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									              CHAPTER 9
 Security Futures Products Introduction

Chapter 9 and 10 explore stock index futures. This chapter
is organized into the following sections:

1. Indexes

2. Stock Index Futures Contracts

3. Stock Index Futures Prices

4. Index Arbitrage and Program Trading

5. Speculating with Stock Index Futures

6. Risk Management with Stock Index futures




                         Chapter 9                       1
                       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.




                         Chapter 9                        2
                                  Indexes
  INDEX                           ACRONYM DESCRIPTION
                                             30 large U.S. companies. Price-
  Dow Jones Industrial Averages   DJIA       weighted index. Dividends are not
                                             included
                                             Largest Japanese firms. Price-
  Nikkei 225                      Nikkei 225 weighted index. Dividends are not
                                             included
                                             Market Capitalization (value) Weighted
  S&P 500                         S&P 500
                                             Index. Dividends are not includes
                                             British 100 index. Market Capitalization
  FT-SE 100                       FT-SE 100 (value) Weighted Index. Dividends are
                                             not includes
                                             German index .Total Return index that
  Deutscher Aktien 30             DAX 30     includes capital gains, dividends, spin
                                             offs, mergers etc
                                             French index Total Return index that
  Compagnie des Agents de
                                  CAC 40     includes capital gains, dividends, spin
  Change 40
                                             offs, mergers etc.
                                             Total Return index that includes capital
  Dow Jones Stoxx
                                             gains, dividends, spin offs, mergers etc


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.


                                    Chapter 9                                           3
           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.




                          Chapter 9                        4
                             DJIA Index

                            Table 9.1
           Stocks in the Dow Jones Industrial Average
Alcoa                      General Electric    Merck
Altria Group               General Motors      Microsoft
American Express           Hewlett-Packard     Minnesota, Mining, Mfg.
American Int. Group        Home Depot          Pfizer Inc.
Boeing                     Honeywell           Procter & Gamble
Caterpillar                Intel               SBC Communications
Citigroup                  IBM                 United Technologies
CocaBCola                  J P Morgan-Chase    Verizon
DuPont                     Johnson & Johnson   Communications
Exxon-Mobil                McDonald= s         WalMart
                                               Walt Disney Company

Source: Dow Jones web site, April 8, 2004




                                   Chapter 9                             5
           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:


                           
                              N
                                     Pi
                 Index       i 1
                           Divisor

 where:
 Pi = price of stock i


                           Chapter 9                         6
                  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

          
              N
                   Pi
Index      i 1
          Divisor
          1,689.375
Index               1900.31
            0.889
After the Change (No New Divisor Is Used)

Total new 30 stock price: $1,689.375 - 6+47 = $1,730.375
            1,730.375
 Index                1946.43
              0.889




                            Chapter 9                      7
          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:


                 New Sum of Prices
New Divisor 
                 Index Value Before Substitution


The new divisor is given by:


                1,730.375
New Divisor               0.9106
                 1900.31



Thus, to keep the index value unchanged, the new
divisor must be 0.9106.




                            Chapter 9                      8
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 S&P 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 S&P 500 index consists of three stocks
ABC, DEF and GHI.

Table 9.2 shows how the value of these 3 firms will be
weighted.




                           Chapter 9                         9
 Market Capitalization-Weighted Indexes

                                        Table 9.2
                                 Calculation of S&P 500
                              Outstanding
                                Shares                   Price                     Value
        Company ABC              100                          $50    =              $ 5,000
        Company DEF              300                           40    =               12000
        Company GHI              200                           10    =                2000
                            Current Market Valuation                  =             $19,000
                    43
        If the 1941B value were $2,000, then $19,000 is to $2,000 as X is to 10.
        Current Market Valuation                           $19,000          X
        1941B Market Valuation
               43                                           $2,000    =     10

                                                          $190,000     =    $2,000X
                                                             95.00     =    X
        Source: CME, AInside S&P 500 Stock Index Futures.@




The S&P index is calculated as:
                 500              
                  N i , t Pi , t 
                 i=1               10
S & P Index t =                   
                      O.V.
                                  
                                  

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


                                            Chapter 9                                          10
               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.


                  Indext = M t  base value
                           Bt
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)




                          Chapter 9                           11
               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     Yes
No. of shares      Yes
Exchange rate      Yes
Dividends                              Yes
Splits                                 Yes
Mergers                                Yes
Repurchase                             Yes
Mergers                                Yes
Spin-offs                              Yes




                           Chapter 9                           12
           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.

                                       Table 9.3
                      Summary of Key Stock Index Futures Contracts
  Contract        Exchange        Currency        Contract Size    Index Compo-       Index
                                                                       sition       Calculation
  DJIA            CBOT            U.S.            10  Index       30 U. S.        Price
                                                                   blueB chip      weighting (no
                                                                                   dividends)
  Nikkei 225      CME             U.S.            5  Index        225 Japanese    Price
                                                                   first section   weighting (no
                                                                                   dividends)
  NASDAQ 100      CME             U.S,            20  Index       100 NASDAQ      Modified
  e-mini                                                           stocks          Market cap
                                                                                   weighting
  S&P 500         CME             U.S.            250  Index      500 mostly      Market cap
                                                                   NYSE            weighting
                                                                                   (no dividend)
  S&P 500         CME             U.S.            50  Index       500 mostly      Market cap
  e-mini                                                           NYSE            weighting
                                                                                   (no
                                                                                   dividends)
  FTSE 100        Euronext        British         10  Index       100 large       Market cap
                                                                   British         weighting
                                                                                   (no
                                                                                   dividends)
  DAX 30          EUREX           Euro            25 x Index        30 German      Total return
                                                                    blue chip
  CAC 40         Euronext          Euro            10 x Index       40 French      Total return
                                                                    blue chip
  DJ Euro        EUREX             Euro            10 x Index       50 European    Total return
  Stoxx 50                                                          blue chip
  Note: Some stock index futures trade on both U. S. and non-U.S. exchanges, and some non-U.S.
  markets dominate in certain 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.
                                             Chapter 9                                             13
       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.

                          Chapter 9                         14
                  E-Mini S&P 500 Futures

                                      s
              Product Profile: The CME= e-mini S&P 500 Futures
                                            s
Contract Size: $50 times the Standard & Poor= 500 stock index.
                                                       s
Deliverable Grades: Cash Settled to the Standard & Poor= 500 stock index.
Tick Size: 0.25=$12.50.
                                                        s
Price Quote: Price is quoted in terms of Standard & Poor= 500 Index points. 1 S&P 500
index point =$50. .
Contract Months: At any time the nearest two delivery months will trade from the March,
June, September, and December cycle.
Expiration and final Settlement: Trading ceases at 8:30 a.m. (Chicago time) on the third
Friday of the contract month. The contract is settled on the morning of the expiration day
based on the opening values of the component stocks, regardless of when those stocks open on
expiration day. However, if a stock does not open on that day, its last sale price will be used.
Trading Hours: Traded on Globex: Monday through Thursday 3:30 p.m.to 3:15 p.m.;
Shutdown period from 4:30 p.m. to 5:00 p.m. nightly; Sunday & holidays 5:30 p.m.-3:15 p.m.
Daily Price Limit: 5 percent increase or decrease from prior settlement price.




                                          Chapter 9                                                15
          E-Mini NASDAQ 100 Futures

                                   s
           Product Profile: The CME= e-mini NASDAQ 100 Futures
Contract Size: $20 times the NASDAQ 100 stock index.
Deliverable Grades: Cash Settled to the NASDAQ 100 stock index.
Tick Size: 0.25=$12.50.
Price Quote: Price is quoted in terms of NASDAQ 100 Index. One NASDAQ 100 index
point =$20.
Contract Months: At any time the nearest two delivery months will trade from the March,
June, September, and December cycle.
Expiration and final Settlement: Trading ceases at 8:30 a.m. (Chicago time) on the third
Friday of the contract month. The contract is settled on the morning of the expiration day
based on the opening values of the component stocks, regardless of when those stocks open on
expiration day. However, if a stock does not open on that day, its last sale price will be used.
Trading Hours: Traded on Globex: Monday through Thursday 3:30 p.m.to 3:15 p.m.;
Shutdown period from 4:30 p.m. to 5:00 p.m. nightly; Sunday & holidays 5:30 p.m.-3:15 p.m.
Daily Price Limit: 5 percent increase or decrease from prior settlement price.




                                         Chapter 9                                                 16
      Dow Jones Euro STOXX Futures

                                s
      Product Profile: The Eurex= Dow Jones Euro STOXX 50 Futures
Contract Size: 10 euros per Dow Jones STOXX 50 index point.
Deliverable Grades: Cash Settled to the Dow Jones STOXX 50.
Tick Size: One index point representing 10 euros.
Price Quote: Price is quoted in terms of Dow Jones STOXX 50 index points with no decimal
places. .
Contract Months: At any time the nearest three months will trade from the March, June,
September, and December expiration cycle.
Expiration and final Settlement: The last trading day is the third Friday of the expiration
month, if that is a trading day, otherwise the day immediately prior to that Friday. Trading
ceases at 12:00 noon on the last trading day. The final settlement price is the average price of
the Dow Jones STOXX 50 index calculated in the final 10 minutes of trading on the last
trading day.
Trading Hours: Eurex operates in three trading phases. In the pre-trading period users may
make inquiries or enter, change or delete orders and quotes in preparation for trading. This
period is between 7:30 and 8:50 a.m. The main trading period is between 8:50 a.m. and 8:00
p.m. Trading ends with the post-trading period between 8:00 p.m. and 8:30 p.m.
Daily Price Limit: . None




                                           Chapter 9                                               17
   Price Quotation Stock Index Futures


Insert Figure 9.1 here




                         Chapter 9       18
          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:

                 F 0, t  S 0(1  C 0, t )

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.



                           Chapter 9                        19
              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.

                                    Table 9.4
                          Cash Flows from Carrying Stock
  t=0
          Borrow $100 for 1 year at 10%.                               + 100
          Buy 1 share of Widget, Inc.                                  B 100
  t = 6 months
          Receive dividend of $2.                                        +$2
          Invest $2 for 6 months at 10%.                                 B$2
  t = 1 year
           Collect proceeds of $2.10 from dividend investment           +2.10
           Sell Widget, Inc., for P1.                                    + P1
           Repay debt.                                               B 110.00
                                Total Profit: P1 + $2.10 B $110.00




 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.

                                           Chapter 9                            20
          Stock Index Futures Prices


From the above example, we can generalize to understand
the total cash inflows from a cash-and-carry strategy.

1. The cash-and-carry strategy will return the future value
   of the stock, P1, at the horizon of the carrying period.

2. 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.

3. Against these inflows, the cash-and-carry trader must
   pay the financing cost for the stock purchase.




                          Chapter 9                          21
          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.
                                        N
             F 0, t  S 0(1  C 0, t )   Di (1  ri )
                                       i 1


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




                              Chapter 9                      22
     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.
                                           Table 9.5
                             Information for Computing Fair Value
    Today's date:                     July 6
    Futures expiration:               September 20
    Days until expiration:            76
    Index:                            Price-weighted index of two stocks
    Index divisor:                    1.80
    Interest rates:                   All interest rates are 10 percent simple interest; 360 day
                                      year

    Stock A
    Today's price:                    $115
    Projected dividends:              $1.50 on July 23
    Days dividend will be invested:   59
    rA:                               .10(59/360) = .0164

    Stock B
    Today's price:                    $84
    Projected dividends:              $1.00 on August 12
    Days dividend will be invested:   39
    rB:                               .10(39/360) = .0108



                                            Chapter 9                                              23
     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:

         
             N
                 Pi
            i 1
 Index 
         Divisor

         $115  84
 Index 
            1.8
 Index  110.56

Step 2: determine the cost of buying the stocks.
Cost Stock A + Cost of Stock B = $115+84 = $199




                           Chapter 9                     24
     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 = ? = $1.52
Stock A: PV = 1.00, N = 39, I = 10/360, FV = ? = $1.01
Total 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:

                 76
Co, t  0.10 X
                 360
Co, t  0.0211




                          Chapter 9                       25
     Fair Value for Stock Index Futures

Step 5: solve for the futures price as follows:
                          N
F 0, t  S 0(1  C 0, t )   Di (1  ri )
                          i 1

F 0, t  199(1  0.0211)  2.53
F 0, t  203.20  2.53
F 0, t  200.67

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.
                        F 0, t
Fair Value of Index 
                      Divisor
                      $200.67
Fair Value of Index 
                        1.8
Fair Value of Index  111.48

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.

                                  Chapter 9                26
   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.

                            Chapter 9                       27
                              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.

                                        Table 9.5
                          Information for Computing Fair Value
 Today's date:                     July 6
 Futures expiration:               September 20
 Days until expiration:            76
 Index:                            Price-weighted index of two stocks
 Index divisor:                    1.80
 Interest rates:                   All interest rates are 10 percent simple interest; 360 day
                                   year

 Stock A
 Today's price:                    $115
 Projected dividends:              $1.50 on July 23
 Days dividend will be invested:   59
 rA:                               .10(59/360) = .0164

 Stock B
 Today's price:                    $84
 Projected dividends:              $1.00 on August 12
 Days dividend will be invested:   39
 rB:                               .10(39/360) = .0108




                                          Chapter 9                                             28
                   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.




                           Chapter 9                          29
                               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.

                                         Table 9.6
                               CashBandBCarry Index Arbitrage
     Date                             Cash Market                           Futures Market
     July 6          Borrow $199 for 76 days at 10%. Buy Stock     Sell 1 SEP index futures
                     A and Stock B for a total outlay of $199.     contract for 115.00.
     July 23         Receive dividend of $1.50 from Stock A
                     and invest for 59 days at 10%.
     August 12       Receive dividend of $1.00 from Stock B
                     and invest for 39 days at 10%.
     September       For illustrative purposes, assume any values for stock prices at expiration.
     20              We assume that stock prices did not change. Therefore, the index value is
                     still 110.56.
                     Receive proceeds from invested dividends      At expiration, the futures price
                     of $1.52 and $1.01. Sell Stock A for $115     is set equal to the spot index
                     and Stock B for $84. Total proceeds are       value of 110.56. This gives a
                     $201.53. Repay debt of $203.20.               profit of 4.44 index units. In
                                                                   dollar terms, this is 4.44 index
                                                                   units times the index divisor of
                                                                   1.8.
                     Loss: $1.67                                   Profit: $7.99

     Total Profit: $7.99 B $1.67 = $6.32




                                            Chapter 9                                                 30
                                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.
                                      Table 9.7
                        Reverse CashBandBCarry Index Arbitrage
    Date                             Cash Market                       Futures Market
    July 6               Sell Stock A and Stock B for a      Buy 1 SEP index futures contract
                         total of $199. Lend $199 for 76     for 105.00.
                         days at 10%.
    July 23              Borrow $1.50 for 59 days at 10%
                         and pay dividend of $1.50 on
                         Stock A.
    August 12            Borrow $1.00 for 39 days at 10%
                         and pay dividend of $1.00 on
                         Stock B.
    September 20         For illustrative purposes, assume any values for stock prices at
                         expiration. We assume that stock prices did not change. Therefore, the
                         index value is still 110.56.
                         Receive proceeds from invest-       At expiration, the futures price is
                         ment of $203.20. Repay $1.52 and    set equal to the spot index value of
                         $1.01 on money borrowed to pay      110.56. This gives a profit of 5.56
                         dividends on Stocks A and B. Buy    index units. In dollar terms, this is
                         Stock A for $115 and Stock B for    5.56 index units times the index
                         $84. Return stocks to repay short   divisor of 1.8.
                         sale.
                         Profit: $1.67                       Profit: $10.01

    Total Profit: $1.67 + $10.01 = $11.68




                                            Chapter 9                                                31
                  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 S&P 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.



                            Chapter 9                           32
   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.

                          Chapter 9                          33
     Distribution of Dividend Payments


Insert Figure 9.2 here




                         Chapter 9       34
  Market Imperfections and Stock Index
            Futures Prices

Recall that four market imperfections could affect the
pricing of futures contracts:

    1. Direct Transaction Costs

    2. Unequal Borrowing and Lending Rates

    3. Margins

    4. 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.




                          Chapter 9                          35
  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.




                          Chapter 9                        36
 Speculating with Stock Index Futures

A trader observe that the DJIA futures is 8603.50 and
the S&P 500 futures is 999. The trader expects the DJIA
to go up more rapidly than the S&P 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.
                                    Table 9.8
                     A Conservative InterBCommodity Spread
 Date                       Futures Market
 April 22            Buy 20 SEP DJIA futures contracts at 8603.50.
                     Sell 5 SEP S&P 500 futures contract at 999.00.

 May 6               Sell 20 SEP DJIA futures contracts at 8857.30.
                     Buy 5 SEP S&P 500 futures contract at 1026.45.

                                                     DJIA             S&P 500
                     Sell                              8857.30             999.00
                     Buy                               8603.50            1026.45
                     Profit/Loss (points)               253.80             B 27.45
                      $ per contract point                10                250
                      number of contracts                 20                 5
                     Profit/Loss $                  $50,760.00         -34,312.50

 Total Profit: $16,447.50




The spread has widened as expected and thus, the
trader was able to realize a $16,447.50 profit.

                                             Chapter 9                               37
  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.

                                      Table 9.9
                       A Conservative IntraBCommodity Spread
   Date                                               Futures Market
   April 22                 Buy 1 DEC S&P 500 contract at 1085.70.
                            Sell 1 JUN S&P 500 contract at 1079.40.
   May 6                    Sell 1 DEC S&P 500 contract at 1109.25.
                            Buy 1 JUN S&P 500 contract at 1102.50.
                                                              June            December
                            Sell                                    1079.40         1109.25
                            Buy                                     1102.50         1085.70
                            Profit (points)                          -23.10           23.55
                             $250 per contract                 B $5,775.00       $5,887.50

    Total Profit: $112.50



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.

                                            Chapter 9                                         38
              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:

       CBOE
       CBOT
       CME




                          Chapter 9                       39
               Single Stock Futures

Single stock futures contracts specify:

       The identity of the underlying security
       Delivery procedures
       The contract size (100 shares)
       Margin
       The trading environment
       The minimum price fluctuation
       Daily price limits
       The expiration cycle
       Trading hours
       Position 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.




                          Chapter 9                        40
               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-Mart’s 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 + .016*119/365) - .09(1 + .016*72/119)

F0,t = $59.45 + .31 - .09

F0,t = $59.67/ share.




                            Chapter 9                          41
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 S&P 500)

S&P 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 S&P 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.




                          Chapter 9                       42
Risk Management with Security Futures
      Contracts: Short Hedging

Assuming that the S&P index futures contract stands at
1060, the advocated futures position would be given by:

     VP   $40 ,000 ,000
                        150 .94  150 contracts
     V F (1060 )($ 250 )


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 S&P 500 index.

Table 9.10 illustrates the potential results.




                              Chapter 9                    43
 Risk Management with Security Futures
       Contracts: Short Hedging

                                          Table 9.10
                                        A Short Hedge
                              Stock Market                        Futures Market
    March 14      Hold $40,000,000 in a stock          Sell 150 S&P 500 December
                  portfolio.                           futures contracts at 1060.00.
    August 16     Stock portfolio falls by 5.40% to    S&P futures contract falls by 4.43% to
                  $37,838,160.                         1013.00.
                  Loss: B$2,161,840                    Gain: 47 basis points  $250  150
                                                       contracts = $1,762,500

    Net Loss: B$399,340


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.

                                           Chapter 9                                            44
Risk Management with Security Futures
      Contracts: Short Hedging

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

         VP
  P        Number of Contracts
         VF

Where:
βP = beta of the portfolio that is being hedged.
Thus, The manager would sell:

          $40 ,000 ,000
 1.22                    -185 .15
         (1060 )($ 250 )




                                Chapter 9                45
 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.

                             Table 9.11
                A Long Hedge with Stock Index Futures
                        Stock Market                          Futures Market
May 19      A pension fund manager anticipates     Buys 600 SEP Nikkei futures on the
            having - 6 billion to invest in        CME at 14,400.
            Japanese equities in three months.
August 15   - 6 billion becomes available for      The market has risen and the Nikkei
            investment.                            futures stands at 14,760.
            Stock prices have risen, so the - 6    Futures profit: 360 points  $5  600
            billion will not buy the same shares   contracts = $1,080,000
            that it would have on
            May 19.



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

                                       Chapter 9                                           46

								
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