Answer-first summary for fast verification
Answer: 2.06%
### Step 1: Compute the ending value of the U.S. loan portfolio - U.S. loans: \$400.0 million at 5.0% - End-of-year value: \$400.0 \times 1.05 = \$420.0 million ### Step 2: Compute the ending value of the euro loan portfolio using the forward hedge - Initial euro amount purchased with \$200.0 million at spot \$1.15/€1: \[ \frac{200.0}{1.15} = 173.9130 \text{ million euros} \] - End-of-year euro value at 8.0%: \[ 173.9130 \times 1.08 = 187.8261 \text{ million euros} \] - Convert euros back to dollars using the one-year forward rate of \$1.12/€1: \[ 187.8261 \times 1.12 = 210.3652 \text{ million dollars} \] ### Step 3: Compute total end-of-year asset value \[ 420.0 + 210.3652 = 630.3652 \text{ million} \] ### Step 4: Compute liability repayment - CDs of \$600.0 million at 3.0% - End-of-year liability value: \[ 600.0 \times 1.03 = 618.0 \text{ million} \] ### Step 5: Compute net return (ROI) Net profit: \[ 630.3652 - 618.0 = 12.3652 \text{ million} \] ROI over the year, based on beginning assets of \$600.0 million: \[ \frac{12.3652}{600.0} = 0.0206 = 2.06\% \] ### Why not net interest margin? Net interest margin is typically based on interest income minus interest expense relative to earning assets, while ROI here reflects the overall net return after the FX hedge and liability funding cost. The nearest answer is **2.06%**.
Author: Manit Arora
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Q-502.3. Suppose a U.S. financial institution has $600.0 million in assets at the start of the year, which are funded by US certificates of deposit (CDs) with a promised one-year of 3.0%. The institution invests $400.0 million domestically in U.S. loans that yield 5.0%, and the remaining $200.0 million are invested abroad in euro-denominated loans that yield 8.0%:
Assets (loans)
Invest:
$400.00 200.00` € @ 8%
(loans made in euros)
Liabilities (CDs)
Lend:
$600.00 $ @ 3%
Rather than match foreign asset position with liabilities (i.e., on balance sheet hedging), the institution uses the forward FX market to employ an off-balance-sheet hedge. The exchange rate of dollars for euros at the beginning of the year is $1.15/€1. The current forward one-year exchange rate between dollars and euros is $1.12/€1; that is, the forward trades at a $0.03 discount to the spot FX rate. Which is nearest to return on investment (ROI or "net return," which is different than the net interest margin) over the year?
A
1.52%
B
2.06%
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