通过提炼多标度分形分析过程中所产生的对描述金融资产收益非对称特征有益的统计信息,提出了一种新的资产收益非对称测度——多标度分形非对称测度(Multifractal asymmetry measurement)Δf,并以沪深300指数长达7年左右的5分钟高频数据为实证样本,通过两种不同的VaR后验分析(Backtesting analysis)方法,实证对比了Δf测度和传统的偏度系数(Coefficient of skewness)测度在市场风险计算准确性方面的差异。实证结果表明:基于Δf测度的市场风险计算模型的VaR计算精度优于基于偏度系数测度的对应模型,Δf测度具有较偏度系数测度更为优异的对金融资产收益非对称特征的刻画能力。
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.
[1] Christofferson P F. Elements of financial risk management[M]. San Diego: Academic Press, 2003.
[2] Korkie B, Sivakumar R, Turtle H J. Variance spillover and skewness in financial asset returns[J]. The Financial Review, 2006, 41(1): 139-156.
[3] Kendall M, Stuart A. The advanced theory of statistics[M]. London: McGraw-Hill Press, 1969.
[4] Engle R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica, 1982, 50(4): 987-1007.
[5] Mandelbrot B B. Fractals and scaling in finance[M]. New York: Springer Press, 1997.
[6] Mandelbrot B B. A multifractal walk down Wall Street[J]. Scientific American, 1999, 298(1): 70-73.
[7] 王鹏, 王建琼. 中国股票市场的多分形波动率测度及其有效性研究[J]. 中国管理科学, 2008, 16(6): 9-15.
[8] Jiang Zhiqiang, Zhou Weixing. Multifractal analysis of Chinese stock volatilities based on the partition function approach[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(19): 4881-4888.
[9] Calvet L, Fisher A. Multifractal volatility: Theory, forecasting, and pricing[M]. London: Academic Press, 2008.
[10] Ramirez J, Alvarez J, Solis R. Crude oil market efficiency and modeling: Insights from the multi-scaling autocorrelation pattern[J]. Energy Economics, 2010, 32(5): 993-1000.
[11] Schmitt F G, Ma Li, Angounou T. Multifractal analysis of the dollar-yuan and euro-yuan exchange rate before and after the reform of the peg[J]. Quantitative Finance, 2011, 11(4): 505-513.
[12] Faruk S, Ramazan G.Intraday dynamics of stock market returns and volatility [J]. Physica A, 2006, 367: 375-387.
[13] Lau H S, Wingender J R, Lau H L. On estimating skewness in stock returns[J]. Management Science, 1989, 35(9): 1139-1142.
[14] Christofferson P F. Elements of financial risk management[M]. San Diego: Academic Press, 2003.
[15] Korkie B, Sivakumar R, Turtle H J. Variance spillover and skewness in financial asset returns[J]. The Financial Review, 2006, 41(1): 139-156.
[16] Kendall M, Stuart A. The advanced theory of statistics[M]. London: McGraw-Hill Press, 1969.
[17] 陈雄兵, 张宗成. 基于修正GARCH模型的中国股市收益率与波动周内效应实证研究[J]. 中国管理科学, 2008, 16(4): 44-49.
[18] Mcmillan D G, Speight A E. Volatility dynamics and heterogeneous markets[J]. International Journal of Finance and Economics, 2006, 11(1): 115-121.
[19] Poshakwale S, Aquino K. The dynamics of volatility transmission and informationflow between ADRs and their underlying stocks[J]. Global Finance Journal, 2008, 19(1): 187-201.
[20] Linden M. A model for return distribution[J]. International Journal of Finance & Economics, 2001, 6(2): 159-170.
[21] 王鹏, 王建琼. 中国股票市场的收益分布及其SPA检验[J]. 系统管理学报, 2008, 17(5): 542-547.
[22] 黄德龙, 杨晓光. 中国股票市场股指收益分布的实证分析[J]. 管理科学学报, 2008, 11(1): 68-77.
[23] Peters E E. Fractal market analysis: Applying chaos theory to investment and economics[M]. New York: Jone Wiley & Sons Press, 1994.
[24] Tolikas K, Gettinby G. Modelling the distribution of the extreme share returns in Singapore[J]. Journal of Empirical Finance, 2009, 16(2): 254-263.
[25] Matto T D. Multi-scaling in finance[J]. Quantitative Finance, 2007, 7(1): 21-36.
[26] Calvet L, Fisher A. Multifractal volatility: Theory, forecasting, and pricing[M]. London: Academic Press, 2008.
[27] Bai Manying, Zhu Haibo. Power law and multi-scaling properties of the Chinese stock market[J]. Physica A: Statistical Mechanics and its Applications, 2010, 389(9): 1883-1890.
[28] 汪富泉, 李后强. 分形几何与动力系统[M]. 哈尔滨: 黑龙江教育出版社, 1993.
[29] Sydney C L, Serena N. The empirical risk-return relation: A factor analysis approach[J]. Journal of Financial Economics, 2007, 83(1): 171-222.
[30] Kupiec P.Techniques for verifying the accuracy of risk measurement models[J]. Journal of Derivatives, 1995, 3(2): 173-184
[31] Engle R F, Manganelli S. CAViaR: Conditional autoregressive value at risk by regression quantiles[J]. Journal of Business and Economic Statistics, 2004, 22(3): 367-381.
[32] Engle R F, Patton A. What good is volatility model?[J]. Quantitative Finance, 2001, 1(2): 237-245.
[33] Mcneil A J, Frey R. Estimation of tail related risk measures forheteroscedastic financial time series: An extreme value approach[J]. Journal of Empirical Finance, 2000, 7(3): 271-300.
[34] Talpsepp T, Rieger M O. Explaining asymmetric volatility around the world[J]. Journal of Empirical Finance, 2010, 17(8): 938-956.
