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Conditioning Information and Variance on Pricing Kernals

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  • Bekaert, Geert
  • Liu, Jun

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 qt9m7392rq.

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Date of creation: 01 Jun 2001
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Handle: RePEc:cdl:anderf:qt9m7392rq

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  1. Geert Bekaert & Michael S. Urias, 1996. "Diversification, Integration and Emerging Market Closed-End Funds," NBER Working Papers 4990, National Bureau of Economic Research, Inc.
  2. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  3. Ferson, Wayne E & Schadt, Rudi W, 1996. " Measuring Fund Strategy and Performance in Changing Economic Conditions," Journal of Finance, American Finance Association, vol. 51(2), pages 425-61, June.
  4. Bekaert, Geert, 1996. "The Time Variation of Risk and Return in Foreign Exchange Markets: A General Equilibrium Perspective," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 427-70.
  5. Gallant, A. Ronald & Hansen, Lars Peter & Tauchen, George, 1990. "Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 141-179.
  6. Dahlquist, Magnus & Söderlind, Paul, 1997. "Evaluating Portfolio Performance with Stochastic Discount Factors," Working Paper Series in Economics and Finance 175, Stockholm School of Economics, revised 01 Sep 1998.
  7. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
  8. Lars Peter Hansen & John Heaton & Erzo Luttmer, 1993. "Econometric Evaluation of Asset Pricing Models," NBER Technical Working Papers 0145, National Bureau of Economic Research, Inc.
  9. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  10. Bekaert, Geert & Hodrick, Robert J, 1992. " Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," Journal of Finance, American Finance Association, vol. 47(2), pages 467-509, June.
  11. Chen, Zhiwu & Knez, Peter J, 1996. "Portfolio Performance Measurement: Theory and Applications," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 511-55.
  12. Kirby, Chris, 1997. "Measuring the Predictable Variation in Stock and Bond Returns," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 579-630.
  13. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  14. Chen, Zhiwu & Knez, Peter J, 1995. "Measurement of Market Integration and Arbitrage," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 287-325.
  15. Kirby, Chris, 1998. "The Restrictions on Predictability Implied by Rational Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 343-82.
  16. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
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