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A pension fund manager is considering three mutual funds
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 sure rate of 5.5%. The probability distributions of the risky funds are: Stock fund (S) Bond fund (B) Expected Return 15% 98 Standard Deviation 32% 23% The correlation between the fund returns is 0.15. a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%? Investment Proportions % Stocks Bonds % b. Calculate the standard deviation of the portfolio which yields an expected return of 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation %
Expert Solution
a
| Return of Portfolio = Weight of Stock fund*Return of Stock fund+Weight of Bond fund*Return of Bond fund |
| 12 = 15*Weight of Stock fund+9*(1-weight of Stock fund) |
| Weight of Stock fund = 0.5 =50% |
| Weight of Bond fund =1-weight of Stock fund=1-0.5=0.5 = 50% |
b
| Variance | =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) |
| Variance | =0.5^2*0.32^2+0.5^2*0.23^2+2*0.5*0.5*0.32*0.23*0.15 |
| Variance | 0.04435 |
| Standard deviation= | (variance)^0.5 |
| Standard deviation= | 21.06% |
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