| The Capital Asset Pricing Model (CAPM) is aimed at measuring the relationship between therisk and returns in the equilibrium market and the β-coefficient is an index to measure thesystemic risk of this model. EMH, as the theoretical basis of CAPM, has been questioned by moreand more studies, including the Fractal Market Hypothesis (FMH). Based on the framework ofFMH, by studying the systemic risk of the portfolio, this paper shows that the fluctuation of theprice of portfolio bears fractal characteristics in2ways:(1) the volatility of the market portfoliopresents a persistence, i.e., the variance of fluctuations shows a time scaling law;(2) thecovariance between portfolio fluctuations and the market portfolio fluctuations presents, too, atime scaling law. This paper argues that when one above-mentioned time scaling exponent differsfrom another，the β-coefficient of portfolio shows a certain time scaling law and this exponent willbe the difference between the2above-mentioned exponents. On that basis, this paper has given adefinition to the Scale-Variable Capital Asset Pricing Model (SVCAPM). A correspondingeconometric method and the varying pattern of the β-coefficient as well as the characteristics ofSVCAPM are all discussed in this paper. Both an empirical result of the CSI300components’5-min high-frequency data and a comparison between the SVCAPM and the conventional CAPMshow the existence of a time scaling law of the β-coefficient and the reasonableness of theSVCAPM presented in this paper. |
