Question on expected return

Question

The Space Bank wants to open a new branch in a distance city with very different economic conditions. Currently, the bank has an expected return of 15% with a standard deviation of 7%. The new branch is expected to have a return of 20% with a standard deviation of 10%. The correlation between the bank and the new branch is -.3. The new branch is expected to be 10% of the bank's revenues. What is the expected return of the bank if they add the new branch?

35. 0%

15. 5%

17. 5%

19. 5%

Answer 1

Correct Answer: B) 15.5%

This is a weighted average expected return problem. We need to calculate the bank's new expected return after adding the branch.

Step 1: Identify the information given.

Existing bank expected return = 15%

New branch expected return = 20%

Existing bank weight = 90%

New branch weight = 10%

The new branch represents 10% of the combined bank's revenues, so the existing bank represents the remaining 90%.

Step 2: Use the weighted average return formula.

Expected Return = (Weight of Existing Bank × Existing Return) + (Weight of New Branch × New Branch Return)

Step 3: Substitute the numbers.

Expected Return = (0.90 × 15%) + (0.10 × 20%)

Expected Return = 13.5% + 2%

Expected Return = 15.5%

Final Answer: B) 15.5%

Why don't we use the standard deviations or correlation?

The problem provides:

1. Existing bank standard deviation = 7%
2. New branch standard deviation = 10%
3. Correlation = -0.3

These numbers are used to calculate the risk (standard deviation) of the combined bank, not its expected return.

The negative correlation suggests that the returns of the existing bank and new branch tend to move in opposite directions, which can provide diversification benefits.

However, correlation does not affect the weighted average expected return.

Easy Way to Remember:

Expected Return = Weighted Average of Returns

Portfolio Risk = Depends on Standard Deviations AND Correlation

For example, imagine you have $90 invested in something earning 15% and $10 invested in something earning 20%.

Your total expected return is not 35%. It is the weighted average of the two returns, which equals 15.5%.

Answer: B) 15.5%