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Statistical Arbitrage Pairs Trading, Long-Short Strategy Cyrille BEN LEMRID  1 Pairs Trading Model 5 1.1 Generaldiscussion ................................ 5 1.2 Cointegration ................................... 6 1.3 Spreaddynamics ................................. 7 2 State of the art and model overview 9 2.1 StochasticDependenciesinFinancialTimeSeries . . . . . . . . . . . . . . . 9 2.2 Cointegration-basedtradingstrategies ..................... 10 2.3 FormulationasaStochasticControlProblem. . . . . . . . . . . . . . . . . . 13 2.4 Fundamentalanalysis............................... 16 3 Strategies Analysis 19 3.1 Roadmapforstrategydesign .......................... 19 3.2 Identificationofpotentialpairs ......................... 19 3.3 Testingcointegration ............................... 20 3.4 Riskcontrolandfeasibility............................ 20 4 Results 22 2 Contents  Introduction This report presents my research work carried out at Credit Suisse from May to September 2012. This study has been pursued in collaboration with the Global Arbitrage Strategies team. Quantitative analysis strategy developers use sophisticated statistical and optimization techniques to discover and construct new algorithms. These algorithms take advantage of the short term deviation from the ”fair” securities’ prices. Pairs trading is one such quantitative strategy - it is a process of identifying securities that generally move together but are currently ”drifting away”. Pairs trading is a common strategy among many hedge funds and banks. However, there is not a significant amount of academic literature devoted to it due to its proprietary nature. For a review of some of the existing academic models, see [6], [8], [11] . Our focus for this analysis is the study of two quantitative approaches to the problem of pairs trading, the first one uses the properties of co-integrated financial time series as a basis for trading strategy, in the second one we model the log-relationship between a pair of stock prices as an Ornstein-Uhlenbeck process and use this to formulate a portfolio optimization based stochastic control problem. This study was performed to show that under certain assumptions the two approaches are equivalent. Practitioners most often use a fundamentally driven approach, analyzing the performance of stocks around a market event and implement strategies using back-tested trading levels. We also study an example of a fundamentally driven strategy, using market reaction to a stock being dropped or added to the MSCI World Standard, as a signal for a pair trading strategy on those stocks once their inclusion/exclusion has been made effective. This report is organized as follows. Section 1 provides some background on pairs trading strategy. The theoretical results are described in Section 2. Section 3
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