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AbstractIn this study benchmark error is tested for as a source of the small firm effect by comparing the results from ordinary least squares and instrumental variable methods. Although the instrument is not perfect, results show that benchmark error could be a cause of the overall (all months) small firm effect. Results from the instrumental variable method indicate that large January abnormal returns are still present, but that they are offset by negative non‐January abnormal returns. As a result, the instrumental variable results show that there is no longer a significant overall "effect," merely a seasonal effect. It is also found that the results are not sensitive to the choice of the market index.

AbstractWe show that E[X(g(Y1, …, Yn)] (where E[.] is the expectation operator) can be decomposed into a product of two expected values plus a sum of n comovement terms, if X, Y1, …, Yn follow a distribution that admits linear conditional expectation (LCE). We then apply this relation to show that if each asset return is LCE distributed with the market and/or the factors, many capital asset pricing models and the mutual fund separation theorem can be obtained. A well‐known example of a class of distributions that admits LCE is the elliptical distributions, of which the normal is a special case. A larger family, not mentioned in the existing literature, that admits LCE is the Pearson system. As a result, the distribution assumption to derive the capital asset pricing theories can be relaxed to the wider LCE family. We also present the relation of the LCE family to Ross's (1978) separating distribution family.