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On the relation between the expected value and the volatility of the nominal excess return on stocks

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  • Lawrence R. Glosten
  • Ravi Jagannathan
  • David E. Runkle

Abstract

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (i) seasonal patterns in volatility, (ii) positive and negative innovations to returns having different impacts on conditional volatility, and (iii) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 157.

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Date of creation: 1993
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Publication status: Published in Journal of Finance (Vol. 48, No. 5, December 1993, pp. 1779-1801)
Handle: RePEc:fip:fedmsr:157

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Keywords: Stock market;

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  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  2. 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.
  3. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
  4. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  6. Andrew B. Abel, 1988. "Stock Prices Under Time-Varying Dividend Risk: An Exact Solution In An Infinite-Horizon General Equilibrium Model," NBER Working Papers 2621, National Bureau of Economic Research, Inc.
  7. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
  8. Alberto Giovannini & Philippe Jorion, 1988. "The Time-Variation of Risk and Return in the Foreign Exchange and Stock Markets," NBER Working Papers 2573, National Bureau of Economic Research, Inc.
  9. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  10. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
  11. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  12. Donald B. Keim, . "Dividend Yields and Stock Returns: Implications of Abnormal January Returns," Rodney L. White Center for Financial Research Working Papers 14-85, Wharton School Rodney L. White Center for Financial Research.
  13. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
  14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  15. Christopher M. Turner & Richard Startz & Charles R. Nelson, 1989. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," NBER Working Papers 2818, National Bureau of Economic Research, Inc.
  16. Josef Lakonishok, Seymour Smidt, 1988. "Are Seasonal Anomalies Real? A Ninety-Year Perspective," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 403-425.
  17. Chan, K. C. & Karolyi, G. Andrew & Stulz, ReneM., 1992. "Global financial markets and the risk premium on U.S. equity," Journal of Financial Economics, Elsevier, vol. 32(2), pages 137-167, October.
  18. Gennotte, Gerard & Marsh, Terry A., 1993. "Variations in economic uncertainty and risk premiums on capital assets," European Economic Review, Elsevier, vol. 37(5), pages 1021-1041, June.
  19. 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.
  20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  21. Breen, William & Glosten, Lawrence R & Jagannathan, Ravi, 1989. " Economic Significance of Predictable Variations in Stock Index Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1177-89, December.
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