夏普概率值:一种新的测度投资绩效的方法

Sharpe Ratio Probability:A New Approach to Measure Investment Performance

夏普概率值即收益率满足非正态分布时计算得到的夏普比率高于给定基准值的概率,该指标可以从三个层面有效地降低夏普比率存在的"虚高"现象。一是通过比较夏普概率值与给定的置信水平,筛选出夏普比率"虚高"的投资组合;二是通过对夏普概率值公式的进一步推导,得到拒绝夏普比率存在"虚高"的原假设所需的最小样本量公式,即门槛样本量公式,将计算得到的门槛样本量与样本区间作比较,同样可以筛选得到"虚高"夏普比率投资组合;三是通过对夏普概率值公式和门槛样本量公式的进一步分析发现,延长样本区间或提高抽样频率可以有效降低收益率满足非正态分布时夏普比率出现的"虚高"现象。在夏普概率值的基础上,我们结合马克维茨的投资组合理论推导得到夏普比率有效前沿并得到收益率服从非正态分布下的投资组合最优配置。

Since hedge fund strategies are non-normality in general, Sharpe ratios from these strategies tend to be ＂inflated＂ as a result. We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns to correct those inflationary effects. This new uncertainty-adjusted investment skill metric can solve the problem from three aspects. Firstly, it can filter the ＂inflated＂ Sharpe ratios by comparing a measured Sharpe ratio with a given confidence level. Secondly, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is below a certain threshold with a given confidence level, by which we can also use to filter the Sharpe ratios with inflationary effects. Thirdly, it explains why track records with those undesirable traits would benefit from reporting performance with the highest sampling frequency such that the IID assumption is not violated.