F303 Intermediate Investments

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F303 Intermediate Investments

• Class 21
• Futures and Forwards
• Andrey Ukhov
• Kelley School of Business
• Indiana University

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Outline of This Subject

• The basics of Futures contracts.
• Mechanics of trading in futures markets.
• Futures market strategies.
• Determination of Futures prices.
• Forward versus Futures pricing.

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Futures and Forwards

• Futures and forward contracts are like
  optionsthey specify purchase or sale of some
  underlying asset at some future date.
• However, in the case of futures or forward
  contracts, we have the case where the holder has
  the obligation to go through with the agreed-upon
  transaction.
• These instruments offer powerful means to hedge
  other investments.

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Futures and Forwards

• Consider the case of an oil production company.
  The revenue of this company depends on oil
  prices, which are extremely volatile. This
  company cannot easily diversify
• On the other hand, consider a company that has to
  buy oil as one of the inputs in the production
  process. This company has a problem that is the
  mirror of the oil production company. This
  subject the company to profit unpredictability
  because of the volatile oil prices.
• Can forwards and futures help these two firms?

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Futures and Forwards

• It turns out that forwards and futures can
  contribute something to reduce this uncertainty
• The parties can reduce the source of risk if they
  enter a forward contract. This requires that the
  oil producer delivers oil at a price agreed upon
  now, regardless of the market price at the time
  when oil is produced.
• This requires that BOTH parties be willing to
  lock in the price to be paid or received for
  delivery of the commodity.

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Forwards versus Futures
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Hedging Using Futures

• A company that knows it is due to sell an asset
  at a particular time in the future can hedge by
  taking a short futures position. This is known as
  a short hedge.
• Case 1 Assets price goes down.
• The company does not fare well on the sale of the
  asset but makes a gain on the short futures
  position.
• Case 2 Assets price goes up.
• The company gains from the sale of the asset but
  makes a loss on the short futures position.

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Futures Contracts

• A futures contract calls for delivery of a
  commodity at a specified delivery or maturity
  date, for an agreed-upon price, called the
  futures price, to be paid on contract maturity.
• The trader taking the long position commits to
  purchasing the commodity on delivery date.
• The trader taking the short position commits to
  delivering the commodity at contract maturity.

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Futures Contracts

• The trader in the long position is said to buy
  a contract the short-side trader sells a
  contract.
• At maturity
• Profit to long Spot price at maturity
  Original futures price
• Profit to short Original futures price - Spot
  price at maturity
• The spot price is the actual market price of the
  commodity at the time of the delivery.

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Payoffs From Futures Contracts
Payoff
LONG POSITION
K
0
Asset price at maturity
K Delivery price
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Payoffs From Futures Contracts
Payoff
SHORT POSITION
K
0
Asset price at maturity
K Delivery price
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Futures Contracts

• The futures contract is a zero-sum game. The
  losses and gains to all positions netting out to
  zero. Every long position is offset by a short
  position.
• The aggregate profits to futures trading, summing
  over all investors, also must be zero, as is the
  net exposure to changes in the commodity prices.

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Types of Futures Contracts

• Foreign Currencies
• Agricultural Products
• Metals and Energy
• Interest Rate Futures
• Equity Indexes

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Marking to Market

• Traders in futures contracts must establish a
  margin account.
• This account is a form of security consisting of
  cash or near cash securities (like Treasury
  bills) that ensures that the trader is able to
  satisfy the obligations of the futures contracts.
  
• Because both parties to a futures contract are
  exposed to losses, both must post margins. The
  initial margin is usually set between 5 and 15
  of the total value of the futures contract.

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Marking to Market An Example

• Let us say that you want to buy two June 2002
  futures contracts. Suppose that the current
  futures price is 400 per ounce the contract
  size is 100 ounces. Hence the investor has
  contracted to buy a total of 200 ounces of gold.
• The broker will require you to deposit funds in a
  margin account.
• The amount that must be deposited at the time the
  contract is first entered is known as initial
  margin.

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Marking to Market An Example

• Let us say that the broker has decided that the
  initial margin is 2,000 per contract (4,000 in
  total).
• At the end of each trading day, the margin
  account is adjusted to reflect the investors
  gain or loss.
• This is the so-called marking to market.

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Marking to Market An Example

• Let us assume that the price on 31 March drops
  from 400 to 397 per ounce.
• How much has the investor lost?
• 200 x 3 600
• What is the new balance in the margin account?
• 3,400
• In this case, you will receive a margin call from
  your broker to top up the margin account by 600.

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Hedging and Speculation

• Futures contracts may be used for hedging or
  speculation.
• Speculators use the contracts to take a stand on
  the ultimate price of an asset.
• Short hedgers take short positions in contracts
  to offset any gains or losses on the value of an
  asset already held in inventory.
• Long hedgers take long positions to offset gains
  or losses in the purchase price of a good.

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Basis Risk

• The difference between the current spot price on
  an asset (the assets price for immediate
  delivery) and the corresponding futures price
  (the price stated in the futures contracts) is
  known as the basis for the futures
• Basis Current spot price Futures price
• The risk that the basis will narrow or widen,
  causing gains or losses to these investors, is
  known as basis risk.

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Convergence of Prices
Prices
Futures Price
Spot Price
Time
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Forwards Prices

• Consider a forward contract on a security that
  provides the holder with no income (no dividends,
  etc). Examples are non-dividend paying stocks.
• We use the no arbitrage argument to obtain the
  following forward price
• F Forward price today
• S Price of underlying asset
• T Time when forward contract matures (years)
• t Current time (years)
• r Risk-free rate with continuous compounding.

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Forwards Prices

• Example Consider a forward contract on a
  non-dividend paying stock that matures in 3
  months. Suppose that the stock price is 40, and
  the 3-month risk free rate is 5 per annum.
• In this case, T-t 0.25, r0.05 and S40

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Forwards Prices

• Consider a forward contract on a security that
  provides the holder with a known dividend yield.
  Examples are currencies and stock indices.
• We use the no arbitrage argument to obtain the
  following forward price
• F Forward price today
• S Price of underlying asset
• T Time when forward contract matures (years)
• t Current time (years)
• r Risk-free rate with continuous compounding
• q dividend yield

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Forwards Prices

• Example Consider a 6-month forward contract on a
  security that is expected to provide a continuous
  dividend yield of 4 per annum. The risk-free
  rate of interest (with continuous compounding) is
  10 per annum. The stock price is 25.
• In this case, T-t 0.5, r0.10, q0.04 and S25

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Futures Prices

• We can invoke the arbitrage argument to show
  that, when the risk-free rate is constant and the
  same for all maturities, the forward price for a
  contract with a certain delivery date is the same
  as the futures price for a contract with the same
  delivery date.
• When interest rates vary unpredictably, forward
  and futures prices are in theory no longer the
  same.
• Having said this, we shall assume that it is
  reasonable to assume that forward and futures
  prices are the same.

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Futures Prices

• Example Consider a 3-month futures contract on
  the SP 500. The stocks underlying the index
  provide a dividend yield of 3 per annum, the
  current value of the index is 400 and the the
  continuously compounded risk-free rate is 8 per
  annum.
• In this case, T-t 0.25, r0.08, q0.03 and S400

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Key Points to Remember

• The basics of futures and forward contracts.
• Hedging and speculative motives
• Forward and futures prices