Question

Interest rates in India are 5.25% p.a. and in Brazil they are currently at 2.5% p.a. The BRL/INR spot rate is 13.37. (a) Calculate the theoretical three-year forward rate of the BRL implied by Interest Rate Parity. (b) Now assume the actual two-year forward rate is BRL/INR 15.20. What, if any, is the percentage return from engaging in Covered Interest Arbitrage? Assume a transaction cost of 0.3% in the spot and the forward market. (Calculate the result as a percentage of your initial borrowing, accurate to 4 decimal places, making sure to include any opportunity cost in your calculations)

Answer 1

As per Interest rate parity

Theoretical three-year forward rate = Spot rate * (1+interest rate in INR)^3/(1+interest rate in BRL)^3

= 13.37*1.0525^3/1.025^3

= 14.4753

So, Theoretical three-year forward rate iin BRL/INR is 14.4753 (rounded to 4 decimal places)

Theoretical two-year forward rate = Spot rate * (1+interest rate in INR)^2/(1+interest rate in BRL)^2

= 13.37*1.0525^2/1.025^2

= 14.0970

Since the Actual Forward rate is BRL/INR 15.20, Covered Interest Arbitrage can be done as follows

i) Borrow INR 100 from the market for two years at 5.25%p.a.,

ii) Convert the INR to BRL at spot market  to get 100*0.997 /13.37 = BRL 7.4570 after transaction cost

iii) Invest the BRL for two years at 2.5% p.a. to get 7.4570*1.025^2 = 7.8345 after two years

iv) Sell 7.8345BRL in forward contract at BRL/INR 15.20 after two years after transaction cost (assuming transaction cost in forward only applicable at the time of delivery)

v) After two years, get BRL 7.8345 as maturity amount from Investment. Deliver BRL to get 7.8345*0.997*15.20 = INR 118.7272

vi) Pay maturity amount of loan INR 100*1.0525^2=INR 110.7756 and make an arbitrage profit of 118.7272-110.7756 = INR 7.9516

So, Arbitrage profit of 7.9516/100 = 7.9516% can be made