【正文】 owth Rates,” Journal of Finance 58 (April 2003), pp. 643–84. Reprinted by permission of the publisher, Blackwell Publishing, Inc. 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.DEFLT = Default spread on corporate bonds (Baa – Aaa rates).Table Threefactor regressions for portfolios formed from sorts on size and booktomarket ratio (B/M)Source: James L. Davis, Eugene F. Fama, and Kenneth R. French, “Characteristics, Covariances, and Average Returns, 1929 to 1997,” Journal of Finance 55, no. 1 (2000), p. 396. Reprinted by the permission of the publisher, Blackwell Publishing, Inc. for example, the S/M portfolio is prised of stocks in the smallest third of firms and the middle third of booktomarket ratio.For each of these nine portfolios, Davis, Fama, and French estimate Equation as a firstpass regression over the 816 months between 1929 and 1997 by using the regression model 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 index. 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. UI = Unanticipated inflation。Table Economic variables and pricing (percent per month 10), multivariate approachVWNY = Return on the valueweighted NYSE index。They first used 5 years of monthly data to estimate the factor betas of the 20 portfolios in a firstpass regression. This is acplished by estimating the following regressions for each portfolio:where M stands for the stock market index. Chen, Roll, and Ross used as the market index both the valueweighted NYSE index (VWNY) and the equally weighted NYSE index (EWNY).UI = Unexpected inflation defined as the difference between actual and expected inflation. 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: i = 1, . . . , 100, and t = 1, . . . , 60.Many firms use the SML to obtain a benchmark hurdle rate for capital budgeting decisions.These practices show that the financial munity has passed a favorable judgment on the CAPM and the APT, if only implicitly.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.Court rulings on torts cases sometimes use the expected return–beta relationship to determine discount rates to evaluate claims of lost future ine.4.In this chapter we consider the evidence along more explicit and rigorous lines. The first part of the chapter presents the methodology that has been deployed in testing the singlefactor CAPM and APT and assesses the results. The second part of the chapter provides an overview of current efforts to establish the validity of multifactor versions of the CAPM and APT. In the third part, we discuss recent literature on socalled anomalies in patterns of security returns and some of the responses to these puzzling findings. Finally, we present interesting research on stock returns that examines the size of the equity risk premium. Conventional wisdom has held for a long time that the history of returns on equities is quite puzzling. Recent studies address the puzzle.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 iswher