The expected returns and standard deviations of the investments are as follows: $.$

a$.$ If Sharon were risk neutral, which investment would she select? Explain why.

b$.$ If she were risk averse, which investment would she select? Why?

c$.$ If she were risk seeking, which investments would she select? Why?

d$.$Suppose a fourth$$ investment, W$,$ is available. It offers an expected return of$15\%,$ and it has a standard deviation of$9\%.$ If Sharon is risk$$ averse, can you say which investment she will$$ choose? Why or why$$ not? Are there any investments that you are certain she will not$$ choose? $($Select the best answer$$ below.$)$

A$.$

If Sharon were risk$$ averse, it is not clear whether she would prefer investment W or Z $.$ From part$($b$),$ Sharon prefers Z to X and$$ Y$,$ but investment W has a higher expected return and standard deviation.$$ Thus, Sharon's preference between W and Z will depend on whether the extra return expected on W is sufficient compensation for the extra risk. In other$$ words, Sharon's choice will depend on her risk tolerance$($i$.$e$,$ her degree of risk$$ aversion$).$

B$.$

If Sharon were risk$$ averse, it is not clear whether she would prefer investment W or Y $.$ From part$($b$),$ Sharon prefers Y to X and$$ Z$,$ but investment W has a higher expected return and standard deviation.$$ Thus, Sharon's preference between W and Y will depend on whether the extra return expected on W is sufficient compensation for the extra risk. In other$$ words, Sharon's choice will depend on her risk tolerance$($i$.$e$,$ her degree of risk$$ aversion$).$

C$.$

If Sharon were risk$$ averse, it is not clear whether she would prefer investment W or X $.$ From part$($b$),$ Sharon prefers X to Y and$$ Z$,$ but investment W has a lower expected return and standard deviation.$$ Thus, Sharon's preference between W and X will depend on whether the return expected on W is sufficient compensation for the extra investment. In other$$ words, Sharon's choice will depend on her risk tolerance$($i$.$e$,$ her degree of risk$$ aversion$).$

D$.$

If Sharon were risk$$ averse, it is not clear whether she would prefer investment W or X $.$ From part$($b$),$ Sharon prefers X to Y and$$ Z$,$ but investment W has a higher expected return and standard deviation.$$ Thus, Sharon's preference between W and X will depend on whether the extra return expected on W is sufficient compensation for the extra risk. In other$$ words, Sharon's choice will depend on her risk tolerance$($i$.$e$,$ her degree of risk$$ aversion$).$

Data table

$.$ Investment $Y.$

C$.$ Investment $Z.$

D$.$ None of the three investments.

$($Click on the icon here $$ in order to copy the contents of the data table below

into a spreadsheet.$)$

c$.$ If she were risk seeking, which investments might she select? $($Select the best answer below.$)$

A$.$ Investment $x$

B$.$ Investment $Z.$

C$.$ None of the three investments.

D$.$ Investment $Y.$

investments that you are certain she will not choose? $($Select the best answer below.$)$

risk aversion$).$

risk aversion$).$

risk aversion$).$

risk aversion$).$