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Brooks et al., 2001, A trading strategy basedon the lead-lag relationship between the spotindex and futures contract for the FTSE 100

陳韋翔1, 陳奕卲2

NCNU Graduate School of International Business Studies

05/23

199212501299212509

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Introduction

Research motivations:Traders frequently take coincident positions in both the cash andfutures marketsAny lead-lag relationship do not last for more than half an hour;this study uses high frequency (10 min data)Emphasis on forecasting accuracy and development of tradingstrategy for market practitioners to gain trading profits

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Theoretical Relationship between Spots and Futures

Consider a cost of carry model,

Ft = Ste[(r−d)(T−t)], ft = st + (r − d)

, where ft = ln(Ft/Ft−1), st = ln(St/St−1).Futures and spot returns perfectly contemporaneously relatedExistence of lead-lag relationships

Market sedimentArbitrage trading

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Theoretical Relationship between Spots and Futures

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Theoretical Relationship between Spots and Futures

Transaction preference for futures (sentiment indicator)Highly liquid marketEasily available short positionsLow marginsLeveraged positionsRapid execution

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The Data

13,035 10-min observationsAll trading days from June 1996 to April 1997FTSE 100

Spot prices calculated every 1 minFutures prices taking average of last bid/ask prices during 10 minperiod

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Methodology

The spot and futures prices should never drift too far apart,suggesting that a cointergrating relationship might beappropriate.We employ the Engle and Granger (1987) single equationtechnique rather than the Johansen (1988) for simplicity.

lnSt = γ0 + γ1 lnFt

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Methodology

We do indeed find, as expected, that the log-price series for thespot and the futures market are I(1).If cointergration exists between the two series, then the Grangerrepresentation theorem states the there is a corresponding errorcorrection model (ECM) as following,

∆ lnSt = β0 + δzt−1 +

r∑i=1

βi∆ lnSt−i +

s∑j=1

αi∆ lnFt + ϵt

where z = lnSt − γ0 − γ1 lnFt.

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Methodology

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Methodology

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Methodology

According to the DF test result of zt, there is a clear evidence ofrejection of the null hypothesis of a unit root in these residualsand we therefore conclude that there indeed exists acointergrating relationship.By using SBIC, we select one lag of each of ft and st for inclusionin the ECM.

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Methodology

The positive coefficient of ft−1 implies that the price discoveryrole of the futures market for the spot market.The coefficient of zt−1 is negative, suggesting that if st is largerelative to the equilibrium relationship at time t-1, then it isexpected to adjust downwards during the next period.

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Methodology

Consider a ECM-COC, the cost of carry theory model.

zt = lnSt − γ0 − γ1 lnFt − γ2(r − d)(T − t)

The coefficient estimates are extremely similar to those observedin the previous case, and the cointergrating regression are indeedstationary.

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Methodology

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Methodology

Consider an ARMA model.

st = α0 +

p∑i=1

αist−i +

q∑j=1

βjut−j + µt

Again the SBIC criterion, it suggests that only one autoregressivelag and no moving average lags are optimal. So, we utilize AR(1)in following context.

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Methodology

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Methodology

Consider a VAR model.

st = θ0 +

p∑i=1

θist−i +

q∑j=1

ϕift−j + vt

A multivariate extension of SBIC is used. Once again selects alag length of one for the variables.

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Methodology

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Methodology

Conduct a forecast by using 1040 10-min observations for May 1997, abullish month, which were not included in the original sample. Wethen compare to the actual return by criteria such as RMSE, MAE.

1 VAR is better than ARMA model.2 ECM is better than VAR and ARMA models. ARMA and VAR

will lose any long-term properties of the data.

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Methodology

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Trading Strategy

Liquid trading strategyBuy and hold strategyFilter strategy

Better predicted return than averageBetter predicted return than first decile, 10%High arbitrary cut-off, by a rigorous standard

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Trading Strategy

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Trading Strategy

Useful applications in financial markets.Active equity market makers (significantly lower transactioncosts)For traders interested in high frequency transactingIn future may generate average returns in excess of transactioncostsForm a more appropriate proxy for the index to reducetransaction costsTrading becoming increasingly automated (slippage timereduced)

Nevertheless, there are potential profitable circumstances for marketmakers.