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 4.4%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	14%	34%
Bond fund (B)	5%	28%

The correlation between the fund returns is 0.0214.

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.)

Answer 1

E(RS) = 14%

E(RB) =5%

SDS = 34%

SDB = 28%

Rf = 4.4%

Correlation between fund returns = 0.0214

Cov(S,B) = SDS * SDB * Correl (S,B) = 34 * 28 * 0.0214 = 20.3728

The Covariance Matrix is Given as

	S	B
S	1156	20.3728
B	20.3728	784

The proportion of the stock fund in the optimal risky portfolio will be:

Ws = [E(Rs) - Rf ] * SDB2 - [E(RB) - Rf ]* Cov (S,B)

        [E(Rs) - Rf ] * SDB2 + [E(RB) - Rf ] * SDS2 - [E(Rs) - Rf + E(RB) - Rf] Cov (S,B)

       = [(14 - 4.4)*784 - (5 - 4.4)*20.3728] / [(14 - 4.4)*784 + (5 - 4.4)*1156 - (14 - 4.4 + 5 - 4.7)*20.3728]

       = (7526.4-12.2237) / ( 7526.4+693.6-201.6907)

       = 7514.176 / 8018.309 = 93.71%

WB = 1 - 93.71% = 6.29%

Expected Return of the portolio (Rp) = WS * E(RS) + WB * E(RB) = 93.71% * 14 + 6.29% * 5 = 13.1198 + 0.3144

                                                                                                                                                  = 13.4342%

Standard Deviation of the portoflio (SDp) = [ WS2* SD2 + WB2* SD2 + 2WS WBCov(S,B)]1/2

                                                                                   = [ 0.93712* 342 + 0.06292* 282 + 2* 0.9371*0.0629*20.3728]1/2

                                                                                   = [ 1015.149+ 3.1018+ 2.4017]1/2 = 1020.6521/2 = 31.95%