Question

You are the bank manager of a bank with 10m. capital and 90m. deposits. -

-Deposits cost you 1%

Choice of two assets:

a)Safe asset earning 5% risk free

b)Risky asset earning 25% and loses 20% with equal probabilities

You are the bank manager of a bank with 10m. capital and 90m. deposits. Deposits cost you 1 % Choice of two assets: a safe asset earning 5% risk free b, Risky asset earning 25% and loses 20% with equal probabilities Calculate the expected ROA and ROE for both choices (Hint: Calculate the profits net of deposit interests for the good/ bad scenario first. Remember: For owners the loss is limited toequity). If the bank only holds the risk free asset, its ROA is If the bank only holds the risky asset, its ROA is To maximize share holder return the bank manager will chose the Would the depositors be happy with 1% interest if they knew what the banker is doing? The interest rate on deposits would (increase decrease) if the depositors had perfect information about the bank's risk profile. Repeat your calculations for the case that the bank uses 30m capital and only 70m deposits. Investing in the risky asset would now have an %and the ROE is % and the ROE is risk free or risky?) asset. expected ROA of % and ROE of Sit back and think of the importance of bank equity for the choices that bank managers will make. Which is better for society? Can you see why we need bank regulation?

It would be nice if you could provide answers explicitly (easy to read ) and explanations as well. Thanks in advance!

Answer 1

Answer:

Given Capital E=10m

and Deposits D=90 m

Payment for deposit P= 1% of deposit=1%*90 m=0.9 m

A) if company invest in risk free asset then return r=5%

So total return for company from risk free asset=5%*(10m+90m)=5 m

So Net return R = 5m - 0.9m=4.1m

ROE= R/E =4.1m/10m= 41%

ROA=R/(E+D)=4.1m/100m=4.1%

B) if company invest in risk free asset then return =25% for profit in good case and -20% for loss in bad case with probability of 50% for each case.

So Profit =25%*100m=25 m

Loss =20%*100 m=20 m but we will take only 10 m because the loss is limited to equity only.

So total expected return for company from risky asset=50%*25+50%*(-10)=7.5m

So Net return R = 7.5m - 0.9m=6.6m

ROE= R/E =6.6m/10m= 66%

ROA=R/(E+D)=6.6 m/100m=6.6%

C)

To maximize his return the bank manager will choose to invest in Risky asset.

D) No , Depositor would not be happy. if they have perfect information then interest rate would increase for depositors.

E) if

Given Capital E=30m

and Deposits D=70 m

if company invest in risk free asset then return =25% for profit in good case and -20% for loss in bad case with probability of 50% for each case.

So Profit =25%*100m=25 m

Loss =20%*100 m=20 m Since here equity is 30m so we will take loss=20 m

So total expected return for company from risky asset=50%*25+50%*(-20)=2.5m

So Net return R = 2.5m - 0.9m=1.6m

ROE= R/E =1.6m/10m= 16%

ROA=R/(D+E)=1.6/100m=1.6%

F) As the equity increase from 10 m to 30 m the ROE and ROA decreases from 66% to 16% .So bank manager will try to have less equity and more depositors fund for higher return in risky asset. So for society this not good and we require bank regulations to monitor bank manager's action.