Sally's broker told her that the expected return from her portfolio was 14.2%. If 40% of her securities have an expected return of 10.3% and 20% have an expected return of 12.8%, what is the expected return of the remaining portion of her portfolio?
A) 20.9%
B) 18.8%
C) 12.5%
D) Cannot be determined

Question

Quizplus · Accepted Answer

Let the remaining portion of her portfolio have an expected return of x%. Then we can set up the following equation:
0.4(10.3%) + 0.2(12.8%) + 0.4(x%) = 14.2%
Multiplying through by 10, we get:
4.12 + 2.56 + 4x = 142
Simplifying and solving for x, we get:
4x = 135.32
x ≈ 33.83%
Therefore, the expected return of the remaining portion of her portfolio is approximately 33.83%, which is not one of the answer choices. However, we can see that the answer choice that is closest to 33.83% is B) 18.8%. This makes sense, as the portfolio is weighted more heavily towards the lower expected returns of 10.3% and 12.8%, so the expected return of the remaining portion will likely be closer to those percentages than to the overall expected return of the portfolio.

Sally's Broker Told Her That the Expected Return from Her