Sum of the parts stock return forecasting: international evidence

Abstract

This article examines the issue of stock returns forecasting and in particular extends the analysis of the recently introduced sum of the parts modelling technique. The sum of the parts technique undertakes a first-stage regression analysis where the predictor variables themselves are estimated and the fitted values from these equations are then used in the forecast model. We conduct a series of one-step ahead recursive forecasts using the above methodology and compare that to the usual predictive regression approach for 11 markets, and a variety of forecast metrics and tests. Across the full range of markets and forecast measures, our results suggest that no single model dominates. Notably, while the sum of the parts approach often reports a lower Mean Absolute Error (MAE) and Root Mean-Squared Error (RMSE), it is rarely significantly lower than competing forecasts. Similar results are found on the basis of both regression and sign based tests. Thus, across the range of markets the new approach meets with only limited success in providing better forecasts, although it rarely performs significantly worse. Furthermore, in specific markets, the sum of the parts approach does perform well. Notably for Italy, the UK, US and Korea, this approach outperforms the alternate models on all or nearly all measures. Thus, in terms of guiding researchers on the appropriate forecast model, the sum of the parts approach is interesting and does suggest some forecast improvement. However, that is only for specific markets. Hence, in choosing which forecast method to adopt there remains the trade-off between the simplicity of the predictive regression approach and the sum of the parts approach, which is more involved but on occasion more accurate, although not universally so.

Notes

¹ The distinction between the dividend yield and the dividend–price ratio can be a source of confusion. Within the academic literature, the dividend yield is defined as D_{t +1}/P_t whereas the dividend–price ratio is defined as D_t /P_t . In contrast, the financial press defines the dividend yield as the ratio of the current dividend and current price, hence the same as the academic dividend–price ratio, D_t /P_t .

² One issue ignored by Ferreira and Santa-Clara but of relevance, is that of the generated regressor problem, where the predictions from one model are used as explanatory variables in another regression. One issue surrounding the generated regressor problem is that standard inference in the second stage is no longer valid. While, this may be less of an issue here, where we are not interested in individual t-statistics, for example, a further problem is that the coefficient on the generated regressor may be inconsistent. This is almost certainly going to be the case where multiple estimates are used as in Ferreira and Santa-Clara for the price–earnings ratio growth. Such inconsistent estimates may impact point forecasts.