Working Paper: NBER ID: w3297
Authors: charles r nelson; myung j kim
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 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.
Keywords: stock returns; predictability; small sample bias; monte carlo experiments
JEL Codes: G12; C12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| small sample biases (C83) | predictability of stock returns (G17) |
| regressing on lagged dependent variables (C22) | bias in expected coefficient (C51) |
| positive autocorrelation of multiperiod returns (C22) | bias in expected coefficient (C51) |
| bias in expected coefficient (C51) | illusion of predictability (D80) |
| overlapping stock returns data (G17) | positive serial correlation (C22) |
| positive serial correlation (C22) | inflated R-squared values (C29) |
| inflated R-squared values (C29) | misinterpretation of relationship strength (D91) |
| small sample biases (C83) | artifacts of historical predictability (B15) |