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: Expected Return Standard Deviation 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? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Given expected return on stock fund E[S] = 10%

standard deviation for stock fund S.D[S] = 39% VAR[S] = 39²= 1521%

expected return on BOND fund E[B] = 5%

standard deviation for bond fund S.D[B] = 33% VAR[B] = 33²=1089

Expected return on portfolio E[P]= W1*E[S] + W2*E[B]

minimum variance =W1²*VAR[S] + W2²*VAR[B]+ 2.W1.W1.correlation[S,B]* S.D[S]*S.D[B]

here,S.D stands for standard deviation and VAR refers to variance of the referred bond

w1 and w2 refer to the proportion of each bond .

calculation of expected return and minimun variance:-

W1	W2	EXPECTED RETURN(%)	MINIMUM VARIANCE(%)
1	0	10	15.21
0.9	0.1	9.5	12.45
0.8	0.2	9	10.19
0.7	0.3	8.5	8.45
0.6	0.4	8	7.24
0.5	0.5	7.5	6.54
0.4	0.6	7	6.37
0.3	0.7	6.5	6.72
0.2	0.8	6	7.60
0.1	0.9	5.5	8.99
0	1	5	10.89

The variance calculation for W1= 0.6 and W2=0.4 is shown below , repeat the same for all other combinations to get the above table value.

VAR for combination W1=0.6 and W2=0.4

= 0.6²*1521 + 0.4²*1089 +2*0.6*0.4*0.0030*39*33

=547.56 + 174.24 +1.8533 = 7.24%

so the minimum variance and expected return of the above portfolio are :-

expected return = 7%

minimum variance = 6.37%