Explanation:
The trader is considering a specific strategy: borrowing Euros and investing in U.S. dollars, then using futures to convert back to Euros to repay the loan. Let's trace the cash flows:
Borrow 1,000 EUR for 1.5 years at 1.36% (annually compounded).
Amount owed at maturity = $1,000 \times (1 + 0.0136)^{1.5} = 1,020.49$ EUR.
Convert the borrowed 1,000 EUR into USD at the spot rate of 1.071 USD/EUR.
Amount in USD = $1,000 \times 1.071 = 1,071$ USD.
Invest 1,071 USD for 1.5 years at 1.55% (annually compounded).
Amount accumulated at maturity = $1,071 \times (1 + 0.0155)^{1.5} = 1,096.00$ USD.
To repay the EUR loan, the trader needs 1,020.49 EUR at maturity. The trader goes long 1.5-year EUR futures (buys EUR forward) at the quoted rate of 1.100 USD/EUR.
Cost to buy 1,020.49 EUR = $1,020.49 \times 1.100 = 1,122.54$ USD.
Arbitrage profit/loss:
The trader has 1,096.00 USD from the investment but needs 1,122.54 USD to settle the futures contract to pay off the loan.
Arbitrage loss = $1,096.00 - 1,122.54 = -26.54$ USD (closest to USD 26.52).
The loss occurs because the trader executed the wrong arbitrage strategy given the market mispricing. The EUR was overpriced in the futures market (1.100 vs theoretical 1.074), so the correct strategy would have been to borrow USD, convert to EUR, invest EUR, and sell EUR futures.
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Q.83 A retail trader is considering borrowing 1000 Euros and investing the proceeds in 1.50-year currency futures contracts on the U.S. dollar. The 1.5-year risk-free interest rates in the Eurozone and the U.S. are 1.36% and 1.55%, respectively (compounded annually), and the spot exchange rate is 1.071 USD per Euro. According to the given data, the futures exchange rate should be 1.074 USD per Euro. However, the 1.5-year futures exchange rate is quoted at 1.100 USD per Euro. Using this information outlined above, which of the following best represents the arbitrage gain or loss from the strategy?
A
Arbitrage gain of USD 26.52
B
Arbitrage loss of USD 26.52
C
Arbitrage gain of USD 27.52
D
Arbitrage loss of USD 27.52
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