Chapter 6
Introduction to Futures
• Because futures are so very similar to forwards, be
sure that you have read Section 3.1.
• A futures contract is an agreement to buy (if you are
long) or sell (if you are short) something in the
future, at an agreed upon price (the futures price).
• Futures exist on financial assets (debt instruments,
currencies, stock indexes), and real assets (gold,
crude oil, wheat, cattle, cotton, etc.)
©David Dubofsky and
Thomas W. Miller, Jr.
6-1
A Comparison of Futures Contracts
and Forward Contracts
• Both types of contracts specify a trade between two
counter-parties:
– There is a commitment to take delivery of an asset (this is
the buyer, or the long)
– There is a commitment to deliver an asset (this is the seller,
or the short)
• Many times, futures contracts and forward contracts
are substitutes.
• However, at specific times, the relative costs, liquidity,
and convenience of using one market versus the
other will differ.
©David Dubofsky and
Thomas W. Miller, Jr.
6-2
Futures and Forwards: A Comparison Table
Futures
Default Risk:
Forwards
Borne by Clearinghouse
Borne by Counter-Parties
Standardized
Negotiable
Agreed on at Time
of Trade Then,
Marked-to-Market
Agreed on at Time
of Trade. Payment at
Contract Termination
Where to Trade:
Standardized
Negotiable
When to Trade:
Standardized
Negotiable
Clearinghouse Makes it
Easy to Exit Commitment
Cannot Exit as Easily:
Must Make an Entire
New Contrtact
How Much to Trade:
Standardized
Negotiable
What Type to Trade:
Standardized
Negotiable
Required
Collateral is negotiable
Offset prior to delivery
Delivery takes place
What to Trade:
The Forward/Futures
Price
Liquidity Risk:
Margin
Typical Holding Pd.
©David Dubofsky and
Thomas W. Miller, Jr.
6-3
Other Unique Features of Futures Contracts
• Some futures contracts have daily price limits.
• Some futures contracts (Euro$, T-bills, stock index futures,
currencies) have one specific delivery date; others (T-bonds, crude
oil) give the short the option of choosing which day (usually in the
delivery month) to make delivery.
• Some futures contracts (e.g., T-bonds) let the seller choose the
quality of good to deliver, within a specified quality range.
• Some futures contracts (Euro$, stock index futures, feeder cattle)
are cash settled.
• Note that a futures contract is like a portfolio of forward contracts
(time series).
©David Dubofsky and
Thomas W. Miller, Jr.
6-4
Futures Contracts
Payoff Profiles
profit
Long futures
F(0,T)
profit
F(1,T)
The long profits if the next day’s futures
price, F(1,T), exceeds the original
futures price, F(0,T).
Short futures
F(0,T)
F(1,T)
The short profits if the next day’s
futures price, F(1,T), is below the
original futures price, F(0,T).
©David Dubofsky and
Thomas W. Miller, Jr.
6-5
Reading Futures Prices (8/28/02)
Crude Oil, Light Sweet (NYM) - 1,000 bbls.; $ per bbl.
Lifetime
Open
Open High
Low
Settle CHG High
Low
Int
Oct
28.87 29.00 28.17
28.34 -0.49 29.65 19.50 175667
Nov
28.62 28.75 28.08
28.23 -0.37 29.35 19.55
53739
Dec
28.64 28.64 28.00
28.12 -0.25 28.90 15.50
58227
Ja03
28.04 28.10 27.83
27.84 -0.12 28.40 19.90
27383
Feb
27.51 27.63 27.43
27.51 -0.05 28.05 19.70
11830
Mar
27.12 27.30 27.04
27.16 -0.01 27.45 20.05
15787
Apr
26.70 26.70 26.70
26.82 0.02 27.10 20.55
8424
May
26.50 26.50 26.50
26.49 0.03 26.68 20.70
5319
June
26.15 26.27 26.10
26.18 0.03 26.45 19.82
18205
July
25.75 25.75 25.75
25.91 0.03 26.05 20.76
4950
Dec
25.05 25.05 24.80
24.86 0.09 25.10 15.92
24864
Jn04
24.30 24.30 24.30
24.28 0.11 24.40 20.53
6804
Dec
23.90 23.90 23.85
23.86 0.17 24.00 16.35
14741
Dc08
22.30 22.30 22.30
22.20 0.17 22.30 19.75
6060
Est vol 209,648; vol Tue 221,229; open int 471,059, +5,139.
©David Dubofsky and
Thomas W. Miller, Jr.
6-6
Margin Requirements, I.
• Futures exchanges require good faith money from counterparties to futures contracts, to act as a guarantee that each will
abide by the terms of the contract.
• This money is called margin.
• Each futures exchange is responsible for setting the minimum
initial margin requirements for their futures contracts.
– The initial margin is the money a trader must deposit into a trading
account (margin account) when establishing a futures position.
– Many futures exchanges establish initial margin requirements by
using computer algorithms, the most popular of which is called
SPAN (Standard Portfolio ANalysis of risk).
©David Dubofsky and
Thomas W. Miller, Jr.
6-7
Margin, August 1, 2001
Contract
Exch.
S&P 500
CME
Nikkei 225
CME
Japanese Yen CME
Euro
CME
British Pound CME
Eurodollar
CME
TBill
CME
TBond
CBOT
10 yr. TNote CBOT
Gold
CMX
Crude Oil
NYM
Init-Spec
$21,563
6750
2835
2349
1418
810
540
2363
1620
1350
3375
Init-Spr Maint-Spec Maint-Spr
$250 $17,250
135
5000
68
2100
250
1740
68
1050
450
600
203
400
350
1750
350
1200
100
1000
1000
3000
$250
135
68
250
68
450
150
350
350
100
1000*
©David Dubofsky and
Thomas W. Miller, Jr.
6-8
Margin Requirements, II.
• SPAN uses historical price data to set initial margin to what is
believed to be a worst case one-day price movement.
• An exchange can change the required margin anytime.
• Initial Margin will increase if price volatility increases, or if the
price of the underlying commodity rises substantially.
• The margin required for trading futures differs from the concept
of margin when buying common stock or bonds.
– Margin for Common Stock: The fraction of the asset's cost that
must be financed by the purchaser's own funds. The remainder is
borrowed from the purchaser’s stock broker.
– Margin for Futures: A good faith deposit, or collateral, designed to
insure that the futures trader can pay any losses that may be
incurred. Futures margin is not a partial payment for a purchase.
©David Dubofsky and
Thomas W. Miller, Jr.
6-9
Margin Requirements, III.
•
•
•
•
If the equity in the account falls to, or below, the maintenance margin
level, additional funds must be deposited to restore the account
balance to the initial margin level.
E.g., suppose the initial margin required to trade one gold futures
contract is $1000, and the maintenance margin level is $750. Then,
an adverse change of $2.60/oz. will result in a margin call.
Because one gold futures contract covers 100 oz. of gold, a decline of
$2.60/oz. in the futures price will deplete the equity of a long position by
$260. The trader with losses must then deposit sufficient funds to bring
the equity in the account back to the initial margin of $1000.
The margin that is deposited in order to meet margin calls is called
variation margin. If the trader does not promptly meet the margin call,
his FCM will liquidate the position.
©David Dubofsky and
Thomas W. Miller, Jr.
6-10
Margin Requirements, IV.
• Note that once a trader receives a margin call, he must meet
that call, even if the price has subsequently moved in his favor.
• For example, suppose the futures price of gold declines to a
level that triggers a margin call on day t.
• On day t+1, the trader who is long a gold futures contract will
receive a margin call, regardless of the futures price of gold on
day t+1.
• Even if the gold futures price has substantially rebounded, the
trader must still deposit variation margin into his account.
©David Dubofsky and
Thomas W. Miller, Jr.
6-11
Margin Requirements, V.
• FCM's will often set initial and maintenance margin requirements at
higher levels than the minimum requirements specified by the
exchanges.
• Margin requirements also differ for different traders, depending on
whether the position is part of a spread, a hedge or a speculative
trade.
• Margin requirements on spreads and hedges are less than those on
speculative positions. Hedgers must sign a hedge account
agreement, declaring that the trades in the account will in fact be
hedges as defined by the Commodity Exchange Act of 1936, and as
specified by the CFTC.
©David Dubofsky and
Thomas W. Miller, Jr.
6-12
Margin Requirements, VI.
• In a spread, a trader will be long one contract, and also be short
another related contract.
• The two contracts may be on the same good, but for different
delivery months (called a calendar spread, or an intermonth
spread), or be on two similar goods for delivery in the same
month (called an intercommodity spread, or an intermarket
spread).
©David Dubofsky and
Thomas W. Miller, Jr.
6-13
Marking to Market, Example.
• The entire daily resettlement process is illustrated with the
following example.
• On November 6, 2001, you sell one gold futures contract for
delivery in December 2001.
• You sell the contract at 10 AM, when the futures price is
$285/oz.
• The initial margin requirement is $1000, and that sum of money
is transferred from your cash account to your margin account.
• The settlement price at the close on November 6 is $286.40/oz.
• Your account is marked to market, and your equity at the close
is $860.
• The futures price rose by $1.40/oz, and one contract covers 100
oz of gold; therefore, you have lost $140 on the short position.
©David Dubofsky and
Thomas W. Miller, Jr.
6-14
Marking to Market, Table.
On all subsequent days, the account is marked to market. If the
futures price falls, your equity rises. If the futures price rises, your
equity declines. Maintenance margin calls will have to be met if
your account equity falls to a level equal to or below $750.
Date
11/6
11/6 (end)
11/7
11/10
11/11
11/12
11/13
11/14
Gold
Cash Begin.
Price
Flow Equity
285.00
1000
286.40 (140)
860
288.80 (240)
620
289.00
(20)
980
288.60
40
1020
290.70 (210)
810
292.80 (210)
600
292.80
0
1000
Maint.
Margin Ending
Call
Equity
0
380
0
0
0
400
0
860
1000
980
1020
810
1000
1000
©David Dubofsky and
Thomas W. Miller, Jr.
6-15
Basis
• Understanding the basis is a key to hedging.
• Basis = futures price - spot price (financial futures)
• Basis = spot price - futures price (agricultural futures)
• Basis = “net cost of carry” (see chapter 5)
– F = S(1 + r) = S + rS = S + carry costs
– F - S = carry costs
– For stock index futures, F = S(1 + r) - FV(divs).
– If we define the dividend yield over the life of the contract as d:
F = S + rS - dS = S(1 + r - d)
F - S = S(r - d) = net cost of carry
©David Dubofsky and
Thomas W. Miller, Jr.
6-16
Convergence
• On the delivery date, ST = FT
• That is, at delivery (expiration) the basis equals zero.
• Question: What if ST did not equal FT?
• BTW, this is not the last time we will ask one of these ‘arbitrage’
questions.
©David Dubofsky and
Thomas W. Miller, Jr.
6-17
Types of Futures Contract Orders
• Every order must include:
–
–
–
–
–
–
–
–
Whether the trader wants to buy or sell
The name of the commodity
The delivery month and year of the contract
The number of contracts
The exchange on which they trade
Day order or “good-til-canceled” order
Market or limit order; if a limit order, then specify a limit price
There are other order types; see section 6.10.
©David Dubofsky and
Thomas W. Miller, Jr.
6-18
Should Futures Prices Equal
Forward Prices?
• Assume perfect markets.
• If interest rates are non-stochastic (i.e., known), then
futures prices = forward prices. This is because futures
can be transformed into forwards and the impact of the
daily resettlement in futures contracts can be eliminated.
• If corr(DF, Dr) > 0, then futures prices > forward prices
• If corr(DF, Dr) < 0, then futures prices < forward prices
©David Dubofsky and
Thomas W. Miller, Jr.
6-19
For More Information
• The major futures exchanges have websites. For links to some
of them, see: http://www.numa.com/ref/exchange.htm.
• The exchanges offer many free brochures, booklets and
information. Call them (or go to their websites) to get catalogs.
For example:
– CBOT: 1-800-843-2268 (1-800-THE-CBOT)
– CME: 1-800-331-3332
©David Dubofsky and
Thomas W. Miller, Jr.
6-20