 0
2 ,0 0 0
250
3,000
2,0 0 0
6,0 0 0
3,000
5,000
700
500
250
300
4,000
600
1,250
30,100
Total
When instead the dollar firmed, a number of corpora
tions and financial institutions began to consider that
the dollar’s long decline had bottomed out. These mar
ket participants reportedly purchased dollars to avoid
losses that might result from having to convert foreign
currency receivables at still higher dollar levels. In this
environment, market professionals perceived that a
large magnitude of dollar buying might come into the
exchange market if exchange rate expectations were to
shift in favor of the dollar, and a sense of upside risk
for the dollar began to emerge.
Under these circumstances, the market’s longstand
ing bearish sentiment toward the dollar lessened, but
was not eliminated. One concern was that tightening
labor markets and capacity constraints in the United
States might undermine further adjustment as well as
lead to a buildup of inflationary pressures. This con
cern was reflected in the exchange markets when, on
May 17, the dollar gained only modest ground from the
announcement of an unexpected improvement in the
U.S. trade deficit for March. This muted response
occurred, in part, because the data recorded a sharp
rise in imports that, if continued, might hinder further
improvement in the trade balance.
Another element of uncertainty about how far the
dollar might advance was the presumed reaction of for
eign monetary authorities to any significant exchange
rate move. For several months, rumors had circulated
in the exchange markets that those central banks that
had intervened heavily to support the dollar in 1987
were taking advantage of opportunities to sell dollars.
Talk of dollar sales by G-7 central banks intensified
shortly after the release of the March trade figures in
mid-May. Throughout late May there was persistent talk
in the market that the Bundesbank was regularly sell
ing dollars. Gradually, market participants became con
vinced that foreign officials would act to contain the
Table 2
Drawings and Repayments by Foreign Central Banks under Special Swap Arrangements
with the U.S. Treasury
In M illions of Dollars; Draw ings ( + ) or Repayments ( - )
C entral Bank Drawing
on the U.S. Treasury
Central Bank of the A rgentine R epublic
National Bank of Yugoslavia
Central Bank of Brazil
Amount of
Facility
550.0
50.0
250.0
Data are on a value-date basis.
*No fa cility
Digitized 92
for FRASER
FRBNY Quarterly Review/Summer 1988
O utstanding
as of
May 1, 1988
160.0
*
May
June
July
- 1 6 0 .0
0
0
0
+ 50.0
0
0
-1 6 .1
+ 232.5
O utstanding
as of
July 29, 1988
*
+ 33.9
+ 232.5
dollar’s rise through intervention. At the end of May, the
Bundesbank began selling small amounts of dollars
o p e n ly at the F ra n k fu rt fix in g . On June 3, the
Bundesbank reported sharp declines in its net mone
ta ry reserves, p a rtic u la rly in the foreign currency
reserves component. From late May through mid-June,
these declines, attributed by the market largely to dol
lar sales, amounted to DM 7.4 billion. Press reports
indicated that other G-7 countries might also seek to
reduce their dollar holdings.
Market participants also began to anticipate that for
eign monetary authorities would take advantage of any
increases in U.S. interest rates to increase their own
interest rates. Monetary aggregates were growing rela
tively rapidly in a number of countries. Also, during the
first week of June, officials of a number of industrial
countries openly expressed concerns about a potential
rise in inflation worldwide against a background of ris
ing commodity prices. German and Japanese officials
also noted the inflationary impact of the dollar’s rise
C hart 3
Rising world com modity prices . . .
P e rce n t
added to concerns about inflationary
pressures in a number of industrialized
countries.
The c h a rt s h o w s m onthly c h a nges in w o rld com m odity
p ric e s as re p o rte d in th e In te rn a tio n a l M onetary Fund’s
In te rn a tio n a l Fin ancial S ta tis tic s and as c o n v e rte d into
German m a rks and J a p a n e s e yen.
and underscored the importance of maintaining domes
tic price stability.
In these circumstances, the dollar fluctuated irregu
larly upward, as market participants adjusted their eval
uations of o ffic ia l a ttitu d e s toward exchange rate
movements. In the middle of June, the dollar was trad
ing about 21/2 percent higher on balance against the
m ark and o th e r E u ro p e a n c u rre n c ie s and was
unchanged on balance against the yen from the begin
ning of the period.
Mid-June through July
As time passed, market participants became increas
ingly impressed with the dollar’s resilience. They noted
that the dollar had shrugged off both intervention and
statements by foreign officials aimed at resisting the
declines of their own currencies. They also watched for
reactions to the Bundesbank’s June 21 decision to
increase the interest rate on its repurchase agree
ments and looked to the upcoming communique from
the Summit meeting in Toronto for further indications of
policy actions that might affect exchange rates.
On June 14, the announcement of a much smallerthan-expected U.S. trade deficit for April reassured
market participants that the correction of global imbal
ances was continuing, even in the face of a relatively
robust U.S. economy. The m arket’s concerns that
strong dom estic demand and ca p a city constraints
would limit the scope for further trade adjustment were
dim inished by the data for April, which showed a
decline in imports. The dollar’s reaction to this set of
trade figures was stronger than that of the previous
month, with dollar exchange rates moving up sharply to
trade at DM 1.7450 and Y 126.50 soon after the trade
figures’ release.
Later in June, the Economic Declaration issued after
the Toronto Summit left the market with the impression
that the G-7 monetary authorities would tolerate a fur
ther rise of the dollar. A lthough the D eclaration
repeated the precise words of the December 1987 G-7
statement, the dollar was already 8 percent higher in
terms of the mark than at the time of the December
statement. This different market environment, together
with comments by several officials following the Toronto
meetings, led to an interpretation that some further rise
was acceptable.
As a result of these developments, the dollar began
to rise more quickly in late June. As the dollar broke
through DM 1.80 and higher levels not previously antici
pated, there were reports of corporations and financial
institutions moving to reduce their short-dollar posi
tions. There were also dollar purchases associated
with the covering of options positions that had been
established in a n ticip a tio n of a continued dollar
FRBNY Quarterly Review/Summer 1988
93
C h a rt 4
Rising capacity u tilization raised concerns
that capacity constraints would lim it
trade adjustm ent . . .
P ercent
84
D eg ree of capacity utilization
83
82
81 - I — I —
80
79
d id
Sep
[Id n.n.n.n.n.ri
O ct Nov
1987
Dec
Jan
Feb
Mar A pr
1988
M ay
Jun
but did not keep the U.S. trade d eficit from
narrowing during the period.
B illio n s o f do lla rs
16
15
14
13
decline.
In these circumstances, the U.S. authorities entered
the market for the first time during the period on June 27.
The authorities continued to operate, intervening on 15
of the remaining 23 business days through the end of
July and working closely in coordination with other cen
tral banks to foster exchange rate stability.
There were several occasions during July when
upward pressure on dollar rates was considerable.
Some of these occurred when new economic statistics
were released confirming the buoyancy of the U.S.
economy. The dollar was especially well bid, for exam
ple, after the July 8 report of a further decline in U.S.
civilian unemployment and after the July 27 release of
GNP data pointing to a 3.1 percent seasonally adjusted
rate of growth for the second quarter. The dollar also
came into demand after the report on July 15 of May
trade figures that reassured market participants that
U.S. trade adjustment remained on track. Meanwhile,
press coverage of Chairman Greenspan’s congressional
testim ony reinforced the expectation that the U.S.
authorities stood ready to counter inflationary pres
sures. Under these circumstances, the dollar generally
moved up during early July, reaching its highs of the
period against the mark and the yen at DM 1.8925 on
July 18 and Y 135.55 on July 15, respectively. But by
the end of July, the dollar was trading off its highs at
DM 1.8780 and Y 133.15, respectively.
Between June 27 and July 29, the U.S. authorities
sold a total of $2.9 billion in the market, all against
marks. Of the total, $1,317.5 million was sold by the
Federal Reserve and $1,612.5 million was sold by the
Treasury’s Exchange Stabilization Fund (ESF). These
operations were conducted in cooperation with other
12
11
Table 3
10
Net Profits ( + ) or Losses ( - ) on
United States Treasury and Federal Reserve
Foreign Exchange Operations
In M illions of Dollars
9
0
1987
1988
The top c h a rt sho w s th e d e g re e o f c ap acity u tiliz a tio n
in U.S. in d u s try . C a p a city u tiliz a tio n data fo r A p ril, May,
and June w e re re le a s e d on M ay 17, June 16, and July 18,
re s p e c tiv e ly . The bottom c h a rt show s the m o nthly U.S.
m e rchan dise tra d e ba la nce, s e a sonally a d ju s te d and
re p o rte d on a cen sus b a s is . The U.S. tra d e fig u re s fo r
M arch, A p ril, and May w e re re le ased on May 17, Jun e 14,
and July 15, re s p e c tiv e ly .
94
FRBNY Quarterly Review/Summer 1988
Period
May 1, 1988 to
July 31, 1988
Valuation profits and losses on
outstanding assets and lia b ilities
as of July 31, 1988
Data are on a value-date basis.
Federal
Reserve
0
+ 1 ,1 0 1 .2
United States
Treasury
Exchange
S tabilization
Fund
0
+ 856.7
central banks.
In other industrialized countries, the authorities also
intervened to sell dollars, on occasion in substantial
amounts. In addition, interest rates in a number of for
eign countries increased as the authorities sought to
limit the decline of their currencies against the dollar or
otherwise respond to signs of quickening price
pressures.
In other operations, the U.S. authorities increased
holdings of foreign currencies by $1,282.3 million
equivalent through sales of Special Drawing Rights
(SDRs) and dollars to other official institutions and
through receipt of principal repayments and interest
payments due to the United States under the Supple
mentary Financing Facility of the International Mone
tary Fund.
As of end July, cumulative bookkeeping or valuation
gains on outstanding foreign currency balances were
$1,101.2 million for the Federal Reserve and $856.7 million
for the ESF. These valuation gains represent the
increase in the dollar value of outstanding currency
assets valued at end-of-period exchange rates, com
pared with the rates prevailing at the time the foreign
currencies were acquired.
The Federal Reserve and the ESF regularly invest
their foreign currency balances in a variety of instru
ments that yield market-related rates of return and that
have a high degree of quality and liquidity. A portion of
the balances is invested in securities issued by foreign
governments. As of end July, holdings of such securi
ties by the Federal Reserve amounted to $1,408.2 mil
lion equivalent, and holdings by the Treasury amounted
to the equivalent of $1,604.8 million.
During the period under review, the U.S. Treasury,
through the ESF, received repayment of its financing
facility for Argentina and participated in multilateral
financing facilities for Yugoslavia and Brazil.
A rgentina . On May 31, the Central Bank of the
Argentine Republic fully repaid the $160 million second
drawing of a $550 million short-term financing facility
provided by the U.S. Treasury through the Exchange
Stabilization Fund, thereby fully liquidating the
facility.
Yugoslavia. On June 10, the U.S. Treasury, through
the ESF, together with the Bank for International Settle
ments (BIS) acting for a number of central banks,
agreed to provide $250 million in short-term financing
facilities to the National Bank of Yugoslavia. On June 15,
the National Bank of Yugoslavia drew the full $50 million
of the ESF facility. On July 1, $16.1 million was repaid.
Brazil. On July 27, the U.S. Treasury, through the
ESF, together with the BIS acting for a number of cen
tral banks, agreed to provide $500 million in short-term
financing facilities to Brazil. The ESF's facility was
$250 million. On July 29, the Central Bank of Brazil
drew $232.5 million from the ESF facility.
FRBNY Quarterly Review/Summer 1988 95
Recent FRBNY Unpublished Research Papers*
8813. McCauley, Robert N., and Christopher Maxwell.
“ Price D iscrim ination in H o te llin g ’s D uopoly
Model: Equilibrium and Efficiency.” April 1988.
8814. Klitgaard, Thomas. “ Managing Exchange Rates:
The Experience of the European Monetary Sys
tem.” May 1988.
8815. Ceglowski, Janet. “ Intertemporal Substitution in
Import Consumption.” June 1988.
8816. Hirtle, Beverly. “ Default and Liquidity Risk in the
Junk Bond Market.” June 1988.
8817. Harris, Ethan S. “A Reexamination of the Inven
tory Buffer Effect with Disaggregated Data.” July
1988.
8818. Hardouvelis, Gikas. “ Margin Requirements, Vol
atility, and the Transitory Component of Stock
Prices.” July 1988.
8819. Bell, Linda A., Elizabeth Hall, and Daniel R.
Hayes. “ The Incidence of Union Concessions in
the 1980s: What, Where, and W hy?” August
1988.
8820. Donahoo, Kathleen, and Sherrill Shaffer. “ The
Impact of Capital Requirements on the Securiti
zation Decision.1’ August 1988.
8821. Sofianos, George. “A Comparison of MarketMaking Structures.” September 1988.
‘ Single copies of these papers are available upon
request. W rite to R esearch Papers, Room 901,
Research Function, Federal Reserve Bank of New
York, 33 Liberty Street, New York, NY 10045.
FRBNY Quarterly Review/Summer 1988
Digitized for96
FRASER
Single-copy subscriptions to the Quarterly Review (ISSN 0147-6580) are free.
Multiple copies are available for an annual cost of $12 for each additional copy.
Checks should be made payable in U.S. dollars to the Federal Reserve Bank of
New York and sent to the Public Information Department, 33 Liberty Street, New
York, N.Y. 10045. (212-720-6134). Single and multiple copies for United States and
for other Western Hemisphere subscribers are sent via third- and fourth-class mail,
respectively. All copies for Eastern Hemisphere subscribers are airlifted to
Amsterdam and then forwarded via surface mail. Multiple-copy subscriptions are
packaged in envelopes containing no more than 10 copies each.
Quarterly Review subscribers also receive the Bank’s Annual Report.
Quarterly Review articles may be reproduced for educational or training purposes
only, providing they are reprinted in full, distributed at no profit, and include credit
to the author, the publication, and the Bank.
Library of Congress Catalog Card Number: 77-646559
@FedFRASER