Risk, return, and dividends

Using only the definition of returns, together with a transversality assumption, we demonstrate that given a dividend process, any one of three variables—expected return, return volatility, and the price–dividend ratio—completely determines the other two. By parameterizing only one of these processes, common empirical specifications place strong, and sometimes counter-factual, restrictions on the dynamics of the other variables. Our findings lend insight into the nature of the risk–return relation and the predictability of stock returns.