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 (cont’d)
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 (cont’d)
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 S&P 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

14. Elements Affecting the Price of A Futures Contract (cont’d)
SPX Dividend Yield
SPX Index
S&P 500
Stock Index Futures
Time until Settlement
T-bill Rate

15. Elements Affecting the Price of A Futures Contract (cont’d)
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

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 (cont’d)
Calculating the Fair Value of A Futures Contract Example
Assume the following information for an S&P 500 futures contract:
Current level of the cash index (S) = 1,484.43
T-bill yield ® = 6.07%
S&P 500 dividend yield (D) = 1.10%
Days until December settlement (T) = 121 = 0.33 years

18. Determining the Fair Value of A Futures Contract (cont’d)
Calculating the Fair Value of A Futures Contract Example
The fair value of the S&P 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 (cont’d)
Treasury Bill Auction Results
Term
Issue Date
Auction Date
Discount Rate %
Investment Rate %
Price Per $100
13-week
0.885
0.901
99.779
26-week
0.995
1.016
99.500
4-week
0.870
0.882
99.935
0.884
99.783
0.970
0.992
99.512
0.830
0.850

23. Characteristics of U.S. Treasury Bills (cont’d)
The “Discount Rate %” is the discount yield, calculated as:

24. Characteristics of U.S. Treasury Bills (cont’d)
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 (cont’d)
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 (cont’d)
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 (cont’d)
Futures position day T-bill T-bill
established delivered matures
91 days
Time

29. The Treasury Bill Futures Contract (cont’d)
T-Bill Futures Quotations
September 15, 2000
Open
High
Low
Settle
Change
Open Interest
Sept
94.03
94.02
-.01
5.98
+.01
1,311
Dec
94.00
93.96
93.97
-.02
6.03
+.02
1,083

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 (cont’d)
Treasury Bill vs Eurodollar Futures
Treasury Bills
Eurodollars
Deliverable underlying commodity
Undeliverable underlying commodity
Settled by delivery
Settled by cash
Transferable
Non-transferable
Yield quoted on discount basis
Yield quoted on add-on basis
Maturities out to one year
Maturities out to 10 years
One tick is $25

33. The Eurodollar Futures Contract (cont’d)
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 (cont’d)
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 (cont’d)
Add-On Yield Computation Example (cont’d)
If a $1 million Treasury bill sold for a discount of $3, 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 (cont’d)
Speculation Example
Assume a speculator purchased a MAR 05 ED futures contract at a price of 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 speculator’s dollar gain or loss?

38. Speculating With Eurodollar Futures (cont’d)
Speculation Example (cont’d)
The initial price is:

39. Speculating With Eurodollar Futures (cont’d)
Speculation Example (cont’d)
The price with the new interest rate of 7.00% is:

40. Speculating With Eurodollar Futures (cont’d)
Speculation Example (cont’d)
The speculator’s 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 (cont’d)
Hedging Example
Assume you are a portfolio managers for a university’s 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, for $1 million in eurodollars if you buy a futures contract at Using the $10 million figure, you decide to buy 10 MAR ED futures, promising to pay $9,969,000.

43. Hedging With Eurodollar Futures (cont’d)
Hedging Example (cont’d)
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 (cont’d)
Hedging Example (cont’d)
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 (cont’d)
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 (cont’d)

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