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87

Compute the implied interest rate/forward ratepanty by dividing the second equation by the first:

James E Hi ens and AHai, M Loc jian, "F. leigi. Exchange Futures," m Han.tt.c t .fFutures Markets, Perry J Kaufban (ed ) . J. .hii W,ley & Sons, New Yor

U.S./DM = U.S./DM,,

For example, if U.S. interest rates are 8%, West German rates are 6%. and the I.S./DM, is 0.5000, the 1-year forward rate would be

U.S./DM,,.. = 0.50001

S./DM I = 0 5094

Crossrate IVIatrix Evaluation

Given the large number of currency exchange rates that can be quoted in terms of any other currency, there are many combinations of rates that might provide an opportunity for arbitrage. The process for uncovering those inconsistencies that offer opportunity Is easier if you put all of the rates into a table format often seen in the newspapers. Using simplified values, this takes the form:

USD DEM CHF JPY

USD 1.00

DEM 2.00 1.00

CHF 1.25 .625 1,00

JPY .001 .00625 .0125

Every crossrate in table T is related to every other crossrate according to:

atj x ajk = for all i. j, k.

where the first subscript is the row. the second is the column, and each value of a represents an dement in the table, with represemii currency i in terms of currency / Because the top right triangle in the table is exactly the inverse of the lower left pan. it is usually omitted. Whenever a value n the empty part of the lable is referenced, substitute the inverse from the mirror image of that location:

For the example In table T, x , = a- Because there is no we substitute and get at/an a2 Replacing this with values in the table gives l.ZS/Z.OO = .625. showi that the exchange rates between the U.S. dollar (USD), Deutschemark (DEM), and Swiss franc (CHF) are equitable. If the two sides of the equation were not the same, there would be a potential aAitrage opportunity. As in all arbitrage, the transaction costs must be subtracted from the opportunity to determine the realistic minimum variance for a profitable trade.

Class Arbihage

To facilitate the process of keeping prices aligned, there is Class arbitrage, which takes advantage of the



difference between the futures and the interbank forward markets. Class actually refers to the categorj of membership on the International Monetary Maricet of the Chicago Mercantile Exchange, which provides exclusively for this tjpe of arbitrage.

Institutional Arbitrage

Arbitrage is most often associated with institutional trading. Because profits on individual positions are small it is necessarj to trade large numbers; hence, the capital requirements

can be equally large. The most well-known of all arbitrages is called program trading, the process by which a stock index futures market and the cadi index (the weighted average of the 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 cadi and futures prices will come together (to within a small price difference) by the time the futures contract expires. At that time the buyers and sellers must settle in cash at the current cadi maricet value. The price of the two markets at delivery will be:

where F is the futures price at delivery, r is the ris ess interest rate, and is the annualized dividend yield. In addition to a deviation fran this relationship, 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 of stocks because of the uptick rule. The uptick rule requires that share prices only he sold on an uptick, which makes it impossible to guarantee that short positions can be entered in eadi stodc or that the trade can be completed in a preset time

in addition to the laie costs involved in setting a position in all of the 500 stocks that comprise the S&P Index, there is competition from other institutions. This limits the profit potential of the frade to the smallest 1 1 amount over the break-even level. Adding the more realistic assumptions of distinct borrowing and lending rates made in the basic

futures aibitrage discussed earlier, plus separate transaction costs for buying stock and selling shon f the normal futures price at delivery can vary within the band;

(5 - 0(1 + - <F<iS + 0(1 + n -y)

Finding a Representative Subset of an Index

An arbitrage would be much easier and less costly if there was a smaller group of stocks or futures maikets that performed the same as the entire index. If the index is weighted by capitalization, volatility, or some other characteristic, then sorting the components of the index in order of largest capitalization, or highest volatility, would allow you to find a reasonable subset. In the case of capitalization, it is likely that a smaller group of stocks would represent 90° of the index value; therefore, that subset would perform in a way very similar to the index. Unfortunately, the S&P 500 is comprised of companies that all have relatively high capitalization.

Another approadi to finding a subset of maikets that closely tracks the index value is by using stepwise regression, inputting all of the maikets that compose the index, and examining the weighting factors assigned to eadi in the answer. TTiose niarkets writh the highest weighting factors are the most significant in the movement of the overall index By creating a smaller badcet from those maikets with the highest weighting factors, you can adiieve a close approximation of the index with few components-at lead tenporarily. The infiuence of the components may change,



causing the weighting factors to change; therefore, the regression would need to be rerun frequently, and the bad;el adjusted to stay aligned with the index. Unless you are sure that the subset of the index that represents 90°o of the movement will continue to reflect the index movement until expiration, you have replaced an arbitrage with a simple speculative position.

Intermaricet Spreads

The propagation of financial and stock index futures markets have expanded the number of markets that are interdependent upon one another. Prior to the influx of financial markets, product substitution (hogs and cattle, feedgrains) and location spreads were the most common activity; silver in New York, London, and Chicago, and gold in New York and Chicago received much attention. Now there are a laie number of interest rate markets of all maturities in many counfries, 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- Even, countrj seems to have infroduced its equity index into the marketplace, all with the idea of competing for their share of hedgers, speculators, and investors.

Spreading two stock indices expresses a particular market opinion. If you consider three popular indices, the Dow, S&P 500, and the NYSE Index, we see that each represents an increasing picture of business economy. The Dow, limited to blue chips, includes very stable companies not affected by minor events. On the other end of the spectrum, the NYSE Index is the average of all shares and expresses the broadest view of the economic health. If you believe thai the economy is headed for a downturn, but do not want to be net short the entire market, then a spread which is long the Dow and short the NYSE Index would be a lower-rid; approach to implementing that position.

Figure 13-2 shows the spread between the Value Line Index, the first stock index market in Kansas City, and the S&P 500 in Chicago, once the most active stock spread. As is often the case, fraders are attracted to the most active market, and there is significantly less liquidity in one leg of the spread.

There are many dependent relationships between futures markets. Because the basis for these are fundamentally sound, spreads are an excellent way to profit fran short-term divergence. The most comprehensive shidy of these relationships can be found in John Mu hys Intermarfcet Technical Analjsis. in which he shidies the leads and lags between markets and examines the interaction in their relationships. Of these. Figure 13-3 shows how two markets can frend in the same direction, but have short periods of extreme divergence. Interest rates, represented by U.S. bonds, are a dominant component in the carrjing charges of most maikets; therefore, when yields rise, phjsical commodity prices rise, as seen in the CRB Index. Other events, however, can overaiiehn this relationship and cause violent distortions.

Traders must be cautious when attempting intermaiket spreads. Because they are on different exchanges, the simultaneous execution of both legs cannot be guaranteed by either exchange, in addition, each leg must be entered al the market with orders placed at almost the same time. Further care must be taken to understand the differences in the contracts; for example, the three wheat contracts in Kansas City, Minneapolis, and Chicago trade wheat of different tjpes for different piwposes, and each of the stock index maikets represents a different view of public participation, Intermaiket wheat spreads can often go the wrong way. Even the Dow will shift relative to the S&P 500 when maifcel participants concentrate on blue chips.

Additional care is needed when exchanges offer lower maigins for intermaiket spreads. A lower maigin can result in exfreme leverage, which may not always be justified for intermaiket spreads. AVhen prices diverge, the leverage can work against you.

Product Spreads

Product spreads are very actively traded. The soybean crush, the most popular among futures fraders, has been used for many years. Product spreads usually involve three mar

4 aij 1 irny.Ir rman Tecuincal Analysis .J..hii W,ley & Sons, NewY.dc. 1991)

FIGURE 13-2 Intermaiket spread between Value Line and S&P 500.



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