Researchers on variance bounds tests of stock price volatility recognized early that risk aversion can increase the volatility of prices implied by the present-value model. This finding suggests that specifying risk neutrality may induce a bias toward rejecting the present-value model insofar as real-world investors are risk averse. However, establishing that risk aversion may increase stock price volatility does not, by itself, have implications for the presence or absence of excess volatility. This is so because risk aversion also affects the upper-bound volatility measure computed from "perfect foresight" (or "ex post rational") stock prices. Consequently, while high risk aversion implies high volatility in some settings, it may or may not imply excess volatility. This paper compares price volatility computed from real-world data to model-predicted volatility measures in a setting that allows for risk aversion. Using variance bounds tests based on the price-dividend ratio, we find evidence of excess volatility in long-run U.S. stock price data for relative risk aversion coefficients below 5. For higher degrees of risk aversion, the evidence for excess volatility is less clear. We also ask whether variance bounds for returns can be established in settings involving risk aversion and autocorrelated dividend growth. We show that the answer is no. Except in special cases, the present-value model does not impose bounds on return volatility in our setting.
