Portfolio Performance Evaluation with Leptokurtic Asset Returns

When asset returns follow multivariate Levy processes, this paper derives a theoretically sound portfolio performance measure (PPM) that takes into account idiosyncratic and common jump risks. We demonstrate that the PPM can reduce to the Generalized Sharpe Ratio introduced by Zakamouline and Koekebakker (2009), resolving the Sharpe ratio paradox presented in Hodges (1998). With the data of iShares MSCI Germany Index fund, SPDR USA S&P 500 and the iShares MSCI Canada Index Fund over the period from January 1, 2001 to September 30, 2010, we attain that the optimal asset allocation obtained by maximizing the PPM can catch more detailed information of financial shock so that fund managers are able to adjust optimal investment strategy to enhance the investment performance during the period of the financial extreme risk.