A fund manager is considering three mutual funds. The 1st is a stock fund, the 2nd is a long-term government and corporate bond fund (investment grade), and the third is a T-bill money market fund that yields a sure rate of 3.00%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 12.00% 41.00% Bond fund (B) 5.00% 30.00% The correlation between the fund returns is 0.0667. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds

Expected return is: 7.37% and the Standard deviation is: 24.96%

Explanation:

Correlation between fund S&B=0,0667

Standard Deviation of Fund S=41%

Standard Deviation of Fund(B)=30%

E(R) of Stock Fund S=12%

E(R) of Stock Fund B=5%

Covariance between the funds = Standard Deviation of Fund(B) × Standard Deviation of Fund S × correlation between these funds

Cov = 0.41 × 0.30 × 0.0667 = 0.008204

Now minimum variance portfolio is found by applying:

W min(S)=(SDB)^2-Cov(B,S) / ((SDS)^2+(SDB)^2-2Cov(B,S)

W min(S) = 0.338431

W min(B) = 1-0.338431=0.661569

1) E(r)min= 0.338431 × 12% + 0.661569 × 5% = 7.37%

2) Standard Deviation:

SD Min = (Ws^2XSDs^2+Wb^2XSDb^2+2XWsWb*Cov(s,B)^1/2

SDmin=(0.338431^2 × 0.41^2 + 0.661569^2 ×   0.3^2   + 2 × 0.338431 × 0.661569 × 0.008204)^1/2

SDmin=24.96%

1) the stages a new product goes through from beginning to end, i.e., the stages that a product passes through from introduction through growth, maturity, and decline. 2) the time from initial research and development to the time at which sales and support of the product to customers are withdrawn. 3) the period of time during which a product can be produced and marketed profitably.

                                          hope it