A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2788330 • Letter: A
Question
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:
The correlation between the fund returns is .15.
What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Expected Return Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 9% 23%
Explanation / Answer
Calculation of portfolio proportion to reduce the risk to minimum level :
Weight (s) = Sd (B)/ sd(S)+sd(B)
= 23/32+23
= 0.4181 or 41.81%
Weight (B) = 1- Weight (S)
= 58.19%
Calculation of expected return of portfolio : 15%*0.42 + 9%*0.58 = 6.3 + 5.22 = 11.52%
Calculation of portfolio risk of portfolip : Root of 0.42*0.42*32*32 +0.58*0.58*23*23+2*0.42*0.58*32*23*0.15
= root of 180 + 178 + 53
= 20.27%
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