Part II Derivative Securities for Financial Risk Management

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Part IIDerivative Securities forFinancial Risk
Management

• Ch 5 Currency futures and futures markets
• Ch 6 Currency options and options markets
• Ch 7 Currency swaps and swaps markets

Butler, Multinational Finance, 4e
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Chapter 5Currency Futures and Futures Markets
Learning objectives ? Currency
futures Contracts Time value
algebra Futures and spot price
convergence ? Hedging with futures
contracts Basis risk and the hedge
ratio Delta, cross, and delta-cross hedges
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A forward hedge of the dollar

• Underlying position of a
• French exporter (long s)
• Sell s forward at Ft/ 0.80/
• (short s and long s)
• Net position

40 million
-Goods
50 million
-40 million
50 million
v/
Long s
Short s
s/
Currency futures contracts
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Currency futures contracts

• Forwards are a pure credit instrument
• Forwards are a zero-sum game, so that
• one 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
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Futures exchanges

• Financial futures exchanges are often associated
  with a commodity futures exchange
• 2006 contract
• Top futures exchanges volume (mil)
• 1 CME - Chicago Mercantile Exchange
  (U.S.) 1,101.7
• 2 Eurex - Eurex (Germany Switzerland) 960.6
  
• 3 CBOT - Chicago Board of Trade (U.S.) 678.3
• 4 Euronext - (Amsterdam/Brussels/Lisbon/Paris/
  London) 420.0
• 5 Mexican Derivatives Exchange - (Mexico
  City) 274.7
• 6 BMF - Bolsa Mercadorias de Futuros
  (Brazil) 258.5
• 7 NYMEX - New York Mercantile Exchange
  (U.S.) 216.3
• 8 Dalian Commodity Exchange - (China) 170.6

Currency futures contracts
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Growth of derivatives trading
Millions of contracts traded
Source Futures Industry Association
(www.futuresindustry.org)
Currency futures contracts
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Forwards versus futures

• Forwards Futures
• Counterparty Bank CME Clearinghouse
• Maturity Negotiated 3rd week of the month (US)
• Amount Negotiated Standard contract size
• Fees Bid-ask Commissions
• Collateral Negotiated Margin account
• Settlement At maturity Most are settled early

Currency futures contracts
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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
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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
• maturity
• currency
• contract size

Hedging with futures
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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 (1id)/(1if)T-t

Hedging with futures
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Spot and futures price convergence at expiration
Futt,Td/f Std/f (1id)/(1if)T-t
Hedging with futures
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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 hedge

Hedging with futures
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An example of a delta hedge
The futures expiration date is after the
underlying exposure
Jan 18
Jun 16
Jun 3
-100 million Underlying obligation
Hedging with futures
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A delta hedge

• std/f a b futtd/f et
• std/f percentage change in the spot rate
• futtd/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 )2

Hedging with futures
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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?

Hedging with futures
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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 contracts

Hedging with futures
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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 f1
• of the underlying exposure
• std/f2 percentage change in the spot
• price of currency f2 of the
• futures contract

Hedging with futures
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A CME cross hedge

• It is now January 18. You need to hedge a DKr 100
  million obligation due on June 16.
• Spot (cross) exchange rates are 0.75/DKr,
  0.75/DKr, and 1.00/.
• A CME futures contract expires on June 16 with
  a contract size of 125,000
• Based on st/DKr a b st/ et , you
  estimate b 0.960 with r2 0.94.
• How many CME futures contracts should you buy to
  minimize the risk of your hedged position?

Hedging with futures
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The cross hedge solution

• Optimal hedge ratio
• NFut (amt in futures)/(amt exposed) -b
• ? (amt in futures) (-b)(amt exposed)
• (-0.960)(-DKr100 million) DKr96 million
• or 72 million at (DKr96m) (0.75/DKr)
• or 576 contracts at 125,000/contract

Hedging with futures
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The delta-cross hedge

• 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 f1
• of the underlying exposure
• futtd/f2 percentage change in the value
• of the futures contract on
• currency f2

Hedging with futures
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A CME delta-cross hedge

• It is now January 18. You need to hedge a DKr 100
  million obligation due on June 3.
• Spot exchange rates are 0.75/DKr, 0.75/DKr, and
  1.00/.
• A CME futures contract expires on June 16 with
  a contract size of 125,000
• Based on st/DKr a b futt/ et , you
  estimate b 1.020 with r2 0.85.
• How many CME futures contracts should you buy to
  minimize the risk of your hedged position?

Hedging with futures
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The delta-cross hedge solution

• Optimal hedge ratio
• NFut (amt in futures)/(amt exposed) -b
• ? (amt in futures) (-b)(amt exposed)
• (-1.020)(-DKr100 million) DKr102 million
• or 76.5 million at (DKr102m) (0.75/DKr)
• or 612 contracts at 125,000/contract

Hedging with futures
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A classification of futures hedges
Hedging with futures