Assume that the First National Bank has the balance sheet shown below, the income gap is currently
Question:
Assume that the First National Bank has the balance sheet shown below, the income gap is currently -$17.5 million, and that interest rates are initially at 10%.
| Assets | Duration | Liabilities | Duration | |||
| Reserves | 5,000,000 | 0 | ||||
| Securities | Checkable Deposits | 15,000,000 | 2 | |||
| <1 Year | 5,000,000 | 0.4 | Money Market Deposits | 5,000,000 | 0.1 | |
| 1 to 2 Years | 5,000,000 | 1.6 | Savings Accounts | 15,000,000 | 1 | |
| >2 Years | 10,000,000 | 7 | CDs | |||
| Residential Mortgages | Variable-rate | 10,000,000 | 0.5 | |||
| Variables-rate | 10,000,000 | 0.5 | < 1 Year | 15,000,000 | 0.2 | |
| Fixed-rate | 10,000,000 | 6 | 1 to 2 Year | 5,000,000 | 1.2 | |
| Commercial Loans | > 2 years | 5,000,000 | 2.7 | |||
| < 1 Year | 15,000,000 | 0.7 | Interbank Loans | 5,000,000 | 0 | |
| 1 to 2 Years | 10,000,000 | 1.4 | Borrowings | |||
| > 2 years | 25,000,000 | 4 | <1 Year | 10,000,000 | 0.3 | |
| Buildings, etc | 5,000,000 | 0 | 1 to 2 Year | 5,000,000 | 1.3 | |
| > 2 years | 5,000,000 | 3.1 | ||||
| Bank Capital | 5,000,000 | |||||
| Total | 100,000,000 | Total | 100,000,000 |
1. Calculate the duration gap for the bank.
2. If the First National Bank sells $10 million of its securities with maturities greater than two years and replaces them with securities maturing in less than one year, what is the income gap for the bank? What will happen to profits next year if interest rates fall by 3 percentage points?
3. Given the estimates of duration above, what will happen to the bank’s net worth if interest rates rise by 10 percentage points? Will the bank stay in business? Why or why not?
4. If the manager of the First National Bank revises the estimates of the duration of the bank’s assets to four years and liabilities to two years, what is the effect on net worth if interest rates rise by 2 percentage points?
5. Given the estimates of duration in Problem 4, how should the bank alter the duration of its assets to immunize its net worth from interest-rate risk?
6. Given the estimates of duration in Problem 4, how should the bank alter the duration of its liabilities to immunize its net worth from interest-rate risk.
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