A Study of the Time Scaling Law of the β-Coefficient:Based on the Fractal Market Hypothesis

魏益华，吉林大学经济学院教授；程九思，吉林大学经济学院博士研究生；周佰成，吉林大学经济学院教授。【中文摘要】资本资产定价模型旨在衡量均衡资本市场中风险与收益之间的关系，β系数是该模型提出的计量系统性风险的一种指标。证券价格的波动具有两类分形特征：一是市场的波动具有状态持续性，其波动的方差具有时间标度性；二是证券的波动与市场的波动之间的协方差具有时间标度性。当这两个标度特征不一致时，β系数具有时间标度性，且其标度指数为两者之差。理论推导和对沪深300成分股5分钟高频数据的实证检验表明，标度可变资本资产定价模型（SV- CAPM)可以有效描述β系数的标度幂律特征，并具有更高的稳健性和对系统性风险的识别度。 【Abstract】The Capital Asset Pricing Model (CAPM) is aimed at measuring the relationship between risks and returns in the equilibrium market，and the β-coefficient is an index to measure the systemic risk of this model. The fluctuation of prices of portfolio bears fractal characteristics in two ways: (1)the volatility of the market portfolio presents persistence，and the variance of fluctuations shows a time scaling law； (2)the covariance between portfolio fluctuations and the market portfolio fluctuations presents，too，a time scaling law. When one scaling exponent differs from another，the β-coefficient shows a certain time scaling law and this scaling exponent will be the difference between the two above-mentioned exponents. Both theoretical and empirical studies of the CSI 300 components'5-min high-frequency data indicate that SVCAPM can effciently describe the existence of a time scaling law of the β-coefficient，and that it posesses greater stability and is able to increase the ability to recognize systemic risks.国家社会科学基金青年项目“中国与全球股票市场价格波动的动态相关性研究”（11CJY105