CHAPTER 9 Security Futures Products Introduction

1
CHAPTER 9Security Futures Products Introduction

• Chapter 9 and 10 explore stock index futures.
  This chapter is organized into the following
  sections
• Indexes
• Stock Index Futures Contracts
• Stock Index Futures Prices
• Index Arbitrage and Program Trading
• Speculating with Stock Index Futures
• Risk Management with Stock Index futures

2
Indexes

• If you have insight into the future direction of
  the stock market, specifically one index or
  another, you may want to trade stock index
  futures.
• Stock index futures allow you to make a bet on
  which direction you think a stock market index is
  headed.
• Stock index futures also allow you to hedge
  various financial positions.
• Stock index futures trade on a number of
  different indexes.

3
Indexes

• The various indexes use differing computational
  methods. To understand the trading and pricing
  of index futures, one must first understand a bit
  about how the underlying indexes are computed.

4
Priced-Weighted Indexes

• In a price-weighted index, stocks with a higher
  price receive a larger weighting in the
  computations.
• Price-weighted indexes do not consider dividends
  paid by the stocks.
• The companies contained in these indexes change
  infrequently. Changes only occur as a result of
  special events like liquidations and mergers.
• In this section, the DJIA is used as a
  representative price-weighted index. The DJIA is
  comprised of 30 stocks. Table 9.1 shows the lists
  of stocks.

5
DJIA Index
6
Priced-Weighted Indexes

• The DJIA is computed by adding the share prices
  of the 30 stocks comprising the index and
  dividing by the DJIA divisor. The divisor is used
  to adjust for stock splits, mergers, stock
  dividends, and changes in the stocks included in
  the index.
• Index Divisor
• The index divisor is a computed number that keeps
  the index unchanged in the event of certain
  occurrences (e.g., dropping one company from the
  index and adding another company, mergers and
  stock splits).
• The DJIA can be computed by using the following
  formula

where Pi price of stock i
7
Priced-Weighted Indexes

• Assume that the Dow Jones company decides to
  delete Boeing from the index and replace it with
  Dow Chemical. Boeing stock trades at 6.00 and
  Dow Chemical trades at 47. The current level of
  the index is 1900.31 with a divisor of .889.
• Before the Change
• Total 30 stock prices 1,689.375

After the Change (No New Divisor Is Used) Total
new 30 stock price 1,689.375 - 647 1,730.375
8
Priced-Weighted Indexes
If the divisor is not changed the DJIA will be 46
points higher as a result of the component
change. Thus, a new divisor must be calculated. A
new divisor is computed as follows

• The new divisor is given by

Thus, to keep the index value unchanged, the new
divisor must be 0.9106.
9
Market Capitalization-Weighted Indexes

• Each of the stocks in these indexes has a
  different weight in the calculation of the index.
  The weight is proportional to the total market
  value of the stock (the price per share times the
  number of shares outstanding).
• The value of the SP 500 index is reported
  relative to the average value during the period
  of 1941-1943, which was assigned an index value
  of 10.
• Assume that the SP 500 index consists of three
  stocks ABC, DEF and GHI.
• Table 9.2 shows how the value of these 3 firms
  will be weighted.

10
Market Capitalization-Weighted Indexes

• The SP index is calculated as

where O.V. original valuation in
1941-43 Ni,t number of shares outstanding for
firm i Pi,t price of shares in firm i
11
Total Return Indexes

• Similar to the Market Capitalization Indexes,
  these indexes reflect the total change in the
  value of the portfolio from inception to the
  current date.

Where Mt market capitalization of the
index at time t Bt adjusted base date
market capitalization of the index at time
t base value the original numerical starting
value for the index (e. g.,100 or 1000)
12
Total Return Indexes

• From the above equation, the numerator reflects
  the total accumulated value of the portfolio and
  the denominator represents the initial value of
  the portfolio. As such, both the numerator and
  denominator are affected by several factors as
  follows
• Affected by Numerator Denominator
• Price of share YesNo. of shares YesExchange
  rate YesDividends YesSplits YesMergers
  YesRepurchase YesMergers YesSpin-offs Y
  es

13
Stock Index Futures Contracts

• Index futures are available on a number of
  different indexes. Table 9.3 provides a summary
  of the features of the most important futures
  contracts.

As Table 9.3 shows, the total value of a futures
position depends on the currency, the multiplier,
and the level of the index.
14
Stock Index Futures Contracts

• The contract size is computed by multiplying the
  level of the index by the appropriate multiplier.
  
• Example
• Assume that The DJIA is 11,000 and the multiplier
  for the DJIA futures contract is 10. What is the
  value of a given contract?
• The futures product has a contract value of
• 11,000 X 10 or 110,000
• Now, assume that DJIA goes up to 11,250. What is
  the value of a given contract?
• The futures product has a contract value of
• 10 X 10,250 112,500
• One point change in the DJIA results in a 10
  change in the value of the futures contract.
• Notice that price changes for a contract depend
  on the contract size and volatility of the index.

15
E-Mini SP 500 Futures
16
E-Mini NASDAQ 100 Futures
17
Dow Jones Euro STOXX Futures
18
Price Quotation Stock Index Futures

• Insert Figure 9.1 here

19
Stock Index Futures Prices

• Stock index futures trade in a full-carry market.
  As such, the Cost-of-Carry Model provides a good
  understanding of index futures pricing.
• Recall that the Cost-of-Carry Model for a perfect
  market with unrestricted short selling is given
  by

Applying this model to stock index futures has
one complication, dividends. If you purchase the
stocks in the index, you will receive dividends.
Recall that most indexes ignore dividends in
their computation, so the Cost-of-Carry Model
must be adjusted to reflect the dividends. The
receipt of dividends reduces the cost of carrying
the stocks from today until the delivery date on
the futures contract.
20
Stock Index Futures Prices

• Today, t0, a trader decides to engage in a
  self-financing cash-and-carry transaction. The
  trader decides to buy and hold one share of
  Widget, Inc., currently trading for 100. The
  trader borrows 100 to buy the stock. The stock
  will pay a 2 dividend in 6 months and the trader
  will invest the proceeds for the remaining 6
  months at a rate of 10. Table 9.4 shows the
  trader's cash flows.

The trader's cash inflow after one year is the
future value of the dividend, 2.10, plus the
value of the stock in one year, P1, less the
repayment of the loan, 110.
21
Stock Index Futures Prices

• From the above example, we can generalize to
  understand the total cash inflows from a
  cash-and-carry strategy.
• The cash-and-carry strategy will return the
  future value of the stock, P1, at the
  horizon of the carrying period.
• At the end of the carrying period, the
  cash-and-carry strategy will return the
  future value of the dividends.
• the dividend plus interest from the time of
  receipt to the horizon.
• Against these inflows, the cash-and-carry
  trader must pay the financing cost for the
  stock purchase.

22
Stock Index Futures Prices

• In order to adjust the Cost-of-Carry Model for
  dividends, the future value of the dividends that
  will be received is computed at the time the
  futures contract expires. This amount is then
  subtracted from the cost of carrying the stocks
  forward.

Where S0 The current spot price F0,t The
current futures price for delivery of the
product at time t C0,t The percentage cost of
carrying the stock index from today until
time t Di The ith dividend ri The interest
earned from investing the dividend from the
time received until the futures
expiration at time t
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Fair Value for Stock Index Futures

• A stock index futures price has a fair value when
  the futures price conforms to the Cost-of-Carry
  Model.
• In this section, we use a simplified example to
  determine the fair value of a stock index futures
  contract. Assume a futures contract on a
  price-weighted index, and that there are only two
  stocks. Table 9.5 provides the information needed
  to compute the stock index fair value.

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Fair Value for Stock Index Futures

• Step 1 compute the current fair value for stock
  index futures.
• The value of the index is given by

Step 2 determine the cost of buying the
stocks. Cost Stock A Cost of Stock B 11584
199
25
Fair Value for Stock Index Futures

• Step 3 compute the future value of the dividends
  for each stock.
• Stock A PV 1.50, N 59, I 10/360, FV ?
  1.52Stock A PV 1.00, N 39, I 10/360, FV
  ? 1.01Total Future Value of Dividends
  2.53
• Step 4 compute the cost of carry.
• We will store the stocks for 76 days at 10
  annual interest. The interest for 76 days will
  be

26
Fair Value for Stock Index Futures

• Step 5 solve for the futures price as follows

The cost of buying the stocks and carrying them
to the future is 200.67.
Step 6 compute the fair price of the index. To
compute the fair value for the index, we
must convert the previous answer into
index units.
Notice that the fair value of the index (111.48)
is different than the current level of the index
(110.56). This difference suggests that
possibility of an arbitrage.
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Index Arbitrage and Program Trading

• Index arbitrages refer to cash-and-carry
  strategies in stock index futures. This section
  examines
• Index arbitrage
• Program trading
• Recall that deviations from the theoretical price
  of the Cost-of-Carry Model give rise to arbitrage
  opportunities.
• If the futures price exceeds its fair value,
  traders will engage in cash-and-carry arbitrage.
• A cash-and-carry arbitrage involves purchasing
  all the stocks in the index and selling the
  futures contract.
• If the futures price falls below its fair value,
  traders can exploit the pricing discrepancy
  through a reverse cash-and-carry strategy.
• A reserve cash-and-carry arbitrage involves
  selling the stocks in the index short and buying
  a futures contract.
• We would expect the futures prices to follow
  those suggested by the Cost-of-Carry Model. To
  the extent that they do not, traders can engage
  in index arbitrage.

28
Index Arbitrage

• To demonstrate how index arbitrage works, we will
  examine a two-stock index. The Information on the
  index futures and the two stocks contained in the
  index are presented in Table 9.5.

29
Index Arbitrage

• Using the previous calculations
• The cash market index value is 110.56.
• Fair price for the futures contract is 111.48.
• Rule 1
• If the futures price exceeds the fair value,
  cash-and-carry arbitrage is possible.
• Rule 2
• If the futures price is below the fair value,
  reverse cash-and-carry arbitrage is possible.
• Table 9.6 and 9.7 show the cash-and-carry and
  reserve cash-and-carry index arbitrage
  respectively.

30
Index Arbitrage

• Suppose the data from Table 9.5 holds, but the
  futures price is 115 which is above the fair
  value. The transactions for a cash-and-carry
  arbitrage are presented in Table 9.6.

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Index Arbitrage
Now suppose that all the information from Table
9.5 holds, but the futures price is 105, which
is below the fair value of 111.48, so a reverse
cash-and-carry arbitrage is possible. Table 9.7
shows the transactions for a reverse
cash-and-carry arbitrage.
32
Program Trading

• When performing index arbitrage, the investor
  must buy or sell all of the stocks in the index.
  
• For example, to perform index arbitrage on the
  SP 500 index, one would need to purchase or sell
  500 different stocks.
• Because of the difficulty in doing this, the
  trading is frequently done by computer. This is
  called program trading.
• The computer will download the prices of all 500
  stocks, compute the fair price of the index and
  compare that to the price of the futures
  contract.
• If a cash-and-carry arbitrage is suggested, the
  computer will initiate trades to purchase all 500
  stocks. It will also sell the futures contract.
• Because of the number of stocks involved,
  performing a successful index arbitrage involves
  very large sums of money and very rapid trading.
  As such, institutional investors (mutual funds
  and the like) are the ones that typically engage
  in index arbitrage.

33
Predicting Dividends Payments and Investment Rates

• Dividend Amount and Timing
• So far we have assumed certainty with regard to
  dividend amount, timing and investment rates.
• In the real market, dividends are predictable,
  but are not certain.
• To the extent that they are not predicted with
  certainty, the cash-and-carry index arbitrage can
  be frustrated.
• For the DJIA with 30 stocks, dividends are
  relatively stable. Thus prediction can be
  moderately accurate.
• For the SEP 500 or NYSE Indexes, many smaller
  companies are involved and dividend prediction
  becomes much less certain.
• Moreover, dividends are paid in seasonal patterns
  as shown in Figure 9.2.
• Predicting the Investment Rate
• Predicting the investment rate for dividends can
  be done with some certainty, as it is a
  relatively short term investment that will occur
  in the near future.

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Distribution of Dividend Payments

• Insert Figure 9.2 here

35
Market Imperfections and Stock Index Futures
Prices

• Recall that four market imperfections could
  affect the pricing of futures contracts
• Direct Transaction Costs
• Unequal Borrowing and Lending Rates
• Margins
• Restrictions on Short Selling
• Market imperfections exist and can be
  substantial, particularly for indexes with large
  numbers of stocks.
• The existence of market imperfections leads to
  no-arbitrage bounds on index arbitrage.
• So the price has to get out of sync by a good bit
  to cover the transaction costs and other market
  imperfections associated with attempting the
  arbitrage.

36
Speculating with Stock Index Futures

• Futures contracts allow speculators to make the
  most straightforward speculation on the direction
  of the market or to enter very sophisticated
  spread transactions to tailor the futures
  position to more precise opinions about the
  direction of stock prices.
• The low transaction costs in the futures market
  make the speculation much easier to undertake
  than similar speculation in the stock market
  itself.
• Tables 9.8 and 9.9 illustrate two cases of stock
  index futures speculation, a conservative
  inter-commodity spread and a conservative
  intra-commodity spread.

37
Speculating with Stock Index Futures
A trader observe that the DJIA futures is 8603.50
and the SP 500 futures is 999. The trader
expects the DJIA to go up more rapidly than the
SP 500 index due to market conditions. To bet on
her intuition the trader enters into an
inter-commodity spread as indicated in Table 9.8.
The spread has widened as expected and thus, the
trader was able to realize a 16,447.50 profit.
38
Speculating with Stock Index Futures
In the event that a trader expects more distant
contracts to be more sensitive to a market move
than the nearby contracts. The trader initiates a
intra-commodity spread as shown in Table 9.9.
In this case, the position is so conservative
that there was little difference in the price
changes, producing only a 112.50 profit, despite
the fact that the market moved in the predicted
direction.
39
Single Stock Futures

• Single stock futures contracts are written on
  shares of common stocks.
• Currently worldwide, 20 exchanges trade single
  stock futures or have announced their intention
  to do so.
• In 2002, NQLX and OneChicago, started trading
  single stock futures.
• NQLX, based in New York, is a joint venture of
• Nasdaq London International Financial
  Futures Exchange
• OneChicago, based in Chicago, is a joint venture
  of
• CBOECBOTCME

40
Single Stock Futures

• Single stock futures contracts specify
• The identity of the underlying
  securityDelivery proceduresThe contract size
  (100 shares)MarginThe trading environmentThe
  minimum price fluctuationDaily price limitsThe
  expiration cycleTrading hoursPosition limits
• They contain provisions for adjustments to
  reflect certain corporate events (e.g., stock
  splits and special dividends).
• They expire on the 3rd Friday of the delivery
  month.

41
Single Stock Futures

• Single stock futures are priced using the
  Cost-of-Carry Model.
• Example
• Today, Feb 20, the current price of Wal-Mart
  stock is 59.45/share. The JUN futures contract
  for Wal-Mart will expires on June 18. Wal-Marts
  quarterly dividend is expected to be 9
  cents/share on April 7. The current financing
  cost is assumed to be 1.6 per year.
• Since there is only a single dividend payment
  during the life of the futures contract, the
  cost-of-carry relationship becomes simple
• F0,t 59.45 (1 .016119/365) - .09(1
  .01672/119)
• F0,t 59.45 .31 - .09
• F0,t 59.67/ share.

42
Risk Management with Security Futures Contracts
Short Hedging

• Hedging with stock index futures applies directly
  to the management of stock portfolios. This
  section examines short and long hedging
  applications for stock index futures.
• Assume that a portfolio manager has a
  well-diversified portfolio with the following
  characteristics
• Portfolio Value 40,000,000
• Portfolio Beta 1.22 (relative to the SP 500)
• SP 500 Index 1060.00
• The portfolio manager fears that a bear market is
  imminent and wishes to hedge his portfolio's
  value against that possibility.
• The manager could use the SP 500 stock index
  futures contract. By selling futures, the manager
  should be able to offset the effect of the bear
  market on the portfolio by generating gains in
  the futures market.

43
Risk Management with Security Futures Contracts
Short Hedging

• Assuming that the SP index futures contract
  stands at 1060, the advocated futures position
  would be given by

where VP value of the portfolio VF value of
the futures contract This strategy ignores the
higher volatility of the stock portfolio relative
to the SP 500 index. Table 9.10 illustrates
the potential results.
44
Risk Management with Security Futures Contracts
Short Hedging

• The manager might be able to avoid this negative
  result by weighting the hedge ratio by the beta
  of the stock portfolio.
• The failure to consider the difference in
  volatility between the stock portfolio and index
  futures contract leads to suboptimal hedging
  results.

45
Risk Management with Security Futures Contracts
Short Hedging

• Using the following equation the manager can
  determine the number of contracts to trade.

Where ßP beta of the portfolio that is being
hedged. Thus, The manager would sell
46
Risk Management with Security Futures Contracts
Long Hedging

• A pension fund manager is convinced an extended
  bull market in Japanese equities is about to
  begin. The current exchange rate is 1 per 140.
  The manager anticipates funds for investing to be
  6 billion ( 42,857,143 43,000,000) in 3
  months. The pension fund manager trades as shown
  in Table 9.11.

The futures profit offsets the additional cost of
purchasing stocks because of an increase in
prices.