Parameter-free robust optimization for the maximum-Sharpe portfolio problem

Abstract

How can we optimize for the Sharpe ratio if we only have limited training data? Estimates of mean asset returns are noisy, and this noise hurts the out-of-sample Sharpe ratio of current methods. The minimum-variance portfolio, which ignores mean returns, often has a better Sharpe ratio. We develop a parameter-free and scalable method called AlphaRob for this problem. AlphaRob ’s portfolio is a convex combination of two prespecified portfolios. To select the best combination, AlphaRob fuses robust optimization with a new notion of a portfolio’s regret that accounts for the training data’s size. Our analysis only needs mild assumptions on the distribution of asset returns. AlphaRob significantly outperforms competing methods on several simulated and real-world datasets, even after adjusting for transaction costs. AlphaRob is 7.5% better on average than the nearest competitor, and 28% better than the next-best combination portfolio method. Using our regret of regret, we are also able to explain the performance of the minimum-variance portfolio.