Abstract
In this paper, a new model is proposed to empirically test the Capital Asset Pricing Theory. This model is based on the EGARCH-type volatilities in Nelson (1991) and the non-Normal errors of SSAEPD in Zhu and Zinde-Walsh (2009). Is the CAPM theory in Sharpe (1964), Lintner (1965) and Mossin (1966) still alive? Returns of Fama-French 25 stock portfolios (1926-2011) are analyzed. The Maximum Likelihood Estimation Method is used. Likelihood Ratio test (LR) and Kolmogorov-Smirnov test (KS) are used to do model diagnostics. Akaike Information Criterion (AIC) is used for model comparison. Simulation results show the MatLab program is valid. Empirical results show with non-Normal errors and the EGARCH-type volatilities, the CAPM theory is not alive. This new model can capture the skewness, fat-tailness, asymmetric effects and volatility persistence in the data. This new model has better in-sample fit than others. Portfolios with smaller size have larger Beta value.
Highlights
Capital Asset Pricing Model (CAPM) is first established by Sharpe (1964), Lintner (1965) and Mossin (1966) [1], based on the investment portfolio theory of Markowitz (1959)
2) Can this new model beat the CAPM-Standardized Standard Asymmetric Exponential Power Distribution (SSAEPD) model of Zhuo (2013) [12]? 3) Can we find any new patterns for Fama-French 25 portfolios? To answer these questions, simulation is done first
Parameter α controls the skewness of SSAEPD
Summary
Capital Asset Pricing Model (CAPM) is first established by Sharpe (1964), Lintner (1965) and Mossin (1966) [1], based on the investment portfolio theory of Markowitz (1959). The hypotheses will be tested as follows: 1) With non-Normal error terms such as SSAEPD in Zhu and Zinde-Walsh (2009), and EGARCH-type volatilities in Nelson (1991), is the CAPM theory of Sharpe (1964), Lintner (1965) and Mossin (1966) still alive?. Empirical results show with non-Normal error terms and EGARCH-type volatilities, the CAPM theory of Sharpe (1964), Lintner (1965) and Mossin (1966) can not explain the US stock market. The estimates of this new model can capture fat-tailness, asymmetric effects, and volatility persistence in the data.
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