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We develop a strategy for utilizing higher moments, variance risk premia, and conditioning information efficiently, and hence improve on the variance bounds computed by Hansen and Jagannathan (1991); Gallant, Hansen, and Tauchen (1990); and Bekaert and Liu (2004). Our bounds reach existing bounds when nonlinearities in returns are not priced. We also use higher moments, variance risk premia, and conditioning information to provide distance measures that improve on the Hansen and Jagannathan (1997) distance measure. Empirical results indicate that when accounting for the impact of higher moments and variance risk premia, the existing pricing kernels have difficulty in explaining returns on the assets and derivatives. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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