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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 Dow Jones Industrial Averages Nikkei 225 S&P 500 FT-SE 100 Deutscher Aktien 30 Compagnie des Agents de Change 40 Dow Jones Stoxx ACRONYM DESCRIPTION 30 large U.S. companies. PriceDJIA weighted index. Dividends are not included Largest Japanese firms. PriceNikkei 225 weighted index. Dividends are not included Market Capitalization (value) Weighted S&P 500 Index. Dividends are not includes British 100 index. Market Capitalization FT-SE 100 (value) Weighted Index. Dividends are not includes German index .Total Return index that DAX 30 includes capital gains, dividends, spin offs, mergers etc French index Total Return index that CAC 40 includes capital gains, dividends, spin offs, mergers etc. Total Return index that includes capital 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 priceweighted 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 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 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: Index N i 1 Pi 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 Index N i 1 Pi Divisor Index 1, 689 . 375 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 Index 1, 730 . 375 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 Divisor New Sum of Prices Index Value Before Substituti on The new divisor is given by: New Divisor 1, 730 . 375 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 100 $50 = 300 40 = 200 10 = Current Market Valuation = If the 1941B43 value were $2,000, then $19,000 is to $2,000 as X is to 10. Current Market Valuation $19,000 X $2,000 = 10 1941B43 Market Valuation Company ABC Company DEF Company GHI $190,000 95.00 = = $ 5,000 12000 2000 $19,000 $2,000X X Source: CME, AInside S&P 500 Stock Index Futures.@ The S&P index is calculated as: 500 N i , t Pi , i= 1 S & P Index t = O .V . where: O.V. Ni,t Pi,t t 10 = original valuation in 1941-43 = number of shares outstanding for firm i = 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. Index t = M t base value Bt Where Mt = Bt = base value = market capitalization of the index at time t adjusted base date market capitalization of the index at time t 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 Price of share No. of shares Exchange rate Dividends Splits Mergers Repurchase Mergers Spin-offs Yes Yes Yes Denominator Yes Yes Yes Yes Yes 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 Composition DJIA CBOT U.S. 10 Index 30 U. S. blueBchip Nikkei 225 CME U.S. 5 Index 225 Japanese first section NASDAQ 100 e-mini CME U.S, 20 Index 100 NASDAQ stocks S&P 500 CME U.S. 250 Index 500 mostly NYSE S&P 500 e-mini CME U.S. 50 Index 500 mostly NYSE FTSE 100 Euronext British 10 Index 100 large British DAX 30 EUREX Euro 25 x Index Index Calculation Price weighting (no dividends) Price weighting (no dividends) Modified Market cap weighting Market cap weighting (no dividend) Market cap weighting (no dividends) Market cap weighting (no dividends) Total return 30 German 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 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 15 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 16 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 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%. Buy 1 share of Widget, Inc. + 100 B 100 t = 6 months Receive dividend of $2. Invest $2 for 6 months at 10%. +$2 B$2 t = 1 year Collect proceeds of $2.10 from dividend investment Sell Widget, Inc., for P1. Repay debt. +2.10 + P1 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 ) D i (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: Futures expiration: Days until expiration: Index: Index divisor: Interest rates: July 6 September 20 76 Price-weighted index of two stocks 1.80 All interest rates are 10 percent simple interest; 360 day year Stock A Today's price: Projected dividends: Days dividend will be invested: rA: $115 $1.50 on July 23 59 .10(59/360) = .0164 Stock B Today's price: Projected dividends: Days dividend will be invested: rB: $84 $1.00 on August 12 39 .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: Index N Pi i 1 Divisor Index $ 115 84 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: C o , t 0 . 10 X 76 360 C o , 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. Fair Value of Index F 0, t Divisor Fair Value of Index $ 200 . 67 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 Costof-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-andcarry 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: Futures expiration: Days until expiration: Index: Index divisor: Interest rates: July 6 September 20 76 Price-weighted index of two stocks 1.80 All interest rates are 10 percent simple interest; 360 day year Stock A Today's price: Projected dividends: Days dividend will be invested: rA: $115 $1.50 on July 23 59 .10(59/360) = .0164 Stock B Today's price: Projected dividends: Days dividend will be invested: rB: $84 $1.00 on August 12 39 .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 cashand-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 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%. 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 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. 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-andcarry 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. 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 investment 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. 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 noarbitrage 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 Sell Buy Profit/Loss (points) $ per contract point number of contracts Profit/Loss $ 8857.30 8603.50 253.80 10 20 $50,760.00 S&P 500 999.00 1026.45 B 27.45 250 5 -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 Sell Buy Profit (points) $250 per contract 1079.40 1102.50 -23.10 B $5,775.00 December 1109.25 1085.70 23.55 $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 VF where: VP VF $ 40 , 000 , 000 150 . 94 150 contracts (1060 )($ 250 ) = = value of the portfolio 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 March 14 August 16 Hold $40,000,000 in a stock portfolio. Stock portfolio falls by 5.40% to $37,838,160. Loss: B$2,161,840 Futures Market Sell 150 S&P 500 December futures contracts at 1060.00. S&P futures contract falls by 4.43% to 1013.00. 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. P VP Number of Contracts VF Where: βP = beta of the portfolio that is being hedged. Thus, The manager would sell: 1 . 22 $ 40 , 000 , 000 -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 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 9 46