Question

26. Assume an investor with the following utility function: U = E(r) - 3/2(s2). To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively.

Select one:

a. 12%; 20%

b. 10%; 15%

c. 10%; 10%

d. 8%; 10%

Answer 1

U = E(r) - 3/2(s2)

Let's find the value of U for each of the given answer options and then pick the one with highest U

a. E(r ) = 12%

(s^2) = 20%

U = 0.12 - 3/2 * 0.20^2

U = 0.12 - 0.06

U = 0.06

b. 10%; 15%

U = 0.10 - 3/2 * 0.15^2

U = 0.10 - 0.03375

U = 0.06625

c. 10%; 10%

U = 0.10 - 3/2 * 0.1^2

U = 0.10 - 0.015

U = 0.085

d.  8%; 10%

U = 0.08 - 3/2 * 0.1^2

U = 0.08 - 0.015

U = 0.065

Option C is correct: 10%; 10%

The asset with an expected rate of return of 10% and a standard deviation of 10% maximizes the expected utility.

U = 0.085 = 8.5%