Exercise_3_Week_5_Solutions

1、CAPM and Market Efficie ncySolutio ns1. Ms EnglandFundVariability (%)Annual Abno rmal Retur n (%)Annual Actual Retur n (%)Expected Retur nP1.234-29-623T1.036-19221R0.824143319Market1.02021Risk-0011freea) Assuming the CAPM holds the market portfolio has a beta of unity (same as fund T) and hence expe

2、cted return on the market is 21%. Compute the risk-free rate from CAPM for any of the fun dsExpected Return for security P = 23 = r f + 1.2 (21 - r f) f 11% or from security R: 19 = rf + 0.8 (21 - r f) gives rf = 11%.(b) New R m=20% and r f=10%. Call this portfolio A. Ms England expects return on se

3、curity with j to be ER j = 10 + j *(20-10)The beta of Portfolio A is (1.2 + 1.0 + 0.8)/3 = 1 hence the expected return of Portfolio A is 20%.To obta in an expected retur n of 25%, she creates a new Portfolio B in which assume she puts an amount x in the risk free asset and 1-x in her Portfolio Athe

4、nx 10 + 20(1-x) = 25.hencex = -0.5.This implies that Portfolio B con sists of -0.5 (i.e. borrows) in the risk free asset and1.5 in her Portfolio A or borrows 15,000 aftd in vests45,000 in Portfolio A of threefun ds.(c) Variability of market is 20%.Note: specific risk, unique risk and diversifiable r

5、isk are all the same terms.Similarly: market risk, systematic risk, and non-diversifiable are all the same termsWe can compute the specific risk of P, T, R fromvar (i)Beta2 *400 (Systematic risk)Specific Risk ( 2i)P1156576580T1296400896R576256320Assu ming in depe ndence of each compa nies specific r

6、isk from the defi niti on of specific risk, we can compute the specific risk in Portfolio A using the standard formula for portfolio risk, but with the assumption that specific risk has ZERO covaria nee: Specific Risk in Portfolio A = (3 )2 (580+896+320) = 200We have already computed the beta of Por

7、tfolio A as unity, and so systematic risk ofPortfolio A = 1 2 *400 = 400. So total risk of Portfolio A is 600 (stdev = 24.5%)% Diversifiable risk in Portfolio A with just three securities =200400 200=33%In the case where she borrows and creates Portfolio B, the relative weights in the risk free asse

8、t and the three securities are -0.5, 0.5, 0.5, 0.5Beta of Portfolio B = 0*(-0.5)+ 0.5*1.2 +0.5*1 + 0.5*0.8(remember beta of risk-free asset is zero)ie Beta of portfolio B = (1.2 + 1.0 + 0.8)*0.5 = 1.5The specific risk of Portfolio B is (?)2 (580+896+320) = 449Total risk of portfolio B =1.5 2 * 400 +

9、 449 = 1,349 (stdev = 36.7%)% diversifiable risk in Portfolio B =44921.5 *400 44933% .Result: You do not alter the percen tage of diversifiable risk by comb ining securities with a riskless asset. You do of course alter the total risk in the portfolio.Mean return25%20%B20%20%24.5%36.7%Stan dard devi

10、ati on2.Giuli ni Pic, Tosca nini Pic and Can telli Pica) Over the period examined the beta of Giulini was estimated to be 1.74, Toscanini to be 0.78, and Cantelli to be 1.53.b) C.A.R. = Rit Bi RmtRft(1)For 12 mon ths, in clud ing the month in with the annual profits were announ cedGiuli ni -periodMa

11、rch 2008Feb 2009Rit0.0852,Rmt0.0618, Rft 0.0753,1.72Uit0.852 11.72x0.06180.0753(1.72 1)0.246Tosca nini - periodFeb 2008Jan 2009Rit0.0789,Rmt0.1273, Rft 0.0768,0.81Uit0.07890.81x0.1273 0.0768(0.81 1)0.167Can telli-periodMarch 2008Feb 2009Rit0.6568,Rmt0.0618, Rft 0.0753,1.50Uit0.65681.50x0.0618 0.0753

12、(1.50 1)0.526For 12 mon ths, up to the month in with the annual profits were announ cedGiuli ni -periodFeb 2008Jan 2009Rit0.1203,Rmt0.1273,Rft 0.0768,1.88Uit0.12031.88x0.1273 0.0768(1.88 1)0.428Tosca nini - periodJan 2008Dec 2009Rit0.1773,Rmt0.2609,Rft0.0773,0.55Uit0.17730.55x0.26090.07773(0.551)0.0

13、70Can telli-periodFeb 2008Jan 2009Rit0.7266,Rmt0.1273,Rft 0.0768,1.51Uit0.72661.501x0.12730.0768(1.511)0.496c) Assu ming that a reas on able expectati ons model for earnings is a ran dom walk and that the earnings acco un ceme nts were on the same dates in 2008 as in 2009, the n, at the begi nning o

14、f each period used above, the market expectati on would have bee n the 2007 profits. Hence the cha nges to expectati ons are as follows:Changes in ProfitsSign of CARGiuli ni Toscan Ca ntelliHence the acco un ti ng earnings figure may be said to show in formatio n content assu ming that the joint hyp

15、othesis of semi-str ong market efficie ncy and the earnings expectati ons model is valid. There is also the experime ntal assumpti on that the CAR so calculated does reflect only firm-specific factors. So the stock market correctly predicts the earnings surprises.d) The acquisiti on of a con troll i

16、ng in terest in Giul in is shares is likely to boost the price of Giulinis share - hence increasing the CAR of Giulini (Empirical evide nee supports the view that takeovers boost the share price and hence retur n of the acquired compa ny).Tosca nini will be affected in 2 ways:? The acquisiti on of p

17、art of Giul in is share capital will slightly in crease the of Toscanini (0.78) since Giulinis of 1.74 is greater than 0.78.? The issue of debt capital to finance the takeover will also in crease theofTosca nini (as debt/equity in creases so does the of the levered firm).? If Tosca nin ishas cha nge

18、d, the n the 0.78 used to calculate the CAR willbe too low. If a high were to be used, the CAR of Tosca nini would be higher since R m is negative for the period July x 8 Jan x 9 (-0.1437).? The of Giul ini will only cha nge if the compa nys fun dame ntal characteristics are cha nged as a result of

19、Tosca nini acquiri ng the 55% in terest.e) The abnormal performance index (API) for a group of N securities measured over T periods is computed asN TAPI lt 1(1jt)j 1 t 1where jt are deviati ons from the market model. It represe nts the average (over N securities) of the compo un ded rate of residual

20、 retur ns.3. Vila and Weeken (2002) un dertake a similar an alysis of PE and DY ratios to exam ine whether the UK stock market was overvalued in 2000. What relati on ship do they ide ntify betwee n DY and stock prices? List the factors that they argue might have affected the equity risk premium.An s

21、wer: They illustrate that divide nds yields have bee n related to historical divide nd and price growth. They show that DY has little relati on ship with divide nd growth, but a stron ger relati on ship with price growth. When DY is low, prices tend to fall over the n ext 10 years.There is a relati

22、on ship betwee n DY and expected retur ns (prices), and prices adjust to bring DY back to mean. Vila and Weeke n suggest that expected retur ns depe nd on equity risk premium and risk-free-rate.They note that mean reversi on in divide nd yields has bee n accompa nied by cha nges in the equity risk pre