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The Log-Linear Return Approximation, Bubbles, and Predictability

Published online by Cambridge University Press:  13 February 2012

Tom Engsted,
Thomas Q. Pedersen and
Carsten Tanggaard
Tom Engsted
Affiliation:
tengsted@creates.au.dk
Thomas Q. Pedersen
Affiliation:
tqpedersen@creates.au.dk
Carsten Tanggaard
Affiliation:
Department of Economics and Business, Aarhus University, Fuglesangs allé 4, DK-8210 Aarhus V, Denmark. ctanggaard@creates.au.dk
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Abstract

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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 that 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.

Information

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 47 , Issue 3 , June 2012, pp. 643 - 665
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2012

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