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The log-linear return approximation, bubbles, and predictability

  • Tom Engsted


    (School of Economics and Management, Aarhus University and CREATES)

  • Thomas Q. Pedersen


    (School of Economics and Management, Aarhus University and CREATES)

  • Carsten Tanggaard


    (School of Economics and Management, Aarhus University and CREATES)

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 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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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-37.

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Length: 32
Date of creation: 01 Jul 2010
Date of revision:
Handle: RePEc:aah:create:2010-37
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