Foreign Currency Arbitrage: The spot exchange rate for converting one US dollar
ID: 2382714 • Letter: F
Question
Foreign Currency Arbitrage: The spot exchange rate for converting one US dollar into an FD (a foreign dollar) is 8.32. The spot rate for converting one FD into USD is 0.1202 (= 1/8.32). A long FD forward contract obligates the holder to buy one FD in 9 months time at the rate 0.10 (USD per FD). Annual continuously compounded US interest rate is 1.0%. Annual continuously compounded foreign interest rate is 4.0%.
What is the fair forward price?
Given that fair forward price does not equal 0.10, propose a set of transactions that will produce an arbitrage. Fill in an arbitrage table with your numerical values assuming that ST = 0.09 at the end of nine months.
Repeat (b) but now provide the table assuming that ST = 0.13.
Explanation / Answer
F = S*[(1+if) /(1+id)]
F= Forward Exchange Rate
S= Current Spot Exchange Rate
Id= Interest Rate in Domestic Currency [Base Currency; USD in this case]
If= Interest Rate in Foreign Currency [Quoted Currency; FD in this case]
Thus, F= 0.1202*[(1+0.01)/(1+0.04)] = 0.116733 ....... [Fair Forward Price= 0.116733 USD for buying
each FD]
Thus, in this case example, FD trades at forward discount vis-a-vis USD
Set of transdactions for producing an arbitrage are as follows:
i. Borrow some amount in USD i.e. @1% p.a.for 9 months
ii. Immediately convert the borrowed USD amount into FD proceeds at spot rate
iii. Invest these converted FD proceeds in an interest-bearing FD-denominated instrument i.e. @4% p.a. for 9 months
iv. Simultaneously buy a 9-month forward contract to convert these FD investment proceeds into USD at the end of 9 months to hedge exchange-rate risk