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dec04_app_campbell - Appendix to “Bad Beta Good Beta”...

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Appendix to “Bad Beta, Good Beta”: Data Construction, Additional Empirical Results, and Robustness Checks John Y. Campbell and Tuomo Vuolteenaho 1 First draft: February 2004 This version: June 2004 1 Department of Economics, Littauer Center, Harvard University, Cambridge MA 02138, USA, and NBER. Email [email protected] and [email protected] We are grateful to Ken French for providing us with some of the data used in this study. All errors and omissions remain our responsibility. This material is based upon work supported by the National Science Foundation under Grant No. 0214061 to Campbell.
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This appendix to “Bad Beta, Good Beta” (henceforth BBGB, Campbell and Vuolteenaho, 2004) contains background material on our empirical methods and re- ports the results of robustness checks. The fi rst section describes in detail how we construct our data. The second section discusses our method for estimating betas. The third section brie fl y reviews the econometrics of predictive regressions, and then asks whether our fi ndings might be driven by fi nite-sample bias in the predictive equations of our vector autoregressive model. The fourth section discusses the evolution of betas over time, and asks whether it is reasonable to work with a model in which betas are fi xed in each of two subsamples as we do in BBGB. The fi fth section asks whether our results would be a ff ected if we estimated a conditional rather than an unconditional asset pricing model. The sixth section explores the sensitivity of the BBGB results to changes in the parameter ρ , which is a constant of loglinearization in our loglinear approximate asset pricing framework. The seventh section asks whether the BBGB results are robust to changes in the data frequency from monthly to quarterly or annual. The eighth section considers alternative VAR speci fi cations with additional explanatory variables. 1 Data construction We construct the variables that enter our VAR as follows. First, the excess log return on the market ( r e M ) is the di ff erence between the log return on the Center for Research in Securities Prices (CRSP) value-weighted stock index ( r M ) and the log risk-free rate. The risk-free-rate data are constructed by CRSP from Treasury bills with approximately three month maturity. Second, the term yield spread ( TY ) is provided by Global Financial Data and is computed as the yield di ff erence between ten-year constant-maturity taxable bonds and short-term taxable notes, in percentage points. Third, the price-earnings ratio ( PE ) is from Shiller (2000), constructed as the price of the S&P 500 index divided by a ten-year trailing moving average of aggregate earnings of companies in the S&P 500 index. Following Graham and Dodd (1934), Campbell and Shiller (1988b, 1998) advocate averaging earnings over several years to avoid temporary spikes in the price-earnings ratio caused by cyclical declines in earnings. We avoid any interpolation of earnings in order to ensure that all components of the time- t price-earnings ratio are contemporaneously observable
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