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COMMENTARY 80 APRIL 2OO4TRADING TRUTHSHow Mis-Measurement of Trading Costs ls Leading lnvestors Astray

Some recently published data argues that large cap stocks are more expensive to trade on theNYSE than small caps. In this Commentary, we debunk that theory by demonstrating that thisconclusion results from incomplete data and faulty logic. We also show that:. lmplementation costs are much higher than those reported using VWAP measures;. So-called "pennying" only accounts for a small fraction of the cost of trading, and. Damning the specialist-" and floor brckers ie nn! an appropriate nor desen.,ed response.

A recent maqazine article' states in the sub-title that'Blue chips now cost more to trade on the Big Board thansmall caps do." lt goes on to state "The higher cost oftrading giant-cap stocks at the NYSE, compared withsmaller names, runs counter to the conventional wisdomthat large, actively traded stocks have lower transactioncosts than smaller, less liquid ones."The author provides a table, (portions of which are

reproduced on the following page), that shows "MicroCap" stocks of less than $250 million capitalizationcosting 0.5 cents De.:r share on the NYSE whi!a "GiantCap" stocks with capitalizations in excess of $25 billioncost 1 .9 cents per sha,re The arlicle gets fairly breathlessabout how 'iransaction costs on the Big Board areactually higher for big, actively traded stocks than theyare for small, lightly traded stocks."The article attributes this phenomenon in part topennying; .... NYSE specialists' and floor brokersputative practice of bidding a stock up or down by onecent and trading for their own accounts ahead ofinvestors."The author recognizes that the finding "runs counter tothe conventional wisdom that large, actively tradedstocks have lower transaction costs." Indeed, it iscounterintuitive; fortunately, the finding is false. And it is

dangerous: it may lead to mis-identification of themagnitude, source and relevance of transaction costsand thus contribute to inferior oerformance.We will develop three important points:1. Using pennies per share as the metric ignores the factthat small cap stocks trade at lower prices than largecap stocks. When expressed in economic terms aspercentage of principal, this key finding is simply false:liquid, large cap stocks trade at nohigher impact cost than smaller

stocks.2. f he actual costs of implementinginvestment ideas is in factsignificantly higher than the figuresnrrnted hcre Indced thc differences orroted here arevvrvvtrivial, while true implementation costs are egregiousand much larqer than can be seen through the narrowperspective of the Volume Weighted Average Price(VWAP) comparison.3. The damning of specialists and floor brokers on thebasis of thrs evidence is faulty logic based on faultymeasurement.

Measu ring Economic CostsCents per share sounds like a simple metric, but it onlyworks if the share prices are reasonably similar. Forexample, a dime cost on a $100 stock is 0.1oh; on a$10 stock, it represents 1.0% -- a big difference.l Schack, Justin: "Trading Places;" Institutional Investor Magazine,November 2003. Po B1-85.


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The share price for NYSE listed stocks with capitalizationless than $250 million is about $7; for stocks in excess of$25 billion the average price is around $35. The tablebelow adjusts VWAP impact differences in stock price. ltshows the expected relationship: large, liquid stocks aretraded with less impact than smaller capitalization stocks.

The picture here is one of impact as a percent of tradeddollars rising as market cap falls. Showing costs as apercent of principal traded shows the expectedrelationship, even though the impact in cents per sharedeclines.The last column provides a partialexplanation of trade size effects:the average trade in the largest capgroup is almost 19 times the dollarsize in the Microcap group. Otherthings being equal, we expect largetrades to cost more than smalltrades. Things are not equal,however, since large cap stocks arefar more liquid and therefore easierto trade. Thus the interplay of trade size and availableli^!i/.,1;+.., /.r^+^-q;h^.,r.a +r2^llro .-.nci nl*eTences i-liquidity are ignored by the VWAP benchmark, whichuses the same benchmark irresoective of trade size.

The Real Cosfs of Implementinglnvestment Needs and ldeasSo far we've identified cents oer share measurement asleading to erroneous conclusions between large cap andsmall cap stocks. But there are hidden costs of tradingbeyond the impact.First there's the commission. The following table showsNYSE commission costs by capitalization group. Thecents per share commissions are fairly steady. Showingthe cost in basis points highlights the higher commissioncosts of trading lower priced stocks.

VWAP defines impact as the difference between theaverage price in the trade being executed and theaverage price in the market during the day. Noie thet thoVWAP impacts in the above table do not net to zero, asthey would be if the game were one that pittedinstitutional buyers against institutional sellers. Theinvestors must be losing to someone else, specificallymarket makers and speculators. Specialists, marketmakers, hedge funds, day traders, speculators, etc. enterthe market opportunistically solely to garner short termtrading profits. In the process they provide liquidity toinvestors.Institutional traders enter the market to implementinvestment decisions. They cannot be opportunistictraders; they have an agenda, a blotter of specific tradesto complete. Therefore investors pay speculators for theprovision of liquidity, leading to frictional costs in therange of five cents per hundred dollars traded (5 bp.)A more inclusive alternative to the VWAP measure iscalled lmplementation Shortfall. lt measures the changein price from the starting gate, where the trader receivesthe orcier, to ihe finish iine vyhen tne eniife iraoe iscompleted. lt answers the question: How much of thepotential return did I lose to the cost of implementing thetrades?The costs below show figures for all buy and sell tradesfor a sample of 89 investment managers during thesecond quarter of 2003.

Giant cap ($ 25B+)Large cap ($SA - $258)Midcap ($1B - $5B)Small cap ($250M - $18Microcao $250M or less

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Another hidden cost of trading is the cost of searching forliquidity. Liquidity search costs are real; they eat into theresearch advantagefor stock purchases,and they cost realdollars on securitysales when oricesdecline beforefinding the liquidity tocomolete the trade.They occur becauseinstitutional orders

VWAP lmpact Measures VWAP lmpact Price/shr VWAP lmpactcap f/shr ($) (basis points)Giant cap ($ 2SA+;Large cap ($se - $258)Midcap ($1B - $58)Small cap ($2SOw - $ta)Microcap $250M or less

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I mplementation Shortfalllmpact Measures lmplShortlmpact: Price/shr . lmplShortlmpact: Trade Size:cap d/shr ($) (basis points) ($thou;

Giant cap ($ 25B+)Large cap ($5B - $25B)Midcap ($18 - $5B)Small cap ($ZSOtttt - $1B)Microcap $250M or less

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are often too large to be simply presented to the market,and it is difficult to search for liquidity without influencingthe price against your interests. When measured fromthe starting-gate price, the search costs easily dwarf theimpact and commission costs, as the table shows. Theyalso show the expected relationship: smaller cap stocksare more exoensive to trade.

Note that searcl^ costs are nuch higher for the Microcapstocks. The trading rn these stocks is describeo as byappointment." The term indicates that the brokers andspecialists find the other sioe when no interest exists onthe flnor A e-n.trv n.o.ess or searehino for the other' J Yside leads io h gn searci cosrs, Orce both buyer and.- - J'e-araf geo quarr ry a'0 srze.aooarent rncact s smai .

Fira v \1 r^roran -rades Ieno to be a much aroer noiron' , ," J'of the Ca '. vo rme. leadirg to a raL-,tology where thetrade s -easu'ed aoa nst itself. lf an nstitution were theonly bu5,er for the Oay tne VWAP costs show as zero, nomatter ,',^at rtre orice act o.r o't"e stoc< drring the dayAdd inn I rvqvr u Icomnnntr^-c a.q t-tr tn,n\!.r- r:h e nr tntgl 6631-

VWAP has its uses, but analyzing trade cost data isnotoriously tricky. When the conclusions don't match theintuition. one needs to be extra careful.

Pennying.' Does this DataSu pport the Accusation?

Now we turn to the assertion that the alleged extra costfor large cap trades comes from pennyinE by thespecialists. The estimates we have seen for the cost ofpennying are in the $150 million dollar range. The NYSEFact Book for 2002 quotes a dollar volume of $10.278trillion We double that figure to account for the fact thatf r.^,^ ^ ^ h,,,/^r ^^r ^ ^^r'^- t^- ^,,^-,, Shafe SOld.IIEIU 5 d UUYtrI d U d JUIIUI IUI UVEIYDividing $'150 million by this number comes to 0.0007basis points or two hundredths of a cent on an averageQ?6 chrro Thiq nrn^llnts tc :a! ta\ltr 2o/" Cf the \1\AAPcost and is not large enough to account for thedifference in cost, Grven the current high sensitivityconcerning specialist behav or, the offhand attribution topenryrng st'rkes us as careless and inflammatory.

In summary, the key to successful trading is tomanage the speed of execution Trade too fastand your demands for liquidity will allow othersto profit from your urgency. Trade too slowand the information edge you are trying tocapture may be discovered by othets, wiping out youradvantage. Thus traders need to weigh the impact costsof urgently executed orders against the search costs of-ore passive trading techniques. VWAP, properly

expressed in economic terms. gauges only the impactcosts. T ming is de-emphasized. A trader judged solelyagainsi a VWAP standard could avoid impact andtransfer the costs into the search costcategory. thus fooling his evaluator andpossibly himself.As Mark Twain said, there are three kinds^{ li^^. r;^^ l^-^^.J li^- anal a+a+ia+inou llub, ll9>, udllllluu llu>J dllu DLdlrJUUs.More charitably, as was said in the movteState And Main, "lt s not a lie, it's a gift forfiction."

2 Readers familiar with the Plexus Group "iceberg" of costs will noticethat we exclude opportunity cost in this article,

The relationships are as we expect: small cap stocks aremore costly to trade when measured in economic termsas percent of principal. In cents per share, costs peak inthe Midcap range, but this is an artifact of the share pricefalling faster than the costs are rising for sequentiallysmaller capitalization catagories. The VWAP - repeatedfrom the first table - ignores the hidden search costs andunderstates the real costs of trading. lt also reverses thecost to capitalization relationship.

Search Costs NYSE Search Costcap (bp) QlshrGiant cap ($ ZSa+;Large cap ($58 - S25B)Midcap (S1B - S5B)Sma lcao rS250M - SlB)Microcap 5250\l or less

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Total lmplementationCosts I mplementation ShoftfallTotal Volume WeightedAveraqe PricevoP (bp) f/shr //chr

Giant cap (S 25B+;Large cap rS5B - 525B;Midcap (S1B - 55B)Small cap (S250M - S1B;Microcap 5250M or less

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