Statistical Arbitrage in South African Equity Markets

93 Pages·2014·1.66 MB·English

Statistical Arbitrage in
South African Equity
Markets
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Khuthadzo Masindi
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Student no : MSNKHU003

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Supervisors : Sugnet Lubbe and Kevin Kotze
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Dissertation presented for the degree of Master of Philosophy in
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Msathematical Finance
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Faculty of Commerce
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University of Cape Town
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17 February 2014
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The copyright of this thesis vests in the author. No
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quotation from it or information derived from it is to be

published without full acknowledgeement of the source.
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The thesis is to be used for private study or non-
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commercial research purposes only.

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Published by the Universit y of Cape Town (UCT) in terms
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of the non-exclusive license granted to UCT by the author.
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Thesis
Khuthadzo Masindi
October 6, 2014
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Plagiarism declaration
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pretend that it is my own.
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contribution to, and quotation in this thesis from the work(s) of other people
has been contributed, and has been cited and referenced.
3. This thesis is my own work.
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Signature :
Date : 17 February 2014
Publication
I hereby grant the University free license to publish this dissertation in whole
or in part, and in any format the University deems fit
Acknowledgements
I would like to express my special appreciation and thanks to my supervi-
sors Professor Sugnet Lubbe and Mr Kevin Kotze, your assistance has been
priceless. A special thanks to my family. Words cannot express how grateful
I am to my father, my mother and my sister for your support and prayers. I
would also like to thank all of my friends who supported me, and encouraged
me to strive towards my goal.
Abstract
The dissertation implements a model driven statistical arbitrage strategy
that uses the principal components from Principal Component Analysis as
factors in a multi-factor stock model, to isolate the idiosyncratic compo-
nent of returns, which is then modelled as an Ornstein Uhlenbeck process.
The idiosyncratic process (referred to as the residual process) is estimated
in discrete-time by an auto-regressive process with one lag (or AR(1) pro-
cess). Tradingsignalsaregeneratedbasedontheleveloftheresidualprocess.
This strategy is then evaluated over historical data for the South African
equity market from 2001 to 2013 through backtesting. In addition the strat-
egy is evaluated over data generated from Monte Carlo simulations as well as
bootstrapped historical data. The results show that the strategy was able to
significantly out-perform cash for most of the periods under consideration.
The performance of the strategy over data that was generated from Monte
Carlo simulations demonstrated that the strategy is not suitable for markets
that are asymptotically efficient.
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Contents
1 Introduction 6
2 Arbitrage 10
2.1 Pure Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Near Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Statistical arbitrage . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Pairs trading and portfolio construction 14
3.1 Principal component analysis . . . . . . . . . . . . . . . . . . 19
3.2 Residual Process . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Ornstein-Uhlenbeck process . . . . . . . . . . . . . . . . . . . 24
3.4 Estimating the OU model . . . . . . . . . . . . . . . . . . . . 26
4 Formulating the Investment Strategy 28
4.1 Signal generation . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.2 Profit and loss and trading signals . . . . . . . . . . . . 30
4.2 Implementing the residual process model . . . . . . . . . . . . 34
4.2.1 Constant OU parameters derived from the original re-
gression residual process . . . . . . . . . . . . . . . . . 35
4.2.2 Dynamic OU parameters derived from a residual pro-
cess that fully incorporates the continued process and
the regression residual process . . . . . . . . . . . . . . 36
4.2.3 Dynamic OU parameters with updating and replacement 36
4.3 Parameter estimation and sample selection . . . . . . . . . . . 37
4.4 Capital allocation . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6 Control experiments . . . . . . . . . . . . . . . . . . . . . . . 40
4.6.1 Monte Carlo simulations . . . . . . . . . . . . . . . . . 41
4.6.2 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . 41
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