Portfolio Performance Evaluation Using Value at Risk

Abstract

Developed here is a value at risk-based measure of portfolio performance called the reward-to-VaR ratio. It is demonstrated that, under normality, the reward-to-VaR ratio gives the same ranking for portfolio performance as the frequently used Sharpe ratio. Under non-normality, the reward-to-VaR ratio at one confidence level may give a ranking for portfolio performance different from the ranking obtained at a different confidence level. This indicates that the risk-taking incentives of a portfolio manager in a VaR-based risk management system can be substantially different from the incentives in a Sharpe ratio-based system.