In this paper we investigate the properties of the standard two‐pass methodology of testing beta pricing models with misspecified factors. In a setting where a factor is useless, defined as being independent of all the asset returns, we provide theoretical results and simulation evidence that the second‐pass cross‐sectional regression tends to find the beta risk of the useless factor priced more often than it should. More surprisingly, this misspecification bias exacerbates when the number of time series observations increases. Possible ways of detecting useless factors are also examined.

In this paper we investigate the properties of the standard two‐pass methodology of testing beta pricing models with misspecified factors. In a setting where a factor is useless, defined as being independent of all the asset returns, we provide theoretical results and simulation evidence that the second‐pass cross‐sectional regression tends to find the beta risk of the useless factor priced more often than it should. More surprisingly, this misspecification bias exacerbates when the number of time series observations increases. Possible ways of detecting useless factors are also examined.

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time‐varying covariances between stock returns and marketwide factors and time‐varying reward‐to‐covariabilities. The model is then applied to examine the effects of firm size and book‐to‐market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book‐to‐market equity ratios. The results indicate that allowing time‐varying covariances and time‐varying reward‐to‐covariabilities does little to salvage the traditional asset pricing models.