Dividend Innovations and Stock Price Volatility

This paper establishes an inequality that may be used to test the null hypothesis that a stock price equals the expected present discounted value of its dividend stream, with a constant discount rate. The inequality states that if this hypothesis is true, the variance of the innovation in the stock price is bounded above by a certain function of the variance in the innovation in the dividend. The bound is valid even if prices and dividends are nonstationary.The inequality is used to test the null hypothesis, for some long term annual U.S. stock price data. The null is decisively rejected, with the stock price innovation variance exceeding its theoretical upper bound by a factor of as much as twenty. The rejection is highly significant statistically. Regression diagnostics and some informal analysis suggest that the results are more consistent with there being speculative bubbles in the U.S. stock market than with a failure of the rational expectations or constant discount rate hypothesis.