chapter 91 chapter 9 security futures products introduction chapter 9 and 10 explore stock index...

Chapter 9 1

CHAPTER 9Security 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 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.

Chapter 9 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.

INDEX ACRONYM DESCRIPTION

Dow Jones Industrial Averages DJIA 30 large U.S. companies. Price-weighted index. Dividends are not included

Nikkei 225 Nikkei 225 Largest Japanese firms. Price-weighted index. Dividends are not included

S&P 500 S&P 500 Market Capitalization (value) Weighted Index. Dividends are not includes

FT-SE 100 FT-SE 100 British 100 index. Market Capitalization (value) Weighted Index. Dividends are not includes

Deutscher Aktien 30 DAX 30 German index .Total Return index that includes capital gains, dividends, spin offs, mergers etc

Compagnie des Agents de Change 40

CAC 40 French index Total Return index that includes capital gains, dividends, spin offs, mergers etc.

Dow Jones Stoxx Total Return index that includes capital gains, dividends, spin offs, mergers etc

Chapter 9 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.

Chapter 9 5

DJIA Index

Table 9.1

Stocks in the Dow Jones Industrial Average Alcoa Altria Group American Express American Int. Group Boeing Caterpillar Citigroup CocaBCola DuPont Exxon-Mobil

General Electric General Motors Hewlett-Packard Home Depot Honeywell Intel IBM J P Morgan-Chase Johnson & Johnson McDonald=s

Merck Microsoft Minnesota, Mining, Mfg. Pfizer Inc. Procter & Gamble SBC Communications United Technologies Verizon Communications WalMart Walt Disney Company

Source: Dow Jones web site, April 8, 2004

Chapter 9 6


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:

Divisor

PIndex

N

ii 1

where:Pi = price of stock i

Chapter 9 7


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

43.1946889.0

375.730,1Index

Divisor

PIndex

N

ii 1

After the Change (No New Divisor Is Used)

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

31.1900889.0

375.689,1Index

Chapter 9 8


The new divisor is given by:

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

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:

9106.01900.31

375.730,1Divisor New

onSubstituti Before ValueIndex

Prices of Sum NewDivisor New

Chapter 9 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 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 10

Market Capitalization-Weighted Indexes

The S&P index is calculated as:

10 .V.O

Index P & S

P N =

t ,it ,i

500

1 = it

where:O.V. = original valuation in 1941-43Ni,t = number of shares outstanding for firm iPi,t = price of shares in firm i

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

If the 1941B43 value were $2,000, then $19,000 is to $2,000 as X is to 10. Current Market Valuation 1941B43 Market Valuation

$19,000 $2,000 $190,000 95.00

=

= =

X 10 $2,000X X

Source: CME, AInside S&P 500 Stock Index Futures.@

Chapter 9 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.

valuebase B

M = Indext

tt

WhereMt = market capitalization of the index at

time tBt = adjusted base date market capitalization of the index at time tbase value = the original numerical starting value for

the index (e. g.,100 or 1000)

Chapter 9 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 Yes

Chapter 9 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.

Table 9.3

Summary of Key Stock Index Futures Contracts Contract

Exchange

Currency

Contract Size

Index Compo-

sition

Index

Calculation DJIA

CBOT

U.S.

10 Index

30 U. S. blueBchip

Price weighting (no dividends)

Nikkei 225 CME

U.S.

5 Index

225 Japanese first section

Price weighting (no dividends)

NASDAQ 100 e-mini

CME

U.S,

20 Index

100 NASDAQ stocks

Modified Market cap weighting

S&P 500 CME

U.S.

250 Index

500 mostly NYSE

Market cap weighting (no dividend)

S&P 500 e-mini

CME

U.S.

50 Index

500 mostly NYSE

Market cap weighting (no dividends)

FTSE 100 Euronext

British

10 Index

100 large British

Market cap weighting (no dividends)

DAX 30 EUREX

Euro

25 x Index

30 German blue chip

Total return

CAC 40

Euronext

Euro

10 x Index

40 French blue chip

Total return

DJ Euro Stoxx 50

EUREX

Euro

10 x Index

50 European blue chip

Total return

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 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.

Chapter 9 15

E-Mini S&P 500 Futures

Product Profile: The CME=s e-mini S&P 500 Futures

Contract Size: $50 times the Standard & Poor=s 500 stock index. Deliverable Grades: Cash Settled to the Standard & Poor=s 500 stock index. Tick Size: 0.25=$12.50. Price Quote: Price is quoted in terms of Standard & Poor=s 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 16

E-Mini NASDAQ 100 Futures

Product Profile: The CME=s 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 17

Dow Jones Euro STOXX Futures

Product Profile: The Eurex=s 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 18

Price Quotation Stock Index Futures

Insert Figure 9.1 here

Chapter 9 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:

)1( ,00,0 tt CSF

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 20


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 21


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 22


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

iiitt rDCSF

1

,00,0 )1()1(

Where: S0 = The current spot priceF0,t = The current futures price for delivery of the product at time tC0,t = The percentage cost of carrying the stock

index from today until time tDi = The ith dividendri = The interest earned from investing the

dividend from the time received until the futures expiration at time t

Chapter 9 23

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 24


Step 1: compute the current fair value for stock index futures.

The value of the index is given by:

Divisor

PIndex

N

ii 1

8.1

84115$ Index

56.110Index

Step 2: determine the cost of buying the stocks.

Cost Stock A + Cost of Stock B = $115+84 = $199

Chapter 9 25


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:

360

7610.0, XC to

0211.0, toC

Chapter 9 26


Step 5: solve for the futures price as follows:

N

i

tt riDiCSF1

,00,0 )1()1(

53.2)0211.01(199,0 tF

53.220.203,0 tF

67.200,0 tF

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.

Divisor

F t,0Index of ValueFair

8.1

67.200$Index of ValueFair

48.111Index of ValueFair

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 27

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 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.

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 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.

Chapter 9 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.

Table 9.6

CashBandBCarry Index Arbitrage Date

Cash Market

Futures Market

July 6

Borrow $199 for 76 days at 10%. Buy Stock A and Stock B for a total outlay of $199.

Sell 1 SEP index futures 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%.

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 invested dividends of $1.52 and $1.01. Sell Stock A for $115 and Stock B for $84. Total proceeds are $201.53. Repay debt of $203.20.

At expiration, the futures price is set equal to the spot index value of 110.56. This gives a profit of 4.44 index units. In dollar terms, this is 4.44 index units times the index divisor of 1.8.

September 20

Loss: $1.67

Profit: $7.99

Total Profit: $7.99 B $1.67 = $6.32

Chapter 9 31

Index Arbitrage

Table 9.7

Reverse CashBandBCarry Index Arbitrage Date

Cash Market

Futures Market

July 6

Sell Stock A and Stock B for a total of $199. Lend $199 for 76 days at 10%.

Buy 1 SEP index futures contract for 105.00.

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.

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-ment of $203.20. Repay $1.52 and $1.01 on money borrowed to pay dividends on Stocks A and B. Buy Stock A for $115 and Stock B for $84. Return stocks to repay short sale.

At expiration, the futures price is set equal to the spot index value of 110.56. This gives a profit of 5.56 index units. In dollar terms, this is 5.56 index units times the index divisor of 1.8.

September 20

Profit: $1.67

Profit: $10.01

Total Profit: $1.67 + $10.01 = $11.68

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.

Chapter 9 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 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 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.

Chapter 9 34

Distribution of Dividend Payments

Insert Figure 9.2 here

Chapter 9 35

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 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.

Chapter 9 37


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 Buy Profit/Loss (points) $ per contract point number of contracts Profit/Loss $

8857.30 8603.50

253.80 10

20 $50,760.00

999.00

1026.45 B 27.45

250 5

-34,312.50

Total Profit: $16,447.50

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.

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

Chapter 9 38


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 Buy Profit (points) $250 per contract

1079.40 1102.50

-23.10 B $5,775.00

1109.25 1085.70

23.55 $5,887.50

Total Profit: $112.50

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.

Chapter 9 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

Chapter 9 40


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.

Chapter 9 41


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 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 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 43


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

contracts 15094.150)250)($1060(

000,000,40$

F

P

V

V

where:VP = value of the portfolioVF = 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 44


Table 9.10

A Short Hedge

Stock Market

Futures Market

March 14

Hold $40,000,000 in a stock portfolio.

Sell 150 S&P 500 December futures contracts at 1060.00.

August 16 Stock portfolio falls by 5.40% to $37,838,160.

S&P futures contract falls by 4.43% to 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 45


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

Contracts ofNumber F

PP V

V

Where:

βP = beta of the portfolio that is being hedged.

Thus, The manager would sell:

15.185-)250)($1060(

000,000,40$22.1

Chapter 9 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.

Table 9.11

A Long Hedge with Stock Index Futures

Stock Market

Futures Market

May 19

A pension fund manager anticipates having -6 billion to invest in Japanese equities in three months.

Buys 600 SEP Nikkei futures on the CME at 14,400.

August 15

-6 billion becomes available for investment.

The market has risen and the Nikkei futures stands at 14,760.

Stock prices have risen, so the -6 billion will not buy the same shares that it would have on May 19.

Futures profit: 360 points $5 600 contracts = $1,080,000

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

chapter 91 chapter 9 security futures products introduction chapter 9 and 10 explore stock index...

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