forward rate parity by dividing the second equation bythe first:
3 James E. Higgens and Allan M. Loosigian, “Foreign Exchange Futures,” in Handbook of Futures Markets, PerryJ. Kaufman (ed.) John Wiley & Sons, New York, 1984).310 SPREADS AND ARBITRAGE
 
“1 tlysLS. = U.S./DM, =.US JDM yp = USD Moe
 
For example, if U.S. interest rates are 8%, West German rates are 6%, and the U.S./DM igo, is0.5000, the 1-year forward rate would be1.08
U.S.JDM; , = 0.5000>=
U.S./DM, y, = 0.5094
Crossrate Matrix Evaluation
Given the large number of currency exchange rates that can be quoted in terms of anyother currency, there are many combinations of rates that might provide an opportunityfor arbitrage. The process for uncovering those inconsistencies that offer opportunity iseasier if you put all of the rates into a table format often seen in the newspapers. Using sim-plified values, this takes the form:
 
 
usD DEM CHF JPYUSD 1,00 'T= DEM 2.00 1.00CHE 1.25 625 1.00yPY 001 00625 0125 1.00
 
Every crossrate in table 7 is related to every other crossrate according to:iy X Ae = Airy for all z, 7, R,
where the first subscript is the row, the second is the column, and each value of a repre-sents an element in the table, with ay representing currency i in terms of currency j.Because the top right triangle in the table is exactly the inverse of the lower left part, it isusually omitted. Whenever a value in the empty part of the table is referenced, substitutethe inverse from the mirror image of that location: \ay = lay
For the example in table J 45; X @,2 = G37. Because there is no a4, we substitute 1/a,; andet &3;/A2, = 452. Replacing this with values in the table gives 1.25/2.00 = .625, showing thatthe exchange rates between the U.S. dollar (USD), Deutschemark (DEM), and Swiss franc(CHE) are equitable. If the two sides of the equation were not the same, there would be apotential arbitrage opportunity. As in all arbitrage, the transaction costs must be subtractedfrom the opportunity to determine the realistic minimum variance for a profitable trade.
Class B Arbitrage -
To facilitate the process of keeping prices aligned, there is Class B arbitrage, which takesadvantage of the difference between the futures and the interbank forward markets. ClassB actually refers to the category of membership on the International Monetary Market ofthe Chicago Mercantile Exchange, which provides exclusively for this type of arbitrage.Institutional Arbitrage
+
Arbitrage is most often associated with institutional trading. Because profits on individual”Positions are small, it is necessary to trade large numbers; hence, the capital requirementsARBITRAGE : 31
 
can be equally large. The most well-known of all arbitrages is called program trading, theprocess by which a stock index futures market and the cash index (the weighted average ofthe actual stock prices) are kept in the proper relationship to one another.
Program Trading
There is nothing secret about program trading. The premise is that cash and futures priceswill come together (to within a small price difference) by the time the futures contractexpires. At that time the buyers and sellers must settle in cash at the current cash marketvalue. The price of the two markets at delivery will be:
FaS(l+r-y)
where F is the futures price at delivery, r is the riskless interest rate, and y is the annualizeddividend yield. In addition to a deviation from this relatiqnship, you must know:
1. The transaction costs of executing both the stock and futures side of the trade. This
includes both commissions and an estimated slippage for each of the stock issues. that must be bought.
2. The trade can only be entered with a short sale in the futures and the purchase ofstocks because of the uptick rule. The uptick rule requires that share prices only besold on an uptick, which makes it impossible to guarantee that short positions canbe entered in each stock, or that the trade can be completed in a preset time.
In addition to the large costs involved in setting a position in all of the 500 stocks thatcomprise the S&P Index, there is competition from other institutions. This limits the profitpotential of the trade to the smallest acceptable amount over the break-even level. Addingthe more realistic assumptions of distinct borrowing and lending rates made in the basicfutures arbitrage discussed earlier, plus separate transaction costs for buying stock ¢, andselling short ¢,, the normal futures price at delivery can vary within the band:
“S-t)dtre~y) < F< (St+tj dtr -~yy
Finding a Representative Subset of an Index
An arbitrage would be much easier and less costly if there was a smaller group of stocks orfutures markets that performed the same as the entire index. If the index is weighted bycapitalization, volatility, or some other characteristic, then sorting the components of theindex in order of largest capitalization, or highest volatility, would allow you to find a rea-sonable subset. In the case of capitalization, it is likely that a smaller group of stocks wouldrepresent 90% of the index value; therefore, that subset would perform in a way very sim-ilar to the index. Unfortunately, the S&P 500 is comprised of companies that all have rela-tively high capitalization.
Another approach to finding a subset of markets that closely tracks the index value isby using stepwise regression, inputting all of the markets that compose the index, andexamining the weighting factors assigned to each in the answer. Those markets with thehighest weighting factors are the most significant in the movement of the overall index. Bycreating a smaller basket from those markets with the highest weighting factors, you canachieve a close approximation of the index with few components—at least temporarily.The influence of the components may change, causing the weighting factors to change;therefore, the regression would need to be rerun frequently, and the basket adjusted tostay aligned with the index. Unless you are sure that the subset of the index that represents90% of the movement will continue to reflect the index movement until expiration, youhave replaced an arbitrage with a simple speculative position.312 SPREADS AND ARBITRAGE
 
Intermarket Spreads -
The propagation of financial and stock index futures markets have expanded the numberof markets that are interdependent upon one another. Prior to the influx of financial mar-kets, product substitution (hogs and cattle, feedgrains) and location spreads were the mostcommon activity; silver in New York, London, and Chicago, and gold in New York andChicago received much attention. Now there are a large number of interest rate markets ofall maturities in many countries, and stock index markets attempting to measure high cap,low cap, and sectors, as well as the old favorites, the S&P 500 and the DJIA. Every countryseems to have introduced its equity index into the marketplace, all with the idea of com-peting for their share of hedgers, speculators, and investors.
Spreading two stock indices expresses a particular market opinion. If you considerthree popular indices, the Dow, S&P 500, and the NYSE Index, we see that each representsan increasing picture of business economy. The Dow, limited to blue chips, includes verystable companies not affected by minor events. On the other end of the spectrum, theNYSE Index is the average of all shares and expresses the broadest view of the economichealth. If you believe that the economy is headed for a downturn, but do not want to benet short the entire market, then a spread which is long the Dow and short the NYSE Indexwould be a lower-risk approach to implementing that position.
Figure 13-2 shows the spread between the Value Line Index, the first stock index mar-ket in Kansas City, and the S&P 500 in Chicago, once the most active stock spread. As isoften the case, traders are attracted to the most active market, and there is significantly lessliquidity in one leg of the spread.
There are many dependent relationships berween: futures markets. Because the basisfor-these are fundamentally sound, spreads are an excellent way to profit from short-termdivergence. The most comprehensive study of these relationships can be found in JohnMurphy’s Intermarket Technical Analysis,‘ in which he studies the leads and lags betweenmarkets and examines the interaction in their relationships. Of these, Figure13-3 shows how two markets can trend in the same direction, but have short periods ofextreme divergence. Interest rates, represented by U.S. bonds, are a dominant componentin the carrying charges of most markets; therefore, when yields rise, physical commodityprices rise, as seen in the CRB Index, Other events, however, can overwhelm this relation-ship and cause violent distortions.
Traders must be cautious when attempting intermarket spreads. Because’ they are ondifferent exchanges, the simultaneous execution of both legs cannot be guaranteed byeither exchange. In addition, each leg must be entered at the market with orders placed atalmost the same time. Further care must be taken to understand the differences in the con-tracts; for example, the three wheat contracts in Kansas City, Minneapolis, and Chicagotrade wheat of different types for different purposes, and each of the stock index marketsrepresents a different view of public participation. Intermarket wheat spreads can often gothe wrong way. Even the Dow will shift relative to the S&P 500 when market participantsconcentrate on blue chips.
Additional care is néeded when exchanges offer lower margins for intermarketspreads. A lower margin can result in extreme leverage, which may not always be justifiedfor intermarket spreads. When prices diverge, the leverage can work against you.
Product Spreads
Product spreads are very actively traded, The soybean crush, the most popular amongfutures traders, has‘been used for many years. Product spreads usually involve three mar-
‘John J. Murphy, intermarket Technical Analysis (John Wiley & Sons, New York, 1991),ARBITRAGE - 313— EEE
 
FIGURE 13-2 Intermarket spread between Value Line and S&P 500,
 
 
 
 
 
 
t : asses ameraAe fy pOee Pee iPop -
 
 
 
 
pec} JAN
 
Source: Commodity Research Bureau Weekly Chart Service.
kets, which may be of different delivery months, depending on the processing time. Themost common product spreads are:
’
 
 
Raw product(s) Resulting primary product(s) -Soybeans Meal and oil .Crude oil Gasoline and #2 heating oilFeeder cattle and grain Fat cattleFeeder pigs and corn Live hogsLive hogs Pork bellies
 
Exchanges often allow reduced margins when these spreads are entered in the proper pro-portion at the same time.314 SPREADS AND ARBITRAGE
 
 
FIGURE 13-3 A comparison of U.S. Treasury bond yields and the CRB Index, 1987-1993.
A very similar trend is disrupted by an occasional large divergence. In most cases, a noticeablerise or fall in the CRB Index is followed by a change in interest rates in a manner intended tooffset the effects of inflation.
ETL meee
 
 
 
 
Source: Charts created with TradeStation® by Omega Research, Inc.
\
Product spreads do not always correct for distortions within the time needed to beprofitable for the trader. When the combined return on soybean meal and oil is below the.cost of crushing the soybeans, processors may execute a reverse soybean crush spread, inwhich they sell the soybeans and buy the products. Even though this appears to be a cleverway of keeping prices in-line, it is not done until the crushing margin is very negative,Processors cannot readily reduce their level of operation and lay off employees; a reversecrush means that they are buying products as well as producing them—a position of sig-nificantly increased risk.
The Crack Spread L
Crude oil is refined primarily into gasoline and heatirig oil. As with the soybean crush,where the processor buys soybeans and produces meal and oil, the refiner expects a profitfrom the business of buying crude oil and selling gasoline and heating oil. A speculator cantheoretically participate in this process by buying crude oil and selling the products in theright proportion and in the correct delivery months. For example, if crude oil was tradingat $20 per barrel, heating oil at 52.40¢ per gallon, and gasoline at 59.50¢ per gallon, thenbased on futures contracts of 1,000 barrels of crude and 42,000 gallons of heating oil andgasoline, we could calculate each contract value:ARBITRAGE ~ 315a
Gasoline component: 59.50 x 42,000 = $24,990Heating oil component: 52.40 x 42,000 = $22,008Total components: $46,998Crude oil component: 20.00 x 1,000 = $20,000Two other important facts are necessary to put this trade together:
1, It takes from 4 to 6 weeks to refine crude oil into its products; therefore, the pricesused in the crack spread should always take the product prices quoted 1 monthafter the crude price.
2, While the refining ratios can vary during the year, based on the higher demand forgasoline in the summer, and the higher demand for heating oil in the winter, thestandard ratios are found in Table 13-1.
Although there are many other by-products of the refining process, the major componentsof fuel oil and gasoline are produced in a ratio of slightly more than two parts gasoline toone part fuel oil on average éach year. This ratio then accounts for the 3-2-1 crack spread,in which three contracts of crude oil are bought, and two contracts of gasoline and onecontract of heating oil are sold. In the example above, we can complete the net transactionas follows: .
 
 
Unit TotalMarket Price Quantity Value Units CostSell 2 Gasoline contracts. 59.50 x 42,000 = $24,990 x 2 = $49,980Sell | Heating oil contract 52.40 x 42,000 = $22,008 x | = $22,008Buy 3 Crude oil contracts 20.00 x 1,000 = $20,000 x 3 = $60,000Net transaction (without costs) $11,998
Transaction costs will include the expectation of buying crude oil higher and selling prod-ucts lower than desired when the trade is entered, the commission, and the cost of hold-ing the contracts until delivery.
TABLE [3-1 Fuel Oil and Gas Production and Ratios, [984-1992
 
 
 
Fuel Oil —_ Gases
Gas/ -
Resid- Gaso- fet Kero- Fuel OitDistillate val =. — Total line Fuel ~~ sene Total Ratio1984 981 326 - 1,307 2,37! 4l4 42 2,827 2.161985 981 322 1,303 2,352 434 34 2,820 2.161986 1,021 324 1,345 2,476 472 33 2,981 2.221987 997 323 1,320 2,506 490 29 3,025 2.291988 1,046 339 1,355 2,555 50! 29 3,085 2.281989 1,152 500 1,652 2,684 544 31 3,259 1,971990 1,067. - 347 1414 2,650 556 16 3,222 2,28(99) 1,081 341 1,422 2,554 525 14 2,820 1.981992 1,088 326 14l4 2,59! 512 (5 3,118 2.20
 
Source:The CRB Commodity Yearbook, 1994 Jahn Wiley & Sans, 1994),316 SPREADS AND ARBITRAGE
 
Reverse Crack .
When the delivered price of the products totals to less than the cost of crude oil, the refinerhas no reason to process the crude oil, and can go to the market to buy the products andsell crude. This is called a reverse crack. In reality, processors can perform a reverse crackto some degree, but shutting down operations to accommodate a temporary market con-dition is not a good policy. The process of shutting down and restarting a large refinery isnot simple, and labor problems make matters more complicated. When executing areverse crack, the same delivery months are used for both crude and products.
CHANGING SPREAD RELATIONSHIPSSome spread relationships will always exist, while others may change due to:
1, Price level, such as during the silver bull market of 1980
2. Consumer tastes, such as a shift away from red meat
3. Health reasons, such as those often concerning nitrates in bacon
4. New competition, such as increased supply of edible oils from the Far East impact-ing the soybean product relationship, or the effect of high-fructose corn sweetenerson the sugar industry
Even though the market absorbs the anticipation of change in an orderly way, unexpectedevents relating to health or interruption of supply can produce a price shock that will affectmany spreads.
Gold/Silver Ratio —
A relationship that has always been followed with keen interest is the gold/silver ratio, tra-ditionally considered normal at 33 : 1. It serves as a good example of the variability of manyperceived spreads. When gold was $35 per ounce and silver about $1 per ounce, the rela-tionship was never very stable. Between 1930 and 1945, silver prices dropped to about$.50 per ounce; from 1951 to 1962, they remained just under $1 per ounce, and afterwardsilver began its accelerating move to $38 per ounce in January 1980. Between 1944 (whenthe International Monetary Fund (IMF) was formed) and 1971, the price of gold was fixedat $35 per ounce, although in a few years before the cancellation of the agreement, theprice varied above the designated value. From the late 1960s until the silver crisis of 1980,the goldfilver ratio ranged from about 20: 1 to 45:1 in a slow cycle. During the crisisattributed to the Hunt brothers (September 1979~September 1980), the ratio fluctuatedaround 33; 1 in a highly volatile pattern moving only slightly above and below its historicpattern. Following the silver crisis, the value of silver declined faster than gold, reaching aratio of 56: 1 in June 1982, with gold at $314 and silver at $5.57. A year later, the ratiotouched 33 ; 1 and rapidly widened to 66 : 1 in June 1986.
Is the gold/silver ratio a tradable spread? Was it ever a good spread trade? Probably not.The relationship is mainly dependent on public perception of both items as an enduringstore of value. The same is true for the platinum/gold ratio (Figure 13-4) or the value ofgems. Prices remain strong as long as the public confidence is unshaken. There is no fun-damental reason for these prices to remain in the same ratio as there is for feedgrain pricesto adjust relative to their protein content.
The public was hurt during the silver crisis. Many peop!e made their purchases duringthe latter part of 1979, then lost heavily in 1980. At the same time that the U.S. dollar wasgaining incredible strength and interest- rates were still high, gold and silver prices weredropping rapidly, -
Naturally, the value of gold did not decline as much as some other investments, Manycountries still hold gold as a store of value. But times change and there has been a notice-CHANGING SPREAw AELATIONSHIPS: 317
 
 
FIGURE 13-4 The platinum/gold spread, similar to gold/silver, shows periods where it mightbe successfully traded; however, markets such as 1980 always remain a possibility.
 
    
 
 
 
 
 
 
 
Dollars per ounce
 
FMAMJ4IASONO JFMAMJJASOND J1980 : 1981 1982
 
Source: New York Mercantile Exchange.
able shift to the U.S. dollar as an international standard. Investors feel safe with theirmoney in U.S. banks and in U.S. dollars; they are willing to suffer short-term currencyswings in exchange for security and diversification. For example, the price of oil, thelargest traded commodity in the world, is quoted in U.S. dollars rather than gold.
There is no doubt the U.S. dollar will lose glamour if U.S. leadership or its economyweakens; if world peace becomes a reality, the security of the dollar will also be less impor-tant, If there is significant economic instability, there may be a return to gold and diamondsas an implied standard. However, these relationships are too uncertain to be tradable,except at great risk.
Intramarket and Intermarket Financial Spreads
Spread relationships in financial markets represent anticipation of economic policy. Thespread values themselves are well defined by the interrelationship of all interest rate vehi-cles, but they will vary on the interpretation of the impact of government policy on moneysupply in reaction to the balance of trade, unemployment, and an expanding economy,and the time period in which the action will occur.
An intramarket spread, or delivery month spread, in a single financial instrument,such as T-bills, is a conservative speculation in changing policies as discussed in the previ-ous section. A bull spread, long the nearby and short the deferred, shows a belief in tem-porarily_declining interest rates. An intermarket financial spread, involving differentmaturities; is 2 speculation in the changing yield curve. A long bonds/short bills positionfavors a negative carry, while long bills/sbort bonds expects a return-to-normal carry (withrespect to futures prices). -
Intercrop Spreads.
A special case involving carrying charges is the intercrop spread, which can be highlyvolatile, even though there is an old crop carryover that ties the two seasonal marketstogether. Soybeans, for example, are harvested mainly in September and October. TheAugust delivery is clearly the old crop, and November is the first new crop month; the Sep-tember contract often reflects the shift from old to new.318 SPREADS AND ARBITRAGE
 
Normally, the old crop trades at a premium to the new crop. Carrying charges, accu-mulating since the previous winter, are part of the August price; export demand may causeshortages in the old crop, which moves prices further above the cost of carry. | Figure 13-5ashows the anticipated price pattern resulting from carrying charges during a normal year.The minimum storage commitment for the 3 months immediately following harvest isshown as a larger increase in price. Normal carry adds equal amounts to the price until thefollowing September, where old and new crop mix. Finally, any carryover must assume theprice of the new crop, which is in greater supply.
The theory behind an intercrop spread is that prices must come together when the oldcrop merges with the new crop. But can it be a profitable trade? Examine the two possibleevents that affect this trade:
1. Problems involving development of the new crop making supply uncertain. This
causes prices in the new crop to rise more quickly than the old crop (Figure 13-58).
2. Export demand in the old crop results in old crop prices rising faster than new cropprices (Figure 13-5c). :
In case 1, the spread between crops narrows and can only be traded as a spread that is
short the old crop, long the new crop. This spread has limited potential since the Novem-
ber delivery cannot exceed the old crop by more than the normal carrying charge. At that
‘
 
FIGURE 13-5 Intercrop spreads. (a) Normal carrying charge relationship. (b) New crop‘supply problems result in narrowing spreads. (c) Export affects the old crop more thanthe new, resulting in a widening spread.
 
—_—_—_—— 01d crop ——-__-————_____> —~<— New crop —>N DB Jd F M AM J J A S ON Dd F(a)
‘N
——_——_—_——— 01d crop ——_________> —<—— New crop —-»>
 
~ Old crop: me New crop. _
 
 CHANGING SPREAD RELATIONSHIPS 319
 
point, processors will buy, store, and redeliver the old crop against the new crop. Whenprices in the new crop are nearing the old crop value, it makes sense to liquidate or evento reverse the spread. Once reversed, there is little risk that the spread can move adversely.A revised crop estimate that showed better yield than originally expected would cause thenew crop to decline sharply and the spread to widen.
In case 2, export demand in the old crop causes the intercrop spread to widen at first.A spread trader will typically wait until export commitments are complete, then sell the oldcrop and buy the new. When old crop prices rise to a large premium over the new crop,many processors will reduce purchasing based on:
1. Low or negative profit margins at the current price levels2. Use of reserves or inventory to carry processing through until the lower new cropprices are available
It is remarkable how demand is inversely related to price, even when it is consideredinelastic, When a delay in purchasing or processing will result in greater profits for thecommercial, it is somehow achieved.
Butterfly Spreads
A butterfly spread, normally referred to as just a butterfly, is a low-risk technique for cap-turing short-term interdelivery distortions. It is most appropriate in highly volatile mar-kets, where the concentration of trading in one or two delivery months causes thosecontract prices to move away from the normal delivery month relationship.
For example, in April a combination of poor planting, declines in the U.S, dollar, andnew export agreements changes the soybean prices as shown in Figure 13-6. Increaseddemand results in sharply higher July futures prices with a tapering-off of the effect in themore deferred contracts. The normal carrying charge relationship is shown as a straightline in the old crop, beginning again in the new crop. A butterfly entered in the old cropwould mean selling two contracts of July soybeans and buying one contract each of Mayand August. This is the same as executing two spreads: long May, short July and short July,long August.
Each spread in the butterfly has a good chance of being profitable; the combination ofthe two is exceptionally good. The July contract cannot remain out-of-line with the deliv-eries on both sides, because a trader could take delivery of the May contract and redeliverit in July at a profit exceeding the cost of carry. Under normal circumstances, commercialusers of soybeans will defer their purchases to later months, depleting their reserves, toavoid paying a short-term premium and causing July prices to drop.
 
FIGURE 13-6 Delivery month distortions in the old crop making a butterfly spread possible.
~~ Old crop New crop
Sell2° Buy 1°
Buy 13° oO ° °
pe ean carry aa
May Jun Jui Aug Sep Oct Noy Dec
 320 SPREADS AND ARBITRAGE
 
The butterfly spread guarantees that any adjustment in the three contracts back to anormal relationship will prove profitable. If the prices of both May and August rise to be in-line with July or if May rises to form an inverted relationship, the spread will be profitable(Figure 13-7).
The problem with such an ideal spread is the short life and difficult execution. Becauseprofits are nearly riskless, opportunity is small. The beneficiaries of these trades are usuallythe floor traders who can act quickly. Once the position is entered, liquidation can be eas-ily accomplished.
Pseudoarbitrage of S&P Day and Night Markets
Intended to take advantage of distortions caused by S&P Market-on-Close orders andGLOBEX session, Conners and Hayward have created a GLOBEX/S&P Fair Value Program.*
1. Determine the daily fair value difference between the S&P futures and cash markets,FV = S&P futures ~ SGP cash. Use the price as soon after the close of the NYSE aspossible, for example, 4:03 EST, leaving 12 minutes to the close of futures trading.
2. Calculate your price entry target, F as T= SEP cash + FV + .50, where the value .50represents 4 an S&P point.
3. Place a sell order at price T If the market is already trading above T just after theNYSE close, then entering the order as Market-on-Close of futures is likely to be best.
4. If filled, cover your short if your profit is 50 during the 16 hours of GLOBEX trading.
5. Close out the trade on the close of GLOBEX if your profit has not been reached. Donot carry the trade into the next session.
The justification for this situation is the investors’ fear of an overnight drop in price. Itdepends on the lack of overnight news that would drive the market higher; however, ana-lysts might note that S&P price shocks always cause prices to drop. It is strongly suggestedthat no position be taken on the evening that the President gives the State of the Union
Message.
CARRYING CHARGES
The carrying charge structure of a market determines the underlying differences in the rel-ative price of each contract. For metals and most storable commodities, these charges con-
> Laurence A. Conners and Blake E. Hayward, Investment Secrets of a Hedge Fund Manager (Probus, 1995),
 
FIGURE 13-7 Corrections to interdelivery patterns.
 CARRYING CHARGES 32
 
sist of interest, storage costs, and insurance. All else being equal, a market with normalcarry can be expected to show steadily higher prices for deferred contracts based entirelyon the cost of carry. Prices that move out-of-line may be corrected by taking delivery of thenearby and redelivering against the next contract.
It is always possible for changes in supply and demand to alter the relationship offutures contracts so that the carrying charge pattern no longer appears normal. Althoughthis is not likely to occur in the metals, it often happens that an immediate demand forfood can cause short-term increases in prices without substantial effect on more deferredmonths. This situation is called an inverted market, or negative carry, even though thecarry