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In this article we investigate portfolio coskewness using a quadratic market model as a return-generating process. We show that the portfolios of small (large) firms have negative (positive) coskewness with the market. We test an asset pricing model including coskewness by checking the validity of the restrictions that it imposes on the return-generating process. We find evidence of an additional component in expected excess returns, which is not explained by either covariance or coskewness with the market. However, this unexplained component is homogeneous across portfolios in our sample and modest in magnitude. Finally, we investigate the implications of erroneously neglecting coskewness for testing asset pricing models, with particular attention to the empirically detected explanatory power of firm size.
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