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Answer: A 200-bps increase in interest rates will cause the bank's net worth to decrease by USD 27.4 million.
## Explanation **A is correct.** The duration of the bank's assets and liabilities are calculated as follows: **Asset Duration (D_A):** - Cash: 400 × 0 = 0 - Federal funds loans: 400 × 1.0 = 400 - Government securities and mortgages: 600 × 5.0 = 3,000 - Loans and leases: 1,100 × 3.0 = 3,300 - Total weighted duration: 0 + 400 + 3,000 + 3,300 = 6,700 - D_A = 6,700 / 2,500 = 2.68 years **Liability Duration (D_L):** - Interest-bearing deposits: 1,000 × 0.5 = 500 - Other borrowings: 1,200 × 4.0 = 4,800 - Total weighted duration: 500 + 4,800 = 5,300 - D_L = 5,300 / 2,200 = 2.41 years The effect of a 200 bps (0.02) increase in interest rates on the bank's net worth is calculated as: ΔNW = -[D_A × Δr × A]/(1 + r) - [-D_L × Δr × L]/(1 + r) Where: - Δr = 0.02 (200 bps increase) - r = 0.02 (current interest rate) - A = 2,500 (total assets) - L = 2,200 (total liabilities) ΔNW = -[2.68 × 0.02 × 2,500]/1.02 - [-2.41 × 0.02 × 2,200]/1.02 ΔNW = -[134]/1.02 - [-106.04]/1.02 ΔNW = -131.37 + 103.96 = -27.41 million **B is incorrect** because it omits cash from the asset duration calculation, resulting in an incorrect asset duration of 3.19 years instead of 2.68 years. **C is incorrect** because cash (with zero duration) would experience no change in value, making it the item with the smallest change, not interest-bearing deposits. **D is incorrect** because using cash to pay off borrowings would reduce the bank's leverage gap and potentially increase net worth, but the calculation shows the scenario would still result in a net worth decrease.
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The treasurer of a US bank is concerned about potential future interest rate increases by the Federal Reserve (FED) and their impact on the bank's net worth. After reviewing the bank's stress testing framework, the treasurer asks a manager to consider including an additional scenario in which the FED increases interest rates by 200 bps and to perform duration analysis on the scenario. The manager gathers information on the bank's balance sheet and the duration of each asset and liability item as provided below:
| Amount (USD million) | Duration (years) | |
|---|---|---|
| Assets | ||
| Cash | 400 | 0 |
| Federal funds loans | 400 | 1.0 |
| Government securities and mortgages | 600 | 5.0 |
| Loans and leases | 1100 | 3.0 |
| Total assets | 2500 | |
| Liabilities | ||
| Interest-bearing deposits (marketable) | 1000 | 0.5 |
| Other borrowings | 1200 | 4.0 |
| Total liabilities | 2200 |
Assuming the current level of interest rates is 2%, which of the following is a correct statement for the manager to make regarding this stress scenario?
A
A 200-bps increase in interest rates will cause the bank's net worth to decrease by USD 27.4 million.
B
A 200-bps increase in interest rates will cause the bank's net worth to decrease by USD 52.4 million.
C
Compared to the bank's other balance sheet items, interest-bearing deposits will experience the smallest change in value given a 200-bps increase in interest rates.
D
In this scenario, utilizing USD 200 million of cash to first pay off USD 200 million of other borrowings in response to a 200-bps increase in interest rates will cause the value of the bank's net worth to increase.