million commercialpaper at 6.63% (IMM index93.37)
4
Buy (offset) 10 September Eurodollar contracts at 6.59% (IMMindex 93.41)
Loss = 113 points
26
Gain = 139 points
Table 24.6 Sell Hedge Eurodollar CDsCash MarketJune 15Inventory of $5 million Eurodollars maturing 12/14/96,yielding 6%(IMM index 94.00)
Basis
65
July 1Sell inventory of $5 millionEurodollars maturing 12/1/96@ 6.2 yield (IMM index 93.80)
Futures MarketSell five September Eurodollarfutures contracts maturing12/14/96 @ 6.65% yield (IMMindex 93.35)Buy five September Eurodollarsfutures maturing 12/14/96 @6.75% yield (IMM index 93.25)
55Loss = 20 points
–10 points
Gain = 10 points
On June 15, the money manager protects his inventory by selling SeptemberEurodollar futures at a 6.65 percent yield. Time passes and rates rise, causing hisinventory to decline in value. On July 1, he decides to liquidate the inventory at aprice to yield 6.2 percent. He buys back the futures at 93.25 to yield 6.75 percent.
246
Hedging Applications for Interest Rate
The basis narrowed from 65 to 55 points. The use of the futures reduced the $500loss in the cash market to a net loss of only $250.
REDUCING BASIS RISKThe whole idea behind hedging is to minimize the risk of unfavorable basis movement. If you can do that, you will have a very successful hedging program. Thereare several concepts to keep in mind in minimizing such risks.One way to reduce risks is through proper selection of the contract month forplacing the hedge. So many hedgers ask, “Which month should I use?” The answerhas several parts:1. Use the futures month that most closely coincides with the maturity ofyour cash position, if possible, or the second most actively traded month.2. Select the futures price that seems most overpriced or underpriced relative to the cash market.This involves some understanding of what causes futures prices for different months to take on different values. Basically, the price differences betweentwo futures months are reflecting two things:1. Cost-of-carry2. ExpectationsCost-of-carry is the difference between the cost to borrow the money to buythe cash instrument and the return received while owning the cash instrument.Cost of borrowing is best reflected in the repo rate. If the cost-of-carry is positive,you would expect futures to be trading at a higher yield (lower price) than thecash. If the cost-of-carry is negative, you would expect futures to trade at a loweryield or a higher price than the cash.Why? If you can make money by borrowing to buy a cash instrument, youwill bid for the futures as an alternative investment until the net futures price provides exactly the same yield. Because futures are not an earning asset until delivery, you will bid only until the two prices are identical after adjustment for timedifference and the cost of money over the time difference. If it is a positive carryof 2 percent, you will give up no more than 2 percent on futures to get the 2 percent income.Expectations sometimes become a more important price influence than costof-carry. Instances arise where people expect the cost-of-carry to change, or theyexpect significant shifts in the level of interest rates. Those expectations usuallyget reflected in distant months more dramatically than in nearby months. Thus,
247
Chapter 24
you need to watch market fundamentals closely to determine which of myriad factors is influencing the market at any particular time.
HEDGING THE PRIME RATEBanks regularly issue six-month CDs to obtain funds to lend at the prime rate.They do this when rates are high and when they are low. Sometimes they getcaught in situations where they have outstanding CDs with several months to run,but their prime lending rate has fallen. In such cases the profitability of these loanshas reduced dramatically and will remain that way until the CDs mature and newmoney can be obtained (new CDs issued) at the lower rates. A banker caught insuch a profit squeeze could protect his profit margin by hedging, by buying 90day T-bill futures. As the prime rate falls, so should rates on 90-day Eurodollars,if the two rates are correlated fairly closely. In such a hedge, a long position infutures will yield a profit which can be used to offset the loss in loan income. Asthe cost of funding the loan comes in line with the prime rate, the banker shouldlift the hedge.A construction company anticipates that, in about three months, it will needto obtain a substantial construction loan for six months priced on a floating-rate basisat 1 percent over prime. By selling Eurodollar futures, or Treasury bill futures contracts, it can hedge against an increase in the prime rate between now and the timethe loan funds will be needed. If interest rates have risen by that time, and futuresprices have declined correspondingly, the profit realized when the futures contracts are liquidated will help to cover the higher rate of interest the company willpay for its construction loan.This may be a risky hedge if it is a short-term hedge, because the prime rateis an administered rate and changes infrequently compared to the market rates forEurodollars and T-bills. Hence, short-term basis risk may be great. In the long run,say two years or more, such basis risk will average out and provide a much betterpotential for an effective hedge.
HEDGING THE FED FUNDS RATESometimes a regional bank has excess Fed funds, so it sells them. When the Fedfunds rate is high, such sales can be a nice source of income. When Fed fundsrates fall, however, revenues fall. A bank can protect against this loss of incomeby buying 30-day Fed fund futures traded at the CBOT. As rates fall, income fromfutures helps offset the loss of income from Fed funds. Again, this hedge has a
248
Hedging Applications for Interest Rate
reasonable chance of success only if the correlation between the futures and the Fedfunds rate is quite high.
PREFUNDING A PORTFOLIOSuppose a bank has a liquid portfolio (very short-term instruments) with maturities in September and December. Assume it expects rates to be lower in thosemonths than the rates currently reflected in futures. To protect against that fall inrates, the bank could buy Eurodollar futures and T-bill futures. As rates fall, thefutures gains will offset the reduced yields received when the bank reinvests themoney from the maturing instruments in September and December.You might ask why the bank doesn’t simply purchase replacement securitiesnow for the securities maturing in September and December. Two reasons: First,it may not have extra cash. Second, it might not want to swap the securities in itscurrent portfolio for others because it would have to reflect the loss on its financial statements. Such a loss would not have to be booked if the securities are keptto maturity, when they will be redeemed at par.
HEDGING LONG-TERM INTEREST RATESCorporations may wish to hedge the cost of long-term borrowing when the timebetween the decision to borrow and the actual process of borrowing is protracted.For example, corporations that have planned to borrow in the future may wish tolock-in today’s futures market rates. This can often be the case when corporationscontract to have capital goods built. The construction process is financed by shortterm borrowing, but after completion of construction, long-term debt is sold tofinance the asset. When the period of construction is lengthy the corporation maynot want to pay both short-term borrowing and long-term borrowing costs, particularly if it does not wish to risk paying higher long-term rates at a later time.To hedge such a risk the borrower can establish his rate today by shortingT-bond futures contracts. To accomplish this the hedger should do the following:1. Complete a correlation study to find which futures contract provides themost constant basis relationship with the debt that will be eventually sold.2. Study changes in the size of the basis, including those caused by credit differences. A mathematical function can be statistically derived throughregression analysis of past relationships.
249
Chapter 24
3. Adjust for changes in rate resulting from differences in maturity.4. On a present value basis, using the expected coupon rate of the bond fora compounding factor, calculate the amount of money that must be madeon the futures to cover increased interest costs.Once these four steps have been taken, the appropriate number of contractsshould be shorted. If interest rates increase between the hedge date and the bondsale date, the profits from the futures would be added to the proceeds of the bondsale to reduce interest costs of the sale. In effect, the corporation would be receiving a premium for its bonds.The recent decision by the CBOT to change the “notional coupon” on itsTreasury complex results in some changes in determining which cash bond is thecheapest to deliver. The steps one must go through to determine which cash bondis the cheapest to deliver are as follows:1. Determine the conversion factors for the bonds you are hedging. These factors are multiplicative grade adjustments that equilibrate the differencesin coupon and maturity of the issues eligible for delivery. In actuality,they represent the value of the bond under consideration.2. Since the contract “tracks” cash securities priced as the cheapest to deliver, one must figure out which cash bond is the cheapest to deliver andregularly check to be sure that it remains the cheapest to deliver. For example, at the present time the CBOT’s cheapest to deliver bond is assumedto be the 8-1/4 of August 2019 cash T-bond. The futures market shouldtrade pretty much in tandem with this bond.3. The theoretical pricing formula for this issue is:
Futures Price =
CTD Cash Price – Cost of Carry – Strategic Delivery Option ValueThe Conversion Factor
WhereCTD
The cheapest to deliver cash bond
Cost of carry
The interest cost of carrying the bond for the period
Strategic DeliveryOption Value
The value of the shorts option to choose which issueto deliver and when to deliver it
The ConversionFactor
For a given rate of change in yields, the rate ofchange in the price of the instrument. (Note, thisshould be adjusted for the probability of a switch inthe cheapest to deliver.)250
Hedging Applications for Interest Rate
This short description of the process of trading bond futures is not intendedto be a complete course in hedging and selecting the bond for delivery. Those readers who are interested in such should check with the exchange or take a course inbond pricing and futures deliveries to get firsthand knowledge about the processof calculating the cheapest to deliver and the delivery process.
CORPORATION HEDGING SINKING FUNDOBLIGATIONSAssume a corporation must purchase $5 million of its 8 percent bonds (six yearsto maturity) by September 1 to fulfill a sinking fund obligation. The treasurer ofthe corporation believes there is at least an 80 percent probability that interest rateswill be 1 percent lower than current rates by September, but does not have thecash available to buy the bonds at this time. That 1 percent fall on a six-year maturity would increase the costs to the fund manager by approximately $210,000.The fund manager can hedge by purchasing approximately 50 contracts ofthe four-to-six-year Treasury note futures.If rates indeed do decline by 1 percent and if that 1 percent decline is reflected fully in T-note futures, then the manager will have an approximate profit of$210,000 in futures to offset the increased cost of his sinking fund bonds.
BANK ISSUING CDSAssume that a regional bank economic forecasting group concludes interest ratesare headed sharply higher with a real possibility that the Fed will tighten monetarypolicy imminently. Assume that bank also was preparing to issue $50 million inCDs, but does not have them issued yet. It needs two weeks.How could the bank protect itself against the possibility that rates might risebefore it got the CDs sold?The answer is to hedge by selling Eurodollar or T-bill futures. Table 24.7shows how the hedge would have worked out.This example teaches you several important points:1. The basis changed. Rates in the cash position increased more than ratesin the futures market. Hence, gains and losses did not offset each otherexactly. This emphasizes the importance of knowing the basis and correlation.2. This was a cross-hedge. The product being hedged in the cash market wasnot identical to the items represented in the futures contract. That is amajor reason why the basis changed.251
Chapter 24
Table 24.7 Bank Hedge for CDsCash MarketBasisOctober 5Long $50 million CDs due April5.80
1.61
October 12$50 million CDs due April6.80–1.00
Futures MarketSell $100 million March Eurodollarfutures4.19$100 million March Eurodollar futures
1.93–.32
4.87+.68
Each basis point for futures = $25 × 68 × 100 = $170,000Each basis point for CDs = $50 × 100 × 50 = $250,000$80,000Loss reduced from $250,000 to $80,000Note: As the CDs are issued, the futures position should be liquidatedproportionately.
3. Because the maturity of the cash item was different from the maturity ofthe futures instrument, a .01 change in the rate for the two instrumentswas not equal. The value of .01 for the 90-day T-bill futures was $25. Thevalue of .01 for the six-month CD was $50. Hence, to get “dollar equivalent” coverage, it was necessary that the futures position be double thatof the cash position.
252
Chapter 25
Stock Index Futures and Options
Kansas City is famous for many things, some of which have been immortalized insong, but it now takes a place in the history of finance as the originator of stockindex futures. Trading in stock index futures, specifically the Value Line Average(VLA), began in February 1982. The Kansas City Board of Trade worked actively on the concept of trading futures on stock indexes for five years before regulatory hurdles were overcome and trading actually began.The last major regulatory hurdle was cleared in mid-1981 when the Commodity Futures Trading Commission finally granted approval for the concept ofcash settlement of futures contracts. Cash settlement means exactly what it suggests: At delivery time, the buyer and the seller exchange cash equal to the difference between the actual price of the product on that day and the price at which theyhad originally made their contract, adjusted for any daily settlements made in themeantime. Thus, in the case of stock indexes, there is no need for the seller toscurry around at delivery time collecting, in the correct proportion, the variousshares of the companies that make up the index.
253Copyright 2001 The McGraw-Hill Companies. Click Here for Terms of Use.
Chapter 25
WHAT’S TRADED AND WHENThe old Wall Street saying that you can’t buy the market averages isn’t true anymore. Now if you have an opinion on the market as opposed to an individual stock,you can buy or sell the whole market—if you buy and the market goes up, theindex will go up and you will make money. It will not be necessary to make an individual decision on each stock. In other words, index futures now allow you to getin on the price action of broad groups of stocks by buying or selling the futures contracts on those indexes.Since Kansas City inaugurated the trading, other exchanges also have listedstock index futures. The Chicago Mercantile Exchange (CME) offers futures onthe Standard & Poor’s 500 (S&P 500), the Nikkei and several others, and the NewYork Futures Exchange lists futures on the New York Stock Exchange (NYSE)Composite Index. The quick success of stock index futures in the U.S. has prompted the listing of stock indexes and options on a variety of other stock groupings,including some highly specialized selections in utility indexes and financial indexes. Further, all of the major stock exchanges of the world now have futures contracts on their stock indexes: e.g., the Nikkei traded in Chicago and Singapore,the FTSE traded in London; et al.Not all of the indexes are the same. The S&P 500 stock index, a widely recognized representation of the stock market as a whole, is based on the equity pricesof 500 different companies: 400 industrials, 40 utilities, 20 transportation firms, and40 financial institutions. The market value of the 500 firms is equal to approximately80 percent of the value of all stocks listed in the NYSE.The S&P 500 is a weighted index of the prices of the 500 firms. Each stockin the index is weighted so that changes in the stock’s price will influence theindex in proportion to the stock’s respective market value. To determine the weightfor the stock of any particular firm, the number of its shares outstanding is multiplied by its market price per share. In other words, a stock’s market value determines the relative importance of the particular stock in the index; for example,General Motors accounts for approximately 1.35 percent of the S&P 500, whilemany other stocks account for only .05 percent or less.The NYSE Composite Index reflects the value of the shares of all companieslisted for trading on the NYSE. In a manner similar to the S&P, company sharesare not weighted equally, but rather are included in the index according to the formula reflecting the stock’s respective market value. The formula takes into accountboth the number of shares outstanding and the market price.So both the S&P and NYSE attempt to measure the total value of the stocksincluded in their indexes. The NYSE measures every common stock on the NYSE.The S&P measures a designed market sample.
254
Stock Index Futures and Options
COMPUTING A STOCK INDEXThe best way to demonstrate the computation of an index is to actually show thecomputation. To illustrate, consider the S&P 500. That index is calculated usingthe base years 1941 to 1943 equal to 10. The price of each stock is multiplied bythe number of shares outstanding for that company. In the case of the S&P 500, thevalue for each of the 500 shares is added, giving a total dollar value. To create theindex, the total dollar value is then compared to the base value and the index is setaccording to the base index of 10. As a simple example, suppose the index was composed of only five issues (see Table 25.1).To some extent, the indexes are substitutes for each other, i.e., they measurethe same thing. The correlation coefficients between the S&P and the NYSE arenormally .90 and above (a perfect correlation equals 1.000); hence, they measurenearly the same thing and will be almost equally useful in hedging a portfolio.However, the VLA and the Dow Jones Industrial Average are not so highly correlated with the other two.
Table 25.1 S&P 500 Index: An Example
Company ACompany BCompany CCompany DCompany E
OutstandingShares100500200400300
PriceValue303,000105,0005010,00041,600206,000Current Market Value = 25,600
If the 1941–94 market value was $2,500, then 25,600 is to 2,500what × is to 10.
Current Market Value
25, 600 ×=2, 500 10
1941–1943 Market Value $256,000 = $2,500 ×× = 102.40
255
Chapter 25
VOLATILITY IN INDEXESLike other futures contracts, index futures offer a way to play price movements witha lot of leverage. Leverage allows you to get more bang for your buck. Substantialmovements in the value of your account will occur with small investments in theindex. Historically, though, the maximum leverage allowed on the stock indexcontracts has been much less than for almost all other futures. Generally, the margin on the S&P 500 has been about 5 percent of contract value. A 10 percent margin investment for one long contract in 1986, when the index was at about 250and continuously rolled over, would have yielded a handsome return indeed, provided you had survived the 1987 crash! (And that’s not likely because marginswere raised to very high levels during the crash, and anyone who couldn’t meet themwould have had their positions liquidated.)The stock market, as represented by the various indices, is highly variablewhen measured over long periods of time. For example, a study by the CME showsthat the average daily change in the S&P 500 was 2.58 points between February2, 1981, and March 12, 1982. In terms of futures contract value, that is equal to$1,290 per day (2.58 x $500). In more recent years, the volatility has increased, andit is not unusual for the index to change by $2,000 to $3,000 from day to day.Although futures prices move in the same direction as the underlying indexes do, the futures tend to be more volatile than the underlying indexes. Wheninvestors are bearish, prices frequently drop below, and fall faster than, the relevant index. In contrast, when investors are bullish, they tend to push futures pricesabove the index, and futures rise faster. This volatility tends to get accentuated insome of the more thinly traded months and more thinly traded futures. As withmost elements of volatility, these swings offer opportunities for making moneyand losing money.In the long run, stock index futures trade like all other futures: Prices for thefutures will stay in close relationship with the current cash price, plus carryingcosts. Generally speaking, when prices of futures stray away from their theoretical values, arbitrageurs push them back into line by buying when the price seemslow and selling when the price seems high relative to its cash market value.
CIRCUIT BREAKERS AND CRASH PROTECTORSIn the fall of 1987, the stock market crashed, falling more than 500 points in oneday. Many people immediately pointed at the futures traders as culprits, not for initiating the price decline, but for exacerbating it. Many studies were completed onthe causes of the crash and the volatility of the market during the day. The conclusionof the Federal Reserve study, and many others, was that the futures traders were256
Stock Index Futures and Options
participants, but certainly did not initiate or cause the problems. They were reacting to outside forces.The upshot of all the hullabaloo was that the commodity exchanges, stockexchanges, and government regulators each set in place a series of procedures thatare designed to protect the stock market from disastrous collapses due to emotionfilled trading. In short, they agreed on a series of steps to shut down the futures markets and the stock markets for short periods of time if the market rises or falls bysome predetermined amount. The shutdowns become increasingly more severe, andfocus more on market declines than on advances, as the volatility increases. Theseare referred to as circuit breakers, to reflect the idea that they work like an electrical circuit breaker that automatically shuts off the electricity when a circuit getsoverloaded.This process is simply an advancement on the daily price limit that had beenin use for decades on virtually all traditional commodities. Those limits had not beenapplied to stock index futures because it was thought they could cause price dislocations (and, therefore, great financial risk to arbitrageurs) between the stockmarket and the futures market, if the futures stopped trading but the stock marketcontinued. Besides, everybody knew that the stock market would generally stay ina reasonable daily volatility range! Didn’t they?
TRADING THE STOCK INDEXESInvestors or money managers may be interested in participating in stock indexfutures for a number of reasons. For example, they might have an overall opinionon the market direction and would buy or sell the market outright—thereby takinga position on market direction. They might want to sell stock index futures to protect an existing investment or in anticipation of a sale of all or part of a portfolio.Traders may take both a long and short position in the market but in different delivery months. That technique of spreading one month against another worksin stock indexes just as it works in other commodities. You can buy near-termfutures and sell distant futures, or vice versa, hoping to gain as the price differencebetween the two months changes. You should be aware that such spreading techniques are not always low-risk, particularly in stock indexes where there is substantial uncertainty about future stock prices, interest rates, and dividend levels.You also may be interested in integrating stock indexes into the overall management of a stock market portfolio. You could take 10 percent of your capital andplace it in stock index futures, for example, putting the remainder in money market funds at a high yield. Assume you had $100,000 in high-yielding bonds and feltthat the stock market was going up, but you didn’t have the time or resources tomake the difficult decisions on individual stocks. Instead, you could buy one NYSE257
Chapter 25
contract worth approximately $125,000. Approximately 10 percent of the capitalwould be necessary to margin those futures positions. The remainder of the money,$90,000, would stay invested at the higher rate of return. This strategy would allowyou to participate in the stock market, while still maintaining a high yield on yourfunds. Of course, you have significant risk with this strategy. If stocks fall, you willget margin calls.
HEDGING ILLUSTRATEDAs noted earlier in this book, a major use of futures markets is for hedging. In thisinstance, you may want to use the market to hedge your current market holdingsor a portfolio of individual stocks. You may hold the stock investments and sell thestock index. If the market goes lower and the value of your individual investmentsdeclines with it, you will have a gain on the futures which can offset the loss onthe value of the individual shares.Suppose you owned a 10-stock diversified portfolio with a current marketvalue of $35,000. In addition, suppose it generally reflected the value movementsin the NYSE index. If the stock market generally declines by 10 percent as reflected in the NYSE index, your market loss would be about $3,500. You could protect against this loss by selling one NYSE index futures. Suppose at the time of thesale, it had an approximate value of $33,000. If you buy it back after the markethas fallen, and if the index has in turn fallen by 10 percent, you will have made$3,300 on your hedge. That hedge will reduce your net market loss from $3,500to $200.While this may not work as an exact hedge, ways can be found to efficiently tailor a futures position to a particular portfolio to give you the most efficienthedge possible (see the next section). Generally, you would not be well-advised touse the futures market to hedge a portfolio unless it could be statistically demonstrated that the stocks that make up the portfolio do move in concert (are highlycorrelated) with the index used. If that can’t be demonstrated in advance, the hedgermight find himself or herself in the unfortunate position of losing on both thestocks and the futures. If the portfolio is composed of small, little-known firms thatare not included in the underlying index or, if included, are a very small proportion of the index, then it is unlikely that you will find efficient hedges. If, on theother hand, you have a portfolio that is composed of a small but diversified groupof stocks that includes such big names as IBM or AT&T, you may indeed find thefutures a reasonable hedge. Of course, if in 1992 you had tried to hedge IBM stockalone using any of the indexes, it would not have worked. IBM fell 50 percent ormore while the indexes went up. You would have had a double whammy!
258
Stock Index Futures and Options
THE PORTFOLIO MANAGER AND HEDGINGA portfolio manager is one who takes responsibility for managing money invested in a group of assets usually including a range of securities. His objective is usually capital appreciation and income. In making investments, the manager must consider the risk or safety of the investment while attempting to achieve a reasonablereturn. Normally, the higher the risk, the higher the potential for return.When a portfolio manager considers hedging, the objective with the hedgeis akin to doing a balancing act with a scale. On one side of the scale, he has a groupof investments with a particular risk associated with them. On the other side of thescale, he attempts to construct a futures position that will maintain a dollar balance with changes in the value of the portfolio. The success of the hedge willdepend on his success in constructing the proper futures position so that a dollarlost on one side of the scale will be offset by a dollar gain on the other side. Hecan construct that by selecting those futures contracts that are most closely correlated (as determined by statistical analysis) with the individual or groups ofstocks in his portfolio.Once he has identified the appropriate futures to use, he then must determine the number of futures contracts necessary to balance the scales. That calculation is usually accomplished through a statistical technique called regressionanalysis. Regression analysis is used to measure past price relationships for individual issues, or groups of related issues, relative to the underlying index chosenfor the hedge. That volatility relationship will be expressed as a “beta” and is a statistical measurement reflecting the average relationship. Although this “beta” isbased on past history, it is probably the best measure of future price relationshipsin the long run.To determine the correct number of futures contracts to sell to balance thescale, the hedger should calculate a weighted beta for his portfolio. If the overallportfolio beta is 1.0 as measured against any of the indexes, it indicates that virtually all of the risk contained in the portfolio is accounted for, or eliminated, if anequal dollar amount of futures contracts are sold. If the portfolio beta is differentthan 1.0, the number of contracts sold must be adjusted accordingly.For example, if a portfolio manager found a beta coefficient of 1.20 for hisportfolio, he would determine the appropriate number of contracts to sell by dividing the value of the portfolio by the value of the futures contract, and multiplyingby 1.20. To illustrate, assume the manager’s portfolio value is $20 million and themanager intends to use the NYSE Composite Index, which we will assume is valued at $35,000. Twenty million dollars divided by $35,000, multiplied by 1.2,equals 685.7 contracts. The manager would round that number up and would sell686 contracts as the appropriate number for his short hedge.
259
Chapter 25
Now, if past relationships hold and the market changes by 10 percent, the valueof the portfolio should change by $2 million and the dollar value of the changereflected in the index futures should be $2 million as well.It would be unusual if the hedge works out as perfectly as just illustrated.Even with all of the statistical techniques mentioned, it is likely there will be somevariation in the total amount of gain or loss on the futures side compared to thetotal amount of gain or loss in the portfolio. This variation will be due in part to thefact that the futures market may move more, or less, than individual stocks in theportfolio. Further, the timing of the two moves may not coincide exactly. One maymove today and the other may move tomorrow or next