Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-15T08:47:56.301Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abel, A. B.; Mankiw, N. G.; Summers, L. H.; and Zeckhauser, R. J.. “Assessing Dynamic Efficiency: Theory and Evidence.” Review of Economic Studies, 56 (1989), 1–20.CrossRefGoogle Scholar
Abreu, D., and Brunnermeier, M. K.. “Bubbles and Crashes.” Econometrica, 71 (2003), 173–204.Google Scholar
Balke, N. S., and Wohar, M. E.. “Market Fundamentals versus Rational Bubbles in Stock Prices: A Bayesian Perspective.” Journal of Applied Econometrics, 24 (2009), 35–75.Google Scholar
Boudoukh, J.; Michaely, R.; Richardson, M.; and Roberts, M. R.. “On the Importance of Measuring Payout Yield: Implications for Empirical Asset Pricing.” Journal of Finance, 62 (2007), 877–915.CrossRefGoogle Scholar
Brunnermeier, M. K. “Bubbles.” In The New Palgrave Dictionary of Economics, Durlauf, S. N. and Blume, L. E., eds. New York, NY: Palgrave Macmillan (2008).Google Scholar
Campbell, J. Y. “Viewpoint: Estimating the Equity Premium.” Canadian Journal of Economics, 41 (2008), 1–21.Google Scholar
Campbell, J. Y.; Lo, A. W.; and MacKinlay, A. C.. The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press (1997).Google Scholar
Campbell, J. Y., and Shiller, R. J.. “Cointegration and Tests of Present Value Models.” Journal of Political Economy, 95 (1987), 1062–1088.Google Scholar
Campbell, J. Y., and Shiller, R. J.. “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors.” Review of Financial Studies, 1 (1988a), 195–228.CrossRefGoogle Scholar
Campbell, J. Y., and Shiller, R. J.. “Stock Prices, Earnings, and Expected Dividends.” Journal of Finance, 43 (1988b), 661–676.Google Scholar
Campbell, J. Y., and Viceira, L. M.. Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford, UK: Oxford University Press (2002).CrossRefGoogle Scholar
Campbell, J. Y., and Yogo, M.. “Efficient Tests of Stock Return Predictability.” Journal of Financial Economics, 81 (2006), 27–60.Google Scholar
Chen, L. “On the Reversal of Return and Dividend Predictability: A Tale of Two Periods.” Journal of Financial Economics, 92 (2009), 128–151.Google Scholar
Cochrane, J. H. “Explaining the Variance of Price-Dividend Ratios.” Review of Financial Studies, 5 (1992), 243–280.Google Scholar
Cochrane, J. H. Asset Pricing (rev. ed.). Princeton, NJ: Princeton University Press (2005).Google Scholar
Cochrane, J. H. “The Dog That Did Not Bark: A Defense of Return Predictability.” Review of Financial Studies, 21 (2008), 1533–1575.Google Scholar
Diba, B. T., and Grossman, H. I.. “The Theory of Rational Bubbles in Stock Prices.” Economic Journal, 98 (1988a), 746–754.CrossRefGoogle Scholar
Diba, B. T., and Grossman, H. I.. “Explosive Rational Bubbles in Stock Prices?” American Economic Review, 78 (1988b), 520–530.Google Scholar
Engsted, T. “Explosive Bubbles in the Cointegrated VAR Model.” Finance Research Letters, 3 (2006), 154–162.Google Scholar
Engsted, T., and Nielsen, B.. “Testing for Rational Bubbles in a Coexplosive Vector Autoregression.” Econometrics Journal, forthcoming (2012).Google Scholar
Engsted, T., and Pedersen, T. Q.. “The Dividend-Price Ratio Does Predict Dividend Growth: International Evidence.” Journal of Empirical Finance, 17 (2010), 585–605.Google Scholar
Evans, G. W. “Pitfalls in Testing for Explosive Bubbles in Asset Prices.” American Economic Review, 81 (1991), 922–930.Google Scholar
Fama, E. F., and French, K. R.. “Dividend Yields and Expected Stock Returns.” Journal of Financial Economics, 22 (1988), 3–25.Google Scholar
Fama, E. F., and French, K. R.. “Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?” Journal of Financial Economics, 60 (2001), 3–43.CrossRefGoogle Scholar
Johansen, S. “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models.” Econometrica, 59 (1991), 1551–1580.CrossRefGoogle Scholar
Leroy, S. F. “Rational Exuberance.” Journal of Economic Literature, 42 (2004), 783–804.Google Scholar
Lewellen, J. “Predicting Returns with Financial Ratios.” Journal of Financial Economics, 74 (2004), 209–235.Google Scholar
Phillips, P. C. B.; Wu, Y.; and Yu, J.. “Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?” International Economic Review, 52 (2011), 201–226.CrossRefGoogle Scholar
Robertson, D., and Wright, S.. “Dividends, Total Cash Flow to Shareholders, and Predictive Return Regressions.” Review of Economics and Statistics, 88 (2006), 91–99.Google Scholar
Santos, M. S., and Woodford, M.. “Rational Asset Pricing Bubbles.” Econometrica, 65 (1997), 19–57.Google Scholar
Shiller, R. J. Irrational Exuberance. Princeton, NJ: Princeton University Press (2000).Google Scholar
Sydsaeter, K., and Hammond, P. J.. Mathematics for Economic Analysis. Englewood Cliffs, NJ: Prentice Hall (1995).Google Scholar
Tirole, J. “Asset Bubbles and Overlapping Generations.” Econometrica, 53 (1985), 1499–1528.Google Scholar
West, K. D. “A Specification Test for Speculative Bubbles.” Quarterly Journal of Economics, 102 (1987), 553–580.CrossRefGoogle Scholar
Wu, Y. “Rational Bubbles in the Stock Market: Accounting for the U.S. Stock Price Volatility.” Economic Inquiry, 35 (1997), 309–319.Google Scholar