Non-normality in asset returns is now a common feature of financial markets. However, many practitioners as well as investors do still refer to classic risk adjusted performance measures to assess their investment. Fo...Non-normality in asset returns is now a common feature of financial markets. However, many practitioners as well as investors do still refer to classic risk adjusted performance measures to assess their investment. For example, Sharpe and Treynor ratios are designed for a Gaussian world. Then, employing them for a performance assessment prospect relative to the risk borne is a biased approach. If we look for consistency in risk assessment and in asset performance valuation, we need to look for robust methods or tools. Moreover, the well-known mathematical consistency and numerical tractability concerns drive our preference for simple methods. Under this setting, we propose to account in a simple way and to some extent for the skewness and kurtosis patterns describing the deviations from normality. We adjust therefore the classic Sharpe and Treynor ratios to asymmetries in the downside and upside deviations from the mean values of asset returns. Specifically, the adjusted Sharpe and Treynor ratios are weighted by the upside and downside deviation risks. Accounting for skewness and kurtosis changes generally the ranking of hedge fund performance. Moreover, the obtained adjusted performance measures capture well the skewness and/or kurtosis patterns in hedge fund returns depending on the targeted investment strategy展开更多
This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one...This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.展开更多
文摘Non-normality in asset returns is now a common feature of financial markets. However, many practitioners as well as investors do still refer to classic risk adjusted performance measures to assess their investment. For example, Sharpe and Treynor ratios are designed for a Gaussian world. Then, employing them for a performance assessment prospect relative to the risk borne is a biased approach. If we look for consistency in risk assessment and in asset performance valuation, we need to look for robust methods or tools. Moreover, the well-known mathematical consistency and numerical tractability concerns drive our preference for simple methods. Under this setting, we propose to account in a simple way and to some extent for the skewness and kurtosis patterns describing the deviations from normality. We adjust therefore the classic Sharpe and Treynor ratios to asymmetries in the downside and upside deviations from the mean values of asset returns. Specifically, the adjusted Sharpe and Treynor ratios are weighted by the upside and downside deviation risks. Accounting for skewness and kurtosis changes generally the ranking of hedge fund performance. Moreover, the obtained adjusted performance measures capture well the skewness and/or kurtosis patterns in hedge fund returns depending on the targeted investment strategy
基金This research is supported by the National Science Foundation for Distinguished Young Scholars under Grant No. 70825002, the National Natural Science Foundation of China under Grant No. 70518001, and the National Basic Research Program of China 973 Program under Grant No. 2007CB814902.
文摘This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset＇s price is governed by an exponential Levy process, the liability evolves according to a Levy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.
