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A R B I T R A G E I N T H E F T S E 1 0 0 I N D E x F U T U R E S b y J o a n n a K a l o g e r o p o u l o u D e p a r t m e n t o f E c o n o m i c s & F i n a n c e B r u n e l U n i v e r s i t y A t h e s i s s u b m i t t e d f o r t h e d e g r e e

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ARBITRAGE IN THE FTSE 100 INDEx FUTURES

by

Joanna Kalogeropoulou

Department of Economics & Finance Brunel University

A thesis submitted for the degree of PhD in Finance

March 1998

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ACKNOWLEDGEMENTS

To my beloved parents, Odysseas and Agapy, for their total

support, love and encouragement and for believing in me.

My achievement is merely a reflection of their unlimited

sacrifices. I own everything to them, even though they never ask for anything. Special thanks to my sister,

Helena, for her understanding, and for those long letters

and many hours on the phone that kept me "warm" all this time. I alýso thank my aunt, Elly, for everything she has done for me all these years.

I am mostly gratefulýto my supervisor, Professor Antonios Antoniou, whose guidance and patience made this thesis possible.

Special thanks to Andrew for being there for me all the time, helping me without questioning and most of all,

offering me a shoulder to cry.

Finally, I wish to acknowledge the support of relatives, colleagues, friends and flatmates not mentioned above.

Joanna Kalogeropoulou March 1998

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AnSTRACT

This thesis presents f ive empirical papers investigating

the issue of arbitrage trading of the FTSE 100 stock index futures. The first paper explores the effects of non- synchronous trading on the spot index and develops a new technique as well as improving current methodologies for removing them. Studies in U. S. have shown that if the problem of non-synchronous trading is severe, the reported

spot index is not reliable affecting the correct pricing of futures contracts. The second paper investigates the elasticity of supply of arbitrage in the futures market and the ability of the spot and the futures markets to respond

to new information. It shows that arbitrage trading is

initiated 4 when spot prices largely drift apart from the futures prices. In addition, the futures prices tend to uncover new information before the spot prices, although

this reýlationship is not stable over time. The analysis

incorporates all possible channels of information to the -markets, which previous research fails to consider. The

third paper analyses the behaviour of the deviation of the actual futures price from its theoretical value. Although this deviation is seen to have decreased its size over the years, it is still significant and persistent.

Furthermore, it cannot be explained by the tax-timing

option on pricing the futures or the effects of non- synchronous trading. The fourth paper examines the presence, size and frequency of the profitability of the observed arbitrage opportunities by applying different

transactions costs bounds to account for different classes of traders. After applying trading simulations arbitrage profitability is found to be frequent and significant,

despite the fact that its size has decreased over the years. Finally, the thesis concludes with the fifth

empirical paper which investigates the impact of futures trading on the spot and futures market volatility. it

finds that arbitrage increases spot and futures price volatility but a volatile market brings the two markets

closer. on the whole, the thesis shows that although profitable arbitrage opportunities are not present in the

long-run, they are not quickly removed in the short-run, allowing the spot and futures prices to drift apart.

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CONTENTS

PAGE

Introduction 1

Chapter 1: The Stock Index Futures Market 9

1.1 The Futures Market 9

1.2 The Stock Index and Index Futures Contracts 17

1.3 The Literature Review 20

1.3.1 Elasticity of Supply of Arbitrage 20

1.3.2 Price Dominance Relationship 26

1.3.3 Mispricing and Arbitrage Opportunities 42

1.3.4 Arbitrage and Market Volatility 50

1.3.5 Non-synchronous trading 64

1.4 Conclusions 73

Chapter 2: The effects of Non-synchronous Trading

on the FTSE 100 Stock Index 75

2.1 Introduction 75

2.2 Methodology 77

2.2.1 Miller, Muthuswamy and Whaley (1994) 77

2.2.2 Antoniou and Garrett (1993) 85

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2.2.3 Evaluation of the Models 90

2.2.4 The Implied Index 95

2.3 Data Description and Sources 105

2.4 Empirical Results 113

2.4.1 The Spot Index adjusted with the modified

AR(1) Model 113

2.4.2 The Spot Index adjusted with the Kalman

Filter Model 121

2.4.3 Comparing both Methodologies, results 127

2.4.4 The Implied Index series 138

2.5 Summary and Conclusions 145

Chapter 3: The Elasticity of Supply of Arbitrage and

Price Dominance 149

3.1 Introduction 149

3.2 Methodology 153

3.2.1 The Generalised Dominance Model 153

3.2.2 Time varying relationships 163

3.2.3 Cointegration 164

3.2.4 Johansen Cointegration Technique 168

3.3 Data Description and Sources 171

3.4 Empirical Results 175

3.4.1 Cointegration results 175

3.4.2 Generalised Dominance Point Estimate Result 181

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3.4.3 Rolling Estimation Results 198 3.4.4 Supply of Arbitrage and Price Dominance in

relation to Time to Maturity 208

3.4.5 Supply of Arbitrage and Price Dominance in

relation to the Nature of News 213

3.5 Summary and Conclusions 218

Chapter 4: Empirical Examination of the Mispricing of

the FTSE 100 Stock Index Futures Contract 225

4'. 1 Introduction 225

4.2 Methodology 230

4.2.1 The Pricing relation between Stock Index and Futures described by the

Cost-of-Carry Model 230

4.2.2 Producing the Mispricing Series 238

4.3 Data Description and Sources 241

4.4 Empirical Results 243

4.4.1 Comparing the use of dividend yield to

actual dividend inflow 243

4.4.2 The theoretical futures price calculation 248

4.4.3 The performance of the mispricing series 256

4.4.4 Mispricing and time-to-maturity 279

4.5 Summary and Conclusions 268

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Chapter 5: Investigation of Arbitrage Profitability in

the FTSE 100 Stock Index Futures Contract. 291

5.1 Introduction 291

5.2 Method6logy 295

5.2.1 Arbitrage Window - The Impact of transaction

costs 296

5.2.2 Simulating Arbitrage strategies 300

5.2.3 Path dependence in Misprice 302

5.2.4 Arbitrage Trading or Statistical Illusion 303

5.3 Data Description and Sources 307

5.4 Empirical Results 310

5'. 4.1 Frequency and Size of Violation of the

non-arbitrage pricing boundaries 310

5.4.2 Arbitrage Profitability 326

5.4.3 Results about Misprice and path dependence 338 5.4.4 Results about Arbitrage based on Miller

et al. (1994) 341

5.5 Summary and Conclusions 346

Chapter 6: Index futures arbitrage and market

volatility 349

6.1 Introduction 349

6.2 Methodology 352

IV

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6.2.1 Chan and Chung (1993) 352

6.2.2 GARCH Analysis 358

6.3 Data Description and Sources 361

6.4 Empirical Results 362

6.4.1 GARCH Results -362

6.4.2 The Auto-correlation of the variables 370

6.4.3 OLS Regression of each equation separately 374

6.4.4 SUR results of the model 387

6.5 Summary and Conclusions 392

Chapter 7: Summary and Conclusion 395

Glossary 406-

Bibliography 407

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I

LiST OF TABLES

PAGE 2.1 Option status for relationship between exercise price

and underlying price. 96

2.2 The Options Contracts analysed based on the U. K. Stock

Index FTSE 100. 108

2.3 The exercise price, closing offer and bid for June 92 options contract on March 13,1992. The reported spot

index value for the same day. 109

2.4 The average value and the standard deviation of the FTSE 100 index and its trading volume for the period

27/10/86 and 31/05/95. 112

2.5 Estimated first-order auto- correlation of observed

FTSE 100 index changes (s). 115

2.6 Estimated first-order auto- correlation of both

observed and adjusted for non-synchronicity FTSE 100

index changes. 119

2.7 Estimated first-order auto- correlation of observed

FTSE 100 index (S). 122

2.8 Estimated first-order auto- correlation of both

observed and adjusted for non-synchronicity FTSE 100

index. 125

2.9 Summary stati'stics of the observed spot index, the adjusted for non-synchronicity through Kalman Filter - Spot Index and the adjusted for non-synchronicity

through Miller et al. Spot Index. 130

2.10 Estimated first-order auto- correlation (Pl) of both

observed and adjusted for non-synchronicity FTSE 100 index acquired from both the Kalman Filter, and Miller

et al., models. 131

2.11 Estimated auto- correlations (0j) of non-synchronous

trading adjustment acquired with the use of both the

Kalman Filter and the Miller et al. AR(1) models. 136 2.12 Estimated first-order auto- correlation (01) of the

observed, the adjusted for non-synchronicity (through

Kalman Filter) FTSE 100 index, and the implied index. 141 2.13 Summary statistics of the estimated Implied Index, the

unadjusted and the adjusted for non-synchronicity

(Kalman Filter) Spot Indices. 142

2.14 Summary statistics and first-order auto-correlation of

the adjusted for non-synchronicity FTSE 100 index serie s

acquired from the Miller et al. model. Period 3/92-5/95. 144 3.1 The Futures Contracts analysed based on the U. K. Stock

Index FTSE 100. 173

3.2 Johansen Tests for Stationarity in the Spot and Futures

Stock Indices. 177

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3.3 Johansen Tests for Cointegration in the Spot and Futures

Stock Indices. 180

3.4 Point estimates of the GDM. 184

3.5 Calculation of the elasticity of supply of arbitrage

based on the GDM. 188

3.6 Calculation of the elasticity of supply of arbitrage

based on the Garbade and Silber (1983) model. 190

3.7 Calculation of coefficient of dominance based on GDM. 193 3.8 Calculation of the coefficient of dominance based on

the Garbade and Silber (1983) model. 195

3.9 FTSE 100 Spot and Futures Returns under the effect of

good vs bad news. 214

4.1 Summary statistics of the annual returns on theoretical futures price calculated using both dividend yields

and dividend inflow, period 10/04/90-31/05/95. 247

4.2 Summary statistics of the observed futures price and the unadjusted and adjusted for non-synchronicity

fair futures price series, (sample: 2,869 observations). 252 4.3 Summary statistics of the observed futures price, the

fair futures based on the Implied index, and the unadjusted and adjusted for non. -synchronicity fair

futures price series (sample: 839 observations). 253

4.4 Summary statistics of the estimated relative mispricing

series based on both the unadjusted and adjusted for non-

synchronicity spot series (sample: 2,869 obs). 260

4.5 Summary statistics of the relative mispricing series based on the Implied index and the unadjusted and

adjusted for non-synchronicity mispricing series

(sample: 839obs). 261

4.6 Summary statistics of the mispricing series, X, in the

near FTSE 100 futures contract after both adjusting and not adjusting the spot index for non-synchronicity

(sample: 2,869). 263

4.7 Summary statistics of the mispricing series, X, in the near FTSE 100 futures contract using all three cases of

spot series (sample: 839 observations). 265

4.8 Estimated first-order auto-correlation (0) of the unadjusted and adjusted for non-synchronicity

mispricing series, sample period 01/06/84-31/05/92. 275 4.9 Estimated first-order auto-correlation (P) of the

mispricing series based on the Implied index and the unadjusted and adjusted for non-synchronicity

mispricing series, sample period 13/03/92-31/05//95. 278 4.10 Regression of adjusted for non-synchronicity mispricing

against time to maturity, sample: 2,869 obs. 281

4.11 Regression of absolute magnitude of mispricing against

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time to maturity after both adjusting and not adjusting

the spot index for non-synchronicity, sample: 2,869 obs. 285 4.12 Regression of absolute magnitude of mispricing against

time to maturity, after both adjusting and not adjusting the spot index for non-synchronicity as well as when

using the Implied Index, sample: 839 observations. 287 5.1 Violations of no-profitable arbitrage pricing conditions

for the FTSE 100 futures contract when non-synchronous

trading is not considered. 311

5.2 violations of no-profitable arbitrage pricing conditions for the FTSE 100 futures contract when non-synchronous

trading is considered. 313

5.3 Violations of no-profitable arbitrage pricing conditions for the FTSE 100 futures contract when using the implied

index from options. 315

5.4 Violations of no-profitable arbitrage pricing conditions

when involving time-to-expiration. Cases of adjusting and

not adjusting for nonsynchronicity. 322

5.4a Regression of number of profitable mispricings against

time. Both cases of adjusting and not adjusting for non- pynchronicity are analysed for the period 01/06/84 to

31/05/95.323 5.5 Violations

' of no-profitable arbitrage pricing conditions when involving time-to-expiration. Both adjusting and not adjusting for non-synchronicity and the implied

index cases are analysed. 324

5.5a Regression of number of profitable mispricings against time. All cases of adjusting, not adjusting for non-

synchronicity and using the implied index are analysed for the period 13/03/92 to 31/05/95.325

5.6 Arbitrage trading profits generated based on the

holding-until-expiration trading rule. 329

5.7 Arbitrage profits in relation to time-to-expiration for the three cases of adjusting and no adjusting for non-

synchronicity and using the Implied Index. 332

5.7a Regression of arbitrage profits against time for all levels of transaction costs. Both cases of adjusting

and not'adjusting for non-synchronicity are analysed for the period June 01,1984 to May 31,1995.333

5.7b Regression of arbitrage profits against time for all levels of transaction costs. All cases of adjusting,

not adjusting for non-synchronicity and using the

implied index are analysed for the period March 13, 1992 to May 31,1995.334

5.8 Arbitrage trading profits generated based on both

holding-until-expiration and early unwinding. 337

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5.9 Mispricing violations consisting of upper and lower

transaction cost bound crossings. 340

5.10 Estimated first-order auto-correlation of the FTSE 100

basis changes. 345

6.1a GARCH(0,1) estimations for spot and futures volatility. 364 6.1b GARCH(1,1) estimations for spot and futures volatility. 365 6.1c GARCH(2,1) estimations for spot and futures volatility. 366 6.1d GARCH(1,2) estimations for spot and futures volatility. 367 6.1e GARCH(2,1) estimations for spot and futures volatility. 368 6.2 Auto-correlation of. futures and spot price volatility,

arbitrage spread and spot trading volume. 372

6.3 The results of the OLS regression of equations (6.4.. 6.7) separately, 27/10/86 - 31/05/95.376 6.4 The results of the OLS regression of equations

(6.4.. 6.7) separately, 13/03/92 - 31/05/95.378

6.5 Correlation coefficients of the error terms of

equations (6.4.. 6.7) after separate OLS regression. 380 6.6 The results of the SUR of the model described by

equations (6.4.. 6.7), 27/10/86 - 31/05/95.388

6.7 The results of the SUR of the model described by Eýquations (6.4

... 6.7), 13/03/926 - 31/05/95.390

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LIST OF FIGURES

PAGE 2.1 Profit and loss of writing a put and a call option. 99

2.2 Profit and loss of writing a put option. 102

2.3a Average yearly trading volume of FTSE 100 stock index during the period 27/10/86 and 31/05/95.

4.3b 2 Average yearly value of FTSE 100 stock index during the period 27/10/86 and 31/05/95.

2.4 The change in the observed spot index. 114

2. Sa The change in the observed spot index. 118

2.5b The change in adjusted spot index using Miller et al.

model. 118

2.6 The observed spot index vs the adjusted spot index using

Kalman Filýer model. 124

2.7 Observed spot index vs adjusted using Kalman Filter and

adjusted using Miller et al model. 129

2.8a The absolute value of the non-synchronous trading

adjustment generated using the Miller et al. method for

. he FTSE 100 Index. 133

2.8b The absolute value of the non-synchronous trading

adjustment generated using the Kalman Filter method for

FTSE 100 Index. 133

2.9 The Implied Index based on Put FTSE 100 Index Option's

for the period 13/03/92-31/05/95. 140

2.10 Unadjusted for non-synchronicity FTSE 100 Spot Index

for the period 13/03/92 - 31/05/95. 140

2.11 Adjusted for non-synchronicity (through Kalman Filter)

FTSE100 Index (13/03/92-31/05/95). 140

3.1 GDM Dominance Ratio for both cases of the spot index is

adjusted and not adjusted for non-synchronicity. 194

3.2 GDM Dominance Ratio for both cases of using the adjusted

for non-synchronicity spot index and the implied index. 194 3.3 Elasticity of supply of arbitrage, 5, with rolling

regression estimation of GDM when. spot index is not

adjusted for non-synchronicity (2,869 observations). 200 3.4 Elasticity of supply of arbitrage, 5, with rolling

regression estimation of GDM when spot index is adjusted

for non-synchronicity (2,869 observations). 200

3.5 Elasticity of supply of arbitrage, 5, with rolling

regression estimation of GDM when spot index is not

adjusted for non-synchronicity spot (839 observ. ). 201 3.6 Elasticity of supply of arbitrage, 5, with rolling

regression estimation of GDM when spot index is adjusted

for non-synchronicity spot (839 observ. ). 201

3.7 Elasticity of supply of arbitrage, 5, with rolling

regression of GDM using the implied index (839 obs). 201

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3 .8 GDM Ratio estimated with rolling regression when spot

index is not adjusted for nonsynchronicity (2,869 obs). 206 3 .9 GDM Ratio estimated with rolling regression when the

spot index is adjusted for nonsynchronicity (2,869 obs). 206 3.10 GDM Ratio estimated with rolling regression when spot

index is not adjusted for nonsynchronicity (839 obs). 207 3.11 GDM Ratio estimated with rolling regression when the

spot index is adjusted for nonsynchronicity (839 obs) 207 3.12 GDM Ratio estimated with rolling regression using the

implied index series (839 obs). 207

3.13a The elasticity of supply of arbitrage plotted for some futures contracts covering seven months of their life

and include the expiration month. 210

3.13b The GDM Dominance Ratio plotted for some futures

contracts which cover approximately seven months of

their life and include the expiration month. 211

3.14a The average elasticity of supply of arbitrage across

all contracts including their expiration month for the

sample period of June 84 to May 95. 212

3.14b The average GDM Dominance Ratio across all contracts

including their expiration month for the sample period of

June 84 to May 95. 212

3.15 The elasticity of supply of arbitrage 5, at the arrival

of good news (unadjusted case). 216

3.16 The elasticity of supply of arbitrage 6, at the arrival

of bad news (unadjusted case). 216

3.17 The price dominance ratio, F, at the arrival of good news

(unadjusted case). 217

3.18 The price dominance ratio, r, at the arrival of bad news

(unadjusted case). 217

4.1 The theoretical Futures Price calculated using dividend

yields for the period 10/04/90 - 31/05/95. 244

4.2 The theoretical Futures Price calculated using dividend

inflow for the period 10/04/90 - 31/05/95. 244

4 .3 Returns on the theor(ptical Futures Price calculated

using dividend yields for the period 10/04/90-31/05/95. 244 4.4 Returns on the theoretical Futures Price calculated

using dividend inflow for the period 10/04/90-31/05/95. 244 4.5 The fair futures using unadjusted and adjusted for

non-synchronicity index and observed futures, 6/84-5/95. 249 4.6 The fair futures using unadjusted and adjusted for non-

synchronicity index and implied index and observed

futures price, 3/92-5/95. 250

4.7 The cost-of-carry element against time-to-maturity for

four contracts. 255

t. 8 The mispricing series unadjusted and adjusted for non-

synchronicity for the period 01/06/84-31/05/95. 257

f

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4.9 The mispricing series unadjusted and adjusted for non- synchronic, ity and based on implied index, 3/92-5/95.258

4.10 Average yearly trading volume of the FTSE 100-futures during the period 01/01/87 and 31/05/95.270

6.1 Daily observed spot and futures volatility of the FTSE 100 for the period October 27,1986 to May 31,1995.369

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INTRODUCTION

The presence of futures markets is directly related to the execution of two very important functions; the transfer of

risk through hedging and the discovery of new information

about future outcomes which facilitates and improves the discovery of prices. Despite the fact that both roles of the futures markets are significant for the enhancement of market conditions, hedging is seen as the most vital aspect of these functions. As a result, futures markets are expected to serve as a tool for reducing risk associated

with unfavourable changes in the future. Futures bring risk management opportunities to asset markets.

The successful performance of futures markets and the fulfilment of their functions can only be guaranteed if the prices of the futures markets and their underlying markets

remain close and do not have the possibility to drift apart without limit. At any point where futures prices and the price of the underlying asset do diverge by more than a given limit, arbitrage trading becomes essential by acting

to enforce the law of one price. An arbitrageur exploits

the spread between prices in the futures market and its underlying market by buying in one market at one price and

simultaneously selling in the other market at a higher price. The purchase in the "cheap, market will drive prices up for that market, while the sale in the

'expensive' market will drive prices down until the efficient pricing relationship between the markets is

restored. Consequently, arbitrage trading is the

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imperative link between the futures market and its underlying spot market. As a result, the presence of

arbitrage is directly related to the closeness of the two markets' prices, which_has also important implications for

futures markets serving their proper functions, namely hedging and price discovery.

Although a simplified view of arbitrage trading suggests that it is a risk-free process of easily ac quired profits without the need of capital investment, arbitrage trading

is somewhat more involved. The main reason is because there, is a wide range of transactions costs to be faced by an arbitrage trader, which can quickly transform an

initially perceived arbitrage opportunity to one where costs could outweigh expected profit. However, if price discrepancies persist for long without triggering

profitable arbitrage opportunities, then the spot and futures markets will drift apart over the long term with potentially devastating consequences for the functions of

the futures market and for hedging in particular.

Given the vital role of arbitrage in maintaining a price discipline between spot and futures markets which ensures

the performance of hedge trades and the discovery of new information, this thesis focuses its attention on arbitrage

in the U. K. stock index futures market. This thesis is motivated by a desire to further the investigation of arbitrage activity in U. K. stock index futures. There are a number of reasons for identifying this field of study as being worthy of further analysis. First, the majority of

the existing studies concentrate only on the U. S. market,

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