The Log-Linear Return Approximation, Bubbles, and Predictability

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.

[1]  Stephen F. LeRoy.  Rational Exuberance ∗ , 2003 .

[2]  Robinson Kruse,et al.  Milestones of European Integration: Which matters most for Export Openness? , 2010 .

[3]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[4]  Testing for Rational Bubbles in a Co-Explosive Vector Autoregression , 2012 .

[5]  Peter J. Hammond,et al.  Mathematics for economic analysis , 1995 .

[6]  On European monetary integration and the persistence of real effective exchange rates , 2011 .

[7]  John Y. Campbell,et al.  Viewpoint: Estimating the Equity Premium , 2008 .

[8]  Herschel I. Grossman,et al.  Explosive Rational Bubbles in Stock Prices , 1988 .

[9]  Jonathan D. Levin.  Bubbles and Crashes , 2006 .

[10]  Richard K. Crump,et al.  Federal Reserve Bank of New York Staff Reports Bootstrapping Density-weighted Average Derivatives Bootstrapping Density-weighted Average Derivatives , 2010 .

[11]  J. Cochrane.  Explaining the Variance of Price Dividend Ratios , 1989 .

[12]  S. Johansen.  Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models , 1991 .

[13]  S. Wright,et al.  Dividends, Total Cash Flow to Shareholders, and Predictive Return Regressions , 2003, Review of Economics and Statistics.

[14]  Rickard Sandberg,et al.  Linearity Testing in Time-Varying Smooth Transition Autoregressive Models under Unknown Degree of Persistency , 2010 .

[15]  E. Fama,et al.  Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay? , 2000 .

[16]  Leonidas Tsiaras.  The Forecast Performance of Competing Implied Volatility Measures: The Case of Individual Stocks , 2010 .

[17]  Robert J. Shiller,et al.  Cointegration and Tests of Present Value Models , 1987, Journal of Political Economy.

[18]  Herschel I. Grossman,et al.  The Theory of Rational Bubbles in Stock Prices , 1988 .

[19]  G. Evans.  Pitfalls in Testing for Explosive Bubbles in Asset Prices , 1991 .

[20]  K. Arrow,et al.  The New Palgrave Dictionary of Economics , 2020 .

[21]  Roni Michaely,et al.  On the Importance of Measuring Payout Yield: Implications for Empirical Asset Pricing , 2007 .

[22]  Stephen Wright,et al.  Dividends, Total Cash Flow to Shareholders, and Predictive Return Regressions , 2003 .

[23]  Manuel S. Santos,et al.  Rational asset pricing bubbles , 1997 .

[24]  Nathan S. Balke,et al.  Market fundamentals versus rational bubbles in stock prices: a Bayesian perspective , 2009 .

[25]  R. Shiller,et al.  Stock Prices, Earnings and Expected Dividends , 1988 .

[26]  J. Cochrane.  Asset Pricing: Revised Edition , 2005 .

[27]  Christian Schlag.  Strategic Asset Allocation: Portfolio Choice for Long‐Term Investors. , 2003 .

[28]  Long Chen.  On the Reversal of Return and Dividend Growth Predictability: A Tale of Two Periods , 2008 .

[29]  Martin M. Andreasen.  Non-Linear DSGE Models and the Central Difference Kalman Filter , 2011 .

[30]  J. Lewellen,et al.  Predicting Returns with Financial Ratios , 2002 .

[31]  Yangru Wu.  RATIONAL BUBBLES IN THE STOCK MARKET: ACCOUNTING FOR THE U.S. STOCK‐PRICE VOLATILITY , 1997 .

[32]  J. Campbell,et al.  Estimating the Equity Premium , 2007 .

[33]  E. Fama,et al.  Dividend yields and expected stock returns , 1988 .

[34]  Tom Engsted.  Explosive bubbles in the cointegrated VAR model , 2006 .

[35]  M. Nielsen,et al.  Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration , 2011 .

[36]  Yangru Wu,et al.  Explosive Behavior in the 1990s' NASDAQ: When Did Exuberance Escalate Asset Values? , 2007 .

[37]  B. Nielsen,et al.  Testing for Rational Bubbles in a Co-Explosive Vector Autoregression , 2010 .

[38]  R. Shiller,et al.  The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors , 1986 .

[39]  K. West.  A Specification Test for Speculative Bubbles , 1986 .

[40]  J. Tirole.  ASSET BUBBLES AND OVERLAPPING GENERATIONS , 1985 .

[41]  Michael Sørensen,et al.  Maximum Likelihood Estimation for Integrated Diffusion Processes , 2010 .

[42]  Mogens Bladt,et al.  Corrigendum to “Simple simulation of diffusion bridges with application to likelihood inference for diffusions” , 2010, Bernoulli.

[43]  Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns , 2010 .

[44]  Tom Engsted,et al.  The Dividend-Price Ratio Does Predict Dividend Growth: International Evidence , 2010 .

[45]  Robinson Kruse.  Forecasting autoregressive time series under changing persistence , 2010 .

[46]  Irrational Exuberance.  Irrational exuberance? , 2006, Nature Biotechnology.