请选择 进入手机版 | 继续访问电脑版
 找回密码
 立即注册

     

16

主题

17

帖子

506

积分

略有小成

Rank: 4

积分
506
发表于 2018-3-5 16:35:11 | 显示全部楼层 |阅读模式
更多科目及中英文对照资料,请加入学术会员后索取。

Calculation Questions Question 1 A pension fund manager isconsidering three mutual funds. The first is a stock fund, the second is along-term government and corporate bond fund, and the third is a T-bill moneymarket fund that yields a sure rate of 5.5%. The probability distributions ofthe risky funds are: file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpgThe correlation between the fundreturns is .15. 1. Tabulate and draw the investment opportunity set of the two riskyfunds. Use investment proportions for the stock fund of 0% to 100% inincrements of 20%. What expected return and standard deviation does your graphshow for the minimum-variance portfolio? Parameters to Opportunity set = E(r Stock) = 15%, E(r Bonds)= 9%, SD (Stock)= 32%, SD(Bonds) =23%, Correlation= .15            
  Bonds    Stocks  
  Bonds    529    110.4  
  Stocks    110.4    1024  
The Minimum Variance:Wmin(Stock)   = SD2(Bonds) – Covariance(Bonds, Stock) / SD2(Stock)+ SD2(Bond) – 2*(Covariance Bond, Stock)                        = 529 – 110.4 / 1024+529 – 2*(110.4)Wmin(Stock)   =0.3142Therefore Wmin(Bonds) = 1-0.3142                                        =0.6858                         The Minimum Variance Portfolio mean and StandardDeviation:E(r) minimum = 0.3142(15) + 0.6858(9) = 10.89%Standard Deviation         = (W2 (Stock)*SD2(Stock)+W2 (Bond)*SD2(Bond)+2W(stock)*W(bond)Covariance (Stock, Bond))1/2                                        =(0.31422(1024)+0.68582(529) + 2(0.3142)(0.6858)(110.4))1/2                                        =19.94%
  % in stocks    % in Bonds    Expected Return    Standard Deviation  
  0    100    9    23  
  20    80    10.2    20.37    Min Variance  
  31.42    68.58    10.89    19.94  
  40    60    11.4    20.18  
  60    40    12.6    22.5    Tangency Portfolio  
  70.75    29.25    13.25    24.57  
  80    20    13.8    26.68  
  100    0    15    32  
file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png                                                                                2. Draw a tangent from therisk-free rate to the opportunity set. What does your graph show for theexpected return and standard deviation of the optimal risky portfolio? E(r)                                          SDMin Variance                   11%             20%Tangency                         13%             25%file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png3. What is the Sharpe ratio of thebest feasible CAL? Ws       = (E(rs) - rf) *SD2b - (E (rb)– rf)* Cov*(rs, rb)/ (E(rs) – rf) + E(rb )- r ]* SD2s - [E(rs)- rf+E(rb ) rf ]*Cov(rs ,rf )            =(15-5.5)*529-(9-5.5)*110.4/(15-5.5)*529+ (9-5.5)*1024 – (15-5.5+9-5.5)*110.4            =4,639.1/7,143.3            =0.6494Wb      =0.3506Mean and Standard Deviation of the optimal risky portfolio:E(rp)    = 0.6494*(15) + 0.3506 *(9) = 12.90%SDp     =(0.64942(1024)+0.35062(529) + 2*(0.6494)(0.3506)(110.4))1/2 = 24.39% Sharpe Ratio:=E(rp)- Rf / Standard Deviation Portfolio= 12.90-5.5/24.39=0.30344. Suppose now that your portfoliomust yield an expected return of 12% and be efficient, that is, on the bestfeasible CAL. a. What is the standard deviationof your portfolio?E (rc)= (rf+ E(rp) – rf/ Standard Deviation portfolio)*Standard Deviation  = 5.5 + 0.3034 *SD12%     =5.5 +0.3034 *SD       SD=11.34% 
b. What is the proportion invested in the T-billfund and each of the two risky funds? E(rc)   = (l − y)* rf + yr * (rp) = rf + y* [E(rp)− rf]                         = 5.5 + y*(12.90-5.5) E(rc)   =12% 12-5.5 = 12.90y - 5.5y6.5       =7.4yY         =6.5/7.4Y         =0.8784, and1-Y= 0.1216, the proportion of T-bill fund.Proportion Invested:In Stocks in a complete portfolio = 0.8784* 0.6494 =0.5704In Bonds in a complete portfolio = 0.8784 *0.3506 = 0.30805. If you were to use only the tworisky funds and still require an expected return of 12%, what would be theinvestment proportions of your portfolio? Compare its standard deviation tothat of the optimal portfolio in the previous problem. What do you conclude? 12        = 15ws +9*(1-ws)12        = 15ws + 9 –9ws12        =9 + 6wsws        = 0.5 So the proportions are 50% invested in the stock fund and50% in the bond fund.The Standard Deviation of this portfolio is:=((0.52*1,024) + (0.52*529) + (2* 0.5* 0.5 * 110.4))1/2=21.06%

本帖子中包含更多资源

您需要 登录 才可以下载或查看,没有账号?立即注册

x
回复

使用道具 举报

您需要登录后才可以回帖 登录 | 立即注册

本版积分规则