Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity

Capital asset pricing model (CAPM) has become a fundamental tool in finance for assessing the cost of capital, risk management, portfolio diversification and other financial assets. It is generally believed that the market risks of the assets, often denoted by a beta coefficient, should change over time. In this paper, we model timevarying market betas in CAPM by a smooth transition regime switching CAPM with heteroscedasticity, which provides flexible nonlinear representation of market betas as well as flexible asymmetry and clustering in volatility. We also employ the quantile regression to investigate the nonlinear behavior in the market betas and volatility under various market conditions represented by different quantile levels. Parameter estimation is done by a Bayesian approach. Finally, we analyze some Dow Jones Industrial stocks to demonstrate our proposed models. The model selection method shows that the proposed smooth transition quantile CAPM–GARCH model is strongly preferred over a sharp threshold transition and a symmetric CAPM–GARCH model.