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Conditioning Information and Variance on Pricing Kernals

  • Bekaert, Geert
  • Liu, Jun

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. Burnside, Craig, 1994. "Hansen-Jagannathan Bounds as Classical Tests of Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 57-79, January.
  2. 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.
  3. Dahlquist, Magnus & Söderlind, Paul, 1997. "Evaluating Portfolio Performance with Stochastic Discount Factors," SSE/EFI Working Paper Series in Economics and Finance 175, Stockholm School of Economics, revised 01 Sep 1998.
  4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  5. Peter J. Knez & Zhiwu Chen, 1998. "Portfolio Performance Measurement: Theory and Applications," Yale School of Management Working Papers ysm48, Yale School of Management.
  6. Geert Bekaert, 1994. "The Time Variation of Risk and Return in Foreign Exchange Markets: A General Equilibrium Perspective," NBER Working Papers 4818, National Bureau of Economic Research, Inc.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Bekaert, Geert, 1994. "Exchange rate volatility and deviations from unbiasedness in a cash-in-advance model," Journal of International Economics, Elsevier, vol. 36(1-2), pages 29-52, February.
  16. 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.
  17. Ferson, Wayne E. & Merrick, John Jr., 1987. "Non-stationarity and stage-of-the-business-cycle effects in consumption-based asset pricing relations," Journal of Financial Economics, Elsevier, vol. 18(1), pages 127-146, March.
  18. 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.
  19. Bekaert, Geert & Urias, Michael S, 1996. " Diversification, Integration and Emerging Market Closed-End Funds," Journal of Finance, American Finance Association, vol. 51(3), pages 835-69, July.
  20. 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.
  21. 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.
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