Some new variance bounds for asset prices: a comment

Engel (2005) derives a theoretical variance inequality involving the change in equilibrium stock prices Var ( p) : Assuming that stock prices are "cum-dividend" and that investors are risk neutral, he shows that Var ( p) must be greater than or equal to the variance of the "perfect foresight" (or "ex post rational") price change Var ( p*) ; where p* is computed from the discounted stream of subsequent realized dividends. This paper expands the analysis to consider "ex-divdend" prices and risk aversion in a standard Lucas-type asset pricing model. I show that the direction of the price-change variance inequality can be reversed, depending on the values assigned to some key parameters of the model, namely the dividend AR(1) parameter, the investor's subjective time discount factor, and the coefficient of relative risk aversion. Overall, the results demonstrate that the present-value model of stock prices does not impose theoretical bounds on price-change volatility except in some special cases.