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

2. 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

3. 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: $ 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

4. 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

5. 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: $ 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:

6. 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

7. U.S. investor Borrow: $100,000 at 7% for 1 year
Suppose that;
The 1-year forward exchange rate = $ 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 $ per CX  CX 166,210 x $ = $ 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: $ 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

8. 1-year forward exchange rate must be $ 0.6438
Receive  $ 108,037
Repay  $107,000
IF, forward exchange rate
> $ : U.S. investors – selling CX forward & buying $ forward
< $ : Investors in country X – selling $ forward & buying CX forward
Conclusion:
1-year forward exchange rate must be $
Otherwise  Arbitrage opportunities
Arbitrage Profit: $ 1,037

9. 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

10. 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 = $
F = $
iA = 0.07
iB = 0.09
$ 100,000(1+0.07) = ($ 100,000 / $ )(1+0.09)($ )
$ 107,000 = $ 107,005
IRP formula: I(1+ iA) = (I/S)(1+ iB)/F
F = S
1+ iA
1 + iB

11. 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

12. Thank you!!