Forwards, Futures, and their Forwards, Futures, and their ApplicationsApplications

2

The Oldest Derivative: The Oldest Derivative: Forward ContractsForward Contracts

Forward ContractsForward Contracts – – ObligatesObligates its owner to buy (if its owner to buy (if in a “long” position) or sell (if in a “short” position) a in a “long” position) or sell (if in a “short” position) a given asset on a specified given asset on a specified datedate at a specified at a specified priceprice (the “forward price”) at the (the “forward price”) at the originationorigination of the of the contract.contract.

Two Key Features:Two Key Features: Credit risk is two-sided (i.e., both buyer and seller of the Credit risk is two-sided (i.e., both buyer and seller of the

forward can default on the deal).forward can default on the deal). No money is exchanged until the forward’s maturity date. No money is exchanged until the forward’s maturity date.

The above features The above features increaseincrease default risk and default risk and restrictsrestricts the availability and liquidity of these contracts.the availability and liquidity of these contracts.

3

Futures ContractsFutures Contracts Futures ContractsFutures Contracts – Similar to Forwards. – Similar to Forwards.

ObligatesObligates its owner to buy (if in a “long” position) or its owner to buy (if in a “long” position) or sell (if in a “short” position) a given asset on a sell (if in a “short” position) a given asset on a specified specified datedate at a specified at a specified priceprice (the “futures (the “futures price”) at the price”) at the originationorigination of the contract. of the contract.

Key Features:Key Features: Credit risk is two-sided but is reduced substantially because Credit risk is two-sided but is reduced substantially because

of two mechanisms: of two mechanisms: 1) 1) marking-to-marketmarking-to-market (daily settling up of the account), and (daily settling up of the account), and 2) 2) margin requirementsmargin requirements (i.e., a good-faith deposit). (i.e., a good-faith deposit).

Standardized contractStandardized contract specifies exact details of term, asset, specifies exact details of term, asset, contract size, delivery procedures, place of trading, etc.contract size, delivery procedures, place of trading, etc.

ClearinghouseClearinghouse reduces transaction costs and de-couples reduces transaction costs and de-couples buyer from seller by providing anonymity. buyer from seller by providing anonymity.

4

Forward Contract CharacteristicsForward Contract Characteristics

Forwards can be created on Forwards can be created on allall types of financial types of financial assets (FX, interest rates, commodities, stock assets (FX, interest rates, commodities, stock prices).prices).

Can require Can require physical deliveryphysical delivery or or cash-settledcash-settled.. The expected NPV of an at-market forward is The expected NPV of an at-market forward is

zerozero.. Notional principalNotional principal is used to determine cash flows is used to determine cash flows

but is but is notnot paid/received at maturity. paid/received at maturity. Most liquid within Most liquid within 1-2 year1-2 year maturities. maturities. Most frequently used with Most frequently used with FX transactionsFX transactions by by

larger corporations with international exposures.larger corporations with international exposures.

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Profit Calculations on a Forward Profit Calculations on a Forward ContractContract

Profit on a forward contract is related to the Profit on a forward contract is related to the differencedifference between the between the price of the underlying price of the underlying assetasset at the forward’s maturity (time = T) and the at the forward’s maturity (time = T) and the forward priceforward price (initially specified at the onset of the (initially specified at the onset of the contract at time = 0).contract at time = 0).

ProfitProfit = = L/S IndicatorL/S Indicator * (P * (PTT – P – PFF00) * Number of units) * Number of units

where,where,L/S indicatorL/S indicator = = +1+1 if in a if in a longlong position or position or

-1-1 if in a if in a shortshort position. position. The objective is to use the forward’s profit to The objective is to use the forward’s profit to offsetoffset

any losses in the underlying asset’s position.any losses in the underlying asset’s position.

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Hedging StrategiesHedging Strategies If you are If you are longlong the underlying asset (i.e., the underlying asset (i.e., increasesincreases in in

the asset’s price increase firm value), then you can the asset’s price increase firm value), then you can enter into a forward contract to enter into a forward contract to sellsell (or “short”) the (or “short”) the asset at the forward price. This can asset at the forward price. This can hedgehedge changes in changes in the asset’s price. the asset’s price.

A classic example is a A classic example is a farmerfarmer producingproducing an agricultural an agricultural commodity. He/she is long wheat and is worried about commodity. He/she is long wheat and is worried about price price declinesdeclines so he/she hedges by so he/she hedges by sellingselling wheat in the wheat in the forward market.forward market.

Conversely, if you are Conversely, if you are shortshort the underlying asset, then the underlying asset, then you should you should buybuy (or “go long”) the asset. For example, (or “go long”) the asset. For example, a baker a baker consumesconsumes wheat and is worried about wheat and is worried about increasesincreases in wheat prices. So, should in wheat prices. So, should buybuy wheat at the wheat at the forward price.forward price.

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Principles of Forward PricingPrinciples of Forward Pricing

A cynic: A cynic: “Someone who knows the price of “Someone who knows the price of everything but the value of nothing”.everything but the value of nothing”.

There are There are costscosts and and benefitsbenefits to all derivatives and to all derivatives and underlying assets.underlying assets.

Storage and insurance costsStorage and insurance costs of the underlying of the underlying asset.asset.

Opportunity costsOpportunity costs (forgone interest, missed (forgone interest, missed opportunities).opportunities).

Benefits such as Benefits such as income generationincome generation (e.g., (e.g., dividends on a stock) and having the asset on-dividends on a stock) and having the asset on-hand (e.g., a hand (e.g., a “convenience yield”“convenience yield” for for commodities).commodities).

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Principles of Forward Pricing Principles of Forward Pricing (cont.)(cont.)

Forward PriceForward Price = F = FPP00 = P = P00 + FV(cost of asset ownership) + FV(cost of asset ownership)

– FV(benefits of asset ownership) – FV(benefits of asset ownership) Forward prices must be Forward prices must be arbitrage-freearbitrage-free.. IfIf F FPP

00 >> P P00 + FV(costs) – FV(benefits) + FV(costs) – FV(benefits)then, then,

1.1. SellSell the forward at F the forward at FPP00,,

2.2. BorrowBorrow proceeds equal to P proceeds equal to P00 and and buybuy asset in spot asset in spot market (at Pmarket (at P00),),

3.3. ReceiveReceive income on long position in the asset. income on long position in the asset.4.4. At maturity, you At maturity, you reversereverse your actions to lock in a your actions to lock in a riskless riskless

profitprofit (receive income, pay back loan, and sell asset at (receive income, pay back loan, and sell asset at FFPP

00).).

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Principles of Forward Pricing Principles of Forward Pricing (cont.)(cont.)

IfIf F FPP00 << P P00 + FV(costs) – FV(benefits) + FV(costs) – FV(benefits)

then, then,

1.1. Buy/go longBuy/go long the forward at F the forward at FPP00,,

2.2. BorrowBorrow the asset (and pay any interest on this the asset (and pay any interest on this borrowing),borrowing),

3.3. SellSell the asset immediately in the spot market (at P the asset immediately in the spot market (at P00) ) and and investinvest proceeds equal to P proceeds equal to P00 in riskless asset, in riskless asset,

4.4. At maturity, At maturity, reversereverse your actions to lock in a your actions to lock in a riskless profitriskless profit (recoup investment in riskless asset, (recoup investment in riskless asset, pay for underlying asset at Fpay for underlying asset at FPP

00, and return borrowed , and return borrowed asset with interest).asset with interest).

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FX Risk: Calculate the indirect quotations FX Risk: Calculate the indirect quotations for euros and Swedish kronafor euros and Swedish krona

Euro: Euro: 1 / 0.8000 = 1 / 0.8000 = 1.251.25 Krona:Krona: 1 / 0.1000 = 1 / 0.1000 = 10.0010.00

Direct Quote: U.S. $ per foreign currency

Indirect Quotes: # of

Units of Foreign

Currency per U.S. $

Euro 0.8000 1.25

Swedish krona 0.1000 10.00

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What is a What is a crosscross rate? rate?

A A cross rate cross rate is the exchange rate is the exchange rate between any two currencies between any two currencies notnot involving U.S. dollars.involving U.S. dollars.

In practice, cross rates are usually In practice, cross rates are usually calculated from direct or indirect U.S. calculated from direct or indirect U.S. rates. That is, on the basis of U.S. dollar rates. That is, on the basis of U.S. dollar exchange rates.exchange rates.

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Calculate the two cross ratesCalculate the two cross ratesbetween euros and krona.between euros and krona.

Euros Dollars Dollar Krona

Krona Dollars Dollar Euros

×

×

= 1.25 x 0.1000= 0.125 euros/krona

Cross Rate =

Cross Rate =

= 10.00 x 0.8000= 8.00 krona/euro

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Example of International Example of International TransactionsTransactions

Assume a firm can produce a Assume a firm can produce a liter of orange liter of orange juicejuice in the U.S. and ship it to Spain for in the U.S. and ship it to Spain for $1.75$1.75. .

If the firm wants a If the firm wants a 50%50% markup on the markup on the product, product, what should the juice sell for in what should the juice sell for in Spain?Spain?

Target price = ($1.75)(1.50)=$2.625Target price = ($1.75)(1.50)=$2.625Spanish priceSpanish price = ($2.625)(1.25 euros/$) = ($2.625)(1.25 euros/$)

= = € 3.28€ 3.28

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Example Example (continued)(continued) Now the firm begins producing the orange juice Now the firm begins producing the orange juice

in Spainin Spain. The product costs . The product costs 2.02.0 euros euros to produce to produce and and ship to Swedenship to Sweden, where it can be sold for , where it can be sold for 2020 kronakrona. .

What is the What is the dollar profitdollar profit on the sale? on the sale?

2.0 euros * (8.0 krona/euro) = 2.0 euros * (8.0 krona/euro) = 1616 krona krona20 - 16 = 20 - 16 = 4.04.0 krona profit. krona profit.Dollar profitDollar profit = 4.0 krona * (0.1000 $ per krona) = 4.0 krona * (0.1000 $ per krona)

= = $0.40$0.40

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What is exchange rate risk?What is exchange rate risk?

Exchange rate risk is the risk that the Exchange rate risk is the risk that the value of a cash flow in one currency value of a cash flow in one currency translatedtranslated from another currency will from another currency will declinedecline due to a change in exchange due to a change in exchange rates.rates.

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Currency Appreciation and Currency Appreciation and DepreciationDepreciation

Suppose the exchange rate goes from Suppose the exchange rate goes from 1010 krona per dollar to krona per dollar to 1515 krona per dollar. krona per dollar.

A A dollardollar now buys now buys moremore krona, so the krona, so the dollar is dollar is appreciatingappreciating, or strengthening., or strengthening.

The The kronakrona buys buys lessless dollars, so the krona dollars, so the krona is is depreciatingdepreciating, or weakening., or weakening.

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Affect of Dollar Affect of Dollar AppreciationAppreciation

Suppose the profit in krona remains Suppose the profit in krona remains unchangedunchanged at at 4.04.0 krona, but the krona, but the dollardollar appreciatesappreciates, so the exchange rate is now , so the exchange rate is now 1515 krona/dollar.krona/dollar.

Dollar profitDollar profit = 4.0 krona = 4.0 krona // (15 krona per (15 krona per dollar) = dollar) = $0.267$0.267

StrengtheningStrengthening dollar dollar hurtshurts profits from profits from internationalinternational sales. sales.

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Forward FX rate contractsForward FX rate contracts FX forward contractFX forward contract – agree on an exchange rate – agree on an exchange rate todaytoday to to

exchange one currency (e.g., the Japanese yen) for another exchange one currency (e.g., the Japanese yen) for another currency (e.g., the U.S. dollar) at some time in the currency (e.g., the U.S. dollar) at some time in the futurefuture..

Interest Rate ParityInterest Rate Parity determines the forward FX rate that determines the forward FX rate that makes the E(NPV) = 0.makes the E(NPV) = 0.

Covered Interest ArbitrageCovered Interest Arbitrage ensures that Interest Rate Parity ensures that Interest Rate Parity holds. holds.

Conceptually equivalent to Conceptually equivalent to a pair of zero coupon bondsa pair of zero coupon bonds..

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FX forward rates…FX forward rates…

Forward exchange rate determined by the current spot FX Forward exchange rate determined by the current spot FX rate and the riskless interest rates in the two countries. rate and the riskless interest rates in the two countries.

The interest rate parity relation can be summarized by:The interest rate parity relation can be summarized by:

Where, Where, rr11 = interest rate for the country that has its = interest rate for the country that has its currency in the currency in the denominatordenominator of the FX rate (e.g., U.S. dollar of the FX rate (e.g., U.S. dollar if FX rate is expressed as Yen / dollar).if FX rate is expressed as Yen / dollar).

rr22 = interest rate for country whose currency is in the = interest rate for country whose currency is in the numeratonumeratorr of the FX rate. of the FX rate.

T

T

tPt r

rSF

)1(

)1(

1

2

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Application for Application for 6-month Colon / 6-month Colon / U.S. DollarU.S. Dollar FX forward rate: FX forward rate:

To synthesize the current Colon / Dollar 6-month forward To synthesize the current Colon / Dollar 6-month forward exchange rate, we must use the current spot FX rate and exchange rate, we must use the current spot FX rate and the (near) riskless interest rates of the two countries. the (near) riskless interest rates of the two countries.

This This interest rate parity relationinterest rate parity relation can be summarized by: can be summarized by:

Where, Where, rr11 = the = the U.S. dollarU.S. dollar interest rate because the FX interest rate because the FX rate is expressed as Colones / U.S. Dollar).rate is expressed as Colones / U.S. Dollar).

rr22 = the interest rate in = the interest rate in ColonesColones).).

9.520)0015.1(

)0895.1(4.499

)1(

)1(2/1

2/1

2/11

2/12

02/1

0

r

rSF P

21

Interest Rate Parity and the Interest Rate Parity and the “Box”“Box”

Forward FX rates Forward FX rates can be can be replicatedreplicated by by following the lines around a box that following the lines around a box that links spot rates, forward rates, and links spot rates, forward rates, and interest rates.interest rates.

U.S. $T

U.S. $0 Colones0

ColonesT

ForwardT

Spot0

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Application of how to Application of how to synthesizesynthesize a a ShortShort Colon / Dollar Forward Colon / Dollar Forward FX RateFX Rate

A A ShortShort ColonesColones position can be position can be synthesizedsynthesized by: 1) by: 1) borrowing in borrowing in ColonesColones at 8.95% for 6 months, 2) at 8.95% for 6 months, 2) investing in U.S. Dollarsinvesting in U.S. Dollars at 0.15% for 6 at 0.15% for 6 months at the Spot FX rate of 499.4.months at the Spot FX rate of 499.4.U.S. $T

U.S. $0 Colones0

ColonesTForwardT=520.9

Spot0=499.4

-1.08951/2+1.00151/2

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Forward Interest Rates (FRAs)Forward Interest Rates (FRAs)

Forward Interest Rate AgreementForward Interest Rate Agreement – agree on an – agree on an interest rate interest rate todaytoday to receive (or pay) at some time in to receive (or pay) at some time in the the futurefuture..

Forward Interest RatesForward Interest Rates are are implicitimplicit in in spotspot yield yield curves.curves.

This is due to a This is due to a “no arbitrage” argument“no arbitrage” argument that says that says that the return on, say, a two-year bond must be that the return on, say, a two-year bond must be equivalent to the return on a equivalent to the return on a “roll-over” strategy“roll-over” strategy of of investing in a 1-year bond and rolling it over into investing in a 1-year bond and rolling it over into another 1-year bond at the beginning of the second another 1-year bond at the beginning of the second year. year.

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FRA pricingFRA pricing

You can use interest rates from the spot You can use interest rates from the spot yield curve to derive forward rates as yield curve to derive forward rates as follows:follows:

Where, Where, R’sR’s with a prefix of with a prefix of “0”“0” are spot are spot rates andrates and jj = the term of the FRA and = the term of the FRA and kk = = the start date of the FRA.the start date of the FRA.

)()(

)(

11

1

0

0

jk

j

j

k

kkj R

RR

25

Currency Risk and Forward Pricing Currency Risk and Forward Pricing ExamplesExamples

Link to Forward Pricing Excel file:Link to Forward Pricing Excel file:

FM 12 Ch 26 Mini Case.xls (Brigham & Ehrhardt file) (Brigham & Ehrhardt file)

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Futures ContractsFutures Contracts

Similar to Forward contracts but are more Similar to Forward contracts but are more structured and structured and standardizedstandardized than forwards. than forwards.

Futures contract Futures contract is a legally binding is a legally binding obligationobligation to to buy or sell a specified quantity of a specific asset buy or sell a specified quantity of a specific asset at a specified date in the future. at a specified date in the future.

StandardizationStandardization features: contract specifies a features: contract specifies a homogeneous asset, maturity date, contract size, homogeneous asset, maturity date, contract size, delivery mechanism, and minimum “tick” size.delivery mechanism, and minimum “tick” size.

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Futures Contracts Futures Contracts (cont.)(cont.)

Institutional Features that: Institutional Features that: Reduce credit riskReduce credit risk, and, and Improve liquidityImprove liquidity

Five key elements:Five key elements: Standardized contractStandardized contract on homogeneous asset on homogeneous asset Daily settlementDaily settlement of positions (like a series of forwards) of positions (like a series of forwards) Margin requirementsMargin requirements (good faith deposit that reduces credit risk) (good faith deposit that reduces credit risk) Price limitsPrice limits (restricts daily movement in futures price to be (restricts daily movement in futures price to be withinwithin margin requirement) margin requirement) ClearinghouseClearinghouse (de-couples buyer and seller by providing anonymity and reduces (de-couples buyer and seller by providing anonymity and reduces

counterparty risk)counterparty risk)

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Pricing of Futures ContractsPricing of Futures Contracts Pricing reflects thePricing reflects the spot price, spot price, PP00, , plusplus the “cost of carry”, the “cost of carry”, cc, , (which includes(which includes the the

risk-free rate, risk-free rate, rrff).).

FF00 = P = P00 + c + c = P = P00 * (1 + r * (1 + rff))TT ifif the only component of c is a constant risk-free rate. the only component of c is a constant risk-free rate.

No arbitrage requirementNo arbitrage requirement enforces the above relation enforces the above relation

Other factorsOther factors can affect the cost of carry, c, such as storage and insurance can affect the cost of carry, c, such as storage and insurance costs, as well as interest/dividend income on the underlying asset.costs, as well as interest/dividend income on the underlying asset.

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Features of Futures PricesFeatures of Futures Prices The concept of The concept of Basis Basis is a key factor when determining the effectiveness of a is a key factor when determining the effectiveness of a

hedge:hedge:

BasisBasistt = = FFtt - P - Ptt See Spreadsheet File.

According to the cost-of-carry model, the basis should correspond to the According to the cost-of-carry model, the basis should correspond to the cost of carry variable, cost of carry variable, cc..

Over time, futures prices will tend to Over time, futures prices will tend to convergeconverge toward the price implied by toward the price implied by cc..

Also, the futures price will Also, the futures price will convergeconverge to the spot price at the futures to the spot price at the futures contract’s expiration (contract’s expiration (FFTT = P = PTT). ).

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Basis RiskBasis Risk Perfect hedgesPerfect hedges are difficult to construct due to basis are difficult to construct due to basis

risk.risk. Basis RiskBasis Risk is the risk that the payoff profile of the is the risk that the payoff profile of the

hedging instrument is hedging instrument is not exactlynot exactly equal to the firm’s equal to the firm’s risk profile associated with a specific financial asset.risk profile associated with a specific financial asset.

FourFour primary primary sourcessources of basis risk: of basis risk: Changes in the convergence rate of Changes in the convergence rate of FFTT toto P PTT Changes in the factors affecting Changes in the factors affecting cc,, Random deviations in Random deviations in cc, , Mismatches between the hedging instrument and the Mismatches between the hedging instrument and the

underlying asset exposure (cross-hedge basis risk) underlying asset exposure (cross-hedge basis risk) Note:Note: basis risk goes to basis risk goes to zerozero ifif hedge’s maturity hedge’s maturity

exactly equals the underlying asset’s purchase/sale exactly equals the underlying asset’s purchase/sale date.date.

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Cross-hedge Basis RiskCross-hedge Basis Risk Cross-hedge Cross-hedge is used when there is no hedging is used when there is no hedging

instrument that is identical to the underlying asset instrument that is identical to the underlying asset exposure (e.g., use T-bond futures to hedge a corp. exposure (e.g., use T-bond futures to hedge a corp. bond portfolio).bond portfolio).

Cross-hedge BasisCross-hedge Basistt = = (F(Ft,Xt,X – P – Pt,Xt,X) + (P) + (Pt,Xt,X - P - Pt,Yt,Y))where, where, X = asset that is used for hedging purposes,X = asset that is used for hedging purposes,Y = underlying asset exposure to the firm.Y = underlying asset exposure to the firm.

Three factorsThree factors that affect the above basis risk: that affect the above basis risk:1) Maturity mismatch, 2) Liquidity, 3) Credit risk.1) Maturity mismatch, 2) Liquidity, 3) Credit risk.

32

Hedging Applications of Hedging Applications of Forwards and FuturesForwards and Futures

Forward contractsForward contracts are normally best for are normally best for situations where the contract details (size, situations where the contract details (size, maturity, underlying asset) need to be tailored maturity, underlying asset) need to be tailored to a specific set of firm cash flows.to a specific set of firm cash flows.

Forwards are usually more cost-effective for Forwards are usually more cost-effective for larger firms with good credit ratings and larger firms with good credit ratings and special needs that suit “custom-tailoring”.special needs that suit “custom-tailoring”.

FuturesFutures are less flexible than forwards in terms are less flexible than forwards in terms of tailoring the payoffs to fit a firm’s exposures.of tailoring the payoffs to fit a firm’s exposures.

However, futures are much more liquid than However, futures are much more liquid than forwards and have much less credit risk. forwards and have much less credit risk.

33

Hedging PrerequisitesHedging Prerequisites ““Appropriates”Appropriates” – specifies the details of the financial – specifies the details of the financial

exposure that the firm plans to hedge (e.g., exposure that the firm plans to hedge (e.g., What What security?, What time/maturity?, How much?security?, What time/maturity?, How much?).).

Hedging Strategies: Hedging Strategies: Do NothingDo Nothing – easiest strategy (but can be very costly!). – easiest strategy (but can be very costly!). Lock in price todayLock in price today – use forwards or futures to hedge exposure – use forwards or futures to hedge exposure

fully (100% of exposure is covered). fully (100% of exposure is covered). Lock in price today for Lock in price today for somesome of the exposure of the exposure - less than 100% - less than 100%

coverage can be cheaper.coverage can be cheaper. Cross-hedgeCross-hedge – when derivative is not available for the firm’s – when derivative is not available for the firm’s

underlying financial exposure.underlying financial exposure.

Note:Note: hedging hedging substitutessubstitutes Basis RiskBasis Risk for for Price RiskPrice Risk..

34

Cross-Hedging ExampleCross-Hedging Example Cross-hedge: Cross-hedge: UseUse New Mexican Peso Futures New Mexican Peso Futures to to

hedge against changes in hedge against changes in Colon / U.S. Dollar rateColon / U.S. Dollar rate).).

Find Futures Contract with Find Futures Contract with closest correlationclosest correlation to to underlying exposureunderlying exposure – Usually use a regression: – Usually use a regression:

PPC.R. Exchange RateC.R. Exchange Rate = a + b * P = a + b * PMexican Exchange RateMexican Exchange Rate + e + e(choose the future that has the highest adj. (choose the future that has the highest adj. RR22, , e.g., our e.g., our RR22 = .333 and b = 0.023 for the peso) = .333 and b = 0.023 for the peso)

Divide total exposure by standard futures contract Divide total exposure by standard futures contract size (0.5M pesos) to get “raw” number of contracts size (0.5M pesos) to get “raw” number of contracts needed.needed.e.g., {[400M colones x 0.023] / 0.5M} = e.g., {[400M colones x 0.023] / 0.5M} = 18.418.4 19. 19.

35

Cross-Hedging Example Cross-Hedging Example (continued)(continued)

Assume:Assume: Peso devalues from 11.1 to 12.3 per U.S. Peso devalues from 11.1 to 12.3 per U.S. dollar and Colon devalues from 513 to 570 per U.S. dollar and Colon devalues from 513 to 570 per U.S. dollar.dollar.

InitialInitial Value of Value of 400M Sale400M Sale::$0.780M = 400M / (513 / $1)$0.780M = 400M / (513 / $1)EndingEnding Value of Sale: Value of Sale: $0.702M$0.702M = 400M / (570 / $1) = 400M / (570 / $1)LossLoss due to Devaluation: due to Devaluation: $0.078M (-10.0%)$0.078M (-10.0%)

InitialInitial SHORT Futures: SHORT Futures: $0.856M = (19 x 0.5M) / 11.1$0.856M = (19 x 0.5M) / 11.1EndingEnding SHORT Futures: SHORT Futures: $0.772M$0.772M = (19 x 0.5M) / 12.3 = (19 x 0.5M) / 12.3GainGain due SHORT Futures: due SHORT Futures: $0.084M (+9.8%)$0.084M (+9.8%)Net Change in Total Value:Net Change in Total Value: +$0.006M+$0.006M = +0.084 – = +0.084 –

0.0780.078

36

Calculating the Overall Effect of Calculating the Overall Effect of a Hedgea Hedge

Calculate Change in Underlying Asset PositionCalculate Change in Underlying Asset Position – – Multiply the spot price Multiply the spot price at maturityat maturity timestimes quantity of the quantity of the underlying positionunderlying position– – Then subtract Then subtract initialinitial asset value (at t=0) from the asset value (at t=0) from the above figure.above figure.

Calculate the Hedge’s Profit/Loss Calculate the Hedge’s Profit/Loss

Hedging Profit/LossHedging Profit/Loss = = L/S IndicatorL/S Indicator * (F * (FTT – F – F00) * Number ) * Number of Futures Contracts * Futures Contract size of Futures Contracts * Futures Contract size Note: must replace FNote: must replace FT T with Pwith PTT if there is if there is nono basis risk basis risk

Add the two figures together to get net effect:Add the two figures together to get net effect: Net Change in Value = Net Change in Value = Underlying + Underlying + HedgeHedge