Consider a risky portfolio, A, with an expected rate of return of 0.15 and a standard deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve? A. E(r) = 0.15; Standard deviation = 0.20.
B. E(r) = 0.15; Standard deviation = 0.10.
C. E(r) = 0.10; Standard deviation = 0.10.
D. E(r) = 0.20; Standard deviation = 0.15.
E. E(r) = 0.10; Standard deviation = 0.20.

C. E(r) = 0.10; Standard deviation = 0.10.

Explanation:

An indifference curve is plotted by graphing the various combinations of portfolios such that the customer in question is indifferent between them as they regard the combinations as giving them equal utility.  

For portfolios to be on the same indifference curve they would have to provide the same reward - risk ratio. The reward to risk ratio of the portfolio in question is;

=Expected return/standard deviation'

= 0.15/0.15

= 1.0

Any portfolio with this same reward - risk ratio will be on the same curve.

The Portfolio in Option C has the same reward - risk ratio (0.1 - 0.1) and so will lie on the same indifference curve.