Robust optimization of time series momentum portfolios

Abstract

Mean-Variance Optimization (MVO) is well-known to be extremely sensitive to slight differences in the expected returns and covariances: if these measures change day to day, MVO can specify very different portfolios. Making wholesale changes in portfolio composition can cause the incremental gains to be negated by trading costs. We present a method for regularizing portfolio turnover by using the ℓ1 penalty, with the amount of penalization informed by recent historical data. We find that this method dramatically reduces turnover, while preserving the efficiency of mean-variance optimization in terms of risk-adjusted return. Factoring in reasonable estimates of transaction costs, the turnover-regularized MVO portfolio substantially outperforms a leverage-constrained MVO approach, in terms of risk-adjusted return.