The log-linear return approximation, bubbles, and predictability
AbstractWe 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 dividendprice 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.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-37.
Date of creation: 01 Jul 2010
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Web page: http://www.econ.au.dk/afn/
Stock return; Taylor expansion; bubble; simulation; predictability;
Other versions of this item:
- Engsted, Tom & Pedersen, Thomas Q. & Tanggaard, Carsten, 2012. "The Log-Linear Return Approximation, Bubbles, and Predictability," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(03), pages 643-665, June.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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- Tom Engsted & Thomas Q. Pedersen, 2012. "Predicting returns and rent growth in the housing market using the rent-to-price ratio: Evidence from the OECD countries," CREATES Research Papers 2012-58, School of Economics and Management, University of Aarhus.
- Pavlidis, Efthymios & Yusupova, Alisa & Paya, Ivan & Peel, David & Martinez-Garcia, Enrique & Mack, Adrienne & Grossman, Valerie, 2014. "Monitoring housing markets for episodes of exuberance: an application of the Phillips et al. (2012, 2013) GSADF test on the Dallas Fed International House Price Database," Globalization and Monetary Policy Institute Working Paper 165, Federal Reserve Bank of Dallas.
- Lof, Matthijs, 2012. "Rational Speculators, Contrarians and Excess Volatility," MPRA Paper 43490, University Library of Munich, Germany.
- Tom Engsted & Thomas Q. Pedersen, 2013. "Housing market volatility in the OECD area: Evidence from VAR based return decompositions," CREATES Research Papers 2013-04, School of Economics and Management, University of Aarhus.
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