Portfolio Optimization Using Conditional Sharpe Ratio

Abstract

In this paper we propose a portfolio optimization model that selects the portfolio with the largest worse-case-scenario sharpe ratio with a given confidence level. We highlight the relationship between conditional value-atrisk based sharpe ratio and standard deviation based sharpe ratio proposed in literature. By utilizing the results of Rockafellar and Uryasev [5], we evaluate conditional value- at- risk for each portfolio. Our model is expected to enlarge the application area of practical investment problems for which the original sharpe ratio is not suitable, however should device effective computational methods to solve optimal portfolio selection problems with large number of investment opportunities. Here conditional sharpe ratio is defined as the ratio of expected excess return to the expected shortfall. This optimization considers both risk and return, of which changes will effect the sharpe ratio. That is the fitness function for dynamic portfolio is the objective function of the model.