Question

The spot rate for the Brazilian Real is $0.1845/R$. The interest rate is 3% in the U.S. and 7% in Brazil.
a) If the 90-day forward rate is $0.1810, can you arbitrage with these rates? If yes, use $1,000,000 or R$1,000,000 as the notional amount.
b) what spot rate will prevent this arbitrage, everything else being constant?

Answer 1

a)

Yes, Arbitrage is possible

Step 1:- Borrow Brazilian Real (BRL) 1,000,000 AT 7% for 90days & take a long position in the forward rate = $0.1810 / BRL

Amount owed in BRL after 90 days = BRL Amount borrowed * (1 + BRL interest rate * 90 / 365)

Amount owed in BRL after 90 days = BRL 1,000,000 * (1 + (7% * 90 / 365))

Amount owed in BRL after 90 days = BRL 1,017,260.274

Step 2:- Covert BRL 1,000,000 to USD at Spot rate = $0.1845 / BRL

Amount in USD = Amount in BRL * Spot rate

Amount in USD = 1,000,000 * 0.1845

Amount in USD = 184,500

Step 3:- Invest USD 184,500 at USD interest rate = 3%

USD Invested amount after 90 days = USD Invested Amount * (1 + USD interest rate * 90 / 365)

USD Invested amount after 90 days = $184,500 * (1 + (3% * 90 / 365))

USD Invested amount after 90 days = $185,864.7945

Convert the invested USD to BRL at the forward rate = $0.1810 / BRL

Amount in BRL after 90 days = USD Invested amount after 90 days * (1 / forward rate)

Amount in BRL after 90 days = $185,864.7945 * (1 / 0.1810)

Amount in BRL after 90 days = BRL1,026,877.318

Arbitrage profit = Amount in BRL after 90 days - Amount owed in BRL after 90 days

Arbitrage profit = BRL1,026,877.318 - BRL 1,017,260.274

Arbitrage profit = BRL 9617.04

b)

No arbitrage spot rate is computed as

Spot rate = Forward rate * (1 + BRL interest rate * (90 / 365)) / (1 + USD interest rate * (90 / 365))

Spot rate = 0.1810 * (1 + 7% * (90 / 365)) / (1 + 3% * (90 / 365))

Spot rate = $0.1828 / BRL