Does the return-state-varying relationship between risk and return matter in modeling the time series process of stock return?

This paper empirically investigates the time series behavior of stock returns and volatility and the relationship between return premium and stock market risk by utilizing a TSV-GARCH(p,q)-Risk-Mean model. The empirical findings of this paper provide evidence for the distinct driving forces in mean and volatility and the state-dependent tradeoff between risk and return. The empirical results demonstrate that the stock market displays four types of dynamic processes (high-return–low-volatility state, low-return–low-volatility state, high-return–high-volatility state, and low-return–high-volatility state) and that the structural change process of stock market returns is greatly at odds with that of stock market volatility. The TSV-GARCH(1,1)-Risk-Mean model provides better in-sample fit compared to the conventional GARCH(p,q) and regime-switching GARCH(p,q) models. Moreover, the relationship between excess returns and risk is positive, and the intensity of this positive relationship during periods of bear market is significantly higher than that during periods of bull market, which provides supporting evidence for the countercyclical risk premiums hypothesis in which the magnitude of compensation for enduring risk is weaker during periods of favorable financial conditions than during periods of adverse conditions.