Explanation:
Since the actual 1.5-year futures exchange rate is lower than the calculated/estimated futures exchange rate, the investor should borrow €1000 for 1.5 years at the rate of 1.25% and convert the €1000 into USD at the current exchange rate: €1000 × 1.098 = $1098
Then, the investor will invest the $1098 at the U.S risk-free rate of 1.5% for 1.5 years:
$1098 × (1.015)^{1.5} = $1,122.7974
After 1.5 years the euro loan payable will equal
€1000 × (1.0125)^{1.5} = €1018.81
The futures contract to buy €1018.81 at the futures exchange rate of 1.100 USD per EUR costs
€1018.808 × 1.100 = $1120.69
The risk-free profit at the end of 1.5 years is $1,122.80 − $1,120.61 = $2.11
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Q.16 Muhammad Zubair is the investment manager of an investment company based in Chicago that invests in almost all financial instruments such as equities, derivatives, currencies, etc. He is considering investing 1000 Euros 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 1.25% and 1.5%, respectively, and the spot exchange rate is 1.098 USD per Euro. According to the given data, the futures exchange rate should be 1.102 USD per Euro. However, the 1.5-year futures exchange rate is quoted at 1.100 USD per Euro. Using this information, what is the arbitrage gain or loss?
A
Arbitrage gain of $2.1.
B
Arbitrage loss of $15.8.
C
Arbitrage loss of $1.8.
D
Arbitrage loss of $7.9.