Essays on Statistical Arbitrage. Der Rechts- und Wirtschaftswissenschaftlichen Fakultät/ dem Fachbereich Wirtschaftswissenschafen

Transcription

1 Essays on Statistical Arbitrage 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

2 Abstract Abstract (deutsche Fassung) Acknowledgements iv v vi 1 Introduction 1 2 Statistical Arbitrage Pairs Trading Strategies: Review and Outlook Introduction Distance approach The baseline approach - Gatev, Goetzmann and Rouwenhorst Expanding on the GGR sample From SSD to Pearson correlation and quasi-multivariate pairs trading Explaining pairs trading profitability Further out-of-sample testing of GGR's strategy Cointegration approach Univariate pairs trading Development of a theoretical framework A large-scale empirical application A deep-dive on the developinent of optimal trading thresholds A review of further empirical applications Multivariate cointegration approach Passive index traeking and enhanced indexation strategies Active Statistical arbitrage strategies Adjacent developments Time series approach Modeling the spread in State Space Applications of the Ornstein-Uhlenbeck process Further concepts from time series analysis Stochastic, control approach 35 vii

3 viii Modeling aaset pricing dynamics with the Ornstein-Uhlenbeck proc.ess Modeling asset pricing dynamics with error correction models Ot-her approaches Machine learning and combined forecasts approach Copula approach Principal components analysis approach Pairs trading in the light of market frictions Conclusion Distance approach Cointegration approach Times series approach Stochastic control approach Other approaches Pairs trading in the light. of market frictions 49 3 On the power and size properties of cointegration tests in the light of high-frequency stylized facts Introduc.tion Data sample and its stylized facts Methodology Simulation of stock prices Simulation of cointegration processes Autoregressive model Generalizcd autoregressive conditional heteroscedasticitv model Multiple regime smooth transition autoregressive model Multiple regime smooth transition autoregressive model with reversible jumps Multiple regime smooth transition autoregressive model with nonreversible jumps Parameter choices common to all Monte Carlo variants The cointegration relation Analysis of power and size properties Cointegration tests Definition of size and power Results Setup of Monte Carlo simulations Results Type I through Type III Results Type IV Results Type V Results Type VI Economic Interpretation Conclusion 98 4 Pairs trading with partial cointegration Introduction Partial cointegration 113

4 ix Representation Estimation of a partial cointegration model Consistency of estimation routine Power and size propcrties of the likelihood ratio test Study design: Comparing partial cointegration with cointegration in the context of pairs trading Data The backtesting framework Building blocks Formation period Trading period Trading on simulated data Results Simulated data Empirical data Performance evaluation Sub-period analysis Conclusions AppendixA. Identifiability AppendixB. Likelihood function AppendixC. Likelihood ratio test Nonlinear dependence modeling with bivariate copulas: Statistical arbitrage pairs trading on the S&P Introduction Data and Software Data Software Methodology Preliminaries Copula concept Goodness-of-fit of copulas 159 Cramer-von Mises test 159 Information criteria Formation period Estimation period Pseudo-trading period 164 Suitable pairs 166 Individualized exit rules Trading period Retuni computation Results Return characteristics and trading statistics Value at risk Annualized risk-return characteristics Drawdown measures Subperiod analysis 172

5 x Common risk factoi's Market frictions Conclusion Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P Introduction Literature review Data and Software Data Software Methodology Generation of training and trading sets Feature generation Model training Deep neural networks Gradient-boosted trees Random forests Equal-weighted ensemble Forecasting, ranking, and trading Results General results Strategy Performance Sub-period analysis Further analyses Variable importances Industry breakdown Robustness check« Conclusion Conclusion 223 Bibliography 227