A bank is planning to set up a new branch. It expects the new branch to generate 5 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 bank's current returns is expected to be 0.20. What is the bank's total expected return and standard deviation after adding this branch? is there a diversification from adding the branch?

a. 12.84 % 3.82%, yes

b. 12.15%, 3.35% no

c. 13.62%, 3.61% no

d. 12.15% , 3.87% yes

e. 12.30%, 6% no