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86

delivery months are a combination of livestock on feed, expectations of marketing, and the price of grain.

Spreads are actively traded between related products. As within a sector of the stock maricet, such as airiines or technologj, there are groups of financial and agricultural maikets that are interdependent. Globalization has made interest rates in the industrialized countries respond to changes in monetary policy by the United States, Germany, and Japan. Changing interest rates then cause changes in foreign exchange rates, which also impact the local equities markets. The meetings of the Group of 7 (G7) further increase the chance of a unified policy by setting common expectations among the largest economies. While there is a clear dependence of one market on the other, the effects are highly variable.

Spreads are often unique to a specific market situation and cannot be generalized for all products. The trader must first understand the basis of the spread relationship before any technical analjsis can be applied. It is most important that a trader understand the conditions under which a spread, or even an arbitrage, will fail. This chapter will present many approadies to spreading that very specific; examples are equally limited in scope and application.

SPREAD AND ARBITRAGE RELATIONSinPS

The relationship between two markets, or between various deliveries and trading vehicles within the same market, will determine the tjpe of trading strategj that may he applied. The tjpes of spreads and arbitrage situations that are most often watched are:

1 . Substitute products, such as wheat and corn or cattle and hogs. Product substitution ranges from those markets that are nearly identical (e.g., 3-month T-bills and 3month Eurodollars), to cotton and soybeans, which share the same land and growing season.

2. Location spreads, including gold in New Yoric Chicago, and London; cocoa and heating oil (gasoil) in New York and London.

3. Carrjmg charge spreads and cash-and-carrj, where one delrvery month is out-ofline with others.

4. Product relationships, such as crude oil versus heating oil and gasoline, and soybeans versus soybean meal and oil.

5. Usage spreads, including the hog-com ratio, feeder catUe-com-fat cattle, cocoasugar, broilers-com, and lumber-pljwood.

6. Pureprice differences, such as exchange and interbank currency rates, interest rates of the same maturity and



the same grade, where there is no actual cost of delivery or carrjing chaiges.

ARBITRAGE

When the two legs of a spread are highly correlated and, therefore, the opportunity for profit fran price diveigence is of short duration (less than 1 or 2 dajs), the trade is called an arbitrage. True arbitrage has, theoretically, no trading ride however, it is offset by small profits and limited opportunity. For example, a spacial arbitrageur using the interbank maiket might call one bank in Tokjo and another in Frankfiirt to find their rates on the Mexican peso, if they differ, the trader would buy the peso fran one bank and sell the peso at another provided:

1. The price difference was greater than the bid-ad;ed spread, representing the cost of converting the currencies.

2. The arbitrageur has proper credit established with both banks.

3. The transaction can be performed simultaneously (by telephone). This requires one trader with a telephone in each ear or two traders woiking side-by-side.

Laige-scale arbitrage has become the domain of major financial institutions who employ many traders, each provided with high-tech computer displajs, sophisticated analytic software, and lots of telephones. These traders specialize in specific interest rate maikets, foreign exchange, individual stock selection, or less often, precious metals. They constantly scan quotes from across the world to find price differences, then act quickly using cadi, forward and ftitures maikets. They trade laige quantities to profit fran small variations. For the interest rate maikets, there are computer programs that compare the various tjpes of coupons and maturities to identifj an opportunity quickly. Such operations have become an integral part of the banking industrj; they keep rates in-line with other banks and generate steadj profits.

Pricing of Futures Contracts

The relationship of one ftitures market delivery month to the spot price of that maiket is different according to the tjpe of product, which has alreadj been described in general terms. The mathematics of some of these relationships can become very complex, and the reader is referred to texts that deal specifically with these subjects. The following sections describe the most important features of these relationships.

Storable Commodities

Storable commodities can be purchased in the cadi maiket, stored, and sold at a later time. They can also be delivered on a ftitures contract, held in storage, and redelivered against another contract. This puts an upper limit on the amount of the carrjing charges that can be added to ftitures prices. The difference in cost between holding the phjsical commodity and bujing it on the ftitures market are:

1. The financing cost involved in the purchase of the phjsical commodity:

added interest cost== spotprice )[l + interestrate]"f"ff"

Where life of ftitures contract is expressed in years. 2 The cost of storage, if any

3. A convenience cost for not buying the phjsical product, and the ability to be able to sell it at any time.

These three cods are added to the ftitures spot price to get the fair value of the ftitures price at the time of delrvery. The strategies that keep the spot and ftitures prices aligned, where F is the ftitures price, S is the spot price, r is the annualized interest rate, t is the life of the ftitures contract (in years) from today to the time of deliverj, and is the net annual storage cost (expressed as a percentage of the spot price) are:

Method 1: Buy the ftitures contract for F; take delivery at expiration. Margin cost can be collateralized. Net cost isF



Method 2: Borrow the cost of the spot commodity S and buy the phjsical product; pay the interest, S)[ 1 -i- -1), and the storage net-of-convenience cost, S x x t, until the corresponding futures market delivery.

nt Valuation ij-lm Wiley & Sons, New York, 19 ,pp 44SA , iriiich pr-vrled tiie basis fortiiese ftniulas, also see IJa-rha

The two methods must have the same net cost; otherwise, everyone would choose the cheaper alternative. Therefore the two strategies are equal, and they form the basic arbitrage relationship between futures and spot prices:

F = S + Si[l+r}-l)+Skt = S(\l + rY + Mt)

This relationship represents the ideal case. If you add more realistic features, including separate borrowing and lending rates, and , where > r, and assume that the short seller cannot recover the saved storage costs and must pay transaction costs. as well, you gel a normal range in which futures pnces can fluctuate:

(S - l,Xl + r) < jF < 5(11 + rY + kt)

When futures prices move outside this range, there is a possibility of arbitrage. Interest Rate Parity

One well-known, second-order arbitrage combines foreign exchange forward rates with interest rate parity Consider the following: A U.S. corporation would like to invest $1 million for the nest 6 months. The current U.S T-bill retum for the next 6 months is lower than the rate in West Germany, and the inflation rate is about the same. The corporation is faced with the decision of whether to convert U.S. dollars to Deutschemarics and invest in West German time deposits or accept the lower U.S. rates. The decision is made easier if the corporation purchases goods from West Germany, since it must eventually convert U.S. dollars to Deutschemarks to satisfj payments; the conversion cost will then exist with either choice.

What if the value of the Deutschemark loses Po against the U.S. dollar durmg the 6month investment period? A corporation whose payment is stated in Deutschemaiks suffers a Po loss in the total interest received. If the 6-month return was 4>o, interest received is now valued at $400 less than the $40,000 total, a small amount for the corporation making payment in Deutschemarics. A speculator would face a different problem because the entire return of $1,040,000 would be reduced by 1% to $1,029,600, netting a return of only 2.96° o, less the additional cost of conversion. For the speculator, shifts in exchange rates often overwhelm the relative improvement in interest rate return.

The interest rateparity tbeorem will normally explain the differences between the foreign exchange rates and the relative interest rates of countries. It states that

the forward rate of a currency is equal to its present value plus the interest earned in that country for the period of the forward rate.

Using the futures or interbank market for the forward rate (DM lyr, is I year forward) and the spot rate for the current value (DM spot,), the annual interest rate in West Germany (Lger.1 is applied to obtain the relationship

Because the forward value of the U.S. dollar can be expressed similarly as

U.S.,yr = U.S.sp,{l+Ias)



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