First Principles: No-Arbitrage and Cross-Border Capital Flows
A is correct. Covered interest rate parity (CIRP) states that the forward rate must equal the spot rate adjusted for interest rate differentials to prevent riskless arbitrage. The no-arbitrage forward rate is given by $$F = S \times \frac{1 + r_{quote} \times \frac{days}{360}}{1 + r_{base} \times \frac{days}{360}}$USD where the quote currency is USD and base currency is EUR. Computing: $F = 1.2500 \times \frac{1 + 0.05 \times 0.5}{1 + 0.035 \times 0.5} = 1.2500 \times \frac{1.025}{1.0175} = 1.2500 \times 1.00737 = 1.2592$$. The market forward (1.2410) is below the no-arbitrage forward (1.2592), meaning EUR is too cheap forward. The arbitrage strategy: borrow USD at 5%, convert to EUR spot, invest EUR at 3.5%, sell EUR forward at 1.2410. Borrowing USD 10,000,000 for 180 days costs $$10,000,000 \times 1.025 = 10,250,000$USD to repay. Converting at spot: $\frac{10,000,000}{1.2500} = 8,000,000$USD EUR. Investing EUR at 3.5%: $8,000,000 \times 1.0175 = 8,140,000$USD EUR at maturity. Selling EUR forward: $8,140,000 \times 1.2410 = 10,101,740$USD USD received. Arbitrage profit: $10,101,740 - 10,250,000 = -148,260$USD USD. This is a loss, indicating the strategy reverses. The correct arbitrage: borrow EUR, convert to USD, invest USD, buy EUR forward. Borrowing 8,000,000 EUR at 3.5% requires $8,000,000 \times 1.0175 = 8,140,000$USD EUR to repay. Converting to USD at spot: $8,000,000 \times 1.2500 = 10,000,000$USD USD. Investing at 5%: $10,000,000 \times 1.025 = 10,250,000$USD USD. Buying EUR forward at 1.2410: $\frac{10,250,000}{1.2410} = 8,258,678$USD EUR received. Net profit in EUR: $8,258,678 - 8,140,000 = 118,678$USD EUR. Converting profit to USD at forward rate: $118,678 \times 1.2410 / 1.2500 \approx 9,040$$ USD after accounting for the rate differential.
B is incorrect because it incorrectly applies the interest differential to the notional without recognizing that the arbitrage profit is the difference between the synthetic forward and market forward applied to the principal after interest, not the simple interest differential multiplied by the spot rate discrepancy.
C is incorrect because it calculates the profit as if the entire interest rate differential (1.5% annualized = 0.75% for 180 days) applies directly to the mispricing without proper compounding and without executing the full arbitrage sequence of borrowing, converting, investing, and hedging, which overstates the achievable gain.