This paper shows that standard corporate finance theory implies that there is potentially a trade off between the variances of dividends and equity prices. We show how the trade off works in a stochastic difference equation model of dividend policy demonstrating that the solution may be unstable for plausible parameter values. At the boundary of the feasible set of price and dividend variances, prices and dividends are perfectly correlated and both follow an AR(1) process. We calculate explicit formulae for the variances, and show that firms could in principle make prices completely predictable, by immediately incorporating all news about the present value of earnings into dividends. By choosing to smooth dividends firms increase the variance of prices, and may also increase the variance of dividends. We show how this can easily result in sample variances which violate variance bounds inequalities
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