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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.
The correct answer is A. The treasurer of a US bank is concerned about the potential impact of a 200 basis point (bps) increase in interest rates by the Federal Reserve on the bank's net worth. To assess this, the manager is asked to perform a duration analysis on the bank's assets and liabilities under this stress scenario. The duration of the bank's assets and liabilities are calculated as follows: - Duration of Assets (D Assets): \((400 \times 0 + 400 \times 1 + 600 \times 5 + 1100 \times 3) / 2500 = 2.68\) years. - Duration of Liabilities (D Liabilities): \((1000 \times 0.5 + 1200 \times 4) / 2200 = 2.41\) years. The effect of a 200 bps increase in interest rates on the bank's net worth is calculated by applying the duration concept to both assets and liabilities and then finding the difference: - Change in Asset Value: \(-(2.68 \times 0.02 \times 2500) / 1.02\) - Change in Liability Value: \((2.41 \times 0.02 \times 2200) / 1.02\) The net effect on the bank's net worth is the change in asset value minus the change in liability value: \(-131.37 + 103.96 = -27.41\) million USD. This calculation shows that a 200 bps increase in interest rates will cause the bank's net worth to decrease by approximately USD 27.4 million, making option A the correct statement. Option B is incorrect because it omits cash from the asset's duration calculation, leading to an inaccurate assessment. Options C and D are not relevant to the question's focus on the impact of interest rate changes on net worth.
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The bank's treasurer is concerned about the potential impact on the bank's value due to a possible future increase in interest rates by the Federal Reserve (FED). To address this concern, the treasurer has requested the manager to include a new scenario in the bank's stress testing system where the FED raises interest rates by 200 basis points. The manager is tasked with performing a duration analysis under this scenario. The following table summarizes the bank's balance sheet and the duration of each asset and liability:
| Amount (USD million) | Duration (years) | Assets/Liabilities |
|---|---|---|
| 400 | 0 | Cash |
| 400 | 1.0 | Federal funds loans |
| 600 | 5.0 | Government securities and mortgages |
| 1100 | 3.0 | Loans and leases |
| 2500 | Total assets | |
| 1000 | 0.5 | Interest-bearing deposits (marketable) |
| 1200 | 4.0 | Other borrowings |
| 2200 | Total liabilities |
Assuming the current interest rate is 2%, what accurate conclusion can the manager draw from this stress test 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.