Question

A pension fund manager is considering three mutual funds for investment. The first one is a stock fund, the second is a bond fund, and the third is a money market fund. The money market fund yields a risk-free return of 4%. The inputs for the risky funds are given in the following table.

Fund   Expected Return   Standard Deviation
Stock Fund 14% 26%
Bond Fund 8% 14%

The correlation coefficient between the stock and the bond funds is 0.20.

a) What is the variance of a portfolio that invests 60% in the stock fund and 40% in the money market fund?

b) What is the expected return of a portfolio that invests 60% in the stock fund and 40% in the bond fund?

c) What is the variance of a portfolio that invests 60% in the stock fund and 40% in the bond fund?

d)What is the expected return of a portfolio that invests 60% in the stock fund and 40% in the money market fund?

(Hint: Note that the correlation between the stock fund and the money market fund is zero, and the money market fund has no risk.) (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

Let be the return from Stock fund, Bond fund and Money market fund respectively.

The expected values are

The standard deviations of return are

(The money market fund is risk free and hence the standard deviation of the return for this fund is 0%)

The correlation coefficient between the stock and the bond funds is 0.20.

The covariance between the stock and the bond funds is

the correlation between the stock fund and the money market fund is zero, and hence the covariance between the stock fund and the money market fund is zero

a) What is the variance of a portfolio that invests 60% in the stock fund and 40% in the money market fund?

The portfolio invests in the stock fund and in the money market fund.

The variance of the portfolio is

ans: the variance of a portfolio that invests 60% in the stock fund and 40% in the money market fund is 243.36

b) What is the expected return of a portfolio that invests 60% in the stock fund and 40% in the bond fund?

The portfolio invests in the stock fund and in the bond fund.

The expected return is

ans: the expected return of a portfolio that invests 60% in the stock fund and 40% in the bond fund is 11.60%

c) What is the variance of a portfolio that invests 60% in the stock fund and 40% in the bond fund?

The portfolio invests in the stock fund and in the bond fund.

The variance of the portfolio is

ans: the variance of a portfolio that invests 60% in the stock fund and 40% in the bond fund is 309.66

d)What is the expected return of a portfolio that invests 60% in the stock fund and 40% in the money market fund?

The portfolio invests in the stock fund and in the money market fund.

The expected return of the portfolio is

ans: the expected return of a portfolio that invests 60% in the stock fund and 40% in the money market fund is 10.00%