Answer-first summary for fast verification
Answer: +2.00%
### Solution Because the institution matches the currency and maturity of the foreign assets and liabilities, the exchange-rate movement affects both sides similarly. #### 1. U.S. loan and U.S. CD - U.S. loan: $100.0 million × 1.04 = **$104.0 million** - U.S. CD liability: $100.0 million × 1.03 = **$103.0 million** - Net U.S. contribution = **$1.0 million** #### 2. U.K. loan and pound CD - Initial pound amount of the U.K. loan: \[ \frac{100.0}{1.60} = 62.5 \text{ million £} \] - End-of-year value of the U.K. loan in pounds: \[ 62.5 \times 1.10 = 68.75 \text{ million £} \] - Convert at end-of-year spot rate $1.20/£: \[ 68.75 \times 1.20 = 82.5 \text{ million dollars} \] - Pound CD liability: \[ 62.5 \times 1.06 = 66.25 \text{ million £} \] - Convert at $1.20/£: \[ 66.25 \times 1.20 = 79.5 \text{ million dollars} \] - Net U.K. contribution = **$3.0 million** #### 3. Total net interest income \[ 1.0 + 3.0 = 4.0 \text{ million dollars} \] #### 4. Net interest margin Using beginning assets of $200.0 million: \[ \frac{4.0}{200.0} = 0.02 = 2.00\% \] ### Final Answer **C. +2.00%**
Author: Manit Arora
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Q-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
-3.75%
B
-0.84%
C
+2.00%
D
+3.33%
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