Chapter 8
Stock Index Futures
• Organization of Slides:
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–
–
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History
Futures Contract Specifications
Risk Management
Index Calculations (Appear in the Extra Section).
©David Dubofsky and 8-1
Thomas W. Miller, Jr.
Stock Index Futures, History I.
• Trading began on February 24, 1982, when the Kansas City
Board of Trade introduced futures on the Value Line Index.
• About two months later, the Chicago Mercantile Exchange
introduced futures contracts on the S&P 500 index.
• By 1986, the S&P 500 futures contract had become the second
most actively traded futures contract in the world, with over 19.5
million contracts traded in that year.
• In May 1982, the NYSE Composite Index futures contract began
trading on the New York Futures Exchange, the NYFE.
©David Dubofsky and 8-2
Thomas W. Miller, Jr.
Stock Index Futures, History II.
• In July 1984, the Chicago Board of Trade began trading futures
contracts on the Major Market Index (MMI).
– Dow Jones and Company went to court to block its attempts
to trade futures on the Dow Jones Industrial Average (DJIA)
• But, in June 1997, Dow Jones and Company agreed to allow
DJIA options, futures, and options on futures to begin trading.
• On October 6, 1997, futures on the DJIA began trading on the
Chicago Board of Trade.
©David Dubofsky and 8-3
Thomas W. Miller, Jr.
In their short trading history, stock index
futures contracts have had a great impact.
• Trading in stock index futures has allegedly made the world's
stock markets more volatile than ever before.
• Critics claim that individual investors have been driven out of the
equity markets because institutional traders' actions in both the
spot and futures markets cause stock values to gyrate with no
links to their fundamental values.
• Many political figures have called for greater regulation, going
so far as to favor an outright ban on stock index futures trading.
• Fortunately, such extreme measures have been avoided.
©David Dubofsky and 8-4
Thomas W. Miller, Jr.
Stock index futures have become
irreplaceable in the modern world of
institutional money management.
• Stock Index futures have revolutionized the art and
science of equity portfolio management as practiced by:
–
–
–
–
–
mutual funds
pension plans
endowments
insurance company
other money managers.
©David Dubofsky and 8-5
Thomas W. Miller, Jr.
2 Important Details
• A futures contract on a stock market index represents
the right and obligation to buy or to sell a portfolio of
stocks characterized by the index.
• Stock index futures are cash settled.
– That is, there is no delivery of the underlying stocks.
– The contracts are marked to market daily.
– On the last trading day, the futures price is set equal to the
spot index level and there is a final mark to market cash flow.
©David Dubofsky and 8-6
Thomas W. Miller, Jr.
What is an Index?
• An index is, in one sense, just a number that is computed in
order to measure the value of a portfolio of stocks.
– Other indices have been constructed to track the values of other
types of securities, such as bonds and futures.
– Still other indices track such economic indicators as the consumer
price index (CPI) or the index of leading indicators.
• When constructing a stock market index, three issues are of
particular interest:
– which stocks are in the index
– how each stock is weighted
– how the average is computed
• We will describe three different stock market indices.
©David Dubofsky and 8-7
Thomas W. Miller, Jr.
A Famous Price-Weighted Index: The
Dow Jones Industrial Average
• When one asks: "How is the market doing?", it is
usually implicit that the question is refers to the DJIA.
• Other stock market indices that are computed in the
same way as the DJIA, and which have futures and
options trading on them include the Nikkei 225 stock
index of Japanese stocks.
©David Dubofsky and 8-8
Thomas W. Miller, Jr.
As of December 2001, the 30
stocks in the DJIA were:
Alcoa
American Express
AT&T
Boeing
Caterpillar
Citigroup
Coca Cola
Disney
DuPont
Eastman Kodak
Exxon Mobil
General Electric
General Motors
Hewlett Packard
Home Depot
Honeywell
IBM
Intel
International Paper
Johnson & Johnson
McDonalds
Merck
Microsoft
3-M
J.P. Morgan Chase
Philip Morris
Procter & Gamble
SBC Communications
United Technologies
Wal-Mart
©David Dubofsky and 8-9
Thomas W. Miller, Jr.
Dow Jones Futures
• Futures on the DJIA trade on the Chicago Board of Trade.
• The value of stock underlying one DJIA futures contract equals
$10 times the futures price.
• One tick is one Dow-point, and this equals $10.
• Thus, if the DJIA futures price rises one tick, i.e., from 10813 to
10814, a trader who is long one contract profits by $10 because
the value of the stock underlying the contract rises from
$108,130 to $108,140.
©David Dubofsky and 8-10
Thomas W. Miller, Jr.
A Famous Value-Weighted Average:
The S&P 500 Stock Index
• A widely quoted benchmark portfolio.
• Vanguard S&P 500 Trust.
• SPDR. (http://www.amex.com).
• Standard and Poor’s (S&P) webpage:
http://www.standardandpoors.com.
©David Dubofsky and 8-11
Thomas W. Miller, Jr.
Many Futures Trade on
Value-Weighted Indices
• Trading on the CME alone:
– The S&P 500 futures (the future’s face value is $250 times
the S&P 500 index level)
– Mini-S&P 500 futures (the future’s face value is only $50
times the S&P 500 index level)
– The S&P Midcap 400 (400 middle-sized firms)
– Nasdaq 100 (100 Largest Nasdaq Stocks)
– Russell 2000 (small cap stocks)
©David Dubofsky and 8-12
Thomas W. Miller, Jr.
S&P 500 stock index
futures contracts
• Perhaps the most actively traded stock index futures
in the world.
• The last trading day for this contract is the Thursday
before the third Friday of the delivery month.
• Therefore, there are four delivery months:
–
–
–
–
March
June
September
December
©David Dubofsky and 8-13
Thomas W. Miller, Jr.
Marking to Market
• The smallest allowed price change (the “tick”) is 0.10 point,
which equals $25.
• Thus, if the S&P 500 futures price falls from 1,019.40 to
1,019.30, the face value of the futures contract declines $25.
That is:
(1,019.40)(250) = $254,850
(1,019.30)(250) = $254,825
• This one tick decrease in the futures price creates a mark to
market profit of $25 for an individual who is short one contract.
©David Dubofsky and 8-14
Thomas W. Miller, Jr.
Portfolio Risk Management
Using Stock Index Futures
•
Portfolio managers often have reasons for
selling parts of their portfolio. For example:
a)
b)
c)
They may feel some stocks no longer offer adequate
returns for the risks the stocks possess;
They may have turned bearish (or less bullish) on the
overall market, or;
They may have to sell in order to provide cash for their
clients.
Stock index futures provide an efficient means to
achieve their objectives for reasons b) and c) above.
©David Dubofsky and 8-15
Thomas W. Miller, Jr.
Stock index futures are also surrogates for the
stock purchases when the portfolio manager:
a)
has received an inflow of cash but has not decided which
stocks or market sectors in which to invest.
b)
has a growing bullishness about the market.
c)
wants to get market exposure in advance of a near-term
expected cash inflow.
d)
wants an investment that can be quickly liquidated to raise
cash, if needed.
©David Dubofsky and 8-16
Thomas W. Miller, Jr.
Changing the Beta of a Portfolio
• Capital Market Theory predicts that rational investors will only
hold combinations of two assets:
– The market portfolio of all assets, (by definition, has a beta of 1.0)
– A risk-less asset, (by definition, has a beta of 0.0)
• If investors are relatively more risk averse or are bearish about
the prospects for the stock market, investors will lower the beta
of their portfolio by shifting a portion of their assets into risk-less
securities.
• If investors are not very risk averse or if they are bullish about
the market, investors will raise their portfolio's beta by borrowing
additional capital and investing the borrowed funds in risky
securities.
©David Dubofsky and 8-17
Thomas W. Miller, Jr.
Example: Adjusting the Beta of a
Portfolio with Stock Index Futures
• Portfolio managers adjust their portfolio betas as they perceive
risk and return changes.
• When they are bullish, i.e., they believe that the stock market
offers a relatively high expected return for a given level of risk,
they will increase the beta of their stock portfolio.
• When they are bearish, (or simply believe that the risk of the
market has increased), they will decrease their portfolio's beta.
©David Dubofsky and 8-18
Thomas W. Miller, Jr.
Equation to Adjust Beta:
• A negative number indicates that futures should be sold in order
to lower the portfolio beta. A positive number means that futures
should be bought.
N=
βD
- βP 
βF
×
Portfolio Value
(Futures Price) × Multiplier
• Note: Generally, bF = 1, and the Futures Multiplier for the S&P500
is 250.
©David Dubofsky and 8-19
Thomas W. Miller, Jr.
Using the Equation, I.
• A portfolio manager is concerned that the stock market will
temporarily decline in the next few days.
• The manager does not wish to incur the commission costs and
price pressure of selling stocks and then repurchasing them
after the anticipated decline.
• Thus, the manager decides to use futures contracts to hedge
against the expected market decline.
©David Dubofsky and 8-20
Thomas W. Miller, Jr.
Using the Equation, II.
• An equity fund manager owns a portfolio of $20 million in stocks with a
portfolio beta of 1.20.
• Suppose, the S&P 500 index level is 1275 and the observed futures
price is 1280. What is the risk-minimizing position?
N=
 0.0 - 1.20 
1
×
$20,000,000
= -75.
(1280) × 250
• The Key: Set the target portfolio beta, bd, equal to 0.0. Then, using the
equation above, we conclude that the manager should sell 75 futures
contracts.
• Suppose the manager was right about the market's movement, and
the S&P 500 declines to 1224, which is a 4% decline in the market.
©David Dubofsky and 8-21
Thomas W. Miller, Jr.
Using the Equation, III.
• If beta was estimated accurately, the value of the manager’s
equity portfolio should decline by 4.8% (1.20 times 4%). This
results in a loss in the capital value of the portfolio of $960,000.
• Now assume that the futures price also declines by 4%, to
1228.80.
• A futures price decline of 51.2 points results in a profit of
$12,800 on one futures contract. On a position of 75 short
futures contracts, the profit would be $960,000.
• Here, the hedge eliminated the effects of the market decline.
©David Dubofsky and 8-22
Thomas W. Miller, Jr.
Stock Index Arbitrage
• Stock Index Arbitrage is an attempt to exploit any futures
mispricing relative to the index level.
• When futures prices lie outside their no-arbitrage bounds,
arbitrageurs will quickly act to realize the (near) riskless profits
by buying cheap stock and selling futures (buy programs), or
buying cheap futures and selling stock (sell programs).
• Between July 1, 2002 and August 30, 2002, program trading
averaged 34.6% of total NYSE volume, and stock index
arbitrage as a percentage of total program trading ranged
between 8.4% and 14.3%, with an average of 11.9%.
©David Dubofsky and 8-23
Thomas W. Miller, Jr.
Arbitrage Bounds
• In practice, if F > S + CC - CR, then arbitrageurs' purchases of
stock increase stock prices (these are called “buy programs”).
• Their sales of futures will depress futures prices, until
equilibrium is again reached (F  S + CC - CR), and no arbitrage
opportunities exist.
• Similarly, if F < S + CC - CR, the buying of cheap futures and
the sale of expensive stock (“sell programs”).
• Their purchases of futures will increase futures prices, until
equilibrium is again reached (F  S + CC - CR), and no arbitrage
opportunities exist.
©David Dubofsky and 8-24
Thomas W. Miller, Jr.
Program Trading
• Program trading is a technique for trading a stock portfolio in one single
order.
• The NYSE defines a program trade as: "a wide range of portfolio trading
strategies involving the purchase or sale of a basket of 15 stocks or more,
and valued at more than $1 million".
• Program trading may involve stock index arbitrage, option replication
strategies, or asset allocation shifts (such as between equities and bonds),
etc.
• Recent growth in program trading has arisen from brokers who offer
institutions the ability to trade large portfolios of stocks with low cost and
little price impact.
• In 2001, program trading accounted for almost 30% of total NYSE volume.
©David Dubofsky and 8-25
Thomas W. Miller, Jr.
An Actual Pricing Example, 2/5/99
•
•
•
•
•
SPH: 1,243.50
S&P Index: 1,239.40
T-bill rate: 4.35%
Days to Expiration: 42
Annual Dividend Yield: 1.32% (assume this is the
dividend yield in terms of its future value)
What is the theoretical futures price, and the Deviation
from Fair Value (DFV)?
©David Dubofsky and 8-26
Thomas W. Miller, Jr.
DFV = Factual – Ftheoretical
•
•
•
•
Let t = the time until delivery, in years.
Note that dividends = dtS
Ftheoretical = S + Srt – Sdt
Ftheoretical = 1239.40 + (1239.40)(0.0435)(42/365) (1239.40)(0.0132)(42/365) = 1243.72
• Fobs is ‘too low’ by –0.22 index points.
• So, if TC are less than 0.22 to perform reverse cash
and carry arbitrage, then do it!
©David Dubofsky and 8-27
Thomas W. Miller, Jr.
Index Arbitrage with Transaction Costs
• Let hb and hl = the unannualized borrowing rate and
lending rate, respectively.
• Let Sbid and Sask = the spot index value, based on
stocks’ bid quotes and asked quotes, respectively.
• Let TC1 and TC2 = transaction costs (commissions,
etc.) necessary to perform reverse cash and carry
arbitrage, and cash and carry arbitrage, respectively.
• Sbid (1+hl(0,T)) - div(1+hb(,T)) - TC1 < F <
Sask(1+hb(0,T)) - div(1+hl(,T)) + TC2
©David Dubofsky and 8-28
Thomas W. Miller, Jr.
The DOT
• In 1976, the New York Stock Exchange introduced its Designated
Order Turnaround (DOT) system, which was improved and
renamed Super DOT in November 1984.
• Super DOT is a computerized order handling system that
guarantees that any market order of less than 2100 shares of a
stock will be executed within three minutes at the prevailing bid
price (for a market sell order) or asked price (for a market buy
order) at the time the order was entered, or at better prices if
possible.
• Today, the average order through SuperDot is transmitted,
executed and reported back to the originating firm in 22 seconds.
©David Dubofsky and 8-29
Thomas W. Miller, Jr.
DOT and Stock Index Arbitrage
• Originally, DOT was designed to alleviate the traffic around
specialists' trading posts by automatically handling the orders of
small individual investors.
• Runners do not have to hand-carry small orders to the
specialist. Instead, they are electronically transmitted from order
rooms to the specialists' posts.
• Little did the designers of DOT realize that their system would
be adopted by index arbitrageurs, who now enter orders to buy
or sell portfolios of stocks, including the composition of any
index replicating portfolio (e.g., 1000 shares of IBM, 1267
shares of GM, etc.).
©David Dubofsky and 8-30
Thomas W. Miller, Jr.
Computerized Trading
• Whenever an arbitrage opportunity arises a trader can literally
push a button to submit these orders to buy (at the asked) or sell
(at the bid) the entire basket of stocks.
• On average, the execution of the trade is reported back to the
buyer or seller in 22 seconds.
• At the same time, the arbitrageur will trade the necessary stock
index futures contracts.
• Larger orders (more than 2099 shares of one stock) are handled
less efficiently, with trades occurring only after an arbitrageur's
human representative carries the order to the specialists' posts.
©David Dubofsky and 8-31
Thomas W. Miller, Jr.
Risks of Stock Index Arbitrage
• Even with Super DOT, there are some risks to index arbitrage.
Large orders to trade securities are not guaranteed any price,
and prices can change quickly in the few minutes that it takes to
execute all of the desired trades.
• Arbitrageurs' orders to buy stock may create upward price
pressure on those stocks unless there happens to be a
contemporaneous flow of sell orders, or the specialist is willing
to reduce his inventory of stock.
• Similarly, program selling will often lead to price declines in the
spot stock market.
©David Dubofsky and 8-32
Thomas W. Miller, Jr.
Some Extra Slides on this Material
• Note: In some chapters, we try to include some extra slides in
an effort to allow for a deeper (or different) treatment of the
material in the chapter.
• If you have created some slides that you would like to share with
the community of educators that use our book, please send
them to us!
©David Dubofsky and 8-33
Thomas W. Miller, Jr.
Three Basic Weighting Schemes
• Capitalization-Weighting (AKA Value Weighting or
Market-Value Weighting):
– Stocks held in proportion to their market value.
– Large-cap companies have more influence on the index.
©David Dubofsky and 8-34
Thomas W. Miller, Jr.
Three Basic Weighting Schemes, Cont.
• Price Weighting: Equal number of shares invested in
each stock, therefore, the price is the weight.
– The highest-priced stocks have the largest weight.
– Berkshire Hathaway
• Equal Dollar Weighting: Same dollar investment in
each stock.
– The lowest-priced stocks have more influence.
©David Dubofsky and 8-35
Thomas W. Miller, Jr.
Assume a $1,000,000 Portfolio,
Value-Weighting, Data from 3/11/1994
Company
Price
Shares Capitalization Value Value
(millions)
(millions)
Weight Shares
Am. Express
28.625
485.445
13,895.9
0.0560
1,956
GE
105.250
852.935
89,771.4
0.3618
3,437
3M
103.250
215.791
22,280.4
0.0898
870
Merck
32.125 1,282.316
41,194.4
0.1660
5,167
Exxon
65.250 1,241.618
81,015.6
0.3265
5,003
248,157.7 1.0000
16,434
Total: 334.500
Total:
Note: Shares = $1,000,000*Weight / Price
©David Dubofsky and 8-36
Thomas W. Miller, Jr.
Assume a $1,000,000 Portfolio,
Price-Weighting, Data from 3/11/1994
Company
Am. Express
Price
Price Price-Weighted
Weight
Shares
28.625
0.086
2,990
GE
105.250
0.315
2,990
3M
103.250
0.309
2,990
Merck
32.125
0.096
2,990
Exxon
65.250
0.195
2,990
334.500
1.000
2,990
Note: Shares = $1,000,000 / 334.500 = 2,990
©David Dubofsky and 8-37
Thomas W. Miller, Jr.
DJIA Index Details, I.
• The DJIA is computed by adding the prices of the thirty
component stocks, and dividing the sum by a divisor.
• The divisor is printed in the Wall Street Journal every day and is
also available in the equity product information area at
http://www.cbot.com.
• For example, on April 24, 2001, the divisor for the DJIA was
0.15369402. On September 9, 1999, the divisor was
0.19740463.
• The divisor is changed when one of two events occurs.
Periodically, one of the thirty stocks in the DJIA may be
removed, and another company's stock is substituted.
• This will happen when a component stock is taken over by
another company or one of the corporations goes bankrupt.
©David Dubofsky and 8-38
Thomas W. Miller, Jr.
DJIA Index Details, II.
• For example, Anaconda, a component of the DJIA, was bought
by Atlantic Richfield (ARCO) in 1976. Thus, a new component
stock (which was MMM) was chosen to replace Anaconda.
• Dow Jones may decide that the DJIA no longer representative of
"the market", so the composition will change.
– This occurred on November 1, 1999
– IN: Home Depot, Intel, Microsoft, and SBC Communications
– OUT: Chevron, Goodyear, Sears Roebuck, and Union Carbide.
• So, anytime there is a change in the portfolio of the constituent
stocks, or if there are splits, stock dividends, or mergers, the
DJIA divisor will change because Dow Jones and Company
wants to remove the impact on the index from these events.
• NB: The DJIA is not adjusted to account for regular dividend
payments.
©David Dubofsky and 8-39
Thomas W. Miller, Jr.
Example: Changing the Divisor
Day 1 of Index:
Company
Am. Express
GE
3M
Merck
Exxon
Sum:
Index:
Price
28.625
105.250
103.250
32.125
65.250
334.500
66.90 (Divisor = 5)
Before Day 2 starts, we want to replace Merck with Intel, selling at $22.
To Keep the value of the Index the same, i.e., 66.90:
Am. Express
GE
3M
Intel
Exxon
Sum:
Sum / Divisor = 66.90 if Divisor is:
28.625
105.250
103.250
22.000
65.250
324.375
4.848654709
©David Dubofsky and 8-40
Thomas W. Miller, Jr.
DJIA Index Details, III.
• To construct a portfolio that is equivalent to the DJIA, an investor
must buy an equal number of shares of each of the component
stocks.
• Maintaining the proper underlying portfolio is complicated by the
payment of cash dividends and stock distributions.
• Still, the DJIA is an easy index to replicate, as it has only 30
stocks, each of which is very actively traded.
• If a stock selling for $100/share increases in value by 5%, then
the DJIA will increase by 5/divisor points.
• If a stock selling for $20/share rises in price by 5%, then the
DJIA will rise by only 1/divisor points.
©David Dubofsky and 8-41
Thomas W. Miller, Jr.
Assume a $1,000,000 Portfolio,
Equal-Weighting, Data from 3/11/1994
Company
Am. Express
Price
Equal Equal-Weighted
Weight
Shares
28.625
0.200
6,987
GE
105.250
0.200
1,900
3M
103.250
0.200
1,937
Merck
32.125
0.200
6,226
Exxon
65.250
0.200
3,065
1.000
20,115
Shares = $1,000,000*0.20 / Price
©David Dubofsky and 8-42
Thomas W. Miller, Jr.
Many stock market indices are ValueWeighted Averages
• In the Capital Asset Pricing Model (CAPM), a stock's correlation
with the market portfolio is the factor that determines its price,
and that market portfolio is value-weighted.
• Besides the NYSE and S&P Indices, other value-weighted
indices include the AMEX Market Value Index, the NASDAQ
Composite Index, the Russell 2000 Index, and the Wilshire
5000.
• The levels of these and yet other indices are presented daily in
the Wall Street Journal. While each index is a different portfolio
of stocks, the method of computing each index is the same.
©David Dubofsky and 8-43
Thomas W. Miller, Jr.
Value-Weighted Index Movements.
Day 1:
Day 2:
Company
Price
Am. Express 28.625
GE
105.250
3M
103.250
Merck
32.125
Exxon
65.250
Total Shares
Market Capitalization
(millions)
(millions)
485.445
13,896
852.935
89,771
215.791
22,280
1,282.316
41,194
1,241.618
81,016
Total MV(1):
248,158
Divisor (Set by Vendor):
248.1576686
Day 1 Index Level:
1000.00
Company
Price
Am. Express 29.000
GE
110.000
3M
92.000
Merck
37.000
Exxon
67.000
Total Shares
Market Capitalization
(millions)
(millions)
485.445
14,078
852.935
93,823
215.791
19,853
1,282.316
47,446
1,241.618
83,188
Total MV(2):
258,388
Day 2 Index Level:
1041.22
©David Dubofsky and 8-44
Thomas W. Miller, Jr.
Note Bene: The Day 3 index can be
calculated in two ways:
Day 3:
Company
Am. Express
GE
3M
Merck
Exxon
Price
25.000
108.500
93.700
37.875
62.000
Total Shares
Market Capitalization
(millions)
(millions)
485.445
12,136.1
852.935
92,543.4
215.791
20,219.6
1,282.316
48,567.7
1,241.618
76,980.3
Total MV(3):
250,447.2
Day 3 Index Level:
1009.23
Day 2 Index 
Market Value Day 2
 Index Level Day 1
Market Value Day 1
Day 2 Index 
Market Value Day 2
 Index Level Day 0
Market Value Day 0
©David Dubofsky and 8-45
Thomas W. Miller, Jr.