【文章內(nèi)容簡介】 hing besides a beta measure of risk.2. Beta is a fickle shortterm performer. Some shortterm studies have shown risk andreturn to be negatively related. For example, Black, Jensen and Scholes found that fromApril 1957 through December 1965, securities with higher risk produced lower returnsthan less risky securities. This result suggests that (1) in some short periods, investorsmay be penalized for taking on more risk, (2) in the long run, investors are not rewardedenough for high risk and are overpensated for buying securities with low risk, and (3)in all periods, some unsystematic risk is being valued by the market.3. Estimated betas are unstable. Major changes in a pany affecting the character ofthe stock or some unforeseen event not reflected in past returns may decisively affect thesecurity’s future returns.4. Beta is easily rolled over. Richard Roll has demonstrated that by changing the marketindex against which betas are measured, one can obtain quite different measures of therisk level of individual stocks and portfolios. As a result, one would make differentpredictions about the expected returns, and by changing indexes, one could change theriskadjusted performance ranking of a manager.14. CFA Examination Level IIThe following information describes the expected return and risk relationship for the stocks of two ofWAH’s Using only the data shown in the preceding table:a. Draw and label a graph showing the security market line and position stocks X and Y relativeto it. [5 minutes]b. Compute the alphas both for Stock X and for Stock Y. Show your work. [4 minutes]c. Assume that the riskfree rate increases to 7 percent with the other data in the preceding matrixremaining unchanged. Select the stock providing the higher expected riskadjusted return and justifyyour selection. Show your calculations. [6 minutes]答案14(a). The security market line (SML) shows the required return for a given level of systematicrisk. The SML is described by a line drawn from the riskfree rate: expected return is 5percent, where beta equals 0 through the market return。 expected return is 10 percent,where beta equal .14(b). The expected riskreturn relationship of individual securities may deviate from thatsuggested by the SML, and that difference is the asset’s alpha. Alpha is the differencebetween the expected (estimated) rate of return for a stock and its required rate of returnbased on its systematic risk Alpha is puted asALPHA (α) = E(ri) [rf + β(E(rM) rf)]whereE(ri) = expected return on Security irf = riskfree rateβi = beta for Security iE(rM) = expected return on the marketCalculation of alphas:Stock X: = 12% [5% + % (10% 5%)] = %Stock Y: = 9% [5% + %(10% 5%)] = %In this instance, the alphas are equal and both are positive, so one does not dominate theother.Another approach is to calculate a required return for each stock and then subtract thatrequired return from a given expected return. The formula for required return (k) isk = rf + βi (rM rf ).Calculations of required returns:Stock X: k = 5% + (10% 5%) = %= 12% % = %Stock Y: k = 5% + (10% 5%) = %= 9% % = %14(c). By increasing the riskfree rate from 5 percent to 7 percent and leaving all other factorsunchanged, the slope of the SML flattens and the expected return per unit of incrementalrisk bees less. Using the formula for alpha, the alpha of Stock X increases to percent and the alpha of Stock Y falls to percent. In this situation, the expectedreturn ( percent) of Stock X exceeds its required return ( percent) based on theCAPM. Therefore, Stock X’s alpha ( percent) is positive. For Stock Y, its expectedreturn ( percent) is below its required return ( percent) based on the CAPM.Therefore, Stock Y’s alpha ( percent) is negative. Stock X is preferable to Stock Yunder these circumstances.Calculations of revised alphas:Stock X = 12% [7% + (10% 7%]= 12% % = %Stock Y = 9% [7% + (10% 7%)]= 9% % = %CFA Examination Level IIIMultifactor models of security returns have received increased attention. The arbitrage pricing theory(APT) probably has drawn the most attention and has been proposed as a replacement for the capitalasset pricing model (CAPM).a. Briefly explain the primary differences between the APT and the CAPM.b. Identify the four systematic factors suggested by Roll and Ross that determine an asset’s riskiness.Explain how these factors affect an asset’s expected rate of return.答案12(a). The basic Capital Asset Pricing Model (CAPM) assumes that investors care only aboutportfolio risk and expected return。 ., they are risk averse. From this assumption esthe conclusion that a portfolio39。s expected return will be related to only one attribute itsbeta (sensitivity) relative to the broadly based market portfolio.Arbitrage Price Theory (APT) takes a different approach: it is not much concerned aboutinvestor preferences, and it assumes that returns are generated by a multifactor model.APT reflects the fact that several major (systematic) economic factors may affect a givenasset in varying degrees. Further, unlike the CAPM, whose single factor is unchanging,APT recognizes that these key factors can change over time (as can investor preferences).Summarizing, APT 1) identifies several key systematic macroeconomic factors as part ofthe process that generates security returns vs. only one factor recognized by the CAPM, 2)recognizes that these key factors can change over time, whereas the CAPM’s singlefactor is unchanging, 3) makes fewer assumptions about investor preferences than theCAPM, and 4) recognizes that these preferences can change over time.12(b). The four systematic factors identified by Roll and Ross are unanticipated changes in: 1)inflation, 2) industrial production, 3) risk premiums, and 4) the slope of the term structur