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ISSN 0007-7011
Federal Reserve Bank of Philadelphia
SEPTEMBER • OCTOBER 1987
SEPTEMBER/OCTOBER 1987
THE UNDERGROUND ECONOMY:
A TROUBLING ISSUE FOR POLICY
MAKERS
Joel F. Houston
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The existence of the underground economy
leads to tax rates and budget deficits that
are higher than necessary, unfairness in
the tax system, and potentially misguided
fiscal and monetary policies. But getting a
handle on the underground economy is
no easy task. Depending on the definition,
economists' estimates of its size range as
wide as 5 to 25 percent of GNP, or $200
billion to $1 trillion! Moreover, how poli
cies will affect the underground economy
also depends on how it is defined.
FACT AND FANTASY ABOUT STOCK
INDEX FUTURES PROGRAM TRADING
John J. Merrick, Jr.
Futures markets in stock indexes, such as
the S&P 500, are an astounding success
story. And some are concerned that arbi
tragers' "program trading," which tries to
profit from abnormal price differences be
tween these futures markets and the cash
market for stocks, has grown too much.
Pointing to the price swings in the stock
market on "Triple Witching Days," they
claim that program trading makes stock
prices volatile overall. But a careful analysis
of the impact of program trading suggests
that limiting arbitrage activity could do
more harm than good.
The Underground Economy:
A Troubling Issue for Policymakers
Joel F. Houston*
In making economic decisions, households,
businesses, and government officials all rely on
information concerning the current and expected
performance of the economy. The most widely
recognized barometer of economic performance
is the measure of gross national product (GN P).
In principle, GNP represents the value of all
final goods and services produced for a given
time period.
*Joel F. Houston, Assistant Professor of Finance at the
University of Florida, prepared this article while he was an
Economist in the M acroeconomics Section of the Phila
delphia Fed's Research Department.
In practice, however, not all economic activity
is accounted for in GNP. Empirical evidence
suggests that a significant portion of economic
activity takes place in a sector that has been
alternatively referred to as the "shadow," "hid
den," "irregular," or "underground" economy,
where goods and services—some legal, some
not—are produced but not reported. For policy
makers who want to account for this activity, the
problems of doing so are daunting. The under
ground economy does not just sit "out there,"
unchanging; rather, many diverse elements
make up the underground economy, and both
the size of its components and its overall size
vary over time. Parts of the underground econ
3
BUSINESS REVIEW
omy, for example, may move in response to
changes in government policy. To the extent
that policymakers do not, or cannot, take the
underground economy into account, they may
not achieve their desired goals.
Interest in understanding and estimating the
size of the underground economy has increased
recently, due in part to the current political envi
ronment in which budget deficits and tax reform
have dominated the news. High budget deficits
have led legislators to search for untapped
sources of revenue. At the same time, tax reform
was designed to lower marginal tax rates and to
promote a more equitable distribution of the tax
burden. And while tax reform was designed
explicitly to be revenue neutral, it represents a
net tax cut for individual taxpayers. By "getting
at" income generated in the underground econ
omy, the potentially contradictory goals of
increasing revenue and lowering tax rates can
both be met. But in order to do so, the two-way
link between the underground economy and
policy should be carefully explored.
AN INTRODUCTION
TO THE UNDERGROUND ECONOMY
What Is the Underground Economy? The
underground economy conjures up a variety of
images. Often, people first think of illegal activi
ties, such as selling drugs, gambling, or loan
sharking. They might also think of income earned
in perfectly legal activities but not reported, for
example, income earned moonlighting "off the
books" to avoid taxes or to supplement social
security or unemployment benefits without
facing a reduction in benefits. More generally,
the underground economy incorporates all
unmeasured economic activity. Thus it includes
other activities as well, such as bartering goods
and services: the dentist wires braces for the
electrician's child, and in return the electrician
wires the dentist's house. It even includes activi
ties like growing your own food or doing your
own repairs.
Obviously, the underground economy defined
this broadly is not homogeneous. It is made up
4
SEPTEMBER/OCTOBER 1987
of lots of different people who are influenced by
many different factors. For example, the factors
influencing whether or not you decide to deal
drugs may be entirely different from the factors
affecting whether or not you neglect to report all
of your income on your taxes.
These differences are especially important to
keep in mind when it comes to interpreting
studies claiming to measure the size and impact
of the underground economy. Estimating the
size of the underground economy cannot be
separated from the fundamental question con
cerning what the underground economy com
prises. Indeed, estimates of the underground
economy vary, at least in part, because they
often focus on different components of the
underground economy.
While the underground economy can be
defined quite broadly, most researchers have
focussed on a more narrow definition that does
not consider activities such as barter and growing
your own food. These activities are often ex
tremely hard to detect, and individuals' reasons
for engaging in them are difficult to pinpoint.
The dentist and electrician, in the previous
example, may be merely exchanging acts of
friendship, as opposed to trying to circumvent
the tax laws. Policymakers, it would appear, have
little or no impact on whether or not acts of
friendship occur, or on whether or not an indi
vidual chooses to grow his own food. Policy
makers, however, can more directly influence
certain other types of underground activity, such
as taxes that are evaded on income that is earned
legally, and income illegally earned, which pre
sumably also is untaxed. These activities repre
sent a more narrow definition of the under
ground economy, and will make up what we
refer to here as the underground economy.1
h n adopting this more narrow definition we are limiting
the discussion to that part of the underground econom y that
has been the primary focus of past research and policy
discussions. This does not imply, however, that there is no
link between public policy and activities such as barter and
growing your own food. As discussed in Donald C. Cox and
FEDERAL RESERVE BANK OF PHILADELPHIA
The Underground Economy
Joel F. Houston
How Big Is the Underground Economy? For
some very obvious reasons, it is impossible to
come up with a direct estimate of the size of the
Robert H. DeFina, "W arm Feelings and Cold Calculations,"
this Business Review (M arch/April 1986) pp. 15-22, even acts
of friendship have important implications for the success or
failure of certain policy initiatives. At the same time, changes
in policy may make barter and growing your own food more
or less attractive. Indeed, the main points concerning the
links between policy and our more narrow definition of the
underground econom y also may directly apply to these
other activities as well.
underground economy. By definition, partici
pants in the underground economy are actively
trying to avoid detection, so there is no simple
and direct place to look for information about its
size. This makes the underground economy
inherently difficult to measure.
Studies that have tried to measure it have
used a variety of indirect techniques. (See
MEASURING THE SIZE OF THE UNDER
GROUND ECONOMY.) The various estimates
differ considerably, ranging from 5 to 25 percent
Measuring the Size of the Underground Economy
A number of techniques have been employed in an attempt to measure the underground economy,
with each giving a somewhat different view of its size and variation.3 Two related issues help explain the
differences among these various estimates. First, each uses a different methodology; for instance, the IRS
estimates rely on audits of tax returns, while others rely on unexplained currency holdings.b Second,
there is no guarantee that the alternative procedures have captured the same portion of the underground
economy. This is true despite the fact that all available estimates focus only on market transactions and
ignore barter transactions. For example, the IRS estimates may be picking up mainly legally earned, but
not reported, income, while currency-based estimates may be capturing mainly illegally earned income.
It is important to keep this lack of perfect comparability in mind when examining the estimates. See
SELECTED BIBLIOGRAPHY, p. 12, for full references.
Study
IRS
Bureau of Economic Analysis
Adjusted Gross Income Gapc
Monetary Based Approaches:
Gutmann
Feige
Tanzi
0'Learyd
Houston
Estimate
(billions $)
Percent
of GNP
Year of
Estimate
145
8
1976
184
5.4
1983
420
600+
118-159
432
400
14-15
27
4.5-6
15.2
14.7
1981
1979
1980
1985
1980
aFor a more comprehensive review of these estimates see, Carol S. Carson, "The Underground Economy: An
Introduction," Survey of Current Business 64 (May 1984 and July 1984). Some of the estimates in the chart follow
directly from a similar chart presented in these articles.
bFor a critical summary of these approaches, see R. Porter and A. Bayer, "A Monetary Perspective on Underground
Economic Activity in the United States," Federal Reserve Bulletin (March 1984) pp. 177-189.
cThe Bureau of Economic Analysis stresses that caution should be taken in interpreting this measure. See Robert
Parker, "Improved Adjustments for Misreporting of Tax Return Information Used to Estimate the National Income
and Product Accounts, 1977," Survey of Current Business (June 1984) pp. 17-25, and Carol S. Carson, "The Underground
Economy: An Introduction," Survey of Current Business 64 (May 1984 and July 1984).
dFor a description, see Leonard Silk, "Underground's Hidden Incom e," New York Times (September 10, 1986)
p. D2.
5
BUSINESS REVIEW
of reported GNP in recent years. Most of the
estimates, however, suggest its size is quite large
and lies in the more narrow range of 5 to 15
percent of reported GNP. At the beginning of
1987, that amounted to between $200 and $650
billion.
The large disparity among the various esti
mates is perhaps not surprising, since the dif
ferent methodologies used probably pick up
different aspects of even our narrow definition
of the underground economy. Estimates from
the Internal Revenue Service (IRS), for example,
rely on information gained from audited tax
returns, and so may be a more accurate measure
of tax evasion of income legally earned. Other
estimates focus on what are believed to be
abnormal holdings of currency. In contrast to
the IRS strategy, these approaches may do a
better job of detecting changes in illegally earned
income.
The wide range of estimates serves as a
reminder of how slippery the underground
economy is, and thus of the difficulties policy
makers face when trying to get a handle on it.
But despite those potential difficulties, policy
makers cannot afford to ignore the underground
economy. For as it happens, the success or failure
of a variety of economic policies may well hinge
on the existence and behavior of the under
ground economy.
THE EXISTENCE
OF THE UNDERGROUND ECONOMY
HINDERS EFFECTIVE POLICYMAKING
For a number of reasons, the viability of the
underground sector makes policy initiatives less
effective than they would otherwise be. It can,
for example, force tax rates or budget deficits to
be higher than is desirable. It can also lead to an
unfair distribution of the tax burden; and, by
obscuring policymakers' view of the overall
health of the economy, it can lead to misguided
fiscal or monetary policies.
The Underground Economy Can Lead to
Higher Taxes or Larger Deficits. A key feature of
underground activity is that it remains untaxed,
6
SEPTEMBER/OCTOBER 1987
and thus represents a potentially large source of
lost revenue. This loss of revenue implies that
the government must either increase taxes, run
a larger deficit, or cut government spending.
While an increase in taxes may offset the lost
revenue due to the underground economy, tax
increases raise the costs of public services for
current taxpayers and reduce the incentives to
work and invest, which in turn may weaken the
economy. Alternatively, increasing deficits may
lead to higher interest rates, which also may
discourage investment and economic growth.
Slashing government spending is not likely to
reduce investment, but it does imply that tax
payers are receiving fewer government services
than they would if all underground activity were
somehow taxed. Consequently, the loss of tax
revenue due to the underground sector poses
serious problems for fiscal policy, regardless of
whether the lost revenue is offset by higher
taxes, higher deficits, or lower spending.
Back-of-the-envelope calculations suggest
that the potential revenue losses due to the
underground economy may be staggering. The
average range of estimates indicate that this
sector currently represents between $200 billion
and $650 billion. If all of this underground
income were taxed at the average marginal tax
rate of 22 percent, then the government would
receive between $44 billion and $143 billion in
additional revenue, everything else equal. This
suggests that if this underground income could
be discovered and taxed, current deficits could
be reduced significantly, or tax rates could be
cut. Alternatively, spending could rise anywhere
between $44 billion and $143 billion with no
corresponding rise in taxes or deficits.
The Underground Economy Diminishes the
Fairness of Our Tax Structure. The loss of tax
revenue due to the underground economy also
raises some important issues concerning fairness
and equity. For example, all of us receive some
benefits from public goods, such as defense
spending, park maintenance, law enforcement,
and pollution control. To finance these services,
we are expected to pay our "fair share" of taxes,
FEDERAL RESERVE BANK OF PHILADELPHIA
The Underground Economy
as determined by Congress and codified in the
tax structure. But those who choose to participate
in the underground economy enjoy the benefits
of these services while paying less than their fair
share of taxes. Some individuals in the under
ground economy may even pay no taxes at all.
Tax evasion necessarily increases the burden on
those who choose not to participate in the
underground economy. Consequently, the
presence of the underground economy leads to
an unfair distribution of the tax burden.
The Underground Economy Can Lead to Mis
guided Policies. There are at least two distinct
ways in which the underground economy may
distort policymakers' perception of the economy,
and hence lead to inappropriate fiscal or m one
tary policy actions. First, it prevents policy
makers from accurately determining the average
level of economic activity. Second, it distorts
policymakers views on how total economic
activity fluctuates over the course of business
cycles.
The key point is that individuals base their
economic decisions on total income (that is,
aboveground plus underground income),
whereas policymakers observe movements in
only the aboveground, or reported, economy.
At least in part, individuals decide how much to
save, how much to work, and even where to
work based on all income opportunities that are
available, as opposed to just the income that is
reported to the IRS. For example, historical data
on reported income and consumption might
lead policymakers to conclude that household
saving rates have been either low or declining.
But if households have been earning money in
the underground economy, this conclusion may
be way off the mark. Instead, if the gap between
consumption and actual income were quite
large, policies designed to encourage savings
would be misguided. In this instance, policy
makers would be making incorrect decisions,
because they do not have complete information
about the average level of the economy's
performance.
At the same time, policymakers' attempts to
Joel F. Houston
stabilize the economy may be limited by their
inability to observe movements in the under
ground economy over the course of business
cycles. Since individuals base their economic
decisions on their total income, it follows that
interest rates and prices respond to changes in
total as opposed to reported income. For ex
ample, we may observe inflationary pressures
in the economy if total income is climbing, even
if reported GNP is sluggish. For this reason,
policymakers may care to stabilize the total
economy. However, they are constrained by the
fact that data exist only for the reported economy.
If policymakers fail to understand the ways in
which the aboveground and underground econo
mies are linked, then they will misread the
strength of the total economy, which may lead
them to make inappropriate stabilization deci
sions.
As an example, consider the following scen
ario: We observe a recession in the reported
economy, although at the same time the under
ground economy is expanding. So while reported
GNP is declining, the total level of economic
activity is not declining as much, or is possibly
even increasing because of the increase in the
underground economy. Observing the recession
in the reported economy, policymakers become
convinced that the economy is quite weak, and
implement countercyclical policies to promote
recovery. However, since the total economy is
stronger than reported figures indicate, counter
cyclical policies that attempt to stimulate the
economy may serve only to increase inflationary
pressures in the total economy.2
Alternatively, the total economy may be
subject to wider swings in performance than
2Policymakers might not care about inflationary pressures
if they affected only illegal goods and services. Higher prices
for narcotics and prostitution, for example, might be con
sidered beneficial since they probably discourage their
consumption. However, it is extremely unlikely that price
increases would be isolated to illegal goods and services. As
a practical matter, then, the main points stressed in this
section represent relevant concerns to policymakers.
7
BUSINESS REVIEW
SEPTEMBER/OCTOBER 1987
reported statistics suggest. In this situation,
policymakers could be lulled into believing that
the economy is growing at a steady rate, while in
fact total economic activity may be subject to
fairly dramatic swings over the course of busi
ness cycles. If policymakers aim to stabilize the
total economy, then countercyclical policies may
actually be appropriate, even if the reported
economy appears to be stable.
The underground economy would present
less of a problem for stabilization policy if it
remained constant in size, or if it remained a
constant percentage of GNP. In either case, at
least the direction in which the overall economy
is moving could be gauged, and policymakers
could successfully stabilize the total economy
by looking only at reported data. Unfortunately,
available estimates suggest that even this may
not be true: indirect measures indicate that the
underground economy may fluctuate signifi
cantly relative to reported GNP (see RATIO OF
THE UNDERGROUND ECONOMY TO GNP).
As a result, policymakers may well be "missing
the boat" by focusing solely on the aboveground
economy.
SOME SECTORS
OF THE UNDERGROUND ECONOMY
MIGHT RESPOND TO POLICY CHANGES
So far, we have looked at one part of the twoway link between the underground economy
and policy, namely, the way the existence of the
underground economy thwarts desired policy
outcomes. Now we focus on the other part of the
link, the way policy changes can affect the behav
ior of the underground economy. The first step
to understanding this link requires a behavioral
theory of the underground economy. With that
in hand, we can then discuss the implications
that policy initiatives have for the underground
economy.
Why Do People Participate in the Underground
FIGURE 1
Ratio of the Underground Economy to GNP
1954 - 1980
Percent
0
L..... JL----- L— J-------1
------- 1
____ I____L
54
56
58
60
62
64
66
68
Year
70
72
74
76
78
80
NOTE: See SELECTED BIBLIOGRAPHY (p. 12) for references to data sources. The BEA-AGI Gap data are from Thae
S. Park, "The Relationship Between Personal Income and Adjusted Gross Income, 1 947-78" Survey o f Current Business
(November 1981) and the updates and revisions published in the Survey thereafter.
8
FEDERAL RESERVE BANK OF PHILADELPHIA
The Underground Economy
Economy? In all likelihood, a variety of consid
erations affect people's decisions to participate
in the underground economy. Social factors, for
example, probably play an important role. For
instance, if an individual's parents, friends, and
neighbors all cheat on their taxes, he might
conclude that "everyone is doing it," and that he
has an obligation to himself to do the same. It is
also conceivable that while someone is at first
reluctant to participate in the underground
economy, once she has taken the plunge, she is
unwilling to leave the underground economy.
This may be in part because she has overcome
any moral obstacles that would have precluded
her from going underground; but it also may be
because she knows that if she did decide to
"com e clean," she might bring attention to past
underground activity.
Many of these social factors are hard to
quantify, however, and hard for economists, in
particular, to address through policy prescrip
tions. As a result, economists look for the
economic factors affecting where and how an
individual chooses to work.
Financial Incentives Are Probably Impor
tant . . . Economic theory suggests that indi
viduals respond to financial incentives, and will
choose to work where they believe they will
receive the greatest net benefit. The total net
benefit from employment in the aboveground
sector equals the dollar wage received plus the
value of any benefits earned, less the amount of
taxes paid. For example, if a worker earns $10 an
hour at his aboveground job, earns no fringe
benefits, and pays 20 percent of his income in
taxes, his net hourly wage is $8.00.
What happens when he decides to go under
ground and not report his income? In this case,
his expected net benefit from working in the
underground economy comprises the dollar
wage received less the expected penalties he has
to pay in the event of being caught. For example,
suppose the worker believes that he has a 10
percent chance of being audited, and that if he is
audited he will have to pay twice the amount of
the taxes owed, or $4.00 for every hour he works
Joel F. Houston
underground, instead of $2.00 in aboveground
taxes. In other words, his expected penalty is 40
cents an hour (10 percent probability of being
caught times the $4.00), so his expected hourly
wage earned from working in the underground
economy is $9.60.
This reasoning also applies to felonious activi
ties, where individuals must assess the chances
of being caught by the police, as well as the
penalties that may be imposed once caught.
These factors must be balanced against the
income earned from the chosen activity in deter
mining the net wage.
. . . As Is People's Aversion to Risk. This
framework highlights one important distinction
between the net wages earned in the two sectors.
While aboveground wages are known and fixed,
people in the underground economy incur some
risk concerning the actual net wage they will
receive, because they are never sure when or if
they will be caught. In the previous example, the
worker's expected net wage was $9.60 an hour,
though the actual net wage received will depend
on whether or not the worker is caught or audited.
In the event that the worker escapes detection,
he would receive the full amount of his under
ground income, or $10.00 per hour. However, if
the person is caught and forced to pay the pen
alty, he must pay $4.00 per hour in taxes and
penalties, so he would receive only $6.00 an
hour for working underground.
It is generally believed that individuals would
rather avoid risk, and all else equal would prefer
certainty over uncertainty. For example, most
people given the choice between receiving
$1,000 with certainty or having a 50 percent
chance of receiving $2,000 would prefer the
$1,000 with certainty, even though they can in
principle expect to receive $1,000 in either case.
This implies that since working in the under
ground economy involves additional uncertainty,
workers must receive a bonus, or "risk-pre
mium," in the form of a higher net wage in order
to induce them to participate in the underground
economy.
While it is hard to pinpoint the factors that
9
BUSINESS REVIEW
affect an individual's willingness to take risks,
one factor that seems to matter significantly is
the individual's level of wealth, which is directly
affected by changes in income.3 Unfortunately,
economic theory is unable to say anything deci
sive about this relation. That is, theory has
identified good reasons why aversion to risk
may rise with income and other reasons why it
may fall with income. Moreover, theory suggests
that while an individual's willingness to risk a
fixed amount probably increases with income,
his willingness to risk a given portion of his
income may decline with income. For instance,
it seems likely that a millionaire would be more
comfortable betting $10 on a coin flip than would
someone who is currently unemployed. How
ever, it is not obvious that a millionaire would be
more willing than an unemployed worker to
wager 10 percent of his wealth on a coin flip.
Since we are hampered by the fact that we cannot
directly observe people's willingness to take
risk, empirical evidence has not been able to
uncover how risk aversion varies with income.
It does, however, seem plausible that income
levels and risk aversion are related, even if the
exact dependency remains unknown.
Policies Can Alter the Risks and Rewards of
Being in the Underground Economy. This eco
nomic perspective suggests that there are two
important considerations that determine whether
or not someone will choose to be in the under
ground economy: the net wages in both the
aboveground and underground economy and
the individual's willingness to take risks. There
fore, policy changes that influence either the net
wages or an individual's willingness to take risks
can affect participation in the underground
economy. Unfortunately, the net impact of such
policy changes is unclear; conceivably a change
in policy may affect net wages and people's
willingness to assume risk simultaneously.
3For a complete discussion on the impact of wealth on risk
aversion, see Kenneth Arrow, Essays in the Theory of RiskBearing (Chicago: Markham Publishing Company, 1971).
Digitized for10
FRASER
SEPTEMBER/OCTOBER 1987
Worse yet, since we cannot directly observe
movements in the underground economy, empir
ical tests cannot completely resolve many of
these issues.
From a conceptual viewpoint, an increase in
tax rates both reduces the effective aboveground
wage and lowers an individual's take-home pay,
which may affect that individual's tolerance of
risk. The reduction in the effective aboveground
wage makes the underground economy more
attractive to would-be tax evaders, and if such
individuals are more willing to take risks as their
after-tax income falls, then this also encourages
their movement into the underground economy.
However, if potential tax evaders are generally
less willing to take risks as their income falls,
then shifts in tax rates have an ambiguous effect
on the underground economy. By the same token,
raising the likelihood of detection or imposing
stiffer penalties works to reduce the net under
ground wage, which makes the tax evasion
component and the illegal activity part of the
underground economy less attractive. But again,
increased enforcement reduces the expected
income of workers in the underground economy,
which may alter both their willingness to take
risks and their willingness to participate in the
underground economy.
Policy decisions regarding the degree of progressivity in the tax structure and the level of
unemployment compensation may also affect
the size of the tax evasion element of the
underground economy. In particular, changes
in the tax structure and in unemployment com
pensation alter the cyclical behavior of the
underground economy, and may ultimately
determine whether or not the underground
economy is procyclical or countercyclical. For
instance, since the U.S. tax structure is progres
sive, an individual finds that his tax bill increases
at a faster rate than does his income. Conse
quently, the financial incentives from working
in the underground economy rise as his income
rises. Assuming his willingness to take risks
remains the same, a self-employed businessperson may decide to hide a greater portion of
FEDERAL RESERVE BANK OF PHILADELPHIA
The Underground Economy
income earned when times are good to avoid
being pushed into a higher tax bracket. This
works to make the underground economy
procyclical.
Alternatively, it seems plausible that the
underground economy is a place where many
turn when times become tough in the reported
economy. For instance, a person laid off in the
middle of a recession may choose to paint houses
“off the books," while collecting unemployment
benefits and waiting to be rehired. If this case
is dominant, the presence of unemployment
benefits may make the underground economy
more attractive in cyclical downturns. In this
case, the underground economy is countercycli
cal and acts to smooth out shifts in the above
ground economy.
Exactly how policy changes will alter the
underground economy will depend on which
conflicting effect dominates. Empirical evidence
is crucial in this regard. But while sorely needed,
reliable evidence is sparse mainly due to the
unobservability of the underground economy.
The scant information that is available regarding
the impact of policy changes chiefly concerns
the effect of tax changes.4 The results of these
4See Charles Clotfelter, "Tax Evasion and Tax Rates: An
Analysis of Individual Returns," Review of Economics and
Statistics (August 1983) pp. 363-373, and S. Crane and F.
Nourzad, "Inflation and Tax Evasion: An Empirical Analysis,"
Review of Economics and Statistics (May 1986) pp. 217-223.
Joel F. Houston
studies suggest that high tax rates may encourage
participation in the underground economy.
WILL TAX REFORM SHRINK
THE UNDERGROUND ECONOMY?
To the extent that high tax rates have been a
factor in increasing the underground economy,
the Tax Reform Act of 1986, which lowers
marginal tax rates, should provide the additional
benefit of reducing the size of the underground
economy. Indeed, if the above evidence is cor
rect, tax reform may be expected to increase tax
revenue by flushing out part of the underground
economy. But here the sociological issues may
also come into play. Conceivably, people are
reluctant at first to participate in the underground
economy. However, once they cross the line it
may be harder to bring them back. Thus, while
the steady increases in tax rates over the years
may have led people into the underground
economy, as empirical evidence suggests they
have, it may not follow that symmetric reductions
in tax rates will bring them back aboveground.
For policymakers, the key point to keep in
mind is that tax reform will affect both the above
ground and underground economies. However,
we will only observe directly how it affects the
reported economy. Difficulties will undoubtedly
persist in trying to assess the economy's overall
performance. This emphasizes the importance of
continuing to study the underground economy.
Selected Bibliography
F
li
BUSINESS REVIEW
SEPTEMBER/OCTOBER 1987
Selected Bibliography
Carol S. Carson. "The Underground Economy: An Introduction," Survey of Current Business 64 (May
1984 and July 1984).
Charles Clotfelter. "Tax Evasion and Tax Rates: An Analysis of Individual Returns," Review of Economics
and Statistics 65 (August 1983) pp. 363-373.
S. Crane and F. Nourzad. "Inflation and Tax Evasion: An Empirical Analysis," Review of Economics and
Statistics 68 (May 1986) pp. 217-223.
Edgar Feige. "A New Perspective on Macroeconomic Phenomena—The Theory and Management of the
Unobserved Sector of the United States Economy: Causes, Consequences, and Implications," paper
presented at the 93rd annual meeting of the American Economic Association, September 6, 1980.
Peter Gutmann. "The Subterranean Economy, Redux," paper presented at the International Conference
on "The Economics of the Shadow Economy," University of Bielefield, October 10-14, 1983.
Joel Houston. "The Macroeconomic Implications of the Underground Economy," unpublished Ph.D.
dissertation, The Wharton School of the University of Pennsylvania, 1986.
Robert Parker. "Improved Adjustments for Misreporting of Tax Return Information Used to Estimate the
National Income and Product Accounts, 1977," Survey of Current Business (June 1984) pp. 17-25.
R. Porter and A. Bayer. "A Monetary Perspective on Underground Economic Activity in the United
States," Federal Reserve Bulletin (March 1984) pp. 177-189.
Leonard Silk. "Underground's Hidden Income," New York Times, (September 10, 1986) p. D2.
Vito Tanzi. "The Underground Economy in the United States: Annual Estimates, 1930-1980," Inter
national Monetary Fund Staff Papers 30 (June 1983) pp. 283-305.
United States Department of Treasury. Internal Revenue Service. Income Tax Compliance Research:
Estimates for 1973-1981 (July 1983).
12
FEDERAL RESERVE BANK OF PHILADELPHIA
Fact and Fantasy About Stock Index
Futures Program Trading
John J. Merrick, Jr*
INTRODUCTION
Exchange-traded stock index futures con
tracts** have been among the most important
financial innovations of the 1980s. With these
products, investors can adjust the exposure of
their portfolio to fluctuations in the average level
of stock prices quickly and cheaply. This capa
bility is extremely attractive to pension fund
managers and other institutional investors. In
* John Merrick, Associate Professor of Finance, New York
University Graduate School of Business Administration,
prepared this article while he was a Visiting Scholar in the
M acroeconomics Section of the Philadelphia Fed's Research
Department.
**See the Glossary (pp. 24-25) for a definition of this and
other terms with ** throughout the text.
fact, in less time than the typical reader will take
to read this article, he or she could buy an index
futures contract, change opinion on the market
and sell it off, and, upon further reflection, revise
opinion once again and buy it back.
Trading in these futures contracts has grown
enormously since their introduction in the early
1980s. During fiscal 1986, the dollar value of the
Standard and Poor's (S&P) 500 stock index**
futures contracts that traded hands was about 60
percent greater than the value of actual stock
trading on the floor of the New York Stock
Exchange. The four major stock index futures
contracts are the Chicago Mercantile Exchange's
S& P500 index contract (by far the most active),
the New York Futures Exchange's New York
13
BUSINESS REVIEW
Stock Exchange Composite** index contract,
the Kansas City Board of Trade's Value Line**
index contract, and the Chicago Board of Trade's
Major Market** index contract.1
Perhaps because of the astounding growth in
these index futures markets, traders, investors,
and the financial press have made much ado
about their possible adverse effects. In particular,
the impact of program trading** between index
futures and cash market** stocks by arbitragers**
has become a hot contract design and market
regulation issue. The concern centers on whether
program trading has increased price volatility**
in the cash stock markets. Excess price volatility
is undesirable because investors may have to
buy stocks at artificially high prices or sell them
at artificially depressed prices, thus creating
windfall gains and losses in a market where the
gains and losses from the "fundamentals" are
variable enough.2
As it turns out, the adverse impacts of arbitrage
program trading probably have been overblown.
It is true that, during the so-called "Triple
Witching Days" that occur four times a year
when the major stock index futures contracts
expire, program trading magnifies stock market
price volatility. However, in more normal circum
stances, available evidence indicates that such
trading has had no significant impact on volatility.
Moreover, the arbitrage process underlying
program trading provides important benefits to
investors, through both enhancing the liquidity**
of futures trading and ensuring fairer relative
pricing between stock and stock index futures
markets. In conjunction with attempts to lessen
the pricing distortions that occur when index
futures expire, the exchanges and their regu
lators should avoid inhibiting overall activity in
the arbitrage sector.
1Options on stock indexes and options on stock index
futures also have attracted large trading interest. In fact,
today, the most actively traded options are the Chicago
Board Options Exchange's S& P100 stock index option
contracts.
2Excess stock price volatility is also undesirable since it
decreases the informational content of prices.
14
SEPTEMBER/OCTOBER 1987
INDEX FUTURES CONTRACTS
AND THEIR MARKETS
A futures contract is a standardized agreement
to buy or sell a particular asset or commodity at
some deferred date.3 The underlying "asset" for
a stock index futures contract is a specific price
index of cash market stocks. For example, the
S&P500 stock index futures contract is based
upon the S& P500 index of stock prices, a
weighted average of the prices of all 500 stocks
comprising Standard and Poor's list.4 (Each
S&P500 index futures contract represented about
$145,000 of stock market value as of May 1987.)
Stock index futures contracts cover only four
expiration m onths a year—March, June,
September and December. Thus, in May 1987,
the June 1987 expiration contract was the "near"
contract. The nearest expiration contract tends
to be the most actively traded of all contracts up
to a short time prior to its expiration day.
Traditional futures contracts, such as those for
gold or Treasury bills, allow final settlement by
delivery of the underlying assets. In stock index
futures, actual physical securities (the individual
stocks themselves) are not involved. Instead,
stock index futures make their final settlement
through a cash payment. For example, on each
third Friday of the months of March, June,
September and December, the nearest S& P500
index contract expires. At the expiration mo
ment, the contract is assigned a value based
upon the current value of the underlying cash
market index. The net gain or loss on an index
futures position depends upon the change in
the futures price between the time when the
contract is entered initially and the date it expires
3For a short introductory guide to financial futures markets,
see John J. Merrick, Jr. and Stephen Figlewski, "An Intro
duction to Financial Futures Markets," Occasional Papers in
Business and Finance, Salomon Brothers Center for the Study
of Financial Institutions, No. 6 (August 1984).
4The weight for each individual stock price in the index is
the ratio of the total dollar value of all outstanding shares of
the stock to the total dollar value of all 500 stocks in the index
(that is, each stock price in the index is "capitalizationweighted").
FEDERAL RESERVE BANK OF PHILADELPHIA
Stock Index Futures Program Trading
or the position is offset**. (Most users of futures
will close their futures contract position out prior
to expiration through a reversing trade—for
example, selling another contract to offset one
previously bought.)
The terms of the S& P500 index futures con
tract are that each one point move in the futures
price is worth $500. For example, a rise in an
S& P500 index futures contract's price from 290
to 291 would entail a gain of $500 to investors
who were long** the contract (that is, those who
had bought) and an equivalent loss to those who
were short** (that is, those who had sold). The
final cash settlement feature of the stock index
futures contract is designed to avoid the costs
and inconvenience of final settlement through
physical delivery which, in the case of the
S& P500 contract, would involve the purchase,
delivery and (probably) resale of the properly
weighted basket of 500 individual stocks.
Stock Index Futures Lower Portfolio Manage
ment Costs. Investors find stock index futures
useful because they are a convenient and rela
tively low-cost way to speculate on future
movements in the stock market or to hedge the
market risk of a stock portfolio. Speculators who
are confident in their ability to predict swings in
stock prices find long or short index futures
positions convenient ways to take on desired
market risk exposure. Other, perhaps less con
fident, investors enter index futures positions
designed to hedge their current cash market
positions. For example, if the hedger is holding a
cash market portfolio of stocks (that is, if he is
long cash stocks), he will sell a properly weighted
number of stock index futures contracts to reduce
his net market risk exposure.5 The hedge works
to reduce total return risk since a loss (gain)
from a fall (rise) in cash market stock prices will
be at least partially offset by a gain (loss) from
5A thorough practical treatment of hedging using financial
futures markets is contained in Hedging with Financial Futures
for Institutional Investors, by Stephen Figlewski with Kose
John and John J. Merrick, Jr. (Cambridge, MA: Ballinger
Publishing Company, 1985).
John J. Merrick, Jr.
the short futures position as long as futures
prices move in the same direction taken by cash
prices.
Of course, investors could speculate or hedge
their risks without resorting to futures market
transactions. The would-be bullish speculator
could simply buy a broad portfolio of stocks (or
shares in a mutual fund). The would-be hedger
could simply sell out the stock portfolio and
invest the proceeds in Treasury bills until a less
uncertain environment prevailed. However,
executing these strategies in the cash market can
be cumbersome. The speculator would be ham
pered because only 50 percent of a stock position
can be financed by margin loans. Similarly, the
hedger who sold off the stock portfolio would
bear not only the direct costs of selling these
stocks, but also the costs of reconstructing the
perhaps painstakingly acquired initial position
at the onset of more favorable market conditions.
While transactions in standardized indexbased futures contracts also entail margin re
quirements and direct trading costs, these are
substantially lower than those for the cash
market. For example, the direct commission cost
of a "round-trip" purchase and sale of 100
S&P500 index futures contracts is about $2,500.
Assuming commission costs in the cash market
of $.07 per share and an average share price of
$45, the cost of buying and then selling an
equivalent amount of stocks (roughly $14.5 mil
lion in May 1987) would be about $45,100. Thus,
stock index futures contract purchases and sales
provide large investors with cost-efficient means
of making desired portfolio adjustments and are
properly viewed as institutional solutions to
trading problems.
INDEX FUTURES ARBITRAGE:
LINKING CASH AND FUTURES MARKETS
Index Futures Prices Versus the Cash Index.
Since an index futures contract is a close substi
tute for the basket of stocks underlying the cash
market index for many users, one might expect
the index futures price to be closely related to
the cash index. Certainly the tie between the
15
BUSINESS REVIEW
futures price and the cash index value is tight on
the contract's expiration day when, by the con
tract's design, the two are equal. However, prior
to expiration day, the potential user of the futures
should “comparison shop" to see whether the
contract is overpriced or underpriced relative to
the prices of the stocks in the cash market. For
example, is it cheaper to buy a one-year-tomaturity S& P500 futures contract at 300 or the
underlying portfolio of stocks if the cash S&P500
index stands at 286? Clearly, the futures should
usually sell for more than the cash index since,
while both futures and cash indexes converge
within a year, there is a net cost to carrying** the
stock portfolio (financing costs less dividends
earned).6*However, is 300 too high or too low?
As it happens, answering the question of fair
relative pricing between futures and cash mar
kets also explains how arbitragers make money
by trading between the two markets following
what are called “program trading" rules. While
comparison shopping by hedgers and specula
tors puts some limits on potentially abnormal
deviations of index futures prices from their
cost-of-carry values, most of the responsibility
for maintaining fair pricing between the futures
and cash markets falls on “program traders"—
members of the arbitrage community who have
come to specialize in intermarket trading. Pro
gram traders attempt to extract profits from any
discrepancy that arises between the futures
contract's price and its cost-of-carry value, follow
ing the old adage “buy cheap, sell dear." That is,
they buy (or sell) index contracts in the futures
market and sell (or buy) the equivalent value of
the actual stocks in the cash market.
Cost-of-Carry Pricing and Arbitrage. The
theoretical difference between the initial futures
price and the initial index value is solely deter
mined by the difference between the stock
portfolio's financing cost and its dividend yield.**
For example, suppose that the S& P500 stock
6The futures position entails no meaningful initial invest
ment but accrues no dividends.
16
SEPTEMBER/OCTOBER 1987
index currently is 286; that the dividend yield on
the underlying cash market S& P500 stock port
folio is 3.2 percent; that the one-year interest
rate is 7.1 percent; and that transactions costs
can be ignored. In this case, the net cost of carry
equals 3.9 percent—the 7.1 percent financing
rate less a 3.2 percent dividend yield. The costof-carry pricing argument would maintain that a
one-year-to-expiration S& P500 index futures
contract should sell for 297.15 index points, or
3.9 percent above the current cash index value.
To see why this pricing structure makes sense,
consider what happens when an arbitrager pur
chases the stocks and sells the futures. He is
assured of making the current futures-cash index
spread** (297.15-286 = 11.15 index points) via
convergence regardless of whether the year-end
level of the index is higher, equal to, or lower
than its current level. For example, if the expira
tion day closing index value is 300, the cash
position gains 14 points (300-286) and the short
futures position loses 2.85 (297.15-300) for a net
gain of 11.15. If, instead, the index closes out at
275, the cash position loses 11 points (275-286),
but the futures position gains 22.15 (297.15275) to again net a gain of 11.15. “Convergence"
ensures that the initial 11.15 point spread be
tween the futures and the cash index (297.15286) is earned. This position also will earn 9.15
points in dividends (.032x286 = 9.15). Thus,
total gross earnings for this riskless investment
will be 20.3 index points. However, this gross
profit is exactly what the initial capital would
return if it were invested at the current interest
rate of 7.1 percent (.071x286 = 20.3).
The futures price of 297.15 is fair relative to
the current cash index value precisely because
the “program" of buying cash stocks and selling
index futures is a perfectly hedged position. If
the futures were selling at 298 instead, this risk
less buy/sell program would gross 21.15 points
(yielding 100x21.15/286 = 7.40 percent). Such
a program would dominate the simple 7.1 per
cent riskless investment. Thus, this particular
program trade by arbitragers, or other investors
seeking to swap the riskless cash/futures program
FEDERAL RESERVE BANK OF PHILADELPHIA
Stock Index Futures Program Trading
for a "plain vanilla" riskless investment (say, a
Treasury bill) whenever rate of return discrep
ancies arise, would drive the futures price down
(and/or the cash price up) if the futures rose
above 297.15. Likewise, if the futures price fell
below 297.15, arbitragers would profit from the
reverse trade of selling the stock basket and buy
ing the underpriced futures. Again, the result
would be pressure on both cash and futures
prices to return to their fair relative values.
These calculations ignore transactions costs.
Typically, the largest players in index futures
program trading are the major stock brokerage
houses. These firms already have invested in
developing economical systems for trading
stocks. For a S& P500 index futures program
trade by a major brokerage house arbitrager,
total transactions costs might be reasonably
approximated as 0.5 percent of the S& P500 cash
index (or, 1.43 index points in the example
above).7 Thus, the futures price actually could
wander anywhere within a band between 298.58
and 295.72 without violating fair pricing bounda
ries.8 Certainly, the proposed price of 300 that
began this discussion is too high in this sense.
However, some hedgers and speculators would
still find the futures an attractive buy at 300 if
their cash market trading costs were relatively
high (greater than 2.85 index points), or if it
were important to avoid delay in executing the
trade.
In sum, deviations from cost-of-carry pricing
7See Hans Stoll and Robert Whaley, "Expiration-Day
Effects of Index Options and Futures," Monograph Series in
Finance and Economics, Salomon Brothers Center for the Study
of Financial Institutions, New York University (1986).
8This 0.5 percent or 1.43 index point transactions cost
estimate overstates the average transactions costs incurred
by active arbitragers who constantly look either to unwind
their positions early at a reversed mispricing or to roll their
hedges into the next contract expiration at a more favorable
price spread. These arbitragers receive additional arbitrage
profits without incurring the full set of additional transactions
costs. Thus, some aggressive players might choose to be
active even at futures prices that lie within the transactions
costs bounds described. One active arbitrager estimates his
average transactions cost at about one S&P500 index point.
John J. Merrick, Jr.
that cannot be attributed to transactions costs
present signals for arbitragers to buy cheap and
sell dear. These program traders enter both a
position in index futures contracts and an off
setting position in an appropriately selected
basket of stocks. The basket is constructed in
such a way that movements in its value mirror
movements in the stock index upon which the
futures contract is based. The position is designed
to deliver a "riskless" hedged return that yields
more than alternative riskless securities.9 The
arbitrage process should continue until the
futures and cash stock markets have returned to
a fair relative pricing relation.
The Economic Role of Arbitragers. As ex
plained above, arbitragers seek to profit from
misaligned relative prices. This last statement
might be construed as an academic way of stating
that "these people make easy money at the
expense of true investors." However, such an
interpretation would be misleading. First, the
arbitrage process itself is costly. Arbitrage firms
must invest heavily in communication, trade
evaluation, and trade execution systems. Second,
the trades themselves are not completely riskless.
Risk enters because of the marked-to-market**
daily settlement feature of futures, because of
restrictions on short sales of stocks, and because
the stock baskets assembled by the arbitrager do
not always track the stock index perfectly.10
But most importantly, it can be argued that
arbitragers actually help true investors. By
working to bring about cost-of-carry pricing,
arbitragers allow speculators and hedgers to
9The hedge underlying intermarket arbitrage trading can
also be constructed by combining the cash market stocks
with index option positions. Thus, arbitragers will use both
options and futures programs depending upon which hedge
yields the highest riskless return.
10Gains and losses from futures price changes are settled
in cash at the end of each day by means of marked-to-market
settlement. Therefore, losses on futures contracts are not
"paper losses," but entail real cash outlays even when the
position has not yet been closed. Likewise, gains on futures
positions entail immediate cash inflows. Short sales of stock
refer to sales of stock temporarily borrowed from other
investors.
17
BUSINESS REVIEW
open and close futures positions at prices that
are fairer relative to the underlying cash market
than those they would have obtained without
arbitrage trade price pressures.11 Thus, arbi
tragers help reduce some of the uncertainty that
users of futures markets bear. Furthermore,
arbitrage trading adds to market liquidity. Addi
tional liquidity in a market benefits all market
users. In particular, it lowers total transactions
costs by shrinking the bid-ask spread** and
allows larger orders to be placed with shorter
time delay.
One useful way to view the contribution of
arbitragers concerns the sequence of events
surrounding the decision of a previously bullish
portfolio manager to turn bearish on the stock
market. However, assume that the portfolio
manager still believes that his individual stock
“picks" will outperform the market over time.12
Consequently, he keeps his portfolio intact, but
sells S& P500 futures contracts of equivalent
value to hedge his position against market risk.
Since no sell order on the cash side is entered,
only the futures market is initially affected by
the portfolio manager's change of heart: In order
to find buyers to absorb this new futures contract
sell order, the index futures price is nudged
down a bit.
If prices were initially in their fair cost-ofcarry relation, now they are slightly misaligned
(futures are cheap relative to cash). This is the
signal for the arbitrager to act. He buys the
underpriced futures contract and sells a basket
of stocks carefully selected to mimic the value
change of the S& P500 index.13 The arbitrager's
11 See John J. Merrick, Jr., "Hedging With Mispriced
Futures," Federal Reserve Bank of Philadelphia Working
Paper No. 87-11, June 1987 for an analysis of the interrelation
ships between arbitrage sector performance and hedging
cost and effectiveness.
12That is, he thinks that the portfolio will lose less than the
S&P500 in bear markets and gain more than this index in
bull markets.
13The arbitrager may accomplish the stock sale half of the
position either by selling out of his firm's preexisting
inventory (a swap) or by short sales.
Digitized 18 FRASER
for
SEPTEMBER/OCTOBER 1987
orders put some upward pressure on the index
futures price and (at last) downward pressure
on the prices of the stocks comprising his
basket.
The net effect of the portfolio manager's shift
to bearish sentiments is to lower both futures
and cash stock prices. In effect, the portfolio
manager made the sell decision, but delegated
responsibility for the actual stock market sales to
the arbitrager. The “fee" collected by the arbi
trager consists of the spread implicit in the
initially underpriced futures. The portfolio
manager was willing to pay this fee (that is, sell
the futures at less than full cost-of-carry) because
the implied transactions costs of accepting this
“low" futures price were lower than his direct
transactions costs of selling out and then sub
sequently rebuilding his cash stock portfolio.
Also, the futures sale is accomplished almost
immediately, whereas the liquidation of a large
portfolio might take some time.
Through implicitly delegating his cash market
sales to the arbitrager, the portfolio manager
shifts the burden of selling a large complex stock
portfolio to an agent who has come to specialize
in such sales (or purchases). Thus, one can
interpret the advent of stock index futures
arbitragers as a response to the institutional
investor's desire to develop low-cost ways to
acquire or liquidate large portfolio holdings. In
fact, the term “program trading" as applied to
futures/cash arbitragers makes perfect sense in
this regard, since investment houses servicing
large-scale portfolio restructurings for institu
tional investors traditionally referred to their
services as “doing a program" long before the
advent of index futures trading. For the case of
arbitrage in futures, however, the stock portfolio
involved is always the index-based basket or a
reasonable facsimile.
ARBITRAGE EFFECTS
ON THE CASH STOCK MARKET
The Historical Evidence. Data on the volume
of futures contracts give us a clear picture of how
active these instruments are and how actively
FEDERAL RESERVE BANK OF PHILADELPHIA
Stock Index Futures Program Trading
John J. Merrick, Jr.
arbitragers have been involved with them.
Between 1983 and 1986, while the dollar volume
of stocks traded on the cash markets of the New
York Stock Exchange broke records, the dollar
volume of S& P500 futures contracts rose even
higher (see Figure la , FUTURES CONTRACTS
SOAR . . .). Arbitrage activity can be inferred
from looking at the growth in the number of
contracts settled in cash on expiration day. Mar
ket participants other than arbitragers, who use
futures contracts to hedge their portfolios or to
speculate, are less inclined to hold expirationmonth contracts to their final settlement day.
Instead, these traders typically would roll their
contract positions over to maintain their hedge
or open speculative position. Between 1983 and
1986, the volume of contracts settled in cash
(presumably by arbitragers) more than quin
tupled, from about 6,000 to almost 33,000. In
addition, the relative importance of arbitragers
has increased. The increased presence of arbi
tragers can be inferred by comparing the growth
in the number of contracts settled in cash relative
to the growth of the average month-end open
interest** (see Figure l b , . . . AND ARBITRAGE
ACTIVITY GROW S, TOO). Over this time per
iod, the proportion of cash-settled contracts rose
from about 28 percent to 38 percent of average
month-end open interest.
Deviations From Cost-of-Carry Pricing. Fig
ure 2 (p. 20) presents a plot of the percentage
deviation of the actual daily closing prices for
near expiration S& P500 index futures contracts
from their theoretical cost-of-carry levels for the
May 17,1 9 8 2 to May 3 0 ,1 9 8 6 period. It is clear
that while most of the deviations are within the
0.5 percent transaction cost bounds (shown as a
shaded band), there have been instances in which
such deviations were large and persistent. For
example, the futures was grossly overpriced
throughout the month of October 1984. In the
1985-86 period, however, instances of mis
pricings in excess of transactions costs are less
frequent than in the earlier 1982-84 period,
FIGURE lb
FIGURE la
Futures Contracts Soar . . .
Average
Number of
Contracts
(Thousands)
Dollar Value
of Trading
(Trillions)
2.5
1983
. . . And Arbitrage Activity
Grows, Too
1984
1985
(Fiscal Year Totals)
1986
1983
1984
1985
(Fiscal Year Averages)
1986
19
BUSINESS REVIEW
SEPTEMBER/OCTOBER 1987
Stock Index Futures Program Trading
John J. Merrick, Jr.
FIGUE 2
Near Contract S&P50 Futures Mispricing
As Percentage ofheoretical Value
Percentage
Points
1982
□ Transactions Cost Bounds
probably because of the marked expansion of
the arbitrage sector during the later years.
Volume, Volatility, and the Arbitrage Devia
tion. It's natural to ask why mispricing might
ever arise in the face of expanded arbitrage
trading activity. While it is certainly true that
index futures arbitrage programs pour millions
of dollars into these trades, arbitragers appar
ently are not always able to bring prices l?ack
into their cost-of-carry relation quickly. Thus,
one might be suspicious of at least some of the
charges linking volume and price volatility ef
fects to arbitrage activity.
In fact, looking at daily data for non-expiration
months over the 1982-1986 period, recent re
search has uncovered virtually no evidence that
arbitrage mispricings predict any significant
percentage of the variation in daily return vola
tility (for both S& P500 and NYSE cash indexes).
There is evidence linking futures/cash arbitrage
Digitized20 FRASER
for
1983
1984
1985
1986
Daily Data: 5/17/82 - 5/30/86
mispricings to increased NYSE cash market
trading volume. Such effects have become more
pronounced in the recent 1985-1986 period.
However, fluctuations in trading volume are
more highly correlated with return volatility
than with arbitrage mispricings.14 In addition,
there is stronger evidence that fluctuations in
trading volume and return volatility portend
larger arbitrage mispricings than vice versa.
The evidence that the volume effects of arbi
trage trading have become more important
recently does not necessarily make arbitragers
the ultimate source of cash stock price move
ments. Certainly arbitragers cause pressures on
14See John J. Merrick, Jr., "Volume Determination in Stock
and Stock Index Futures Markets: An Analysis of Volume
and Volatility Effects," Federal Reserve Bank of Philadelphia
Working Paper No. 87-2, January 1987 (forthcoming in The
Journal of Futures Markets, October 1987).
FEDERAL RESERVE BANK OF PHILADELPHIA
cash market prices. However, such price pres
sures generated by arbitrage trading only bring
the cash market in line with the valuation re
flected by the previous movement in the futures.
For instance, suppose that, as in the earlier
"bearish portfolio manager" example, the futures
shifts down suddenly from an initial full cost-ofcarry equilibrium and becomes underpriced
relative to the cash index. Suppose further that,
as the prices become realigned through arbitrage
activity, cash prices fall more than futures prices
rise. Indeed, while cash market selling by program
traders directly leads to the cash index decline,
in this instance the cash market fell because of
the previous weakness in the futures price. The
futures market "discovered" the new bearish
sentiments of the investing public.15*Arbitragers
15The available evidence suggests that the S& P500 index
futures market has played the dominant price discovery role
ensured that this "bad news" was transmitted to
the cash markets in individual stocks. While
investors holding positions in these stocks need
not be pleased, there is no reason to adopt a "kill
the m essenger" attitude.
"Triple Witching Hour" Congestion Effects.
One adverse effect of index futures arbitrage on
cash stock markets that does receive strong
empirical support is the so-called "Triple Witch
ing Hour" congestion. Prior to the June 1987
expirations, the Triple Witching Hour occurred
at the 4:00 p.m. close of trading on the New York
(relative to the cash market) since 1985. Prior to 1985, the
cash stock market dominated the price discovery process.
This reversal in price discovery dominance roles occurred
not long after the volume of trading in the futures market
eclipsed that in the cash market. For details, see John J.
Merrick, Jr., 'T rice Discovery in the Stock Market," Federal
Reserve Bank of Philadelphia Working Paper No. 87-4,
March 1987.
21
BUSINESS REVIEW
Stock Exchange on the quarterly expiration
Fridays of the stock index futures contracts.
Stock index options and options on individual
stocks also have expirations that occur at this
time.
Taken at face value, contract expirations would
not appear to be such dramatic events. After all,
trade in the various commodity and other finan
cial futures contracts has occurred for years, and
individual contract expirations have come and
gone with very little public attention. However,
the cash settlement design of the stock index
futures (and index options) contracts presents
special problems on expiration days when
arbitragers "unw ind" their positions.
Recall that arbitragers hold offsetting positions
in stocks and index futures. Their return is hedged
perfectly if they liquidate their stock basket at
the moment the futures contract expires, since
the futures price is marked to the value of the
cash stock index at that time. Thus, the planned
expiration day strategy of the arbitrager was to
submit market-on-close** orders to the special
ist** on the floor of the exchange trading each
stock held in the stock basket.16 On expiration
days that the net (long or short) aggregate stock
position of arbitragers was large, order imbal
ances appeared in each specialist's book at the
market's close, which produced unusual tempo
rary price swings in one direction or the other.
The imbalance occurs because the index futures
are settled in cash, not through delivery of the
securities. In brief, at market close on expiration
day, arbitragers supplied or demanded an abnor-
16Actually, the trigger for the unwinding is related more
closely to the return of the futures price to its cost-of-carry
relationship. Of course, this return is assured at expiration
by the contract's convergence feature. But if a return to costof-carry pricing (or an appearance of a reverse mispricing)
occurs before the expiration, arbitragers who close out early
will earn higher returns than they initially expected. For
example, early close-outs were optimal for short futures/
long cash positions during the weeks leading up to the
September 1986 contract expiration since the previously
overpriced September futures became substantially underpriced (in fact, futures were trading at a discount to the cash
market stock index).
22
SEPTEMBER/OCTOBER 1987
mal quantity of stocks, but nothing in the futures
settlement process provided an automatic mecha
nism to generate offsetting stock orders to absorb
the disturbance.
Congestion effects in the cash markets during
the last hour of trading on index futures expira
tion days have been documented. Specifically,
three effects have been found for index compo
nent stocks: cash market volume in the last hour
of trading is approximately double that of non
expiration Fridays; last-hour cash market return
volatility for index component stocks is signifi
cantly higher than for non-expiration days; and
abnormal price reversals occur on the morning
following these quarterly expirations.17 The
symptoms accompanying expiration days have
been likened to the temporary cash market distor
tions of "block" trades in individual stocks.
Since these expiration day effects are so local
ized, two reactions are defensible. The first would
be to live with the problem in its present form,
though endeavoring to educate investors con
cerning the increased uncertainties of trading
during these four days of the year. There is some
reason to believe that, with proper market educa
tion, the expiration day problem would correct
itself. Small investors would be wary of trading
on expiration days. In contrast, large investors
might choose to act strategically, altering their
normal behavior to pick up "bargains" through
either selling at the temporarily high or buying
at the temporarily low cash market prices in
duced by expiration day price "spikes".18 Both
sets of market responses would tend to amelior
ate expiration day pricing distortions.
The second response would be to attempt
some fine-tuning of either the design of the
17These results are found in Stoll and Whaley, "ExpirationDay Effects of Index Options and Futures." Stoll and Whaley
find smaller price and volume effects on days on which
index options expire but index futures do not.
18Such strategic positioning is not without risks, in that
the direction of expiration day congestion price effects is not
perfectly predictable.
FEDERAL RESERVE BANK OF PHILADELPHIA
Stock Index Futures Program Trading
stock index futures contracts or trading proce
dures. However, many of the solutions proposed
to date have adverse effects on the smooth func
tioning of the market—especially in diminishing
market liquidity—which may outweigh their
calculable benefits.19 One major change effective
with the June 1987 contracts for the S& P500 and
NYSE index futures is to shift the expiration of
these contracts to the cash market's open rather
than its close. This change should help reduce
excess expiration day volatility since it effectively
expands the amount of time that NYSE specialists
have to assemble large orders to offset any im
balances created by arbitragers. First, arbitragers
must submit their market-on-open unwinding
orders prior to 9:00 a.m. on expiration day. Sec
ond at 9:00 a.m., the New York Stock Exchange
will announce any buy or sell order imbalances
of 50,000 shares or more in 50 selected "blue
chip" stocks. Furthermore, as on any other day,
the specialists will be able to advertise unusual
excess demand or supply situations by indicating
the expected opening price prior to the actual
opening of trading. Finally, as on any other day,
each specialist will retain the prerogative to delay
the opening of trading for stocks faced with
unusual pricing patterns. In turn, potential buy
ers or sellers of the stock, given extra time and
more complete information about the nature of
net arbitrager activity, should find it easier to
19These anti-congestion proposals include (1) altering the
cash settlement procedure on the index futures contract, (2)
telescoping of position limits on the futures, (3) restricting
expiration day market orders, and (4) requiring early dis
closures of expiration day futures and options positions by
large traders (the Securities and Exchange Commission
sponsored a 3:30 p.m. expiration day stock position disclosure
policy which came into effect as of the September 1986
expiration). See Franklin R. Edwards, "Stock Index Futures
and Stock Market Volatility: Evidence and Implications,"
Commodities Law Letter, 6 (N ovem ber/Decem ber 1986) pp.
3-6, and Stoll and Whaley for discussion.
]ohn J. Merrick, Jr.
respond to perceived imbalances with offsetting
orders.
CONCLUSIONS
"Program trading" based upon stock index
futures arbitrage is growing in practical impor
tance. The positive effects of arbitrage trading
include increased market liquidity and fairer
pricing. Both factors benefit "true investors"
(hedgers and speculators). One adverse effect
of arbitrage is the temporary distortion in the
cash stock markets caused by the unwinding of
positions by arbitragers on the days of the
quarterly futures contract expirations. However,
these distortions are not particularly serious,
especially since their effects are so localized.
The evidence that arbitragers distort cash
markets on non-expiration days is scant. There
is very little evidence that daily cash index return
volatility is affected by observed index futures
mispricing. In fact, the evidence suggests that
the degree of mispricing itself is influenced by
fluctuations in volatility.
The periods of persistent mispricing of index
futures contracts observed since the beginning
of trading in 1982 appear to indicate that the
arbitrage sector has historically been under
capitalized or otherwise impeded. Because of
these implied imperfections in this sector,
futures-cash mispricing inefficiencies tended to
persist, and hedgers were forced to bear un
desired excess risk on positions closed out prior
to contract expiration. Pricing performance by
an expanded arbitrage sector has improved in
recent years. For this reason, as they grapple
with the expiration-day congestion issue, futures
exchanges and their regulators should ensure
that any possible contract redesign or other
trading change does not hamper the arbitrage
sector in a manner that will eliminate the recent
gains in contract pricing efficiency.
23
BUSINESS REVIEW
SEPTEMBER/OCTOBER 1987
Glossary
Arbitrage
A strategy designed to create riskless profits through taking matched opposite positions in
two investments that have identical payoffs but are trading at different prices.
Bid-ask spread The difference between the price currently bid on the exchange floor for the
purchase of a stock (or futures contract) and the price currently asked for the sale of that same stock.
"Market" orders to buy a stock will be transacted at the asked price. "Market" orders to sell a stock will be
transacted at the bid price.
Cash market
The market for (immediate) exchange of title of a security or other asset for cash.
Dividend yield
The dividend income accruing to, say, a portfolio of stocks expressed as a fraction of
the stock or portfolio value.
Futures contract
A standardized agreement to buy or sell a particular asset or commodity at some
deferred date.
Liquidity
The continuity of the order flow and therefore the orderliness of price changes in an asset
market. Other things held constant, a market's liquidity rises with its size.
Long position
The position created through the purchase of a contract.
M arked-to- market settlement The procedure by which all open accounts are debited or credited
the cash amount of the change in contract value due to the daily change in the futures price.
Major Market index
An equally-weighted index of 20 "blue-chip" stocks which tends to track the
popular Dow Jones Industrial Average.
Market-on-close order
Order placed with the specialist to buy or sell the stock at the market asked or
bid price at the 4:00 p.m. close of trading. This type of order was particularly attractive to program traders
who want to unwind their cash stock positions at the futures expiration.
Net cost-of-carry
The difference between the financing cost and the productive yield of a cash
market position over the period ending with the future's expiration date.
24
FEDERAL RESERVE BANK OF PHILADELPHIA
Stock Index Futures Program Trading
New York Stock Exchange Composite index
John J. Merrick, Jr.
A capitalization-weighted index of the prices of all
stocks traded on the New York Stock Exchange.
Open interest
The number of contracts entered but as yet neither offset nor otherwise satisfied by a
final settlement such as delivery.
Option contract
A contract that gives the right but not the obligation to buy an asset (a "call" option)
or sell an asset (a "put" option) at a fixed price on or before a specified expiration date.
Position offset
An equal and opposite ("reversing") transaction to counteract a previously established
position. For example, a sale of a June futures contract on May 15 to close out a position established
previously by an April 25 purchase of a June futures contract.
Program trading The popular name given to arbitrage trading between the stock index futures
market and the cash market in stocks.
S&P500 index An index number that relates the current value of a weighted average of the prices of
the stocks that comprise Standard and Poor's list of 500 stocks to that of a historical base period.
Short position
The position created through the sale of a futures contract or the sale of borrowed stock.
Specialist The marketmaker—price setter and order flow matcher—for a stock in the New York Stock
Exchange system for stock trading.
Spread
The difference between the prices of two assets.
Transactions costs Costs of executing a trading strategy. For the program trader, these costs consist of
commissions and the bid-ask spread on the cash stock side and the commission and one-half of the bidask spread on the futures side.
Value Line composite index
A geometric average of 1,700 stock prices. It is the broadest of the four
indexes on which actively traded futures contracts are based. This stock index places relatively more
weight on smaller stocks than the other major indexes.
Volatility
A measure of the dispersion of possible percentage price changes about their mean
value.
25
Philadelphia/RESEARCH
Working Papers
The Philadelphia Fed's Research Department occasionally publishes working papers based on the current
research of staff economists. These papers, dealing with virtually all areas within economics and finance, are
intended for the professional researcher. The 11 papers added to the Working Papers Series so far in 1987 are
listed below.
A list of all available papers may be ordered from WORKING PAPERS, Department of Research, Federal
Reserve Bank of Philadelphia, 10 Independence Mall, Philadelphia Pennsylvania 19106-1574. Copies of paper
may be ordered from the same address. For overseas airmail requests only, a $2.00 per copy prepayment is
required.
1987
No. 87-1
Paul Calem, “Deposit Market Segmentation: The Case of MMDAs and Super-NOWs." (Super
sedes No. 86-3, "MMDAs, Super-NOWs, and the Differentiation of Bank Deposit Products.")
No. 87-2
John J. Merrick, Jr., "Volume Determination in Stock and Stock Index Futures Markets: An
Analysis of Arbitrage and Volatility Effects."
No. 87-3
Richard P. Voith, "Compensating Variation in Wages and Rents."
No. 87-4
John J. Merrick, Jr., "Price Discovery in the Stock Market."
No. 87-5
Loretta J. Mester, "Testing for Expense Preference Behavior Using Cost Data."
No. 87-6
Paul Calem and Janice Moulton, "Competitive Effects of Interstate Bank Mergers and Acquisi
tions."
No. 87-7
Joel Houston, "The Policy Implications of the Underground Economy."
No. 87-8
Mitchell Berlin and Paul Calem, "Financing, Commitment, and Entry Deterrence."
No. 87-9
Joel F. Houston, "Estimating the Size and Implications of the Underground Economy."
No. 87-10
Joel F. Houston, "Participation in the Underground Economy: A Theoretical Analysis."
No. 87-11
John J. Merrick, Jr., "Hedging with Mispriced Futures."
FEDERAL
RESERVE B A N K O F
PH ILA D ELPH IA
@FedFRASER