Hedging with Foreign Exchange Derivatives

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Hedging with Foreign Exchange Derivatives

• Alex Russell
• Ben Davidson

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Mona Lisa
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History

• August 21,1911 Louis Béroud, a painter, walked
  into the Louvre and went to the Salon Carré where
  the Mona Lisa had been on display for five years.
  However, where the Mona Lisa should have stood,
  he found four iron pegs.
• Béroud contacted the section head of the guards,
  who thought the painting was being photographed.
  A few hours later, Béroud checked back with the
  section head of the museum, and it was confirmed
  that the Mona Lisa was not with the
  photographers. The Louvre was closed for an
  entire week to aid in the investigation of the
  theft.

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History Continued

• At the time, the painting was believed lost
  forever. It turned out that on August 20,1911
  Louvre employee Vincenzo Peruggia stole it by
  simply by entering the building during regular
  hours, hiding in a broom closet, and walking out
  with it hidden under his coat after the museum
  had closed.
• Con-man Eduardo de Valfierno master-minded the
  theft, and had commissioned the French art forger
  Yves Chaudron to make copies of the painting so
  he could sell them as the missing original.
  Because he didn't need the original for his con,
  he never contacted Peruggia again after the
  crime. After keeping the painting in his
  apartment for two years, Peruggia grew impatient
  and was caught when he attempted to sell it to a
  Florence art dealer it was exhibited all over
  Italy and returned to the Louvre in 1913.

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Present Day

• A short time after the theft Yves Chaudron
  escaped to the United States where he hid from
  the international art community. Two weeks ago,
  his great grandson Frances contacted us with a
  business proposal.
• Frances Chaudron, grandson of the great art
  forger Yves Chaudron is currently one of the best
  painters in the world. As an artist, he has made
  a small fortune painting old masterpieces.
  Recently, in his studio in Salem, Oregon, Francis
  presented a profitable scheme inspired by his
  great grandfather.

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The Plan

• Francis wants us to steal the Mona Lisa so that
  he can make precise forgeries to sell on the
  black market. Current technology requires that he
  actually have the original painting in his
  possession so that the borders match that of the
  original. Although the borders are not seen by
  the public, and are never photographed, a few
  collectors know their exact composition.
• Acting in our capacity as an art broker, we were
  intrigued by the idea and contacted our associate
  in Rome, Italy. She believes that she can steal
  the painting and transport it to the United
  States, but requires payment of 15,000,000 upon
  delivery.
• After consulting our thief, we decided to take
  the job on the condition that Francis pays us for
  our services up front. He agrees, but says that
  we will only deal with dollars since foreign
  exchange rates confuse him. Because of this
  complication, he offers us 19,000,000 for the
  painting.

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The Problem

• As an intermediary, how do hedge our positions to
  make the most money on the transaction?
• Long 19,000,000
• Short 15,000,000

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Hedging

• Used to manage against risk
• Delta Hedgeattempts to offset the change in the
  value of the exposure with an opposite change in
  the value of the hedge position.
• Matching longs and shorts.

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Hedging With a Currency Future

• To hedge a foreign exchange exposure, the
  customer assumes a position in the opposite
  direction of the exposure.
• For example, if the customer is short the Euro,
  they would go long in the futures market (which
  we will do).
• A customer that is long in the futures market is
  betting on an increase in the value of the
  currency, whereas with a short position they are
  betting on a decrease in the value of the
  currency.

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Futures Contracts

• Four fixed Dates a year 3rd Wednesday of March,
  June, September and December.
• Exchange traded, price determined through market
  trading, Liquidity.
• Standard sizes (by Date).
• Available only in a few currencies (Cross-hedge).
• Daily settlement and Margin Requirements.

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Forward Contracts

• Written by Banks
• Tailor Size and Date (large and precise,
  respectively).
• Traded Inter-Bank
• No Settlement, only on Date.

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Our Homework Applied

• Remember the last assignment?
• We buy 120 (E15 mil / E125,000) June Euro Futures
  contracts at (1.2247 E125,000) 120 costing
  us 18,370,500.
• Break even (just on the contract) at 2.4494.
• Current Profit 629,500
• Change in Account (Buy Price Settle)
  Contracted Amount.
• Maintain Margin Levels.

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Futures Time Line

• When hedging with a foreign currency there are
  three important dates that you must consider.
• t--------------tn-------------------T
• Inception liquidation Maturity

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Future Equation (To Maturity)

• Gain(Loss) X(Stn- bSt) - (Ztn,T-Zt,T)
• X Amount of Exposure
• b 1it,tn1/a/ 1 it,tn1/a (The
  interest rate ratio)
• a annualized factor for the interval from t to
  tn
• (S tn - bSt) is the deviation of the future
  spot exchange rate (or forward rate) at inception
  of the position
• (Z tn,T-Z t,T) is the change the price of a
  futures contract maturing time T, over the time
  period from ,t inception of the position, to tn,
  liquidation of the position

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Futures Equation 2

• Previous equation was for a contract held to
  maturity.
• If a futures contract is held to maturity, it is
  the same as a forward contract.
• Why?

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Futures Equation (Not held to Maturity)

• Gain (loss)
• X((Stn bSt) c (Stn bSt)
• C is
• C (1itn,T)1/a / (1itn,T)1/a

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Futures Contracts (Not held to Maturity) 2

• Remaining time to maturity prices using Covered
  Interest Parity.
• Interest rates at liquidation are not known in
  advance, and subject to change during the
  interval.
• Futures price has not had the full interval to
  converge to spot price.
• Optimal hedge involves 1/c units of foreign
  currency futures, since c(1/c) 1.
• C gt 1 smaller amount, C lt 1 larger amount.

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Difficulties

• Using a hedge ratio of 1/c sets the expected gain
  (loss) to zero, but does not create a perfect
  hedge.
• C is stochastic
• Interest rates, etc. are unpredictable.
• Frequently adjusted.

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How much risk can we Hedge?

• of un-hedged risk eliminated by futures
  contracts
• (1- (Var(Stn bSt) (Ztn,T Zt,T)) /
  (Var(Stn bSt))) 100
• Or as a of open risk
• SQRT (Var(Stn bSt) (Ztn,T Zt,T)) /
  (Var(Stn bSt))) 100

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Summary

• Futures contracts, unlike forward contracts,
  nearly always fail to be a complete hedge.
• Futures are used when the transaction date is not
  definite.
• Futures are used when the transaction amount is
  not precise.
• Futures are used if the transaction is too small
  for the forward market.

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Options

• Foreign Currency options are financial contracts
  that give the holder the right, but not the
  obligation, to buy or sell a specified amount of
  foreign currency on or before a specified
  maturity date.
• Types of Options
• American
• European

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Calls and Puts

• Calls
• Gives the owner of the option the right but not
  the obligation to buy currency at a specified
  exercise price (X)
• This is a long position
• Puts
• Gives the owner of the option the right but not
  the obligation to sell currency at a specified
  exercise price
• This is a short position

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Why use an Option?

• Your exposure to foreign exchange rate risk is
  uncertain
• We are not sure that our thief will succeed
• If our thief fails we no longer have exchange
  exposure
• With Futures and Forwards we now will have an
  open position
• You are uncertain about exchange rates in the
  future and want to capture the upside
• Allows you still to hedge against risk

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Black Scholes Pricing

• Developed by Fischer Black and Myron Scholes in
  1973
• Assumptions
• European exercise terms are used
• Markets are efficient
• No commissions
• Interest rates are known and remain constant

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The Model

• C SN(d1) Ke(-rt)N(d2)
• S Current spot price
• t Time until option is exercised
• K Option strike price
• r Risk free interest rate
• N Cumulative standard deviation
• s standard deviation of returns
• d1 ln(S/K) (rs2/2)t s?t
• d2 d1 - s?t

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Results of the Model

• Spot price 1.2178
• Risk free rate 4.75
• 62,500 Euro European style
• Strike Date Call Put

1180 Jun 0.0466 0.03
1200 Jun 0.0277 0.015
1220 Jun 0.0129 0.066
1240 Jun 0.043 0.018
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How do we Hedge our Position?

• We are short 15,000,000
• We need to take a long position to offset this
  position
• This requires 240 contracts
• 62,500 each
• The price of each 1200 contract is 1,731.25
• Equals the number of Euros in the contract times
  price per Euro
• Total price of the position 415,500

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Our Position
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The Resulting Position

• The 1200 contract gives us an effective rate of
• 1.2477 /
• Why is this so much more than the Forward
  contracts?
• Protects against the appreciation of the Euro
• Allows for capture of falling Euro prices
• Locks in the maximum loss
• No maximum gain

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Resulting Position
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Exit

• The foreign exchange options market is very
  liquid
• Time of payment is not dependant upon the
  contract date
• Execution of the options are not required
• Buy 15,000,000 at the spot rate
• Sell 240, 1200 Euro Call options
• Final cost 18,115,500 to 18,715,500
• Compare to 17,700,000 to 19,500,000 at
  original spot rate
• 1.18 / to 1.30 /

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Methods of Offsetting the Price of Options

• Straddle
• Requires selling puts offsetting the gain when
  the price of the Euro falls against the dollar
• The premium from the sale (price) offsets the
  cost of the call options
• Generally used when both the call and the put are
  bought and sold out of the money
• Straddle using the same strike price for both
  calls and puts
• Effectively creates a forward contract

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Questions?