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 5%. The inputs for the risky funds are given in the following table.

Fund	Expected Return		Standard Deviation
Stock fund	13%		33%
Bond fund	6%		16%

The correlation coefficient between the stock and the bond funds is 0.4.

a. What is the expected return and the variance for a portfolio that invests 54% in the stock fund and 46% in the bond fund? (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Expected return	?%
Variance	? %2

b. What is the expected return and the variance for a portfolio that invests 54% in the stock fund and 46% in the money market fund? [Hint: Note that the correlation coefficient between the portfolio and the money market fund is zero.] (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Expected return	?%
Variance	?%2

c. Compare the portfolios in parts a and b with a portfolio that is invested entirely in the bond fund. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)

• The portfolios in parts a and b have lower variances than the bond alone.unanswered
• The portfolios in parts a and b offer better expected returns than the bond alone.unanswered
• The portfolios in parts a and b have higher variances than the bond alone.unanswered
• The portfolios in parts a and b offer lower expected returns than the bond alone.

Answer 1

a)

expected return =0.54*13+0.46*6=9.78

variance=(0.54*33)²+(0.46*16)²+2*0.54*33*0.46*16*0.4=476.65

b)

Expected return =0.54*13+0.46*5=9.32

Variance =317.55

c)

The portfolios in parts a and b offer better expected returns than the bond alone

The portfolios in parts a and b have higher variances than the bond alone.