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), with x being a vector of state variables, which tightens the well-known Hansen-Jagannathan bound by a ratio of one over the multiple correlation coefficient between x and the standard minimum variance SDF, m0. In many applications, the correlation is small, and hence the bound is much improved. For example, when x is the growth rate of consumption, the new variance bound can be 25 times greater than the Hansen-Jagannathan bound, making it much more difficult to explain the equity-premium puzzle.