Antoniou and Garret (1993)

8/2/2019 Antoniou and Garret (1993)

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To What Extent did Stock Index Futures Contribute to the October 1987 Stock Market Crash?

Author(s): Antonios Antoniou and Ian GarrettReviewed work(s):Source: The Economic Journal, Vol. 103, No. 421 (Nov., 1993), pp. 1444-1461Published by: Blackwell Publishing for the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2234476 .

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TheEconomic ournal, 03 (November),444-I46I. ( Royal Economic Society I993. Published by BlackwellPublishers, io8 Cowley Road, Oxford OX4 iJF, UK and 238 Main Street, Cambridge, MA 02I42, USA

TO WHAT EXTENT DID STOCK INDEXFUTURES CONTRIBUTE TO THE OCTOBER 1987

STOCK MARKET CRASH?*AntoniosAntoniou nd Ian Garrett

The October I987 worldwide stock market crash has been labelled variously apanic, a debacle, a long overdue price correction and the burstof a speculativebubble to name but a few. As noted in the Presidential Task Force Report(I988) establishing the cause(s) of the crash is important given the profoundeffect it had on confidence (see Roll (i 988) for one explanation of the cause ofthe crash). Of at least equal, if not greater, importance, however, is why theinitial downward pressureon priceswas converted into the rather bewilderingcollapse that followed. This issue has received quite a substantial amount ofattention in the United States (see interalia Blume et al. (i 989), Furbush (i 989)and especially Harris (I989)). A number of these studies of the crash in theUnited States have focused on various aspectsof the relationshipbetween stockindex futures and the underlying stock index (see especially Harris (I989)) todetermine whether there was a breakdown between the two markets, althoughnone have examined the crash in quite the same way as we do here. The issueof market breakdown was also considered quite extensively in the PresidentialTask Force Report.Essentially the argument is that the two markets,that is, the underlying spotmarket and the derivative futures market, should effectively function as onemarket if futures are to serve their designated role as, amongst other things, ameans for hedging stock market risk and a vehicle for price discovery. Duringthe crash, however, the question arises as to whether the two marketsfunctioned as one or whether the link between the two markets broke such thatthey effectively functioned as two separate entities. The point here is that if acascade effect is observed, the two markets did not operate as one and futurescould not effectively perform their prescribed role. The evidence in Harris(i 989) suggeststhat this was the case in the United States. Unfortunately therehas, to our knowledge, been little systematic empirical investigation of thecrash in the United Kingdom. We aim to rectify this here. Using minute byminute values of the FTSE ioo Index and minute by minute transaction pricesfor the December I987 stock index futurescontract, we investigate the pricingrelationship between these two marketson October igth and 20th, I987 to tryand determine whether the link between the two markets broke, once theeffects of non-synchronoustrading are accounted for. To anticipate the results,

* We would like to thank two anonymous referees and the Editor, John Hey, for their very helpful andinsightfulcomments which have substantially improved the paper.We would also like to thankJohn Hunter,Deborah Mabbett and seminarparticipantsat ManchesterUniversity forhelpfulcommentson earlier draftsof the paper. Finally, we would like to thank George Constantinides and especially Merton Miller for somevery illuminating discussions. The usual disclaimer applies.[ 1444 ]


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[NOV. I993] I987 STOCK MARKET CRASH I445we find that the link between the markets did indeed break on October igth,manifesting itself in a cascade effect in both markets,although it was restoredon the 20th. The evidence seems to suggest that whilst the futures marketexacerbated the decline, the cause of the breakdownlies with the stockmarket.The rest of the paper is organisedas follows. Section I providesa brief overviewof events surrounding and during the crash. Section II discusses the nature ofthe pricing relationship between the two markets. In Section III, we proposea method for removing the effects of non-synchronoustrading from the FTSEIOO ndex and analyse the pricing relationshipbetween the adjustedindex andthe stock index futures price. Section IV concludes.

I. THE CRASHThe downturn in share pricescommenced on October 6th and they fell almostcontinuously over the next two trading weeks. The most telling evidence ofwhat was to come can be found by examining the New York market on theI4th, I5th and I6th October, where the Dow Jones Index fell by 95 points, 58points and io8 points on successive days (Bank of England (I988)). Thissubstantial downturn signalled the worldwide collapse that was to follow, theFTSE Ioo Index opening I 38 points down and closing 250 points down onMonday October igth' (Bank of England, I988). There is a surprisingdifference in attitudes between the United States and United Kingdomauthorities as to the role derivative markets, and stock index futures inparticular, played in the decline. The Presidential Task Force Report (I988)pays considerable attention to the importance of stock index futures in thedecline. This singularly contrasts with the view taken by the Bank of Englandthat

' ... the interaction of the cash and derivative products markets seems tohave played a very limited direct role in the crash in London.' (Bank ofEngland (I988) p. 57).Whilst this may be true, figuresfor the daily trading volume of the Decemberfutures contract on the Igth and 20th show that approximately i O,OOOcontracts traded on each day, nearly double that of any other near-maturitycontract in i 987.2 This reinforces the fact that we cannot overlook theimportance of stock index futures in the market decline and in particular thechange (if any) in the pricing relationship on these two crucial days in stockmarket history.

II. THE PRICING RELATIONSHIPIn considering the pricing relationship between stock index futures marketsand the underlying stock market, there are two quite distinct strandsthat haveemerged in the extant literature: those studies that analyse mispricing by1 The London Stock Exchange did not open on the i6th October due to severe storms in the south ofEngland. Consequently the collapse in share prices seems all the more bewildering.2 At the time of the crash, the December contract was nearest to maturity. The other expiration monthsfor the FTSE IOOstock index futurescontract are March, June and September.

(CRoyalEconomicSociety 99349-2


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I446 THE ECONOMIC JOURNAL [NOVEMBERcomparing the actual futures price with its fair, or theoretically correct, valueto determine whether profitable arbitrage opportunities are available (see interalia MacKinlay and Ramaswamy (I988) and Chung (i99i)) and those thatanalyse the lead-lag relationship between the two markets (Kawaller et al.(i 987), Harris (i 989) and Stoll and Whaley (i 990)). Most studiestend to focuson either the former or the latter issue, but not both. Whilst we focus more onthe latter issue here, the former does provide some valuable insights andindicates that results from studies of the lead-lag relationship must be viewedwith some caution as the models typically used to analyse lead-lag relationshipsmay well be misspecified, as we shall see.A. MispricingStudies that analyse mispricing and the existence of arbitrage opportunitiestypically compare the differential between the actual futures price quoted attime t for delivery at time T, F,T, with the fair futures price, F*T. The fairfutures price is given by either of two commonly used fair pricing formulae.First we have (MacKinlay and Ramaswamy, I988)

F* = Ste(r-d) (T-t) (I)where St is the value of the underlying index and (r- d) ( T- t) is the cost ofcarrying the portfolio to maturity, (r-d) being the differential between theyield on the risk-free interest rate and the dividends from the portfolio and(T-t) being the time to expiration. Alternatively we have (Cornell andFrench, I983 a, b),

F*T = Ster(T-t)_Dker(T-k) (k = t+ I,..., T), (I')k

where D is the dividend inflow from the underlying portfolio and all othervariables are as defined above. For ease of exposition, we will work with (i),though similar arguments follow for (i'). The theoretical basis,3 , -F*T) iscompared with transactions costs to determine if arbitrage opportunities arepresent.4 If the theoretical basis falls outside of the no arbitrage windowdetermined by transactions costs, then dependent on whether the futurescontract is undervalued (overvalued) due to, say, bearish (bullish) speculationin the stock index futures market, arbitrageurswill buy (sell) futures and sell(buy) stocks.It is clear that the theoreticalbasisis very important in the pricingrelationship given that index arbitrage links the two markets and thetheoretical basisdetermines whether arbitrage opportunitiesare available. Thebasis itself, however, is equally important in the pricing relationship. To see

3One must be careful in talking about the basis for there are several definitions. Where there may beconfusion, we will refer to the futures to cash price differentialas the simple basis. When there is no risk ofconfusion, we will refer to it as the basis. The futures to fair price differential will be referred to as thetheoretical basis.4 Note that since the yield on dividendsis typically less than the yield on the risklessasset, the basisshouldbe positive.

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I993] I987 STOCK MARKET CRASH I447this, take natural logs of (i) (lower case letters denote variables in naturallogarithms):

X*,T = St+ (r- d (T- t). (2)Clearly, if the futures market is pricing the stock index futures contractcorrectly then

ft, T XJ t, =?O' (3)Now, to see the importance of the basis in the pricing relationship, substitute(2) into (3) and rearrange to obtain

ft, T-St = (r-d) (T-t). (4)It is clear from (4) that the simple basis also has an important role to play inthe arbitrage process. It is also apparent that upon expiration (t = T), the basiswill equal zero whilst before expiration it will, theoretically, equal the cost ofcarry, though if the contract is near to maturity carrying costs become trivial.From a theoretical viewpoint, the basis is crucial given that arbitrage providesan important link between the two markets. From an econometric point ofview, the basis also has the rather appealing interpretation as the errorcorrection mechanism which prevents prices in the two markets drifting apartwithout bound. The importance of the basis cannot be understated, for asHarris (i989, p. 77) points out,

'The (simple) basis is studied because it is a key determinant of whetherarbitrage opportunities exist, because variance in the basis is a measure ofhow well integrated the markets are, and because the basis is related totests for causality among the prices in the two markets.'

B. Lead-lag RelationshipsThe second component of the pricing relationship is the lead-lag relationshipbetween the two markets. In general terms, the argument that underlies theanalysis of lead-lag relationships between indices and index futures is predicatedon the observation that, because of the existence of market imperfections, mostnotably transactions costs and short sale restrictions, the stock index futuresprice will lead the underlying spot index. This is because taking a position inthe futures contract requires little capital outlay (in fact, margins can be postedin the form of interest-bearing securities so that the opportunity cost iseffectively zero) and the trade can be effected quickly given the highly liquidnature of futures markets. Moreover, since the stock index futures contractrepresents a claim on the shares comprising the underlying index proportionateto their allocated weights, its price will reflect the equilibrium (true) value ofthe Index with each trade, whereas each share within the underlying indexwould have to trade before it reaches its equilibrium value. Thus, the futurescontract will act as a vehicle for price discovery in the stock market. Of course,this relationship may in principle be two-sided. If the stock index futures pricereacts to economy-wide information rather than security-specific, theninformation about a group of securities may cause the index to lead the futuresprice. Thus a feedback relationship may exist. These propositions concerning(C Royal Economic Society I993


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I448 THE ECONOMIC JOURNAL [NOVEMBERthe lead-lag relationship between the two markets are typically tested withinthe context of the following model :'

= +aift-i+ali ft+j + t(5)i jwhere Ast is the percentage change in the index value, Aft is the percentagechange in the futures price6 and summations run from i,j = I,..., k. If the a.

are statistically zero while the ai are not, then the futures leads the cash and viceversa. If both the ai and a, (or at least some of them) are non-zero then afeedback relationship exists. There are, however, problems with this approachto testing lead-lag relationships, particularly with the specification of (5).Essentially, (5) is a VAR, specified in first differences with st andft being I(i)in the terminology of Engle and Granger (i 987), such that their first differencesare stationary (i.e. I (o)). However, it is well known from the GrangerRepresentation Theorem (Engle and Granger (I987)) that if two I(i) seriescointegrate, then there will exist a linear combination of these series which is1(o) and an error correction representation of the VAR will exist. From thepreceding discussion, it is clear that the error correction term in this case is thearbitrage link, that is, the basis. Thus, any analysis of lead-lag relationshipsmust necessarily be tied to the arbitrage link between the two markets and assuch tests of this sort should be conducted within the framework of the errorcorrection representation of the VAR, with any restrictions tested. Failure todo so may well result in invalid inference because the arbitrage link iseffectively ignored.

III. MODELLING THE PRICING RELATIONSHIPA. The DataThe data we use to model the pricing relationship are minute by minute valuesof the FTSE I00 Stock Index and minute by minute transactions prices7 for theDecember I987 FTSE IOOStock Index futures contract for the Igth and 20thOctober I987. The data used are for the period 09.IO to I6.05 on both days.The data were kindly provided by the London Stock Exchange and LIFFEand are plotted in Figs. I and 2. One of the interesting features of the data isthe fact that the futures appears to have traded at a discount which was at timessubstantial. This is indicative of the presence of arbitrage opportunities (see fn.4). An interesting issue to be analysed is why these apparent opportunities forarbitrage persisted. However, one must be careful in uncritically using the datafor the FTSE IOO Index since the recorded value is unlikely to reflect its truevalue. This arises because not all shares within the Index will necessarily tradein any one given minute. Some will react to new information with a time lag,leading to the so-called problem of non-synchronous trading whereby the

From now on, as there is no risk of confusion, t,T will be referred to asft.Usually, Aft is included to make (5) 'structural', in which case instrumental variablesshould be usedin its estimation. The omission of Aft does not alter the substance of the arguments that follow.7There are a few minutes during both days where transactionsnever took place. In this case, we use anaverage of the bid-ask quotes for that minute. These periods of no trading are, however, very few and farbetween.(C Royal Economic Society I993


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I993] I987 STOCK MARKET CRASH I4492185

2100

2015 ....

19319:10 10:55 12:40 14:25 16:05Futures Index --

Fig. i. Minute by minute FTSE ioo futures and index prices i9 October I987.

1985

1840

1695

15509:10 10:55 12:40 14:25 16:05Futures Index--

Fig. 2. Minute by minute FTSE ioo futures and index prices 20 October i987.reported value of the Index contains old, or stale, prices. The implications ofnon-synchronous trading should be fairly obvious, particularly with regard tothe perceived presence or otherwise of arbitrage opportunities given that theexistence of arbitrage opportunities is determined by comparing the basis(adjusted for the cost of carrying) with transaction costs. If the basis itself is notC)RoyalEconomicSociety 993


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I450 THE ECONOMIC JOURNAL [NOVEMBERcorrect, as will be the case if non-synchronoustrading is severe, then arbitrageopportunities may simply be statistical illusions (see Miller et al. (i99i)). Weconsider this issue in more depth in the next section.B. RemovingNon-synchronousradingEffectsIn recent years attention has re-focused on non-synchronous trading and itseffectson prices and returns.The issue of non-synchronoustrading is not new(see, for example, Fisher (I966)) but there has been a shift in emphasis awayfrom its effect on the empirical application of asset pricing models (Dimson(I979), for example) to its effect on prices and returns (MacKinlay andRamaswamy (I988), Blume et al. (I989), Harris (I989), Lo and MacKinlay(i99o) and Stoll and Whaley (I990)). The problem non-synchronoustradinginduces is that if the Index does contain stale prices, spurious autocorrelationin prices and returns will be observed. There is also another aspect to thisargument. The FTSE IOO Index is constructed by taking a weighted averageof the mid-quotes, at which market makersare forced to trade, of the prices ofthe securities that comprise the Index. Therefore, the issue of non-synchronoustrading is also essentially one of whether all previous information isincorporatedin the current price quotes. If informationarrives randomly, thenin the presenceof non-synchronoustrading, one would expect to find a movingaverageerror.To demonstrate, supposethat returnscomprisetwo components:the expected return and the unexpected return, which is a random process. Ifinformation also arrives randomly, then by definition, its effects will be feltthrough the unexpected return component. If this information is notincorporated immediately, however, then the unexpected return componentwill be correlatedsince previousinformationwill also have an effect. Therefore,non-synchronous trading will generate a moving average error structure inreturnsand as such, any model of non-synchronoustrading must capture thesefeatures.The problem of removing non-synchronoustrading effects can be thought ofas a signal extraction problemwhere the signal to be extracted is the true valueof the Index. Thus, we can formulate the problem as

St = St*+ ut, (6)where St is the observed value of the Index, St* s the signal to be extracted,thereby representingthe true value of the Index, and ut s the non-synchronoustrading adjustment. Following Garrett (i99i), (6) can be viewed as anunobserved components model and we can extract S* using the Kalman Filter.The advantage of using the Kalman Filter in this situation is that it only makesuse of past information and as such, can be applied in real time. In theterminology of the Kalman Filter, (6) is known as the measurementequation.To make the model complete, we also require what are known as transitionequations which describe the evolution of the unobserved component. Wespecify the transition equations for the evolution of St*as

St*= St*-,+I?t- + et) (7a)Alt = At-l + Cts(7b)

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I993] I987 STOCK MARKET CRASH 145ISpecifying the transition equations in this way means that S* evolves as arandom walk, with the trend in St*also being allowed to evolve in a stochasticfashion. The intuition behind this specification of the problem stems from thearguments in Ross (I989). Ross (I989), for example, shows theoretically thatprices, and hence the rate of change of prices, will move in response to newinformation. Given the assumption that information arrives in a stochasticfashion, prices, and the trend in prices, will evolve stochastically. This iscaptured by the transitionequations given by (7). Further, the systemgiven by(6) and (7) can be written as an ARIMA(o, 2, 2) process.Therefore, the modeltakes account of the moving average component that is presentwhen there arenon-synchronous trading effects. In addition, if observed returns are highlyautoregressivebecause of non-synchronous trading, this model will provide agood approximation to the true value of the Index. A final advantage of thisapproach is that, if there is no apparent trend in the observedprice series, then, can be constrained to zero. If fi is constrainedto zero, then St can be writtenas an ARIMA(o, i, i) process.This legitimises the apparently adhocapproachof including an MA( i) errorin models of returns to capture non-synchronoustrading (see, for example, Hamao et al. (I990)).To demonstrate the workingsof the Kalman Filter in estimating (6) and (7),using the notation in Harvey (I987), we can set up the model in state spaceform as follows. Define the following vectors and matrices

Z = ?)a [ ) 0= I] [tThen the measurement and transition equations can be written as

St Zt/ t+8t) (8)at = O(3t-1 + Vt) (9)

where uthasvariance o2htand vt has variance o-2Qt. If we defineA&-1s the bestestimate of 0tY1 and Pt_1 as the covariance matrix of &t-l then we have thefollowing prediction equations:o tlt-l= CZt-1) (Io)

Ptit-l =OPt-- +Qt (I I)As observations on St become available, so we can update the predictionequations and thereby update the estimate of St*.The updating equations aregiven by

at= 0tit-l + Ptit- Zt St- zA

t-/z,) -1zt + htk (I 2)Pt=tit-- Ptt-1 zt zt Ptt-l/Zt Ptit-1 zt + ht. (I 3)The predictionand updating equationsdefine the Kalman filter. The likelihoodfunction can then be expressedas a function of the one-step-ahead predictionerrors and the model can be estimated by maximum likelihood.This seems a more natural and intuitive way to address the non-synchronoustrading problem. The model is entirely compatible with the class of ARMA(p,( Royal Economic Society 1993


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1452 THE ECONOMIC JOURNAL [NOVEMBERq) models for returnsproposed by Stoll and Whaley (I99O), without incurringthe identification problems that occur, not only through identifying p and q,but through estimating over-parameterised versions of such models. Inaddition, the model is similar in spirit to that proposed by Harris (I989), whoessentially uses factor analysis to extract a factor common to each securitycomprising the S & P 500 Index. However, this approach does not require thedetailed data that Harris' (I989) method requires.8The system (6) and (7) was estimated using (the log of the) minute-by-minute recordedvalue of the FTSE ioo Index to generate the non-synchronoustrading adjustment. Graphsof the non-synchronoustrading adjustmentto theIndex9 are presented in Figs. 3 and 4. As can be seen, the adjustment is

0.01

-0 01

9:10 10:55 12:40 14:25 16:05Adjustment

Fig. 3. Minute by minute non-synchronoustrading adjustment I9 October I987.

relatively small on both days (the meansof the absolute value of the adjustmentand the absolute value of the adjustmentrelative to the Index on the igth, forexample,areoooo8 andooooI respectively ndoo002ando0oo3forthe 20th)perhaps reflecting the fact that the Index only comprises iOO shares. Further,although very small, non-synchronicity is lessof a problem at the opening thanit is at the closing. One explanation for this observed behaviour is that, at thetime of the crash, the stock market closed after the futures market, such thatorders could still be processed. In addition, certainly for the igth, the Bank ofEngland (I988) observed that

8 Specifically, to implement Harris' (I989) approach, transaction by transaction data on each individualsecurity is required to construct a measureof St*.' The figures are multiplied by IOOfor readability.K RoyalEconomicSociety1993


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I993] I987 STOCK MARKET CRASH I453001

-0-01

9:10 10:55 12:40 14:25 16:05Adjustment

Fig. 4. Minute by minute non-synchronoustrading adjustment 20 October I987.

'The capital resources readily available to the London market makersallowed them, in the initial stages of the crash at least, to absorbsubstantialamounts of stock. The marketimbalance was spreadamong allthe major firms active in the equities market, three quartersof which arepart of well-capitalised financial conglomerates.' (Bankof England (i 988)p. 56).This is a point we will return to later on.C. Did theLink Break?From the preceding discussion, any analysis of the pricing relationship shouldbe conducted in the context of a VAR. However, we also argued that anyattempt to analyse lead-lag relationships between the stock market and thestock index futures market must take into account the arbitrage link betweenthe marketswhich, from the discussion in Section II, can be identified as thebasis. The basis provides this link theoretically through its role in indexarbitrage and econometrically through its role as the error correctionmechanism which ensuresthat the two pricesdo not driftapartwithout bound,that is, it ensuresthat in the long-runf = s. To incorporatethesefeatures,beginby specifying the following unrestrictedN-variable VAR:

x j+H1xt-1+ * I* kxt-k+ t (I4)where tt is a vector of intercept terms, x = [f, s*'] and ? is a vector of errorterms. Following Johansen (i 988) and Johansen and Juselius (i 990),reparameterise (I 4) to give

Axt = t+ r1 AXt1 +*** + rk-1 AXt k+l + nxt-k + ?t* (5)K Royal Economic Society I993


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I454 THE ECONOMIC JOURNAL [NOVEMBEREquation (I 5) is now a VAR reparameterised in error correction form whereHI= - (I -Hll-. .. .-Hk) represents the long-run response matrix. Writing thelong-run response matrix as H = op', then the linear combinations P'Xtk will beI (o) if there is cointegration, with a being the adjustment coefficients, and thelong-run response matrix will be of reduced rank. The Johansen test forcointegration is then based on testing the rank of the matrix H. Denoting rank(H) by r, there are three possibilities. First, r = o in which case all of thevariables are I (i) and there are no co-integrating vectors. Second, r = N inwhich case all of the variables are I(o) and there will be N co-integratingvectors given that any linear combination of stationary variables will also bestationary. Finally, o < r < N in which case there will be r linear combinationsof the non-stationary variables that are stationary, that is, there will be r co-integrating vectors or, equivalently, N- r common stochastic trends. Theadvantage of using the Johansen procedure is that it is possible to testrestrictions on the co-integrating vectors, the statistics being X2 istributed. Thisis particularly useful in this case since we know the form the co-integratingvector should take. For the basis to be the co-integrating vector, we requireproportionality to hold, that is, in terms of the equationft = yo +y ls* + et, werequire Yi to be equal to one. yo can be interpreted as the cost of carry in thiscase since on an intra-day basis it will be constant and if the futures contractis near maturity, it should be near zero. Table i reports the test statistics

Table iTestsfor Number of Co-integratingVectors

Igth October 20th OctoberNull Alternative Amax Atrace Amax Atrace

r = 0 r < I 2I-7I 25s3I i8-sI 23-83r I r= 2 3-606 3-606 5-38 5-38Restrictions

Yo = %:' (I) I4-I7 2-339Yi = I% (I) I4.I3 2-233

discussed in Johansen and Juselius (i990) for the number of co-integratingvectors and also tests the restrictions on the co-integrating vectors. The nullhypothesis of zero co-integrating vectors is rejected at the 5%0 level on bothdays whilst the null of one co-integrating vector cannot be rejected.10 It is clear,then, that both variables are I(i), with the linear combination being I(o).What is interesting from these results is the form of the co-integrating vector for

10 For critical values seejohansen andJuselius (I990), table A3. Given that the robustnessof thejohansenprocedure to relaxation of the Gaussian assumptions s unknown, and we find evidence of significant ARCHeffects (see the GARCH models in table 2), we also tested forco-integration and tested for a unit root in thebasis using the Phillips-Ouliaris ( 990) and Phillips-Perron (i 988) testswhich allow for such heterogeneity.Whilst, in the interest of brevity, we do not report these resultshere, they confirm the conclusions reachedin the main text. These results are available from the authors upon request.? Royal Economic Society I993


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I993] I987 STOCK MARKET CRASH I455the two days and this provides us with a first idea as to what happened on thesetwo days. The important restriction here is the proportionality restriction,though the cost of carry restriction does have minor interest.11 Theproportionality restriction is strongly rejected for the igth October, as, lessimportantly, is the zero cost of carry restriction. The implication of this is thatwhilst the two markets were linked on the igth, that link was not the basis(adjusted for the cost of carry) and therefore, by implication, the link was notthe one provided by index arbitrage. Indeed, for the igth, the co-integratingvector is given byft = I27045* - 2~o765, which clearly shows thatft s*. Theevidence, then, suggests that the arbitrage link did not operate effectively onthe i gth October: the important link between the two markets broke down.The implication of this is that the mechanism that serves to stabilise prices inboth markets, index arbitrage, would not serve its purpose. If stock indexfutures prices were falling such that the futures price was below its fair valueand outside of the no-arbitrage window then arbitrageurs would buy futuresand sell stock. Thus, initial selling pressure would be transmitted from the stockindex futures market to the stock market. If the futures price then rose so thatit lay outside the upper no-arbitrage window, then the reverse trade would beinitiated and buying pressure would be transmitted from the stock indexfutures market. Thus, the futures price would fluctuate around its equilibriumvalue and the basis would be stationary. However, the basis on the igth has aunit root12 and thus of little guide in determining the existence of arbitrageopportunities. This was not the case on the 20th, when the link between the twomarkets was the basis and again, by implication, the arbitrage link wasrestored. We will return to the question of how this might have occurred later.What we appear to observe, then, is different behaviour by the markets on thetwo different days. On the 20th, the error correction term was the basis whilston the i gth it was not. This suggests that the important link, index arbitrage,did not function effectively.

It must be noted, however, that some link did still exist on the igth becauseboth prices continued to fall in unison. The implication of this is that we shouldobserve differences in the behaviour of the pricing relationship between the twomarkets on both days. From the earlier discussion and the results of theJohansen procedure, we know that the pricing relationship should be modelledin the context of the error correction representation of the VAR. We began byestimating the VAR with io lags of each variable (except the error correctionterm, which is lagged once),"3 with each equation showing the presence ofsignificant ARCH effects. This is perhaps not surprising given the rathervolatile events on those two days. To capture this volatility, we reestimate the

" The zero restriction is not so important for if the homogeneity restriction were valid but the zero costof carry restriction were not, the error correction term would simply be the basis adjusted for the cost ofcarryingand this is what arbitrageurswould comparewith transactionscosts to see if arbitrage opportunitieswere available.12 For example, ADF testson (ft-S*) and A(ft-st*) yield values of - 245 and -I 438 respectively.The5% critical value is approximately- 2'87.13 We realise of course that the choice of lag length is somewhat adhoc.However, i o minutes does not seeman unreasonablestarting point for our analysis given the extraordinary events that took place on those twofateful days. Full results for the VAR without GARCH are available from the authors upon request.

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I456 THE ECONOMIC JOURNAL [NOVEMBERmodels using the GARCH (i, i) specification (see Bollerslev (i986)), wherebythe conditional variance evolves according to C2 = j + cxe62+ 3o,21. Par-simonious models for both marketson both days are reported in table 2. The

Table 2Modelling the Pricing Relationship

I9 October I987Futures Aft = I II 98Ast* - 0-o5oeCmt,

(30o83) (-2.5IO)G,t= 0-132+0o2I8 t_1+o 605O_(5 294) (3 973) (IO 99)

Q%c(I6) = I5 86, QH(IO) = 5-o6Index AS*=?oIoAft-l+o?oI4Aft-2+00OII ft-3+0ooI5Aft-4+0 0OI ft-5(2-768) (5-02I) (3 367) (4423) (2-760)+ oo7Aft-6+ o003ft7 + 001 2Aft-8 + 0022Aft9 +O-I94AS*1

(2-045) (2-934) (4-IOI) (8 I46) (3-6I3)+ 0-2 I I ASt-2 + o I43ASt_3+ O I46ASt-4 + ?0049ASt-5

(3-6I3) (4 446) (3-497) (2-022)0t2 =0-002 + o-988t2 i + oo46y2_

(6-765) (I2 27) (I *02 I)Qsc(io) = I6-35, QH(IO) = "IO

20 October I987Futures Aft =-0-294ft-

(-4-60)Ct2 = 2-490 + 0-464e2 1+0-272 02(4-076) (6-o87) (2-328)

QSC(IO) = I5525, QH(IO) IO-38Index AS - ooo4f + o484S* 1 + o293ASt*2 + oo004ecm,

(2-708) (9-I90) (5 I54) (3.574)at2 = 0-002 + O- I 054-1 + 0760oTtL

(2-969) (3-557) (I I -93)QSC(IO) = I2 7I, QH(IO) = 9-46

Notes:ecm s the error correction term.Figures in parentheses are t ratios.Constants in the variance equation are multiplied by Io5 for readability.QSC and QH are portmanteau tests for serial correlation and heteroscedasticity, distributed X2(.).

models seem to be adequately specified with none of the diagnostic tests beingsignificant at the i 00 level.Turning our attention to the results,an interesting scenario emerges. If boththe equity and futures markets were effectively functioning then the basisshould be significantin explaining price movements in both markets. However,we observe something very different on both the igth and the 20th OctoberI987. The first indication of breakdownis the fact that, as was discussedearlier,the basis was not the error correction term on the igth. The results also tendto support those found in studies of the United States markets (for example,Kawaller et al. (I987), Stoll and Whaley (I990)) in the sense that the evidencesuggests that the stock index futures market tended to lead the stock marketwith some evidence of a weaker feedback relationship. However, what is ofinterest here is the extent of the feedback from the stock market to the stockt Royal Economic Society I993


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I993] I987 STOCK MARKET CRASH 1457index futures market on the igth October forwhilst some of the feedbackoccursthrough the errorcorrection term the interestingpoint to note is the coefficienton As* 1: it is approximately I 2. Thus, whilst the stock marketwas reacting todeclines in the stock index futuresmarket, the stock index futures market wasreacting (indeed one could argue overreacting) to declines in the stockmarket.Therefore, a vicious downward spiral in prices, or cascade effect, ensued.Moreover, given the evidence presented earlier that the arbitrage linkeffectively broke on the i gth, there was nothing to counteract the fall (see theearlier discussion in section II.A and III.C).This conclusion of market breakdown is reinforced when we consider thebehaviour of the conditional variance for the markets on both days. Aninterestingaspect of the interaction between conditional variances is the notionof co-integration in variance (fora brief discussion,see Bollerslevetal. (I 992)).There is a great deal of evidence (see the review and bibliographyin Bollerslevet al. (I992)) showing that for many financial time series the restriction thata+ fl = i in the conditional variance equation cannot be rejected such that theconditional variance has a unit root (Integrated GARCH, or IGARCH, in theterminology of Engle and Bollerslev (I986)) such that shocks to the variancepersist indefinitely. This obviously raises the question about whether theconditional variances of two similar series co-integrate such that a linearcombination of them shows no persistence.Through the similarityof the stockindex and stock index futures prices one would expect their conditionalvariances to co-integrate, and this is indeed the case on the 20th since shocks tothe conditional variances for both markets are not persistent and therefore alinear combination would not be persistent.However, the i gth again showsanaltogether different state of affairs, with the conditional variance for the indexexhibiting I(i) behaviour (a test of the restriction cz+fl = i yields x2(I) =O0I93) as opposed to the apparent I(o) type behaviour of the conditionalvariance for the futures. Given that co-integration requires the same order ofintegration in the individual series, it is apparent that the two are not co-integrated in variance and this is a further indication of market breakdown.Thus, there is clear evidence that there was a breakdown. Moreover, theoverreaction of the futuresprice would appear to provide primaacie evidencethat the anti-futureslobby is correct: futures destabilise. However, this is notthe case, as we shall see.D. Why Did TheLinkBreakand Why Was, t Restored?It would seem that the initial downward pressureon prices manifested itself inthe decline that followed because the arbitrage link between the two marketsbroke down. The important question is why this should be the case. Given thatthe appropriate arbitrage strategy to undertake was to buy futures and shortstock, any restrictions on short sales may provide at least some explanation ofwhy the link broke. This certainly goes some way to explaining why the cascadeeffect occurred in the United States, for stock cannot be sold short unless theprevious movement was a price increase (the so-called up tick rule). However,there are very few, if any, restrictions (certainly at the time of the crash thereC RoyalEconomicSociety 993


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I458 THE ECONOMIC JOURNAL [NOVEMBERwas no up tick rule) on the short sale of stock within the account period14 onthe London market. Moreover, given that the crash occurred during anaccount period (the account began on I 2th October, with settlement of anytrades during the account to take place on 2nd November), the answer to thequestion of why arbitrage could not function effectively must lie elsewhere.Conversations with specialists have revealed that a major problem, certainly onthe i gth, was the drying up of liquidity in the stock market to the extent thatarbitrage transactions became impossible to undertake. This same point ismade by the Bank of England (I988) who note that the response of marketmakers to the increased selling pressure, which they were able to absorbinitially, was a widening of the bid-ask spread in order to compensate first forlong positions they had accumulated by absorbing the selling pressure but werenot themselves in a position to liquidate fully and second to the perceivedpossibility of default by investors come the end of the account. Indeed, as isdocumented by the Bank of England ((I988), p. 57, table D) the averagespread for the period I9-23 October I987 was some 3300 higher than theaverage spread for the whole of September I987. This widening of the spreadis indicative of a liquidity problem. Since the structure of the London marketemphasises the provision of liquidity through increased competition, and hencenarrow spreads, the implication is that market makers either significantlyreduced their bid prices and/or significantly increased their ask prices, makingtrading unattractive. This action then removes liquidity from the market.In addition, during the crash market makers reduced the average quote sizeby half and finally, some market makers even refused to answer theirtelephones, thereby failing to fulfil their obligation to make markets in alltrading conditions (Bank of England, I 988). Given that, with the futures beingundervalued the appropriate arbitrage strategy would be to buy futures andsimultaneously sell stock, it is hardly surprising that the arbitrage link brokedown. To illustrate, consider the following scenario. An investor perceives theexistence of an arbitrage opportunity. We have already seen that marketmakers widened their spread, increasing the cost of the stock market side of thetransaction. Further, the quote size was halved, again increasing the cost of thestock market side of the transaction. Finally, the investor had to find a marketmaker willing to transact in the first place. Taken together, arbitrage waseffectively prohibited. The cause of the breakdown, then, appears to be aliquidity problem. Moreover, because this liquidity problem occurred in thestock market, the stock market was the cause of the break.

Consider now the 20th. We see a partial reversal of what occurred on theIgth: we see -that the stock index futures market leads the stock market, boththrough Aft-l and through the error correction term, with no feedback from thestock market to the futures, even though the futures sold at a discount. This alsocoincides with the restoration of the basis as the arbitrage link. It wouldappear, then, that the reaction of participants in the stock index futures marketon the 20th was effectively to ignore price movements in the stock market whilst

14 The settlement systemin the London market is based on the notion of an account period, whereby anytrades are not settled until the end of the account. The account period is typically two to three weeks.? Royal Economic Society I993


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I993] I987 STOCK MARKET CRASH I459the stock market utilised the information provided by price movements in theindex futures market. There are several points to note about the behaviour ofthe markets which may explain why this apparent 'reversal' took place.Considerfirst of all the conclusions reached in the Quality of Markets Report(see the discussion in Kleidon and Whaley (I992)) about why sellers werewilling to trade futures at a discount. They argue that two factors were at work:sellers did not believe they could transact immediately in the stock market atquoted prices and second, sellers may not have believed that the prices quotedwere the correct ones. Consider now the non-synchronoustrading adjustmentplotted in Figs. 3 and 4. These show that the non-synchronoustrading problemwas more severe on the 20th and therefore, by implication, there was lesstrading in the stock market on the 20th relative to the Igth. Add to this theargument that liquidity dried up and the results confirm the conclusionsreached in the Quality of Markets Report.This situation helps to explain why the basis was restored as the link. Thereason for the break in the link on the igth was the absence of liquidity. TheQuality of Markets Report suggest that this liquidity problem drove sellersaway from the stock market to the futures market. By implication, there wasless trading in the stock market on the 20th relative to the Igth, therebyalleviating the liquidity problem and in turn, alleviating the original source ofthe breakdown. Drawing all these points together, the evidence points to thestock market as the cause of the breakdown.

IV. CONCLUSIONSIn this paper, we have set out to analyse the pricing relationship between theFTSE IOOIndex, a representativemeasure of stock market performance,andthe FTSE IOOstockindex futures contract on the igth and 20th October i987,the periodof the stock market crash. In particularwe have set out to investigatethe extent to which the FTSE IOO utures contract contributed to the crash.

To address this question, we examine the pricing relationship between thestock market and stockindex futuresmarketon these two fatefuldays. In doingthis, we synthesis two apparently diversestrandsof the literatureon modellingpricing relationships between stock and stock index futures markets into anerror correction framework. The advantage of this framework is that itimmediately yields testable propositions with regard to the functioning of thesemarkets. Before modelling the pricing relationship, however, we address thenon-synchronous trading problem prevalent in high frequency price data onindices. Utilising a new method for removing these effects, we find that non-synchronicity explains little of the observed behaviour of the markets, a resultconsistent with Harris' (i989) findings for the United States.Despite the fact that the futures traded at a discount, which is indicative ofarbitrage opportunities, we find that the link between the two markets on theIgth was not the link provided by arbitrage. We also find that the futures pricestronglyleads the Index with some weakerevidence of feedbackfromthe Indexto the futures on the Igth, a resultapparently consistent with evidence from the( RoyalEconomicSociety 993


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I460 THE ECONOMIC JOURNAL [NOVEMBERUnited States for stable time periods. However, in this turbulent period weobserve the futures price on the i gth overreacting to information contained inthe previous minute's Index price. On the basis of this evidence, it is temptingto conclude that the futures market was to blame. This is not the case. Whatwe observe on the i gth is a situation where arbitrage trades could not beexecuted effectively because of liquidity problems in the stock market. As aresult, the arbitrage link broke down, the outcome being a vicious downwardspiral in prices in both markets.

For the 20th, the futures continued to trade at a discount, again pointing tothe presence of unexploited arbitrage opportunities. In addition, we alsoobserve a change in the nature of the pricing relationship with the restorationof the basis as the link between the two markets, the futures still leading the spotbut this time with no feedback from the spot to the futures. As the Quality ofMarkets Report suggest, the liquidity problem drove sellers away from thestock market to the futures market. This is precisely what restored the basis asthe link.

What seems clear, then, is that the futures market did not serve its purposeon the igth. Indeed, it helped exacerbate the downward movement in prices.However, the blame for this does not lie with the futures market, for the initialsource of the problem was the stock market, in particular the drying up ofliquidity. The message from this is clear. There is no need to look towardsfurther regulating the futures market as a separate entity because the futuresmarket was not the source of the problem. To regulate the futures marketfurther is to alleviate the symptoms without curing the illness. Regulating thetwo markets as a single entity, as recommended in the Presidential Task ForceReport (i 988) is only part of the solution. In addition, it is necessary to considerthe trading practices in both markets. Kleidon and Whaley (I992) suggest thatthe solution for the United States is more efficient trading systems for the stockmarket. Similar conclusions must apply for the United Kingdom, with reformsof trading practices bringing trading systems in both markets closer together."5We cannot know for sure, but we suspect that had this been the case the crashmight never have taken hold in the way it did.Brunel UniversityDate of receiptoffinal typescript:March I993

REFERENCESBank of England (I988). 'The equity market crash.' Bank of EnglandQuarterlyulletin,February,pp. 5 I-8.Blume, M. E., MacKinlay, A. C. and Terker, B. (I989). 'Order imbalances and stock price movements onOctober 19 and 20, I987.' Journalof Finance,vol. 44, pp. 827-48.Bollerslev, T. (I986). 'Generalised autoregressive conditional heteroscedasticity.'Journalof Econometrics,vol. 3I, pp. 307-27-

15 For example, in the United Kingdom there are two markets closely linked yet with different tradingsystems. The stock market is a purely screen-basedsystem whilst the futures market has trading based onopen outcry. Whilst in theory there is no reason as to why purely screen-basedsystemsshould not executetrades efficiently,in practice human and technical factors will ensure this is not the case in times of marketturbulence.? Royal Economic Society I993


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I993] I987 STOCK MARKET CRASH I46IBollerslev, T., Chou, R. Y. and Kroner, K. F. (I992). 'ARCH modelling in finance: a review of theory andempirical evidence.' Journalof Econometrics,ol. 52, pp. 5-59.Chung, Y. P. (i 99i). 'A transactions data test of stock index futures market efficiency and index arbitrageprofitability.' Journalof Finance,vol. 46, pp. I79I-809.Cornell, B. and French, K. R. (i983a). 'The pricing of stock index futures.' Journalof FuturesMarkets,

vol. 3, pp.- I4-Cornell, B. and French, K. R. (i 983 b). 'Taxes and the pricing of stock index futures.' Journalof Finance,vol. 38, pp. 675-94-Dimson, E. (I979). 'Risk measurement when shares are subject to infrequent trading.' Journalof FinancialEconomics, ol. 7, pp. I97-226.Engle, R. F. and Bollerslev, T. (I986). 'Modelling the persistence of conditional variances.' EconometricReviews, ol. 5, pp. I-50.Engle, R. F. and Granger, C. W. J. (i 987). 'Cointegration and errorcorrection:representation,estimationand testing.' Econometrica,ol. 55, pp. 25I-76.Fisher, L. (I966). 'Some new stock market indexes.' Journalof Business,vol. 39, pp.I 9I-225.Furbush, D. (i 989). 'Programtrading and price movement: evidence from the October i 987 market crash.'FinancialManagement,ol. I9, pp. 68-8I.Garrett, I. (I99I). 'Nonsynchronous trading and the stock market crash.' Mimeo, Centre for EmpiricalResearch in Finance, Department of Economics, Brunel University, London.Hamao, Y., Masulis, R. W. and Ng, V. (I990). 'Correlations in price changes and volatility acrossinternational stock markets.' Reviewof FinancialStudies, ol. 3, pp. 28I-307.Harris,L. H. (I989). 'The October I987 S&P 500 stock-futuresbasis.' JournalofFinance, ol. 44, pp. 77-99.Harvey, A. C. (I987). 'Applications of the Kalman filter in econometrics.' In Advancesn Econometrics:ifthWorldCongress, ol. I (ed. T. F. Bewley). Econometric Society Monograph No. I3. Cambridge:Cambridge University Press.Johansen, S. (i 988). 'Statistical analysis of cointegration vectors.' Journalof Economic ynamics ndControl,vol. I2, pp. 23I-54.Johansen, S. and Juselius, K. (I990). 'Maximum likelihood estimation and inference and cointegration-with applications to the demand for money.' OxfordBulletinof EconomicsndStatistics,vol. 52, pp.

I69-2I0.Kawaller, I. G., Koch, P. D. and Koch, T. W. (I987). 'The temporal price relationshipbetween S&P 500futures and the S&P 5oo Index.' Journalof Finance,vol. 42, pp. I309-29.Kleidon, A. W. and Whaley, R. E. (I992). 'One market?Stocks,futures and options during October I987.'Journalof Finance,vol. 47, pp. 85I-77.Lo, A. W. and MacKinlay, A. C. (i ggo). 'An econometric analysis of nonsynchronoustrading.' JournalofEconometrics,ol. 45, pp.I 8I-2II.MacKinlay, A. C. and Ramaswamy, K. (I988). 'Index-futures arbitrageand the behaviour of stock indexfuturesprices.' Reviewof FinancialStudies,vol. I, pp. I37-58.Miller, M. H., Muthuswamy,J. and Whaley, R. E. (I99I). 'Predictabilityof S&P 500 Index basischanges:arbitrage-inducedor statistical illusion?' CRSPWorking aperno.33i, Graduatechool f Business,Universityof Chicago.Phillips, P. C. B. and Perron,P. (I988). 'Testing for a unit root in time seriesregression.'Biometrika,ol. 75,pp. 335-46.Phillips, P. C. B. and Ouliaris, S. (iggo). 'Asymptotic properties of residual-basedtests for cointegration.'Econometrica,ol. 58, pp. I65-93.Presidential Task Force (i 988). Presidential askForceReport nMarketMechanisms,ubmittedto the President,The Secretaryof the Treasury and Chairman of the Federal Reserve Board, January I988.Roll, R. (i 988). 'The international stock market crash of October I987.' FinancialAnalystsJournal,vol. 44,pp. I9-35.Ross, S.A. (I989). 'Information and volatility: the no-arbitrage martingale approach to timing andresolution irrelevancy.' Journalof Finance,vol. 44, pp. I-I 7.Stoll, H. R. and Whaley, R. E. (i 990). 'The dynamics of stock index and stockindex futures returns.' Journalof FinancialandQuantitative nalysis,vol. 25, pp. 44I-68.

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