1. Chapter 14
Futures Contracts

2. Forward Contract Agreement made today between buyer and seller
Both are obligated to complete a transaction at a date in the future
Buyer and the seller know each other
Customized agreements are negotiated
All contract terms can be customized to the requirements of the buyer and seller

3. Forward Contract Forward Price Default Risk
Price at which the trade will occur
Determined when the agreement made
Default Risk
Counterparty may have incentive to default on the contract
To cancel the contract, both parties must agree
Cancellation payment may be required

4. Futures Contract Agreement made today between buyer and seller
Both obligated to complete a transaction at a date in the future.
Buyer and the seller do not know each other.
Any "negotiation" occurs in a futures pit.
Standardized contract terms
What to trade; Where to trade; When to trade; How much to trade; what quality of good to trade—all standardized under the terms of the futures contract.

5. Futures Contract Futures Price No default risk
Price at which the trade will occur
Determined "in the pit"
No default risk
Futures Clearing and the exchange guarantees each trade
Offsetting trade "in the pit" cancels a contract
Trader may experience a gain or a loss

6. Forward & Futures Contracts
Both:
Are a firm commitment by both buyer and seller
Specify a price today for a future transaction
Specify a delivery date
Clearly define what is to be delivered and where
Forward contracts and futures contracts are really quite similar.
Both involve firm commitments by both the buyer and seller.
Both contracts, at origination, specify what is to be delivered and where delivery will take place as well as the price and date of delivery.
The primary difference is that forward contracts are individually negotiated between a buyer and seller, for example, a corporation and a bank.
The specific terms such as exact amount of the underlying asset to be delivered and the delivery date are chosen by the parties involved.
A forward contract keeps the buyer and seller linked throughout the term of the contract.

7. Forward & Futures Contracts
BUT:
Forward contracts:
Between a specific buyer and seller who remain linked throughout the life of the contract
Counterparties have negotiated an exact delivery date and terms
Futures contracts:
Fundamentally standardized, exchange-traded forward contracts.
Futures contracts, on the other hand, have standardized terms – size, delivery date, etc. They are traded on exchanges such as the Chicago Board of Trade.
Buyers and sellers of exchange-traded futures contracts need not ever know each other. Everything is handled through the exchange.
Our focus in this chapter is on futures contracts.

8. Organized Futures Exchanges
Chicago Board of Trade (CBOT)
Established in 1848
Oldest organized futures exchange in US
CME Group
CME (1874) and CBOT merge 2007
CME and NYMEX (1872) merge 2008
In 2007, the Intercontinental Exchange (ICE) purchased the New York Board of Trade (NYBOT)
Originally all traded storable agricultural commodities (soybeans, corn, wheat…)

9. Financial Futures Important milestones:
Currency futures trading 1972
Gold futures trading
December 31, 1974
= day ownership of gold by U.S.
citizens legalized.
U.S. Treasury bill futures
U.S. Treasury bond futures
Eurodollar futures
Stock Index futures
Today, financial futures = bulk of all futures trading.

10. Futures Contract Terms
Five basic terms:
Identity and description of the underlying commodity or financial instrument
Contract size.
Maturity or expiration date
Delivery or settlement procedure
Futures price

11. Futures Prices in the Wall Street Journal

12. Futures Prices on the Web

13. Futures Price Quotes Cocoa futures
Traded on the NY Board of Trade (ICE)
Contracts: March, May, July, September, December
Contract Size: 10 tonnes (metric tons) = 22,046 lbs
Price quote: $ per metric ton
COCOA (NYBOT) – 10 metric tons $ per ton.
let’s look at how futures prices are quoted.
The table on the slide recaps some of the quotes on cocoa futures for July 2, 2008.
Cocoa is traded on the New York Board of Trade (NYBOT) with contracts maturing in March, May, July, September and December. Maturity months are chosen by the listing exchange to match investor needs. In the case of agricultural commodities such as cocoa, they typically match harvest times.
The contract size for cocoa is ten metric tons (tonnes) and prices are quoted in U.S. dollars per metric ton.
Looking now at the quotes. Much like other financial quotes we have looked at, futures quotes include the opening price (OPEN), and intraday high and low prices. The closing price for the day is in the column marked “SETT” for settlement price. As we’ve seen before, quotes report the change since yesterdays closing price, volume and open interest.
Source: WSJ 07/02/2008

14. Why Futures? Futures contract = zero-sum game Hedging and Speculation
Buyer’s gains = seller’s losses
Futures exchanges track daily gains/losses
“Marking to market”
Hedging and Speculation
Hedging and speculating = complementary
Hedgers shift price risk to speculators
Speculators absorb price risk

15. Speculating with Futures: Long
Buying a futures contract:
= establishing a long position
= “going long”
Profit and Loss from a Speculative Long Position
Every day a new futures price is established.
If new price > previous day’s price
Long position profits
If new price < previous day’s price
Long position loses

16. Speculating in Gold Futures
You believe the price of gold will go up.
You go long 100 futures contracts that expire in 3 months.
Gold futures price today = $800 per ounce.
Gold futures contract = 100 ounces
“Position value" = $800 ×100 × 100 = $8,000,000
If the price of gold is $820 when the futures contract expires:
Position value = $820 × 100 × 100 = $8,200,000
Long speculation gain = $200,000

17. Speculating with Futures: Short
Selling a futures contract:
= establishing a short position
= “going short”
Profit and Loss from a Short Speculative Position
Every day before expiration, a new futures price is established.
If new price > previous day’s price
Short position loses
If new price < previous day’s price
Short position profits

18. Speculating in Gold Futures
You believe the price of gold will go down.
You go short 100 futures contracts that expire in 3 months.
Futures price today = $800 per ounce.
Gold futures contract size = 100 ounces
Position value = $800 × 100 × 100 = $8,000,000
If the price of gold is $770 when the futures contract expires:
Position value now = $770 × 100 × 100 = $7,700,000
Short speculation gain = $300,000

19. Hedging with Futures
A hedger trades futures contracts to transfer price risk.
Hedgers transfer price risk by adding a futures contract position that is opposite of an existing position in the commodity or financial instrument.
When the hedge is in place:
The futures contract “throws off” cash when cash is needed.
The futures contract “absorbs” cash when cash is available.

20. Hedging
Hedging = doing NOW in the futures market what you will have to do in the future in the cash market in order to transfer your risk.
Hedger = a “natural” in the market
The farmer plants in the spring
He must sell into the cash market at harvest time in the fall.
He can hedge his risk by selling into the futures market now.
A major application of futures contracts is hedging.
Hedging is simply doing NOW in the futures market what you will have to do later in the cash market in order to transfer the price risk to a counterparty.
A hedger is considered a “natural” in the market, meaning he is seeking to offset the risk of a normal part of his business.
The most obvious example of a hedger is a farmer who plants his crops in the spring, anticipating selling into the cash market at harvest time in the fall.
In order to offset some of his risk, he can sell his crop into the futures market now, locking in a delivery price.

21. Natural Long and Short Hedges
The farmer who plants soybeans in the spring will need to sell in the fall.
He is a natural long.
To hedge his risk, he needs to go short in the futures market.
He sells his expected crop output now to transfer his risk
Here are two examples of hedgers ..
The soybean farmer is a “natural long” so he needs to go short (sell) into the futures market.

22. Natural Short and Long Hedges
A cereal maker needs a continuous supply of grains.
He is a natural short.
To hedge his risk, he needs to go long in the futures market.
He buys futures contracts now to lock in his futures costs.
A cereal maker would be a “natural short” as he must have a continual supply of grain to maintain his production lines. To hedge his risk he would go long, buying into the futures market to lock in his supply and price.

23. Hedging with Futures: Short Hedge
A company has a large inventory that will be sold at a future date.
The company will suffer losses if the value of the inventory falls.
To protect the value of their inventory:
Selling futures contracts today offsets potential declines in the value of the inventory.
Selling futures contracts to protect against falling prices is called short hedging.

24. Short Hedging with Futures Contracts
Starbucks has 950,000 pounds of coffee in inventory, valued at $0.57 per pound
Starbucks fears coffee prices will fall in the short run
Data:
NYBOT trades coffee futures contracts
Each contract is for 37,500 pounds of coffee
Coffee futures price with three month expiration = $0.58/lb
Selling futures contracts provides current inventory price protection
25 futures contracts covers 937,500 pounds
26 futures contracts covers 975,000 pounds

25. Short Hedging with Futures Contracts
Starbucks sells 25 near-term futures contracts.
Over the next month:
Price of coffee falls
Starbucks sells its inventory for $0.51/lb
Futures price also falls to $0.52
How did this short hedge perform?

26. The Short Hedge Performance
The hedge was not perfect.
Short hedge “threw-off” cash ($56,250) which offset the decline in the inventory value ($57,000).
What would have happened if prices had increased by $0.06 instead?

27. Long Hedging with Futures
A company needs to buy a commodity at a future date.
To "fix" the price they’ll pay:
Buying futures contracts today offsets potential increases in price
Buying futures contracts to protect against rising prices is called long hedging

28. Long Hedging with Futures Contracts
Nestles plans to purchase 750 metric tons of cocoa next month.
Current cocoa prices = $3,400 per tonne
Nestle fears the price will increase before next month and wants to “lock in” the price it will pay
Data:
NYBOT trades cocoa futures contracts
Contract size = 10 metric tons (22,046 lbs)
Cocoa futures price with three months to expiration = $3,440 per tonne
Buying futures contracts locks in “acquisition” price
75 futures contracts covers 750 metric tonnes

29. Long Hedging with Futures Contracts
Nestles decides to buy 75 near-term futures contracts.
Over the next month:
The price of cocoa increases to $3,490.
The futures price increases to $3,525.
How did this long hedge perform?

30. The Long Hedge Performance
Date
Nestles
Cocoa Price
Nestles Inventory Acquisition
Near-Term Cocoa Futures Price
Value of 75 Cocoa Futures Contracts
Now
$3,400
$2,550,000
$3,440
$2,580,000
1-Month
From now
$3,490
$2,617,500
$3,525
$2,643,750
Gain (Loss)
$90
$67,500
$85
$63,750
This is a reference price to show the difference in what will be paid.
The hedge was not perfect. But, the long hedge “threw-off” cash ($63,750) when Nestles needed some extra cash to offset the increase in the cost of their cocoa inventory acquisition ($67,500).
What would have happened if cocoa prices fell by $85 instead?

31. Hedging Currency Transactions
Your company has contracted to buy products from Japan in three months for 2 million yen.
Today’s exchange rate =105.99¥ to the US$
2 million yen = $18,869.70
Looking at the forward rates, you fear prices will move against your company in 3 months.
Is your company “short” or “long” yen?
How would you hedge your company’s exposure to possible changes in the US$-Yen exchange rate?
Futures contracts are used extensively to hedge the exchange rate risk in foreign currency transactions.
In this example, your company will need 2 million yen in three months to pay for product on order.
Today’s exchange rate is Yen to the U.S. dollar.
At that rate, 2 million yen equals $18,
Is your company long or short yen?
How would you hedge your exchange rate risk?
We’ll continue this example on the next slide.

32. Hedging Currency Transactions
Company is short; they will need to buy Yen in 3 months.
With the quotes shown above, 2 million yen would currently = $18, (2,000,000/105.99)
At the 3-month forward rate 2 million yen = $18,
Entering into a 3-month forward contract for 2 million yen at the above rate will lock in the exchange rate.
Since you will need to buy yen in the market in the future, you are short yen.
Looking at the quotes shown above, we saw 2 million yen convert to $18, at the current spot market exchange rate.
Using the 3-month forward rate, 2 million yen would equal $18,969.93, a difference of about $100.
If you entered into the 3-month forward contract you will lock in your exchange rate. This could be good or bad depending on which way exchange rates move over the three month period. Whichever way they move, you have eliminated your risk and are certain of your exchange rate.

33. Hedging Currency Transactions
Suppose the situation is reversed:
In 6 months your company will receive 4 million yen for product you will deliver.
How do you hedge your exposure?
Let’s look at a reverse situation. In 6 months your company will receive 4 million yen. How do you hedge this exposure?

34. Hedging Currency Transactions
Your company has a long position in Yen – you’re going to receive Yen in 6 months.
Now 4 million Yen = $37,
If spot rates move as expected, you’ll be OK.
In 6 months, 4 million Yen will result in $38,
You can lock in that price now by shorting a 6-month forward contract in Yen at the rate of Yen per US$.
In this case, you are long yen.
If the exchange rate in 6 months equals today’s spot rate, 4 million yen would equate to $37,
If these forward rates truly reflect the way exchange rates will move over the next six months then you’ll be OK. 4 million yen at the 6-month forward rate translates to $38, a gain.
But rates might not move that way. You can lock in the 6-month forward rate now, by shorting the 6-month forward contract on yen.

35. Futures Trading Accounts
Margin required
Initial margin
Level depends on the price volatility of the underlying asset
Can differ by type of trader
Maintenance margin
A futures position can be closed out at any time by entering a reverse trade.
In the hedging examples, Starbucks and Nestles entered reverse trades at the time they adjusted inventories.

36. Marking to Market
Daily adjustment of a futures trading account value based on market settlement price (closing price)
If balance < maintenance margin  margin call
Margin call = demand by broker for more money to be deposited into the trading account.

37. Margin and Marking to Market
Molly believes gold prices will increase.
She takes a long position in gold futures.
Futures price = $400 per oz
Her broker requires:
Initial margin of $1,000 per contract
Maintenance margin of $750 per contract
Molly deposits $1,000 into her trading account.
Note: A reputable brokerage firm would actually require more, perhaps as much as $10,000.

38. Initial Margin Deposit
Molly’s Trading Account for a Long Position in One Gold Futures Contract
Day
Deposits
Closing
Futures Price
Equity Value of
Account
Maint. Margin Level
Diff.
Action
$1,000
$750
+$250
Initial Margin Deposit 1
$400
Molly buys at close 2
$398
$800
+$50 3
$394
-$350
Margin Call for $600 4
$600

39. Cash Prices Cash price: Cash market = spot market = spot price
= price for immediate delivery.
Cash market = spot market
Where commodities or financial instruments are traded for immediate delivery.
“Immediate" delivery can be 2 or 3 days later.

40. Quoted Cash Prices

41. Cash-Futures Arbitrage
Earning risk-free profits from an unusual difference between cash and futures prices is called cash-futures arbitrage.
In a competitive market, cash-futures arbitrage has very slim profit margins.
Cash prices and futures prices are seldom equal.

42. Cash-Futures Arbitrage
Basis = Cash price – Futures price
Carrying charge market :
Basis = Cash price – Futures price < 0
Commodities with storage costs
Inverted market:
Basis = Cash price – Futures price > 0
Basis is kept at an economically appropriate level by arbitrage.

43. Spot-Futures Parity
The Spot-Futures Parity relationship must hold to prevent arbitrage opportunities.
where:
F = futures price
S = spot price
r = risk-free rate
T = number of periods to contract maturity
The relationship between spot and futures prices is call spot-futures parity.
As shown in the equations above, the futures price should equal the current spot price multiplied by the cost of money, represented by one plus the risk-free rate.
The basic equation shown in (14.2) is generalized for multiple periods in equation (14.3) where “T” is the number of periods to contract maturity.
Note that “T” may be a fraction such as ½ representing 6 months to maturity.

44. Spot-Futures Parity: Example
Suppose the current price on a non-dividend paying stock is $25. The risk-free rate is 5.5%.
If a futures contract on this stock is available with a 6 month maturity, what should it’s price be?
(14.3) F = S(1+r)T
F = $25(1+.055).5
F = $
Suppose the current market price on a non-dividend-paying stock is $25.
The risk-free rate is 5.5%.
What should be the price of a 6-month futures contract on this stock?
Using equation (14.3) with “T” equal to .5, we find a price of $

45. Spot Futures Parity with Dividends
Particularly important for stock index futures
If D represents a dividend paid at or near the end of the futures contract’s life, the spot-futures parity formula is:
If there is dividend yield (d = D/S), the spot-futures parity formula is:

46. Spot-Futures Parity: Example
Suppose the current price on a stock is $25. The stock has an annual dividend yield of 2.5%.
The risk-free rate is 5.5%.
If a futures contract on this stock is available with a 6 month maturity, what should it’s price be?
(14.6) F = S(1+r-d)T
F = $25( ).5
F = $
Using our same $25 stock. Now we have an annual dividend of 2.5% and a 5.5% risk-free rate.
Using equation (14.6), we find the 6-month contract should be priced at $

47. Stock Index Futures Futures contracts on stock market indexes:
The S&P 500
The Dow Jones Industrial Average
Cash Settled
Difficult to actually deliver
At expiration, no delivery of shares of stock.
Positions are "marked-to-market" for the last time and cash settled.

48. Stock Index Futures
In September 2008, you believe the broad market is going to decline over the next three months.
You sell (short) one December 2008 S&P500 index futures contracts at
Your total short position = $250 X or $316,675.00
Stock index futures are very popular as vehicles to hedge or speculate on broad market movements.
In this example, you believe the market is going to fall over the next three months.
You sell short a December S&P500 index futures contract.
The S&P500 Index futures contract size is $250 times the index value.
With a December price of , your position would equal times $250 or $316,675.

49. Stock Index Futures
At maturity, the value of the S&P500 Composite Index is
You shorted the December 2008 S&P500 index futures contracts at
The buyer of your short sale contract owes you:
(Contract price – Current value) X $250
( – ) X $250 = $4,125
Index Futures contracts are not delivered, but rather use a process call “cash settlement”. With cash settlement, the buyer and seller exchange cash based on the futures price and the current price of the index at maturity.
In our example, you shorted a December S&P500 futures contract at
At maturity, the index is valued at
The difference is minus or 16.5 points.
Since the index declined as you anticipated, the buyer owes you 16.5 times $250 or $4,125 in cash.

50. Single Stock Futures
OneChicago began trading single stock futures in November 2002.
Joint venture of the CBOE, CME and the CBOT.
Single Stock Futures contracts listed on 80 stocks
Underlying asset = 100 Shares of common stock.
Shares are delivered at expiration.
Industry Basket Futures
14 industry sectors
Each “basket” = 5 stocks
Cash settled

51. Index Arbitrage Index arbitrage
Trading stock index futures and underlying stocks to exploit deviations from spot-futures parity.
Often implemented as a program trading strategy.
Program trading accounts for about 15% of total trading volume on the NYSE.
About 20% of all program trading involves stock-index arbitrage.
Index Arbitrage attempts to exploit discrepancies between the futures price of an index contract and the price of the assets making up the index.
Index arbitrageurs use the spot-futures parity relationship to find trading opportunities.

52. Index Arbitrage The S&P500 is currently at 1262.9.
The annual risk-free rate is 4.5%.
The annual dividend yield on the S&P500 is 2.5%.
How can you determine if the futures contracts are mispriced?
Suppose the S&P500 index is currently at
The annual risk free rate is 4.5%.
The annual dividend yield on the S&P500 is 2.5%.
On the next slide we’ll see how we used the spot-futures parity to identify this mispricing.

53. Index Arbitrage
Using our given data, the column labeled “should be” reflects the price indicated by the spot-futures parity equation.
The “Diff” column records “LAST” minus “SHOULD BE.”
Clearly there are mispricing opportunities in these contracts.
Since the “DIFF” (difference) column is negative, it indicates that the last or closing futures contract price is too low relative to the current spot price.
We should buy the futures contract and sell the index short.

54. Cross Hedging
Hedging a particular spot position with futures contracts on a related, but not identical, commodity or financial instrument.
For example:
You decide to protect your stock portfolio from a fall in value by selling S&P 500 stock index futures contracts.
This is a “cross-hedge” if changes in your portfolio value do not move in tandem with changes in the value of the S&P 500 index.

55. Hedging Stock Portfolios with Stock Index Futures
Suppose you want to protect the value of a portfolio against changes in the underlying market.
bD = desired Beta = zero
bP = beta of portfolio to be hedged
VP = dollar value of portfolio to be hedged
VF = dollar value of one S&P 500 futures contract = 250 × S&P 500 index futures price
Formula:

56. Example: Hedging a Stock Portfolio with Stock Index Futures
You want to protect the value of a $185,000,000 portfolio over the near term (so, you will "short-hedge").
βp = 1.25
βD = 0
S&P futures contract with 3-months to expiration has a price of 1,480.
How many futures contracts do you need to sell?

57. Example: Hedging a Stock Portfolio with Stock Index Futures
3-month S&P futures contract = 1,480
S&P 500 Multiplier:

58. Hedging Interest Rate Risk
To protect a bond portfolio against changing interest rates, we may cross-hedge using futures contracts on U.S. Treasury notes.
It is called a “cross-hedge” if the value of the bond portfolio held does not move in tandem with the value of U.S. Treasury notes.
A short hedge will protect your bond portfolio against the risk of a general rise in interest rates during the life of the futures contracts.
Bond prices fall when interest rates rise.
Selling bond futures throws off cash when bond prices fall.

59. Hedging Bond Portfolios with T-note Futures: Formula
Information needed for the formula:
DP = Duration of the bond portfolio
VP =Value of the bond portfolio
DF = Duration of the futures contract
VF =Value of a single futures contract

60. Handy Estimate for the Duration of an Interest Rate Futures Contract
Rule of Thumb Estimate: The duration of an interest rate futures contract, DF, is equal to:
The duration of the underlying instrument, DU, plus
The time remaining until contract maturity, MF.
That is:

61. Example: Hedging a Bond Portfolio with T-note Futures
You want to protect the value of a $100,000,000 bond portfolio over the near term (so, you will "short-hedge").
Suppose the duration of the underlying T-note is 6.5, and the futures contract has 0.5 years to expiration.
Also suppose the T-note futures price is 110 (which is 110% of the $100,000 par value.)

62. Example: Hedging a Bond Portfolio with T-note Futures
VP = $100,000,000
DF = = 7.0
VF = 1.10 * $100,000
How many futures contracts do you need to sell?

63. Example: Hedging a Bond Portfolio with T-note Futures

64. Futures Contract Delivery Options
Cheapest-to-deliver
Seller’s option to deliver the cheapest instrument when a futures contract allows several instruments for delivery.
Complicates hedging
Increases futures liquidity
U.S. Treasury note futures allow delivery of any Treasury note with a maturity between 6 1/2 and 10 years.

65. Useful Websites Futures Exchanges: www.cmegroup.com www.nymex.com
(Search for LIFFE)
(Sydney Futures Exchange)
(Tokyo International Financial Futures Exchange)
(Singapore Exchange)
(Extensive list of world’s futures exchanges)
For Futures Prices and Price Charts: