Question

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's returns and the returns from the new branch is -0.3. The new branch is expected to contribute 10% of the bank's revenues. What is the standard deviation of returns for the bank if they add the new branch? (Round your answer to the nearest 0.1%)

Answer 1

Assume A = Existing Bank

B = New Branch

Bank with New Brach as Portfolio.

Particulars	Amount
Weight in A	0.9000
Weight in B	0.1000
SD of A	7.00%
SD of B	10.00%
r(A,B)	-0.3

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.9*0.07)^2)+((0.1*0.1)^2)+2*(0.9*0.07)*(0.1*0.1)*-0.3]
=SQRT[((0.063)^2)+((0.01)^2)+2*(0.063)*(0.01)*-0.3]
=SQRT[0.0037]
= 0.0608
= I.e 6.08 %

SD of Bank with new branch is 6.08%