A Markov regime switching model for asset pricing and ambiguity measurement of stock market

Based on the theoretical framework of expected utility with uncertain probabilities, this paper uses actual prices of CSI300 and Hang Seng index to empirically measure ambiguity degrees in the Chinese mainland and Hong Kong stock markets. A Markov regime-switching model is proposed to divide the stock market into bear and bull states, and then test whether there exist significant differences in the ambiguity degrees under different states. An ambiguity factor and a risk factor are then proposed to analyze the time-varying relationship among risk, ambiguity, and return under different states. In addition to the mean and variance, the high-order moments, including skewness and kurtosis, are used to test whether they affect the relationship among them. The results show that the ambiguity degrees in the Chinese mainland stock market are significantly higher than those in the Hong Kong stock market, and there are significant differences between bear and bull states for the two markets. Moreover, the regression results among risk, ambiguity, and return indicate that with ambiguity, the effects of risk factors on excess returns is significantly negative under bear state, and significantly positive under bull state, while it is significantly negative under the two states without ambiguity.