Risk Control of Mean-Reversion Time in Statistical Arbitrage

Abstract

This paper deals with the risk of mean-reversions in statistical arbitrage. The basic concept of 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 a certain amount of time, but literature on the assessment of risk on this belief is rare. In this paper, we propose a simple scheme that controls the risk on mean-reversions, via portfolio selections and screenings. Realizing that each residual exhibits different mean-reversion time, the residuals that have fast mean-reverting speed are selected to form portfolios. In addition, further control is imposed by allowing the trading activity only when the goodness-of-fit of the estimation for trading signals is sufficiently high. Furthermore, we design the dynamic asset allocation with the market- and dollar-neutrality conditions as a constrained optimization problem, which can be solved numerically. The improved reliability and robustness of the strategy from our method is demonstrated through back-testing results. It has been found that the performance of this investment framework is robust to market fluctuations. We further provide an answer to a puzzled relation among the number of factors, lengths of estimation window, and transaction costs, which are crucial parameters that have direct impacts on the strategy.