A Markov model of heteroskedasticity, risk, and learning in the stock market

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Abstract

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.

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    Advice from the referee, James D. Hamilton, and the editor, G. William Schwert, both substantive and expositional, is gratefully acknowledged. Thanks also to Wing Suen and Walter Fisher for valuable criticism of earlier drafts. Of course, any remaining errors remain the responsibility of the authors. Nelson's participation was sponsored in part by the Center for the Study of Banking and Security Markets, University of Washington. The opinions expressed in this paper are those of the authors, not those of the Federal Reserve System.

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