Principles of Futures Contract Pricing

1
Principles of Futures Contract Pricing

• The expectations hypothesis
• Normal backwardation
• A full carrying charge market
• Reconciling the three theories

2
The Expectations Hypothesis

• The expectations hypothesis states that the
  futures price for a commodity is what the
  marketplace expects the cash price to be when the
  delivery month arrives
• Price discovery is an important function
  performed by futures
• There is considerable evidence that the
  expectations hypothesis is a good predictor

3
Normal Backwardation

• Basis is the difference between the future price
  of a commodity and the current cash price
• Normally, the futures price exceeds the cash
  price (contango market)
• The futures price may be less than the cash price
  (backwardation or inverted market)

4
Normal Backwardation (contd)

• John Maynard Keynes
• Locking in a future price that is acceptable
  eliminates price risk for the hedger
• The speculator must be rewarded for taking the
  risk that the hedger was unwilling to bear
• Thus, at delivery, the cash price will likely be
  somewhat higher than the price predicated by the
  futures market

5
A Full Carrying Charge Market

• A full carrying charge market occurs when the
  futures price reflects the cost of storing and
  financing the commodity until the delivery month
• The futures price is equal to the current spot
  price plus the carrying charge

6
A Full Carrying Charge Market (contd)

• Arbitrage exists if someone can buy a commodity,
  store it at a known cost, and get someone to
  promise to buy it later at a price that exceeds
  the cost of storage
• In a full carrying charge market, the basis
  cannot weaken because that would produce an
  arbitrage situation

7
Reconciling the Three Theories

• The expectations hypothesis says that a futures
  price is simply the expected cash price at the
  delivery date of the futures contract
• People know about storage costs and other costs
  of carry (insurance, interest, etc.) and we would
  not expect these costs to surprise the market
• Because the hedger is really obtaining price
  insurance with futures, it is logical that there
  be some cost to the insurance

8
Spreading with Futures

• Intercommodity spreads
• Intracommodity spreads
• Why spread in the first place?

9
Intercommodity Spreads

• An intercommodity spread is a long and short
  position in two related commodities
• E.g., a speculator might feel that the price of
  corn is too low relative to the price of live
  cattle
• Risky because there is no assurance that your
  hunch will be correct
• With an intermarket spread, a speculator takes
  opposite positions in two different markets
• E.g., trades on both the Chicago Board of Trade
  and on the Kansas City Board of Trade

10
Intracommodity Spreads

• An intracommodity spread (intermonth spread)
  involves taking different positions in different
  delivery months, but in the same commodity
• E.g., a speculator bullish on what might buy
  September and sell December

11
Why Spread in the First Place?

• Most intracommodity spreads are basis plays
• Intercommodity spreads are closer to two separate
  speculative positions than to a spread in the
  stock option sense
• Intermarket spreads are really arbitrage plays
  based on discrepancies in transportation costs or
  other administrative costs

12
Pricing of Stock Index Futures

• Elements affecting the price of a futures
  contract
• Determining the fair value of a futures contract
• Synthetic index portfolios

13
Elements Affecting the Price of A Futures Contract

• The SP 500 futures value depends on four
  elements
• The level of the spot index
• The dividend yield on the 500 stock in the index
• The current level of interest rates
• The time until final contract cash settlement

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Elements Affecting the Price of A Futures
Contract (contd)
SPX Dividend Yield
SPX Index
SP 500 Stock Index Futures
Time until Settlement
T-bill Rate
15
Elements Affecting the Price of A Futures
Contract (contd)

• Stocks pay dividends, while futures do not pay
  dividends
• Shows up as a price differential in the futures
  price/underlying asset relationship
• Stocks do not accrue interest
• Posting margin for futures results in interest
• Shows up as a price differential in the futures
  price/underlying asset relationship

16
Determining the Fair Value of A Futures Contract

• The futures price should equal the index plus a
  differential based on the short-term interest
  rate minus the dividend yield

17
Determining the Fair Value of A Futures Contract
(contd)

• Calculating the Fair Value of A Futures Contract
  Example
• Assume the following information for an SP 500
  futures contract
• Current level of the cash index (S) 1,484.43
• T-bill yield 6.07
• SP 500 dividend yield (D) 1.10
• Days until December settlement (T) 121 0.33
  years

18
Determining the Fair Value of A Futures Contract
(contd)

• Calculating the Fair Value of A Futures Contract
  Example
• The fair value of the SP 500 futures contract
  is

19
Synthetic Index Portfolios

• Large institutional investors can replicate a
  well-diversified portfolio of common stock by
  holding
• A long position in the stock index futures
  contract and
• Satisfying the margin requirement with T-bills
• The resulting portfolio is a synthetic index
  portfolio
• The futures approach has the following advantages
  over the purchase of individual stocks
• Transaction costs will be much lower on the
  futures contracts
• The portfolio will be much easier to follow and
  manage
• Basic Convergence As time passes, the difference
  between the cash index and the futures price will
  narrow
• At the end of the futures contract, the futures
  price will equal the index (basic convergence)

20
Interest Rate Futures

• Exist across the yield curve and on many
  different types of interest rates
• T-bond contracts
• Eurodollar (ED) futures contracts
• 30-day Federal funds contracts
• Other Treasury contracts

21
Characteristics of U.S. Treasury Bills

• Sell at a discount from par using a 360-day year
  and twelve 30-day months
• 91-day (13-week) and 182-day (26-week) T-bills
  are sold at a weekly auction

22
Characteristics of U.S. Treasury Bills (contd)

• Treasury Bill Auction Results

23
Characteristics of U.S. Treasury Bills (contd)

• The Discount Rate is the discount yield,
  calculated as

24
Characteristics of U.S. Treasury Bills (contd)

• Discount Yield Computation Example
• For the first T-bill in the table on slide 6,
  the discount yield is

25
Characteristics of U.S. Treasury Bills (contd)

• The discount yield relates the income to the par
  value rather than to the price paid and uses a
  360-day year rather than a 365-day year
• Calculate the Investment Rate (bond
  equivalent yield)

26
Characteristics of U.S. Treasury Bills (contd)

• Bond Equivalent Yield Computation Example
• For the first T-bill in the table on slide 6,
  the bond equivalent yield is

27
The Treasury Bill Futures Contract

• Treasury bill futures contracts call for the
  delivery of 1 million par value of 91-day
  T-bills on the delivery date of the futures
  contract
• On the day the Treasury bills are delivered, they
  mature in 91 days

28
The Treasury Bill Futures Contract (contd)

• Futures position 91-day T-bill T-bill
• established delivered matures
• 91 days
• Time

29
The Treasury Bill Futures Contract (contd)

• T-Bill Futures Quotations
• September 15, 2000

30
Characteristics of Eurodollars

• Applies to any U.S. dollar deposited in a
  commercial bank outside the jurisdiction of the
  U.S. Federal Reserve Board
• Banks may prefer eurodollar deposits to domestic
  deposits because
• They are not subject to reserve requirement
  restrictions
• Every ED received by a bank can be reinvested
  somewhere else

31
The Eurodollar Futures Contract

• The underlying asset with a eurodollar futures
  contract is a three-month, 1 million face value
  instrument
• A non-transferable time deposit rather than a
  security
• The ED futures contract is cash settled with no
  actual delivery

32
The Eurodollar Futures Contract (contd)

• Treasury Bill vs Eurodollar Futures

33
The Eurodollar Futures Contract (contd)

• The quoted yield with eurodollars is an add-on
  yield
• For a given discount, the add-on yield will
  exceed the corresponding discount yield

34
The Eurodollar Futures Contract (contd)

• Add-On Yield Computation Example
• An add-on yield of 1.24 corresponds to a
  discount of 3,124.66

35
The Eurodollar Futures Contract (contd)

• Add-On Yield Computation Example (contd)
• If a 1 million Treasury bill sold for a
  discount of 3,124.66 we would determine a
  discount yield of 1.236

36
Speculating With Eurodollar Futures

• The price of a fixed income security moves
  inversely with market interest rates
• Industry practice is to compute futures price
  changes by using 90 days until expiration

37
Speculating With Eurodollar Futures (contd)

• Speculation Example
• Assume a speculator purchased a MAR 05 ED
  futures contract at a price of 97.26. The ED
  futures contract has a face value of 1 million.
  Suppose the discount yield at the time of
  purchase was 2.74. In the middle of March 2005,
  interest rates have risen to 7.00.
• What is the speculators dollar gain or loss?

38
Speculating With Eurodollar Futures (contd)

• Speculation Example (contd)
• The initial price is

39
Speculating With Eurodollar Futures (contd)

• Speculation Example (contd)
• The price with the new interest rate of 7.00 is

40
Speculating With Eurodollar Futures (contd)

• Speculation Example (contd)
• The speculators dollar loss is therefore

41
Hedging With Eurodollar Futures

• Using the futures market, hedgers can lock in the
  current interest rate

42
Hedging With Eurodollar Futures (contd)

• Hedging Example
• Assume you are a portfolio managers for a
  universitys endowment fund which will receive
  10 million in 3 months. You would like to invest
  the money now, as you think interest rates are
  going to decline. Because you want a money market
  investment, you establish a long hedge in
  eurodollar futures. Using the figures from the
  earlier example, you are promising to pay
  993,150.00 for 1 million in eurodollars if you
  buy a futures contract at 98.76. Using the 10
  million figure, you decide to buy 10 MAR ED
  futures, promising to pay 9,969,000.

43
Hedging With Eurodollar Futures (contd)

• Hedging Example (contd)
• When you receive the 10 million in three
  months, assume interest rate have fallen to
  1.00. 10 million in T-bills would then cost
• This is 6,000 more than the price at the time
  you established the hedge.

44
Hedging With Eurodollar Futures (contd)

• Hedging Example (contd)
• In the futures market, you have a gain that will
  offset the increased purchase price. When you
  close out the futures positions, you will sell
  your contracts for 6,000 more than you paid for
  them.

45
Treasury Bonds and Their Futures Contracts

• Characteristics of U.S. Treasury bonds
• Pricing of Treasury bonds
• The Treasury bond futures contract
• Dealing with coupon differences
• The matter of accrued interest
• Delivery procedures
• The invoice price
• Cheapest to deliver

46
Characteristics of U.S. Treasury Bonds

• Very similar to corporate bonds
• Pay semiannual interest
• Have a maturity of up to 30 years
• Are readily traded in the capital markets
• Different from Treasury notes
• Notes have a life of less than ten years
• Some T-bonds may be callable fifteen years after
  issuance

47
Characteristics of U.S. Treasury Bonds (contd)

• Bonds are identified by
• The issuer
• The coupon
• The year of maturity
• E.g., U.S. government six and a quarters of 23
  means Treasury bonds with a 6¼ coupon rate that
  mature in 2023

48
Dealing With Coupon Differences

• To standardize the 100,000 face value
  T-bond contract traded on the Chicago Board of
  Trade, a conversion factor is used to convert all
  deliverable bonds to bonds yielding 6

49
Dealing With Coupon Differences (contd)
50
Cheapest to Deliver

• Normally, only one bond eligible for delivery
  will be cheapest to deliver
• A hedger will collect information on all the
  deliverable bonds and select the one most
  advantageous to deliver