Question

The Cd Bank wants to open a new branch in a distant city with very different economic conditions. 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 expected return for the bank if they add the new branch

Answer 1

The expected return for the bank if they add the new branch is 15.5%.

Let New bank =10%

Let Old bank=1-10% = 90%

Using this formula

E(R)=(W1×R1)+[(1-W)×R2]

Where:

E(R)=Expected return=?

W1=New branch expected contribution=10%

R1=New branch expected return=20%

(1-W)=Old branch expected contribution=(1-10%)=90%

R2=Old branch expected return=15%

Let plug in the formula

E(R)=(.10×20%) + [(1-.10)×15%)]

E(R)= (.10×20%) + (.90×15%)

E(R)=0.02+0.135

E(R)=0.155×100

E(R)=15.5%

Inconclusion the expected return for the bank if they add the new branch is 15.5%.

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