A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market*

We examine a variety of models in which the variance of a portfolio’s excess return depends on a state variable generated by a first-order Markov process. A model in which the state is known to economic agents is estimated. It suggests that the mean excess return moves inversely with the level of risk. We then estimate a model in which agents are uncertain of the state. The estimates indicate that agents are consistently surprised by high-variance periods. so there is a negative correlation between movements in volatility and in excess returns.