The Research Of Open-end Fund Risk Measurement And Performance Evaluation Index On Fractal Theory

The paper bases on the fractal theory, studies the non-linear characters of our country's open-end fund market-multifractal characters. Based on the MF-DFA method, we uses a risk measurement indicatorσhandσhto measure the risk level of our country's open-end fund market and single open-end fund; we studies the performance persistent of our country's open-end fund with the help of V/S analysis method. The empirical study of this paper mainly includes the following content:(1) This article uses the multifractal detrended fluctuation analysis (MF-DFA) method to analysis the indexes of Shanghai and Shenzhen fund market, and the yield time series of Shanghai and Shenzhen fund market indexes that have multifractal characters; and the yield time series of Shanghai fund index's multifractal due to long-range correlation and fat-trail distribution while the yield time series of Shenzhen fund index's multifractal not only due to long-range correlation and fat-trail distribution but some other factors; Using a risk measurement indicatorσh to measure the risk level of Shanghai and Shenzhen fund market and the result is Shanghai fund market's risk level is smaller than Shenzhen fund market and check the validity of the indicatorσh.(2) Usingσhto measure the risk level of single open-end fund. Defining a new risk measurement indicatorσh to measure the risk level of different types and style investing of open-end fund. According to different types investing, the risk level of equity fund is bigger than hybrid fund and bond fund, the risk level of bond fund is smallest; According to different style investing, the risk level of index fund is the biggest, the next is growth fund, the risk level of balanced fund is the smallest.(3) Using the V/S method which applied by Cajueiro (2005) to analysis the performance persistent of our country's open-end fund, and it shows that most of the open-funds have performance persistent and different types and style investing of open-end fund have performance persistent, but with the different intensity. According to the different style investing, the performance persistent of equity fund is the biggest, the next is hybrid fund, the performance persistent of bond fund is the smallest; According to different style investing, the performance persistent of index fund is the biggest, the next is growth fund, the performance persistent of balanced fund is the smallest.