Equity Markets under Stress: Tests for
Arbitrage Anomalies in the Stock-futures Basis*
Joe Ganley
Bank of England

Giorgio Trebeschi
Bank of England

Abstract
World markets in the 1990s appear to have been subject to greater turbulence andto more shocks than hitherto. At the same time we observe a wide variety ofmarket structures and trading platforms. This raises the question of whether, for acommon shock, markets will respond differently. In particular, is it possible torank the performance of different market structures during turbulent trading
conditions? We examine the performance of four equity markets—Frankfurt,
London, New York and Toronto—during the stressful trading conditions of October 1997. We propose six econometric tests for normal index arbitrage between
spot and futures markets. Counter-intuitive results to these tests are classified as“arbitrage anomalies.” A differential concentration of anomalies allows us to rank
the robustness of different markets in response to shocks. Tentatively, the tests
suggest that during October 1997 markets with a larger dealer component sustained the arbitrage link more robustly than others.

1

Introduction

Twenty or thirty years ago most economists might have argued that prices infinancial markets were efficient, fully reflecting all available information andadjusting instantaneously to news. But the gradual emergence of market microstructure ideas questions this, suggesting that the performance of financial mar*
The views expressed are those of the authors and do not necessarily reflect those of the Bank ofEngland. We are indebted to Ravi Pindoria, Jim Hughes, Rachel Charlton, Matt Davies andDalbinder Kalarahi for excellent research assistance. Comments and assistance with the paper werereceived from Ian Bond, Rob Bliss, Dick Brealey, Francis Diebold, Ian Garrett, Gordon Gemmill,
Allison Holland, Jim Mahoney, Paul Mizon, Vicky Saporta, Anne Vila and Ingrid Werner. We are
grateful to them all, but remaining errors are ours, not theirs. Correspondence tojoe.ganley@bankofengland.co.uk.

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Joe Ganley and Giorgio Trebeschi

kets could be “constrained,” at least temporarily, by the way they are set up andorganised. This seems plausible, given the wide variety of actual market structures that can be seen in operation around the world today. Do these all yield identical outcomes, for given shocks? Or can we rank them in some way?
These are important questions, since in recent years there has been a tendency
for organised equity markets to converge on electronic order-books, moving awayfrom traditional dealer structures. What has driven this? There are, from firstprinciples, arguments on the qualities of different market structures. For example,
a classic dealer system should prevent liquidity withdrawal and trading halts intimes of stress, because, on the back of various privileges, market makers are
required to quote continuous two-way prices regardless of market conditions. By
contrast, electronic order-matching systems offer open, non-privileged access,with no requirement that participants remain in the market. This, and other aspects of electronic trading like anonymity, could be problematic—particularly intimes of stress.
There are a number of practical ways of measuring market performance which
we can use to make comparisons of real market structures. A natural episode toevaluate market performance is at times of stress, notably during sharp downward
price movements, such as in October 1987 or October 1997. How well did different markets cope with these disturbances? Several possible measures suggest
themselves, such as the size of price changes, market turnover (relative to desired
trading quantities), or the number of trading halts. But where a futures market
exists, the link between the spot and the futures price—the “stock-futures basis”—is a preferable measure because it is readily observable and embodies a
simple theoretical underpinning, namely arbitrage principles.
Using data from the market correction in October 1997, this paper tests for thearbitrage link in spot and futures prices for the headline stock indices in four
markets—Frankfurt, London, New York, and Toronto. We have chosen theseparticular centres because they allow a number of interesting comparisons. At thesame time we have two North American and two European markets; two “large”
and two “small” markets; and an interesting diversity of trading platforms.
The focus of the paper is on trading over the 10 business days from 20 October to 31 October 1997. Since the Correction occurred on 27 October, we have inthis sample period 5 days of trading under “stress,” and 5 days of “normal”
trading from the week before. We also include, for London and New York, datafrom the October 1987 Crash. These allow us also to assess the impact, not onlyof different market structures, but also of shocks of differing severity. The underlying causes of these shocks are not the concern of this paper. Rather, this is acomparative study of the performance of different market structures, illustrated
during times of stress. We draw on the approach of Antoniou and Garrett (1993)
to propose six econometric tests for normal arbitrage between spot and futures
markets. Counter-intuitive results are classified as “arbitrage anomalies.” Anydifferential concentration of anomalies allows us to rank the robustness of different markets in response to shocks.

Equity markets under stress

437

The remainder of this paper is divided into four sections. In section 2 wediscuss the theory underlying the arbitrage link between spot and futures prices.
The details of the econometric methodology used to test for anomalies in thearbitrage link are outlined in section 3. Section 4 begins with a description of the
difficult trading conditions encountered during October 1997, before going on toreport our econometric results. Section 5 draws some very tentative conclusions.
Figures covering all the data are in Annex I. Annex II very briefly describes themarket structures in operation during October 1997.

2

Arbitrage and the stock-futures basis

This section defines the stock-futures basis and outlines the kind of arbitrage
relationship which can be expected to hold between cash and futures prices innormal trading conditions. In practice, two definitions of the basis are commonly
cited: the “theoretical” and the “simple” basis. The theoretical basis is a comparison of the actual futures price, Ft,T, with the fair value futures price, F*t,T, while
the simple basis is the difference between the futures price and the spot price. In
the former case the basis is:
Ft,T - F*t,T(1)

where t is the date the price is quoted and T is the contract expiry date. The
definition of fair value is:
F*t,T = St.e(r-d)(T-t)(2)

St is the price of the underlying equity index and (r-d)(T-t) is the cost of carrying
the index portfolio to the expiry date of the futures contract: (r-d) being the difference between the risk-free rate of interest, r, and, d, the dividend yield on theequity portfolio. (T-t) is the number of days to expiry. Trading between the twomarkets occurs if the cost of carry is less than (or equal to) the difference between
actual and fair values of the futures contract.
Taking natural logarithms of (2) we can re-write this in terms of the simple
basis to get:
f*t,T = st + (r-d)(T-t)(3)

where lower case letters denote natural logs. In equilibrium the futures market
correctly prices the equity portfolio (the contract gives fair value), so:
f*t,T - ft,T = 0.

(4)

Substituting for f*t,T in (4) and rearranging for the difference between the future

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Joe Ganley and Giorgio Trebeschi

and the spot price we find that the simple basis spread is equal to the cost of
carry:
ft,T - st = (r-d)(T-t)(5)

This is the most commonly used measure of the basis in both market practice andin the literature—in the equity market it is usually referred to as the stock-futuresbasis—and it is the measure used throughout this paper. Since the dividend yieldis usually lower than the interest rate on cash, it is expected to be positive.1 When
we come in section 3 to think in econometric terms, it will be convenient to write
equation (5) as:
ft = a + bst(6)That is, the futures price is equal to a constant plus the spot rate. To date empirical studies like that of Antoniou and Garrett (1993) have assumed that the cost of
carry is a constant within a single day. I think there is an issue here about thedefinition (and measurement) of d—which unlike r is not observable in a forward-looking sense. This seems to be a reasonable assumption. We have examined intra-day observations on r during October 1997, and these suggest thatwithin the course of a single day the cost of carry is (approximately) unchanging,so that it can be included in the constant term, a. Notice also that the coefficient,b, on the spot rate equals unity.
In normal conditions basis trading is a form of relative value trading, in that
positions taken in one market will be offset in the other; a trader might buy (sell)
the cash and sell (buy) the future, but would not simultaneously buy or sell both.
In this context, the cost of carry defines a “no-arbitrage window” within which itis uneconomic to undertake new trades. If the spread widens outside this window,i.e., if |ft - st| ³ a, arbitrage trading will occur because the expected profit fromdoing so exceeds the cost of holding the index to delivery.

3

Six tests for stock-futures arbitrage

3.1

Definitions

We now have to consider how in practice we can model and test the arbitrage link
between the future and the spot price. Drawing on Antoniou and Garrett (1993),
we suggest six simple tests for normal arbitrage. Since these tests form the backbone of our results in the next section, we will outline each of them in detailbelow. We can summarise them first in terms of the following six Questions:1
As maturity of the future’s contract approaches, the cost of carry diminishes until at t = T it
equals zero.

Equity markets under stress439· Q.1. Is the stock-futures basis stationary (ADF test)?
· Q.2. Is there a long-run relationship between the spot and future (is there a
cointegrating vector)?
· Q.3. Does the spot price equal the futures price (proportionality test)?
· Q.4. Do price changes in the future lead changes in the spot (in terms of (a) theECM coefficient and (b) “Granger-feedback” effects)?
· Q.5. Do shocks to the variances in the GARCH equation persist?
· Q.6. Do shocks to the variances in the GARCH equations cointegrate?
Let us consider each of these in turn, beginning with Question 1. In normal
trading, index arbitrage should stabilise prices in both markets. Imagine a situation in which the futures price is below its fair value and outside the no-arbitrage
window. The future is cheap, so basis traders will buy the future and sell the spot.
If the futures price then rose above fair value (and is again outside of the noarbitrage window), the reverse trade will be initiated with arbitrageurs buying
stock and selling the future. In this way, the futures price should fluctuate around
its equilibrium value and the basis will be stationary. This is equivalent to an
Augmented Dickey Fuller (ADF) test for a unit root in the basis.
We can begin to explain the remaining Questions in terms of a general
econometric model of the pricing relationship between spot and futures markets.
That is, consider a VAR-type model like equation (7):Dft = m0 + SimiDft-i + SjmjDst-j + l1Ecmt-1 + et1(7A)

Dst = g0 + SigiDft-i + SjgjDst-j + l2Ecmt-1 + et2(7B)

where D indicates first differences in the variables and et are white noise residuals.
The rationale for this specification is that it restricts the future and spot price,through the error correction term, to converge on their “long-run” equilibrium
relationship, while at the same time allowing a wide range of short-run dynamics
in the lagged first differences. Thus “Ecmt-1” denotes the error correction
model and is essentially the basis as defined earlier in equation (6); that is,
Ecmt-1 = (ft-1 - bst-1 - a). Inclusion of the basis in this way is justified theoreticallythrough its role in index arbitrage; econometrically it amounts to an equilibrium
condition that keeps f and s in proportion to one another in the long run (without
this they would drift apart which would suggest that no arbitrage is taking place
and the two markets are trading independently of one another).
In order to include an Ecm term in equation (7), we need to establish firstwhether f and s are cointegrated; that is, whether there is a linear combination ofthem that is stationary. This linear combination of f and s is called the cointegrating equation (or vector). If there is no cointegration, this implies there is noequilibrium condition that keeps f and s in proportion in the long run. We will

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Joe Ganley and Giorgio Trebeschi

already have some feel for whether f and s are non-stationary from the ADF tests
which we have used to examine the basis for Question 1 and indeed cointegration
requires the same order of integration in f and s. But we can directly estimate thecointegrating equation using the framework established by Johansen (1991). Thisapproach is advantageous, in that it allows us in addition to test for restrictions on
the Ecm term.
We will not here say any more about the well-known details of Johansen
estimation, except to add that in a two-variable model there could be up to two
cointegrating vectors. If we find a single cointegrating vector, this indicates that
there is a long-run relationship between f and s and we have an answer to Question 2. But for this relationship to have any economic meaning, we require thatthe future and spot price are equal, subject to the wedge created by the cost of
carry. This recalls equation (5) in section 2 and is equivalent to the null hypothesis that b = 1 in equation (6). We label this the “proportionality” test.
Moving on to Question 4, an established stylised fact in empirical studies ofthe link between spot and future is that of price leadership in the futures price (seeHolland and Vila (1998) or Schwarz and Szakmary (1994), for example). Since
this is an almost universal finding we would expect that, in normal trading, theprice of the equity future will move before, i.e. lead, that in the cash market. In
equation (7) there are two ways we can consider this. The first, and perhaps
usually the clearest, is in terms of the coefficient l on the Ecm term. From our
two pricing equations there will be two versions of the estimated coefficient, l1
and l2. The smaller of the two will indicate the variable that leads, so we expect|l1| < |l2|. Intuitively, a smaller coefficient means that for a given shock thatvariable gets less out of equilibrium and so returns to equilibrium sooner, aheadof the other.
Of course, we can examine the price leadership Question in a classic Granger
Causality setting. If, in equation (7A), the lags on the future are statistically zero
while those on the spot are not, the spot leads the future; analogously, if equation(7B) contains significant lags only on the future, then the future leads the spot. If
both sets of lags are significantly non-zero then a feedback relationship exists.
No estimates of a relationship on very high frequency financial data would becomplete without some sort of examination for the effects of volatility in theresiduals, i.e. for ARCH and GARCH effects. Where ARCH effects are present
we will wish to model these explicitly, including an equation for the conditionalvariance of the residuals. The commonest form used in the literature is the
GARCH(1,1) specification whereby the conditional variance evolves accordingto:
st2 = w + aet-12 + bst-12(8)

The presence of volatility effects brings us to Questions 5 and 6 which focus on
the behaviour of the conditional variance in the spot and futures markets. The
work surveyed in Bollerslev et al. (1992) indicates that for many financial timeEquity markets under stress

441

series the restriction that a + b = 1 in the conditional variance equation cannot berejected such that the conditional variance has a unit root. An interesting aspect of
the interaction between conditional variances is the idea of cointegration invariances. Clearly, if the conditional variance is non-stationary, this raises thequestion as to whether the conditional variances from the separate spot and futures equations cointegrate such that a linear combination of them shows nopersistence. If it is apparent that the two are not cointegrated in variance this is afurther indication of an anomaly in the arbitrage link between the spot and futures
price.

3.2

Interpretation of the arbitrage tests

We have now outlined six Questions which form our tests for normal arbitrage. At
the end of the day, we are looking for an interpretation of these which allows us tosay something about the effects of market structure. But a breakdown in thearbitrage link could be the result of non-microstructure imperfections—for example, in the way transactions have to be financed or in restrictions on short selling.
So we are testing a joint hypothesis where both microstructure and nonmicrostructure factors will play a role in determining the quality of the arbitrage
link.
It is also worth saying a little more at this stage on the interpretation of ourtests and how we might wish to prioritise the results from each one. Naturally, allof the Questions are related, but we would argue that Questions 1, 2 and 4a areperhaps the most decisive in detecting market anomalies and these could be
regarded as our “core” Questions. Question 2 is clearly fundamental, because it
addresses the very existence of a (long-run) relationship between the spot andfutures price. A negative answer to this Question would suggest that there is nofirm, systematic link between the two markets—flatly contradicting the principles
of normal arbitrage. Question 1 is important in the same way. A stationary basis
implies a continuous process of convergence between the future and the spot, andhence it also implies the existence of a long-run pricing relationship.
Though Question 4a is not motivated by any specific theory, there is plenty of
empirical evidence to suggest that, as a stylised fact, the futures price leads the
spot (see the early evidence in Kawaller, Koch and Koch (1987), Harris et al.
(1995) and most recently in Holland and Vila (1998)). There are important practical realities to trading which provide some underpinning to the finding of priceleadership. Basket trading the components of a spot index has always proved tobe costly because it involves large numbers of transactions in individual stocks—
up to 500 in the case of the headline S&P index. On the other hand, trading in the
future involves one standard product on a single exchange. For this reason, generic market information tends to be pooled and traded in the futures market firstand as a consequence index price discovery occurs in that market first. It is also
the case that if investors are capital constrained, they will have incentives to trade
first in the future where their initial outlay will be only the margin call on the442

Joe Ganley and Giorgio Trebeschi

contract, rather than the full price of the asset as in the cash market. The results of
the Granger causality test in Question 4b are based on adjustments in the very
short term. The minute-by-minute lags in the equation are likely to be noisy andpotentially misleading, since they are merely short-lived deviations around thelong-run relationship.
Question 3, the proportionality test, indicates whether the coefficients on the
spot and the future are equal. But there are caveats to its interpretation. If there is
price leadership, it might be the case in high frequency data that even in the “longrun” the spot price is “catching up” with the future. Given this catching-up effect,
it is perhaps unlikely that the b coefficient in equation (6) will in practice be
precisely equal to one. The existence of transactions costs and other “frictions” in
trading will also cause minor departures from exact proportionality. In line withthe literature to date, our daily model assumes that the intra-day cost of carry isconstant. From the data we have examined, it does appear that the cost of carry isunvarying intra-day. If this were not the case, we would need to model the cost of
carry explicitly, rather than in the intercept term. Without this, a time-varying costof carry would engender an omitted variables problem, biasing our estimate of b
and invalidating our hypothesis test for proportionality.
We would not regard Question 5 as a core test because it is not a sign, in itself,
of a market anomaly. The literature, for example in Bollerslev et al. (1992), has
shown that most high frequency financial time series modelled in a GARCH(1,1)
setting have a unit root (i.e. a+b=1). So the finding that in both the future and thespot equation the variance is I(1) is not in any sense unusual. It is more relevant toexamine whether the two conditional variances from the GARCH equations
cointegrate. Failure to cointegrate can be regarded as a sign of market anomaly.

4

The october 1997 market correction

4.1

Stressful trading conditions

Before describing our results in detail, it is useful to begin Section 4 by providing
an overview of the difficult trading conditions encountered in the equity markets
during October 1997. In this context, developments in the week beginning 27
October will be described as the “Correction.” Later, when we come to discuss
the markets in October 1987, we shall refer to the “Crash.”
The purpose of this overview is to convey some sense of the practical difficulty that may be faced by basis traders during times of stress—and hence how
the markets were tested last year. In London these market problems coincidedwith an important structural change, the introduction of the new Stock Exchange
Trading System (“SETS”)—the electronic order book for the top 100 equities—
on 20 October.
The conjunctural background to the Correction is interesting. While theCorrection began in the US markets on Monday, 27 October, market turbulence
generally had been growing since the summer in the east Asian region. World

Equity markets under stress443

equity prices had been rising steadily since January 1995, more than doubling in
the US before the October Correction. Inevitably, this raised questions of valuation—most famously those of Alan Greenspan in his warnings of “irrational
exuberance” in December 1996 and March 1997. These set the markets backtemporarily, but the trend in prices remained upwards. In London and New York,the equity markets finally peaked in the first week of October 1997 before falling
sharply in the second half of the month. Thereafter prices recovered, so that by
year-end there was little remaining evidence of a downturn. This recovery fromthe Correction was mirrored in most non-emerging equity markets by the end of
1997.
The general background of difficult trading during October is reflected inlevels of market volatility. The implied volatility from options traded on the S&P
500 future more than doubled to 42% on Monday, 27 October. A sharp increase involatility on the T35 contract was also recorded in Toronto on the same day.
Owing to the time zone differences which saw Europe correct a day later, volatility on the headline indices rose by a third or more in both Frankfurt and London
on the 28th. By close of business on the 27th, the S&P 500 spot price was down
about 6.3% and the futures price by almost 8% (Figures 3 and A2). As documented in Cochrane (1998), this triggered the New York Stock Exchange’s circuit
breaker Rule 80B for the first time since the rule had been adopted in 1988.
Trading was halted for half an hour at 2.36p.m.; it resumed at 3.06p.m. before afurther halt was invoked at 3.30p.m., closing the US markets for that day. It isclear from Figure 4 that the stock-futures basis became distorted and more volatile during this time, becoming negative in the last period of trading on the 27thand early on the morning of the 28th.
Trading in the European markets ended before the US collapse got into fullswing and caught up on Tuesday 28th: in London spot prices opened 6% down on
the previous night’s close (Figures 1 and A1). Order-book trading halts werenecessary in a few stocks, but the market as a whole functioned without a break.
Although the basis spread remained positive, it was clearly very volatile for ashort while (Figure 2). Both here and in the US, prices bounced back sharply the
day following the Correction, regaining much of the ground they had lost initially(Figures A1 and A2). While price levels recovered rapidly, the sharply increased
volatility in the markets persisted for several days.

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Joe Ganley and Giorgio Trebeschi

Figure 1: The UK equity markets FT-SE 100 index: Spot and futures priceMonday, 27 October, 1997 and Tuesday, 28 October, 1997
Jan. 1984 = 1000

Futures Index
5050

Spot Index

Monday, 27
27 October,
October 1997
Monday,5050

Tuesday, 28
28 October,
October 1997
Tuesday,

16:00

15:00

14:00

4350
13:00

4350
12:00

4450

11:00

4450

10:00

4550

09:00

4550

15:35

4650

14:35

4650

13:35

4750

12:35

4750

11:35

4850

10:35

4850

09:35

4950

08:35

4950

Source : FTSE
Internationaland LIFFE
Source:FTSE
Internationaland LIFFE

Figure 2: The UK equity markets: The stock-futures
Monday, 27 October, 1997 and Tuesday, 28 October, 1997
100
100

Monday, 2727October
19971997
Monday,October,

Tuesday, 2828October
19971997
Tuesday,
October,

100
100

80
80

80
80

60
60

60
60

40
40

40
40

20
20

20
20

00

0

-20
-20

-20
-20

-40
-40

-40
-40

-60
-60

-60
-60

-80
-80

-80
-80

08:35 09:35
09:35 10:35
10:35 11:35
11:35 12:35
12:35 13:35
13:35 14:35
14:35 15:35
15:35 09:00
09:00 10:00
10:00 11:00
11:00 12:00
12:00 13:00
13:00 14:00
14:00 15:00
15:00 16:00
16:00
08:35

445

Equity markets under stress

Figure 3: The US equity markets S&P 500 index: Spot and futures
Monday, 27 October, 1997 and Tuesday, 28 October, 1997
Jan. 1941 = 10
Futures Index
Futures
Index
960
960

Spot Index
Spot
Index

Monday, 27
19971997
Monday,27October
October,960
960

Tuesday, 2828
October
19971997
Tuesday,
October,

940
940

940
940

920
920

920
920

900
900

900
900

880
880

880
880

860
860

860
860

840
840

840
840

09:30
11:30
12:30
13:30
10:30 Reserve
11:30
13:30
09:30
10:30
11:30
12:30
13:30
Source: Federal
Bank 12:30
of
New York

14:30
14:30
14:30

15:30
15:30
15:30

10:30
10:30
10:30

11:30
11:30

12:30
12:30
12:30

13:30
13:30

14:30
14:30

15:30
15:30
15:30

Source:Source: Federal
FederalReserve
ReserveBank
BankofofNew
NewYork
York

Figure 4: The US equity markets: The stock-futures basis
Monday, 27 October, 1997 and Tuesday, 28 October, 1997
20

20
20

Tuesday, 2828
October
19971997
Tuesday,
October,

Monday, 27
19971997
Monday,27October
October,

-15
-15

-20
-20

-20
-20

-25
-25

-25
-25

15:30
15:30

-15
-15

14:30
14:30

-10
-10

13:30
13:30

-10
-10

12:30
12:30

-5

11:30
11:30

-5
-5

10:30
10:30

00

15:30
15:30

00

14:30
14:30

5

13:30
13:30

5

12:30
12:30

10
10

11:30
11:30

10
10

10:30
10:30

15
15

09:30
09:30

15
15

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4.2

Joe Ganley and Giorgio Trebeschi

Econometric answers to Questions 1 to 6

Our sample is made up of end-minute observations on the spot and the nearcontract futures price for the headline stock indices in each market, covering thefive days before and after the October 1997 shock; that is, from Monday 20 to
Friday 31 October. We estimate a separate pricing model for each day and in
addition we estimate a “pooled” model which examines the aggregate relationshipover all ten days. The estimation of separate daily models before and after theshock on the 27th allows us to make a comparison between market performancein the “stressful” conditions of the Correction with the more normal trading theweek before.2 On each day we initially estimate a Vector Error Correction Model(VECM) to test for cross correlation between the errors in the spot and futuresequations. Based on this we have identified an appropriate lag length to use in asingle equation approach. In most cases we have used a 10-lag specification.3 For
the October 1987 Crash we have included data on London and New York for two
trading days: Monday 19 and Tuesday 20. Due to a trading halt which occurred
around noon on the Chicago Mercantile Exchange, the data for Tuesday 20 are
split into two trading sessions.
Estimation of the Ecm term in the daily model requires that the interest rate
and the dividend yield are constant throughout the day and hence that the intraday cost of carry is constant. The data suggest that this is a valid assumption.
Obviously, over several days the cost of carry will vary and so we have allowed
for discrete day-by-day changes in the cost of carry in a pooled, 10-day model.
One of the purposes of the pooled model is to provide a counterfactual against
which to judge the stability of the daily estimates. With this in mind we haveestimated a full pooled model on all 10 days and a second version which dummies
out the shock day (that is, 28th in London and Frankfurt and 27th in New Yorkand Toronto).4 It turns out that this adjustment has little impact on the pooledmodel in either London or New York.
The results to Questions 1 to 6 are very bulky to report in full, so we havecondensed them for each market into the summary Tables 1 to 4 reported below.
The full results are available from the authors on request. We will discuss London
and New York first, referring to Tables 1 and 2, respectively.

London and New York2
It is worth observing that some or all of the characteristics of stressful trading conditions(wider spreads, more volatility) might be evident in very quiet trading periods, for example aroundseasonal lulls like Christmas Eve.
3
Most of the relevant literature using minute-by-minute data, e.g. Holland and Vila (1998), uses
a 10-lag specification. The only exceptions in our own results are the 23rd and 28th in the US andthe 20th, 23rd and 30th in the UK where we have used 20 lags to remove cross-correlation between
the residuals of the future and the spot equation.
4
Figure A1 in the appendix shows that London reopened on Tuesday down about 6% withrespect to the previous day. That is the main reason why we have dummied out the 28th rather thanthe 27th.

Equity markets under stress

447

The London spot market switched from a traditional dealer market to a new orderbook system, SETS, on 20 October, 1997. A lot of bilateral trading has continued,
off order book, in the “upstairs” market, but the spot index is calculated from
SETS trades. The futures index was traded on LIFFE in a traditional open-outcry
format.5 Based on the answers to Questions 1 to 6, it appears that there is little
evidence of arbitrage anomalies during the October 1997 Correction in the UK
equity markets. It is worth noting that the answer to what we have called the threecore questions (1, 2, 4a) is always intuitive. That is, the basis is stationary, there isa long-run relationship between the two indices and the futures market always
leads the spot. Apart from the mixed picture that appears from Question 3 andQuestion 5, the only anomalies we have observed are on 29 October, where thefuture fails to Granger-cause the spot, and on the 20th where the shocks in thevariances do not cointegrate.6
The picture in the London markets ten years earlier, during the 1987 Crash, iscompletely reversed. On both 19 and 20 October that year the basis is nonstationary and the tests for the existence of a cointegrating vector give borderline
results. In line with the findings of Antoniou and Garrett, the situation appears to
be worse on the 19th. On this day we clearly reject the proportionality test,7 andthe spot market leads the futures market, both in the long-run analysis (ECM
term) and the short-term one (Granger lags). One reason for this sharp difference
might be the magnitude of the two events: the 1987 Crash was a much severer test
for the market than the 1997 Correction (see Figure 1 and Figure A5). It is worth
noting that in October 1987 the future traded at a lower price than the spot
throughout both days in the sample, while in October 1997 the futures contract isalways traded at a price above the spot, except in the first few minutes after
opening on 28 October. Of course, a further important difference in explaining
events in 1987 and 1997 could be the change in market structure in London. But
the introduction of the new electronic order book, SETS, was so recent that thisseems unlikely.

5

Fuller details of how the market operates can be found in Annex II.
The variance in the spot equation is I(0) whereas in the future equation it is I(1).
The coefficient on the spot is 1.27436 as opposed to 1.17652 on the 20 October, 1987 and to
1.0053 in the pooled model in 1997.
6
7

448

Joe Ganley and Giorgio Trebeschi

Table 1: UK econometric results: Summary of findings
Questions:
Dates

1

2

3

4a

4b

20/10/97

Yes

Yes

No

Yes

Yes

5

6

Yes

No

(No in Future)

21/10/97
22/10/97
23/10/97
24/10/97

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
No
No
No

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

N/A
N/A
Yes
Yes

N/A
N/A
Yes
Yes

27/10/97

Yes

Yes

Yes

Yes

Yes

N/A

28/10/97
29/10/97

Yes
Yes

Yes
Yes

No
Yes

Yes
Yes

Yes
No

30/10/97
31/10/97

Yes
Yes

Yes
Yes

No
Yes

Yes
Yes

Yes
Yes

Yes
(Spot N/A)
Yes
No
(Spot N/A)
Yes
Yes
(Future N/A)

Pooled Model
20th - 31st Oct.

Yes

Yes

No

Yes

Yes

No

Yes

19/10/87

No

Yes(Borderline)

No

No

No

No

Yes

20/10/87

No

Yes(Borderline)

Yes

Yes

No

Yes
(Borderline)

Yes

Yes in 11/13 Yes in 13/13 Yes in 5/13 Yes in 12/13 Yes in 10/13 Yes in 13/19
days
days
cases
days
days
days
(6 in Spot,
7 in Future)

Yes
N/A
Yes
N/A

Yes in 7/8
days

449

Equity markets under stress

Table 2: US econometric results: Summary of findings
Questions:
Dates

1

2

3

4a

4b

5

6

20/10/97

Yes

Yes

No

Yes

N/A

N/A

21/10/97
22/10/97
23/10/97
24/10/97

Yes
Yes
Yes
Yes

Yes
(borderline)
Yes
Yes
Yes
Yes

No
Yes
No
No

Yes
Yes
No
No

Yes
Yes
Yes
Yes

No
N/A
Yes
N/A

Yes
N/A
Yes
N/A

27/10/97

Yes

No

N/A

N/A

Yes

No

28/10/97

Yes

Yes

No

No

Yes

29/10/97

Yes

Yes

Yes

Yes

No

30/10/97

Yes

Yes

No

No

Yes

31/10/97

Yes

Yes

No

Yes

Yes

Yes
(No in Future)Yes(No in Future)
Yes(Borderline)
No(Future N/A)Yes
(No in Spot)

Pooled Model
20th -31st Oct.
19/10/87

Yes

Yes

No

No

Yes

N/A

N/A

No

Yes
(Borderline)

No

Yes?

Yes

N/A

N/A

20/10/87 a.m.

No

Yes

No

Yes?

No

N/A

N/A

20/10/87 p.m.

No

No

N/A

N/A

No

Yes
(Spot N/A)

N/A

Yes in
11/14 days

Yes in10 or 12/14
days

Yes in3/12 days

Yes in6/12 days

Yes in
11/14 days

Yes in8/14 cases(4 in Spot,
4 in Future)

Yes in4/6 days

No
Yes
N/A
Yes

Table 2 shows the results of the arbitrage tests in the US equity markets.
Nearly all of the stocks in the S&P 500 are traded on the NYSE. The market there
is based around an order book run by a specialist who, where necessary, balancesorders on the book. The futures contract is traded in a pit on the Chicago Mercantile Exchange. Compared to London, it seems that there is greater evidence of
anomalies in the US data. As far as the core questions are concerned, it is particularly striking that we fail to detect a long-run relationship between the future
and the spot (i.e. no cointegrating vector) on Monday, 27th. Other striking
anomalies are found in the answers to Question 4a. In 5 cases out of 9, the spot
market leads the future in the daily models—the pooled models exhibit the same

450

Joe Ganley and Giorgio Trebeschi

pattern—whereas we find in London that the future always leads in the 1997 data.
Other interesting results in the non-core questions are the lack of futures leadership in the short term lags on the 29th, and the lack of a cointegrating vector in
the conditional variances on the 27th and 28th. The proportionality test, as for
London, gives mixed results.
A comparison of the US markets in October 1987 and October 1997 gives thesame picture as in London, in that market performance is much poorer in the 1987
data. Remember that the US data for 20 October, 1987 have been split into two
samples (morning and afternoon) following a trading halt in the middle of thatday. The afternoon of the 20th is by far the worst period in terms of market performance, although there are probably too few observations to draw firm conclusions. We therefore concentrate on trading on the 19th and in the morning of the
20th. We find that the arbitrage link broke down on both days. The basis is nonstationary, while it is not clear whether there is a cointegrating vector on the 19th,
and the proportionality test is rejected.8
The overall picture that emerges from Tables 1 and 2 is that there are similarities in a comparison of London and New York in the Crash, but differences during
the Correction. Thus in both London and New York the markets seem to be undermuch more pressure in October 1987, when there is clearer (econometric) evidence of arbitrage breakdown. The reason for this may lie in the difference in themagnitude of the two Crashes.
During October 1997 the London markets appear to trade with less evidenceof difficulty than in New York. This may be because the Correction occurred
during New York trading hours, whereas it happened overnight in Europe. Consequently, the European markets were able to open a single step down in responseto the news rather than undergoing a process of adjustment with greater uncertainty in the middle of the trading day (which might be more disruptive). It is alsointeresting to observe that the informal split we suggested between normal trading
and stressful trading is not accurately reflected in the results. For example, in the
US markets the price leadership responses are equally counter intuitive both in
the week before and the week of the Correction, rather than during the stressful
conditions alone.

Frankfurt and Toronto
We now turn briefly to our results on Frankfurt. Until October 1997, the Frankfurt
stock exchange operated a hybrid system of floor trading and an electronic orderbook called IBIS.9 Floor trading operated in parallel with the order book from10.30a.m. to 13.30p.m. While the floor was open, the official DAX 30 prices
were calculated from floor trades (rather than from trading in the order book). Ourdata set includes only floor trades and so our daily model was estimated over this8
The coefficient on the spot is 1.5338 on the 19th and 1.3437 on the 20th in the morning as
opposed to 1.0516 in the 1997 pooled model.
9This was replaced by the new electronic Xetra system in November 1997.

451

Equity markets under stressshorter, 3-hour period, excluding the IBIS trading either side. In the 10 days of thesample period, we find that there are three days which show evidence of weakness in market performance, based on our core Questions. Again, these are notconfined to the week of the shock itself. Other than on the proportionality test, theaggregate pooled model performs well.
In Toronto the spot market trades through an electronic order book, CATS(Computer Assisted Trading System); floor trading ended in April 1997. Futurestrades are conducted through a traditional open-outcry floor system. Last Octobertrading in the future was not liquid enough to allow minute-by-minute samplingof prices, so we have taken observations every 2 minutes. No daily model isestimated at all on 20 and 21 October, where the future trades too infrequently toallow this, so in the case of Toronto we have 8 daily models rather than 10. Likewise, the pooled model is estimated over 8 rather than 10 days. The overall picture in the intra-day analysis shows many instances of anomalies. With the single
exception of 28 October, no long-run relationship can be identified in the data.
The pooled model gives rather more favourable results, in that the basis appears
to be stationary and there is a cointegrating vector. One possible interpretation ofthis may be that anomalies in arbitrage will persist over short periods of a day or
two but will be removed over one- or two-week horizons (as embodied in thepooled model).

Table 3: Frankfurt econometric results: Summary of findings
Questions:
Dates

1

2

3

4a

4b

5

6

20/10/97
21/10/97

Yes
No

Yes
No

No
N/A

No
N/A

Yes
Yes

N/A
N/A

22/10/97
23/10/97

Yes
No

Yes
No

No
N/A

Yes
N/A

No
Yes

24/10/97

Yes

Yes

No

No

No

N/A
Yes (in the
Future)N/A
Yes (in the
Future)
N/A

27/10/97
28/10/97
29/10/97
30/10/97
31/10/97

Yes
Yes
Yes
Yes
No

Yes
Yes
Yes
Yes
No

No
Yes
Yes
Yes
N/A

Yes
Yes
No?
Yes
N/A

No
Yes
Yes
No
Yes

N/A
N/A
N/A
N/A
Yes (in the
Future)

N/A
N/A
N/A
N/A
N/A

Pooled Model
20th - 31st Oct.

Yes

Yes

No

Yes?

Yes

No

Yes

8/11 Yes

8/11 Yes

3/8 Yes

5/8 Yes

7/11 Yes

Yes in 3 cases(3 in Future)

1/1 Yes

N/A
N/A
N/A

452

Joe Ganley and Giorgio Trebeschi

Table 4: Toronto econometric results: Summary of findings
Questions:
Dates

1

2

3

4a

4b

5

6

22/10/97
23/10/97

Yes?
Yes?

No
No

N/A
N/A

N/A
N/A

No
Yes?

N/A
N/A

24/10/97

No

No

N/A

N/A

Yes

N/A
Yes (in theSpot)
Yes (in the
Future)27/10/97
28/10/97

Yes?
Yes?

No
Yes

N/A
Yes

N/A
No

No
No

N/A
N/A

29/10/97
30/10/97

No
Yes?

No
No

N/A
N/A

N/A
N/A

Yes?
Yes

31/10/97

Yes?

No

N/A

N/A

Yes

N/A
Yes (in the
Future)N/A
Yes (in the
Spot)
N/A

Pooled model
22nd - 31st Oct.

Yes

Yes

No

No

Yes

No

N/A

7/9 Yes

2/9 Yes

1/2 Yes

0/2 Yes

6/9 Yes

Yes in 4 cases(2 in Spot,
2 in Future)

N/A

N/A
N/A
N/A

Note: There is no daily model on the 20th and 21st of October because of lack of liquidity in the
futures market.

Summary
Taking the four markets as a whole, London seems to produce the best resultswith little, if any, evidence of a break in the arbitrage link in October 1997. However, it could be argued that the London market—and European markets generally—were not tested to the same extent as those in North America, since theinitial shock occurred outside European trading hours. As a consequence, theCorrection is for them embodied in a single observation at the Open on Tuesday,
28th. If the Correction had begun during the trading day, providing a continuous
period of stress, the picture in London might have been different. However, inboth London and New York in the 1987 Crash there is clear evidence of market
breakdown in all three core Questions. In New York in 1997 the only real evidence of a problem is on 27 October, the day of the Correction when the market
fell over 6%. Frankfurt shows rather more evidence of problems. But still more
often than not, the arbitrage link appears to hold. On the criteria we have selected, Toronto is the weakest performer. The lack of a long-run relationship in 7
out of 8 days in the data is striking. We will speculate below whether these conclusions have any clear market structure interpretation.

Equity markets under stress5453

Did market structure make a difference?

The results we have presented are of statistical anomalies observed while markets
were trading under stress. We need to ask if they are any more than this. In particular, can we plausibly attribute departures from econometric benchmarks to theeffects of market structure? This is a tantalising question. On the one hand, there
appears to have been a trend towards order-driven trading systems in both spot
and futures markets since the mid-1980s. Consider for example the introductionof the CAC system in Paris, its precursor CATS in Toronto, IBIS and latterly
Xetra in Frankfurt and SETS in London. In practice, these systems are rarely pureauction markets, but usually incorporate some of the characteristics of a dealer
market as well. In London more than half the trading on SETS shares is donebilaterally off order book, while in New York, monopoly specialists take out
imbalances in the book. Consequently, the distinction between market structures
is in practice blurred, at least relative to text book cleanliness.
So we are forced to make dirty comparisons. Bertero and Mayer (1990) madeone such attempt. They observed that while stock markets were responding to a
global shock, the price collapse observed during the 1987 Crash varied widely
across markets, from under 5% in Austria to over 25% in Singapore. This obviously raised questions about the interdependence of markets and of the link
between structure and performance. Their analysis undertook cross-section regressions of price changes on market structure variables, but was unable to find aconclusive link. Based on our own results we would also wish to be tentative indrawing firm conclusions. But the facts of the tests do suggest that during October 1997 the market with the largest dealership component—London—sustained
the arbitrage link more robustly than in the other markets in this study. This need
not imply that these other markets had profound or terminal difficulties. But at themargin, in difficult trading conditions, they may at least show more noise in thearbitrage link between spot and futures pricing.

454

Joe Ganley and Giorgio Trebeschi

Annex I
Figure A1: The UK equity markets FT-SE 100 index: Spot and futures price20 October, 1997 - 31 October, 1997
Jan. 1984 = 1000

Futures
Index
Futures Index

Spot
Index
Spot Index

5400
5400

5400
5400

5200
5200

5200
5200

5000
5000

5000
5000

4800
4800

4800
4800

4600
4600

4600
4600

4400
4400

4400
4400

4200
4200
20/10/97 21/10/97
21/10/97 22/10/97
22/10/97 23/10/97
23/10/97 24/10/97
24/10/97
20/10/97

4200
4200
27/10/97 28/10/97
28/10/97 29/10/97
29/10/97 30/10/97
30/10/97 31/10/97
31/10/97
2710/97

Figure A2: The US equity markets S&P 500 index: Spot and futures prices
20 October, 1997 - 31 October, 1997
Jan. 1941 = 10

Futures
Index
Futures Index

Spot
Index
Spot Index

1000
1000

1000
1000

980
980

980
980

960
960

960
960

940
940

940
940

920
920

920
920

900
900

900
900

880
880

880
880

860
860

860
860

840
840
20/10/97 21/10/97
21/10/97 22/10/97
22/10/97 23/10/97
23/10/97 24/10/97
24/10/97 27/10/97
27/10/97 28/10/97
28/10/97 29/10/97
29/10/97 30/10/97
30/10/97 31/10/97
31/10/97
20/10/97840
840

Equity markets under stress

455

Figure A3: The UK equity markets FT-SE 100 index: Spot and futures price19 and 20 October, 1987
Futures
Index
Futures index

Spot
Index
Spot index

2300
2300

2300
2300

2200
2200

2200
2200

2100
2100

2100
2100

2000
2000

2000
2000

1900
1900

1900
1900

1800
1800

1800
1800

1700
1700

1700
1700

1600
1600

1600
1600

1500
1500
19/10/87
19/10/87

1500
1500
20/10/87
20/10/87

Figure A4: The UK equity markets: The stock-futures basis
19 and 20 October, 1987
100
100

100
100

50
50

50
50

00

00

-50
-50

-50
-50

-100
-100

-100
-100

-150
-150

-150
-150

-200
-200

-200
-200

-250
-250

-250
-250
19/10/87
19/10/87

20/10/87
20/10/87

456

Joe Ganley and Giorgio Trebeschi

Figure A5: The US equity markets S&P 500 index: Spot and futures price19 and 20 October, 1987
Futures
Index
Futures index

Spot
Index
Spot index

290
290

290
290

270
270

270
270

250
250

250
250

230
230

230
230

210
210

210
210

190
190

190
190

170
170
19/10/87
19/10/87

170
170
20/10/87
20/10/87

Figure A6: The US equity market: The stock-futures basis
19 and 20 October, 1987
20
20

20
20

10
10

10
10

00

00

-10
-10

-10
-10

-20
-20

-20
-20

-30
-30

-30
-30

-40
-40

-40
-40

-50
-50
19/10/87
19/10/87-50-50
20/10/87
20/10/87

Equity markets under stress457

Annex II
Microstructure of the equity markets
The purpose of this Annex is to outline the microstructure of the UK, US, Toronto
and Frankfurt equity markets. Trading systems are described as they were in
operation during our sample period, i.e. from 20 October, 1997 to 31 October,
1997.

LondonLondon Stock Exchange (LSE)· Index characteristics: The FT-SE 100 index comprises the top 100 UK-registeredcompanies listed on the London Stock Exchange measured by market capitalisation.
· Trading system: Before 20 October, 1997 the LSE was a quote-driven market,
based on competing, dual-capacity market makers who quoted bid and ask
prices through SEAQ screens. Trading with customers occurred through bilateral negotiation over the telephone. Market makers were compelled by the Exchange’s rules to execute a trade size up to 1 NMS (normal market size = 2.5%of the daily average trading volume) between 8:30 a.m. and 16:30 p.m. at, orwithin, the quoted ask and bid. Trading among market makers occurred directly
over the telephone or indirectly through one of the four inter-dealer broker(IDB) screens which provided an anonymous electronic order-driven trading
facility.
· SETS (Stock Exchange Electronic Trading Service) was introduced on 20
October, 1997 and functions in parallel with the traditional telephone-based
system. SETS is an order book for trading FT-SE 100 stocks, on which there is
no requirement for dealers to post firm bid and ask quotes. The order bookopens at 8:00 a.m. for order addition and deletion and then starts execution withan uncrossing process at 8:30 a.m. It closes at 16:30 p.m.
The London International Financial Futures and Option Exchange (LIFFE)· The FT-SE 100 index future: Contract size: Valued at GBP 25 per full index point.
Delivery method: Cash settlement.
Trading hours: 08:35 a.m. – 16:10 p.m.
· Trading system: The FT-SE 100 futures contract is traded through open-outcry
negotiation in a pit on the trading floor at LIFFE.

458

Joe Ganley and Giorgio Trebeschi

TorontoToronto Stock Exchange (TSE)· Index characteristics: The Toronto 35 index is composed of 35 Canadian blue
chip stocks. It is a modified, capitalisation-weighted index (i.e. larger stocks
have greater weight). However, there is a ceiling of 10% on the weight of eachstock.
· Trading systems: The trading system at the Toronto Stock Exchange used to bea hybrid of order book (called CATS) and floor trading. Stocks were listed either as floor stocks or CATS stocks. Orders were handled according to the typeof stock and the nature of the order. The trading floor closed in April 1997 andnow all stocks are traded electronically through CATS. Orders for CATS are
entered through terminals located in brokerage-firm offices and they are bookedin price and time priority. The CATS system is to be replaced by another moreadvanced electronic system called TOREX.
Toronto Futures Exchange (TFE)· The Toronto 35 Index (TXF): Contract size: CAD 500 times Toronto 35 Index level.
Trading hours: 09:15 a.m. – 16:15 p.m.
· Trading system: The trading system of the TFE is an open outcry (last trade
market) with floor traders.

Frankfurt
Deutsche Bõrse AG· Index characteristics: The DAX 30 index comprises 30 German blue chips. It is
calculated for both floor trades and for IBIS (now XETRA). Our research inthis paper concentrates on the floor-based index.
· Trading system: In our sample period the Frankfurt stock exchange trading
system is a hybrid between a floor and an electronic trading system called IBIS.
IBIS is a country-wide computer-assisted trading system that allows dealers totrade anonymously between 8:30 a.m. and 17:00 p.m. In 1996, 38.6% of the
DAX 30 shares were electronically traded on IBIS. Floor trading is organised as
an auction market where market participants (banks, official and unofficial brokers) are responsible for fixing the official daily price (called “einhetskurs” orsingle price) which is determined once a day commencing at 12:00 noon forshares. The single price is the price that maximises the volume traded after
matching supply and demand. Brokers are allowed to trade on their account any
imbalance between demand and supply that should arise at the single price.
Highly liquid stocks are also traded continuously on the floor in lots of 50

Equity markets under stress459

shares between 10:30 a.m. and 1:30 p.m. The residues of orders exceeding theround lot are traded at the single price. Therefore it might happen that a trade is
executed at two different prices.
Deutche Terminbõrse (DTB)· The DAX German Stock index: Contract size: DEM 100 per DAX Index point.
Trading hours: 09:00 a.m. – 17: 00 p.m.
· Trading system: Trading at the DTB is based on an international electronic
network. The system displays best bids and offers, allows traders to query themarket for better or additional quotes and matches orders and quotes electronically.

New York
New York Stock Exchange (NYSE)· Index characteristics: The Standard and Poor’s (S&P) Composite Index comprises 500 stocks mostly traded on the NYSE, but also including a few AMEX(American Stock Exchange) and some OTC stocks.
· Trading system: Trading at NYSE is conducted as a centralised continuous
auction at a designated location on the trading floor between 9:30 a.m. and 4:00
p.m. The market participants are mainly member-firms than can act both asagent dealer, member-firm broker, independent broker, and, lastly, dealers
known as specialists. The specialist’s functions are three: as a dealer he tradeson his own account—after giving precedence to public orders—when there isan absence of public buyers or sellers; as an agent he executes orders entrusted
by other brokers which have arrived electronically; as auctioneer he quotes current bid/ask prices for each of the stocks assigned to him. However, the majority of the trades are processed electronically through SuperDot, an electronicsystem which links member firms’ order processing and trading operations tothe specialist post at the floor. The market is subject to circuit breakers if the
DJIA (Dow Jones industrial average) falls 350 points from the previous trading
day’s close. AMEX, which comprises some of the S&P 500 stocks, works withthe same principles as NYSE.
There are dual-function specialists and an automated system called PER,
which is similar to SuperDot.
The Chicago Mercantile Exchange (CME)· S&P 500 Index future: Trading unit: USD 500 times S&P 500 index value.
Trading hours: 08:30 a.m. – 15:15 p.m. (Central time).

460

Joe Ganley and Giorgio Trebeschi· Trading system: Trading is effected in outcry pits. There is also a system forafter-hours trading called GLOBEX. This allows trading around the clock, on
Sundays and on public holidays.
Sources of information:
The IFR Handbook of World Stock & Commodity Exchanges. London: IFR Publishing, 1997.
The Salomon Smith Barney Guide to World Equity Markets 1998. London: Euromoney Books, 1998.
Sofianos, G, and I. Werner, 1997, “The Trades of NYSE Brokers,” NYSE Working Paper, #97-04.

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461

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