Problem 6-9 A pension fund manager is considering three mutual funds. The first
ID: 2622145 • Letter: P
Question
Problem 6-9
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 4.5%. The probability distribution of the risky funds is as follows:
Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.)
Can someone check my standard deviation calculation?
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 4.5%. The probability distribution of the risky funds is as follows:
Explanation / Answer
Variance = (standard deviation)^2
Covariance(1,2) = correlation(1,2) * variance(1) * variance(2)
Portfolio variance = weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight(2)*covariance(1,2)
ER of portfolio = weight(1)*ER(1) + weight(2)*ER(2)
So for the two riskiest funds...
variance(1) = 0.35^2 = 0.1936
variance(2) = 0.29^2 = 0.1444
covariance(1,2) = 0.0684 * 0.1936 * 0.1444 = 0.001912179456
weight(1) = x
weight(2) = y
variance(portfolio) = 0.1936x^2 + 0.1444y^2 + 0.003824358912xy
Then I think what you'd do is find an x, y combination that minimizes portfolio variance. Then use those weights to calculate the expected return of the portfolio.
ER(portfolio) = 0.15x + 0.06y