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 4.9%. The probability distributions of the risky funds are:

Stock fund (S)	10%	39%
Bond fund (B)	5%	33%

The correlation between the fund returns is 0.0030.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? Hint: Use the formula and parameters:

The parameters of the opportunity set of possible portfolios are:

E(r_S) = 10%, E(r_B) = 5%, S = 39%, σ_B = 33%, ρ = 0.0030, r_f = 4.9%

The covariance between stocks and bonds is calculated as:

Cov(r_S, r_B) = ρσ_Sσ_B

wmin(S)	=	σB2 – Cov(rS, rB)
		σS2 + σB2 – 2Cov(rS, rB)

Variance for the min-var portfolio:

σ_Min = [w_S²σ_S² + w_B²σ_B² + 2w_Sw_B Cov(r_S, r_B)]^1/2

Answer 1

Return of Stock Fund (Rs) = 10%

Return of Bond Fund (Rb) = 5%

SDs = 39%

SDb = 33%

Correlation(s.b) R(s,b) = 0.0030

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

= 0.0030 * 39 * 33

= 3.861

Optimum weight of Bond (Wb) =

=

= 1517.139 / 2602.278

= 58.30%

Weight of Stock Fund (Ws) = 100 % - 58.30% = 41.70%

Expected Return = Ws * Rs  + Wb * Rb

= .4170 * 10% + .5830 * 5%

= 7.085%

SD =

=

=

= 41.66%