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The Short Sample Evidence
The value premium puzzle is the empirical observation that the CAPM cannot explain the value premium, the difference between the high average excess returns of value stocks and the low average excess returns of growth stocks. To put it a bit technically, but precisely, the CAPM betas cannot account for the observed variation of average excess returns (the difference between returns and the yield on three month Treasury Bills) across book-to-market sorted portfolios. Recall indeed the main implication of the CAPM: Differences is average returns between two assets are solely due to differences in their betas, which is a measure of how much do the returns of a particular asset commove with the returns of the market portfolio.
There is obviously an intimate connection between the value premium and the value premium puzzle and thus it is not surprising that the papers that showed rigorously the presence of the value effect in the data are also the ones which immediately tested whether the CAPM could capture such an extraordinary regularity. The paper by Barr Rosenberg, Kenneth Reid and Ronald Lanstein entitled "Persuasive Evidence of Market Inefficiency" in the Journal of Portfolio Management (1985: 11, 9-17) takes the view, as the title indicates, that the rejection of the CAPM is conclusive evidence that financial markets are not efficient. Instead Gene Fama and Ken French ("The Cross Section of Expected Stock Returns," Journal of Finance, 1992: 47, 427-465) take a more circumspect attitude: Variation in CAPM betas does not seem related to variation in average returns but whether one can jump to the conclusion that markets are inefficient is a very different matter. We explore this subtle issue in another QL. The value premium and value premium puzzle can be nicely seen in Table IV (page 442) of Fama and French's classic 1992 paper. The extreme growth portfolio has an average value weighted monthly return of .30 and a beta of 1.36 whereas the extreme value portfolio has a return of 1.83% and a beta that is essentially the same as that of the growth portfolio, 1.35. This is indeed a striking rejection of the CAPM, one that barely requires a rigorous test. The long sample evidence is less clear and we study it in a different QL. A word on Fama and French's 1992's paper: It is remarkable piece not only for the role it has in establishing conclusively the presence in the data of the value premium and its puzzle but also because it provides a wonderful synthesis of the empirical problems of the CAPM identified over a decade of empirical research in academia. For a wonderful summary of these issues you can read the piece by Fama and French "The Capital Asset Pricing Model: Theory and Evidence," The Journal of Economics Perspectives, vol. 18, no. 3, Summer, 2004.
The table below shows both the value premium and the value premium puzzle where we have extended the sample used by Fama and French until July 2011. The initial data point is January of 1963. Notice that the returns increase with book to market whereas the betas stay roughly constant. The plot shows these results in striking fashion. There are ten points in the plot, where the extreme ones correspond to the growth and value portfolios. In the vertical axis we report the CAPM fitted excess return, that is, the average excess return that the portfolio should yield given the estimated beta. In the horizontal axis the empirically observed average excess return. If the CAPM was a good representation of risk, the "dots" should be on the diagonal line. The plot is conclusive: The CAPM cannot explain the remarkable spread between value and growth stocks. This is the value premium puzzle.
|Returns (ann. %)||4.55||5.53||6.08||6.16||5.91||6.94||7.67||8.18||9.32||10.83|
|CAPM Fitted Returns||5.86||5.56||5.39||5.44||4.99||5.08||4.77||4.90||5.11||5.87|
Sample: 1963-01 to 2011-07. Average excess returns (in %), CAPM betas and CAPM fitted excess returns for ten book-to-market sorted portfolios of all stocks in Compustat; annualized; value weighted.; the portfolios are resorted at the end of June and BE/ME is book equity at the last fiscal year end of the prior calendar year divided by ME at the end of December of the prior year. Data: Ken French databse.