We develop asset pricing models' implications for portfolio efficiency with conditioning information in the form of lagged instruments. A model identifies a portfolio that should be minimum-variance efficient with respect to the conditioning information. Our framework refines tests of portfolio...

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...