A New Capital Asset Pricing Model with GARCH-type Volatility and Asymmetric Exponential Power Distribution Error Terms

Abstract

The Capital Asset Pricing model (CAPM) is recognized as one of the most important models in researching the relationship between the systematic risk and the expected returns for the stocks. However, the assumption of normal distribution is the main shortage of the original model. In this paper, a new distribution of Standardized Standard Asymmetric Exponential Power Distribution (SSAEPD) is introduced to replace the normal distribution assumption in the original CAPM to eliminate the inaccurate element in assumption and extend the function of CAPM. Meanwhile, this research also includes the discussion of error term volatility by introducing the Generalized AutoRegressive Conditional Heteroskedasticity model (GARCH). To test the hypotheses of the model, the paper collects the data from China300 index from the year 2000 to 2010 and applies maximum likelihood to estimate models. Method of maximum likelihood estimation is used to estimate the model. Markov Chain Monte Carlo (MCMC) method is used to generate random variables from Asymmetric Exponential Power Distribution (AEPD) for simulation. Akaike Information Criterion (AIC) is used to compare the model between different conditions. The results will shed lights on the decision making of risk management. What’s more, this will also benefit the certain group of investors in the financial markets.