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

The author develops a strategy for utilizing higher moments and conditioning information efficiently, and hence improves on the variance bounds computed by Hansen and Jagannathan (1991, the HJ bound) and Gallant, Hansen, and Tauchen (1990, the GHT bound). The author's bound incorporates variance risk premia. It reaches the GHT bound when non-linearities in returns are not priced. The author also provides an optimally scaled bound with conditioning information, higher moments, and variance risk premia that improves on the Bekaert and Liu (2004, the BL bound) optimally scaled bound. This bound reaches the BL bound when nonlinearities in returns are not priced. When the conditional first four moments are misspecified, the author's optimally scaled bound remains a lower bound to the variance on pricing kernels, whereas the BL bound does not. The author empirically illustrates the behaviour of the bounds using Bekaert and Liu's (2004) econometric models. He also uses higher moments and conditioning information to provide distance measures that improve on the Hansen and Jagannathan distance measures. The author uses these distance measures to evaluate the performance of asset-pricing models. Some existing pricing kernels are able to describe returns ignoring the impact of higher moments and variance risk premia. When accounting for the impact of higher moments and variance risk premia, these same pricing kernels have difficulty in explaining returns on the assets and are unable to price non-linearities or higher moments.