The bank has an expected return of 25% with a standard deviation of 7.5% the new

Question

The bank has an expected return of 25% with a standard deviation of 7.5% the new branch is expected to have a return of 20% with standard deviation of 15%. The correlation between the banks returns and the returns from new bank is 0.7 the new branch is expected to contribute 10% of the banks revenues. What is the expected return for the bank if they add the new branch? What is the standard deviation of returns for the bank if they add the new branch? The bank has an expected return of 25% with a standard deviation of 7.5% the new branch is expected to have a return of 20% with standard deviation of 15%. The correlation between the banks returns and the returns from new bank is 0.7 the new branch is expected to contribute 10% of the banks revenues. What is the expected return for the bank if they add the new branch? What is the standard deviation of returns for the bank if they add the new branch?

Explanation / Answer

We have Expected return of bank r1 = 25%

And expected return of new branch r2 = 20%

Standard deviation of bank 1 = 7.5%

Standard deviation of new branch 2 = 15%

The correlation between the banks returns and the returns from new bank 12 = 0.7

The new branch is expected to contribute w2 = 10% of the banks revenues

Therefore banks contribution in revenue without new branch w1 = 100% -10% = 90%

The expected return for the bank if they add the new branch

= w1 * r1 + w2 *r2

= 90% * 25% + 10%*20%

= 24.50%

Standard deviation of the bank if they add the new branch can be calculated by the following formula

= sqrt (w1^2 * 1^2 + w2^2 * 2^2 + 2* w1 * w2 *1 *2* 12)

= sqrt (0.90^2 * 7.5%^2 + 0.10^2 * 15%^2 + 2* 0.90 * 0.10 *7.5% *15%* 0.7)

= sqrt (45.5625% + 2.25% + 14.175%)

= sqrt (61.9875%)

= 7.87%

Standard deviation of the bank if they add the new branch is 7.87%

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