The Specification of Conditional Expectations

71 Pages Posted: 28 Apr 2005

See all articles by Campbell R. Harvey

Campbell R. Harvey

Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER)

Date Written: August 1991


This paper explores different specifications of conditional expectations. The mostcommon specification, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in financial data, in particular, asymmetric responses of security returns to the direction and magnitude of market returns. The technique is ideally suited for empirically modeling returns of securities that have complicated embedded options. The conditional mean and variance of the NYSE market return are also examined. Forecasts of market returns are not improved with the nonparametric techniques which suggests that linear conditional expectations are a reasonable approximation in conditional asset pricing research. However, the linear model produces a disturbing number of negative expected excess returns. My results also indicate that the relation between the conditional mean and variance depends on the specification of the conditional variance. Furthermore, a linear model relating mean to variance is rejected and these tests are not sensitive to the expectation generating mechanism nor the conditioning information. Rejections are driven by the distinct countercyclical variation in the ratio of the conditional mean to variance. A revised version of this paper was published in the Journal of Empirical Finance in 2001.

Keywords: nonparametric density estimation, forecasted returns, forecasted volatility, asymmetric volatility, reward to risk, time-varying expected returns

JEL Classification: G12

Suggested Citation

Harvey, Campbell R., The Specification of Conditional Expectations (August 1991). Available at SSRN: or

Campbell R. Harvey (Contact Author)

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States
919-660-7768 (Phone)


National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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