Tests of risk premia in linear factor models

Abstract

We show that statistical inference on the risk premia in linear factor models that is based on the Fama–MacBeth (FM) and generalized least squares (GLS) two-pass risk premia estimators is misleading when the β’s are small and/or the number of assets is large. We propose novel statistics, that are based on the maximum likelihood estimator of Gibbons [Gibbons, M., 1982. Multivariate tests of financial models: A new approach. Journal of Financial Economics 10, 3–27], which remain trustworthy in these cases. The inadequacy of the FM and GLS two-pass t/Wald statistics is highlighted in a power and size comparison using quarterly portfolio returns from Lettau and Ludvigson [Lettau, M., Ludvigson, S., 2001. Resurrecting the (C)CAPM: A cross-sectional test when risk premia are time-varying. Journal of Political Economy 109, 1238–1287]. The power and size comparison shows that the FM and GLS two-pass t/Wald statistics can be severely size distorted. The 95% confidence sets for the risk premia in the above-cited work that result from the novel statistics differ substantially from those that result from the FM and GLS two-pass t-statistics. They show support for the human capital asset pricing model although the 95% confidence set for the risk premia on labor income growth is unbounded. The 95% confidence sets show no support for the (scaled) consumption asset pricing model, since the 95% confidence set of the risk premia on the scaled consumption growth consists of the whole real line, but do not reject it either.