Predictable Stock Returns: The Role of Small Sample Bias

Abstract

Predictive regressions are subject to two small sample biases: the coefficient estimate is biased if the predictor is endogenous, and asymptotic standard errors in the case of overlapping periods are biased downward. Both biases work in the direction of making t‐ratios too large so that standard inference may indicate predictability even if none is present. Using annual returns since 1872 and monthly returns since 1927 we estimate empirical distributions by randomizing residuals in the VAR representation of the variables. The estimated biases are large enough to affect inference in practice, and should be accounted for when studying predictability.

Financial Economics, Return Predictability and Market Efficiency

“…[46], [55], [2], [27], and [58] conclude that the statistical evidence of forecastability is weaker once tests are adjusted for high persistence. [1], [2], [16], [42], [57], and [20] derive asymptotic distributions for predictability coefficients under the assumption that the forecasting variable follows a local-to-unit root, yet stationary, process.…”

Reconciling the Return Predictability Evidence In-Sample Forecasts, Out-of-Sample Forecasts, and Parameter Instability*

“…For example, Stambaugh (1986Stambaugh ( , 1999, Mankiw and Shapiro (1986), Nelson and Kim (1993), and Lewellen (1999) considered the following model:…”

“…First, correct inference is problematic because financial ratios are extremely persistent; in fact, standard tests leave the possibility of unit roots open. Nelson and Kim (1993), Stambaugh (1999), Ang and Bekaert (2001), Ferson, Sarkissian, and Simin (2003), and Valkanov (2003) conclude that the statistical evidence of forecastability is weaker once tests are adjusted for high persistence. Second, financial ratios have poor out-of-sample forecasting power, as shown in Bossaerts and Hillion (1999) and Goyal andWelch (2003, 2004), but see Campbell and Thompson (2005) for a different interpretations of the out-of-sample evidence.…”

“…Appropriately adjusting the dividend-price ratio for the structural break strengthens the evidence for return predictability, but not dividend growth predictability. Finally, the in-sample return predictability evidence stands up to the usual problem of persistent regressor bias (Nelson and Kim (1993), Stambaugh (1999), Ang and Bekaert (2001) and Valkanov (2003)) because the adjusted dividend-price ratio is much less persistent.…”

Real exchange-rate prediction over long horizons

“…A problem arises because changes in the log real exchange rate at horizons exceeding the sampling interval (k > 1) of the observations are used as the dependent variable which induces (k -1)-th order serial correlation into the error term. As Hodrick (1992) and Nelson and Kim (1993) have shown for the least squares case, the asymptotic distribution of heteroskedastic and autocorrelation consistent r-ratios can differ considerably from their exact finite sample distributions when the extent of the overlap is large relative to the sample size. To bypass this problem, we examine regressions of the one-period change in the log real exchange rate on the k-period moving average of the regressor as suggested by Jegadeesh (1991).…”