Question

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?

	A.	Expected return is: 7.37% and the Standard deviation is: 24.96%
	B.	Expected return is: 5.08% and the Standard deviation is: 24.96%
	C.	Expected return is: 7.37% and the Standard deviation is: 28.13%
	D.	Expected return is: 5.08% and the Standard deviation is: 28.13%

Answer 1

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)XStandard Deviation of Fund SXcorrelation between these funds

Cov=.41*.30*.0667=0.008204

Now minimum variance portfolio is found by applying:

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

Wmin(S)=0.338431

Wmin(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=(0.338431^2X.41^2+0.661569^2X0.3^2+2X0.338431X0.661569X0.008204)^1/2

SDmin=24.96%

Hence option 1 is correct