A bank is planning to set up a new branch.It expects the new branch to generate 20 percent of the total business of the bank after it is opened.The bank expects the returns on this branch to be 15 percent with a standard deviation of 5 percent.Currently the bank has a 12 percent rate of return with a standard deviation of 4 percent.The correlation between the returns on the new branch and the bank's current returns is expected to be 0.25.What is the bank's expected standard deviation after adding this branch?
A)12.84 percent
B)3.35 percent
C)4.36 percent
D)3.58 percent
E)6.8 percent

Question

Quizplus · Accepted Answer

To calculate the bank's expected standard deviation after adding the branch, we need to use the following formula:

σ_total = √(σ_1^2 + σ_2^2 + 2ρσ_1σ_2)

Where:
σ_total = the expected standard deviation of the bank after adding the branch
σ_1 = the standard deviation of the bank's current rate of return (12% with a standard deviation of 4%)
σ_2 = the standard deviation of the new branch's rate of return (15% with a standard deviation of 5%)
ρ = the correlation between the returns on the new branch and the bank's current returns (0.25)

Plugging in these values, we get:

σ_total = √(0.16 + 0.25 + 2(0.25)(0.04)(0.05)) = √0.1735 = 0.4161

So, the expected standard deviation of the bank after adding the branch is 4.16%, or approximately 3.58% (option D) after rounding to two decimal places.

A Bank Is Planning to Set Up a New Branch