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

31 Pages Posted: 9 Mar 2004 Last revised: 15 Sep 2022

Date Written: 1989


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.

Suggested Citation

Turner, Christopher M. and Startz, Richard and Nelson, Charles R., A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market (1989). NBER Working Paper No. w2818, Available at SSRN: https://ssrn.com/abstract=447232

Christopher M. Turner

Black Rock Financial Management, Inc. ( email )

345 Park Avenue
New York, NY 10154

Richard Startz

UCSB ( email )

Department of Economics
University of California
Santa Barbara, CA 93106-9210
United States
805-893-2895 (Phone)

Charles R. Nelson (Contact Author)

Dept of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States