Consider the following utility function introduced in the lecture.

U = E(r) 1/2 A2

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; ₁ = .3

E(r2) = .15; ₂ = .5

E(r3) = .20; ₃ = .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?