Hedging Transaction Hedging Transaction ExposureExposure

Forward ContractsForward Contracts Forward contracts are purchases/sales Forward contracts are purchases/sales

of currencies to be delivered at a of currencies to be delivered at a specific forward date (30,90,180, or 360 specific forward date (30,90,180, or 360 days)days)

ExampleExampleCAD/USDCAD/USD .7641.7641

1 month 1 month .7583 .75833 months 3 months .7563.75636 months 6 months .7537.753712 months 12 months .7525.7525

Forward contracts are individualized agreements between the bank and the customer

Futures ContractsFutures Contracts Forward contracts are written on an individual Forward contracts are written on an individual

basis. Futures are standardized, traded basis. Futures are standardized, traded commodities (Chicago Mercantile Exchange)commodities (Chicago Mercantile Exchange) JPY: 12,500,000 YenJPY: 12,500,000 Yen GBP: 62,500 PoundsGBP: 62,500 Pounds Euro: 125,000 EuroEuro: 125,000 Euro CAD: 100,000 Canadian DollarsCAD: 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

% Change in e ($/GBP)

Mean: -1.6%

Std. Dev: 2%

%Change

e

-1.6%

[ -3.6% , 0.4%]

[ -5.6% ,2.4%]

[ -7.6%, 4.4%]

Given a standard deviation, we can approximate a distribution for the exchange rate in 90 days.

Standard Standard DeviationDeviationss

Percentage Percentage ChangeChange

Exchange RateExchange Rate ProbabilityProbability

-3-3 -7.6-7.6 $1.74$1.74 1%1%

-2-2 -5.6-5.6 $1.77$1.77 4%4%

-1-1 -3.6-3.6 $1.81$1.81 25%25%

00 -1.6-1.6 $1.85$1.85 40%40%

11 .4%.4% $1.89$1.89 25%25%

22 2.4%2.4% $1.93$1.93 4%4%

33 4.4%4.4% $1.96$1.96 1%1%

Current Spot Rate: $1.88

Given the distribution of exchange rates, we can estimate the expected cost of the hedge

Exchange Exchange RateRate

ProbabilitProbabilityy

Cost Cost w/out w/out hedgehedge

Cost Cost w/hedgew/hedge

Value of Hedge

$1.74$1.74 1%1% $174,000$174,000 $185,000$185,000 -$11,000

$1.77$1.77 4%4% $177,000$177,000 $185,000$185,000 -$8,000

$1.81$1.81 25%25% $181,000$181,000 $185,000$185,000 $-4,000

$1.85$1.85 40%40% $185,000$185,000 $185,000$185,000 $0

$1.89$1.89 25%25% $189,000$189,000 $185,000$185,000 $4,000

$1.93$1.93 4%4% $193,000$193,000 $185,000$185,000 $8,000

$1.96$1.96 1%1% $196,000$196,000 $185,000$185,000 $11,000

Current Spot Rate: $1.88

Expected Value: $0

From the previous table, we can show the distribution of gains from the hedge

0

5

10

15

20

25

30

35

40

Pro

bability

($11,000) ($8,000) ($4,000) $0 $4,000 $8,000 $11,000

Hedge Cost

If forward rates are unbiased, most of the weight will be at zero!

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

GBP 100,000

1.026

Present Value of 100,000 in 90 days

$1.88 = $183,236 (1.01) = $185,000

Borrow $183,236 @ 1% for 90 Days

Convert to GBP @ $1.88

Invest in 90 Day British Asset @ 2.6%

Collect GBP 100,000 to pay for imports

Pay of loan + interest = $185,000

Money Market Hedges VS.

Forward/Futures Hedge

Recall Covered Interest Parity

ee = (1+i)= (1+i)(1+i*)F(1+i*)F

Forward Rate

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 OptionsCurrency Options With options, you have the right to buy/sell With options, you have the right to buy/sell

currency, but not the requirementcurrency, but not the requirement Call: The right to buy at a specific “strike price”Call: The right to buy at a specific “strike price” Put: The right to sell 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 The option belongs to the buyer of the contract. If you sell a put, you are REQUIRED to buy if the you sell a put, you are REQUIRED to buy if the holder of the put chooses to exercise the option.holder of the put chooses to exercise the option.

The buyer must pay an up front price for the The buyer must pay an up front price for the contract contract

Payout from a CallPayout from a Call

0

0.05

0.1

0.15

0.2

0.9

5 1

1.0

5

1.1

1.1

5

1.2

1.2

5

1.3

1.3

5

1.4

Exchange Rate ($/ E)

Pro

fit per

Euro

Suppose you buy a 30 Suppose you buy a 30 day call on 125,000 day call on 125,000 Euros at a strike price of Euros at a strike price of $1.20$1.20

For spot rates less than For spot rates less than $1.20, the option is $1.20, the option is worthless (“out of the worthless (“out of the money”)money”)

If the spot rate is $1.25, If the spot rate is $1.25, your profit is your profit is

($.05)*($125,000) = ($.05)*($125,000) = $6,250$6,250

Payout from a PutPayout from a Put Suppose you buy a put Suppose you buy a put

on 125,000 Euros at a on 125,000 Euros at a strike price of $1.20strike price of $1.20

For spot rates greater For spot rates greater than $1.20, the option is than $1.20, the option is worthless (“out of the worthless (“out of the money”)money”)

For example, if the spot For example, if the spot rate is $1.15, your profit rate is $1.15, your profit is is

($.05)*($125,000) = ($.05)*($125,000) = $6,250$6,250

0

0.05

0.1

0.15

0.2

0.25

0.9

5

1.0

5

1.1

5

1.2

5

1.3

5

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!

ExchangExchange Ratee Rate

ProbabilitProbabilityy

Cost Cost w/out w/out hedgehedge

Cost Cost w/hedgew/hedge

Value of Hedge

$1.74$1.74 1%1% $174,000$174,000 $179,000$179,000 -$5,000

$1.77$1.77 4%4% $177,000$177,000 $182,000$182,000 -$5,000

$1.81$1.81 25%25% $181,000$181,000 $186,000$186,000 -$5,000

$1.85$1.85 40%40% $185,000$185,000 $190,000$190,000 -$5,000

$1.89$1.89 25%25% $189,000$189,000 $190,000$190,000 $1,000

$1.93$1.93 4%4% $193,000$193,000 $190,000$190,000 $3,000

$1.96$1.96 1%1% $196,000$196,000 $190,000$190,000 $6,000

Current Spot Rate: $1.88

Expected Value: -$3,070

0

10

20

30

40

50

60

70

Pro

bability

($5,000) $1,000 $3,000 $6,000

Hedge Value

Option Hedge The option hedge is more expensive on average, but protects you from large negative outcomes!

Hedging Techniques

Type of Type of ExposureExposure

Forward/Forward/FuturesFutures

Money MarketMoney Market OptionOptionss

Payables Payables (Cash (Cash Outflow)Outflow)

Long PositionLong Position Borrow Borrow Domestically/Lend Domestically/Lend AbroadAbroad

Call Call OptionOption

ReceivableReceivables (Cash s (Cash Inflow)Inflow)

Short PositionShort Position Lend Lend Domestically/Borrow Domestically/Borrow AbroadAbroad

Put Put OptionOption

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)

e ($/L)

Value

1.85 e ($/L)

Value

1.85

e ($/L)

Value

1.85

Cost = $0.06/LCost = $0.06/L

Cost = $0.12/L(L 100,000) = $12,000

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 Call Expire

Use Put to sell GBP

NCF = - L100,000, e > $1.85

Let Put Expire

Use Call to Buy GBP

NCF = - L100,000, e < $1.85

Let Call Expire

Buy GBP in Spot Market

Sell GBP with Put

e ($/L)

Value

1.89 e ($/L)

Value

1.84

e ($/L)

Value

1.84

Cost = $0.03/LCost = $0.04/L

Cost = $0.07/L(L 100,000) = $7,000

Straddles hedge your exposure under all circumstances, but are very expensive (in this case, $12,000 in premium costs)

1.89

Un-hedged Region

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.

e ($/L)

Value

1.85 e ($/L)

Value

1.89

Cost = $0.08/LCost = $0.05/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

e ($/L)

Value

1.85 e ($/L)

Value

1.89

Cost = $0.08/LCost = $0.05/L

Value

1.85

Cost = $0.08 - $0.05 = $0.03

e ($/L)1.89

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!!