E ssays on S ta tistical A rbitrage

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Διόσκουροι Λειβαδάς
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1 E ssays on S ta tistical A rbitrage Der Rechts- und Wirtschaftswissenschaftlichen Fakultät/ dem Fachbereich Wirtschaftswissenschafen der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr. rer. pol vorgelegt von Diplom-Wirtschaftsingenieur Univ. Christopher Krauß aus Nürnberg

2 Contents Abstract iv Abstract (deutsche Fassung) V Acknowledgements vi 1 Introduction 1 2 Statistical Arbitrage Pairs Trading Strategies: Review and Outlook Introduction Distance ap p ro ach The baseline approach - Gatev, Goetzmann and Rouwenhorst Expanding on the GGR sam ple From SSD to Pearson correlation and quasi-multivariate pairs trading Explaining pairs trading profitability Further out-of-sample testing of GGR S strategy.. ٠ ٠ Cointegration approach Univariate pairs tra d in g Development of a theoretical framework A large-scale empirical application A deep-dive on the development of optimal trading thresho ld s A review of further empirical applications Multivariate cointegration ap p ro ach Passive index tracking and enhanced indexation strategies Active statistical arbitrage strategies Adjacent developments Time series approach Modeling the spread in state sp ace Applications of the Ornstein-Uhlenbeck process Further concepts from time series analysis Stochastic control approach... 35

3 2.5.1 Modeling asset pricing dynamics with the Ornstein-Uhlenbeck proc e s s ٠ Modeling asset pricing dynamics with error correction models Other approaches Machine learning and combined forecasts approach ٠. ٠ Copula approach Principal components analysis approach Pairs trading in the light of market frictions Conclusion Distance approach Cointegration ap p ro ach Times series approach Stochastic control approach Other approaches Pairs trading in the light of market frictions. ٠ On the power and size properties of cointegration tests in the light of high-frequency stylized facts Introduction Data sample and its stylized f a c ts M ethodology Simulation of stock p ric e s Simulation of cointegration processes Autoregressive m o d e l Generalized autoregressive conditional heteroscedasticity m odel Multiple regime smooth transition autoregressive model Multiple regime smooth transition autoregressive model with reversible ju m p s Multiple regime smooth transition autoregressive model with nonreversible ju m p s Parameter choices common to all Monte Carlo variants The cointegration relation Analysis of power and size properties Cointegration tests Definition of size and power Setup of Monte Carlo sim ulations Results Results Type I through Type I I I Results Type I V Results Type V Results Type V I Economic interpretation Conclusion Pairs trading with partial cointegration Introduction...I ll 4.2 Partial cointegration...113

4 4.2.1 R epresentation Estimation of a partial cointegration m o d e l Consistency of estimation routine Power and size properties of the likelihood ratio test Study design: Comparing partial cointegration with cointegration in the context of pairs trading D a ta The backtesting fram ew ork Building blocks Formation period Trading perio d Trading on simulated d a ta Results Simulated d a t a Empirical d a t a Performance evaluation Sub-period an aly sis Conclusions AppendixA. Identifiability AppendixB. Likelihood function Appendixe. Likelihood ratio t e s t Nonlinear dependence modeling with bivariate copulas: Statistical arbitrage pairs trading on the S&P Introduction Data and so ftw are D a ta Software M ethodology Prelim inaries Copula concept G0 0 dness0 f-fit of copulas Cramér-νοη Mises t e s t Information criteria Formation period Estimation p e rio d period Pseudo-trading.. Suitable p a irs Individualized exit ru le s Trading p e rio d Return com putation Results Return characteristics and trading statistics Value at r i s k Annualized risk-return characteristics Drawdown m easures Subperiod analysis

5 Gouteuts Common risk factors Market frictions Conclusion Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the s& p Introduction Literature review Data and so ftw are D a ta Software Methodology Generation of training and trading sets Feature generation Model tra in in g Deep neural netw orks Gradient-boosted trees Random forests Equal-weighted ensem ble Forecasting, ranking, and trading Results General re s u lts Strategy performance Sub-period analysis Further analy ses Variable im portances Industry breakdown Robustness checks Conclusion Conclusion 223 Bibliography 227

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