[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 efficiency by using the given conditioning information optimally. The optimal use of the lagged variables is economically important; by using the instruments optimally, we reject several efficiency hypotheses that are not otherwise rejected. The Sharpe ratios of a sample of hedge fund indexes appear consistent with the optimal use of conditioning information.]

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 variables. We also study optimized HJ bounds with conditioning information from Gallant, Hansen, and Tauchen (1990) and based on portfolios derived in Ferson and Siegel (2001). We document striking finite-sample biases in the HJ bounds, where the bounds reject asset-pricing models too often. We provide a useful bias correction. We also evaluate asymptotic standard errors for the bounds from Hansen, Heaton, and Luttmer (1995).

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 efficiency by using the given conditioning information optimally. The optimal use of the lagged variables is economically important; by using the instruments optimally, we reject several efficiency hypotheses that are not otherwise rejected. The Sharpe ratios of a sample of hedge fund indexes appear consistent with the optimal use of conditioning information.

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 variables. We also study optimized HJ bounds with conditioning information from Gallant, Hansen, and Tauchen (1990) and based on portfolios derived in Ferson and Siegel (2001). We document striking finite-sample biases in the HJ bounds, where the bounds reject asset-pricing models too often. We provide a useful bias correction. We also evaluate asymptotic standard errors for the bounds from Hansen, Heaton, and Luttmer (1995).