Question

Suppose the spot USD/INR is 46.75 and 1 year US interest rate is 5% while it is 11% in India. A bank is quoting 1 year forward rate as 43.35. The spot rate at maturity (360 days) USD/INR is 45. As a trader on the foreign exchange market you wish to speculate and take advantage of an arbitrage opportunity.
Using covered interest rate parity does an arbitrage opportunity exist? Calculate the profit.
Using uncovered interest rate parity does an arbitrage opportunity exist? Calculate the profit.
       

Answer 1

Covered interest rate parity:

For covered interest rate parity, we have to use the forward rate in order to lock in the profit. Hence, we start with borrowing $100, convert it to INR with the spot rate, and get = INR 4675. Then, we put this money on interest in India and get after one year = 1.11 x 4675 = 5189.25. On the borrowed money we have to payback = 100 x 1.05 = $105 after one year. So, we convert the INR with the help of the forward and get = 5189.25/43.35 = $119.7058. So, we pay back the $105 borrowed and make an arbitrage profit of = 119.7058 - 105 = $14.7058. So, there is an arbitrage opportunity and the profit percentage is 14.7058%.

Uncovered Interest rate parity:

For this, we can't use the forward rate and have to use the spot rate after 1 year. Hence, we start by borrowing $100, convert it to INR with the spot rate into 4675 INR. Then, we put this money on interest in India and get after one year = 1.11 x 4675 = 5189.25. On the borrowed money we have to payback = 100 x 1.05 = $105 after one year. So, we convert the INR with the help of the spot rate after one year and get = 5189.25/45 = $115.3166. So, we pay back the $105 borrowed and make an arbitrage profit of = 115.3166 - 105 = $10.3166, So, there is an arbitrage opportunity and the profit percentage is 10.3166%.