A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6%. An investor has the following utility function: U = E (r) - (A/2) s2. Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset?

a. 5

b. 6

c. 7

d. 8

The value of A is 8

Explanation:

To answer this question, we plug the given figures into the utility function given above

First U = E (r) - A/2 (SD) ∧2.

The expected return rate = 0.15

The standard deviation = 0.15

The risk-free rate = 6%

Therefore find A

U = E (0.15) - A/2 (0.15) ∧2.

U is already given as 6%

0.06 = E (0.15) - A/2 (0.15) ∧2.

0.06-0.15 = - A/2 (0.0225)

= - 0.09 = - 0.01125A

A = 8

the value of A is 8

Finally, if we plug A as 8 into the Utility function given in the question, we still arrive at 6% which validates the use of 8 as our value for A.