【正文】 x. These additional factors are empirically motivated by the observations, documented in Chapter 11, that historicalaverage returns on stocks of small firms and on stocks with high ratios of book equity to market equity (B/M) are higher than predicted by the security market line of the CAPM. These observations suggest that size or the booktomarket ratio may be proxies for exposures to sources of systematic risk not captured by the CAPM beta and thus result in the return premiums we see associated with these factors.DEFLT = Default spread on corporate bonds (Baa – Aaa rates). 2005 with permission from Elsevier Science. The strategy is to estimate parameters b0 through b4 and then fit beta using the parameter estimates and the values at each date of the four state variables. In this way, they can estimate beta in each period.The booktomarket ratio reflects past growth, but not future growth prospects. B/M tends to fall with ine growth experienced at the end of a 5year period, but actually increases slightly with future ine growth rates.Source: . Chan, J. Karceski, and J. Lakonishok, “The Level and Persistence of Growth Rates,” Journal of Finance 58 (April 2003), pp. 643–84. Reprinted by permission of the publisher, Blackwell Publishing, Inc. Of course, this additional factor presents further conundrums of interpretation. To characterize the original FamaFrench factors as reflecting obvious sources of risk is already a bit of a challenge. A momentum factor seems even harder to position as reflecting a risk–return tradeoff. But as we saw in Chapter 9, recent work has resulted in a growing appreciation of the importance of liquidity, and particularly an illiquidity premium, in asset pricing. We will see in the next section that a good part of the momentum effect may be related to liquidity.The sample average excess returns on each stock and the market portfolio are taken as estimates of expected excess returns, and the values of bi are estimates of the true beta coefficients for the 100 stocks during the sample period. σ2(ei) estimates the nonsystematic risk of each of the 100 stocks.p. 409CONCEPTCHECKAccording to the CAPM, what should be the intercept in each of these regressions?These results are inconsistent with the CAPM. First, the estimated SML is “too flat”。4.s efficiency. Furthe。In any sample of observations of individual returns there will be an infinite number of ex post (., after the fact) meanvariance efficient portfolios using the sample period returns and covariances (as opposed to the ex ante expected returns and covariances). Sample betas calculated between each such portfolio and individual assets will be exactly linearly related to sample average returns. In other words, if betas are calculated against such portfolios, they will satisfy the SML relation exactly whether or not the true market portfolio is meanvariance efficient in an ex ante sense. the average standard deviation of annual returns of the stocks included in these tests is probably even higher.Do high or lowbeta stocks tend to outperform the predictions of the CAPM?c.How many observations are there in each of the regressions?But B/M at the beginning of a 5year period shows little or even a positive association with subsequent growth (the solid colored line), implying that market capitalization today is inversely related to growth prospects. In other words, the firms with lower B/M (glamour firms) experience no better or even worse average future ine growth than other firms. The implication is that the market ignores evidence that past growth cannot be extrapolated far into the future. Booktomarket may reflect past growth better than future growth, consistent with extrapolation error.Finally, Petkova and Zhang examine the relationship between beta and the market risk premium. They define the state of economy by the size of the premium. A peak is defined as the periods with the 10% lowest risk premiums。TB = 1month Tbill rate.They estimate a firstpass regression, but first substitute these state variables for beta as follows:p. 423Figure Difference in return to factor portfolios in year prior to aboveaverage versus belowaverage GDP growth. Both SMB and HML portfolio returns tend to be higher in years preceding better GDP growth.Source: J. Liew and M. Vassalou, “Can BooktoMarket, Size and Momentum Be Risk Factors That Predict Economic Growth?” Journal of Financial Economics 57 (2000), pp. 221–45. 169。RiskBased InterpretationsLiew and Vassalou17 show that returns on style portfolios (HML or SMB) seem to predict GDP growth, and thus may in fact capture some aspects of business cycle risk. Each bar in Figure is the average difference in the return on the HML or SMB portfolio in years before good GDP growth versus in years with poor GDP growth. Positive values mean the portfolio does better in years prior to good macroeconomic performance. The predominance of positive values leads them to conclude that the returns on the HML and SMB portfolios are positively related to future growth in the macroeconomy, and so may be proxies for business cycle risk. Thus, at least part of the size and value premiums may reflect rational rewards for greater risk exposure.To create portfolios that track the size and booktomarket factors, Davis, Fama, and French16 sort industrial firms by size (market capitalization or market “cap”) and by booktomarket (B/M) ratio. Their size premium, SMB, is constructed as the difference in returns between the smallest and largest third of firms. Similarly, HML in each period is the difference in returns between high and low booktomarket firms. They use a broad market index, the valueweighted return on all stocks traded on . national exchanges (NYSE, AMEX, and NASDAQ) to pute the excess return on the market portfolio relative to the riskfree rate, taken