Conditioning Information and Variance Bounds on Pricing Kernels with Higher- Order Moments: Theory and Evidence

We develop a strategy for utilizing higher moments, variancerisk premia, and conditioning information efficiently, and henceimprove on the variance bounds computed by Hansen and Jagannathan(1991); Gallant, Hansen, and Tauchen (1990); and Bekaert andLiu (2004). Our bounds reach existing bounds when nonlinearitiesin returns are not priced. We also use higher moments, variancerisk premia, and conditioning information to provide distancemeasures that improve on the Hansen and Jagannathan (1997) distancemeasure. Empirical results indicate that when accounting forthe impact of higher moments and variance risk premia, the existingpricing kernels have difficulty in explaining returns on theassets and derivatives.