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 7%. The probability distribution of the risky funds is as follows:
Expected Return | Standard Deviation | |||||
Stock fund (S) | 16 | % | 38 | % | ||
Bond fund (B) | 12 | 21 | ||||
The correlation between the fund returns is 0.12.
You require that your portfolio yield an expected return of 11%, and that it be efficient, on the best feasible CAL.
a. What is the standard deviation of your portfolio? (Round your answer to 2 decimal places.)
b. What is the proportion invested in the T-bill fund and each of the two risky funds? (Round your answers to 2 decimal places.)
Proportion Invested in:
T-bill funds = ____ %
Stocks = ____ %
Bonds = ____ %
First we need to find the weight of stock and bond within in the risky portfolio through the equation of the optimal portfolio:
Now we need to calculate the expected return and the standard deviation of this risky portfolio:
Risky Portfolio Expected return is calcualted by solving the following equation:
Risky Portfolio standard deviation is calculated by solving the following equation:
Now we need to combine this risky portfolio with the tbill to generate the expected return of 11%
Portfolio Expected return is calcualted by solving the following
equation:
Now as the Tbill has no risk so the entire risk comes from the risky portfolio so that is calculated is as follows:
Below is the calcualtion of each asset:
Asset | Portfolio weight | Asset weight | Final weights = Portfolio Weigh x Asset Weight |
Tbill | 37.50% | 100.00% | 37.50% |
Stock | 62.50% | 35.00% | 21.88% |
Bond | 62.50% | 65.00% | 40.63% |
A pension fund manager is considering three mutual funds. The first is a stock fund, the...
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