Recent research indicates that results of variance-bounds tests of stock price volatility may depend on the definition of cash flows deemed relevant to shareholders: Tests using regular (or "narrow") dividends repeatedly have suggested that stock prices fluctuate more than can be explained by a simple present value hypothesis, while some tests using "broad dividends" (i.e., narrow dividends plus proceeds from share liquidations) do not detect such excess price volatility. Researchers disagree as to the cause and meaning of these differences. This paper derives and analyzes the broad-dividend version of the present value hypothesis to show that under common assumptions, these differences in variance-bounds tests have only two possible causes: Either narrow-dividend tests have rejected the present value hypothesis because of bubbles (either rational bubbles, or "empirical" bubbles as might be effected by dividend-smoothing or dividend-nonpayment); or broad-dividend tests simply have lacked power to detect mispricing. Using simulation and results from previous studies, this paper demonstrates that the second possible cause -- the lack of power in broad-dividend tests -- most likely explains the differences between narrow- and broad-dividend variance-bounds tests.
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