CITY UNIVERSITY OF HONG KONG 香港城市大學. Inter-Market Pairs Trading Strategy Construction Using Stochastic Approach 基於隨機過程的跨市場配對交易策略研究

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1 CITY UNIVERSITY OF HONG KONG 香港城市大學 Inter-Market Pairs Trading Strategy Construction Using Stochastic Approach 基於隨機過程的跨市場配對交易策略研究 Submitted to Department of Management Sciences 管理科學系 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 哲學博士學位 by Huang Ying 黃瑩 August 2014 二零一四年八月

2 Inter-Market Pairs Trading Strategy Construction Using Stochastic Approach by Huang, Ying Department of Management Sciences College of Business City University of Hong Kong Abstract Pairs trading, a strategy used for statistical arbitrage, is a popular market-neutral trading strategy that matches a long position with a short position in two correlated stocks. It works by finding two stocks that move together, and taking long or short positions when they diverge abnormally, expecting that their prices will converge in the future. There are three categories of approaches to pairs trading: the distance method, the co-integration method and the stochastic method. In this paper, we mainly study strategy construction based on stochastic approach. It shows that there exists statistical arbitrage opportunities between commodities markets, currency exchange market and stock market, indicating the deficiency of market efficiency between different sectors of financial market. The main work of this paper includes two parts: constructing a novel stochastic bid-ask spread approach in inter-market as well as evaluating the performances of classic pairs trading strategies, and developing a loss protection pairs trading strategy focusing on the control of positions in pairs trading. Stochastic approach incorporates mean reversion process into pairs trading framework, and this property is the most important statistical relationship required for success. If the value of a portfolio is known to fluctuate around its i

3 equilibrium value over time, then any deviations from this equilibrium can be traded against. Especially in this thesis, pairs trading strategies are developed based on stochastic forecasting process in terms of bid-ask spread between a pair of assets. The mean reverting stochastic process, described as Ornstein- Uhlenbeck (OU) process, is used to analyze the properties of price time series of assets. Two OU processes based on two bid-ask spreads are developed. Least square regression method is adopted to estimate the parameters of two models. To evaluate the performances of the proposed strategies, several classic pairs trading strategies are discussed in this thesis. We also investigate the profitability of classic pairs trading strategies in high frequency trading, when both bid-ask spread and transaction costs are included. We apply the pairs trading strategy to three selected categories of equities in inter-market, to examine whether positive excess return can be generated in heterogeneous groups. We find that pairs trading is able to achieve statistically significant daily excess returns on average for almost all the approaches if no transaction costs or bid-ask spreads are included. But once the transaction costs or bid-ask spreads are included in the experiments, their performances become bad, except that the stochastic model with transaction cost embedded can still achieve good returns if only transaction cost is included. Based on this phenomenon, we develop a new stochastic approach based on bid-ask price spread for pairs trading by constructing the model with both factors. It is an extension of the stochastic model proposed by Bertram. In this model, we integrate two bid-ask OU processes, assuming that the two bid-ask spread time series are highly correlated and both follow the mean-reverting process, which is tested by co-integration method. Our empirical results show that the proposed strategy is profitable with a daily average excess return of 0.03%, taken as the mean of all returns of different frequencies, when including only the bid-ask spreads. ii

4 The issue of effective bid-ask spread and transaction cost is also discussed. We find that the steady effective bid-ask spread and transaction costs can be estimated as 70 bp. and 80 bp., respectively, providing evidence for argument about effective bid-ask spread and transaction costs in GateV et al. (2006)[59]. We also present the performances of top 10 profitable pairs during the total trading periods in 1-minute frequency, and find that the pair lists of top 10 for all approaches are almost the same, and active pairs always exist between foreign currency and precious metal assets. Moreover, according to the empirical comparisons between the classic strategies and the proposed strategy, the tiny difference between parameters of entry rule, might lead a negative excess return to positive return. In addition, we develop another model to obtain a minimum return per trade to control positions in pairs trading, acting as a complementary part for the s- tochastic approach based on bid-ask prices. Combining the optimal entry and exit rules with the loss protection model, more returns can be generated by controlling the number of trade units at every run. iii

5 Table of Contents Abstract i Acknowledgements vii Table of Contents ix List of Figures xii List of Tables xiii 1 Introduction Background Research Problems and Contribution Thesis Organization Literature Review Statistical Arbitrage Statistical Arbitrage Models for Investment Market Efficiency and Statistical Arbitrage Pairs Trading Market Neutrality and the Law of One Price Distance Method Cointegration Method ix

6 2.2.4 Stochastic Method Combined Forecast Method Summary A Novel Stochastic Approach Based on Bid-ask Prices in Pairs Trading Introduction Problem Formulation Optimal Solutions Cointegration Test Unit Root Test Empirical Analysis Strategy Formulation Data Empirical Results Summary A Strategy with Minimum Return Bounds Based on Bid-Ask Prices Introduction Problem Formulation Return Generated by a Completely Pair Trade The Definition of Minimum Return per Trade Strategy Construction Empirical Analysis Summary Conclusions Summary x

7 5.2 Future Work xi