【作者】 李雪；

【导师】 梁志彬；

【作者基本信息】 南京师范大学 ， 应用统计（专业学位）， 2017， 硕士

【摘要】 夏普比率是人们在构建资产组合或对基金业绩进行评价时广泛应用的一个工具,但是由于夏普比率具有时变特征,因此人们在选择投资组合或对其进行评定时会面临很多不确定的因素。本文利用多重分形去趋势波动分析法对中国股市近几年的部分数据进行了实证分析并用R程序进行实现,证实了夏普比率的时变特征是具有多重分形的特点的,而此特点是相关多重分形和分布多重分形共同引起的。在传统的夏普比率中,是用资产组合的标准差来度量风险的,但是由于夏普比率具有多重分形的时变特征,仅用收益的标准差并不能合理地刻画投资资产的表现,因此本文利用多重分形波动测度指标代替收益标准差来对夏普比率进行修正,并用该修正后的夏普比率进行实证分析和程序实现。在实证研究中,本文用平均收益率、传统夏普比率以及基于多重分形波动测度指标的夏普比率对中国股市上的十只股票在2011-2016年间的表现进行了评价和排序,分析了股票在不同的风险测度下表现的差别,证实了基于多重分形波动测度指标的夏普比率比传统夏普比率更加合理。更多还原

【Abstract】 Sharpe ratio is a tool widely used in portfolio construction or evaluation of fund performance, but the time-varying of Sharpe ratio will bring a lot of uncertainties when people face the portfolio selection and evaluation. In this paper, we use the method of multifractal detrended fluctuation analysis to analyze some of the data from the Chinese stock market in recent years and achieve it by R program. Results show that the Sharpe ratio are non-linear timing-varying,present the multifractal characteristics, which is caused by dependence multifractal and distribution multifractal. Traditional Sharpe ratio takes investment standard deviation as the risk meature, but because of the multifractal time-varying characteristics, standard deviation of investment can not reasonably describe the performence of investment assets. We adjust the way of evaluating risk by multifractal volatility measurement ,and use the modified Sharpe ratio in empirical analysis and programming implementation. In the empirical studies, three indexes of the average rate of return,traditional Sharpe ratio and Sharpe ratio adjusted by multifractal volatility meaturement are employed to evaluate and sort the performence of ten stocks in Chinese stock market from 2011 to 2016. Besides, the stocks have different performance under the different risk measure. The paper confirms that Sharpe ratio adjusted by multifractal volatility meaturement is more reasonable than the traditional Sharpe ratio.更多还原