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#### WORKING PAPER

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The Specification of Conditional Expectations

**
Campbell R. Harvey**

*
Fuqua School of Business*

*
Duke University*

Abstract

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.