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Conditioning Information and Variance on Pricing Kernals

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Author Info
Geert Bekaert (Columbia University and NBER)
Jun Liu (Anderson School of Management)

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Abstract

Gallant, Hansen and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound on pricing kernels. The literature predominantly resorts to a simple, 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, when the first and second conditional moments are known, coincides with the bound derived by Gallant, Hansen and Tauchen (GHT bound). When these moments are mis-specified, our optimally scaled bound still yields a valid lower bound for the standard deviation of pricing kernels, unlike the GHT bound. Moreover, the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns because it only achieves the maximum when the conditional mean and conditional variance are correctly specified. The illustration in this article adds time-varying volatility to the familiar Hansen-Singleton (1983) set-up of an autoregressive model for consumption growth and bond and stock returns. Both an unconstrained version and a version with the restrictions of the standard consumption-based asset pricing model imposed, serve as the data-generating processes to illustrate the behavior of the bounds. In the process, we explore an interesting empirical phenomenon: asymmetric volatility in consumption growth

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Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number 1009.

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Date of creation: 01 Jun 2001
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    Other versions:
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  6. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
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  27. Kandel, Shmuel & Stambaugh, Robert F, 1990. "Expectations and Volatility of Consumption and Asset Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(2), pages 207-32. [Downloadable!] (restricted)
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  32. Geert Bekaert & Jun Liu, 1999. "Conditioning Information and Variance Bounds on Pricing Kernels," NBER Working Papers 6880, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  33. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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