Question

A pension fund manager is considering 3 mutual funds. The 1st is a stock fund, the 2nd is a long-term government and corporate bond fund, and the 3rd is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:

	Expected Return	Standard Deviation
Stock Fund (S)	18%	35%
Bond Fund (B)	15	20

The correlation between the fund returns is 0.12.

What are the investment proportions in the minimum-variance portfolio of the two risky funds? (decimals rounded to 4 places.)

Portfolio invested in the stock
Portfolio invested in the bond

What is the expected value and standard deviation of its rate of return? (decimals rounded to 4 places.)

Expected Return
Standard Deviation

Answer 1

Return of Stock Fund (Rs) = 18%

Return of Bond Fund (Rb) = 15%

SDs = 35%

SDb = 20%

Correlation(s.b) R(s,b) = 0.12

Cov(s,b) = R(s,b) * SDs * SDb

= 0.12 * 35 * 20

= 84

Optimum weight of Bond (Wb) =

= 1141 / 1457

= 78.31%

Weight of Stock Fund (Ws) = 100 % - 78.31% = 21.69%

Expected Return = Ws * Rs  + Wb * Rb

= .2169 * 18% + .7831 * 15%

= 15.65%

SD =

=

=

= 18.21% OR 0.1821