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.

why

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