Intermediary and downside risk asset pricing theories lay the foundations for spanning the multi-asset return space by a small number of risk factors. Recent studies show strong empirical support for such factors across major asset classes. We revisit these results and show that robust evidence for common factor pricing remains elusive. Importantly, the proposed risk factors do not seem to provide incremental information to the traditional market factor. We argue that most of the economic and statistical challenges are not specific to these analyses and, with the aid of a placebo test, offer general recommendations for improving empirical practice, thus adding to the prescriptions in Lewellen et al. (2010).

We study some seemingly anomalous results that arise in possibly misspecified, reduced-rank linear asset-pricing models estimated by the continuously updated generalized method of moments. When a spurious factor (that is, a factor that is uncorrelated with the returns on the test assets) is present, the test for correct model specification has asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large.The rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1.

We propose a methodology for estimating and testing beta-pricing models when a large number of assets is available for investment but the number of time-series observations is fixed. We first consider the case of correctly specified models with constant risk premia, and then extend our framework to deal with time-varying risk premia, potentially misspecified models, firm characteristics, and unbalanced panels. We show that our large cross-sectional framework poses a serious challenge to common empirical findings regarding the validity of beta-pricing models. In the context of pricing models with Fama-French factors, firm characteristics are found to explain a much larger proportion of variation in estimated expected returns than betas. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.