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The Shape of the Risk Premium: Evidence from a Semiparametric Garch Model

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  • LINTON, Olivier
  • PERRON, Benoît

Abstract

We examine the relationship between the risk premium on the S&P 500 index return and its conditional variance. We use the SMEGARCH - Semiparametric-Mean EGARCH - model in which the conditional variance process is EGARCH while the conditional mean is an arbitrary function of the conditional variance. For monthly S&P 500 excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic. Moreover, we find considerable persistence in the conditional variance as well as a leverage effect, as documented by others. Moreover, the shape of these relationships seems to be relatively stable over time.

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File URL: http://hdl.handle.net/1866/475
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 9911.

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Length: 35 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:mtl:montde:9911

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Keywords: ARCH models; asset icing; backfitting; Fourier series; kernel; risk emium;

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  1. Braun, Phillip A & Nelson, Daniel B & Sunier, Alain M, 1995. " Good News, Bad News, Volatility, and Betas," Journal of Finance, American Finance Association, vol. 50(5), pages 1575-1603, December.
  2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  3. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  4. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
  5. Backus, David K & Gregory, Allan W, 1993. "Theoretical Relations between Risk Premiums and Conditional Variances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 177-85, April.
  6. Andrew B. Abel, 1998. "Risk Premia and Term Premia in General Equilibrium," NBER Working Papers 6683, National Bureau of Economic Research, Inc.
  7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  8. 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.
  9. Backus, David K. & Gregory, Allan W. & Zin, Stanley E., 1989. "Risk premiums in the term structure : Evidence from artificial economies," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 371-399, November.
  10. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  11. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
  12. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  13. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  14. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  15. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
  17. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  18. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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Cited by:
  1. Bent Jesper Christensen & Christian M. Dahl & Emma M. Iglesias, 2008. "Semiparametric Inference in a GARCH-in-Mean Model," CREATES Research Papers 2008-46, School of Economics and Management, University of Aarhus.
  2. Anisha Ghosh & Oliver Linton, 2009. "Consistent estimation of the risk-return tradeoff in the presence of measurement error," Economics Working Papers we094928, Universidad Carlos III, Departamento de Economía.

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