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 rate of 4.6%. 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.)

  

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

Explanation / Answer

COV(rs,rb) = 0.16 * 36 * 30 = 172.8

potifolio invested in stock

= (16- 4.6) * 30^2 - (7 - 4.6) * 172.8 /[(16-4.6)*30^2 + (7-4.6) * 36^2]-[(16-4.6+7-4.6)*172.8]

= 9845.28/10985.76

= 0.8962

= 89.62%

portifolio invested in bonds = 100 - 89.62 = 10.38%

expected return

= (0.8962 * 16) + (0.1038 * 7)

= 15.07%

standard deviation

= sqrt[(0.8962^2 * 36^2) + (0.1038^2 * 900) +(2*0.8962 *0.1038*172.8)]

= 32.91%

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