中文摘要：

夏普比率的时变特征将给资产投资组合构建带来很大的不确定性。在资产收益率及其波动序列呈现分形特征的背景下，利用多重分形的相关方法对夏普比率的统计特征进行了刻画，并对其多重分形程度进行了量化分析。结果显示，夏普比率时变特征是非线性的，呈现多重分形特征，其成因是由相关多重分形与分布多重分形共同导致。在此基础上，提出了一种修正夏普比率的猜想。为应用夏普比率评价基金业绩、构建有效投资组合等奠定了理论与方法基础。

英文摘要：

The Time-varying of Sharpe ratio will be a big challenge for the portfolio construction. This paper uses the related methods of multifractal to analyze the statistical characteristic of Sharpe ratio and quantitatively analyze its degree,under the background of the return and its volatility of assets present fractal characteristics. Results show that the Sharpe ratios are non-linear time-varying, present the multifractal characteristics, which is caused by dependence muhifractal and distribution multifractal. On this basis, this paper proPoses a suspect of a modified Sharpe ratio. The conclusion of this paper laid a foundation for studyies on fund performance and building effective portfolio by Sharpe ratio.