Constructing and Trading Sparse Mean-Reverting Portfolios

Abstract

We explore how to construct and trade sparse mean-reverting portfolios. We find that the statistical techniques given by d'Aspremont (2008) give us a statistically higher mean reversion rate than a simple benchmark portfolio, though the economic significance is limited to lower bankruptcy risk and not profitability. We empirically test two portfolio trading strategies - the optimal trading rule given by Jurek and Yang (2007) and the simple threshold rule given by Gatev et al. (2006) - and evaluate the results based on a few metrics: observed terminal wealth, Sharpe ratio and fraction of trading days in which the return on the portfolio exceeds the risk-free return. We find that the optimal trading rule is better but is empirically unstable.