Consider two investors that abide by the following utility function. Ui = γiEi [r]/Aiσ 2 i , where the subscript indicates investor i = 1, 2. A) Explain the motivation behind this utility specification. How does it con- form to the ideas of risk presented in class?
B) Explain the role of Vi.
C) Find an analytical expression for the level of expected return for investor 1 that makes these two investors equally satisfied with their portfolios.
D) Suppose that both investors hold the same assets. How can El[r] not equal E2[r]?
E) Suppose investors 1 and 2 are family (e. g. husband and wife). Investor 1 utility has a 60% weight and investor 2 utility has a 40% weight in determining the overall family utility.
i. Write out the utility function for the family.
ii. Suppose investor 1 has a higher risk aversion than investor 2. Sketch the expected return versus standard deviation for each of these investors. Next, sketch the family's expected return versus standard deviation.
iii. Suppose a car crash makes investor's 1 risk aversion increase. Overlay on the above graph the effect of this increase on both of the investors and on the family as a whole.
F) Suppose the family wants to remain just as happy as before, despite the in- crease in investor l's risk aversion. How much would a financial advisor have to increase the expected return of investor 2 in order to maintain the previous level of happiness?