P$83$ Risk preferences Sharon Smith, the financial manager for Barnett Corporation,

wishes to select one of three prospective investments: X$,$ Y$,$ and Z$.$ Assume that the

measure of risk Sharon cares about is an asset$$s standard deviation. The expected

returns and standard deviations of the investments are as follows:

Investment

Expected

return

Standard

deviation

X $14\%7\%$

Y $148$

Z $149$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 investment 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?