Sharpe Ratio With Multifractal Volatility Measurement And Its Appliacation In Empirical Analysis

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.