The Log-Linear Return Approximation, Bubbles, and Predictability

42 Pages Posted: 9 Aug 2010 Last revised: 28 Feb 2013

See all articles by Tom Engsted

Tom Engsted

University of Aarhus - CREATES

Thomas Quistgaard Pedersen

Aarhus University - CREATES

Carsten Tanggaard

affiliation not provided to SSRN

Date Written: March 11, 2011

Abstract

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

Engsted, Tom and Pedersen, Thomas Quistgaard and Tanggaard, Carsten, The Log-Linear Return Approximation, Bubbles, and Predictability (March 11, 2011). Journal of Financial and Quantitative Analysis, Vol. 47, Nr. 3, 2012, s. 643-665.. Available at SSRN: https://ssrn.com/abstract=1655265 or http://dx.doi.org/10.2139/ssrn.1655265

Tom Engsted (Contact Author)

University of Aarhus - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Thomas Quistgaard Pedersen

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Carsten Tanggaard

affiliation not provided to SSRN

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