【正文】 5.s efficiency and therefore are not independently testable. There is an “if and only if” relation between the expected return–beta relationship and the efficiency of the market portfolio.p. 4112a.Figure , from a study by Chan, Karceski, and Lakonishok,20 makes the case for overreaction. Firms are sorted into deciles based on ine growth in the past 5 years. By construction, the growth rates uniformly increase from the first through the tenth decile. The booktomarket ratio for each decile at the end of the 5year period (the dashed line) tracks recent growth very well. B/M falls steadily with growth over past 5 years. This is evidence that past growth is extrapolated and then impounded in price. High past growth leads to higher prices and lower B/M ratios.Similarly, one can estimate the determinants of a timevarying market risk premium, using the same set of state variables:We can estimate the expected market risk premium for each period using the regression parameter estimates and the values of the state variables for that period. The fitted value from this regression is the estimate of the market risk premium.TERM = Term structure spread (10year–1year Treasury rates). or H, M, L). The nine portfolios thus formed are labeled in the following matrix。How can we make the FamaFrench model operational? Fama and French propose measuring the size factor in each period as the differential return on small firms versus large firms. This factor is usually called SMB (for “small minus big”). Similarly, the other extramarket factor is typically measured as the return on firms with high booktomarket ratios minus that on firms with low ratios, or HML (for “high minus low”). Therefore, the FamaFrench threefactor assetpricing model is15p. 420The coefficients bi, si, and hi are the betas of the stock on each of the three factors, often called the factor loadings. According to the arbitrage pricing model, if these are the relevant factors, excess returns should be fully explained by risk premiums due to these factor loadings. In other words, if these factors fully explain asset returns, the intercept of the equation should be zero. Note that tstatistics are in parentheses.Source: Modified from NaiFu Chen, Richard Roll, and Stephen Ross, “Economic Forces and the Stock Market,” Journal of Business 59 (1986). Reprinted by permission of the publisher, The University of Chicago Press.CG = Unexpected changes in risk premiums measured by the difference between the returns on corporate Baarated bonds and longterm government bonds.Identification of portfolios that hedge these fundamental risk factors.Estimates of the variance of the residuals for each of the 100 stocks. Tests of Multifactor CAPM and APTThe multifactor CAPM and APT are elegant theories of how exposure to systematic risk factors should influence expected returns, but they provide little guidance concerning which factors (sources of risk) ought to result in risk premiums. A test of this hypothesis would require three stages: p. 418P 500 index over the sample period.P 500) is assumed to represent the factor, or one of the factors. Furthermore, to obtain more reliable statistics, most tests have been conducted with the rates of return on highly diversified portfolios rather than on individual securities. For both of these reasons, tests that have been directed at the CAPM actually have been more suitable to establish the validity of the APT. We will see that it is more important to distinguish the empirical work on the basis of the factor structure that is assumed or estimated than to distinguish between tests of the CAPM and the APT. The Index Model and the SingleFactor APTp. 408The Expected Return–Beta RelationshipRecall that if the expected return–beta relationship holds with respect to an observable ex ante efficient index, M, the expected rate of return on any security i iswhere βi is defined as CovCourt rulings on torts cases sometimes use the expected return–beta relationship to determine discount rates to evaluate claims of lost future ine.4.IIIp. 407IN THIS CHAPTER, we consider the empirical evidence in support of the CAPM and APT. At the outset, however, it is worth noting that many of the implications of these models already have been accepted in widely varying applications. Consider the following: 1. i = 1, . . . , 100, and t = 1, . . . , 60. View Equation as a security characteristic line (SCL), as in Chapter 8. For each stock, i, you estimate the beta coefficient as the slope of a firstpass regression A time series regression to estimate the betas of securities or portfolios. equation. (The terminology firstpass regression is due to the fact that the estimated coefficients will be used as input into a secondpass regression A crosssectional regression of portfolio returns on betas. The estimated slope is the measurement of the reward for bearing systematic risk during the period..)You will use the following statistics in later analysis:UI = Unexpected inflation defined as the difference between actual and expected inflation. UI = Unanticipated inflation。Note in Table that the two market indexes EWNY and VWNY are not statistically significant (their tstatistics of and ?.633 are less than 2). Note also that the VWNY factor has the “wrong” sign in that it seems to imply a negative marketrisk premium. Industrial production (IP), the risk premium on corporate bonds (CG), and unanticipated inflation (UI) are the factors that appear to have significant explanatory power.Chapter13: Empirical Evidence on Security Returns The FamaFrench ThreeFactor ModelThe multifactor model that occupies center stage these days is the threefactor model introduced by Fama and The systematic factors in the FamaFrench model are firm size and booktomarket ratio as well as the market inde