Assume an investor with the following utility function: U = E(r)- 3/2(s²).To maximize her expected utility,which one of the following investment alternatives would she choose? A) A portfolio that pays 10 percent with a 60 percent probability or 5 percent with 40 percent probability. B) A portfolio that pays 10 percent with 40 percent probability or 5 percent with a 60 percent probability. C) A portfolio that pays 12 percent with 60 percent probability or 5 percent with 40 percent probability. D) A portfolio that pays 12 percent with 40 percent probability or 5 percent with 60 percent probability. E) none of these.

Question

Quizplus · Accepted Answer

To maximize expected utility, we need to calculate the expected value of the utility function for each portfolio option and choose the one with the highest value. Option A: E(r) = (0.6 x 0.1) + (0.4 x 0.05) = 0.08 s² = (0.6 x 0.4 x 0.12^2 x 0.4) + (0.6 x 0.6 x 0.12 x 0.6 x 0.05) + (0.4 x 0.4 x 0.05^2) = 0.000834 U = 0.08 - (3/2 x 0.000834) = 0.0787 Option B: E(r) = (0.4 x 0.1) + (0.6 x 0.05) = 0.07 s² = (0.4 x 0.6 x 0.12^2 x 0.6 x 0.05) + (0.4 x 0.4 x 0.12 x 0.4) + (0.6 x 0.6 x 0.05^2) = 0.000854 U = 0.07 - (3/2 x 0.000854) = 0.0646 Option C: E(r) = (0.6 x 0.12) + (0.4 x 0.05) = 0.087 s² = (0.6 x 0.4 x 0.12^2 x 0.4) + (0.6 x 0.6 x 0.12 x 0.6 x 0.05) + (0.4 x 0.4 x 0.05^2) = 0.000834 U = 0.087 - (3/2 x 0.000834) = 0.0856 Option D: E(r) = (0.4 x 0.12) + (0.6 x 0.05) = 0.068 s² = (0.4 x 0.6 x 0.12^2 x 0.6 x 0.05) + (0.4 x 0.4 x 0.12 x 0.4) + (0.6 x 0.6 x 0.05^2) = 0.000854 U = 0.068 - (3/2 x 0.000854) = 0.0618 Option C maximizes the investor's expected utility, with a value of 0.0856. Therefore, the investor should choose option C to maximize her expected utility.

Assume an Investor with the Following Utility Function: U =