8/14/2019 Research: How Are PAEG/Ls Formed

1/4

9rorrltuilding Betler Perf ormernceCOMMENTARY 77 JULY 2OO3

RESEA RCH: HOW ARE PAEG/L@S FORMED?Market discipline and regulatory pressure are forcing traders to evaluate the quality of theirtrading. This can be done by peer group comparisons or against a cost benchmark,preferably both. As the benchmark becomes more relevant to trade evaluations, traderswant to know what's behind the PAEG/L concept applied by Plexus since 1994. ThisCommentary discuss the benchmarking process in detail.

Why Did Plexus CreateThe PAEG/L Concept?

PAEG/L - Plexus Average Execution Gain/Loss -is a benchmark for evaluating the quality ofexecution of a trade. The Alpha Capture@implementation shortfall approach answers theouestion: What did it cost to execute this trade?The PAEG/I- puts this cost measuring in contextby answering the question "What should it cost toexecute this trade?""What should it cost?" refers to the typicalexperience of professional investment managers,traders, and brokers executing simtlar trades insi milar circumstances.The PA.trGi! r'neasrrre of eynacted coqt i-e d45ir.rarlfrom a statistical regression applied to recenttrade data. Plexus' unique database contains avery large sample of manager-to-trader-to-brokerlinked trade data and provides the ability to createintelligent estimates of costs through time.Why fs lhr's Important?

A good benchmark signals whether actualtransaction costs reflect good or poorperformance by managers, traders, and brokers.The benefits of better benchmarks include:1. Trading and brokerage skills are more

accu rately attributed ;2. Managers and traders develop a better senseof when and why trading costs rise; and3. Valuable insights lead to action items thatdirectly enhance future pedormance.

Without a good benchmark, organizations oftencannot make the critical first leap frommeasurement to evaluation that leads toimprovement.Sfafisfrcally Speaking, What Is theGoal of PAEG/L Research?

The objective of PAEG/L research is to explain thevariation in trade cost. This requires:1. A rich database of observations, consisting ofthe experienced costs (the dependent variable)and a variety of potential causative factors;2. A high-power regression package, capable of

running very large problems;3. A test-bed facility to determine not only howwell we can explain the variation within thesample (explanatory power) and moreimportantly, the ability to explain costs in out-of-sample, i ntothe-futu re appl ications (forecasti n gpower);4. A deep understanding of the economics oftrading and the vagaries of trading data.

8/14/2019 Research: How Are PAEG/Ls Formed

2/4

How Do You SelectExplanatory Factors?An appropriate benchmark should take intoaccount trade- and stock-specific factors. Forexample, it should reflect the fact that moredifficult trades such as large trades usually costmore than small trades. A regression-basedapproach, such as PAEG/L, permits us to tryvarious combinations of variables to see whatworks best as a forecaster.Every trade is different and traders assess manyfactors as they work trades. Defining anexhaustive list of variables and conditions thatcapture ihe fuii essence of trading is impossible.The trick is to identify a set of factors thataccount for as much of the variability in tradecost as possible. Finding these factors is a trial-and-error process. The modeling process isquite similar in scope and in accuracy to what aresearch director would go through whiledeveloping a stock valuation model.Over the past fifteen years, we have identifiedand tested dozens of factors in combination,including various measures of liquidity, volatility,trend, market, size, and nature of the tradingdesk (size, style, etc.) We often find, sometimesmuch to our surprise, that important-soundingfactors do not add forecasting power. Thishappens when one of the existing factors is astrong surrogate for another and, so to speak,steals its thunder. For example, tagging tradesaccording to manager style (e.9. growth, value)doesn't help because the trade size, companycapitalization and short-term price momentumalready capture the differences betweenmanager styles.How Are The Equations Produced?

PAEG/Ls are derived quarterly through a multi.step process:1. Measure total transaction cost from time-stamped manager order through completion;2. Form a rolling six month client data universefor trades world-wide. Equations are updated

quarterly to reflect evolving market structureand conditions;3. Art as well as science is reouired. Theregression equations are carefully screenedfor outlier observation effects that can easilydistort the equations. An example: a verylarge trade that fortuitously found the otherside for a cross al near-zero cost. lt would beunfair to expect a trader to duplicate thosecircumstances, so these irreproducibleobservations are d iscarded ;4. A parallel procedure is used to calculateBroker PAEG/Ls, which benchmark costsfrom broker release through execution basedon the most recent quarter's data.What Are The StrengthsOf The Database?

Probably the greatest strength is the diversity ofsample trades. The sample runs the gamut ofinstitutional trading from the simplest to the mostcomolex. lt includes trades from hundreds ofmanagers, traders, and brokers, all striving toproduce "best execution" and maximalperformance. lt is an unbiased, peer-based total-cost comparative standard.The second strength is the number ofobservations: over a million orders go into thecomputation of U.S. PAEG/Ls each quarter, andover 300,000 orders are used in the computationof non-U.S. equations. Each observation contains+lr^ .l^+^ +^ m^^^!rra aaa*a f.^* ^^:^+ -r .- -rr-ti-tl l(' (lcll,cl ((J I llEdDUlY tJtJ>l,D ll t/r | | PUil r! \Jr Pvr !rvllvmanager inception through all partial completions.Finally, we go to extraordinary efforts to scrub thedata to avoid the GIGO principle. We estimatethat we spend 2-4 man-years per quartervalidating the data submitted to us.

8/14/2019 Research: How Are PAEG/Ls Formed

3/4

Factor Interpretation Co-efficient StandardError T-testIntercept Absent any other factor effects, transacting is expected tolead to costs. -62.39 2.54 -24.5MomSize Market buy/sell balance effect, measured as the product ofthe size of the trade and the two dav price momentum. -4.23 0.023 182.0PercVol Liquidity demand, measured by the percentage of dailyvolume this trade reDresents. -0.53 0.0'18 -29.4

Size Size of the trade. in shares. 0040622 0.0000030 -20.6LogCap Log of the Capitalization of the company 8.29 0.61 13.6

SizeDummy A small-trade dummy factor equal to 1 if the trade is under10.000 shares 17.i3 0.99 17.4

What Does a Typical PAEG/L Equation Look Like?

The PAEG/L equation is estimated separately for!.1' qrr rrc call nrr.{nr^ ih li.:+4/.1 qtanlzc onr{ hr rrr trc eallorders in NASDAQ stocks. The equation aboveis the Buy/listed equation applied to the fourthquarter of 2004. A parallel set of equationsevaluates broker executions. In addition, wecalculate separate PAEG/L equations eachquarter for Canada. Latin America, Europe (ex-UK), UK, Emerging Europe, Japan, Asia (ex-Japan), and Emerging Asia,P/ease lnterpretThe Factors For Me. The Intercept is negative: in the absence of any

other factors. the expectation is that transactingwill lead to costs.. MomSize captures the movement of the stockand provides a measure of the degree to whichthe trade is liquidity demanding or supplying.Rising orices during a buy execution is anadverse situation, so the coefficient should benegative.Percent Volume is a measure of relative tradesize. We exoect that it will be more difficult tofind the other side of the trade for high levels ofPercVol, so its coefficient should be negative.Large orders are more difficult to transact andshould imply higher costs, so the Sizecoefficient is also expected to be negative.Log Cap is a proxy for stock liquidity, so it isexpected that it should have a positivecoefficient.Trades less than 10,000 shares are easier toexecute, so we would also expect a positivecoefficient for the Small Trade Dummv factor.

The T-Test column shows that all factors aresignificent at the 99%+ !eve!. l-lcv;ever, theexplanatory power is dominated by the MomSizefactor, which reflects the compounded effect oftrading Iarge orders into strongly favorable oradverse market conditions. This is the situation inwhich trades are most likelv to be costlv.Is the Equation StatisticallySignificant?The table below compares the in-sampleexplanatory power of the equations developed onsecond and third ouarter 2002 data to thepredictive power as applied in the fourth quarter,2002.

Remember that the equation is tuned formaximum forecasting power (the secondcolumn.) We can easily come up with better R-squareds for the in-sample model, but the powerderives from over-fitting and is spurious. For thefour equations above, the deterioration as wemove out of sample is about 25%.

PAEG/L equation In-SampleExplanatory PowerNext QuarterForecasting Power

ru/v "09'i4Listed Stocks - Sells 1 130 .0848NASDAQ Stocks -

Buys.1202 091 3

NASDAQ Stocks -Sells .1236 0778

8/14/2019 Research: How Are PAEG/Ls Formed

4/4

Can We Trust PAEG/L?What's the Quality of the Estimate?Absolutely YES, but it is important to understandwhat the PAEG/L is telling you. lVarkets, in theclassic understatement. fluctuate. which meansthe costs we are trying to explain vary stronglyfrom day to day depending on market conditions.The PAEG/L is subject to the same rules as anystatistical analysis. Therefore, the statistic carriesmore weight when there are more trades toreference. We always highlight and recommendto clients that they should be skeptical about anystatistic.Can I Have Accessto the PAEG/L equations?

Yes. Ask your consultant to discuss them withyou. Our research is open to clients and weencourage independent testing and review of ourequations.How Do I Use PAEG/Ls in a PredictiveEnvironment Such as TransPort@?The conundrum of prediction is that today wedon't know tomorrow's market environment" lf themarket rises, sells will be cheap and buys will bemore expensive; vice versa if the market falls.Our method for dealing with that uncertainty is tobuild a Monte Carlo distribution of possible costsby computing the benchmark cost for each of thelast 100 days. Buys will be more expensive onrising days and cheaper on falling days. Thedistribution shows managers and traders therange of possible outcomes in tomorrow'smarkets.Of course, when we know the market conditionqafter the fact, we can make the appropriateadjustment and hone in the estimate.

What's the future of PAEGIL?Research is a continuing challenge and wealways welcome new ideas and newtechnologies. We've hired the best academicianswe can find to come up with better forecastingpower. What we use now is the best result todate. lt is not, and never will be, the final answer.Where Can I Gofor More Information?Check out the Co m me nta ries onwww"plexusgroup,com particularly the one entitled"A Look Under the Hood of U.S. PAEG/Ls."

Plexus NeursPlexus Group's Ninth conference will be held September 21-24, 2003 at Silverado Country Club & Resod located inNapa Valley, California. Please look for the program and allreseruation forms on our website at: www.plexusgroup.com

Plexus canferences gather together managers, traders,brokers, exchanges and regulators in a format of openinterchange af ideas on markets, trading and investmentperformance. This year's conference will feature an updatedformat, enhancing the take-away value for the pafticipants.

Re/ease 2.0 of our lceBreaker'drill-down'tool, and a newon-line application for reviewing daily trading activity will beavailable mid-August. More detailed descriptions andinstructions will be communicated very soon, or contact yourconsultant to qet the latest infarmation.

Reprint any portion with credit given to:Dlexrrsgrorrpexrr11150 W. Olympic Blvd., #9AA Los Angeles, CA90064PH: 31 0.312.5505 FAX: 31 0.31 2.5506www.plexusgroup.com

Plexus Group is a wholly owned subsidiary of JPMorganlnvestor Services Company, a division of JPMorgan Chase.@ 2Affi Pbxus Group, lnc.