International Finance Professor, Jasper Kim 072SIS07 Yang Il Kim Currency (FX) Forward International Finance Professor, Jasper Kim 072SIS07 Yang Il Kim

Currency Forward Contracts Maturity: Contractual commitment to buy or sell a specified amount of foreign exchange at a future date (maturity of contract) and for a specified price (forward exchange rate) Most Forward Contracts Less than 2 years Relatively large bid-ask spreads Longer-dated Forward Contracts are not attractive for hedging long-dated foreign currency exposure

Pricing Currency Forward Contracts Deposit $100,000 in a U.S. bank at 7% for 1 year $100,000  $107,000 Exchange $100,000  CX Spot rate: $0.6558 of 1 CX Deposit CX152,486 in a bank in country X at 9% for 1 year CX152,486  CX 166,210 $100,000  CX 166,210 x F CX: unit of currency for Country X F: exchange rate btw CX & $ $100,000 x 1.07 CX 152,486 x 1.09 Alternative 1: Now 1 year later Alternative 2: Alternative 1: Deposit $100,000 in a U.S bank at 7% for 1 year Alternative 2: Deposit $100,000 in country X’s currency in a bank in country X at 9% for 1 year

Pricing Currency Forward Contracts (cont’) $100,000  $107,000 = Investors will be indifferent btw 2 alternatives F = $0.6438/CX $100,000  CX 166,210 x F IF, >$0.6438: the investor receives more than $107,000 <$0.6438: the investor receives less than $107,000

Pricing Currency Forward Contracts (cont’) Alternative 1: Deposit CX 152,486 in a bank in country X at 9% for 1 year Alternative 2: Deposit CX 152,486 in $ in a U.S. bank at 7% for 1 year Deposit CX 152,486 at 9% for 1 year CX 152,486  CX 166,210 Exchange CX 152,486  $ Spot rate: $0.6558 of 1 CX Deposit $100,000 in a U.S. bank at 7% for 1 year $ 100,000  $ 107,000 CX 152,486  $ 107,000 / F CX: unit of currency for Country X F: exchange rate btw CX & $ CX 152,486 x 1.09 $100,000 x 1.07 Alternative 1: Now 1 year later Alternative 2:

Pricing Currency Forward Contracts (cont’) $100,000  $107,000 $100,000  CX 166,210 x F = Investors will be indifferent btw 2 alternatives F = $0.6438/CX CX 152,486  CX 166,210 CX 152,486  $ 107,000 / F The 1-year forward exchange rate fixes today the exchange rate 1 year from now. IF, 1-year forward exchange rate =$0.6438: no arbitrage >$0.6438: arbitrage

U.S. investor Borrow: $100,000 at 7% for 1 year Suppose that; The 1-year forward exchange rate = $0.6500 for 1 unit of CX The borrowing rates = the lending rates w/i each currency’s country U.S. investor Borrow: $100,000 at 7% for 1 year Agree: Deliver CX 166,210 1 year from now at $0.6500 per CX  CX 166,210 x $0.6500 = $ 108,037 Deposit $100,000 in a U.S. bank at 7% for 1 year $100,000  $107,000 Exchange $100,000  CX Spot rate: $0.6558 of 1 CX Deposit CX152,486 in a bank in country X at 9% for 1 year CX152,486  CX 166,210 $100,000  CX 166,210 x F CX: unit of currency for Country X F: exchange rate btw CX & $ $100,000 x 1.07 CX 152,486 x 1.09 Alternative 1: Now 1 year later Alternative 2: Profit: $ 1,037

1-year forward exchange rate must be $ 0.6438 Receive  $ 108,037 Repay  $107,000 IF, forward exchange rate > $ 0.6438 : U.S. investors – selling CX forward & buying $ forward < $ 0.6438 : Investors in country X – selling $ forward & buying CX forward Conclusion: 1-year forward exchange rate must be $ 0.6438 Otherwise  Arbitrage opportunities Arbitrage Profit: $ 1,037

Determination of the Forward Exch. R. Interest rate parity (IRP) : The relationship among the spot exch. R, the int. R in 2 countries & the forward R. Covered interest arbitrage : The arbitrage process that forces int. R parity * IRP btw the currencies of 2 countries A & B I = amount of A’s currency to be invested for a time period of length t S = spot exch. R: price of foreign currency in terms of domestic currency (units of domestic currency per unit of foreign currency) F = t-period forward rate: price of foreign currency t periods from now iA = int. R. on an investment maturing at time t in country A iB = int. R. on an investment maturing at time t in country B I(1+ iA) = (I/S)(1+ iB)/F

IRP formula: I(1+ iA) = (I/S)(1+ iB)/F Suppose that: Country A = the U.S. Country B = the country X I = $100,000 for 1 year S = $ 0.6558 F = $ 0.6438 iA = 0.07 iB = 0.09 $ 100,000(1+0.07) = ($ 100,000 / $ 0.6558)(1+0.09)($ 0.6438) $ 107,000 = $ 107,005 IRP formula: I(1+ iA) = (I/S)(1+ iB)/F F = S 1+ iA 1 + iB

Theoretical Forward Exchange Rate Assumptions No commissions or bid-ask spread The borrowing & lending rates are same in each currency Ignoring taxes Arbitrageurs could borrow and invest in another country The actual forward exchange rate may deviate from the theoretical forward exchange rate

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