Theoretical Relations between Risk Premiums and Conditional Variances

David Backus and Allan Gregory

Journal of Business & Economic Statistics, 1993, vol. 11, issue 2, 177-85

Abstract: Many statistical models of time-varying risk premiums, including the autoregressive conditional heteroskedasticity-in-mean, attempt to exploit a relation between risk premiums and conditional variances or covariances of asset returns. The authors examine this relation in numerical versions of a dynamic asset-pricing theory and show that it can be increasing, decreasing, flat, or nonmonotonic. Its shape depends on both the preferences of the representative agent and the stochastic structure of the economy. Without additional structure, the theory does not provide either a general foundation for autoregressive conditional heteroskedasticity-in-mean specifications or a simple interpretation of their parameters.

Date: 1993
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