Ned Dennis, a financial planner and CFA charterholder, is working with two clients:
Client One is strongly opposed to taking on risk in his investment portfolio.  Client One will only accept additional risk in his portfolio if he is well compensated for that additional risk by receiving a large amount of additional expected return.
Client Two also does not like risk; however, Client Two is not as risk averse as is Client One.  Relative to Client One, for taking on the same amount of additional risk in her portfolio, Client Two does not require as much additional expected return as compensation.
Based on this information, which of the following statements about these two clients is most accurate?

a. Client One’s investment utility curves are steeper than Client Two’s, and Client One’s optimal portfolio is located higher on the efficient frontier.

b. Client One’s investment utility curves are flatter than Client Two’s, and Client One’s optimal portfolio is located lower on the efficient frontier.

c. Client One’s investment utility curves are steeper than Client Two’s, and Client One’s optimal portfolio is located lower on the efficient frontier.

d. Client One’s investment utility curves are flatter than Client Two’s, and there is only one optimal portfolio, which they share.

 

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Choice "c" is correct.  Risk-averse investors have steeper utility curves because they demand more return for assuming one additional unit of risk relative to less risk-averse investors.  Client One is clearly the more risk averse of the two.  Therefore, Client One has steeper investment utility curve than Client Two.  The optimal portfolio for any investor is the point of tangency between his or her highest utility curve and the efficient frontier.  Steeper utility curves will be tangent to the efficient frontier at a point below flatter utility curves.

Client One’s utility curves are steeper than Client Two’s.  Note that Client Two is willing to assume quite a bit more risk than Client One for the same increase in return.  Client One’s optimal portfolio is the point of tangency at point C, while Client Two’s optimal portfolio is at point D.  Because Client Two is less risk averse than Client One, his optimal portfolio resides higher on the efficient frontier.

My Conclusion :

A is more risk averse than B.
A’s investment utility curves are steeper than B’s.
A’s optimal portfolio is located lower on the efficient frontier.