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:

	Expected Return	Standard Deviation
Stock fund (S)	16%	45%
Bond fund (B)	7%	39%

The correlation between the fund returns is 0.0385.

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.)

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:

	Expected Return	Standard Deviation
Stock fund (S)	16%	45%
Bond fund (B)	7%	39%

The correlation between the fund returns is 0.0385.

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?

Answer 1

Answer 2

7% B15 X fic = (B8-B9)/(B8+B7-2*B9) A 1 Expected return on stock fund [E(rs)] 16% 2 Expected return on bond fund [E(rb)] 3 SD of stock fund (os) 45% 4 SD of bond fund (ob) 39% 5 Correlation between fund returns (r(sb)] 0.0385 6 7 Variance of stock fund (os^2) 0.2025 8 Variance of bond fund (ob^2) 0.1521 9 Covariance of stock and bond funds [COV(sb)] 0.0068 10 (r(sb)xobxos) 11 12 Minimum portfolio variance (Ws) = [lob^2 [(ob^2)-COV(sb)]/[(os^2)+(ob^2)-2xCOV(sb)] 13 (Portfolio invested in stock) 14 15 Portfolio invested in stock (Ws) 42.61% 16 Portfolio invested in bond (Wb) 57.39% 17 (1-Portfolio invested in stock) 18 19 Expected return on minimum variance portfolio || E(rs)xWs+E(rb)xWb Expected return on minimum 20 variance portfolio 21 22 SD of minimum variance portfolio ((Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWb)^(1-2) SD of minimum variance 23 portfolio 10.84% 30.03%

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