Explanation:
The investor borrows €1000 for 1.5 years at the rate of 1.36% and converts the €1000 into USD at the current exchange rate:
€1000 × 1.071 = USD 1071
Then, the investor will invest the USD 1071 at the U.S. risk-free rate of 1.55% compounded for 1.5 years:
USD 1071 × (1.0155)¹·⁵ = USD 1,096.00
After 1.5 years, the euro loan payable will equal €1000 × (1.0136)¹·⁵ = €1,020.47
The futures contract to buy €1,020.61 at the futures exchange rate of 1.100 USD per EUR costs
€1,020.47 × 1.100 = USD 1,122.52
The risk-free gain/loss at the end of 1.5 years is USD 1,096.00 − USD 1,122.52 = −USD 26.52
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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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