Question 1 - Bank Risk (20 points). Suppose you are the sole shareholder of a bank with deposits of $1.2 million and assets of $1 million. There is no reserve requirement. Your liability in the bank is limited by law to your investment (if it fails, you need not make up losses to depositors). You are risk neutral.

1. What is the net worth of your bank?

Suppose you may reinvest your assets into one but only one of the following projects before the examiners audit your books: Project A: risk free return of 7 percent Project B: 50 percent chance of a 21 percent net return and a 50 percent chance of a net return of -21 percent Project C: 10 percent chance of doubling your assets and a 90 percent chance of losing everything

2. Rank the three projects according to which will benefit you personally.

3. How would your ranking change if the assets of your bank were $1, 200, 000?

4. How would your ranking change if the assets of your bank were $2, 000, 000?

5. If you have the chance to abscond with $100, 000 at the cost of losing ownership in the bank, would you do it (setting aside questions of morality)? How does your answer depend on the net worth of the bank?

6. If banks are covered by government deposit insurance, why should the government take an active role in closing down failed banks as soon as they can be discovered? Answer with references to the examples in this exercise.