Exchange Market

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Exchange Market

• Physical or virtual location where buyers and
  sellers meet in order to trade securities or
  commodities

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Exchange Market

• Anonymous trading
• Risks are assumed by the clearing corporation

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Exchange Market

• Types of available products
• Futures contracts
• Financial futures contracts
• Interest rates
• Currencies
• Indexes
• Commodities
• Agricultural products
• Metals
• Livestock, etc.

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Exchange Market
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Futures Contract

• A futures contract is an agreement that obliges
  the buyer to take delivery of a specific quantity
  of an underlying asset, at a specific date, and
  at a price established at the time of the
  transaction.
• Conversely, the seller is obliged to deliver a
  specific quantity of an underlying asset, at a
  specific date, and at a price established at the
  time of the transaction.

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Futures Contract

• The value of a futures contract is zero when
  initiated
• Delivery price identical to the forward price
• The contract develops value as the forward price
  change
• Zero-sum game
• What is lost by one is gained by the other
• No initial payment
• Performance bond required

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The Payoff of a Forward Contract

• The payoff of a long position
• Pt D
• The payoff of a short position
• D Pt
• where
• Pt Price of the underlying asset at the
  maturity of the contract
• D Delivery price

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The Payoff of a Forward Contract

• Futures contracts have a linear profit and loss
  profile
• Zero-sum game
• What is lost by one is gained by the other

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The Payoff of a Forward Contract
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Futures Contract

• Example
• Suppose we are in June and a coffee producer
  wants to sell his September harvest at the
  current market price of 2 per pound. At this
  price, the producer would realize a return of 25.

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Futures Contract

• Example
• A futures contract expiring in September will be
  sold at a price of 2.
• The producer is committing himself to deliver the
  coffee at a price of 2 per pound in September.
  He is obliged to do so even if the price of
  coffee rises.
• However, he is protected against a drop in the
  price since the buyer is obliged to purchase the
  coffee at a price of 2.

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Futures Contract
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Contract Specifications

• Contract size and value
• Minimum price fluctuations
• Daily price limits
• Delivery month
• Trading hours
• Delivery location

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Settlement

• Delivery by an offsetting transaction
• Taking an opposite position to the initial
  position
• Settlement by delivery
• The short position holder initiate the delivery
  process at any time after the first notice day
• Cash settlement
• The long and the short must pay or receive a
  payment in cash instead of having to accept or to
  make delivery of the merchandise

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Specifications
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Specifications
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Specifications
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Margin Requirements and Marking to Market

• Margin
• Good faith deposit or performance bond
• Determined by the exchange or clearinghouse as a
  fixed amount per contract or as a percentage of
  the total contract value (3 to 10 of the
  contract value)
• Initial margin
• The required deposit at the contract inception
• Adjustments are being made at the end of every
  days (daily settlement, mark to market)
• Maintenance margin
• The amount that must be maintained in the account
  at all time

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Margin Requirements and Marking to Market

• Margin call
• A margin call is issued when the account falls
  under the maintenance margin level. The account
  must then be immediately brought back to the
  initial margin level.

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Margin Requirements and Marking to Market

• Example
• Long position on 1 Coffee futures
• Size 37,500 pounds
• Initial margin 2,500 per contract
• Maintenance margin 2,000 per contract

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Margin Requirements and Marking to Market
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Pricing of Futures/Forwards
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Cost of Carry Model

• Price of a futures contract
• Priced so that the investor is indifferent about
• buying the asset immediately and paying the
  carrying costs associated with holding the asset
  until the delivery date, or
• buying a futures contract
• Carrying costs
• Financing, storage, and insurance.

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Cost of Carry Model

• Futures price
• The price of a futures is established by
  determining the arbitrage free price (the
  indifference price).
• Two possible choices
• Buy the asset immediately and keep it until
  needed
• Loss of interest rate income
• Storage fees
• Buy a futures contract in order to buy the asset
• Interest rate income
• No storage fees
• What do you do?

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Basis

• Basis
• The spread between the spot and the futures price
• Contango (Normal)
• The futures price is higher than the spot price
• Backwardation (Inversion)
• The futures price is lower than the spot price

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Basis

• Contango (Normal)
• The basis is widening when futures prices
  increase faster or decline slower than the spot
  price.
• The basis is narrowing when futures prices
  decline faster or rise slower than the spot
  price.
• Backwardation
• The basis is widening when futures prices decline
  faster or rise slower than the spot price.
• The basis is narrowing when futures prices rise
  faster or decline slower than the spot price.

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Normal Market

• A normal market is characterized by adequate
  supplies of the underlying asset through all
  delivery months. Prices reflect all or at least
  some of the carrying costs.

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Cash and Carry Arbitrage

• Arbitrage
• According to the law of one price in finance, two
  assets generating the same cash flows should sell
  for the same price.
• Arbitrage consist of taking advantage of price
  discrepancies between two or more assets
  generating the same cash flows.

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Cash and Carry Arbitrage

• Example
• Asset XYZ
• Spot (cash) price 100
• Futures price expiring in one year 110
• Storage costs per year 8
• Fair or theoretical value of the futures 108

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Cash and Carry Arbitrage

• Example
• 108 is the indifference price. Since the futures
  price is 110 than there is an arbitrage
  opportunity.
• Purchase of the undervalued asset (in the cash
  market) and sale of the overvalued asset (the
  futures contract).

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Cash and Carry Arbitrage

• Arbitrage

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Reverse Cash and Carry Arbitrage

• Example
• Asset XYZ
• Spot (cash) price 100
• Futures price expiring in one year 105
• Storage costs per year 8
• Fair or theoretical value of the futures 108

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Reverse Cash and Carry Arbitrage

• Example
• 108 is the indifference price. Since the futures
  price is 105 than there is an arbitrage
  opportunity.
• Purchase of the undervalued asset (the futures
  contract) and sale of the overvalued asset (in
  the cash market).

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Reverse Cash and Carry Arbitrage

• Arbitrage

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Conditions Which Facilitate Arbitrage

• Ease of short selling
• A large supply of the underlying asset
• High storability
• Non-seasonal production and/or consumption

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Conditions Which Facilitate Arbitrage

• Arbitrage can easily be performed with financial
  futures
• Arbitrage is more difficult to execute on
  commodities.
• When shortages occur, market participants places
  a higher value on the benefits of owning the
  physical commodity.
• The spot price will be values at a higher price
  then the futures price (backwardation or inverted
  market)

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Inverted Markets

• An inverted market typically results from a
  shortage of the underlying asset in the cash
  market. The spot price increases above the
  futures price. Futures prices for the nearest
  delivery months are also above the deferred month
  prices.

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The Relationship Between Forward Prices and Spot
Prices

• The futures price of an asset providing no income
  is always higher than the spot price
• The futures price of an asset providing a known
  income could be lower than the spot price

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Types of operations

• Hedging with futures contracts
• Speculation with futures contracts
• Arbitrage with futures contracts

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Hedging with futures contracts

• Hedging is an operation that aims to reduce or
  eliminate risk
• Short hedge and long hedge
• Perfect and imperfect hedge
• Basis risk
• The optimal hedge ratio

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Long Hedge

• A long hedge aims to protect against rising
  prices between the present and the time when the
  asset is needed.
• Example of a perfect hedge
• You want to buy 1000 troy ounces of gold in 3
  months
• Actual price 350 per ounce
• Storage fees 10 per ounce per month, which
  implies that the fair futures price should be
  equal to 380 per troy ounce
• Buy 10 gold futures contracts on the New York
  Mercantile Exchange (COMEX division) at 380 per
  troy ounce
• Spot price at expiry 400 per ounce
• Futures price at expiry 400 per ounce

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Long Hedge

• Example of a perfect hedge

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Perfect Hedge

• Conditions for a perfect hedge
• The holding period matches the expiration date of
  the futures contract
• The asset being hedged matches the asset
  underlying the futures contract
• When these conditions are not met, the hedger is
  exposed to a basis risk

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Imperfect Hedge

• Basis
• The spread between the spot and the futures price
• At expiry, the basis is worthless
• Prior to expiry, the basis can fluctuate
  unexpectedly

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Imperfect Hedge

• Example of an imperfect hedge
• You want to buy 1000 troy ounces of gold in 3
  months
• Actual price 350 per ounce
• Storage fees 10 per ounce per month, which
  implies that the fair futures price should be
  equal to 380 per troy ounce
• Buy 10 gold futures contracts on the New York
  Mercantile Exchange (COMEX division) at 380 per
  troy ounce
• You must close the position one month prior to
  expiry
• Spot price in two months 400 per ounce
• Futures price in two months 400 per ounce

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Imperfect Hedge

• Example of an imperfect hedge

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Optimal Hedge Ratio

• The basis risk is usually linked to the interest
  rate fluctuations (changes in the cost of
  financing)
• Commodities including agricultural and energy
  based assets entail higher basis risk then other
  products.
• In case of shortage, holding the physical
  commodities is more valuable then holding the
  futures contract.
• The spot or cash price will be worth much more
  than the futures contract (inverted or
  backwardation market).

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Optimal Hedge Ratio

• There is a high basis risk when one of the
  following conditions is not met
• A large supply of the underlying asset
• Storability of the underlying asset
• Non-seasonal production and/or consumption
• Ease of short selling

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Optimal Hedge Ratio

• When the basis risk is not high, a hedge ratio of
  1 is appropriate
• If there is not maturity or asset match, the
  hedge ratio needs to be adjusted to reflect the
  historical or expected price correlation between
  the futures contract and the asset.

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Optimal Hedge Ratio

• A hedge where the futures contract uses an
  underlying asset similar but not the same as the
  physical asset being hedged is called a
  cross-hedge.
• The hedge ratio might be different than 1.
• The correlation between the assets and their
  respective volatility have to be taken into
  account.

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Optimal Hedge Ratio

• The optimal hedge ratio (H)
• H Corr(PF) (SDP / SDF)
• where
• SDP standard deviation of changes in the spot
  price (P),
• SDF standard deviation of changes in the
  futures price (F),
• Corr(PF) coefficient of correlation between
  changes in CP and F.

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Optimal Hedge Ratio

• Example
• A portfolio manager wants to reduce, by 10 M,
  for three months, the market risk of her
  portfolio composed of shares of American
  companies.
• The three-month standard deviation of the
  portfolio is 0.25, and the three-month standard
  deviation of the SP/TSX 60 index is 0.20. The
  correlation between the portfolio and the index
  is 0.88.

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Optimal Hedge Ratio

• Example
• SDP 0.25 SDF 0.20 Corr(PF) 0.88
• H Corr(PF) (SDP / SDF)
• H 0.88 (0.25 / 0.20) 1.10
• The size of the futures on the SP/TSX 60 index
  is 200 times the index level. If the index is
  valued at 500 then each contract has a value of
  100,000 (200 x 500). In order to hedge the
  portfolio manager must sell
• 1.10 x (10 M / 100,000) 110 contracts
• If she is not taking into account the volatility
  or the correlation then she has to sell only 100
  contracts (10 M/100,000).

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Speculation with futures contracts

• The futures market is particularly attractive to
  speculators for the following reasons
• Ease of entry and exit
• Variety of opportunities
• Leverage
• Excitement