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

• Deposits cost you 1%
• Choice of two assets:

1. Safe asset earning 5% risk free
2. 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?