Predictable Stock Returns: Reality or Statistical Illusion?

Abstract

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 ssmple bias in these reaults. 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.

Efficient Capital Markets: II

“…But how much of it is real? The standard errors of the slopes for the forecasting variables in the return regressions are typically large and so leave much uncertainty about forecast power (Hodrick (1990), Nelson and Kim (1990)). Inference is also clouded by an industry‐level data‐dredging problem.…”

Predictability of Equity Returns over Different Time Horizons: A Nonparametric Approach

“…There are quite a few works which examine the predictive power of the dividend yield on excess stock returns over various time horizons. Fama and French (1988), Campbell and Shiller (1988a,b), and Nelson and Kim (1993) document evidence of predictability. However, empirical studies increasingly cast doubt on the forecasting power of price-based predictors of equity returns.…”

“…First, several authors expressed concern that the apparent predictability of stock returns might be spurious given the fact that many predictor variables, such as valuation ratios, used are highly persistent. Nelson and Kim (1993) and Stambaugh (1999) pointed out that persistence leads to biased coe¢ cients in predictive regressions if innovations in the predictor variable are correlated with returns (as is strongly the case for valuation ratios, although not for interest rates). Under the same conditions, the standard t-test for predictability has incorrect sizes in …nite samples (Cavanagh et al, 1995).…”

“…Third, there exists serial correlation in the forecast error particularly when the time horizon h is large relative to the sample size. As a result, there exist some …nite sample problems for reliable statistical inference (Hodrick (1992), Nelson and Kim (1993)). An active recent literature discusses alternative econometric methods or propose new statistical tests for correcting the bias and conducting valid inference on estimation of long-horizon predictive regression models with persistent variables and errors.…”

“…Hodrick (1992) examines the implications for hypothesis testing of using di¤erent speci…cations of the forecasting equation. Nelson and Kim (1993) analyze small-sample biases in simulations of a VAR system for returns and yields, under the null hypothesis of no predictability of returns. Using U.S. returns sampled annually, they report that the simulated distributions of t-statistics are displaced upward, and still …nd some spurious evidence of predictability at conventional signi…cance levels.…”