Explaining the Variance of Price–Dividend Ratios

Abstract

I report a bound on the variance of price–dividend ratios and a decomposition of their variance into terms that reflect changes in dividend growth and discount rates. The specification is not restrictive. The test statistics do not require construction of ex post present values; instead, they are restrictions on means, variances, and covariances of price–dividend ratios, dividend growth, and discount rates. I consider implications for the mean price–dividend ratio, and I evaluate whether a low mean discount rate can rationalize the mean and variance of price–dividend ratios. The results do not indicate any striking rejections of present-value models. However, the bulk of the variance of price–dividend ratios must be accounted for by changingforecasts of discount rates and discount rates must possess some unusual characteristics.