Hansen and Jagannathan (1991) (hereafter HJ) derive restrictions on the volatility of stochastic discount factors that price a given set of returns. This article studies the sampling properties of HJ bounds that use conditioning information. One approach is to multiply the returns by the lagged...

This paper studies the estimation of asset pricing model regressions with conditional alphas and betas, focusing on the joint effects of data snooping and spurious regression. We find that the regressions are reasonably well specified for conditional betas, even in settings where simple...

Even though stock returns are not highly autocorrelated, there is a spurious regression bias in predictive regressions for stock returns related to the classic studies of <link rid="b49">Yule (1926)</link> and <link rid="b21">Granger and Newbold (1974)</link>. Data mining for predictor variables interacts with spurious regression bias. The...

Three concepts: stochastic discount factors, multi-beta pricing and mean-variance efficiency, are at the core of modern empirical asset pricing. This chapter reviews these paradigms and the relations among them, concentrating on conditional asset-pricing models where lagged variables serve as...