Question

You are the bank manager of a bank with 10m. capital and 90m. deposits. Deposits cost you 1% Choice of two assets: Safe asset earning 5% risk free 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 ____% and the ROE is ____%. If the bank only holds the risky asset, its ROA is ____% and the ROE is ____%. To maximize share holder return the bank manager will chose the (risk free or risky?) asset. 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 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?

Answer 1

A) Calculation of ROA and ROE in case of investment in Safe Assets

1) Return on assets -ROA = NET PROFIT / AVERAGE ASSETS

= 4.1m /100m = 4.1%

Net profit = return on safe asset - cost of deposit  

= (100*5%) - (90* 1%)

= 4.1m

2) Return on equity -ROE = net profit/ Equity fund

= 4.1m/10m

=41%

B) Calculation of ROA and ROE in case of investment in risky asset

1) Return on assets -ROA = NET PROFIT / AVERAGE ASSETS

= 1.6m /100m = 1.6%

Net profit = return on risky  asset - cost of deposit  

={100* [ (25%*0.5) - (20%*0.5)]} - [(90* 1%)]

= 1.6 m

2) Return on equity -ROE = net profit/ Equity fund

= 1.6 m/10m

=16 %

To mazmise the shareholder return the banker should invest in safe return asset. Investment must be made prudently and by maintaing the balance risk.  

No the depositer would not be happy with the interest rate of deposit provided to them.

The deposit rate will increase if the depositer know about the risk of the investment made by banker. With the incresed level of risk the epectation of the invester increases.  

If bank uses 30% equity and 70% deposit then results are as under -

A) Calculation of ROA and ROE in case of investment in Safe Assets

1) Return on assets -ROA = NET PROFIT / AVERAGE ASSETS

= 4.3m /100m = 4.3%

Net profit = return on safe asset - cost of deposit  

= (100*5%) - (70* 1%)

= 4.3m

2) Return on equity -ROE = net profit/ Equity fund

= 4.3m/30m

=14.33%

B) Calculation of ROA and ROE in case of investment in risky asset

1) Return on assets -ROA = NET PROFIT / AVERAGE ASSETS

= 1.8m /100m = 1.8%

Net profit = return on risky  asset - cost of deposit  

={100* [ (25%*0.5) - (20%*0.5)]} - [(70* 1%)]

= 1.8 m

2) Return on equity -ROE = net profit/ Equity fund

= 1.8 m/30m

=6 %

Investment in risk free asset must be made.

Banking regulation are very much necessary to safeguard the interest of depositer. Otherwise bankers in order to provide more returns to equityholders invest in very risky assets which can be very harmful for the depositer in the adverse circumstances.