Abstract: For describing asymmetry of financial returns, the validity of traditional measurement, i.e., skewness coefficient, is heavily dependent on the assumption that the data is independently and normally distributed. However, actual data in financial markets often has non-independent and non-normal distribution. So a new measurement should be explored to fit stylized facts of actual financial data. After a preliminary exploration for a long time, fractal analysis are found to provide highly targeted solutions for many problems in traditional research about asymmetry of financial returns. By refining useful statistical information to describe the asymmetric features of financial assets' yields during the process of multifractal analysis, a new asymmetry measurement (Δf) is constructed in this paper,whose theoretical properties is more excellent and are more suitable for typical statistical characteristics of actual financial data. Unconditional coverage test and conditional coverage test are used to compare the VaR computation accuracy differences for CSI 300 index between risk models augmented by the skewness coefficients and the Δf measurement. Empirical results show that the latter has higher VaR estimation accuracy. The new measurement which we present in this paper provides a more suitable tool for asymmetry testing to financial returns. Furthermore, this is a typical result of making use of statistical information embedded in the process of fractal analysis.

Key words: multifractal theory, asymmetry measurement, value at risk, backtesting analysis