Statistical Arbitrage in the U.S. Equities Market

We study model-driven statistical arbitrage in U.S. equities. The trading signals are generated in two ways: using Principal Component Analysis and using sector ETFs. In both cases, we consider the residuals, or idiosyncratic components of stock returns, and model them as mean-reverting processes. This leads naturally to “contrarian” trading signals. The main contribution of the paper is the construction, back-testing and comparison of market-neutral PCAand ETFbased strategies applied to the broad universe of U.S. stocks. Back-testing shows that, after accounting for transaction costs, PCA-based strategies have an average annual Sharpe ratio of 1.44 over the period 1997 to 2007, with much stronger performances prior to 2003. During 2003-2007, the average Sharpe ratio of PCA-based strategies was only 0.9. Strategies based on ETFs achieved a Sharpe ratio of 1.1 from 1997 to 2007, experiencing a similar degradation after 2002. We also introduce a method to account for daily trading volume information in the signals (which is akin to using “trading time” as opposed to calendar time), and observe significant improvement in performance in the case of ETF-based signals. ETF strategies which use volume information achieve a Sharpe ratio of 1.51 from 2003 to 2007. The paper also relates the performance of mean-reversion statistical arbitrage strategies with the stock market cycle. In particular, we study in detail the performance of the strategies during the liquidity crisis of the summer of 2007. We obtain results which are consistent with Khandani and Lo (2007) and validate their “unwinding” theory for the quant fund drawdown of August 2007. ∗Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012 USA †Finance Concepts, 49-51 Avenue Victor-Hugo, 75116 Paris, France.