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 offer lower expected returns 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 have lower variances than the bond alone.

Answer 1

Let S be the percentage return for the stock fund.

The expected value of S is

The standard deviation of return for the stock fund is

Let B be the percentage return for the bond fund.

The expected value of B is

The standard deviation of return for the bond fund is

Let M be the percentage of return for the Money market fund

M=5% is a constant

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

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.)

Let be the proportion invested in stock fund and be the proportion invested in the bond fund.

The expected return of the portfolio is

The variance of the portfolio  return is

ans:

Expected return	9.78%
Variance	476.65%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.)

Let be the proportion invested in stock fund and be the proportion invested in the money market fund.

The expected return of the portfolio is

The variance of the portfolio  return is

ans:

Expected return	9.32%
Variance	317.55%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 expected return of Bond alone is 6% and it is lower than the expected returns from the portfolios in a) and b)

The variance of bond alone is . This is lower than the variances of the portfolios

ans:

• 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.