Risk Control of Mean-Reversion Time in Statistical Arbitrage

This paper deals with the risk associated with the mis-estimation of mean-reversion of residuals in statistical arbitrage. The main idea in statistical arbitrage is to exploit short-term deviations in returns from a long-term equilibrium across several assets. This kind of strategy heavily relies on the assumption of mean-reversion of idiosyncratic returns, reverting to a long-term mean after some time. But little is known regarding the assessment of this kind of risk. In this paper, we propose a simple scheme that controls the risk associated with estimating mean-reversions by using portfolio selections and screenings. Realizing that each residual has a different mean-reversion time, the ones that are fast mean-reverting are selected to form portfolios. Further control is imposed by allowing the trading activity only when the goodness-of-fit of the estimation for trading signals is sufficiently high. We design a dynamic asset allocation strategy with market and dollar neutrality, formulated as a constrained optimization problem, which is implemented numerically. The improved reliability and robustness of this strategy is demonstrated through back-testing with real data. It is observed that its performance is robust to a variety of market conditions. We further provide some answers to the puzzle of choosing the number of factors to use, the length of estimation windows, and the role of transaction costs, which are crucial issues with direct impact on the strategy