Hedging Transaction
Exposure
Forward Contracts


Forward contracts are purchases/sales of
currencies to be delivered at a specific
forward date (30,90,180, or 360 days)
Example
CAD/USD
1 month
3 months
6 months
12 months
.7641
.7583
.7563
.7537
.7525
Forward contracts are individualized agreements
between the bank and the customer
Futures Contracts

Forward contracts are written on an individual basis.
Futures are standardized, traded commodities
(Chicago Mercantile Exchange)
 JPY: 12,500,000 Yen
 GBP: 62,500 Pounds
 Euro: 125,000 Euro
 CAD: 100,000 Canadian Dollars
To hedge or not to hedge….that is the
question”
Suppose that you have signed an agreement to purchase
GBP 100,000 worth of goods from England payable 90
days from now.
Spot Rate: $1.88
90 Day Forward: $1.85 (-1.6%)
If you were to “lock in” your price with the forward/futures
contract, you would pay $185,000 for the goods (with
certainty)
Suppose you have the following forecast for the
percentage change in the British pound over the
upcoming 90 days
e
% Change in e ($/GBP)
Mean: -1.6%
Std. Dev: 2%
-1.6%
[ -3.6% , 0.4%]
[ -5.6% ,2.4%]
[ -7.6%, 4.4%]
%Change
Given a standard deviation, we can
approximate a distribution for the exchange
rate in 90 days.
Current Spot Rate: $1.88
Standard
Deviations
Percentage
Change
Exchange Rate
Probability
-3
-7.6
$1.74
1%
-2
-5.6
$1.77
4%
-1
-3.6
$1.81
25%
0
-1.6
$1.85
40%
1
.4%
$1.89
25%
2
2.4%
$1.93
4%
3
4.4%
$1.96
1%
Given the distribution of exchange rates, we can
estimate the expected cost of the hedge
Current Spot Rate: $1.88
Exchange
Rate
Probability
Cost w/out
hedge
Cost
w/hedge
Value of
Hedge
$1.74
1%
$174,000
$185,000
-$11,000
$1.77
4%
$177,000
$185,000
-$8,000
$1.81
25%
$181,000
$185,000
$-4,000
$1.85
40%
$185,000
$185,000
$0
$1.89
25%
$189,000
$185,000
$4,000
$1.93
4%
$193,000
$185,000
$8,000
$1.96
1%
$196,000
$185,000
$11,000
Expected Value: $0
From the previous table, we can show the
distribution of gains from the hedge
If forward rates are
unbiased, most of the
weight will be at zero!
40
Probability
35
30
25
20
15
10
5
0
($11,000) ($8,000) ($4,000)
$0
$4,000
Hedge Cost
$8,000
$11,000
Money Market Hedges
Suppose that you have signed an agreement to purchase
GBP 100,000 worth of goods from England payable 90
days from now.
Spot Rate = $1.88
British 90 Day Interest Rate = 2.6%
US 90 Day interest rate = 1%
Spot Rate = $1.88
Money Market
Hedges
British 90 Day Interest Rate = 2.6%
US 90 Day interest rate = 1%
Today
90 Days
Borrow $183,236 @ 1% for 90 Days
Convert to GBP @ $1.88
Invest in 90 Day British Asset @ 2.6%
GBP 100,000
1.026
Present Value of
100,000 in 90 days
Collect GBP 100,000 to pay for
imports
Pay of loan + interest = $185,000
$1.88 = $183,236 (1.01) = $185,000
Money Market
VS.
Hedges
Forward/Futures
Hedge
Recall Covered Interest Parity
Forward Rate
(1+i*)F
= (1+i)
e
Spot Rate
If covered interest parity holds (and it does!), then the forward rate
reflects the interest differential and the money market hedge is
identical to the forward/future hedge!
Currency Options



With options, you have the right to buy/sell currency,
but not the requirement
 Call: The right to buy at a specific “strike price”
 Put: The right to sell at a specific “strike price”
The option belongs to the buyer of the contract. If
you sell a put, you are REQUIRED to buy if the holder
of the put chooses to exercise the option.
The buyer must pay an up front price for the contract
Payout from a Call

0.15

0.1
0.05
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0

0.95
Profit per Euro
0.2
Exchange Rate ($/E)
Suppose you buy a 30 day
call on 125,000 Euros at a
strike price of $1.20
For spot rates less than
$1.20, the option is
worthless (“out of the
money”)
If the spot rate is $1.25,
your profit is
($.05)*($125,000) = $6,250
Payout from a Put
0.2
0.15
0.1
0.05
1.35
1.25
0
1.15

0.25
1.05

Suppose you buy a put on
125,000 Euros at a strike
price of $1.20
For spot rates greater than
$1.20, the option is
worthless (“out of the
money”)
For example, if the spot rate
is $1.15, your profit is
($.05)*($125,000) = $6,250
0.95

Hedging with Options
Suppose that you have signed an agreement to purchase
GBP 100,000 worth of goods from England payable 90
days from now.
Spot Rate: $1.88
3 Month Call w/strike price of $1.85 is selling at a
premium of $.05 (GBP 100,000)
You pay $.05(100,000) = $5,000 today. Your cost of GBP
in 90 days = MIN [ spot rate, $1.85]
Remember, you pay (.05)*100,000 = $5,000
Today!
Current Spot Rate: $1.88
Exchange
Rate
Probability
Cost w/out Cost
hedge
w/hedge
Value of
Hedge
$1.74
1%
$174,000
$179,000
-$5,000
$1.77
4%
$177,000
$182,000
-$5,000
$1.81
25%
$181,000
$186,000
-$5,000
$1.85
40%
$185,000
$190,000
-$5,000
$1.89
25%
$189,000
$190,000
$1,000
$1.93
4%
$193,000
$190,000
$3,000
$1.96
1%
$196,000
$190,000
$6,000
Expected Value: -$3,070
The option hedge is more
expensive on average, but
protects you from large
negative outcomes!
Option Hedge
70
Probability
60
50
40
30
20
10
0
($5,000)
$1,000
$3,000
Hedge Value
$6,000
Hedging Techniques
Type of
Exposure
Forward/Futures Money Market
Options
Payables
(Cash
Outflow)
Long Position
Borrow
Domestically/Lend
Abroad
Call
Option
Receivables
(Cash
Inflow)
Short Position
Lend
Domestically/Borrow
Abroad
Put
Option
Cross Hedging
Suppose that you have entered an agreement to
buy PLN 100,000 (Polish Zloty) worth of
imports. ($1 = 3.17PLN). Zloty futures are not
traded. What do you do?
You notice that the Zloty is highly correlated
with the Euro (E 1 = 4.09 PLN)
Act as if you are hedging (100,000/4.09) = E 24,454
Some more advanced hedging
strategies…
Suppose that you have signed an agreement to purchase
GBP 100,000 worth of goods from England payable 90
days from now. You are in the process of negotiating a
deal to sell GBP 200,000 worth of goods to Britain.
Case #1: The export deal falls through and you will
need to buy GBP 100,000 in one 90 days
Case #2: The export deal succeeds and you will need
to sell GBP 100,000 in one 90 days
How do you hedge this?
A currency straddle is a combination of a put
(the right to sell) and a call (the right to buy)
Value
Value
Cost = $0.06/L
1.85
e ($/L)
Value
Cost = $0.06/L
1.85
e ($/L)
Cost = $0.12/L(L 100,000) = $12,000
1.85
e ($/L)
Currency Straddles: Four
Possibilities
NCF = L100,000, e > $1.85
NCF = L100,000, e < $1.85
Let Put Expire
Let Call Expire
Buy $ in Spot Market
Use Put to sell GBP
Buy GPB with Call
Sell GBP in Spot Market
NCF = - L100,000, e > $1.85
NCF = - L100,000, e < $1.85
Let Put Expire
Let Call Expire
Use Call to Buy GBP
Buy GBP in Spot Market
Sell GBP with Put
Straddles hedge your exposure under all
circumstances, but are very expensive (in this case,
$12,000 in premium costs)
Value
Value
Cost = $0.04/L
1.89
e ($/L)
Value
Cost = $0.03/L
1.84
e ($/L)
Cost = $0.07/L(L 100,000) = $7,000
Un-hedged
Region
1.84
1.89
e ($/L)
Another way to save money is to only hedge particular
ranges (i.e. a 95% confidence interval!)
Suppose that you have signed an agreement to purchase
GBP 100,000 worth of goods from England payable 90
days from now.
Value
Cost = $0.05/L
1.85
e ($/L)
Value
Cost = $0.08/L
1.89
e ($/L)
You could hedge the range from $1.85 to $1.89 by
selling a call w/ a strike price of $1.85 and using the
proceeds to buy a call with a strike price of $1.89
Value
Value
Cost = $0.05/L
Cost = $0.08/L
e ($/L)
1.85
Value
1.89
Cost = $0.08 - $0.05 = $0.03
e ($/L)
1.85 1.89
e ($/L)
Hedging…the possibilities are
endless!
There are many different types of hedges
available. Each hedge has a cost and a level of
protection. Its your choice to decide what
coverage you need and how much you are willing
to pay for it!!