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Predictable Stock Returns: Reality or Statistical Illusion?

  • Charles R. Nelson
  • Myung J. Kim

Recent research suggests that stock returns are predictable from fundamentals such as dividend yield, and that the degree of predictability rises with the length of the horizon over which return is measured. This paper investigates the magnitude of two sources of small simple bias in these results. First, it is a standard result in econometrics that regression on the lagged value of the dependent variable is biased in finite samples. Since a fundamental such as the price/dividend ratio is a statistical proxy for lagged price, predictive regressions are potentially subject to a corresponding small sample bias. This may create the illusion that one can buy low and sell high in the sample even if the relationship is useless for forecasting. Second, multiperiod returns are positively autocorrelated by construction, raising the possibility of spurious regression. Standard errors which are computed from the asymptotic formula may not be large enough in small samples. A set of Monte Carlo experiments are presented in which data are generated by a version of the present value model in which the discount rate is constant so returns are not in fact predictable. We show that a number of the characteristica of the historical results can be replicated simply by the combined effects of the two small sample biases.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3297.

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Date of creation: Mar 1990
Date of revision:
Publication status: Published as "Predictable Stock Returns: The Role of Small Sample Bias", JF, Vol. 48, no. 2 (1993): 641-661.
Handle: RePEc:nbr:nberwo:3297
Note: ME
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  1. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  2. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  3. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  4. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  5. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  6. 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.
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
  9. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  10. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1990. "Speculative Dynamics," NBER Working Papers 3242, National Bureau of Economic Research, Inc.
  11. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
  12. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  13. Myung Jig Kim & Charles R. Nelson & Richard Startz, 1991. "Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 515-528.
  14. Campbell, John Y & Shiller, Robert J, 1988. " Stock Prices, Earnings, and Expected Dividends," Journal of Finance, American Finance Association, vol. 43(3), pages 661-76, July.
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