Homework Answers
| Stock Fund=Asset 1,Bond Fund=Asset 2 | |||||||||
| Return of asset1=R1=15% | |||||||||
| Return of asset2=R2=9% | |||||||||
| Standard deviation of asset 1=S1=32% | |||||||||
| Standard deviation of asset 2=S2=23% | |||||||||
| Correlation of asset 1 and 2=Corr(1,2)=0.15 | |||||||||
| Covariance(1,2)=Corr(1,2)*S1*S2=0.15*32*23 | 110.4 | %% | |||||||
| w1=Investment in asset 1 | |||||||||
| w2=Investment in asset 2 | |||||||||
| Portfolio Return=Rp | |||||||||
| w1*R1+w2*R2=w1*15+w2*9 | ……..Equation (1) | ||||||||
| Portfolio Variance=Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2) | |||||||||
| Portfolio Variance=(w1^2)*(32^2)+(w2^2)*(23^2)+2*w1*w2*110.4 | 1024 | 220.8 | |||||||
| Portfolio Variance=(w1^2)*1024+(w2^2)*529+w1*w2*220.8……………Equation (2) | |||||||||
| Sp=Portfolio Standard Deviation=Square root of Variance(Vp) | |||||||||
| (b) | ALL POSSIBLE PORTFOLIOS | ||||||||
| w1 | w2 | Rp=w1*15+w2*9 | Vp(Using Equation (2) | Sp=Square root of Vp | |||||
| Weight of | Weight of | Portfolio | Portfolio | Portfolio | Portfolio | ||||
| STOCK | BOND | Return(%) | Variance | Std. Deviation | Return | ||||
| 0 | 1 | 9 | 529 | 23.00% | 9.00% | ||||
| 0.1 | 0.9 | 9.6 | 458.602 | 21.41% | 9.60% | ||||
| 0.2 | 0.8 | 10.2 | 414.848 | 20.37% | 10.20% | ||||
| 0.3 | 0.7 | 10.8 | 397.738 | 19.94% | 10.80% | ||||
| 0.31 | 0.69 | 10.86 | 397.492 | 19.94% | 10.86% | ||||
| 0.4 | 0.6 | 11.4 | 407.272 | 20.18% | 11.40% | ||||
| 0.5 | 0.5 | 12 | 443.45 | 21.06% | 12.00% | ||||
| 0.6 | 0.4 | 12.6 | 506.272 | 22.50% | 12.60% | ||||
| 0.7 | 0.3 | 13.2 | 595.738 | 24.41% | 13.20% | ||||
| 0.8 | 0.2 | 13.8 | 711.848 | 26.68% | 13.80% | ||||
| 0.9 | 0.1 | 14.4 | 854.602 | 29.23% | 14.40% | ||||
| 1 | 0 | 15 | 1024 | 32.00% | 15.00% | ||||
| Minimum Variance Portfolio : (Variance) | 397.49242 | %% | |||||||
| Min. Variance Portfolio Standard Deviation | 19.94% | ||||||||
| Weight of Stock Fund | 0.31 | 31% | |||||||
| Weight of Bond Fund | 0.69 | 69% | |||||||
| Min. Variance Portfolio Return | 10.86% | ||||||||
 |
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A pension fund manager is
considering three mutual funds. The first is a stock fund, the
second is a long-term government and corporate bond fund, and the
third is a T-bill money market fund that yields a rate of 8%. The
probability distribution of the risky funds is as follows:
Expected Standard Deviation Return Stock fund (S) Bond fund (B) 17% 30% 22 11 The correlation between the fund returns is 0.10 a-1. What are the investment proportions in the...
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probability distribution of the risky funds is as follows:
Expected Standard Deviation Return Stock fund (S) Bond fund (B) 17% 30% 22 11 The correlation between the fund returns is 0.10 a-1. What are the investment proportions in the...
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