Ed5 05 Currency Futures and Futures Markets(1)

Multinational Finance

Part IIDerivative Securities forFinancial Risk ManagementChapter 5 Currency Futures and Futures Markets

Chapter 6 Currency Options and Options Markets

Chapter 7 Currency Swaps and Swaps MarketsButler / Multinational FinanceChapter 5 Currency Futures and Futures Markets5-#

These technical chapters focus on currency derivatives, with some coverage of related derivative instruments where appropriate. Chapter 5Currency Futures and Futures MarketsLearning objectives

Currency futures

Credit risk and the futures contract solution

Currency futures exchanges

Currency forwards versus currency futures

Hedging with futures contracts

Basis risk and the hedge ratio

Delta, cross, and delta-cross hedgesButler / Multinational FinanceChapter 5 Currency Futures and Futures Markets5-#

Chapter 5 topics:5.1Financial Futures Exchanges5.2The Operation of Futures Markets5.3Futures Contracts5.4Forward versus Futures Market Hedges5.5Futures Hedges Using Cross Exchange Rates5.6Hedging with Currency Futures5.7Summary

Credit risk and the futures contract solution

Forwards are a pure credit instrument

Forwards are a zero-sum game, so thatone party always has an incentive to default

The futures contract solution

A futures exchange clearinghouse takes one side of every transaction (and makes sure that its exposures cancel one another)

Initial and maintenance margins ensure settlement

Contracts are marked-to-market daily Currency futures contracts and exchangesHedging with currency futures

Credit risk and the futures contract solution Currency futures exchangesCurrency forwards versus currency futures

Butler / Multinational FinanceChapter 5 Currency Futures and Futures Markets5-#

Forward markets for agricultural products and commodities such as gold and silver have existed throughout recorded history.

Futures markets are a more recent innovation

Agricultural futures contracts

Europe: Agricultural futures contracts first appeared in as the lettre de faire in medieval times.

Asia: Rice futures were traded at Osaka, Japan in the early 1700s. These standardized contracts were traded through a futures exchange clearinghouse and specified weight, quality, and contract life.

North America: Agricultural futures were introduced on the Chicago Board of Trade (CBOT) in the 1860s.

Currency futures contracts

Currency futures began trading at the Chicago Merc (CME) in 1972 following the 1971 collapse of the Bretton Woods Agreement.Financial futures exchanges are often associated with commodity futures or options exchanges

Contract volume (trillions)20102000Location(s)1Korea Exchange 3,749 23 Korea2CME Group 3,080 471US3Eurex 2,642 290EU4NYSE Euronext 2,155 202 US & EU 5Natl Stock Exchange of India 1,616 -India6BM&F Bovespa 1,422 80 Brazil7CBOE Group 1,124 47 US8Nasdaq OMX 1,099 21 US & Nordic9Multi-Commodity Exch of India 1,082 -India10Russian Trad Sys Stock Exchange 624 -Russia

Source: Futures Industry Association (www.futuresindustry.org)Credit risk and the futures contract solutionCurrency futures exchanges Currency forwards versus currency futures

Currency futures contracts and exchangesHedging with currency futures


Figure 5.2 lists the Top 20 futures exchanges by volume, based on data from the Futures Industry Association. This table includes both financial and commodity futures. Here are numbers 11-20.

2010200011Shanghai Futures Exchange 622 4China 12Zhengzhou Commodity Exchange 496 -China 13Dalian Commodity Exchange 403 -China 14Intercontinental Exchange 329 -US UK Canada15Osaka Securities Exchange 196 9 Japan 16JSE 170 22South Africa17Taiwan Futures Exchange 140 2Taiwan18Tokyo Financial Exchange 121 51 Japan 19London Metal Exchange 120 61 UK20Hong Kong Exchanges and Clearing 116 5Hong Kong

A forward hedge of the dollar

Underlying position of a French exporter (long $s)

Sell $s forward at Ft/$ = 0.75/$ (short $)

Net position-Goods+30 million -$40 millionv/$Long $ss/$Short $s+$40 million+30 million-GoodsCredit risk and the futures contract solutionCurrency futures exchangesCurrency forwards versus currency futures

Currency futures contracts and exchangesHedging with currency futures


The forward contract provides a perfect hedge of a transaction exposure (that is, a known future cash flow in a foreign currency) because the size and timing of the hedge transaction can be set to exactly offset the size and timing of the underlying exposure. Forwards versus futures

ForwardsFutures

CounterpartyBankCME Clearinghouse

MaturityNegotiated3rd week of the month (US)

AmountNegotiatedStandard contract size

FeesBid-askCommissions

CollateralNegotiatedMargin account

SettlementAt maturityMost are settled early Currency futures contracts and exchangesHedging with currency futures

Credit risk and the futures contract solutionCurrency futures exchangesCurrency forwards versus currency futures


Forward contracts are created by commercial and investment banks, whereas futures contracts are usually found on futures exchanges.

Forwards are negotiated. Dealers profit on the bid-ask spread.

Futures contracts are standardized. Futures brokers profit by charging a commission on each trade. Standardized contracts promote liquidity, but are not as flexibility as forwards.

On U.S. exchanges, futures contracts expire on the Monday before the 3rd Wednesday of a contract month. The previous Friday is the last trading day.

Contract sizes vary by exchange. For example, CME: 12,500,000 and 100,000 contract sizes PBOT: 6,250,000 and 50,000 contract sizes

Just for fun (not in the text)The text says $30 is a typical fee for a futures contract. In fact, fees are negotiable and can range from around $10 to $100 depending on the size of the trade and the broker-client relationship. Been there, done that...

Futures contracts are similar to forward contracts

Futures contracts are like a bundle of consecutive one-day forward contracts

Futures and forwards are nearly identical in their ability to hedge risk

The biggest difference between a forward and a futures contract is daily marking-to-market Currency futures contracts and exchangesHedging with currency futures

Credit risk and the futures contract solutionCurrency futures exchangesCurrency forwards versus currency futures


Futures contracts are like a bundle of consecutive one-day forward contracts. This is a consequence of daily marking-to-market.

Each day, the previous days forward contract is replaced by a new one-day forward contract with a delivery price equal to the closing price from the previous days contract.

At the end of each day, the previous days forward contract is settled and a new one-day forward contract is formed.

The hedging properties of futures and forwards are nearly equivalent:

As with forward contracts, futures contracts allow you to hedge against nominal, but not real, changes in the foreign exchange rate. Hedging with forwards and futures

Forward contracts can be tailored to match the underlying exposure

Forward contracts thus can provide a perfect hedge of a transaction exposure to currency risk

Exchange-traded futures contracts are standardized

They will not provide a perfect hedge if they do not match the underlying exposures

maturitycurrencycontract size Currency forwards versus currency futures Maturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


The three biggest potential mismatches between a futures contract and the underlying transaction exposure are:

Currency mismatch - there may not be a futures contract in the currency that you would like to hedgeMaturity mismatch - there may not be a futures contract expiring on the same day as your underlying transaction exposureContract size mismatch - the underlying transaction exposure may not be an even increment of existing futures contracts

These mismatches are not a problem for forward contracts because forward contracts can be custom tailored to the particular circumstance. Interest rate parity revisited

Some definitions

Std/f = spot price at time t

Ft,Td/f = forward price at time t for expiry at time T

Futt,Td/f = futures price at time t for expiry at time T

Currency forward and futures prices are equal through interest rate parity

Futt,Td/f = Ft,Td/f = Std/f [(1+id)/(1+if)]T-t

Currency forwards versus currency futures Maturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


TInterest rate parity is usually expressed as a forward-looking relation from time zero to time t.

(Ftd/f / S0d/f) = [(1+id)/(1+if)]t

In this slide, IRP is expressed as a backward-looking relation from the expiration date T backward toward time t.

Futt,Td/f = Ft,Td/f = Std/f [(1+id)/(1+if)]T-t t0t

Futt,Td/f = Std/f [(1+id)/(1+if)]T-tSpot & futures price convergence at expiryCurrency forwards versus currency futures Maturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


Futures prices converge to spot prices at expiration. This convergence can be seen through the interest rate parity condition.Futt,Td/f = Ft,Td/f = Std/f [(1+id)/(1+if)]T-t

As time to expiry (T-t) approaches zero, the [(1+id)/(1+if)]T-t term goes to one and forward and futures prices converge to the spot price.

If interest rates do not change, then the convergence of futures prices to spot prices is linear in time. In particular, the futures price converges to the spot price at a rate of (1+id)/(1+if) per period.

This nearly linear convergence makes futures contracts and forward contracts nearly identical in their ability to hedge exposure to currency risk.Maturity mismatches and basis risk

If there is a maturity mismatch, futures contracts may not provide a perfect hedge

The difference (id-if) is called the basis

The risk of change in the relation between futures and spot prices is called basis risk

When there is a maturity mismatch, basis risk makes a futures hedge slightly riskier than a forward hedgeCurrency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedgeDelta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


Interest rate differentials [(1+id )/(1+if )] are often approximated by the simple difference in nominal interest rates, (id-if). This difference (id-if) is called the basis. The basis determines the relation of futures prices to spot prices through interest rate parity.The basis changes as interest rate levels in the two currencies rise and fall.

The risk of unexpected change in the relation between futures prices and spot prices is called basis risk. Basis risk arises from changes in the basis; that is, in relative interest rates. Jan 18Jun 16Jun 3-100 million

Underlying obligationThe futures expiration date is after the underlying exposureAn example of a delta hedgeCurrency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedgeDelta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


In a delta hedge:The futures hedge involves a purchase of the June 16 futures contract, which expires shortly after the June 3 underlying exposure. The futures contract is then cancelled (or sold) on June 3, when the underlying exposure no longer exists.This is the reason most futures contracts are not held until expiration.

Buying futures contracts with an expiration date prior to June 3 would leave the underlying cash flow exposed to currency risk between the expiration date and the June 3 date of the underlying cash flow.A delta hedge

std/f = a + b futtd/f + et

std/f=percentage change in the spot ratefuttd/f=percentage change in the futures price

The hedge ratio is used to minimize the variance of the hedged position

NFut*=(Amount in futures)/(Amount exposed) =-b

Hedge quality is measured by (rs,fut )2Currency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedgeDelta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


A delta hedge (Equation 5.7)This regression estimates basis risk over the hedges maturity. A delta hedge estimates the number of futures contracts that minimizes the variance (the D or delta) of the hedged position.The slope coefficient = s,fut (s /fut ) measures the sensitivity of changes in spot prices to changes in futures pricesThe hedge ratio provides the optimal amount in the futures hedge per unit of value exposed to currency risk.

Hedge quality is measured by the r-square of the regression; r2 = s,fut2. r2 measures the % variation in std/f explained by variation in futtd/f.High r2 low basis risk and a high-quality hedge. Low r2 high basis risk and a relatively poor hedge.

Just for fun (not in the text)Volatilities change over time, and so the slope coefficient in Equation (5.8) is often estimated with conditional volatilities and a conditional correlation. See Kroner & Sultan, Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures, Journal of Financial and Quantitative Analysis, 1993.A CME delta hedge

It is now January 18. You need to hedge a 100 million obligation due on June 3.

The spot exchange rate is S0$/ = $1.10/

A 125,000 CME euro futures contract expires on June 16

Based on st$/ = a + b futt$/ + et , you estimate b = 1.040 with r2 = 0.98.

How many CME futures contracts should you buy to minimize the risk of your hedged position?Currency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedgeDelta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


In a delta hedge, there is a currency match but a maturity mismatch.

It is difficult to construct a sample of futures prices of constant maturity t because exchanged-traded futures come in only a limited assortment of maturities. Exchange-traded futures expire only every three months, and the futures prices on any single contract converge to the spot rate at maturity. Fortunately, interest rate parity determines both the forward price and the futures price for a given maturity. Because it is easier to construct a sample of forward prices of constant maturity than a sample of futures prices of constant maturity, the hedge ratio is conventionally estimated from the relation of forward price changes to spot rate changes over the desired maturity.

Although not mentioned in the text, current research is focusing on time-varying (ie. GARCH-type) volatilities and correlations (or comovements) in spot and futures prices.The delta hedge solution

The optimal hedge ratio for this delta hedge is given by

NFut* =(amount in futures)/(amount exposed) = -b

(amount in futures) = (-b)(amount exposed) = (-1.040)(-100 million) = 104 million

or (104 million) / (125,000/contract) = 832 contractsCurrency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedgeDelta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


Hedge ratio NFut* = -b, where b = (ss,fut)/(sfut2) = rs,fut (ss / sfut )

Solution to the delta hedge example:

Given the estimated relation from Equation 6.7, a futures position equivalent to 104 million (832 contracts at 125,000 per contract) will minimize the variance of the hedged position.

The relatively high r2 (0.98) of this regression suggests that this should be a relatively high quality hedge. Currency mismatches and cross hedges

std/f1 = a + b std/f2 + et

A cross hedge is used when there is a maturity match but a currency mismatch

std/f1=percentage change in the currency f1of the underlying exposure

std/f2=percentage change in the spot price ofcurrency f2 of the futures contractCurrency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


In the delta hedge, spot rate changes (std/f) were regressed on changes in futures prices (futtd/f).

In the currency cross hedge (Equation 5.11), the currency of the underlying exposure (f1) is different from the currency of the futures contract (f2).

Spot prices std/f2 are substituted for the independent variable futtd/f2 because

the maturity of the futures contract is the same as that of the underlying transaction in the spot market, andfutures prices converge to spot prices at maturity.A CME cross hedge

It is now January 18. You need to hedge a DKK 100 million obligation due on June 16.

Spot (cross) exchange rates are $0.75/DKK, 0.75/DKK, and $1.00/.

A CME futures contract expires on June 16 with a contract size of 125,000

Based on st$/DKK = a + b st$/ + et , you estimate b = 0.960 with r2 = 0.94.

How many CME futures should you buy to minimize the risk of your hedged position?Currency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


In this cross hedge, there is a maturity match but a currency mismatch.The cross hedge solution

Optimal hedge ratio:

NFut* = (amt in futures)/(amt exposed) = -b

(amt in futures) = (-b)(amt exposed) = (-0.960)(-DKK100 million) = DKK96 million

or 72 million at (DKK96m) (0.75/DKK)

or 576 contracts at 125,000/contractCurrency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedge Delta-cross hedgesCurrency futures contracts and exchanges Hedging with currency futures


Solution to the cross hedge example:

The optimal amount in the futures position of this cross hedge is: (amt in futures) = (-0.96)(-DKK100m) = DKK96m, or (0.75/DKK)(DKK96m) = DKK72m at the 0.75/DKK exchange rate.

With an r-square of 0.94, this is a fairly high quality hedge.

Note that a cross hedge does not have basis risk because the futures price converges to the spot price at expiration. A delta-cross hedge

std/f1 = a + b futtd/f2 + et

A delta-cross hedge is used when there is both a currency and a maturity mismatch

std/f1=percentage change in the currency f1of the underlying exposure

futtd/f2=percentage change in the value of thefutures contract on currency f2Currency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedgeDelta-cross hedges Currency futures contracts and exchanges Hedging with currency futures


A delta-cross hedge (Equation 5.10): std/f1 = a + b futtd/f2 + et

The currency of the underlying exposure (f1) is different from the currency of the futures contract (f2).

The maturity date of the futures contract does not match the maturity of the underlying exposure, so there is basis risk.

Spot rate changes std/f1 in the exposed currency f1 are regressed on futures prices changes futtd/f2 in the currency f2 used to hedge. This compensates for the difference in currencies (f1 vs. f2) and maturities (spot prices vs futures prices). A CME delta-cross hedge

It is now January 18. You need to hedge a DKK 100 million obligation due on June 3.

Spot exchange rates are $0.75/DKK, 0.75/DKK, and $1.00/.

A CME futures contract expires on June 16 with a contract size of 125,000

Based on st$/DKK = a + b futt$/ + et , you estimate b = 1.020 with r2 = 0.85.

How many CME futures should you buy to minimize the risk of your hedged position?Currency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedgeDelta-cross hedges Currency futures contracts and exchanges Hedging with currency futures


In this delta-cross hedge, there is both a maturity and a currency mismatch.The delta-cross hedge solution

Optimal hedge ratio:

NFut* = (amt in futures)/(amt exposed) = -b

(amt in futures) = (-b)(amt exposed) = (-1.020)(-DKK100 million) = DKK102 million

or 76.5 million at (DKK102m) (0.75/DKK)

or 612 contracts at 125,000/contractCurrency forwards versus currency futuresMaturity mismatches and the delta hedgeCurrency mismatches and the cross hedgeDelta-cross hedges Currency futures contracts and exchanges Hedging with currency futures


Solution to the delta-cross hedge example:

The optimal amount in the futures position of this cross hedge is: (amt in futures) = (-1.02)(-DKK100m) = DKK102m, or (0.75/DKK)(DKK102m) = DKK76.5m at the 0.75/DKK exchange rate.

With an r-square of 0.85, this is far from a perfect hedge. However, it will eliminate most of the risk from the underlying DKK exposure.

A classification of futures hedgesCurrency forwards versus currency futuresMaturity mismatches and the delta hedge Currency mismatches and the cross hedge Delta-cross hedges Currency futures contracts and exchanges Hedging with currency futures


Keystd/f = (Std/f-St-1d/f)/St-1d/f and futtd/f = (Futtd/f-Futt-1d/f)/Futt-1d/f d = domestic currencyf1 = currency in which the underlying exposure is denominatedf2 = currency used to hedge against the underlying exposure f = foreign currency when f1 = f2

The most general case is the delta-cross hedge.If the underlying exposure and the futures contracts are in the same currency, then f1 = f2 = f and the hedge is a delta hedge. If there is a maturity match but a currency mismatch, then futtd/f2 = std/f2 and the hedge is a cross hedge. If there is both a maturity and a currency match, then a futures hedge is nearly equivalent to a forward market hedge.

0

TFutTd/f = STd/f

Forward

premium

Fut0d/f

S0d/f

Currency

Hedge

Hedge ratio estimation

Mismatch

Exact match

Mismatch

Perfect hedge

std/f = +std/f+et

such that =0, , & et=

Exact

match

Cross hedge

std/f1 = +std/f2+et

Maturity

Delta hedge

std/f = +futtd/f+et

Delta-cross hedge

std/f1 = +futtd/f2+et

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Ed5 05 Currency Futures and Futures Markets(1)

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