1、1,CAPM模型认为资产组合收益可以由得到最好的解释。a.经济因素b.特有风险c.系统风险d.分散化c,2,按照C A P M模型，假定市场预期收益率=1 5%，无风险利率=8%X Y Z证券的预期收益率=1 7%X Y Z的贝塔值=1.2 5以下哪种说法正确？a.X Y Z被高估b.X Y Z是公平定价c.X Y Z的阿尔法值为-0.2 5%d.X Y Z的阿尔法值为0.2 5%d,第3至第5题中假定无风险利率为6%，市场收益率是1 6%。,3、一股股票今天的售价为5 0美元，在年末将支付每股6美元的红利。贝塔值为1.2。预期在年末该股票售价是多少？为股票的 等于1，它的预期收益率应该等于市
2、场收益率，即6+1.2(1 6-6)=18%。E(r)=(D1+P1-P0)/P0 0.1 8=(6+P1-5 0)/5 0=5 3美元,4、投资者购入一企业，其预期的永久现金流为1 000美元，但因有风险而不确定。如果投资者认为企业的贝塔值是0.5，当贝塔值实际为1时，投资者愿意支付的金额比该企业实际价值高多少？,假定1 000美元是永久型债券。如果是0.5，现金流应该按利率折现：6%+0.5(1 6%-6%)=11%PV=1 000/0.11=9 090.91美元但是，如果等于1，则投资的收益率就应等于1 6%，支付给企业的价格就应该为：PV=1 000/0.16=6 250美元，其中的差
3、额为2 840.91 美元，是你多支付的部分，如果你错误地将视为0.5而不是1的话。,5、一股票预期收益率为4%，其贝塔值是多少？利用证券市场线：4=6+(1 6-6)=-2/1 0=-0.2,6、证券市场线描述的是：a.证券的预期收益率与其系统风险的关系。b.市场资产组合是风险性证券的最佳资产组合。c.证券收益与指数收益的关系。d.由市场资产组合与无风险资产组成的完整的资产组合。a,7、如果rf6%，E(rM)1 4%，E(rP)1 8%的资产组合的值等于多少？,E(rP)=rf+E(rM)-rf 1 8=6+(1 4-6)=1 2/8=1.5,8、以下说法是对还是错？a.值为零的股票的预期
4、收益率为零。b.CAPM模型表明如果要投资者持有高风险的证券，相应地也要求更高的回报率。c.通过将0.7 5的投资预算投入到国库券，其余投入到市场资产组合，可以构建值为0.7 5的资产组合。,a.错。=0说明E(rP)=rf，而不是零。b.错。投资者仅要求承担系统风险(不可分散的或市场风险)的风险溢价。全部波动包括不可分散的风险。c.错。你的资产组合的75%应投资于市场，25%投资于国库券。因此，=0.751+0.250=0.75,如果简单的C A P M模型是有效的，下列各题中哪些情形是有可能的，试说明之。每种情况单独考虑。9、,不可能。资产组合A的比B高，但其预期收益率却低。因此A不会处于
5、均衡。,10,可能。如果C A P M是正确的，预期的收益率仅仅补偿用来表示的系统(市场)风险而不是包含非系统风险的标准差。因此，A的较低的收益率可能有一个较高的标准差，要A的值比B小即可。,11,不可能。资产组合A的酬报与波动性比率要高于市场，根据C A P M这是不可能的，因为C A P M 认为市场是最有效率的资产组合。使用提供的数据，有SA=(1 6-10)/12=0.5 SM=(1 8-1 0)/2 4=0.3 3数字结果表明资产组合A会提供一个比市场组合更高的风险报酬补偿收益。,12,不可能。资产组合A明显优于市场组合。它的标准差较低而预期收益率却更高。,13,不可能。这种情况下的
6、证券市场线为：E(r)=1 0+(1 8-1 0)，为1.5的资产组合的预期收益率为：E(r)=1 0+1.5(1 8-1 0)=2 2%。A的预期收益率为1 6%，也就是说A在证券市场线下有一负的阿尔法值-6%，因此，是一定价过高的资产组合。这与C A P M模型不一致。,14,不可能。与1 0题中的证券市场线相同。这里资产组合A要求的预期收益率为：1 0+0.9 8=1 7.2%，仍然高于1 6%。A定价过高，其阿尔法值为-1.2%。,15,可能，与8题中的证券市场线相同。资产组合A位于C M L的下方，这与C A P M并不矛盾。,16、一证券的市场价格为5 0美元，期望收益率为1 4%
7、，无风险利率为6%，市场风险溢价为8.5%。如果这一证券与市场资产组合的协方差加倍(其他变量保持不变)，该证券的市场价格是多少？假定该股票预期会永远支付一固定红利。,如果证券的协方差加倍，则它的值和风险溢价也加倍。现在的风险溢价为8%(=1 4%-6%)，因此新的风险溢价为1 6%，新的折现率为1 6%+6%=2 2%。如果股票支付某一水平的永久红利，则我们可以从红利D的原始数据知道必须满足永久债券的等式：价格=红利/折现率 5 0=D/0.1 4 D=5 00.1 4=7.0 0美元在新的折现率2 2%的条件下，股票价值为7美元/0.2 2=3 1.8 2美元。股票风险的增加使得它的价值降低
8、了3 6.3 6%。,17,根据CAPM模型，贝塔值为1.0，阿尔法值为0的资产组合的预期收益率为：a.在rM和rf之间b.无风险利率rf c.(rM-rf)d.市场预期收益率rM d,18,假定短期国库券(被认为是无风险的)的收益率约为5%。假定一贝塔值为1的资产组合市场要求的期望收益率是12%，根据资本资产定价模型(证券市场线)：a.市场资产组合的预期收益率是多少？b.贝塔值为0的股票的预期收益率是多少？c.假定投资者正考虑买入一股股票，价格为40美元。该股票预计来年派发红利3美元。投资者预期可以以41美元卖出。股票风险的=-0.5，该股票是高估还是低估了？,a.因为市场组合的定义为1，它
9、的预期收益率为12%。b.=0意味着无系统风险。因此，资产组合的公平的收益率是无风险利率，为5%。c.运用证券市场线，=-0.5的股票公平收益率为：E(r)=5+(-0.5)(12-5)=1.5%利用第二年的预期价格和红利，求得预期收益率：E(r)=44/40-1=0.10 或10%因为预期收益率超过了公平收益，股票必然定价过低。,19,a.A mutual fund with beta of 0.8 has an expected rate of return of 14%.If rf 5%,and you expect the rate of return on the market po
10、rtfolio to be 15%,should you invest in this fund?What is the funds alpha?b.What passive portfolio comprised of a market-index portfolio and a money market account would have the same beta as the fund?Show that the difference between the expected rate of return on this passive portfolio and that of t
11、he fund equals the alpha from part(a).,a.E(rP)=rf+E(rM)-rf=5%+0.8(15%5%)=13%=14%13%=1%You should invest in this fund because alpha is positive.b.The passive portfolio with the same beta as the fund should be invested 80%in the market-index portfolio and 20%in the money market account.For this portfo
12、lio:E(rP)=(0.8 15%)+(0.2 5%)=13%14%13%=1%=,20、根据上表参照证券市场线作出的资产组合R的图形，R位于：a.证券市场线上b.证券市场线的下方c.证券市场线的上方d.数据不足d,21、参照资本市场线作出的资产组合R的图形，R位于：a.资本市场线上b.资本市场线的下方c.资本市场线的上方d.数据不足d,22、Karen Kay,a portfolio manager at Collins Asset Management,is using the capital asset pricing model for making recommendations
13、to her clients.Her research department has developed the information shown in the following exhibit.a.Calculate expected return and alpha for each stock.b.Identify and justify which stock would be more appropriate for an investor who wants toi.add this stock to a well-diversified equity portfolio.ii
14、.hold this stock as a single-stock portfolio.,B、i.Kay should recommend Stock X because of its positive alpha,compared to Stock Y,which has a negative alpha.In graphical terms,the expected return/risk profile for Stock X plots above the security market line(SML),while the profile for Stock Y plots be
15、low the SML.Also,depending on the individual risk preferences of Kays clients,the lower beta for Stock X may have a beneficial effect on overall portfolio risk.,ii.Kay should recommend Stock Y because it has higher forecasted return and lower standard deviation than Stock X.The respective Sharpe rat
16、ios for Stocks X and Y and the market index are:Stock X:(14%5%)/36%=0.25Stock Y:(17%5%)/25%=0.48Market index:(14%5%)/15%=0.60The market index has an even more attractive Sharpe ratio than either of the individual stocks,but,given the choice between Stock X and Stock Y,Stock Y is the superior alterna
17、tive.When a stock is held as a single stock portfolio,standard deviation is the relevant risk measure.For such a portfolio,beta as a risk measure is irrelevant.Although holding a single asset is not a typically recommended investment strategy,some investors may hold what is essentially a single-asse
18、t portfolio when they hold the stock of their employer company.For such investors,the relevance of standard deviation versus beta is an important issue.,23,投资者是一家大型制造公司的咨询顾问，考虑有一下列净税后现金流的项目(单位：百万美元)项目的贝塔值为1.8。假定rf8%，E(rM)1 6%，项目的净现值是多少？在其净现值变成负数之前，项目可能的最高估计值是多少？,该项目适当的折现率为：E(rP)=rf+E(rM)-rf=8+1.8(18
19、-8)=26%使用该折现率，NPV=-40+.(10)(15/1.26t)=-40+15年金因素(26%,10年)=11.97 该项目的内部收益率为35.73%。在边界利率超过无风险利率之前，可取的的最高值由下式决定：35.73=8+(1 8-8)=2 7.7 3/1 0=2.7 7 3,24,Joan McKay is a portfolio manager for a bank trust department.McKay meets with two clients,Kevin Murray and Lisa York,to review their investment objecti
20、ves.Each client expresses an interest in changing his or her individual investment objectives.Both clients currently hold well-diversified portfolios of risky assets.a.Murray wants to increase the expected return of his portfolio.State what action McKay should take to achieve Murrays objective.Justi
21、fy your response in the context of the CML.b.York wants to reduce the risk exposure of her portfolio but does not want to engage in borrowing or lending activities to do so.State what action McKay should take to achieve Yorks objective.Justify your response in the context of the SML.,a.McKay should
22、borrow funds and invest those funds proportionately in Murrays existing portfolio(i.e.,buy more risky assets on margin).In addition to increased expected return,the alternative portfolio on the capital market line will also have increased risk,which is caused by the higher proportion of risky assets
23、 in the total portfolio.b.McKay should substitute low beta stocks for high beta stocks in order to reduce the overall beta of Yorks portfolio.By reducing the overall portfolio beta,McKay will reduce the systematic risk of the portfolio,and therefore reduce its volatility relative to the market.The s
24、ecurity market line(SML)suggests such action(i.e.,moving down the SML),even though reducing beta may result in a slight loss of portfolio efficiency unless full diversification is maintained.Yorks primary objective,however,is not to maintain efficiency,but to reduce risk exposure;reducing portfolio
25、beta meets that objective.Because York does not want to engage in borrowing or lending,McKay cannot reduce risk by selling equities and using the proceeds to buy risk-free assets(i.e.,lending part of the portfolio).,零贝塔证券的预期收益率是什么？a.市场收益率b.零收益率c.负收益率d.无风险收益率d,两个投资顾问比较业绩。一个的平均收益率为1 9%，而另一个为1 6%。但是前者的
26、贝塔值为1.5，后者的贝塔值为1。a.你能判断哪个投资顾问更善于预测个股(不考虑市场的总体趋势)吗？b.如果国库券利率为6%，这一期间市场收益率为1 4%，哪个投资者在选股方面更出色？c.如果国库券利率为3%，这一时期的市场收益率是1 5%吗？,r1=19%；r2=16%；1=1.5；2=1 a.要找出哪个投资者是更好的个股预测家，我们来考察他们的不正常收益，即超过正常的阿尔法值的部分，也就是在实际收益和根据证券市场线估计的收益之间的差额。没有公式中的有关信息(无风险利率和市场收益率)，我们无法得出哪个投资者的预测更准确。,b.如果rf=6%且rM=1 4%，则(用表示非正常收益)有1=19-
27、6+1.5(14-6)=19-18=1%2=16-6+1(14-6)=16-14=2%这里，第二个投资者有更高的非正常收益，因此他表现为更准确的预测者。通过更好的预测，第二个投资者得以在他的资产组合中添加定价过低的股票。,c.如果rf=3%且rM=1 5%，则有 1=19-3+1.5(15-3)=19-21=-2%2=16-3+1(15-3)=16-15=1%这里，不仅第二个投资者表现为更佳的预测者，而且第一个投资者的预测显得毫无价值(或更糟)。,27,假定借款受到限制，因此零贝塔C A P M模型成立。市场资产组合的期望收益率为1 7%，而零贝塔资产组合的期望收益率为8%。贝塔值为0.6的资
28、产组合的预期收益率是多少？在0贝塔值C A P M模型中，0贝塔值资产组合代替了无风险利率，因此，E(r)=8+0.6(1 7-8)=1 3.4%,28、上表给出了一证券分析家预期的两个特定市场收益情况下的两只股票的收益。a.两只股票的值是多少？b.如果市场收益为5%与2 5%的可能性相同，两只股票的预期收益率是多少？c.如果国库券利率6%，市场收益为5%与2 5%的可能性相同，画出这个经济体系的证券市场线(S M L)。d.在证券市场线图上画出这两只股票，其各自的阿尔法值是多少？e.激进型企业的管理层在具有与防守型企业股票相同的风险特性的项目中使用的临界利率是多少？,a.是股票的收益对市场收
29、益的敏感程度。称A为一激进型股票，而D为一保守型股票。则是市场收益每变化一个单位，股票收益的相应变化。因此，我们可以通过计算在两种假设情况下股票的收益差别除以市场的收益差别来计算出该股票的值。A=(-2-3 8)/(5-2 5)=2.0 0 B=(6-1 2)/(5-2 5)=0.3 0,b.在每种情况的可能性相等的情况下，预期收益率是两种可能结果的平均数。E(rA)=0.5(-2+3 8)=1 8%E(rB)=0.5(6+1 2)=9%c.证券市场线由市场预期收益0.5(2 5+5)=1 5%决定，此时为1；国库券的收益率为6%时，为零。见下图。,证券市场线的公式为：E(r)=6+(15-6
30、),d.激进型股票有一公平的预期收益为：E(rA)=6+2.0(15-6)=24%但是，分析家得出的预期收益是1 8%。因此他的阿尔法值是18%-24%=-6%。相似的，保守型股票要求的收益率为E(rD)=6+0.3(15-6)=8.7%，但是分析家对D的预期收益率是9%，因此，股票有一正的阿尔法值：=实际的预期收益-要求的收益(风险既定)=9-8.7=+0.3%。在图上每种股票的点如上所示。,e.边界利率由项目的值0.3决定，而不是由企业的值决定。正确的折现率为 8.7%，即股票D的公平的收益率。,29,a.McKay should borrow funds and invest those
31、 funds proportionately in Murrays existing portfolio(i.e.,buy more risky assets on margin).In addition to increased expected return,the alternative portfolio on the capital market line will also have increased risk,which is caused by the higher proportion of risky assets in the total portfolio.b.McK
32、ay should substitute low beta stocks for high beta stocks in order to reduce the overall beta of Yorks portfolio.By reducing the overall portfolio beta,McKay will reduce the systematic risk of the portfolio,and therefore reduce its volatility relative to the market.The security market line(SML)sugge
33、sts such action(i.e.,moving down the SML),even though reducing beta may result in a slight loss of portfolio efficiency unless full diversification is maintained.Yorks primary objective,however,is not to maintain efficiency,but to reduce risk exposure;reducing portfolio beta meets that objective.Bec
34、ause York does not want to engage in borrowing or lending,McKay cannot reduce risk by selling equities and using the proceeds to buy risk-free assets(i.e.,lending part of the portfolio).,a.Agree;Regans conclusion is correct.By definition,the market portfolio lies on the capital market line(CML).Unde
35、r the assumptions of capital market theory,all portfolios on the CML dominate,in a risk-return sense,portfolios that lie on the Markowitz efficient frontier because,given that leverage is allowed,the CML creates a portfolio possibility line that is higher than all points on the efficient frontier ex
36、cept for the market portfolio,which is Rainbows portfolio.Because Eagles portfolio lies on the Markowitz efficient frontier at a point other than the market portfolio,Rainbows portfolio dominates Eagles portfolio.b.Nonsystematic risk is the unique risk of individual stocks in a portfolio that is div
37、ersified away by holding a well-diversified portfolio.Total risk is composed of systematic(market)risk and nonsystematic(firm-specific)risk.Disagree;Wilsons remark is incorrect.Because both portfolios lie on the Markowitz efficient frontier,neither Eagle nor Rainbow has any nonsystematic risk.Theref
38、ore,nonsystematic risk does not explain the different expected returns.The determining factor is that Rainbow lies on the(straight)line(the CML)connecting the risk-free asset and the market portfolio(Rainbow),at the point of tangency to the Markowitz efficient frontier having the highest return per
39、unit of risk.Wilsons remark is also countered by the fact that,since nonsystematic risk can be eliminated by diversification,the expected return for bearing nonsystematic is zero.This is a result of the fact that well-diversified investors bid up the price of every asset to the point where only syst
40、ematic risk earns a positive return(nonsystematic risk earns no return).,30,Wilson is now evaluating the expected performance of two common stocks,Furhman Labs Inc.and Garten Testing Inc.He has gathered the following information:The risk-free rate is 5%.The expected return on the market portfolio is
41、 11.5%.The beta of Furhman stock is 1.5.The beta of Garten stock is.8.Based on his own analysis,Wilsons forecasts of the returns on the two stocks are 13.25%forFurhman stock and 11.25%for Garten stock.Calculate the required rate of return for FurhmanLabs stock and for Garten Testing stock.Indicate w
42、hether each stock is undervalued,fairly valued,or overvalued.,E(r)=rf+E(rM)rfFuhrman Labs:E(r)=5+1.5 11.5 5.0=14.75%Garten Testing:E(r)=5+0.8 11.5 5.0=10.20%If the forecast rate of return is less than(greater than)the required rate of return,then the security is overvalued(undervalued).Fuhrman Labs:
43、Forecast return Required return=13.25%14.75%=1.50%Garten Testing:Forecast return Required return=11.25%10.20%=1.05%Therefore,Fuhrman Labs is overvalued and Garten Testing is undervalued.,31,简要说明根据C A P M模型，投资者持有资产组合A是否会比持有资产组合B获得更高的收益率。假定两种资产组合都已充分分散化。,在CAPM模型的条件下，投资者仅可以得到不能被分散化(系统)的风险的补偿。因为系统风险(以来测度)对两种资产组合都为1.0，投资者将预期这两种资产组合A和B有相同的收益率。而且，因为这两种资产组合都是充分分散化的，个别证券的特有风险高或低并不产生影响。两种资产组合中企业特有的风险都被分散掉了。,