A New Variance Bound on the Stochastic Discount Factor*

In this paper, we construct a new variance bound on any stochastic discount factor (SDF) of the form m = m(x), where x is a vector of random state variables. In contrast to the well known Hansen-Jagannathan bound that places a lower bound on the variance of m(x), our bound tightens it by a ratio of 1/ ,x,m0 where x,m0 is the multiple correlation coecient between x and the standard minimum variance SDF, m0. In many applications, the correlation is small, and hence our bound can be substantially tighter than Hansen-Jagannathan’s. For example, when x is the growth rate of consumption, based on Cochrane’s (2001) estimates of market volatility and x,m0, the new variance bound is 25 times greater than the Hansen-Jagannathan bound, making it much more dicult,to explain the equity-premium puzzle based on existing asset pricing models.