Small-Sample Tests for Stock Return Predictability with Possibly Non-Stationary Regressors and GARCH-Type Effects

Abstract

We develop a simulation-based procedure to test for stock return predictability with multiple regressors. The process governing the regressors is left completely free and the test procedure remains valid in small samples even in the presence of non-normalities and GARCH-type effects in the stock returns. The usefulness of the new procedure is demonstrated both in a simulation study and by examining the ability of a group of financial variables to predict excess stock returns. We find robust evidence of predictability during the period 1948-2014, driven entirely by the term spread. This empirical evidence, however, is much weaker over subsamples. RésuméNous développons une méthode de simulation pour tester la prévisibilité du rendement des actions à l'aide de multiples variables de régression. Le processus déterminant les variables de régression n'est aucunement restreint et la méthode de simulation reste valide à distance finie même en présence de distributions autres que la loi normale et d'effets GARCH sur le rendement des actions. L'utilité de la nouvelle méthode est démontrée à la fois dans une étude de simulation et par l'examen de la capacité d'un ensemble de variables financières à prévoir le rendement excédentaire des actions. Nous observons, pour la période 1948-2014, des signes probants de prévisibilité qui s'expliquent entièrement par l'écart de taux. Toutefois, ces résultats empiriques sont beaucoup plus faibles dans le cas des souséchantillons.A long-standing question in finance is whether asset returns can be predicted by economic and financial variables. This question has important and broad economic implications. However, the robustness of the evidence on asset return predictability remains controversial. A common practice in the literature is to estimate an ordinary least squares (OLS) regression of asset returns on the lagged values of the predictor variable under study. Such predictive regressions are then evaluated using a t-test, which often appears significant when compared to traditional critical values. As a result, the prevailing tone in the literature is that asset returns are predictable using financial and economic variables.Common features of the predictability regressions are the feedback from returns to the future values of the predictor variable and the persistent behavior of the predictor variable. The problem in this case is that the t-statistic often rejects the null hypothesis of no predictability much too often. This problem has generated substantial interest in both econometrics and empirical finance, and a number of econometric solutions have been proposed. All of these proposed approaches, however, depend on a very specific model for the predictor variable.In sharp contrast, in this study, we propose a simulation-based procedure without any modelling assumptions being imposed on the predictor variable. In addition, this new procedure does not impose any parametric assumptions on the distribution of stock return innovations, and it can be applied for hypothesis testing in pr...