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

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

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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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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  1. Keim, Donald B., 1985. "Dividend yields and stock returns: Implications of abnormal January returns," Journal of Financial Economics, Elsevier, vol. 14(3), pages 473-489, September.
  2. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  3. 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.
  4. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  5. K.C. Chan & G. Andrew Karolyi & Rene M. Stulz, 1992. "Global Financial Markets and the Risk Premium on U.S. Equity," NBER Working Papers 4074, National Bureau of Economic Research, Inc.
  6. 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.
  7. 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.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  9. 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.
  10. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
  11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  12. 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.
  13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  14. 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.
  15. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  16. Turner, Christopher M. & Startz, Richard & Nelson, Charles R., 1989. "A Markov model of heteroskedasticity, risk, and learning in the stock market," Journal of Financial Economics, Elsevier, vol. 25(1), pages 3-22, November.
  17. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
  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. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  20. 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.
  21. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
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