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E V ID E N C E O N T H E IM P A C T O F F U T U R E S
M A R G IN S P E C IF IC A T IO N S O N T H E
P E R F O R M A N C E O F F U T U R E S AND
C A SH M A R K E T S
Jam es T. M oser
W orking Paper Series
Issues in Financial Regulation
Research D epartm ent
Federal Reserve B ank o f Chicago
Decem ber, 1990 (W P-90-20)
Not for quotation
Revised: December 1990
Evidence on the Impact of Futures Margin Specifications
on the Performance of Futures and Cash Markets
by
James T. Moser
Research Department
Federal Reserve Bank of Chicago
230 S. LaSalle
Chicago, IL 60604-1413
Phone: (312) 322-5769
FAX: (312) 322-5231
The analysis and conclusions of this paper are those of the
author and do not indicate concurrence by other members of the
research staff, the Board of Governors or the Federal Reserve
Banks.
Abstract
Changes in margin requirements for S&P and silver futures
contracts are examined to determine their impacts on various
measures of market performance.
Margin changes are found to be
unrelated to the subsequent volatility of futures prices after
controlling for exchange interventions in the silver market.
Speculative margin appears to be positively related to cash
market volatility in both contracts. We find evidence of a
positive relationship between margin changes and the volatility
of open interest in the S&P contract. This suggests margin
changes may increase the risk of realizing thin market
conditions. No relationship is found between margin changes and
other measures of market participation. A cost-of-carry model
is introduced which relates compensation for nonperformance risk
to margin changes. We find evidence favoring the hypothesized
negative relation between margin changes and nonperformance.
Keywords: FUTURES MARGIN, NONPERFORMANCE, COST OF CARRY, BASIS
Evidence on the Impact of Futures Margin Specifications
on the Performance of Futures and Cash Markets
I . Introduction
Recent volatility in stock and futures markets motivates
further examination of margin and market performance.
This
paper investigates several paths through which linkages between
futures margin changes and market performance may be
expressed.
Section II relates margin requirements to some
traditional measures of performance.
The first of these
examines the role of margin in fulfulling the often-stated
regulatory goal of controlling volatility.
Second, we examine
the impact of futures margin changes on volatility in the cash
market.
The third considers the role of margin in the
determination of market participation.
Our measures of market
participation are the levels and volatilities of trading volume
and open interest.
For the futures markets, we examine levels
and volatilities for both volume and open interest in each
contract.
Trading volume in the stock market is examined for
evidence of a change in cash-market participation owing to
margin changes in associated futures contracts.
This study of the correlation between margin changes and
market performance suggests three conclusions.
First, in
itself, margin changes do not appear to affect the volatility of
futures prices.
A relation between margin changes and futures
price volatility is supported only during periods when other
1
forms of exchange intervention are used.
Second, we find modest
evidence that speculative margin changes in futures contracts
produce higher volatility in associated cash markets.
Maintenance margin changes which are generally concurrent with
changes in speculative margin do not repeat this finding.
Third, we reject linkages of margin changes with most of our
market participation measures.
The exception is a finding that
margin changes appear to precede increases in the volatility of
open interest for S&P contracts.
This result may indicate
increased risk of liquidity problems.
This correlative evidence motivates consideration of a model
in section III for the impact of margin on the prices of cash
and futures contracts.
The cost-of-carry model is specialized
to include compensation for nonperformance risk.
This approach
emphasizes the role of margin as a performance bond in the
futures markets.
Simply stated, if margin balances bond
performance, then compensation for the risk of nonperformance
should be negatively related to changes in margin. Section IV
reports estimates of the parameters of our model, finding
evidence favoring the hypothesized negative relation with margin
changes.
This suggests that exchanges seek to control
nonperformance risk through the setting of margin.
summarizes the paper.
2
Section V
II. The Impact: of Margin Changes on Market Performance
This section examines three possible impacts from changes in
margin requirements: futures return volatility, cash return
volatility, and futures market participation.1
Schwert
(1989a,1989b) suggests an iterative approach to examine the
relationship between margin changes and price volatility.
Variations on this approach are used to obtain inferences on the
impact of margin on return volatilities for futures and
underlying cash markets.
The approach is also extended to
examine margin implications for the volatility of volume and
open interest.
A. Description of Data Set
Data used in these preliminary tests are from two contracts
having a history of volatility and margin adjustments: the
Chicago Merchantile Exchange (CME) stock index— S&P— contract
and the Comex Silver contract.
The data are daily observations
of: futures prices, futures volume, open interest, and values of
the underlying cash market index or price.
The sample period
for the S&P contract is June 30, 1982 through November 30, 1989.
The sample period for the silver contract is September 27, 1974
through November 30, 1989.
In both cases, series are
The literature on margin also addresses the issue of
regulatory constraints on credit allocated to speculative
purposes. See for example, Moore (1966) and Luckett (1982).
This issue is not taken up here.
3
constructed for the nearest-to-expiration contract prior to its
delivery month.
As contracts enter the delivery month, the
next-to-nearest delivery month is used.
This sampling procedure
avoids inferences regarding futures markets which are unique to
delivery months.
Margin requirements are from the respective clearing
organizations.
Margin specifications are categorized according
to type of position and time of requirement.
Margins differ
depending on whether the position is speculative or hedging with
the former generally larger.
Margin is required at the time
either type of position is established— its initial margin— and
as accounts are marked to market— its variation margin.
2
Figures 1 and 2 graph required margin amounts for stock
index futures on the their effective dates for each margin
category.
Figure 3 graphs required initial margin amounts for
silver futures on their effective dates.
Margin minimums are
set by the clearinghouse after examining historical volatility
in the cash and futures markets and, when available, ex ante
volatilities implied by option prices.
Margins for both
contracts demonstrate a relation to market events.
Peak margins
in the S&P contract occur during the period beginning October
19, 1987 which coincides with the extreme stock price changes of
2 Only initial margin amounts for the silver contract are
available.
4
that period.
Peak margins in the silver contract appear during
the period when the Hunt brothers attempted to corner the silver
market.
The focus of this section is to associate these margin
changes with some plausible measures of market performance.
Figlewski (1984) points out that clearing members are at
risk when maintenance margin levels are reached.
Their risk
derives from customer failure to comply with calls for margin
made on reaching the maintenance level.
Thus, an appropriate
assessment of exchange risk considers the level of maintenance
margin.
He develops a model for the probability of margin
violations over a given number of days.
His model implies that
maintenance margin levels of 10% or higher provide virtually
sure protection against margin violations at reasonable mean and
variance levels of the stock index.
Comparing Figures 1 and 2, changes in initial margin after
October 1987 are more frequent than changes in maintenance
margin.
This suggests an incompleteness in the model of
Figlewski.
If adjustments to margin are made to control
nonperformance risk, maintenance margin changes should occur at
least as frequently as changes to initial margins.
One
explanation is that changes in initial margin serve additional
purposes.
The tendency of regulators to focus on initial margin
suggests this purpose is to limit entry into the market.
High
initial margins may prevent unsophisticated investors from
opening positions or reduce volatility due to speculation.
5
Gay, Hunter and Kolb (1986) find that margin setting appears
to maintain a constant probability of exhausting margin
balances.
For example, assuming a normal distribution for price
changes, setting margins at two standard deviations of price
change maintains a 5% probability of exhausting margin.
Warshawsky (1989) considers the sufficiency of exchange-imposed
margin requirements to cover price changes.
He finds that
margins on index futures contracts provide sufficient coverage
at the 99th percentile of absolute price changes.
These studies consider risk from the perspective of clearing
members who face losses if margin calls are not met.
Generally,
this perspective provides an insight to the risk faced by the
clearing association and the payments system, but not in the
case of the CME.
The CME uses a gross margining system.
The
difference is that all margin balances are held by the clearing
association.
Other clearing associations operate net margining
systems, holding the net of margins collected from long and
short positions.
For example, clearing members with ten open
contracts— six long and four short— at $1000 margin per contract
must post margin with the association as follows: $10,000 under
gross margining rules [10 x $1000], $2,000 under net rules [(6 4) x $ 1000].
The difference alters the potential liabilities of the
clearing association.
Under both methods, the clearing
association guarantees the performance of each clearing member.
6
All else equal, gross margining rules increase resources
available to the clearing association over that obtained from
net margining systems.
Thus, in terms of the nonperformance
risk faced by the exchange, a given margin amount provides
greater protection in a gross margining system than in a net
margining system.
In terms of the risk that customer margin
calls will not be met, clearing members face identical risks.
B. The Relation Between Margin and Futures-Price Volatility
B.l Tests of the Relation
Schwert (1989a,1989b) suggests a procedure to test the
notion that margin changes influence volatility.
He expresses
the idea as a hypothesis of conditional heteroskedasticity.
Estimation of the hypothesized variance function permits a
simple test for the relevance of margin changes for changes in
volatility.
Using the procedure of Davidian and Carroll (1987),
he begins with two specifications as follows:
Rt
iuit'
-
si=ia iDit +
-
si-i°iD it +
+
s j i i ^ e t-ji
it
+
<*>
<*t
<2>
where R^. is the time-t change in futures prices, D^t are
indicator variables for the months of the year, and u ^ and
are the respective error terms.
The procedure is a generalized
least squares approach iterating on three steps.
7
First, fit
equation (1) to obtain the conditional mean and collect residual
terms.
Second, using the absolute values of these residuals,
fit equation (2).
This gives an estimate of the standard
deviation of ult conditional on the month and past residuals.
Third, these residuals become weights used in re-fitting
equation (1) to produce GLS estimates used for the next round.3
The hypothesis that volatility is conditional on margin
changes is tested by augmenting equation (2) with percentage
margin changes for the period t-12 through t+12 giving:
|ult(
"
2i=la iD i t +
j|e t-j!
+
Sk=-125lkdmt-k +
^lt*
(3)
The coefficients 6 ^ allow inferences on the relation between
leads or lags of margin changes and volatility.
for
Nonzero values
imply that leads or lags of margin changes are related
to volatility.
For k in the interval {-1,-12}, a nonzero value
implies that margin changes are in response to earlier
volatility.
For example, a positive
,
8~
.
X —X
implies that
volatility leads margin changes by one dane day: margins
increase in response to past increases in volatility.
Nonzero
values of k in the interval {1,12} suggest a volatility response
from margin changes.
Thus, a negative
+1 implies that
The monte carlo experiments of Davidian and Carroll (1987)
suggest the procedure provides a fairly robust estimator for
variance functions.
8
volatility lags margin changes: margin increases are correlated
with subsequent volatility.
Table 1 reports sums of these coefficients estimated in the
fifth iteration of the above procedure and tests for their
significance.
Inspecting the change in coefficients after each
iteration, the fifth iteration produces unimportant differences
in coefficients.
(1980)
Test statistics are computed using White's
adjustment for heteroskedasticity.
Estimates are made
separately for changes in speculative or hedging margin required
either initially or as variation margin.
For the S&P contract,
coefficient sums are generally negative, but not significant at
the usual levels and we can reject any relationship between
futures-price volatility and margin changes.
Silver contract
results are uniformly negative, significantly so for lags of
speculative margin changes.
This suggests that the volatility
of these futures prices declines following increases in initial
margins.
To illustrate the result, figure 4 plots the
individual coefficient t statistics on the order of the
lead/lag.
The significantly negative coefficients at lags +4
and +7 weigh most heavily in this result.
Interpreting this in
a Granger-causal sense, increases in margin decrease volatility
4 The number of negative predicted values from the variance
estimation equation is another indication of convergence.
This number declines after each iteration. In each case this
number was zero at the fifth iteration.
9
with the bulk of the impact on volatility coming on the fourth
and seventh trading days following the margin increase.
The negative signs of the sums of leads and lags for both
speculative and hedging positions suggest more is happening.
Retaining the previous Granger-causal perspective, negative lead
coefficients imply volatility falls prior to margin changes.
This seems to obviate the need for changing margin.
The margin
change might instead be regarded as part of an overall policy
intended to reduce volatility.
This interpretation may be
particularly apt given exchange intervention in the silver
contract to reduce the impact of an apparent corner by the Hunt
brothers.
To investigate this possibility, the procedure was
re-run for the post-corner period.
For this subsample, t
statistics for speculative positions were: leads -.68, lags 1.51, leads and lags -1.55.
For the hedging positions these
were: leads -.12, lags -1.39, leads and lags -1.07.
The general
decline in t statistics for the post-corner period appears to
weaken the relationship between margin changes and volatility
suggesting other exchange interventions did play a role in the
earlier period.
The evidence suggests exchange intervention in
the cornered silver contract of late-1979 and early 1980 did
5 Barnhill and Powell (1981) describe exchange interventions in
the silver contract performance during this period. Following
their description of exchange interventions, we begin the
post-corner sample after May 31, 1980.
10
precede a decrease in futures-price volatility.
This
intervention included substantial margin increases.
After this
period, margin changes do not appear to play a role in the
determination of futures price volatility.
B.2 Comparison to Previous Research
Much of the investigation of the relation between margin
requirements and volatility concentrates on stock markets.6
The
impact of margin changes on futures prices generally finds no
link between futures margins and futures volatility.
A 1967 report prepared for the Economic Research Service
[hereinafter cited as ERS (1967)] of the Department of
Agriculture studies the impact of speculative margin policy for
grain contracts during the period 1948-1966.
The impact from
changes in initial margin requirements for speculative positions
depends on the amount of change.
The large margin changes
during the earlier portion of the sample period are negatively
related to daily price ranges, suggesting reductions in
volatility.
The effect of the smaller margin changes occuring
Largay (1973), Largay and West (1973), Eckhardt and Rozoff
(1976), Hardouvelis (1988,1989) examining U.S stock markets
and Hardouvelis and Peristiani (1989) examining Japanese stock
markets find a negative relationship between margin changes
and stock price volatility. Grube, Joy and Panton (1979) find
a d a positive relation. Other researchers find no relation.
These are: Officer (1973), Ferris and Chance (1988), Kupiec
(1989), Schwert (1989a,1989b), Hseih and Miller (1990),
Salinger (1989) and Kumar, Ferris and Chance (1990).
11
after 1948 is less clear.
Most of the effect (which is
positive) appears to be limited to changes followed by important
events subsequent to the margin change.
Hartzmark (1986) examines price volatility for twenty-five
days before and after thirteen instances of changed margin in
wheat, cattle, pork bellies and US bonds.
Volatility is
measured as the squared absolute value of price changes.
Volatility comparisons are made with F statistics.
He finds
volatility increasing in eight of the thirteen cases, but not
significantly at usual levels.
7
One significant decrease in
volatility is found in the June 17, 1981 increase in margin for
the wheat contract.
C. The Relation Between Margin and Cash-Price Volatility
C.l Tests of the relation
These tests are similar to those of the previous subsection.
We begin with the specifications:
7
Indeed, using a simple sign test the number of volatility
increases suggests a positive relation between margin and
volatility. For the null of a negative relation between
margin changes and volatility, no more than three positive
cases is required for the five percent level of significance.
The eight reported positives are better than two standard
deviations above the number required for a negative relation.
12
r.
lu2t'
=
u 2t
zi^ia iD it
"
Si-l“ iD it +
+
(4)
^-IZ^k^-k +
"2f
(5)
where r^. is the cash market rate of price change and u2^. is an
error conditional on the calendar month and previous rates of
return.
Iterating as before, $2k measures the impact of changes
in futures margin on cash market volatility.
Table 2 reports results from these regressions.
For the
stock-index samples, there is no evidence of a relationship at
the five percent level of significance.
At slightly lower
levels of significance, the evidence favors a positive relation
for lagged margin changes: increasing margin implies higher
cash-market volatility.
Figure 5 plots individual coefficient t
statistics on the order of the lead/lag.
Comparing volatilities
before and after the period of the margin change indicates a
persistent positive relationship with margin changes following
the margin change.
Results for speculative silver margins differ from the
pattern for futures volatility.
At the 10% level of
significance, the evidence favors an increase in cash-price
volatility prior to changes in initial margin for speculative
silver contracts; Table 1 reports a negative, but insignificant
relationship between futures price volatility prior to a margin
13
change.
Margin changes appear to precede decreases in
volatility for both the futures contract and its corresponding
cash market.
Increases in initial hedging margins appear to be
unrelated to cash market volatility.
To investigate the
importance of the Hunt brother episode, a subsample for the
post-corner period was constructed.
The t statistics for summed
regression coefficients of initial speculative margins are:
leads .37, lags 1.75, leads and lags 1.50.
For the hedge
positions these are: leads -1.19, lags -.05, leads and lags .87.
For the subsample, the pattern is comparable to results
from the S&P contract.
statistics.
Figure 6 plots individual coefficient t
The pattern is similar to that for S&P cash
volatility— margin increases are positively related to increased
cash market volatility.
Thus, omitting the results which
include the Hunt episode, the evidence from both contracts
appears to slightly favor an increase in cash price volatility
following increases in speculative margins.
The evidence does
not support a relation between hedging margins and cash price
volatility.
C.2 Comparison to previous research
Several researchers compare price volatility of cash assets
preceding and following introduction of related futures
contracts.
Working (1960) finds a reduction in cash price
volatility associated with the level of open interest in onion
contracts.
Gray (1964) cites evidence of a decline in potato
14
price volatility after introduction of futures contracts in that
commodity.
Edwards (1988) finds lower volatility for the S&P
500, the Value Line index, the Tbill and 90-day Eurodollar
contracts except during 1987 and on expiration days of the
stock-index contracts.
Harris (1988) finds increased volatility
for individual stocks included in the computation of the S&P
Q
index.
Damodaran (1990) finds modest increases in cash market
volatility following the introduction of S&P500 futures
contracts.
The increase appears to be in systematic risk.
He
also reports evidence of higher trading volume in stocks
included in the index.
Kupiec (1990) conducts two tests for changes in stock index
volatility from margin changes in the S&P contract.
First,
regressing index volatility on margin rates he finds a positive
association between volatility and margin rates.
Second, he
regresses intraday volatility on lags of volatility and margin
rates, finding a positive association for the one-day lag of the
margin rate.
The sum of the lag coefficients is not significant
suggesting the effect on volatility is short-term.
Further,
specifications including lags of rates of price change produce
insignificance for the margin rate coefficients.
Kupiec
interprets this as adjusting for the changes in return variance
Q
This result corresponds to the higher volatility found in S&P
stocks during the October 1987 market break. See Blume,
Mackinlay and Terker (1989).
15
which have been found to accompany price declines.
Thus, the
positive relation between margin change and volatility appears
to be spurious. Both results are consistent with prudential
.
.
9
setting of futures margins.
The results of our tests conform with those of Kupiec with
the exception of those for hedging margin changes.
Figures 2
and 3 suggests that hedging and speculative margin changes are
generally coincident.10
for the reasons
If the positive association is spurious
Kupiec suggests, hedging margin changes should
also enter significantly with the same sign.
Hedging margin
changes are not significant and in two cases, S&P variation
margin and silver initial margin, differ in sign from results
for speculative positions.
Thus, while the evidence is not
particularly strong, it does suggest that speculative margin
changes are positively related to subsequent cash market
volatility.
Somewhat troubling is the reported lack of evidence of
variance persistence. Both Chou (1987) and Kupiec (1989) find
persistence in conditional variances.
1 For the S&P contract, concurrent changes in initial margins
for hedging and speculative positions occurred six times.
There were 15 changes in speculative margin and 11 changes in
hedging margin. S&P maintenance margins were concurrently
changed 10 times. There were 10 changes in speculative
margin and 11 changes in hedging margin. For the silver
contract, initial margins changed concurrently 108 times.
There were 116 changes in speculative margin and 108 changes
in hedging margin.
16
D. Examination of Some Relations Between Margin and Volume
D.l Tests of the relation
Additional measures of market performance are examined for
relationships with margin changes.
Two of these are the changes
in the level of futures-market and cash-market volume.
Volume
levels are often used as measures of market participation.
Clearly, inferences drawn from volume evidence rely on the
indirect association between volume and participation.
For
example, reductions in the number of participants may be offset
by increased trading activity of those who remain.
Nevertheless, changes in volume associated with changes in
futures margin might imply that the relative cost of trading has
changed.
For example, if maintaining margin balances is costly,
an increase in futures margin might make the relative cost of
trading in the cash market more favorable.
Thus, increases in
futures margin should be negatively associated with changes in
futures market volume and positively associated with changes in
cash market volume.
To examine these possibilities the following specifications
are used:
dV ft
2i-la iD it
+
s A b jd v ft-j+
2 k~lrf 3j?"t-k +
V £t
(6 )
.12
dvCt -
2i-la iD it
+
K
2 j=lb ^ V ct-j +
17
12
2 k— 1# 41?” t-k +
v ct
(7 )
where dV^t and dVct are the changes in volume at t for,
respectively, the futures market and the cash market.
Our
volume measure for the futures contracts are those reported by
the exchange for the nearest-to-expiration contract.11
Cash
market volume for the stock market is total volume on the New
York Stock Exchange.
This volume figure encompasses trading in
most of the stocks included in the Standard and Poor's index.
The figure also includes trading in stocks listed on the NYSE
but not included in the S&P 500.
Our results may be biased if,
for example, margin changes were to differentially impact
trading in the S&P stocks.
trades are not available.
Volume figures for cash silver
Tables 3 and 4 report these results.
In no case, do we find evidence supporting a relation between
margin changes and volume in the futures or cash markets.
The method used previously to examine futures and cash
return volatility was also used to examine the relation between
the volatility of volume and margin changes.
The volatility of
futures volume can be used as a measure of the risk of market
thinness.
Increases in the volatility of volume suggest a
greater risk that investors will encounter a thin market.
A
relationship between past margin changes and volume volatility
As before, contracts entering their expiration months are
replaced by the next-to-nearest expiration month.
18
would then imply changes in this risk.
from these tests.
Table 5 reports results
The evidence does not support a relationship.
This series of tests can be summarized as finding no support
for a volume impact.
Thus, results from these indirect measures
of participation would imply no changes in futures or cash
market participation can be attributed to changes in margin.
D. 2 Comparison to previous research
ERS (1967) find that margin changes are negatively related
to volume.
Fishe and Goldberg (1986) and Hartzmark (1986) find
reductions in open interest for nearby contracts following
margin increases.
Presumably, at some level, reduced open
interest would impact trading volume, Hartzmark (1986) is unable
to confirm an impact on volume.
Fishe and Goldberg (1986)
report ambiguous results linking margin and volume.
They find
significant changes in three-day average volume following margin
changes, but no significance for five-day average volume.
E. Examination of Some Relations Between Margin and Open
Interest
E.l Tests of the Relation
Open interest figures state the number of contracts
outstanding at the close of trading.
The measure provides an
alternative measure of market participation.
We examine the
effect of margin changes on open interest as another route to
obtain insight on the role of margin in the determination of
market participation.
Following the previous method we define:
19
doft "
s i=la iD it
+
sA b ^ ° f t - j +
w
E ki-lf 5 ^ t-k +
ft
(8 )
where dOft are changes in open interest at time t.
Open
interest is for the nearest-to-expiration contract save for
contracts entering their expiration months.
results.
Table 6 reports the
We find no evidence of linkage between margin changes
and the level of open interest for any of the samples.
As before, volatility of open interest might indicate the
risk of market thinness.
To examine the impact of margin
changes on the volatility of open interest we again use the
method of Schwert.
Table 7 reports the results.
For the S&P
contract, we find evidence of an increase in open interest
volatility following changes in margin.
coefficient t statistics.
Figure 7 plots the
The pattern suggests the bulk of the
response occurs within two periods of the margin change.
This
result is not corraborated in the silver contract.
E .2 Comparison to previous research
Fishe and Goldberg (1986) and Hartzmark (1986) find
reductions in open interest for nearby contracts following
margin increases.
This result is consistent with a higher cost
of trading.
20
F. Some Anecdotal Evidence and Summary
Evidence can also be obtained from specific instances of
margin increases.
Figlewski (1984) reports that in 1965 the
Johnson Administration requested margin increases in the Comex
copper contract.
After a series of margin increases amounting
to more than a 300% increase in margin, volume on the contract
declined from 832 contracts in November to 260 in January.
The
final days of trading in the Mexican Peso contract at the CME
illustrate an alternate link between margin and volume.
After
the depreciation of the peso in 1985, the CME raised margins to
100% of contract value.
Trading in the contract persisted.
The
explanation for this continued trading is that maintaining
margin balances provided a way to circumvent Mexican
restrictions on currency exports. 12
This anecdotal evidence urges a cautious interpretation of
the correlation evidence reported in the previous subsections.
The common feature of these anecdotes is the extreme changes
made in margin requirements.
Since extreme changes are unusual,
sample sizes limit our ability to draw inferences from these
cases.
In the realm of usefully sized samples, our evidence
supports three conclusions.
First, in the silver contract we
find a negative relation between futures margin and futures
I am indebted to John Davidson of the CME Clearing House
Division for this story.
21
volatility in samples which include exchange intervention
through margin rules as well as other forms.
This evidence is
not corraborated by the results from the S&P contract, nor in
the silver contract when margin is the principal mechanism for
exchange intervention.
Second, we find modest evidence that cash market volatility
increases with speculative margin changes.
This phenomena does
not appear to be explained along the lines offered by Kupiec
(1989).
Third, we find no evidence of a volume effect from
margin changes in either the mean or volatility.
The
examination of open interest suggests an increase in the
volatility of open interest following margin changes, but no
relation between the level of open interest and margin changes.
III. A Cost-of-Carry Specification Incorporating Nonperformance
Premiums
A. Forces Affecting Compensation for the Risk of Nonperformance
This section examines the relationship between margin rules
for futures contracts and the cash-futures basis.
The cost-of-
carry model implies that prices for futures contracts eliminate
any arbitrage profits from simultaneously held futures and cash
positions.
Observed differences in these prices are, therefore,
interpreted as market-determined compensation for the marginal
costs of holding these positions.
These costs include the
riskless rate used to finance the position, the net of any
convenience yields obtained from holding the good and its
22
storage costs, and, lastly, compensation for nonperformance on
the futures contract.
The nonperformance premium is featured in this section.
Kane (1980) emphasizes the role of nonperformance in the
determination of futures prices.
Futures contracts are
executory contracts; that is, contracts specifying terms which
must be executed by parties to the contract.
Failure to live up
to these specifications is termed nonperformance.
Since
nonperformance imposes costs on the counterparties to open
contracts, the risk of nonperformance should be compensated.
Brennan's (1986) Theory of Efficient Contract Design argues that
competition between exchanges results in contracts which
minimize these costs.
Exchanges minimize nonperformance costs through two jointly
determined routes.
First, exchange guarantees of contract
performance involve the exchange clearing members in each
futures contract as third-party guarantors.
describes the form of these guarantees.
Edwards (1982)
Clearing members
guarantee the performance of their matched long and short
positions.
Exchange clearinghouses guarantee the performance of
the net positions of each clearing member.
Since all trades
must be conducted through clearing members, all contracts traded
on the exchange involve a third-party guarantor.
As a second route to minimizing nonperformance costs,
exchange rules committees alter contract specifications.
23
Contract nonperformance is rational only when losses from
futures positions exceed the wealth of the contractholder.
Margin requirements play a key role in controlling
nonperformance risk.
risk in two ways.
Margin reduces exposure to nonperformance
First, these balances reduce nonperformance
risk by assuring the availability of a minimum level of wealth.
Second, delays in posting margin signal clearing members of the
potential liquidity problems of its clients.
Combining these
separate roles, margin balances provide a mechanism to assess
and manage exchange exposure to nonperformance.
Increasing
margin requirements decreases the potential liability of the
exchange to cover losses.
B. A Cost-of-Carrv Model for Nonperformance Premiums
The cost-of-carry model developvelops the futures price from
the cost of holding the underlying asset to delivery of the
futures contract. Absent arbitrage opportunities, the futures
price at t for a contract delivering the underlying good or
asset at T is:
f(T,t)
-
P(t)exp{Efc(r+s-c+n)r + € t ^
(8)
where f(T,t) is the futures price at t delivering the underlying
good or asset at T, P(t) is the cash market price at t, Efc() is
the expectations operator conditional on information available
at t, e.
is the time-t error which is fully realized at time
T, and at continuously compounded annual rates:
24
r
= the riskless rate of interest
s
= the cost of storing the good
c
= the convenience yield obtained by holding the good
n
= the nonperformance premium.
Finally, r is the number of years until contract expiration;
that is, (T-t)/365.
Equation (4) is useful for its insight into the
determination of futures prices.
For example, the variables r,
s, and n are regarded as relevant costs to agents doing business
in the underlying good or asset.
The variable c would be
regarded as a revenue source.13
From the discussion in the previous subsection, n is related
to the level of margin denoted as M and nonperformance risk
denoted
a.
Thus, n=n(M,a) with sn/5M<0 and sn/Ser>0.
Thus,
increasing margin decreases market-determined compensation
required for nonperformance risks while increases in
nonperformance risk increase required compensation for this
risk.
Fishe and Goldberg (1986) use an options framework to
express a similar point.
They note that nonperformance of a
futures contract can be regarded as putting the contract to the
Interestingly, a positive convenience yield implies the
marginal price setter is not a pure speculator. Since
convenience yields decrease the cost of holding the position,
agents having a business purpose for inventories of the good
will have lower carrying costs.
25
exchange.
Clearinghouse guarantees require the clearing members
of the exchange to make good on the contract.
(1989)
Bailey and Ng
further develop this insight to examine changes in
nonperformance premiums for exchanges experiencing substantial
increases in nonperformance risk.
We use this insight to
motivate an investigation into the relation between margin and
cost of carry.
One period later, the cost of carry relation will be
/ (T,t+1)
=
P(t+l)exp{Et+1(r+s-c+n)r(-l)+ e t+1^
(9)
where r(-l) is the number of years under contract expiration
after one period.
Taking logs, subtracting equation (8) from
equation (9), and re-arranging gives
lo a f£ iS it± U )
■L^ 1 P(t+i) '
+
{E^.+1 (r+s-c+n) - Et(r+s-c+n) }r
-
Et+1(r+s-c+n) r
+
Ct+1,T
“
^
et ,T*
The LHS and first term on the RHS are the continuously
compounded bases at, respectively, time T+1 and t.
The second
term on the RHS is the difference in expected cost of carrying
the position over the period t to t+1.
The third term on the
RHS is the negative of the time t+1 cost of carrying the
position.
The last two terms are the errors.
26
Defining B(T,t) as the log basis at time t for a contract
expiring at time T, we estimate equation (10) as follows:
B(T,t+l)
-
pQ
+
+
+ jS4lxt +
et+1
where hfc is the holding period in years from t to t+1.
model
(11)
From the
gives the relationship of the basis at t+1 to the prior
period basis.
p2
is an estimate of the relation between
riskfree rates of interest and the basis.
borrowing opportunities, ^2==1'
in margin.
With riskless
^3 re^ates the basis to changes
Increases in margin should lower any nonperformance
premiums incorporated into the market's determination of basis.
Thus, margin changes should be negatively related to changes in
basis.
£4 is our estimate for s-c under the assumption that the
net of storage costs and convenience yields is constant.
The error term, e^+1, includes the remaining terms of
equation (10).
This includes the difference in expected costs
of carry and the difference in realized errors.
Changes in
expectations cannot persist over long periods, thus the mean of
changed expectations are zero.
Nevertheless, expected costs of
carry might well vary systematically over the lives of futures
contracts.
components.
For example, convenience yields might have seasonal
Such seasonality would suggest autocorrelation at
lags of e^+1.
The difference in the error terms of equation (10) implies
an MA(1).
Combining these inferences for the error term
27
suggests that estimation of equation (11) must use an ARMA(p,l)
model for the process where p is determined from the data.
IV. Estimates of the Cost-of-Carry Model
A.
Description of the Data Set
The previously described data set is augmented with daily
cash market prices used to compute the basis.
Riskfree rates of
interest are from the Federal Reserve Bank of New York.
This
series is described as a three-month Treasury Bill series.
Since three-month maturity bills are not issued daily, actual
maturities depend on the day of the week.
Monday bills are
"same-day" quotes obtained from dealers for bills issued the
previous Thursday, maturities are 86 days.
Tuesday and
Wednesday bills are Thursday "when-issued" bills auctioned on
Monday, maturities for both are 91 days.
Thursday and Friday
bills are "next-day" quotes obtained from dealers for 91-day
maturities issued on Thursday, maturities are, respectively, 90
and 89 days.
Bill rates used in our specifications are
converted to continuously compounded annual rates calculated as
follows:
rt
log(l
____l ______
“
qt
365 .
dtm” ) ( dtm”'
36000
where qfc is the quoted discount rate and dtm is the days to
maturity as determined by the day of the week for each quote.
28
B. Regression Results
Equation (11) was estimated for an MA(1) with a variety of
autoregressive lags included.
Model selection was determined by
examining residual autocorrelations from each.
Including lags 2
and 8 for the S&P contract and lags 2, 7 and 8 for the Silver
contract seems appropriate.
Box-Ljung Q(k) statistics were
calculated to detect autoregressive problems through the twelfth
lag.
At the twelfth lag the critical value for the five percent
level is 21.03.
None of the Q(12) statistics exceed this
critical value.
Table 8 reports results from the cost of carry model for the
S&P and silver contract for the available margin categories.
Results are consistent across the margin categories.
Panel A reports the results for the S&P contract.
implies the intercept is zero,
pQ
The model
is well within two standard
errors of zero,
p^
significant.
is greater than one and the difference is sign
ificant.
p2
is less than one and the difference is
The model implies the
p^
coefficient equals one if
positions can be financed at riskless rates of interest,
p^
is
negative and differs reliably from zero for all but the initial
speculative margin category where it does not’differ
significantly from zero.
The evidence suggests that
nonperformance premiums are negatively related to changes in
margins.
p
estimates the average net of convenience yield and cost
29
of carry.
These estimates do not differ reliably from zero.
Convenience yields for financial assets are the return to
holding the asset.
This yield should equal its cost of carry,
else an arbitrage opportunity exists.
asset a zero value for
p^
Hence, for a financial
is consistent with zero arbitrage
opportunities.
Estimates of the cost-of-carry model for silver contracts
are reported in Panel B.
Again using the intercept as a
specification check, estimates of
pQ
are more than four standard
errors from zero. This result implies a persistent return in
excess of the costs included in the specification from holding a
hedged position in silver.
The post-corner subsample dating
from May 31, 1980 yields similar results.
The evidence from the
intercept estimates is inconsistent with zero arbitrage
opportunities.
^
is less than unity, falling much below the estimates
obtained from the S&P contract.
p2
exceeds unity and is much
larger than coefficients from the S&P contract,
p^
is negative
for both hedging and speculative positions; significantly so,
for speculative positions.
The negative relation between margin
and compensation for nonperformance risk repeats results from
the S&P contract,
p^
is significantly negative for both
speculative and hedging positions suggesting the net of
convenience yield and storage costs is negative.
C. Comparison to Previous Research
30
Fama and French (1987) investigate cost of carry models for
a variety of commodity futures contracts using monthly
observations on twenty-one contracts.
Their specification
includes 12 dummy variables which control for monthly seasonals
and an interest rate variable.
They obtain coefficients on
interest rates ranging from -4.32 to 2.71.
None of the reported
coefficients, however, differ significantly from one.
Averaging
coefficients across the contracts they study gives an average
interest-rate coefficient of 1.06.
Bailey and Ng (1989) use a cost of carry model to interpret
changes in nonperformance premiums.
They use an event-study
approach to investigate innovations in the excess of the basis
over the riskfree rate for contracts trading on distressed
exchanges.
They find increases in these excess returns which
coincide with announcements indicating increased likelihood of
exchange failure.
Hirshleiffer (1988) links transactions costs to residual
risk premiums.
His model predicts that increased transactions
costs reduce market participation by speculators.
Hedgers
respond by compensating speculators for portions of their
residual risk.
Margin balances are frequently argued to represent a cost of
transacting futures.
Thus, the percentage changes in margin
included in our cost of carry specification might be interpreted
as capturing this residual risk premium.
31
However, one would
expect to see some evidence of a change in market participation.
Our previous investigations on the effect of margin changes on
market participation suggest no change in the level of
participation.
Further, one would expect to find this premium
only in specifications which include changes in speculative
margin.
This suggests that we are more likely to be capturing
changes in nonperformance premiums.
V. Summary
Linkages between market performance and margin
specifications for futures contracts on the S&P index and silver
are investigated.
results.
Our series of causality tests finds three
First, in the silver contract we find a negative
relation between futures margin and futures volatility in
samples which include exchange intervention beyond setting
margin.
This evidence is not corraborated by results from the
S&P contract nor in the silver market when exchange intervention
principally involves margin setting.
Second, we find modest
evidence that cash market volatility increases with speculative
margin changes.
Third, we examine several measures of market
participation.
In this series of tests, we find evidence that
margin changes precede volatility in open interest for the S&P
contract.
This result is not corraborated by the silver
contract.
This might suggest an increased risk that traders
will encounter a thin market.
Such a risk would suggest
increases in bid-offer spreads for futures contracts as
32
opportunities to unwind contract positions become less certain.
Other market participation measures are examined, these are:
volume of futures trading, volume of cash market trading,
volatility of futures volume, and levels of open interest.
Examination of margin links to these other market participation
measures leads us to reject any link.
A model is developed linking the cost of carrying the cash
asset with the risk of nonperformance.
We argue that
nonperformance risk should diminish when margin increases.
This
implies that compensation for nonperformance risk should be
negatively related to the level of margin.
Estimates of the
model are generally consistent with the model— margin changes
are negatively related to basis when other costs of carry are
included.
The results have implications for policy makers.
Links
between margin changes and the volatility of futures prices are
absent.
Margin appears to be an ineffective tool for
controlling futures market volatility.
Our results imply that
changes in futures market margin are positively related to cash
market volatility.
be perverse.
Indeed,
the effect of changing margin may
Our evidence suggests that margin changes are
positively related to volatility in the cash market.
On the other hand, our results suggest that the margin
specifications of futures exchanges do impact nonperformance
risk.
Thus, potential losses from clearinghouse guarantees of
33
performance serve to motivate exchanges to control
nonperformance risk.
The margin-setting behavior of the
exchange obtains a positive externality— residual nonperformance
risk borne by holders of futures contracts is reduced.
34
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38
Table 1
Relation of Futures Price-Change Volatility
with Margin Requirements
'ul t '
-
s i= l“ iDi t +
Futures P o s itio n
t-j
-
I n i t i a l Marain
s s ik
T- s t a t i s t i c
12*lkdmt - k +
" It
V a ria tio n Maroin
S 6 lk
T"s t a t i s t i c
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
-.0 0 0 0
-.0 0 0 4
-.0 0 0 4
- .0 3
-1 .0 6
- .7 7
-.0 0 0 2
-.0 0 0 1
-.0 0 0 3
- .5 0
- .1 6
- .4 6
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
(k— 1 . . 12 ;1 . .12)
.0001
-.0 0 0 3
-.0 0 0 2
.16
- .6 7
- .3 7
-.0 0 0 4
.0003
-.0 0 0 2
-1 .2 0
.74
- .3 1
S p e c u la tiv e S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; 1 ..12)
-.0 0 0 1
-.0 0 0 2
-.0 0 0 4
-1 .2 1
-2 .2 6 *
-2 .4 5 *
Hedging
le a d s
la g s
le a d s
-.0 0 0 3
-.0 0 0 1
-.0 0 0 4
-1 .4 2
- .6 7
-1 .5 6
S ilv e r
(k— 1 ..- 1 2 )
(k = 1 ..1 2 )
& la g s
(k— 1. .12;l. .12)
* s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
39
Table 2
Relation of Cash Price-Change Volatility
with Margin Requirements
lU2 t'
“
Si = l “ iDi t +
Futures P o s it io n
S j = 3 ^ U t-J
+
^ --^ S k ^ t-k +
i n i t i a l Marg in
S5
T -s ta tis tic
S p e c u la tiv e S&P
le a d s (k = -1 ..^ 1 2 )
la g s (k=*1..12)
le a d s & la g s
( k = - l ..1 2 ? 1 ..12)
-.0 0 0 2
.0004
.0003
- .5 9
1 .69
.78
Hedging S&P
le a d s ( k = - l . .-1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . .1 2 j l . .12)
.0000
.0004
.0004
.16
1.34
1.0 8
S p e c u la tiv e S ilv e r
le a d s ( k = - l . .-1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
.0002
-.0 0 0 6
-.0 0 0 4
-4 .0 9 *
-1 .7 3
Hedging S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
-.0 0 0 0
.0004
.0004
- .1 8
.65
.56
vay l at l gn .Mar g in
S5
T -s ta tis tic
.0001
.0004
.0004
-.0 0 0 2
.0001
-.0 0 0 0
1.66
* s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W hite’s (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
40
^ 2t
.29
1.62
1 .36
- .7 4
.52
- .1 5
Table 3
Relation of Futures Volume Levels with Margin Requirements
dvf t -
2 “ l a i Di t
Futures P o s itio n
+
z j ^ j dvt t - j +
2 k = -l^ 3 $ m t - k +
v ft
I n i t i a l Margin
V a ria tio n Margin
2S3k T' • s t a t i s t i c
25 3k
T -s ta tis tic
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s ( k -1 ..1 2 )
le a d s & la g s
(k— 1. .1 2 ;1 . .12)
-.4 5 5 0
-.6 5 7 2
-1 .1 1 2 2
- .1 8
- .2 7
- .3 2
.4693
-.3 0 6 5
.1628
.22
- .1 5
.06
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
(k— 1. . 1 2 ; l . .12)
.6638
-.3 5 5 3
.3084
.27
- .1 5
.09
.4928
-.2 6 7 2
.2256
.26
- .1 4
.08
S p e c u la tiv e S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k - 1 ..1 2 )
le a d s & la g s
( k = - l..1 2 ; 1 . .12)
-1 1 .1 2 1 3
10.9652
-.1 5 6 2
- .4 9
.48
- .0 1
Hedging S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k * 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
-2 0 .0 1 4 0
15.2325
-4 .7 8 1 5
- .6 8
.52
- .1 2
* s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
41
Table 4
Relation of Cash Market Volume Levels with Margin Requirements
dvc t -
s i = i a i Di t
Futures P o s it io n
+
E A b jdVc t - j +
s k = - l $ 4$® t - •k +
v ct
I n i t i a l Margin
V a r ia tio n Margin
25 4k T“• s t a t i s t i c
25 4k
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . .1 2 ; 1 . .12)
.3950
-.3 0 5 1
.0898
.68
- .5 3
.11
.2032
-.3 4 2 3
-.1 3 9 1
.41
- .7 0
- .2 0
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s (k==1..12)
le a d s & la g s
(k— 1. .1 2 ;1 . .12)
.3154
-.5 3 3 4
-.2 1 8 0
.55
- .9 3
- .2 7
.5616
-.4 0 2 4
.1592
1 .2 6
- .9 1
.25
* s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
42
T‘- s t a t i s t i c
Futures P o s itio n
I n i t i a l Margin
5k T - s t a t i s t i c
■k+
ft
i
s
>§
+
Ul
t-J
2 i= l0t iD i t +
*
|u 5 t'
II H
I to
H
Table 5
Relation of Futures-Volume Volatilities with Margin Requirements
^5t
V a ria tio n Margin
S* 5 k
T‘- s t a t i s t i c
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s ( k = l . .12)
le a d s & la g s
( k = - l . . 1 2 ; 1 . .12)
-.0 1 0 1
-.0 0 3 3
-.0 1 3 4
- .1 6
- .0 5
- .1 5
.0545
-.0 1 5 6
.0388
.79
- .2 3
.40
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s ( k = l . .12)
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
.0361
-.0 9 9 0
-.0 6 3 0
.47
-1 .3 2
- .5 9
-.0 0 6 1
.0249
.0188
- .1 2
.51
.27
S p e c u la tiv e S ilv e r
le a d s ( k = - l..- 1 2 )
la g s
( k = l . .12)
le a d s & la g s
(k— 1. .12 j l . .12)
.0714
-.0 9 8 2
-.0 2 6 8
.67
- .9 2
- .1 8
Hedging S ilv e r
le a d s ( k = - l..- 1 2 )
la g s ( k = l . .12)
le a d s & la g s
(k = -l. .1 2 H . .12)
.1365
-.0 3 7 2
.0993
1.25
- .3 4
.64
s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
43
Table 6
R e la tio n o f Open I n t e r e s t w ith Margin Requirem ents
2 i-ia iD it
doft -
F utures P o s itio n
Enter Table Data
+
+
I n i t i a l Margin
6k T- s t a t i s t i c
E
t-k +
w ft
V a r ia tio n Margin
25 6k
T"• s t a t i s t i c
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
(k— 1. . 1 2 ; l . .12)
.3658
.1516
.5175
.39
.17
.40
-.0 2 4 1
-.0 6 2 8
-.0 8 6 9
- .0 3
- .0 8
- .0 8
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; 1 . .12)
-.0 2 0 4
-.0 1 9 9
-.0 4 0 4
- .0 2
- .0 2
- .0 3
-.0 4 5 2
-.1 3 0 6
-.1 7 5 9
- .0 6
- .1 9
- .1 8
S p e c u la tiv e S ilv e r
le a d s (k— 1. .-1 2 )
la g s (k**l.. 12)
le a d s & la g s
(k = -l.. . 1 2 ; l . .12)
-1 .8 3 6 5
-1 .4 2 5 7
-3 .2 6 2 2
- .0 6
- .0 4
- .0 7
-1 5 .7 8 5 9
.3577
-1 5 .4 2 8 3
- .3 8
.01
- .2 6
Hedging
le a d s
la g s
le a d s
S ilv e r
( k = - l..- 1 2 )
( k - 1 . .12)
& la g s
(k— 1. .12|1. .12)
•ft
s i g n i f i c a n t l y d i f f e r s from zero a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
44
Table 7
Relation of Open Interest Volatility with Margin Requirements
'U7 tl
-
t-j1 +
2 i= l“ iDi t +
Futures P o s itio n
2 k i - l l 7&m t - k +
I n i t i a l Margin
V a ria tio n Margin
25 7k T‘ s t a t i s t i c
26
S p e c u la tiv e S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
(k— 1 . . 1 2 ;1 . .12)
-.0 0 3 0
.0148
.0118
Hedging S&P
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; 1 . .12)
.0007
.0291
.0298
S p e c u la tiv e S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; l . .12)
.0067
-.0 1 9 1
-.0 1 2 4
.15
- .4 2
- .1 9
Hedging S ilv e r
le a d s ( k = - l..- 1 2 )
la g s (k = 1 ..1 2 )
le a d s & la g s
( k = - l . . 1 2 ; 1 . .12)
-.0 2 3 2
-.0 0 0 7
-.0 2 3 9
- .6 7
.0172
.0298
.0470
1.51
2.66*
2.94*
.06
2.64*
1.89
.0065
.0300
.0365
.69
3.24*
2.77*
- .4 8
a t th e 5% l e v e l .
Note: T - s t a t i s t i c s u se W h ite's (1980) c o r r e c tio n fo r
h e t e r o s k e d a s t ic it y .
45
T -s ta tis tic
- .2 7
1.42
.78
-.02
* s i g n i f i c a n t l y d i f f e r s from
^7t
Table 8
Estimates for Cost-of-Carry Model
B (T ,t+1)
-
pQ + P
^B(T,t) + ) 8 f h t +
+
p ^
+
et+1
Panel A: S&P C ontract
I n itia l
S p e c u la tiv e
Hedging
V a ria tio n
Hedging
S p e c u la tiv e
-.0 0 0 3
(.0 0 0 2 )
-.0 0 0 4
(.0002)
-.0 0 0 4
(.0002)
-.0 0 0 3
(.0002)
.8529
(.0147)
.8934
(.0 1 3 2 )
.8695
(.0140)
.8637
( .0143)
*2
4.6625
(1 .2 3 1 )
3 .3750
(1.1 2 2 )
4.0565
(1.186)
4.2231
(1 .2 0 3 )
*3
-.0 2 5 5
(.0035)
.0018
(.0035)
-.0 1 5 3
(.0027)
-.0 1 8 7
(.0030)
*4
-.1 3 2 8
(.1129)
-.0 4 3 0
(.1067)
-.0 8 5 2
(.1104)
-.1 0 3 4
(.1113)
*0
MA(1)
.33
.39
.36
.35
AR param eters
in clu d ed
2 ,8
2 ,8
2 ,8
2 ,8
Q(12)
18.61
14.66
15.80
11.93
(Standard e r r o r s in p a r e n th e se s.)
46
Table 8— continued
Estimates for Cost-of-Carry Model
B (T, t + 1)
-
+ £ jB (T, t ) +
P f h t +
^dir^ + ^h*.
Panel B: S ilv e r C ontract
I n itia l
Hedging
S p e c u la tiv e
Po
.0037
(.0008)
.0037
(.0008)
P,X
.6450
(.0236)
.6449
(.0234)
P7
14.0775
(3.410)
14.3542
(3.397)
P3
-.0 0 6 4
(.0056)
-.0 1 4 9
(.0044)
-1 .3 1 6 1
(.3235)
-1 .3 3 6 5
(.3224)
17.22
18.48
(Standard e r r o r s in p a r e n th e se s.)
00
Q(12)
.12
CM
AR param eters
in clu d ed
.12
00
MA(1)
to
H
r
1. S&P initial margin requirements
for speculative ana hedge positions
Spec, positions ------ Hedge positions
2. S&P maintenance margin requirements
for speculative and hedge positions
Required margin amount
25000
20000-
15000-
10000-
5000-
o
Jan-82
Dec-82
Nov-83
Oct-84
^
Sep-85
Aug-86
Jul-87
Jun-88
Spec, positions ------ Hedge positions
May-89
Required margin amount
3. Silver initial margin requirements
for speculative and hedge positions
Jan-74Dec-74Nov-75 Oct-76Sep-77 Aug-78 Jul-79 Jun-80May-81 Apr-82 Mar-83 Feb-84 Jan-85 Jan-86Dec-86 Nov-87 Oct-88Sepn89
Spec, positions ------ Hedge positions
T-statistic on lead/lag coefficient
4. Silver futures price volatility
Initial margin on speculative positions
n
LU ,........ n t.J.].n
UUQ... 0
TT
-4-
-^ '-n '-io ' -9 ' -8' -7 ' -6 ' -5 ' -4' -3 ' -2' -1 '
V
1
‘ 1 ' 2 ' 3 ' 4 ' 5 '6 ' 7 ‘ e' 9' l o' l l ' l 2
Order of lead/lag of margin change
T-statistic on lead/lag coefficient
5. S&P cash price volatility
Initial margin on speculative positions
Order of lead/lag of margin change
T-statistic on lead/lag coefficient
6. Silver cash price volatility
Initial margin on hedge positions
T-statistic on lead/lag coefficient
7. S&P open interest volatility
Initial margin on hedge positions
Working Papers and Staff Memoranda
The following lists papers developed in recent years by the Bank’s research staff. Copies
of those materials that are currently available can be obtained by contacting the Public
Information Center (312) 322-5 111.
W o rk in g P a p e r S eries
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
REG IO N A L ECO N OM IC ISSUES
Taxation of Public Utilities Sales: State Practices
and the Illinois Experience
WP-86-1
Diane F. Siegel and William A. Testa
Measuring Regional High Tech Activity with Occupational Data
WP-87-1
Alenka S. Giese and William A. Testa
Alternative Approaches to Analysis of Total Factor Productivity
at the Plant Level
WP-87-2
Robert H. Schnorbus and Philip R. Israilevich
Industrial R&D An Analysis of the Chicago Area
WP-87-3
Alenka S. Giese and William A. Testa
Metro Area Growth from 1976 to 1985: Theory and Evidence
WP-89-1
William A, Testa
Unemployment Insurance: A State Economic Development Perspective
WP-89-2
William A. Testa and Natalie A. Davila
A Window of Opportunity Opens for Regional Economic Analysis:
BEA Release Gross State Product Data
WP-89-3
Alenka S. Giese
Determining Manufacturing Output for States and Regions
WP-89-4
Philip R. Israilevich and William A. Testa
The Opening of Midwest Manufacturing to Foreign Companies:
The Influx of Foreign Direct Investment
WP-89-5
Alenka S.Giese
t
Walking paperseriescontinued
A New Approach to Regional Capital Stock Estimation:
Measurement and Performance
W P-89-6
Alenka S. Giese and Robert H. Schnorbus
Why has Illinois Manufacturing Fallen Behind the Region?
William A. Testa
W P -89-7
Regional Specialization and Technology in Manufacturing
W P-89-8
Alenka S. Giese and William A. Testa
Theory and Evidence of Two Competitive Price Mechanisms for Steel
W P-89-9
Christopher Erceg, Philip R. Israilevich and Robert H. Schnorbus
Regional Energy Costs and Business Siting Decisions:
An Illinois Perspective
W P-89-10
David R. Allardice and William A. Testa
Manufacturing's Changeover to Services in the Great Lakes Economy
W P-89-12
William A. Testa
Construction of Input-Output Coefficients
with Flexible Functional Forms
WP-90-1
Philip R. Israilevich
Regional Regulatory Effects on Bank Efficiency
W P-90-4
Douglas D. Evanoffand Philip R. Israilevich
Regional Growth and Development Theory: Summary and Evaluation
W P-90-5
Geoffrey JD . Hewings
Institutional Rigidities as Barriers to Regional Growth:
A Midwest Perspective
W P-90-6
Michael Kendix
ISSUES IN FIN A N C IA L REGULATION
Technical Change, Regulation, and Economies of Scale for Large Commercial
Banks: An Application of a Modified Version of Shepard's Lemma
WP-89-11
Douglas D. Evanojf, Philip R. Israilevich and Randall C. Merris
2
W orking paper series continued
Reserve Account Management Behavior: Impact of the Reserve Accounting
Scheme and Carry Forward Provision
WP-89-12
Douglas D. Evanojf
Are Some Banks too Large to Fail? Myth and Reality
WP-89-14
George G. Kaufman
Variability and Stationarity of Term Premia
W P-89-16
Ramon P. De Gennaro and James T. Moser
A Model of Borrowing and Lending with Fixed and Variable Interest Rates
WP-89-17
Thomas Mondschean
Do "Vulnerable” Economies Need Deposit Insurance?: Lessons from the
U.S. Agricultural Boom and Bust of the 1920s
W P-89-18
Charles W. Calomiris
The Savings and Loan Rescue of 1989: Causes and Perspective
W P-89-23
George G. Kaufman
The Impact of Deposit Insurance on S&L Shareholders' Risk/Retum Trade-offs
WP-89-24
Elijah Brewer III
Payments System Risk Issues on a Global Economy
WP-90-12
Herbert L. Baer and Douglas D. Evanojf
Deregulation, Cost Economies and Allocative
Efficiency of Large Commercial Banks
WP-90-19
Douglas D. Evanoff and Philip R. Israilevich
Evidence on the Impact of Futures Margin Specifications
on the Performance of Futures and Cash Markets
WP-90-20
James T. Moser
M ACR O ECO N OM IC ISSUES
Back of the G-7 Pack: Public Investment and Productivity
Growth in the Group of Seven
WP-89-13
David A. Aschauer
3
Working paperseriescontinued
Monetary and Non-Monetary Sources of Inflation: An Error
Correction Analysis
W P -89-15
Kenneth N. Kuttner
Trade Policy and Union Wage Dynamics
W P-89-19
Ellen R. Rissman
Investment Cyclicality in Manufacturing Industries
W P-89-20
Bruce C. Petersen and William A. Strauss
Labor Mobility, Unemployment and Sectoral Shifts:
Evidence from Micro Data
W P-89-22
Prakash Loungani, Richard Rogerson and Yang-Hoon Sonn
Unit Roots in Real GNP: Do We Know, and Do We Care?
W P-90-2
Lawrence J. Christiano and Martin Eichenbaum
Money Supply Announcements and the Market's Perception
of Federal Reserve Policy
W P-90-3
Steven Strongin and Vefa Tarhan
Sectoral Shifts in Interwar Britain
W P-90-7
Prakash Loungani and Mark Rush
Money, Output, and Inflation: Testing the P-Star Restrictions
W P-90-8
Kenneth N. Kuttner
Current Real Business Cycle Theories and Aggregate Labor
Market Fluctuations
W P-90-9
Lawrence J. Christiano and Martin Eichenbaum
The Output, Employment, and Interest Rate Effects of
Government Consumption
W P-90-10
S. Rao Aiyagari, Lawrence J. Christiano and Martin Eichenbaum
Money, Income, Prices and Interest Rates after the 1980s
W P -90-11
Benjamin M. Friedman and Kenneth N. Kuttner
Real Business Cycle Theory: Wisdom or Whimsy?
W P-90-13
Martin Eichenbaum
4
Working paperseriescontinued
Macroeconomic Models and the Term Structure of Interest Rates
W P-90-14
Steven Strongin
Stock Market Dispersion and Real Economic Activity:
Evidence from Quarterly Data
W P-90-15
Prakash Loungani, Mark Rush and William Tave
Term-Structure Spreads, The Money Supply Mechanism,
and Indicators of Monetary Policy
W P-90-16
Robert D. Laurent
Another Look at the Evidence on Money-Income Causality
W P-90-17
Benjamin M. Friedman and Kenneth N. Kuttner
Investment Smoothing with Working Capital:
New Evidence on the Impact of Financial Constraints
W P-90-18
Steven Fazzari and Bruce Petersen
5
S ta ff M e m o ra n d a
A series of research papers in draft form prepared by members of the Research
Department and distributed to the academic community for review and comment. (Series
discontinued in December, 1988. Later works appear in working paper series).
Risks and Failures in Banking: Overview, History, and Evaluation
SM-86-1
George J. Benston and George G. Kaufman
The Equilibrium Approach to Fiscal Policy
SM -86-2
David Alan Aschauer
Banking Risk in Historical Perspective
SM -86-3
George G. Kaufman
The Impact of Market, Industry, and Interest Rate Risks
on Bank Stock Returns
SM -86-4
Elijah Brewer, III and Cheng Few Lee
Wage Growth and Sectoral Shifts: New Evidence on the
Stability of the Phillips Curve
SM-87-1
Ellen R. Rissman
Testing Stock-Adjustment Specifications and
Other Restrictions on Money Demand Equations
SM -87-2
Randall C. Merris
The Truth About Bank Runs
SM -87-3
George G. Kaufman
On The Relationship Between Standby Letters of Credit and Bank Capital
SM -87-4
Gary D. Koppenhaver and Roger Stover
Alternative Instruments for Hedging Inflation Risk in the
Banking Industry
SM -87-5
Gary D. Koppenhaver and Cheng F. Lee
The Effects of Regulation on Bank Participation in the Market
SM -87-6
Gary D. Koppenhaver
Bank Stock Valuation: Does Maturity Gap Matter?
SM -87-7
Vefa Tarhan
6
S taff M em oranda continued
Finite Horizons, Intertemporal Substitution and Fiscal Policy
SM -87-8
David Alan Aschauer
Reevaluation of the Structure-Conduct-Performance
Paradigm in Banking
SM -87-9
Douglas D. Evanoffand Diana L. Fortier
Net Private Investment and Public Expenditure in the
United States 1953-1984
SM -87-10
David Alan Aschauer
Risk and Solvency Regulation of Depository Institutions:
Past Policies and Current Options
SM-88-1
George J. Benston and George G. Kaufman
Public Spending and the Return to Capital
SM -88-2
David Aschauer
Is Government Spending Stimulative?
SM -88-3
David Aschauer
Securities Activities of Commercial Banks: The Current
Economic and Legal Environment
SM -88-4
George G. Kaufman and Larry R. Mote
A Note on the Relationship Between Bank Holding Company
Risks and Nonbank Activity
SM -88-5
Elijah Brewer, III
Duration Models: A Taxonomy
SM-88-6
G. O. Bierwag, George G. Kaufman and Cynthia M. Latta
Durations of Nondefault-Free Securities
G. 0. Bierwag and George G. Kaufman
Is Public Expenditure Productive?
SM -88-7
David Aschauer
1
StaffMemoranda continued
Commercial Bank Capacity to Pay Interest on Demand Deposits:
Evidence from Large Weekly Reporting Banks
SM -88-8
Elijah Brewer, III and Thomas H. Mondschean
Imperfect Information and the Permanent Income Hypothesis
SM -88-9
Abhijit V. Banerjee and Kenneth N. Kuttner
Does Public Capital Crowd out Private Capital?
SM -88-10
David Aschauer
Imports, Trade Policy, and Union Wage Dynamics
SM-88-11
Ellen Rissman
8
@FedFRASER