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 5.9%. The probability distributions of the risky funds are: B RESSER Expected Return Standard deviation Stock fund (S) 208 Bond fund (b) 498 98 2 sted Return 435 The correlation between the fund returns is 0.0721 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 < Prev 4 of 22 !!! Next

Answer 1

Answer:

Expected Return of a portfolio = W1*R1 + W2*R2

Portfolio Standard Deviation = W1^2 * Variance 1 + W2^2 * Variance 2 + 2 W1* W2* Standard deviation of asset 1 * standard deviation of asset 2 * correlation coefficient between asset 1 and 2

S.No.	R1	R2	W1	W2	Stdev 1	Stdev 2	Portfolio Return	Portfolio Varinace	Portfolio Standard deviation
1	20	9	1	0	49	43	20	2401	49
2	20	9	0.9	0.1	49	43	18.9	1990.645	44.61664091
3	20	9	0.8	0.2	49	43	17.8	1659.213	40.73343472
4	20	9	0.7	0.3	49	43	16.7	1406.704	37.50605516
5	20	9	0.6	0.4	49	43	15.6	1233.119	35.11579496
6	20	9	0.5	0.5	49	43	14.5	1138.457	33.74103362
7	20	9	0.4	0.6	49	43	13.4	1122.719	33.5070001
8	20	9	0.3	0.7	49	43	12.3	1185.904	34.43695942
9	20	9	0.2	0.8	49	43	11.2	1328.013	36.44190862
10	20	9	0.1	0.9	49	43	10.1	1549.045	39.35790449
11	20	9	0	1	49	43	9	1849	43

From the calculation mentioned above, we can see that minimum portfolio variance is 1122.719 for the portfolio consisting of 40% of asset 1 and 60% of aorsset. The expected return of this portfolio is 13.4% and standard deviation is 33.51%.