Statistical Arbitrage & Optimality
Readers interested in statistical arbitrage (statarb) strategies may enjoy brief review of two recent articles: Statistical Arbitrage in the U.S. Equities Market by Avellaneda and Lee (15 Jun 2009 draft) and Analytic Solutions for Optimal Statistical Arbitrage Trading by Bertram (12 Nov 2009 draft).
Avellaneda and Lee survey the results of statarb over 1997 – 2007, focusing on both classic approaches: co-integration (beta-neutralized sector ETFs) and PCA (factors and market-neutralized eigenportfolios). One of the better concise summaries of statarb methodology, outside the few early Ph.D. thesis published on the topic (e.g. Burgess). Section 6 is interesting, as it draws an equivalence between volume-weighting returns (originally popularized by technical analysis) and measuring returns in “trading time” (recently popularized by Dacorogna et al.); using such adjustment increases Sharpe by 37% sharpe (1.51 from 1.1, admittedly neither stellar). Given the broad applicability of both volume-weighting and “trading time” across diverse quantitative strategies, this article is worth review.
Bertram presents closed-form solutions for “optimal statistical arbitrage strategies with transaction costs”, derived from Taylor series approximation of real-valued integral. One interesting result, from § 3.1 is the assertion that optimal entry and exit bands are symmetric around zero (which differs from historical practice, in which such expectations were both ad hoc and tended to be asymmetric). Other interesting results are closed-form solutions for mean and variance of trade length and strategy return.
Bertram’s article follows the technical style, with heavy emphasis on stochastic processes, from his 2005 dissertation: Modelling Asset Dynamics via an Empirical Investigation of Austrialian Stock Exchange Data. Both are worth reading, albeit both being a bit formal.