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Management of Transaction ExposureChapter Eight

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Chapter Outline• Forward Market Hedge• Money Market Hedge• Options Market Hedge• Cross-Hedging Minor Currency Exposure• Hedging Contingent Exposure• Hedging Recurrent Exposure with Swap Contracts• Hedging Through Invoice Currency• Hedging via Lead and Lag• Exposure Netting• Should the Firm Hedge?• What Risk Management Products Do Firms Use?

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Forward Market Hedge: Imports• If you expect to owe foreign currency in the future, you can hedge by

agreeing today to buy the foreign currency in the future at a set price by entering into a long position in a forward contract.

Forward Contract 

Counterparty

Importer

Foreign Supplier

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Forward Market Hedge: Exports• If you are going to receive foreign currency in the future, agree to

sell the foreign currency in the future at a set price by entering into short position in a forward contract.

Forward Contract 

Counterparty

Exporter

Foreign Customer

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Forward Contract 

Counterparty

U.S. Importer

Italian Supplier

A U.S.-based importer of Italian shoes has just ordered next year’s inventory. Payment of €100M is due in one year. If the importer buys €100M at the forward exchange rate of $1.150/€, the cash flows at maturity look like this:

Importer’s Forward Market Hedge

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Exporter’s Futures Market Cross-Currency Hedge

U.S. $ Equivalent Bid Ask

Pound $1.1990 $1.2000 1 Month Forward $1.2290 $1.2300

3 Months Forward $1.2690 $1.2700 6 Months Forward $1.3190 $1.2800

12 Months Forward $1.3590 $1.3600 Euro $1.0500 $1.1250

1 Month Forward $0.9500 $1.1260 3 Months Forward $0.8500 $1.1270 6 Months Forward $0.8000 $1.1280

12 Months Forward $0.7500 $1.1290

Your firm is a U.K.-based exporter of bicycles. You have sold €2,500,000 worth of bicycles to an Italian retailer. Payment (in euros) is due in six months. Your firm wants to hedge the receivable into pounds.

Sizes of forwards on this exchange are £62,500 and €125,000.

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1. The exporter has to convert the €2,500,000 receivable first into dollars and then into pounds.

2. If we sell the €2,500,000 receivable forward at the six-month forward bid rate of $0.80/€, we can do this with a SHORT position in 20 six-month euro futures contracts.

20 contracts = €2,500,000€125,000/contract

3. Selling the €2,500,000 forward at the six-month forward bid rate of $0.8000/€ generates $2,000,000:

$2,000,000 = €2,500,000 × €1$0.800

4. At the six-month forward ask rate of $1.280/£, $2,000,000 will buy £1,562,500. We can secure this trade with a LONG position in 25 six-month pound futures contracts:

25 contracts = £1,562,500

£62,500/contract

Futures Market Cross-Currency Hedge: # contracts

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Exporter’s Futures Market Cross-Currency Hedge: Cash Flows at Maturity

Exporter Customer€2,500,000

€2,500,000 $2,000,000

Short position in 20 six-month euro futures on

€125,000at $0.8000/€1

Long position in 25 six-

month pound futures on £62,500 at $1.2800/£1

Bicycles

$2,000,000

£1,562,500

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Importer’s Money Market Hedge• This is the same idea as covered interest

arbitrage.• To hedge a foreign currency payable, buy the

present value of that foreign currency payable today and put it in the bank at interest.– Buy the present value of the foreign currency payable

today at the spot exchange rate.– Invest that amount at the foreign rate.– At maturity your investment will have grown enough

to cover your foreign currency payable.

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Importer’s Money Market HedgeA U.S.–based importer of British bicycles owes £100,000 to an Italian supplier in one year.– The spot exchange rate is $1.50 = £1.00.– The one-year interest rate in the U.K. is i£ = 4%.– The importer can hedge this payable by buying

and investing £96,153.85 at 4% in Italy for one year. At maturity, he will have £ 100,000 = £96,153.85 × (1.04).

$1.50£1.00Dollar cost today = $144,230.77 = £96,153.85 ×

£100,0001.04£96,153.85 =

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Importer’s Money Market Hedge• With this money market hedge, we have redenominated

a one-year £100,000 payable into a $144,230.77 payable due today.

• If the U.S. interest rate is i$ = 3%, we could borrow the $144,230.77 today and owe $148,557.69 in one year.

$148,557.69 = $144,230.77 × (1.03)

$148,557.69 =£100,000(1+ i£)T

(1+ i$)T×S0($/£)×

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$144,230.77

Importer’s Money Market Hedge: Cash Flows Now & at Maturity

Importer

Supplier

Spot Foreign Exchange

Market $144,230.77

£96,153.85

U.S Bank

$148

,557

.69

Brit Bank

£100,000 T= 1 cash

flows

deposit i£ = 4%

£96,153.85

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$119,047.62

Exporter’s Money Market HedgeExporter

Customer

Spot Foreign Exchange

Market $119,047.62

€95,238.10

U.S Bank$1

27,5

00.0

0

CréditAgricole

€100,000

T= 1 cash

flows

deposit i$ = 7.10%

€95,238.10Borrow i€ = 5%

An American exporter has just sold €100,000 worth of shoes to a French customer. Payment is due in one year.Interest rates in dollars are 7.10 percent in the U.S. and 5 percent in the euro zone.The spot exchange rate is $1.25/€1.00. Use a money market hedge to eliminate the exporter’s exchange rate risk.

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Importer’s Money Market Cross-Currency Hedge

Your firm is a U.K.-based importer of bicycles. You have bought €750,000 worth of bicycles from an Italian firm. Payment (in euros) is due in one year. Your firm wants to hedge the payable into pounds.

– Spot exchange rates are $2/£ and $1.55/€– The interest rates are 3% in €, 6% in $ and 4% in

£, all quoted as an APR. What should you do to redenominate this 1-year €-denominated payable into a £-denominated payable with a 1-year maturity?

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• Sell pounds for dollars at spot exchange rate, buy euro at spot exchange rate with the dollars, invest in the euro zone for one year at i€ = 3%, all such that the future value of the investment equals €750,000. Using the numbers we have:

– Step 1: Borrow £564,320.39 at i£ = 4%.– Step 2: Sell pounds for dollars, receive $1,128,640.78.– Step 3: Buy euro with the dollars, receive €728,155.34.– Step 4: Invest in the euro zone for 12 months at 3% APR (the

future value of the investment equals €750,000).– Step 5: Repay your borrowing with £586,893.20.

(see next slide for where the numbers come from)

Importer’s Money Market Cross-Currency Hedge

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Where Do the Numbers Come From?

£586,893.20 = £564,320.39 × (1.04)

€728,155.34 =€750,000

(1.03)

= $1,128,640.78 = €728,155.34 × €1$1.55

£564,320.39 = $1,128,640.78 × $2£1

The present value of the euro payable =

The dollar cost of buying the present value of the

euro payable today

Cost today in pounds of the present dollar value of the

euro payable

FV in pounds of the cost in pounds of being able to pay

the supplier €750,0008-16

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Importer’s Money Market Cross-Currency Hedge: Cash Flows Now and at Maturity

Importer

Supplier

Spot Foreign Exchange

Market

£564,320.39

$1,128,640.77

Spot Foreign Exchange

Market

$1,128,640.77 €728,155.34

€728,155.34 deposit i€ = 3%

U.K Bank£564,320.39 £5

86,8

93.2

0

Italia Bank

€750,000 T= 1 cash

flows

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Options• A motivated financial engineer can create

almost any risk-return profile that a company might wish to consider.

• An important consideration when using options is the hedge ratio that we covered in the last chapter.

• Without due consideration of the hedge ratio, the careless use of options can undo attempts at hedging.

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Using Options to Hedge: Exports• A British exporter who is owed €100,000 in one period has

many choices:– Buy call options on the pound with a strike in dollars while

also buying put options on the euro with a strike in dollars.– Buy call options on the pound with a strike in euros.– Buy put options on the euro with a strike in pounds.

• For any options market hedge, the exporter should consider the hedge ratio to know how many options are needed.

• To see why, let’s consider some at-the-money currency options.

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Using Options to Hedge: Exports• Consider an at-the-money put option on €10,000 with a strike

price in pounds sterling.• The current spot exchange rate is S0(£/€) = £0.80/€ and • Interest rates in pounds and euro are i£ = 15½% and i€ = 5%. • In the next year, suppose that there are two possibilities:

– S1u(£/€) = £1.00/€ or– S1d(£/€) = £0.75/€

• Recall our work in Chapter 7, option valuation with risk neutral probabilities.

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Options Market Cross-Currency Hedge:review of option valuation

Step One: Draw the tree diagram £10,000 = €10,000 × £1.00/€

£7,500 == €10,000 × £0.75/€

€10,000 × £0.80/€ = £8,000

p1u = £0

p1d = £500

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= payoff from ability to sell €10,000 for £8,000 when €10,000 is worth £10,000

= payoff from ability to sell €10,000 for £8,000 when€10,000 is worth £7,500

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Options Market Cross-Currency Hedgereview of option valuation

Step 2: Calculate the risk neutral probability, q.We solve for q by setting the expected value of the underlying currency at expiry equal to today’s forward price.

𝑞Step 3: Find the value today of the option

Calculated as the present value of the expected value of the option payoffs, computed using the risk neutral probabilities and the right discount rate.

𝑝 𝑞 𝑝 1 𝑞 𝑝1 𝑟

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Options Market Cross-Currency Hedgereview of option valuation

The current exchange rate is S0(£/€) = £0.80/€, interest rates are i£ = 15½% and i€ = 5% we can find the forward price as

𝐹 £/€ 𝑆 £/€ ££

£ .€1.00

.. £0.8800/€

We can solve for the risk‐neutral probability, q, as 

𝑞 £0.8800/€   £0.7500/€£1.00/€   £0.7500/€ 0.52The price of the put option using risk neutral valuation is

𝑝 𝑞 𝑝 1 𝑞 𝑝1 𝑟0.52 £0 0.48 £500

1.155 £207.79

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Options Market Cross-Currency HedgeAt first it seems logical that a British exporter with a €100,000 receivable should buy 10 put options on €10,000—but that doesn’t work well.The hedge ratio of this option is − 1/5

£10,000 = €10,000 × £1.00/€

£7,500 = €10,000 × £0.75/€

€10,000 × £0.80/€ = £8,000

p1u = £0

p1d = £500

With a hedge ratio of –0.20 our exporter would actually be better hedged with a long position in 50PHLX puts.

p0 = £207.79

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𝐻 𝑝 𝑝𝑆 𝑆£0 £500

£10,000 £7,500 0.20

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Option Dealer

£80,000PutBuyingExporter €100,000

Option Dealer

T = 1 Spot MarketSell €100,000£100,000

€100,000

PutBuying Exporter S1(£/€) = £1.00/€.

S1(£/€) = £0.75/€K0(£/€) = £0.80/€

Out‐of‐the‐Money:S1(£/€) = £1.00/€K0(£/€) = £0.80/€

10 Puts on €10,000 (Strike £8,000) is Not a Hedge

10×p0 = £2,077.92

customer Notice that our exporter doesn’t have a hedge when he buys 10 put options.

The future value of the receivable net of the cost of 10 options is either

£97,600 = £100,000 − £2,077.92 × 1.155or £77,600 = £80,000 − £2,077.92 × 1.155

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Option Dealer

£400,000PutBuyingExporter €500,000

Option Dealer

T = 1 Spot MarketSell €100,000£100,000

€100,000

PutBuying Exporter S1(£/€) = £1.00/€.

In‐the‐Money PutsS1(£/€) = £0.75/€K0(£/€) = £0.80/€

Out‐of‐the‐Money:S1(£/€) = £1.00/€K0(£/€) = £0.80/€

Long 50 Puts = Perfect Hedge

customer

The future value of the receivable net of the cost of 50 puts is

£88,000 = £100,000 − £10,389.61 × 1.155 or £88,000 = £400,000 − £10,389.61 × 1.155 − £300,000

T = 1 Spot MarketBuy €400,000S1(£/€) = £0.75/€.

50 × p0 = £10,389.61

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Options Hedges and Money Market Hedges and Forward Market Hedges

• The next two slides show that the hedge of buying 50 puts has the exact same payoffs as a forward market hedge and a money market hedge.

• Recall the story: A British exporter is owed €100,000 in one period.

• S0(£/€) = £0.80/€, S0($/€) = $2.00/€, S0($/£) = $2.50/£– i£ = 15½% and i€ = 5% – In the next year, there are two possibilities:

• S1(£/€) = £1.00/€ or• S1(£/€) = £0.75/€

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Money Market Cross-Currency Hedge

Exporter

Customer

Spot Foreign Exchange

Market

$95,238.10

£76,190.48

Spot Foreign Exchange

Market

€95,238.10

$95,238.10€95,238.10

U.K Bank

£76,

190.

48£8

8,00

0

Italia Bank

€100,000 T= 1 cash

flows

S0(£/€) = £0.80/€ i£ = 15½% i€ = 5%

Perfect hedge whether S1u(£/€) = £1.00/€ or S1d(£/€) = £0.75/€.Borrow PV of €100,000 at i€ = 5%

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Forward Market Cross-Currency HedgeA U.K.-based exporter sold a €100,000 order to an Italian retailer. Payment is due in 1 year and the exporter used a forward hedge.

Exporter Customer€100,000

€100,000 $104,761.90

Euro Forward Contract

Counterparty

PoundForward Contract

Counterparty

Goods

$104,761.90

£88,000

Perfect hedge whether S1u(£/€) = £1.00/€ or S1d(£/€) = £0.75/€.

S0(£/€) = £0.80/€, S0($/€) = $1.00/€, S0($/£) = $1.25/£i£ = 15½% i€ = 5% i$ = 10%

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𝐹 $/€ $1.00 1 .10€1.00 1 .05$1.0476

€1.00

𝐹 $/£ $1.25 1 .10£1.00 1 .155$11905£1.00

𝐹 £/€ £0.80 1 .1550€1.00 1 .05£0.8800€1.00

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Call-Buying Importer Consider a British importer who owes €100,000 in one year.The importer can use a money market or forward market hedge to redenominate this into a £88,000 liability.He could also use OTC call options on the euro with a pound strike.

£10,000

£7,500

£8,000

c1u = £2,000

c1d = £0

c0 = £900.43

With a hedge ratio of .80 our importer can hedge with a long position in 1 OTC call on €125,000.

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𝐻 𝑐 𝑐𝑆 𝑆£2,000 £0

£10,000 £7,500 0.80

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Option Dealer

£100,000CallBuyingImporter €125,000

Option Dealer

£75,000€100,000

Call Buying Importer S1(£/€) = £0.75/€.

In‐the‐Money Calls:S1(£/€) = £1.00/€K0(£/€) = £0.80/€

Out‐of‐the‐Money:S1(£/€) = £0.75/€K0(£/€) = £0.80/€

1 Call on €125,000 = Perfect Import Hedge

Supplier

The future value of the receivable net of the cost of the call is £88,000 = £75,000 + £13,000 or £88,000 = £100,000 + £13,000 − £25,000

T = 1 Spot MarketSell €25,000

S1(£/€) = £1.00/€.

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T = 1 Spot MarketBuy €100,000

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Cross-Hedging Minor Currency Exposure• The major world currencies are the U.S. dollar,

Canadian dollar, British pound, euro, Swiss franc, Mexican peso, and Japanese yen.

• Everything else is a minor currency (for example, the Swedish krona).

• It is difficult, expensive, and sometimes even impossible to use financial contracts to hedge exposure to minor currencies.

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• Cross-hedging involves hedging a position in one asset by taking a position in another asset.

• The effectiveness of cross-hedging depends upon how well the assets are correlated.– An example would be a U.S. importer with liabilities in

Swedish krona hedging with long or short forward contracts on the euro. If the krona is expensive when the euro is expensive, or even if the krona is cheap when the euro is expensive, it can be a good hedge. But they need to co-vary in a predictable way.

Cross-Hedging Minor Currency Exposure

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Hedging Recurrent Exposure with Swaps

• Recall that swap contracts can be viewed as a portfolio of forward contracts.

• Firms that have recurrent exposure can usually hedge their exchange risk at a lower cost with swaps than with a program of hedging each exposure as it comes along.

• It is also the case that swaps are available in longer-terms than futures and forwards.

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Exposure Netting• A multinational firm should not consider deals in isolation, but should

focus on hedging the firm as a portfolio of currency positions.• Once the residual exposure is determined, we hedge that.• Multilateral netting is an efficient and cost-effective mechanism for

settling interaffiliate foreign exchange transactions and thus determining the firm’s residual exposure.

• In the following slides, a firm faces the following exchange rates:

£1.00 = $2.00€1.00 = $1.50

SFr 1.00 = $0.90

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€150

€150

£150

£150

$150

$150

SFr150

SFr1

50

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€150

€150

£150

£150

$150

$150

Exposure Netting

$225

$225

=

=

$135

$135

SFr1

50

SFr150=

=

$300=

$300

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€150

€150

£150

£150

$150

$150

$225

$225

=

=

$135

$135

SFr1

50

SFr150=

=

$300=

$300

Exposure Netting

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$225

$225

$300

$300

$150

$150

$135

$135

$15

$75

$75

$165

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Exposure Netting: How to Double Check Your Answer

• It’s always good practice to check your work.• It’s better for you to find your mistakes than for

your professor to (or your boss!).• You can check your work in exposure netting by

adding up each subsidiary’s debits and credits.• When you’re done, check that you haven’t

destroyed or “created” any money.• A new example follows for practice checking

answers.8-40

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$125

$125

$155

$155

$100

$100

$80

$80

–$240

$100+$125+$155

$140

–$465

$80+$100+$125

–$160–$375

$100+$80

+$155

–$40

–$300

$125+$80

+$155

$60

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$25

$30

$75

$20 +$75

$20+$45

$140

–$30–$75–$55

–$160–$25

+$30–$45

–$40

$25+$55–$20$60

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$100

+$40$100

$140

–$60–$100

–$160–$40

$60

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8-44

$140

$140

–$20–$140

–$160–$40

$60

$40

Alternative Solution

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Netting with Central DepositorySome firms use a central depository as a cash pool to facilitate funds mobilization and reduce the chance of misallocated funds.

Central depository

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Other Hedging Strategies• Hedging through invoice currency.

– The firm can shift, share, or diversify:• Shift exchange rate risk by invoicing foreign sales in home currency• Share exchange rate risk by pro-rating the currency of the invoice

between foreign and home currencies• Diversify exchange rate risk by using a market basket index

• Hedging via lead and lag.– If a currency is appreciating, pay those bills denominated in that

currency early; let customers in that country pay late as long as they are paying in that currency.

– If a currency is depreciating, give incentives to customers who owe you in that currency to pay early; pay your obligations denominated in that currency as late as your contracts will allow.

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8-47

Should the Firm Hedge?• Not everyone agrees that a firm should

hedge.– Hedging by the firm may not add to

shareholder wealth if the shareholders can manage exposure themselves.

– Hedging may not reduce the non-diversifiable risk of the firm. Therefore, shareholders who hold a diversified portfolio are not benefitted when management hedges.

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What Risk Management Products do Firms Use?

• Most U.S. firms meet their exchange risk management needs with forward, swap, and options contracts.

• The greater the degree of international involvement, the greater the firm’s use of foreign exchange risk management.

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EXHIBIT 8.11A Survey of Knowledge and Use of Foreign Exchange Risk Management Products by U.S. Firms

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Summary• The firm is subject to a transaction exposure when it faces

contractual cash flows denominated in foreign currencies.• Transaction exposure can be hedged by financial contracts

like forward, money market, and options contracts, as well as by such operational techniques as the choice of invoice currency, lead/lag strategy, and exposure netting.

• If the firm has a foreign-currency-denominated receivable (payable), it can hedge the exposure by selling (buying) the foreign currency receivable (payable) forward. – The firm can expect to eliminate the exposure without incurring costs

as long as the forward exchange rate is an unbiased predictor of the future spot rate.

– The firm can achieve equivalent hedging results by lending and borrowing in the domestic and foreign money markets.

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Summary (continued)• currency options provide flexible hedges against

exchange exposure. With the options hedge, the firm can limit the downside risk while preserving the upside potential. – Currency options also provide the firm with an effective hedge

against contingent exposure.• The firm can shift, share, and diversify exchange

exposure by appropriately choosing the invoice currency. • The firm can reduce transaction exposure by leading

and lagging foreign currency receipts and payments, especially among its own affiliates.

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8-52

Summary (concluded)• When a firm has a portfolio of foreign currency positions,

it makes sense only to hedge the residual exposure rather than hedging each currency position separately. The reinvoice center can help implement the portfolio approach to exposure management.

• In a perfect capital market where stockholders can hedge exchange exposure as well as the firm, it is difficult to justify exposure management at the corporatelevel. In reality, capital markets are far from perfect, and the firm often has advantages over the stockholders in implementing hedging strategies. There thus existsroom for corporate exposure management to contribute to the firm’s value. 8-52

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