A New Variance Bound on the Stochastic Discount Factor*

Hansen and Jagannathan (1991) provide a lower bound on the variance of a stochastic discount factor (SDF). As many asset pricing models can be represented by using an SDF (see, e.g., Cochrane [2001] and references therein), this bound became instantly known as the Hansen-Jagannathan bound and has been applied widely in a variety of finance problems. On developing related bounds, Snow (1991) derives a bound in terms of higher moments, Stutzer (1995) obtains a bound using Bayesian information criterion, Bansal and Lehmann (1997) investigate a growth form of the bound, Balduzzi and Kallal (1997) relate the bound to risk premia, and Chrétien (2003) derives a bound on the autocorrelation of SDFs. Moreover, Bernardo and Ledoit (2000) and Cochrane and SaáRequejo (2000) derive similar bounds in incomplete