
Explanation:
Step-by-step solution:
This is an on-balance sheet (balance-sheet) hedge, where the bank matches the currency of its foreign assets and liabilities to neutralize FX risk.
Convert UK loan principal to pounds at start:
$100.0M / $1.60/£ = £62.5MIncome at end of year (year 1):
$100M × 1.04 = $104.0M$1.20/£ = $82.5M$104.0M + $82.5M = $186.5MExpenses at end of year (year 1):
$100M × 1.03 = $103.0M$1.20/£ = $79.5M$103.0M + $79.5M = $182.5MNet income:
$186.5M − $182.5M = $4.0MNet Interest Margin (NIM):
$4.0M / $200.0M = +2.00%Key insight: The balance-sheet hedge successfully neutralizes the FX risk on the UK book. The pound depreciation does not affect the bank's net position because both the UK assets and UK liabilities depreciate by the same percentage (from $1.60/£ to $1.20/£). The NIM of 2.0% reflects only the true interest-rate spreads (1% on US book + 1% on UK book = 2%).
The answer is (c) +2.00%.
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Q-2 (502.2). Suppose that a U.S. financial institution has $200.0 million in assets at the start of the year. Half of its assets are invested domestically in US loans, while the other $100.0 million is invested abroad in the United Kingdom. The (default risk-free) US loans yield 4.0%, and the (default-free) loans in the United Kingdom, which denominated in pound sterlings, yield 10.0%:
| Assets (loans) | Liabilities (CDs) |
|---|---|
| Invest: | Lend: |
$100.0 US $ @ 4% | $100.0 US $ @ 3% |
$100.0 UK £ @ 10% | $100.0 UK £ @ 6% |
| (loans made in pounds) | (deposits made in pounds) |
This institution employs what Saunders calls an "on-balance sheet hedge;" it hedges by matching the maturity and currency of its foreign asset-liability book. The promised one-year U.S. CD rate is 3.0%, to be paid in dollars at the end of the year. The institution funds the British loans with $100.0 million equivalent one-year pound CDs at a rate of 6.0%. The exchange rate of dollars for pounds at the beginning of the year is $1.60/£1; i.e., GBPUSD is $1.60. At the end of the year, assume the pound sterling plummets (depreciates) against the dollar to $1.20. Which is nearest to the implied net interest margin? (Note: variation on Saunders' Question #16)
A
a) -3.75%
B
b) -0.84%
C
c) +2.00%
D
d) +3.33%
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