Mean-Reverting Portfolios: Tradeoffs between Sparsity and Volatility

Mean-reverting assets, namely assets whose price oscillates predictably around a long-term mean, provide investors with an ideal investment opportunity. Statistical arbitrage strategies attempt to find portfolios that exhibit mean reversion. This chapter shows that the semidefinite programs (SDP) can handle sparsity and volatility constraints while still aiming at mean reversion. A common econometric tool to find mean reverting portfolios is based on co-integration. The chapter examines the problem of estimating baskets that have maximal mean reversion, while being at the same time sufficiently volatile and supported by as few assets as possible. It presents numerical evidence that taking into account sparsity and volatility can significantly boost the performance of mean-reverting trading strategies in trading environments where trading costs are not negligible. The chapter also shows that, under realistic trading costs assumptions, selecting sparse and volatile mean-reverting baskets translates into lower incurred costs and thus improves the performance of trading strategies.