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 $6\%.$ The inputs for the risky funds are given in the following table.

Fund Expected Return Standard Deviation

Stock fund $19\%33\%$

Bond fund $10\%11\%$

The correlation coefficient between the stock and the bond funds is $0\mathrm{.}42.$

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

b$.$ What is the expected return and the variance for a portfolio that invests $46\%$ in the stock fund and $54\%$ 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.$)$

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.$)$

check all that apply

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

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

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

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