Robust Portfolio Optimization with Value-at-Risk Adjusted Sharpe Ratio

Abstract

We propose a robust portfolio optimization approach based on Value-at-Risk (VaR) adjusted Sharpe ratios. Traditional Sharpe ratio estimates based on limited historical return data are subject to estimation errors. Portfolio optimization based on traditional Sharpe ratios ignores this uncertainty in parameter estimation from historical data and is therefore not robust. In this paper, we propose a robust portfolio optimization framework that selects the portfolio with the largest worse-case-scenario Sharpe ratios. We show that this framework is equivalent to maximizing the Sharpe ratio reduced by the VaR of the Sharpe ratio and highlight the relationship between the VaR-adjusted Sharpe ratios and other modi ed Sharpe ratios proposed in the literature. In addition, we present both numerical and empirical results comparing optimal portfolios generated by the approach advocated here and those generated by alternative optimization approaches.