U.S. Interest rate : 2%
India interest rate : 6%
Current spot rate INR/USD : 40
An Indian software company is expecting to receive a USD payment in 3 months time. It is considering a forward contract to hedge movements in the USD.
If the 3 month forward contract is quoted as INR 41 instead of the arbitrage free price of INR 40.38, could someone please kindly show me the maths to exploit the mispricing.
The answer to the qn states to: borrow INR for 3 months at 6%, convert today into USD at INR40 and invest at 2%, agreeing today to sell USD three months forward at INR 41.
Thanks very much!
This is a simple one . . . once you look at it the right way.
The arbitrage-free exchange rate is INR/USD 40.38, and the quoted rate is INR/USD 41.
The quoted rate is paying you too many INR.
Here’s the simple rule: you _ always _ want to be paid too many (or too much).
If you end with INR, you must start with INR.
Here you go:
- Borrow INR1,000,000 @ 6% for 3 months
- Convert to USD25,000 @ INR/USD 40
- Invest USD25,000 @ 2% for 3 months
- Enter into a forward contract to sell USD25,124 @ INR/USD 41 in 3 months
- Wait 3 months
- Collect USD25,124 (= USD25,000 × 1.02^(3/12)) from the bank
- Convert to INR1,030,087 @ INR/USD 41
- Pay off loan for INR1,014,674 (= INR1,000,000 × 1.06^(3/12))
- Wallow in the profit of INR15,413 (= INR1,030,087 − INR1,014,674)