A portfolio is entirely invested into Buzz's Bauxite Boring Equity, which is expected to return 16%, and Zum's Inc. bonds, which are expected to return 8%. Sixty percent of the funds are invested in Buzz's and the rest in Zum's. What is the expected return on the portfolio?
A) 9.6%.
B) 12.8%.
C) 24%.
D) 6.4%.

Question

Quizplus · Accepted Answer

To find the expected return on the portfolio, we need to take the weighted average of the returns of both investments.

Weighted Average = (Weight of Investment A × Return on Investment A) + (Weight of Investment B × Return on Investment B)

Let's say the portfolio is worth $100.
60% of the portfolio is invested in Buzz's, therefore $60 is invested in Buzz's.
The rest of the portfolio, 40%, is invested in Zum's, therefore $40 is invested in Zum's.

The expected return from Buzz's is 16%, hence the dollar amount of return from Buzz's is:
0.6 × $60 × 0.16 = $5.76

The expected return from Zum's is 8%, hence the dollar amount of return from Zum's is:
0.4 × $40 × 0.08 = $1.28

The total dollar amount of return from both investments is:
$5.76 + $1.28 = $7.04

The total value of the portfolio is $100, hence the expected return is:
$7.04/$100 = 0.0704 or 7.04%

However, this is not the final answer. We need to convert this percentage into a compounded annual growth rate (CAGR).

To do that, we use the following formula:

CAGR = (1 + Total Return)^(1/Number of Years) - 1

Assuming we are looking at a one-year period, the CAGR will be:

CAGR = (1 + 0.0704)^(1/1) - 1
CAGR = 1.074 - 1
CAGR = 0.074 or 7.4%

Therefore, the expected return on the portfolio is 7.4%.
However, none of the answer choices match this, so the closest answer is B, which is 12.8%. It is unclear where this answer came from, as it is not the correct answer.

A Portfolio Is Entirely Invested into Buzz's Bauxite Boring Equity