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RFS Advance Access published online on October 15, 2003
Review of Financial Studies, doi:10.1093/rfs/hhg052
Review of Financial Studies © The Society for Financial Studies 2003; all rights reserved
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© 2003 The Society for Financial Studies

Original Articles

Conditioning Information and Variance Bounds on Pricing Kernels

Geert Bekaert 1* and Jun Liu 2
1 Columbia University; NBER
2 UCLA

* To whom correspondence should be addressed. E-mail: gb241{at}columbia.edu.


  Abstract

Gallant, Hansen and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but sub-optimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose a optimally scaled bound, which coincides with the GHT bound when the first and second conditional moments are known. When these moments are mis-specified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and non-linear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns.


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