1. Consider an economy with a bank and two types of risky borrowers. Each type of borrower requires a loan for a project with an uncertain return.  Borrower A’s project has a return of either 10% or 0%, and each return is equally likely. Borrower B’s project has a return of 100% with probability 0.1, otherwise the return is 0%.

The bank can make money by issuing loans to the borrowers but also has the option to purchase a Government bond with a guaranteed return of 2%. Borrowers will always repay the face value of their loans, but will only be able to repay the interest payments if it is less than the return on their project.

(a) What are expected returns of the two risky projects?

(b) Suppose the bank can distinguish between the two types of borrowers.  What is the smallest interest rate the bank would charge each type of agent to make the loans worthwhile?

(c) Now suppose that the bank cannot distinguish between the two types of bor- rowers. If 75% of borrowers are type A, what is the lowest common interest rate i that the bank could charge for the loans to be worthwhile?

(d) Which types of borrowers would agree to borrow at the interest rate you calcu- lated in part (c)? Would the bank agree to lend at this interest rate?

(e) Repeat parts (c) and (d) if only 25% of borrowers are Type A.

2.  Consider a bank with two depositors, Jamie and Alison, each of whom has deposits of $100. The bank uses these deposits to issue loans, keeping only 5% as reserves to facilitate withdrawals.  These loans are risky and have a default probability of z.  Alison knows this but Jamie thinks that the loans are perfectly safe.

Each depositor has the option to withdraw their deposits or do nothing. The bank operates under a sequential service constraint, but Alison is faster so if both agents try to withdraw their funds she will arrive at the bank first.

(a) Calculate the expected payoffs for Jamie and Alison for each potential outcome. (b) Using your answer from part (a), write down the payoff matrix.  What is the largest value of z for which both agents doing nothing is a Nash equilibrium?       (c) Now suppose the government introduces deposit insurance that guarantees 100% of each depositor’s losses up to a maximum of $80. Calculate expected payoffs for each potential outcome.

(d) Using your answer from part (c), write down the payoff matrix.  What is the largest value of z for which both agents doing nothing is a Nash equilibrium? Does deposit insurance help prevent bank runs in this model? Why or why not?

3. Go to the OSFI website and find data for the consolidated balance sheets of the Tangerine Bank as of 31 August 2022.

(a) There are six types of asset holdings.  Calculate and report the total holdings of each type of asset.

(b) What is the bank’s primary source of funding? What is its primary asset?      (c) Calculate bank capital as the sum of all components in Shareholders’ equity. What is the bank’s leverage ratio? Is Tangerine Bank well capitalized?

(d) Now calculate and report the bank’s risk-weighted leverage ratio using the risk-based capital requirement under the Basel Accord. Give “land, buildings, and equipment” and “other assets” a risk weight of 0.

(e) Compare the two leverage ratios you calculated in parts (c) and (d). Which do you think more accurately reflects the riskiness of Tangerine Bank’s portfolio?

4. The Dodd-Frank act includes annual stress tests on banks with more than $10 billion in assets.  While the results of these tests are released to the public, the criteria and specifics of the tests are private, unknown even to the banks being examined. Why do you think the Federal Reserve does not release this information? What do you think are the pros and cons of this approach. Answer in one or two paragraphs.