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