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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: 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 Chapter 9

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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

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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. Chapter 9

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**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 shows the lists of stocks. Chapter 9

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DJIA Index Chapter 9

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**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 Chapter 9

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**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 with a divisor of .889. Before the Change Total 30 stock prices = $1, After the Change (No New Divisor Is Used) Total new 30 stock price: $1, = $1, Chapter 9

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**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 Chapter 9

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**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 , 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

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**Market Capitalization-Weighted Indexes**

The S&P index is calculated as: where: O.V. = original valuation in Ni,t = number of shares outstanding for firm i Pi,t = price of shares in firm i Chapter 9

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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) Chapter 9

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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

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**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. Chapter 9

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**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? $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

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E-Mini S&P 500 Futures Chapter 9

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E-Mini NASDAQ 100 Futures Chapter 9

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**Dow Jones Euro STOXX Futures**

Chapter 9

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**Price Quotation Stock Index Futures**

Insert Figure 9.1 here Chapter 9

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**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. Chapter 9

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**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 $ 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. Chapter 9

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**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. Chapter 9

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**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 Chapter 9

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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. Chapter 9

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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 = $ = $199 Chapter 9

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**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 = ? = $ Stock A: PV = 1.00, N = 39, I = 10/360, FV = ? = $ 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: Chapter 9

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**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 $ 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. Chapter 9

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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. Chapter 9

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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 Chapter 9

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**Index Arbitrage Using the previous calculations:**

The cash market index value is Fair price for the futures contract is 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

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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. Chapter 9

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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. Chapter 9

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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 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

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**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

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**Distribution of Dividend Payments**

Insert Figure 9.2 here Chapter 9

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**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. Chapter 9

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**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

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**Speculating with Stock Index Futures**

A trader observe that the DJIA futures is 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, profit. Chapter 9

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**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 $ profit, despite the fact that the market moved in the predicted direction. Chapter 9

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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

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**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

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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 = *( *119/365) - .09( *72/119) F0,t = $ F0,t = $59.67/ share. Chapter 9

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**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 = 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

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**Risk Management with Security Futures Contracts: Short Hedging**

Assuming that the S&P index futures contract stands at , 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 S&P 500 index. Table 9.10 illustrates the potential results. Chapter 9

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**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. Chapter 9

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**Risk Management with Security Futures Contracts: Short Hedging**

Using the following equation the manager can determine the number of contracts to trade. Where: βP = beta of the portfolio that is being hedged. Thus, The manager would sell: Chapter 9

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**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. Chapter 9

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