A pension fund manager is considering three mutual funds. The first is a stock f

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 4.6%. The probability distributions of the risky funds are:

  

  

   What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Expected Return Standard Deviation    Stock fund (S) 16%         36%             Bond fund (B) 7%         30%         

Explanation / Answer

COV(rs,rb) = 0.08 X 36 X 30 = 86.4

potifolio invested in stock = (16 - 4.6) X 30^2 - (7 - 4.6) X 86.4 / [(16 - 4.6) X 30^2 + (7-4.6) X 36^2]-[(16-4.6+7-4.6) X 172.8]

..........................................= 10052.64 / 12178.08

..........................................= 0.82547

..........................................= 82.55%

portifolio invested in bonds = 100 - 82.55 = 17.45%

expected return = (0.8255 X 16) + (0.1745 X 7)

..........................= 14.43%

standard deviation = sqrt[(0.8255^2 X 36^2) + (0.1745^2 X 900) +(2 X 0.8255 X 0.1745 X 86.4)]

...............................= 30.59%

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