Tài chính doanh nghiệp - Chapter 9: Stock index futures

© 2004 South-Western Publishing1Chapter 9Stock Index Futures2OutlineIntroductionStock indexes and their futures contractsUses of stock index futuresHedging with stock index futures3IntroductionThe fastest growing segment of the futures market is in financial futuresIn 1972, physical commodities comprised over 95 percent of all futures volumeToday, physical commodities amount to only one-third of total futures volume4Stock Indexes and Their Futures ContractsStock indexesStock index futures contractsThe S&P 500 stock index futures contractPricing of stock index futuresBasis convergence5Stock IndexesIntroductionCapitalization-weighted indexes6IntroductionThe S&P 500 index represents about 90% of all U.S. stock index futures tradingFirst published in 1917Currently one of the Commerce Department’s leading indicators7Capitalization-Weighted IndexesThe S&P 500 index is capitalization-weightedEach of the 500 share prices in the index is multiplied by the number of outstanding shares in that particular firmStandard and Poor’s calculates the index by adding these figures and dividing by the index divisor8Capitalization-Weighted Indexes (cont’d)Assume only three firms are in an indexAssume the initial divisor is arbitrarily set at 2,700,0009Capitalization-Weighted Indexes (cont’d)Day 1Index = 270,000,000/2,700,000 = 100.00StockShares OutClosing PriceShares x PriceA1,000,000$1010,000,000B5,000,000$22110,000,000C10,000,000$15150,000,000Total270,000,00010Capitalization-Weighted Indexes (cont’d)Day 2Index = 271,000,000/2,700,000 = 100.37StockShares OutClosing PriceShares x PriceA1,000,000$1111,000,000B5,000,000$20100,000,000C10,000,000$16160,000,000Total271,000,00011Capitalization-Weighted Indexes (cont’d)Day 3 – B splits two for oneIndex = 262,000,000/2,700,000 = 97.04StockShares OutClosing PriceShares x PriceA1,000,000$1212,000,000B10,000,000$11110,000,000C10,000,000$14140,000,000Total262,000,00012Stock Index Futures ContractsAs with other futures, a stock index future is a promise to:Buy or sell Standardized units Of a specific index At a fixed price At a predetermined future date13Stock Index Futures Contracts (cont’d)Stock index futures are similar in every respect to a traditional agricultural contract except for the matter of deliveryIndex futures settle in cash rather than by delivery of the underlying asset14The S&P 500 Stock Index Futures ContractThere is no actual delivery mechanism at expiration of an S&P 500 futures contractYou actually deliver the dollar difference between the original trade price and the final price of the index at contract termination15Pricing of Stock Index FuturesElements affecting the price of a futures contractDetermining the fair value of a futures contractSynthetic index portfolios16Elements Affecting the Price of A Futures ContractThe S&P 500 futures value depends on four elements:The level of the spot index The dividend yield on the 500 stock in the indexThe current level of interest ratesThe time until final contract cash settlement17Elements Affecting the Price of A Futures Contract (cont’d)S&P 500 Stock Index FuturesSPX IndexT-bill RateTime until SettlementSPX Dividend Yield18Elements Affecting the Price of A Futures Contract (cont’d)Stocks pay dividends, while futures do not pay dividendsShows up as a price differential in the futures price/underlying asset relationship19Elements Affecting the Price of A Futures Contract (cont’d)Stocks do not accrue interestPosting margin for futures results in interestShows up as a price differential in the futures price/underlying asset relationship20Determining the Fair Value of A Futures ContractThe futures price should equal the index plus a differential based on the short-term interest rate minus the dividend yield:21Determining the Fair Value of A Futures Contract (cont’d)Calculating the Fair Value of A Futures Contract Example Assume the following information for an S&P 500 futures contract:Current level of the cash index (S) = 1,484.43T-bill yield ® = 6.07%S&P 500 dividend yield (D) = 1.10%Days until December settlement (T) = 121 = 0.33 years22Determining the Fair Value of A Futures Contract (cont’d)Calculating the Fair Value of A Futures Contract Example The fair value of the S&P 500 futures contract is:23Synthetic Index PortfoliosLarge institutional investors can replicate a well-diversified portfolio of common stock by holdingA long position in the stock index futures contract andSatisfying the margin requirement with T-billsThe resulting portfolio is a synthetic index portfolio24Synthetic Index Portfolios (cont’d)The futures approach has the following advantages over the purchase of individual stocks:Transaction costs will be much lower on the futures contractsThe portfolio will be much easier to follow and manage25Basic ConvergenceAs time passes, the difference between the cash index and the futures price will narrowAt the end of the futures contract, the futures price will equal the index (basic convergence)26Uses of Stock Index FuturesSpeculationSpreadingArbitrageAnticipation of stock purchase or saleHedging27SpeculationEach one-point movement in the S&P 500 index translates to $250A person who is bullish could obtain substantial leverage by buying S&P contracts28SpreadingSpreads using index futures can be used to speculate with reduced riskE.g., a speculator believing the Nasdaq will outperform the Dow Jones could employ an intermarket spread by buying Nasdaq 100 futures and selling DJIA futures29ArbitrageSometimes the market price of a futures contract temporarily deviates from the price predicted by pricing theoryAn arbitrageur could short the futures contracts and buy stock if the price deviates upwardAn arbitrageur could short the stock and buy futures contracts if the price deviates downward30Anticipation of Stock Purchase or SaleFutures contracts can be used to lock in a price in anticipation of a stock purchase or saleE.g., a portfolio manager might want to get out of the market, but for tax reasons does not want to sell securities until the new year31HedgingThe primary purpose of S&P futures is to facilitate risk transfer from one who bears undesired risk to someone else willing to bear the riskS&P futures are used by most large commercial banks and by many pension funds and foundations to hedge32Hedging With Stock Index FuturesSystematic and unsystematic riskThe need to hedgeThe hedge ratioHedging in retrospectAdjusting market risk33Systematic and Unsystematic RiskSystematic factors are those that influence the stock market as a wholeE.g., interest rates, economic indicators, political climate, etc.Systematic risk or market risk34Systematic and Unsystematic Risk (cont’d)Unsystematic factors are unique to a specific company or industryE.g., earnings reports, technological developments, labor negotiations, etc. Unsystematic risk35Systematic and Unsystematic Risk (cont’d)Proper portfolio diversification can virtually eliminate unsystematic riskThe market assumes that you have been smart enough to reduce risk through diversificationBeta measures the relative riskiness of a portfolio compared to a benchmark portfolio like the S&P 50036Systematic and Unsystematic Risk (cont’d)Portfolio VarianceNumber of Securities37The Need to HedgeUsing Futures Contracts to Hedge Portfolios You are the manager of a $100 million equity portfolio. You are bullish in the long term, but anticipate a temporary market decline. How can you use futures contracts to hedge your stock portfolio? 38The Need to Hedge (cont’d)Using Futures Contracts to Hedge Portfolios (cont’d) If you are long stock, you should be short futures. You need to calculate the number of contracts necessary to counteract likely changes in the portfolio value. 39The Hedge RatioIntroductionThe market fallsThe market risesThe market is unchanged40IntroductionTo construct a proper hedge, you must realize that portfolios are ofDifferent sizesDifferent risk levelsThe hedge ratio incorporates the relative value of the stock and futures, and accounts for the relative riskiness of the two portfolios41Introduction (cont’d)To determine the hedge ratio, you need:The value of the chosen futures contractThe dollar value of the portfolio to be hedgedThe beta of the portfolio42Introduction (cont’d)Determining the Factors for A Hedge Suppose the manager of a $75 million stock portfolio (with a beta of 0.9 and a dividend yield of 1.0%) wants to hedge using the December S&P 500 futures. On the previous day, the S&P 500 closed at 1,484.43, and the DEC 00 S&P 500 futures closed at 1,517.20. 43Introduction (cont’d)Determining the Factors for A Hedge (cont’d) The value of the futures contract is: $250 x 1,517.20 = $379,30044Introduction (cont’d)Determining the Factors for A Hedge (cont’d) The hedge ratio is:45The Market FallsUsing the Hedge in A Falling Market Assume the S&P 500 index falls 5%, from 1,484.43 to 1,410.20 after three months. Given beta, the portfolio should have fallen by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. However, you receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,410.20) x $250 x 178 = $4,761,500. 46The Market Falls (cont’d)Using the Hedge in A Falling Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,636,500. 47The Market RisesUsing the Hedge in A Rising Market Assume the S&P 500 index rises from 1,484.43 to 1,558.70 after three months. Given beta, the portfolio should have advanced by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. You still receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will lose (1,517.20 – 1,558.70) x $250 x 178 = $1,846,750.48The Market Rises (cont’d)Using the Hedge in A Rising Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,778,250. 49The Market is UnchangedUsing the Hedge in An Unchanged Market Assume the S&P 500 index remains at 1,484.43 after three months. There is no gain on the stock portfolio. However, you still receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,484.50) x $250 x 178 = $1,455,150.50The Market is Unchanged (cont’d)Using the Hedge in An Unchanged Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,705,150. 51Hedging in RetrospectA hedge will usually not be perfect because:It is not possible to hedge exactlyStock portfolios seldom behave exactly as their beta suggestsThe futures price does not move in lockstep with the underlying index (basis risk)The dividends on the S&P 500 index do not occur uniformly over time52Adjusting Market RiskFutures can be used to adjust the level of market risk in a portfolio:53Adjusting Market Risk (cont’d)Determining the Number of Contracts Needed to Increase Market Exposure Suppose the manager of a $75 million stock portfolio with a beta of 0.9 would like to increase market exposure by increasing beta to 1.5. Yesterday, DEC 00 S&P 500 futures closed at 1517.20 How can the manager use futures to accomplish this goal, assuming the composition of the stock portfolio remains unchanged?54Adjusting Market Risk (cont’d)Determining the Number of Contracts Needed to Increase Market Exposure (cont’d) The manager should go long futures and hold them with the stock portfolio. Specifically, he should purchase 119 S&P 500 futures contracts: