The Log-Linear Return Approximation, Bubbles, and Predictability
42 Pages Posted: 9 Aug 2010 Last revised: 28 Feb 2013
Date Written: March 11, 2011
We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional expectation, and we investigate the magnitude of the approximation error in those cases. We find that surprisingly the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find evidence that bubbles generate large approximation errors. Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented.
Keywords: Stock return, Taylor expansion, bubble, simulation, predictability
JEL Classification: C32, C52, C65, G12
Suggested Citation: Suggested Citation