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

Abstract

Risk premia in the stock market are assumed to move with time varying risk. We present a model in which the variance of time excess return of a portfolio depends on a state variable generated by a first-order Markov process. A model in which the realization of the state is known to economic agents, but unknown to the econometrician. is estimated. The parameter estimates are found to imply that time risk premium declines as time variance of returns rises. We then extend the model to allow agents to be uncertain about time state. Agents make their decisions in period t using a prior distribution of time state based only on past realizations of the excess return through period t-1 plus knowledge of the structure of the model. These parameter estimates from this model are consistent with asset pricing theory.