One of the main reasons futures have been such successful trad-ing instruments is that they almost always are cheaper to tradethan their related cash instruments. As a result, we have attracteda cost sensitive clientele. And with every passing year, our mar-kets have become more liquid and more efficient to trade.

Even so, one area in which the futures industry lags behind thesecurities industry is in providing clients with estimates of marketimpact and transaction costs. In the U.S. equities market, trans-action cost analysis has been an area of real competition amongbroker-dealers for some time, and a lot of interesting quantitativework has been done in that area.

This is now beginning to happen in the futures industry. The rapidgrowth and expansion of electronic trading now makes it possibleto study transaction costs in a way that conventional pit tradingdid not allow.

In talking about transaction costs, this discussion is not referringto brokerage commissions or exchange fees. Rather, electronictrading makes it possible to analyze the cost of market impactwith much greater mathematical precision than ever before. Toput it another way, we can use the vast amount of data generatedby electronic trading to analyze the daily ebb and flow of liquidityand use that information in trading strategies. This is especiallyimportant for institutional customers, such as money managers orhedge funds, that want to trade in size and can benefit from quan-titative estimates of the potential cost from moving the marketone way or the other.

MeasuringMarketImpact:TransactionCost AnalysisComes to theFuturesMarketBy Galen Burghardt

62 Futures Industry

We now have several years of electronictrading in the major interest rate contractsunder our belts, and even longer with thestock index products. More than 80% ofEurodollar futures are traded electronically,and average daily volume in the E-mini stockindex contracts far outstrips their largerbrethren still traded on the floor. In addition,the falling cost of computing power makes itmore feasible for the large broker-dealers andthe large funds to perform complex calcula-tions on very large amounts of data.

So it is entirely possible to compile a con-tinuous series of tick-by-tick market data for awide range of futures contracts. CalyonFinancial recently completed just such a proj-ect, and the results have proved to be quiteuseful in helping our clients minimize themarket impact of their trades. And we arewell aware that a number of money managerswith experience in these markets are under-taking similar projects, and in some caseshave already modified their trading strategies.

Having the ability to make precise meas-urements of market impact can be useful inat least three trading applications. Theseinclude optimal trading strategies, that is,those that are designed to minimize marketimpact or produce the best trade-off betweenmarket impact and tracking error. A secondis the design of tactical execution rules forworking orders, such as in determining thelikelihood for being filled at the bid or theoffer. A third is in the analysis of bench-marks, tracking error, and execution costs.

The remainder of this article providessome examples of the kind of transactioncost analysis that is now possible with elec-tronic trading. The examples are drawn froma longer paper published by Calyon, whichexplains in detail how the various calcula-tions were made. One interesting aspect ofthe analysis is that the results confirm severaltheoretical insights into market behavior.

Building the Data Set Calyon Financial has invested heavily in

gathering a continuous time market depthdatabase that allows us to observe the limitorder book in nearly continuous time and totrack the flow of actual trades. In the case ofthe limit order book, we are tracking the bestfive bids and best five offers. This data set isexceptionally valuable for studying marketliquidity and the impact of trades of varioussizes throughout the course of a trading day.

For example, it allows us to calculate asweep-to-fill measure of market impact—theeffect on the price of instantaneously tradingas far into the order book as necessary to fillan order of a given size. For large orders, itmay be necessary to go well beyond the num-

ber of contracts available at the best bid orbest ask, and the resulting average price isknown as a sweep-to-fill price.

As of this writing, we are gathering datafor 51 markets—16 equity, 12 bond, 6 moneymarket, 7 currency and 10 energy. We arealso gathering data on calendar spread trad-ing for 24 of these markets. And we continueto add to the list as quickly as we can.

We also have learned more than wethought possible about the peculiarities thesedata sets present. For one thing, synchroniz-ing clock times is a challenge. Filtering outspecial trades from actual market trades isanother. Paying attention to the way thatexchanges aggregate data is a third.

November/December 2006 63

Exhibit 1

Sweep to Fill Costs Versus Order Size E-mini S&P 500 futures trades at 8:40 a.m. during the first quarter of 2006

Source: Calyon Financial

64 Futures Industry

Market Impact in PracticeExhibits 1 and 2 provide two different

perspectives on market impact. Exhibit 1shows the sweep-to-fill market impact cost ata particular time of day over the course of anentire quarter. The reason for picking a par-ticular time of day is that market impact is afunction of both volume and volatility,which vary systematically and predictablywith time of day. In this case, the datasetcontains all trades in the E-mini S&P 500 at8:40 a.m. for every trading day in the firstquarter of 2006. Typically the E-mini marketis very active at that time of day.

While there is considerable variability inmarket impact for trades of a given size, thescatter makes it clear that the impact of atrade on the market is less than linear—thatis, market impact is not directly proportionalto the size of the trade. And the convex shareof the curve indicates that larger trades—more than 1,000 lots—are not as expensive interms of market impact as one would expect.

Exhibit 2 looks at the same contract, butthis time the dataset covers the entire tradingday. We can see that the market impact of atrade can vary a lot over the course of a trad-ing day. In this case, we find that the most

liquid time of day for E-mini S&P futures cor-responds to 3:00 p.m. Chicago time, which iswhen the cash market closes. We can also seethat the futures market loses some liquidityafter the cash close but is still more liquid atthe futures close than at other times of thetrading day, including the futures open at8:30 a.m. Exhibit 2 also confirms the non-lin-ear nature of market impact, in that thesweep-to-fill cost for a 2,000 lot order is nottwice the cost for a 1,000 lot order.

Analyses like these can be very useful totraders. For one thing, traders can identifythe most liquid times of the trading day. Foranother, traders can make informed choicesbetween tracking error and the costs of trad-ing, rather than relying on subjective impres-sions or past experience.

Market Impact in TheoryOur research on liquidity and market

impact suggests that we can explain what wesee in Exhibits 1 and 2 using the simplestpossible theory. In particular, if we assumethat the great pool of traders whose businessit is to provide liquidity can be representedby a single, risk averse market maker, we canfirst get an idea of how risk averse this hypo-

thetical market maker is by fitting a curve tothe scatter plot in Exhibit 1.

The rest of the theory suggests that thebid/ask spread that the market maker wouldquote is directly related to the volatility ofthe price (i.e., its standard deviation) and isinversely related to the square root of tradingvolume. From the same data set that we usefor calculating sweep-to-fill prices andimpacts, we can calculate trading volumeand price volatility profiles by time of day.

Then, armed with our estimate of riskaversion and our estimates of trading volumeand price volatility, we can produce theoret-ical estimates of market impact like thoseshown in Exhibit 3. For someone in research,the beauty of this exercise is that the theoret-ical market impact profiles in Exhibit 3 con-form almost perfectly to the empirical marketimpact profiles found in Exhibit 2. In otherwords, the simple theory works.

Hidden LiquidityWhat you see with a limit order book is

not necessarily what you get. First, it showsphantom liquidity—bids and offers to whichtraders are not really committed and that arewithdrawn either for no apparent reason orbecause the market begins to move in theirdirection. Whether these are available forsweep-to-fill orders is to some extent a mat-ter of timing and fast action. Also, the limitorder book does not reveal hidden liquid-ity—all of those potential bids and offerscontrolled by traders who don’t want to showtheir hands.

Of the two, it seems that hidden liquidityis the more important consideration whenanalyzing market impact. As have others, wefind that the apparent impact of trades tendsto be smaller than sweep-to-fill measures ofmarket impact would suggest.

Using data for the first quarter of 2006,we first calculated the distributions of sweepto fill prices at the beginning of each minuteof each trading day. For each of these snap-shots, we calculate five sweep-to-buy prices(exhausting the number of contracts offeredat each price) and five sweep-to-sell prices(again, exhausting the contracts bid at eachprice). We then calculate the absolute valueof the difference between these sweep-to-fillprices and the true market price at eachmoment. We then proceeded to see howmany contracts actually traded in the inter-val immediately following each snapshot

Exhibit 2

Sweep to Fill Cost by Time of DayE-mini S&P 500 futures during the first quarter of 2006

Source: Calyon Financial

66 Futures Industry

(five seconds in the case of E-mini S&Ps)and calculated the volume-weighted averageprice at which these trades were done.

Comparing the two distributions, we findthat actual trade prices reveal more liquiditythan is apparent in the limit order book. Asshown in Exhibit 4, the effect of hidden liq-

uidity was worth slightly more than a cent forsmall orders and just under two cents forfairly large trade sizes. For intermediate-sizedtrades, though, the presence of hidden liq-uidity was worth considerably more. Fortrades between 500 and 1,000 contracts, hid-den liquidity was worth 4.4 cents, while for

trades between 2,000 and 3,000 contracts,hidden liquidity was worth about 3.8 centsper contract.

Practical ApplicationsThe range of possible applications for

these insights into market liquidity is fairlybroad. We find, for example, that the mostcommon trade size, at least in the E-miniS&P 500 futures market, has become a onelot, that is, a single contract. This suggeststhat computerized trading platforms arebeing used to minimize transaction costs byminimizing market impact. The trading vol-ume profiles also can be used to conductwhat are known as VWAP (volume-weighted average price) trades, which arecommon in the equity world and which aregaining a foothold in the futures world.

Market liquidity measures are useful inchoosing how to work orders over time andallow those of our clients who are less timesensitive than others to be providers ratherthan consumers of liquidity. To this end, partof our research has been devoted to scopingout what might be called the efficient execu-tion frontier—those ways of working ordersthat offer the greatest possible benefit inexchange for the least amount of risk.

The same data set that allows us to meas-ure and monitor market liquidity also allows usto evaluate the quality of trade executionagainst objective benchmarks such as arrivalprice, VWAP, or closing price. Our experiencesuggests that brokers and their clients haveselective memories that give too much weightto unusually bad fills and, as result, they tend tochoose execution strategies that give too muchweight to risk and not enough weight topotential reward. Being able to assess tradesobjectively will allow everyone to make moreinformed decisions about how to trade.

We find too that this theory in practiceallows us to anticipate the effects of key sched-uled economic announcements. We find, forexample, that FOMC announcements pro-duce predictable spikes in both volume andvolatility that, in turn, radically change theshape of the day’s market impact profiles ■.

Galen Burghardt is senior vice president anddirector of research at Calyon Financial Inc. and amember of the editorial advisory board of FuturesIndustry. He is also an adjunct professor offinance at the University of Chicago’s GraduateSchool of Business, where he teaches an MBA-level class on derivatives.

Exhibit 4

Hidden Liquidity Summary for E-mini S&P 500 Futures (1/3/06 - 3/31/06)

Order Size Average Impact

Sweep to Fill Vwap Difference

0-500 0.129 0.117 0.011

500-1000 0.189 0.145 0.044

1000-2000 0.243 0.202 0.042

2000-3000 0.332 0.295 0.038

3000-5000 0.428 0.411 0.017

Source: Calyon Financial

Exhibit 3

Theoretical Market Impact for E-mini S&P 500 Futures on a Typical Day (Projected spread to the “true” price)

Source: Calyon Financial