Prediction of stocks: a new way to look at it

While the traditional $R^{2}$ value is useful to evaluate the quality of a fit, it does not work when it comes to evaluating the predictive power of estimated financial models in finite samples. In this paper we introduce a validated $R_{V}^{2}$ value that is Taylor made for prediction. Based on data from the Danish stock market, using this measure we find that the dividend-price ratio has good predictive power for time horizons between one year and five years. We explain how the $R_{S}^{2}$ s for different time horizons could be compared, respectively, how they must not be interpreted. For our data we can conclude that the quality of prediction is almost the same for the five different time horizons. This is in contradiction to earlier studies based on the traditional $R^{2}$ value, where it has been argued that the predictive power increases with the time horizon up to a horizon of about five or six years. Furthermore, we find that while inflation and interest rate do not add to the predictive power of the dividend-price ratio then last years excess stock return does.