Stochastic Discount Factor Bounds with Conditioning Information

Hansen and Jagannathan (HJ, 1991) describe restrictions on the volatility of stochastic discount factors (SDFs) that price a given set of asset returns. This paper compares the sampling properties of different versions of HJ bounds that use conditioning information in the form of a given set of lagged instruments. HJ describe one way to use conditioning information. Their approach is to multiply the original returns by the lagged variables, and much of the asset pricing literature to date has followed this “multiplicative” approach. We also study two versions of optimized HJ bounds with conditioning information. One is from Gallant, Hansen and Tauchen (1990) and the second is based on the unconditionally-efficient portfolios derived in Ferson and Siegel (2000). We document finite-sample biases in the HJ bounds, where the biased bounds reject asset-pricing models too often. We provide useful correction factors for the bias. We also evaluate the asymptotic standard errors for the HJ bounds, from Hansen, Heaton and Luttmer (1995).