Four essays in statistical arbitrage in equity markets

135 Pages·2011·1.74 MB·English

Four Essays in Statistical Arbitrage in Equity Markets

Jozef Rudy

Liverpool Business School

A thesis submitted in partial fulfillment of the
requirements of Liverpool John Moores University
for the degree of Doctor of Philosophy.

June 2011

i
Declaration

I declare that with the exception of the assistance acknowledged,
this dissertation is the result of an original investigation and that it
has not been accepted or currently submitted in candidate for any
other degree.

Candidate

….…………………(signed)

Supervisor

….…………………(signed)

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Committee

Supervisory Team
Prof. Christian Dunis (Director of Studies)
Mr Jason Laws (1 Supervisor)
st

Examination Team
Prof. Roy Batchelor (External)
(Cass Business School)

Dr Gianluigi Giorgioni (Internal)
(Liverpool John Moores University, School of
Accounting Finance and Economics)

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Acknowledgements

I would like to thank, first and foremost, my Director of Studies,
Professor C. Dunis, without whom this dissertation would not exist. I am
grateful for his grant offer at the beginning. Also his invaluable insights
and our frequent discussions about trading approaches have helped me
in coming up with original yet simple and practical ideas.

I would also like to thank my Supervisor Jason Laws, for his support
and help during the time spent at LJMU.

I am also very thankful to my work colleagues, friends and family for
their lasting support and encouragement.

“Any intelligent fool can make things bigger and more complex. It takes a
touch of genius and a lot of courage to move in the opposite direction.”

Albert Einstein
(1879 – 1955) a physicist and a Nobel Prize winner
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Abstract

This thesis deals with the statistical arbitrage in shares and Exchange traded
funds (ETFs) markets. It addresses pair trading strategies in various time frames
ranging from a minute to daily data and it also addresses various modeling
techniques. The modeling techniques used range from a simple ordinary least
square (OLS) regression to the Kalman filter.

Although market neutral trading strategies originated in 1980 on Wall Street, it is
shown in this dissertation that they can still be attractive for investors, when certain
nontraditional adjustments are implemented.

After the introductory chapter and the relevant literature review in Chapter 2, in
Chapter 3 we show that when high-frequency data (ranging from minutes to hours)
are used for market neutral strategies, they offer more attractive results compared to
only using daily closing prices. In the same chapter it is also shown that the Kalman
filter is superior to various versions of OLS regression (rolling, fixed) for the
calculation of the spread between the shares.

In Chapter 4 we show that pair trading on ETFs is more attractive for investors
than pair trading on shares. We also show that to obtain attractive results, one does
not have to resort to high-frequency data as in Chapter 3. It is enough that one uses
both opening and closing prices instead of only closing prices.

In Chapter 5 we describe yet another version of statistical arbitrage strategy
based purely on autocorrelation criteria of the pair spread. This proves much more
profitable for ETFs than for shares yet again.

Finally, in Chapter 6 we present a mean reversion strategy based on the well-
known academic theory "buy losers, sell winners" described in Thaler and De Bondt
(1985). We divide a trading session into day (open to close) and night (close to
open) and show that an investor can make money following a simple principle of
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buying daily losers and holding them overnight, or buying nightly losers and holding
them during the following day.

In conclusion it is found that simple yet innovative adjustments to already well-
known investment approaches can be of value to investors.

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Table of Contents
Chapter 1 ______________________________________________________________ 1
1.1 INTRODUCTION _________________________________________________ 1
1.2 BACKGROUND TO THE THESIS ______________________________________ 2
1.3 MOTIVATION ___________________________________________________ 2
1.4 CONTRIBUTIONS TO KNOWLEDGE __________________________________ 3
1.5 STRUCTURE OF DISSERTATION _____________________________________ 4
Chapter 2 - Literature review ____________________________________________ 6
2.1 MARKET NEUTRAL STRATEGIES _____________________________________ 6
2.2 COINTEGRATION ________________________________________________ 7
2.3 TIME ADAPTIVE MODELS _________________________________________ 10
2.4 EXCHANGE TRADED FUNDS _______________________________________ 10
2.5 HEDGE FUNDS __________________________________________________ 11
Chapter 3 - Statistical Arbitrage and High-Frequency Data with an Application to
Eurostoxx 50 Equities _______________________________________________________ 12
3.1 INTRODUCTION ________________________________________________ 13
3.2 THE EUROSTOXX 50 INDEX AND RELATED FINANCIAL DATA _____________ 14
3.3 METHODOLOGY ________________________________________________ 17
3.3.1 Cointegration model ________________________________________________________ 17
3.3.2 Rolling OLS ________________________________________________________________ 18
3.3.3 Double exponential-smoothing prediction model _________________________________ 19
3.3.4 Time-varying parameter models with Kalman filter ________________________________ 20
3.4 THE PAIR TRADING MODEL _______________________________________ 20
3.4.1 Spread calculation __________________________________________________________ 21
3.4.2 Entry and exit points ________________________________________________________ 21
3.4.3 Indicators inferred from the spread ____________________________________________ 24
3.5 OUT-OF-SAMPLE PERFORMANCE AND TRADING COSTS ________________ 26
3.5.1 Return calculation and trading costs ____________________________________________ 26
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3.5.2 Preliminary out-of-sample results ______________________________________________ 27
3.5.3 FURTHER INVESTIGATIONS ___________________________________________________ 31
3.6 A DIVERSIFIED PAIR TRADING STRATEGY ____________________________ 36
3.7 CONCLUDING REMARKS__________________________________________ 43
3.8 APPENDICES ___________________________________________________ 44
Chapter 4 - Profitable Pair Trading: A Comparison Using the S&P 100 Constituent
Stocks and the 100 Most Liquid ETFs ___________________________________________ 49
4.1 INTRODUCTION ________________________________________________ 50
4.2 THE S&P 100 INDEX AND ETFs _____________________________________ 51
4.3 METHODOLOGY ________________________________________________ 52
4.3.1 Bollinger bands ____________________________________________________________ 52
4.4 THE PAIR TRADING MODEL _______________________________________ 53
4.4.1 Calculation of the spread _____________________________________________________ 53
4.4.2 Entry, exit points and money-neutrality of positions _______________________________ 54
4.5 OUT-OF-SAMPLE TRADING RESULTS ________________________________ 55
4.5.1 Returns calculation _________________________________________________________ 55
4.5.2 Results for all pairs __________________________________________________________ 56
4.5.3 Some reasons for the superior performance of ETFs _______________________________ 57
4.5.4 RESULTS FOR THE BEST FIFTY PAIRS ____________________________________________ 59
4.6 CONCLUDING REMARKS__________________________________________ 61
4.7 APPENDICES ___________________________________________________ 63
Chapter 5 - Mean Reversion Based on Autocorrelation: A Comparison Using
the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs ______________________ 64
5.1 INTRODUCTION ________________________________________________ 65
5.2 THE S&P 100 INDEX AND ETFs _____________________________________ 67
5.3 METHODOLOGY ________________________________________________ 68
5.3.1 Outline ___________________________________________________________________ 68
5.3.2 Forming pairs ______________________________________________________________ 68
5.3.3 Calculation of the spread _____________________________________________________ 69
5.3.4 Conditional Autocorrelation __________________________________________________ 70
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5.3.5 Normalized return __________________________________________________________ 71
5.3.6 Measure of spread profitability: Information ratio ________________________________ 71
5.3.7 Optimization_______________________________________________________________ 72
5.4 TRADING RESULTS ______________________________________________ 72
5.4.1 Returns calculation _________________________________________________________ 72
5.4.2 Results for the daily data and pairs of shares _____________________________________ 73
5.4.3 Results for the daily data and pairs of ETFs ______________________________________ 74
5.4.4 Results for the half-daily data and pairs of shares _________________________________ 76
5.4.5 Results for the half-daily data and pairs of ETFs ___________________________________ 78
5.5 CONSISTENCY OF THE OUT-OF-SAMPLE RESULTS ______________________ 81
5.6 CONCLUDING REMARKS__________________________________________ 82
5.7 APPENDICES ___________________________________________________ 84
Chapter 6 - Profitable Mean Reversion after Large Price Drops: A story of Day and
Night in the S&P 500, 400 Mid Cap and 600 Small Cap Indices ______________________ 90
6.1 INTRODUCTION ________________________________________________ 91
6.2 LITERATURE REVIEW ____________________________________________ 92
6.2.1 Predictability of returns ______________________________________________________ 92
6.2.2 Contrarian strategies ________________________________________________________ 92
6.2.3 Overreaction hypothesis _____________________________________________________ 93
6.2.4 Stock returns following large price declines ______________________________________ 94
6.2.5 Bid-ask bounce effect _______________________________________________________ 94
6.2.6 Opening gaps and periodic market closures ______________________________________ 95
6.3 RELATED FINANCIAL DATA AND TRANSACTION COSTS _________________ 96
6.3.1 Data sources _______________________________________________________________ 96
6.3.2 Day and night return characteristics ____________________________________________ 97
6.4 TRADING STRATEGY _____________________________________________ 99
6.5 STRATEGY PERFORMANCE _______________________________________ 101
6.5.1 Strategy performance by decile ______________________________________________ 101
6.5.2 Strategy performance by year ________________________________________________ 104
6.5.3 Bid-ask bounce ____________________________________________________________ 106
6.6 MULTI-FACTOR MODELS ________________________________________ 107
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6.7 CONCLUDING REMARKS_________________________________________ 111
6.8 APPENDICES __________________________________________________ 112
Chapter 7 - General Conclusions _______________________________________ 116
References ___________________________________________________________ 119

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