دانلود رایگان مقاله نسبت سود سهام و قیمت اصلاح شده

Abstract

We show that log-dividends (d) and log-prices (p) are cointegrated, but, instead of de facto assuming the stationarity of the classical log dividend–price ratio, we allow the data to reveal the cointegration vector between d and p. We define the modified dividend–price ratio (mdp), as the long run trend deviation between d and p. Using S&P 500 data for the period 1926 to 2012, we show that mdp provides substantially improved forecasting results over the classical dp ratio. Out of sample, while the dp ratio cannot outperform the “simplistic forecast” benchmark for any useful horizon, an investor who employs the mdp ratio will do significantly better in forecasting 3-, 5- and 7-year returns with an ROS2 of 7%, 26% and 31% respectively. In some sense mdp can be considered as a de-noising of the classical ratio as it addresses the major weakness in dp, its presumed inability in revealing business cycle variation in expected returns. Unlike dp, mdp exhibits positive correlation with the risk free return component, and can discern if a low dividend state coincides with a low yield state.

4. Conclusion

While dividends are a critical component of the total return an investor enjoys from her stock holdings, and dividend–price ratio can predict returns, extant literature has largely avoided tackling head-on the possibility of a nonstationary dividend–price ratio. After failing to reject the null of a unit root in the classical dividend–price ratio (dp), we assume away dividend yield stationarity, and show that a cointegrating relationship, not spanned by [1,−1], between dividends and prices exists. We estimate a relation of the type d=α+βp, and define the modified dp ratio as the stationary cointegration error of this long-run equilibrium. We think of β as the unique parameter that “fine tunes” dp, and reveals the true long-run equilibrium between d and p, by removing a possibly small I(1) “noise” component. Indeed, using S&P 500 data for the period 1926 to 2012, we show that mdp is more informative than classical dp, and provides substantially improved forecasting results over the classical dp ratio for medium and long horizons from 3 to 7 years. As we show, one source for the gain of the modified ratio in forecasting returns is due to its enhanced ability to forecast their risk free component. Depending on whether one uses the recursive or population methodology to form mdp, the performance gain of modifying dp lies between a low of 30% and a high limit to the tune of 50% for the population method.