Question

FIN343 Bank estimates that building a new branch office in the newly developed New Heaven township will yield an annual expected return of 10 percent with an estimated standard deviation of 6 percent. The bank's marketing department estimates that cash flows from the proposed New Heaven branch will be strongly positively correlated (with a correlation coefficient of + 0.70) with the bank's other sources of cash flow. The expected annual return from the bank's existing facilities and other assets is 8 percent with a standard deviation of 5 percent. The branch will represent just 15 percent of Lifetime's total assets. Will the proposed branch increase FIN343's overall rate of return? Its overall risk?

Answer 1

The proposed new branch will represent just 15% of the bank's total assets.

Let the weight/proportion of the bank's total assets be denoted as W_a.

Let the weight/proportion of the bank's new branch's total assets be denoted as W_b.

Therefore, as per the above mentioned data, we get :-

W_b = 0.15 ;

W_a = (1 - W_b) = (1 - 0.15) = 0.85

The standard deviation of the bank :- = 5%

The standard deviation of the bank's proposed new branch :- = 6%

The correlation between the bank and the branch :- =  0.7

Therefore, Cov(R_a, R_b) = ( * * ) = 0.7 * 5 * 6 = 21

The expected annual return of the bank :- R_a = 8%

The expected annual return of the bank's proposed new branch :- R_b = 10%

Let the expected overall rate of return be denoted as R_p.

Hence, R_p can be calculated as follows :-

E(R_p) = (W_a * R_a) + (W_b * R_b)

= (0.85 * 8) + (0.15 * 10)

= 8.3%

Hence, the bank's expected overall rate of return = 8.3%.

The standard deviation of the bank if they add a new branch is given by :-

=  [(W_a² * ²) + (W_b² * ²) + (2 * W_a * W_b * Cov(R_a, R_b)]^1/2

Or, = [(0.85² * 5²) + (0.15² * 6²) + (2 * 0.85 * 0.15 * 21)]^1/2

^Or, = (24.2275)^1/2

Or, = 4.9221%

Hence, the overall standard deviation of the bank if it adds the proposed new branch would be = 4.9221%

Hence, since the the overall rate of return is 8.3% which is slightly higher than the bank's expected annual return i.e. 8%, we can say that adding the new branch will increase the overall rate of return. Again, the overall risk of the bank will marginally reduce to 4.9221% from the present 5%.