Question

Consider the following utility function introduced in the lecture.

U = E(r) − 1/2 Aσ2

Suppose there are 3 types of financial securities one can choose to invest in. Expected return and standard deviation of each of these securities are as follows.

E(r1) = .13; σ₁ = .3

E(r2) = .15; σ₂ = .5

E(r3) = .20; σ₃ = .2

(a) Which of these three securities would a risk averse investor with A = 4 choose to invest, given that she can only invest in one of these three securities?

(b) For the same investor (with A = 4), if there is also a risk free asset with expected return 5%, will she invest in the risk free asset or one of those three securities?

(c) Which of these three securities would a risk neutral investor choose to invest, given that she can only invest in one of these three securities?

Answer 1

37 U = E(r) - 0.5x A xoe 1st type U=0.13-0.5 x 4 x 0.3 = 0.13 -0.5 X 4 XO-09 = 0.13-0.18 -0.05 = -52 - nd u=0.15 -0.5x4 x 0.5 = 0.15 - 2x0.25 = 0.15 -0.5 = -0.35 = -35% U= 0.20-0.5x4 x 0.2 -0.20 - 2x0.04 - 0.20 O 08 = 0.12 = 12 % 3rd type th 4 type U= 0.05-0.5x4 XO =0.05 5%

41 three a) A risk averse investor would choose type 3 security because it has the lowest risk the of first financial Securities b) This same investor when offered with pick fice asset with expected return of 5% would go for this one because it has no brisk involved and the investor will investment. get a confirmed return of c) A risk peutzrad investor will choose type 3 because it has the highest expected return.