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The Specification of Conditional Expectations

Campbell R. Harvey

Fuqua School of Business

Duke University


This paper explores different specifications of conditional expectations. The most common 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.