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The Log-Linear Return Approximation, Bubbles, and Predictability

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  • Engsted, Tom
  • Pedersen, Thomas Q.
  • Tanggaard, Carsten

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 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.

Suggested Citation

  • 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(3), pages 643-665, June.
    • Handle: RePEc:cup:jfinqa:v:47:y:2012:i:03:p:643-665_00
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • 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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