FIN 40500: International
Finance
Hedging Foreign Exchange Risk
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 $185,000 for the goods (with
certainty)
Suppose you have the following forecast for the percentage change in the
British pound over the upcoming 90 days
pr
% Change in e ($/GBP)
Mean: -1.6%
Std. Dev: 2%
[ -3.6% , 0.4%]
[ -5.6% ,2.4%]
[ -7.6%, 4.4%]
%e
-1.6%
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%
Money Market
Hedges
Spot Rate = $1.88
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
Collect GBP 100,000 to pay for
imports
Pay of loan + interest = $185,000
$1.88 = $183,236 (1.01) = $185,000
Present Value of 100,000 in 90 days
Money Market
Forward/Futures
VS.
Hedges
Hedge
Recall Covered Interest Parity


F
*
  1  i  (1  i )
e
If covered interest parity holds (and it does!), then the forward rate
reflects the interest differential and the money market hedge is
identical to the forward/future hedge!
Currency Options

With options, you have the right to buy/sell currency, but not the
requirement
 Call: The right to buy at a specific “strike price”
Put: The right to sell at a specific “strike price”
The option belongs to the buyer of the contract. If you sell a put,
you are REQUIRED to buy if the holder of the put chooses to
exercise the option.
The buyer must pay an up front price for the contract



Payout from a Call

0.15

0.1

1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
0
1
0.05
0.95
Profit per Euro
0.2
Exchange Rate ($/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 Probability
Rate
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!
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
Lend
Domestically/Borro
w Abroad
Put
Option
Receivables Short Position
(Cash
Inflow)
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
Cost = $0.06/L
e ($/L)
Value
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
Let Put Expire
Buy $ in Spot Market
Buy GPB with Call
Sell GBP in Spot Market
NCF = - L100,000, e > $1.85
Let Put Expire
Use Call to Buy GBP
NCF = L100,000, e < $1.85
Let Call Expire
Use Put to sell GBP
NCF = - L100,000, e < $1.85
Let Call Expire
Buy GBP in Spot Market
Sell GBP with Put
Value
Value
Cost = $0.04/L
1.89
e ($/L)
Value
Straddles hedge your
exposure under all
circumstances, but
are very expensive
(in this case, $12,000
in premium costs)
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 = $0.08/L
1.85
e ($/L)
Value
Cost = $0.05/L
1.89
e ($/L)
You could hedge the range from $1.85 to $1.89 by selling a call
w/ a strike price of $1.89 and using the proceeds to buy a call
with a strike price of $1.85
Value
1.85
Value
Value
Cost = $0.08/L
e ($/L)
Cost = $0.08 - $0.05 = $0.03
e ($/L)
1.85 1.89
Cost = $0.05/L
1.89
e ($/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!!
Transaction Exposure vs. Economic Exposure
Profits = e (Price – Unit Costs) Q
Economic exposure refers to changes in the $
value of costs/revenues due to changes in
demand (caused by exchange rate movements)
Transaction exposure refers to changes in the
$ value of costs/revenues due to exchange rate
movements
Example: Suppose that Pepsi has subsidiaries in
both the US and Canada. Below is Pepsi’s income
statement.
Sales
US
Canadian
Total
$300
C$4 * .75 = $3
$303
Costs of Goods Sold
US
Canadian
Total
$50
C$200 * .75 = $150
$200
Operating Expenses
US: Fixed
US: Variable
Total
EBIT
$30
$30
$60
$43
Canadian sales and costs
are unaffected by exchange
rate movements, but are
subject to transaction
exposure
US costs are independent
of the Exchange rate, but
US sales rise when the
Canadian dollar
strengthens (Canadian
goods become more
expensive)
If the Canadian Dollar Strengthens, both Costs and Sales are
Affected.
1 CD = $.75
1 CD = $.80
Sales
US
Canadian
Total
Sales
$300
C$4 * .75 = $3
$303
Costs of Goods Sold
US
Canadian
Total
EBIT
$310
C$4 *. 80 = $3.20
$313.20
Costs of Goods Sold
$50
C$200 * .75 = $150
$200
Operating Expenses
US: Fixed
US: Variable
Total
US
Canadian
Total
US
Canadian
Total
$55
C$200 * . 80 = $160
$215
Operating Expenses
$30
$30
US: Fixed
US: Variable
$60
$43
$30
$33
$63
EBIT
$35.20
Example: Suppose that Pepsi has subsidiaries in both the
US and Canada. Below is Pepsi’s income statement.
Sales
US
Canadian
Total
$300
C$4 * .75 = $3
$303
Costs of Goods Sold
US
Canadian
Total
$50
C$200 * .75 = $150
$200
Operating Expenses
US: Fixed
US: Variable
Total
EBIT
$30
$30
$60
$43
If Pepsi could
raise its Canadian
Sales and lower
its Canadian
costs, it would be
better insulated
from exchange
rate changes
Increasing Canadian sales and lowering Canadian
costs lowers exposure
1 CD = $.75
1 CD = $.80
Sales
US
Canadian
Total
Sales
$300
C$20 * .75 = $15
$315
Costs of Goods Sold
US
Canadian
Total
EBIT
$310
C$20 *. 80 = $16
$326
Costs of Goods Sold
$140
C$100 * .75 = $75
$215
Operating Expenses
US: Fixed
US: Variable
Total
US
Canadian
Total
US
Canadian
Total
$145
C$100 * . 80 = $80
$225
Operating Expenses
$30
$30
US: Fixed
US: Variable
$60
$40
$30
$33
$63
EBIT
$38
Increasing Canadian sales and lowering
Canadian costs lowers exposure
EBIT
Old Structure
New Structure
$43
$40
$38
$35.20
E $/CD
.75
.80
Searching for economic exposure
Economic exposure is much more general than
transaction exposure (it can come from many
sources). Therefore, it can be much more
difficult to find!
Exchange rates change market competition
Exchange rates are correlated with
Macroeconomic conditions
Exchange rates change the value of foreign
currency cash flows (transaction exposure)
Changes in currency prices can have all kinds of economic
impacts. A general way to estimate economic exposure would be
as follows:
PCFt  a  bet   t
Percentage change in cash
flows (measured in home
currency)
Percentage change in the
exchange rate ($/F)
Regression Results
Variable
Coefficients
Intercept
% Change in
Exchange Rate
Regression Statistics
R Squared
Standard Error
Observations
.63
Standard Error
t Stat
.05
1.5
.03
-3.35
.97
-3.45
PCFt  a  bet  
1.20
1,000
Every 1% depreciation in the dollar relative to the British
pound lowers cash flows from England by 3.35%
Suppose you have three different facilities …
Plant C
Plant A
Overall, your cash flows
are negatively related to
the value of the Euro
Plant B
You first run a regression using consolidated income statements
Regression Results
Variable
Coefficients
Standard Error
t Stat
Intercept
.001
2
.0005
% Change in e
($/Euro)
-4.35
.5
-8.70
Now, try isolating the exact location …
Plant C
Plant A
Aha!!! Plant B is the
culprit! (And they
would’ve gotten away
with it if it weren’t for
those meddling kids!!!)
Plant B
Now, run a regression using individual plant income statements
Regression Results
Variable
Coefficient
T-Stat
Plant A
Plant B
Plant C
1.50
-4.6
-.4
1.2
-6.50
-1.5
Now, try isolating the specific income statement items …
Sales
Costs of Goods Sold
Plant B
Operating Expenses
Ultimately, it looks like
sales from plant B are the
underlying currency
problem
Now, run a regression using individual plant income statements
Regression Results
Variable
Sales
Cost of
Goods
Expenses
Coefficient
-3.67
-2.23
0.02
T-Stat
-5.59
-.65
4.0
Now, what do we do about it?
Pricing Policy: If sales drop when the Euro
appreciates, then consider lowering prices
during strong Euro periods to maintain
market share
Cash flow matching: If sales (and hence,
cash inflows) are dropping during periods
with a weak dollar, try adjusting production
locations so that your costs will drop at the
same time.
Futures, Forwards, and Options