F446 Carvalho Problem Set 3 Solutions Updated PDF

Preview

Summary

Download F446 Carvalho Problem Set 3 Solutions Updated PDF

Description



F446: Banking and Financial Intermediation Spring 2021 Problem Set #3 SUGGESTED SOLUTIONS

Due Date: March 5 2021 (by 5:00PM) Please submit by e-mail to: [email protected] Please submit the file using the following format: F446_SectionNumber_LastName_FirstName_PS3

Question 1: Imagine a lender facing a choice between one of two strategies: high-risk strategy or moderate-risk strategy. For simplicity, there is only two dates in this example (today and tomorrow). The lender chooses its strategy today and the return on this strategy is delivered tomorrow (cash flows only take place tomorrow). The bank has $270M in funds (total funding raised) and 90% of the funds raised by the lender were deposits paying no interest. In the high-risk strategy, the assets (loans) generate a return equal to 7% with probability 90% and there is a 10% chance that the assets generate a return equal to -40%. On the other hand, in the moderate-risk strategy, the assets (loans) generate a return equal to 5% with probability 95% and there is a 5% chance that the assets generate a return equal to -20%. Deposits are fully insured. The lender (and the government/ deposit insurance fund) discount tomorrow’s cash flows using a 3% discount rate (independently of their risk). (a) Suppose that the deposit insurance premium paid by the bank equals zero. Compute the value of the implicit subsidy (or implicit transfer) provided by the deposit insurance fund to the bank under the two strategies. The deposit insurance fund will cover losses to depositor that take place when the bank is insolvent. Deposits are equal to (90%) × ($270M) = $243M and, since there is no interest, the bank has to pay $243M to depositors tomorrow. When the value of the assets drops below $243M tomorrow, additional losses are covered by the deposit insurance fund. Under the moderate-risk strategy, assets are equal to (1 - 0.2) × ($270M) = $216M after bad news and the losses to depositors equal $243M -$216M = $27M with probability = 5%. The expected

payment tomorrow (from the deposit insurance fund) to the bank is (5%) × ($27M) = $1.35M. The implicit subsidy today is then given by (1/1.03) × $1.35M = $1.31M. Under the high-risk strategy, assets are equal to (1 - 0.4) × ($270M) = $162M after bad news and the losses to depositors equal $243M -$162M = $81M with probability = 10%. The expected payment tomorrow (from the deposit insurance fund) to the bank is (10%) × ($81M) = $8.1M. The implicit subsidy today is then given by (1/1.03) × $8.1M = $7.9M.

(b) Suppose now that the government wants to set this implicit subsidy equal to zero by asking the bank to pay a deposit insurance premium today. What should be the value of this premium (paid only today) under each of the two strategies? The value today of the expected transfer from the deposit insurance fund is $1.31M and $7.9M under the medium- and high-risk strategies, respectively (values calculated in part (a)). If the bank requires the bank these same values today (upfront), then there will be no implicit subsidies. In this case, the bank is simply paying today for the expected payment tomorrow. In other words, the premium should be is $1.31M and $7.9M under the medium- and high-risk strategies, respectively.

(c) How would your answer to parts (a) and (b) change if only 60% of the deposits from the bank were covered by deposit insurance? If only 60% of the deposits from the bank are covered by deposit insurance, the payments from the deposit insurance fund will now cover only 60% of the losses from depositors. Consequently, the implicit subsidies in part (a) under the moderate- and high-risk strategies are now given by (0.6) × ($1.31M) = $0.79M and (0.6) × ($7.9M) = $4.7M. Similarly, the premium in part (b) should be is $0.79M and $4.7M under the medium- and high-risk strategies, respectively.

Question 2: Describe three important new requirements imposed on banks after the increased prudential supervision standards associated with the Dodd-Frank Act. A first important requirement was the creation of stress tests, where banks are required to have enough capital in future potential adverse scenarios. A second important requirement is the existence of restrictions on banks’ leverage ratios, in addition to capital requirements – capital requirements are based on risk-weighted assets, as opposed to total assets – as in a leverage ratio. A third requirement is the use of restrictions on liquidity ratios – intended to check if the bank has enough liquid funds during adverse conditions. A bank might meet capital requirements without much liquidity, e.g. a bank with low leverage has a significant amount of equity capital but might be holding a small amount of liquid assets.

Question 3: In a repurchase agreement between two banks, bank A sells $20.00M in asset-backed securities (ABS) to bank B today that will be repurchased at a value equal to $20.12M in 15 days. The current market value of these securities equals $21.00M. (a) Describe the lender, borrower, principal amount, and the value of the collateral in this secured loan. Today: Bank A gets $20.00M in cash from Bank B and gives ABS with value $21.00M until the end of the transaction. Tomorrow: Bank A pays $20.12M in cash to Bank B and gets back ABS. The borrower is bank A. The lender is bank B. The principal amount is $20.00M. The collateral is the ABS and its value is $21.00M.

(b) Determine the repo rate for this contract. Repo Rate = (Repayment – Loan Amount)/Loan Amount = ($20.12M - $20.00M)/$20.00M = $120K/$20M = 0.6%.

(c) Determine the haircut for this contract. Haircut = (Collateral Value – Loan Amount)/Loan Amount = ($21.00M - $20.00M)/$20.00M = $1M/$20M = 5%.

...