$($Security market line$)$ James Fromholtz is considering whether to invest in a newly formed investment fund. The fund's investment objective is to acquire home mortgage securities at what it hopes will be bargain prices. The fund sponsor has suggested to James that the fund's performance will hinge on how the national economy performs in the coming year. Specifically, he suggested the following possible outcomes: $($In table$).$ James has estimated the expected rate of return from this investment is $20\mathrm{.}75$ percent. James wants to apply his recently acquired understanding of the security market line concept to his analysis.

a$.$ If the risk$-$free rate of interest is currently $2\mathrm{.}0$ percent and the beta for the investment is $3\mathrm{.}0,$ what is the slope of the security market line for the real estate mortgage security investment?

b$.$ James is also considering the investment of his money in a market index fund that has an expected rate of return of $8$ percent. What is the slope of the security market line $($i$.$e$.,$ the reward$-$to$-$risk ratio$)$ for this investment opportunity?

c$.$ Based on your analysis of parts a and b above, which investment should James take? Why?

a$.$ If the risk$-$free rate of interest is currently $2\mathrm{.}0$ percent and the beta for the investment is $3\mathrm{.}0,$ the slope of the security market line for the real estate mortgage security investment is $\%.($Round to two decimal places.$)$

b$.$ James is also considering the investment of his money in a market index fund that has an expected rate of return of $8$ percent. The slope of the security market line $($i$.$e$.,$ the reward$-$to$-$risk ratio$)$ for this investment opportunity is $\%.($Round to two decimal places.$)$

c$.$ Based on your analysis of parts a and b above, which investment should James take? Why? $($Select the best choice below.$)$

A$.$ The real estate portfolio.

B$.$ The market index fund.

C$.$ Cannot be determined from the information given in this problem.