The spot exchange rate E = $0.95 US / FOREX. The U.S. interest rate is 2% per an

Question

The spot exchange rate E = $0.95 US / FOREX. The U.S. interest rate is 2% per annum. The interest rate in the foreign country is 3% per annum. A futures contract for delivery of 1 million units of the foreign currency one year from today is trading now at F = $0.92 US / FOREX. Which of the following is true? An arbitrage strategy:

Doesn’t exist

Would involve buying the futures contract and borrowing in the foreign currency

Would involve selling the futures contract and borrowing in U.S. dollars.

Show your work to arrive at the choice above.

Explanation / Answer

Answer:

Since interest rates of both the countries are different, there is an arbitrage opportunity available.
Hence, the first statement is not true.

For Proving another statement, let we take an example.

Example: Let us assume other foreign currency as EURO.

Spot Rate : 1 EURO = $ 0.95

Forward Rate: 1 EURO = $ 0.92

US Interest Rate : 2% p.a.

Foreign Interest Rate : 3% p.a.

Units : 10,00,000

Case 1: Buy Future contract (Invest in US ) and borrowing in the foreign currency.

Borrow Euro 10,00,000 from foreign for 1 year. After 1 year, amt to be paid on borrowing:

Euro 10,00,000 + Euro 10,00,000 X 3 % = EURO 10,30,000 (A)

Convert Euro 10,00,000 into $ using Spot Rate : 10,00,000 X 0.95 = $ 9,50,000

Invest $ 9,50,000 in US for 1 year & receive : $ 9,50,000 + $9,50,000 X 2% = $ 9,69,000

Reconvert $ 9,69,000 after 1 Year using FR : $ 9,69,000 / 0.92 = Euro 10,53,260.869 (B)

Arbitrage Gain :

Amount Paid (A) = Euro 10,30,000

Amount Receive (B) = Euro 10,53,260.869

Arbitrage Gain (B - A ) = Euro 23,260.869
  

Case 2: Sell Future contract (Invest in Foreign ) and borrowing in the US doller.

Borrow $ 10,00,000 from US for 1 year. After 1 year, amt to be paid on borrowing:

$10,00,000 + $ 10,00,000 X 2 % = $ 10,20,000 (A)

Convert $ 10,00,000 into Euro using Spot Rate : 10,00,000 / 0.95 = Euro 10,52,631.578

Invest Euro 10,52,631.578 in Foreign for 1 year & receive :

Euro 10,52,631.578 + Euro 10,52,631.578 X 3% = Euro 10,84,210.5263

Reconvert Euro 10,84,210.5263 after 1 Year using FR : Euro 10,84,210.5263 X 0.92 =

$ 9,97,473.684 (B)

Arbitrage Gain :

Amount Paid (A) = $ 10,20,000

Amount Receive (B) = $ 9,97,473.684

Arbitrage Loss (B - A ) = $ 22,526.315

Conclusion :

Case 1 : Gain Euro 23,260.869

Case 2 : Loss $ 22,526.315

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