Question

Forever Savings Bank estimates that building a new branch office in the newly developed Washington township will yield an annual expected return of 12 percent with an estimated standard deviation of 10 percent. The bank’s marketing department estimates that cash flows from the proposed Washington branch will be mildly positively correlated (with a correlation coefficient of + 0.15) with the bank’s other sources of cash flow. The expected annual return from the bank’s existing facilities and other assets is 10 percent with a standard deviation of 5 percent. The branch will represent just 20 percent of Lifetime’s total assets. Will the proposed branch increase Forever’s overall rate of return? Its overall risk? 

Answer 1

The estimated total rate of return would be:

E (R) = 0.20 (12%) + 0.80 (10%) = 10.4%

The risk attached to this overall return rate would be:

σ2 = (0.20)2 (0.10)2 + (.80)2 (0.05)2 + 2(0.20)(0.80)(0.15)(0.10)(0.05)

σ2 =0.00224

σ = 4.73%

Thus, σ = 4.73%, and the branch will slightly increase the bank's expected return but slightly increase its overall risk. The bank should proceed with this project.