1.What are the expected return and expected standard deviation for the two-asset portfolio described as: Expected Return/Correlation | Variance | Weight | E(R1) = 10% | Var(1) = 9% | w1 = 30% | E(R2) = 15% | Var(2) = 25% | w2 = 70% | r1,2 = 0.4 |
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A) E(Rport) = 11.5%, σport = 3.95%. B) E(Rport) = 12.5%, σport = 1.60%. C) E(Rport) = 13.5%, σport = 39.47%. D) E(Rport) = 10.5%, σport = 15.58%. The correct answer was C) E(Rport) = w1E(R1) + w2E(R2) = (0.3)(10.0) + (0.7)(15.0) = 13.5% σport = [(w1)2(σ1)2 + (w2)2(σ2)2 + 2w1w2σ1σ2ρ1,2]1/2
= [(0.3)2(.09) + (0.7)2(.25) + 2(0.3)(0.7)(.3)(.5)(0.4)]1/2 = 39.47% 2.Allen Marko, CFA, is analyzing the diversification benefits available from investing in three equity funds. He is basing his analysis on monthly returns for the three funds and an appropriate market index over the past twenty years. He feels that there is no reason that the past performance should not carry forward into the future. Treasury bills currently pay 5 percent. Table 1: Expected Returns, Variances, and Covariance for Funds A, B, & C
| Equity Fund A | Equity Fund B | Equity Fund C | Average Return | 12% | 9% | 8% | Variance | 0.0256 | 0.0196 | 0.0172 | Correlation of A & B is 0.5
Correlation of A & C is 0.38
Correlation of B & C is 0.85 |
Marko has also obtained information about a fourth fund, Fund D. He does not have any information regarding the covariance of Fund D with Funds A, B, and C. The average return and variance for fund D are 10 percent and 0.018, respectively. The beta of Fund D is 0.714. Based on this data, what is the expected return of a portfolio that is made up of 60 percent of Fund A, 30 percent of Fund B, and 10 percent of Fund C? A) 10.2%. B) 9.1%. C) 11.4%. D) 10.7%. The correct answer was D) Expected return for the portfolio = (0.6)(0.12) + (0.3)(0.09) +(0.1)(.08)= 0.107 or 10.7%. 3.Which of the following is closest to the standard deviation of a portfolio that is made up of 60 percent of Fund A, 30 percent of Fund B, and 10 percent of Fund C? A) 13.062%. B) 2.205%. C) 14.840%. D) 1.731%. The correct answer was A) Standard deviation of a three asset portfolio:
σportfolio = [(0.6)2(0.0256) + (0.3)2(0.0196) + (0.1)2(0.0172) + 2(0.60)(0.30)(0.50)(0.16)(0.14) + 2(0.60)(0.10)(0.38)(0.16)(0.13)+ 2(0.3)(0.1)(0.85)(0.14)(0.13)]0.5
= [0.017062]1/2 = 0.13062 or 13.062%. 4.With respect to the relative efficiencies of the Funds, which of the following is TRUE? A) Fund B and D are both inefficient. B) Fund B is inefficient relative to Fund D. C) No determination is possible. D) Fund D is inefficient relative to Fund B. The correct answer was B) To be inefficient, the return must be lower while the variance is higher. The only case where that relationship exists is with respect to Fund B and D. 5.If Marko had to choose to form a portfolio using only T-bills and one of the four funds, which should he choose? A) Fund B. B) Fund C. C) Fund D. D) Fund A. The correct answer was D) The easiest way to approach this question is to calculate the Sharpe ratio for each fund and choose the one with the highest ratio. The highest Sharpe ratio reflects the highest excess return for a given level of risk. The Sharpe ratios are as follows: Fund A = (12 - 5)/16.00 = .44 Fund B = (9 - 5)/14.00 = .29 Fund C = (8 - 5)/13.11 = .23 Fund D = (10 - 5)/13.42 = .37 Fund A has the highest Sharpe ratio and therefore would be the best one to combine with T-bills. An alternative way to answer the question can be seen by combining Fund A with T-bills in a portfolio to get an average/expected return equal to each of the other portfolios and computing the variance for each of those portfolios. Then compare the variance of the portfolio composed of A and the T-bills to the corresponding variance of the other asset. To find the appropriate weights for the portfolio to earn the return of Fund B, solve for W in the following equation: 9% = W*12% + (1-W)*5%. The solution is W=0.5714. 0.5714 in Fund A and 0.429 in T-bills has a variance equal to (0.5714)(0.5714)(0.0256)=0.00836. Applying this procedure to Fund C gives W = 1.333. Obviously, this weighting is impossible. Applying the same procedure to Fund D gives W = 0 .80 0.80 in Fund D and 0.20 in T-bills has a variance equal to (0.80)(0.80)(0.018) = 0.01152. Thus, a CAL formed with Fund A can dominate the CAL of each of the other three portfolios.
[此贴子已经被作者于2008-4-14 16:50:50编辑过] | 
发表于 2008-4-14 16:20
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