Question

A bank is thinking about building a new branch. They think this new branch will generate 20 percent of the business of the bank after it is opened. The bank expects the return for this branch will 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 branch and the bank is expected to be .25. What is this bank's expected standard deviation after adding this branch

Answer 1

Answer: 12.6%

Step-by-step explanation:

The bank's expected standard deviation after adding this branch will be calculated thus:

= (Total invested in new branch × Expected rate of return) + (1 - Investment in new branch) × Other assets

= (0.2 × 0.15) + (1 - 0.2) × 0.12

= 0.03 + 0.8 × 0.12

= 0.03 + 0.096

= 0.126

= 12.6%

Therefore, the bank's expected standard deviation after adding this branch is 12.6%.