breakdown of standard microstructre techniques, jacobsen, 2011

7/29/2019 Breakdown of Standard Microstructre Techniques, Jacobsen, 2011

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The Breakdown of Standard Microstructure Techniques:

And What to Do About It*

Craig W. Holden**

Indiana University

Stacey JacobsenSouthern Methodist University

August 2011

Abstract

U.S. equity markets have explosively increased their trade and quote frequency and the decline of thedominance of the NYSE has increased the importance of National Best Bid and Offer (NBBO) quotes.We address three NBBO issues: (1) millisecond versus second timestamps, (2) withdrawn quotes, and (3)cancelled quotes. We find that each of these three issues is a significant and independent source ofdistortion in standard measures of market quality. The distortions are so massive that standardmicrostructure techniques essentially fail. We test fourteen different methods for matching trades toquotes based on different combinations of three clean-up techniques, two alternative quote sources, andthree quote timing techniques. We conclude that the first best solution is to use the NBBO file in the Daily Trade And Quote (DTAQ) database, because this is the only way to avoid major distortions onmost performance criteria. If a researcher is financially constrained to using only theMonthly Trade AndQuote (MTAQ) database, then the second best solution is to use two clean-up techniques (WithdrawnQuotes and exclude the remaining NBBO Crossed and Locked observations) and use Interpolated Timeas the quote timing technique. Each of these three techniques independently contributes to reducingdistortion on most performance criteria and the combination of all three goes the furthest distancepossible in reducing distortion. Looking to the future, we anticipate the ultimate demise of the NBBO andpropose to replace it with a Relative Best Bid and Offer (RBBO) that is different for each market center.

JEL classification: C15, G12, G20.

Keywords: Milliseconds, high-frequency trading, NBBO, DTAQ.

* We thank Hung-Neng Lai, Jim Upson, andseminar participants at Indiana University. We are solelyresponsible for any errors.

** Corresponding author. Address: Kelley School of Business, Indiana University, 1309 E. Tenth St.,Bloomington, IN 47405-1701. Tel.: 812-855-3383; fax: 812-855-5855; email address: [email protected]


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The Breakdown of Standard Microstructure Techniques:

And What to Do About It

Abstract

U.S. equity markets have explosively increased their trade and quote frequency and the decline of the

dominance of the NYSE has increased the importance of National Best Bid and Offer (NBBO) quotes.

We address three NBBO issues: (1) millisecond versus second timestamps, (2) withdrawn quotes, and (3)

cancelled quotes. We find that each of these three issues is a significant and independent source of

distortion in standard measures of market quality. The distortions are so massive that standard

microstructure techniques essentially fail. We test fourteen different methods for matching trades to

quotes based on different combinations of three clean-up techniques, two alternative quote sources, and

three quote timing techniques. We conclude that the first best solution is to use the NBBO file in the

Daily Trade And Quote (DTAQ) database, because this is the only way to avoid major distortions on

most performance criteria. If a researcher is financially constrained to using only theMonthly Trade And

Quote (MTAQ) database, then the second best solution is to use two clean-up techniques (Withdrawn

Quotes and exclude the remaining NBBO Crossed and Locked) and use Interpolated Time as the quote

timing technique. Each of these three techniques independently contributes to reducing distortion on most

performance criteria and the combination of all three goes the furthest distance possible in reducing

distortion. Looking to the future, we anticipate the ultimate demise of the NBBO and propose to replace it

with a Relative Best Bid and Offer (RBBO) that is different for each market center.


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1. Introduction

Twenty-first century equity markets have gone electronic (Jain 2005), algorithmic (Hendershott,

Jones, and Menkveld 2011), become much faster (Hendershott and Moulton 2011; Angel, Harris, and

Spatt 2011) (AHS), and become more competitive (AHS). On the speed dimension, AHS document a

radical increase in the frequency of bid-ask quote updates. They report a nearly 20-fold increase in the

frequency of quote updates for stocks in the S&P 500 from 0.17 per second in May 2003 to 3.3 per

second in October 2009. Similarly, Chordia, Roll, and Subrahmanyam (2010) report a 33-fold increase in

the value-weighted frequency of trades in NYSE stocks from 0.13 per second January 2003 to 4.3 per

second in June 2008. On the competition dimension, AHS document that the NYSEs market share in

NYSE-listed stocks has dropped from 80% in February 2005 to 25% in February 2009. The shift from a

dominant player to many relatively co-equal players means that researcher reliance on NYSE quotes only

(e.g., Chordia, Roll, and Subrahmanyam 2000, 2001, 2002) is no long sufficient that the use of National

Best Bid and Offer (NBBO)1 quotes has now become a necessity.

This paper explores how this explosive increase in trade and quote frequency and two other

technical data problems impact the computation of the NBBO. Specifically, we address three issues: (1)

millisecond versus second timestamps of trades and quotes, (2) withdrawn quotes where an exchange or

market maker momentarily quotes nothing, and (3) cancelled quotes where a limit sell (buy) setting the

current ask (bid) is cancelled, but the exchange or market makers quote is not updated. We find that each

of these three issues is a significant and independent source of distortion in standard measures of market

quality compared to the corresponding benchmark.

Overall, we find the following distortions compared to the corresponding benchmark: (1) crossed

and locked markets happen nine times more often, (2) outside the BBO trades happen seven times more

often, (3) the dollar quoted spread is four times smaller, (4) the dollar effective spread is more than two

times larger, (5) the effective spread is greater than the quoted spread four times more often, (6) the dollar

realized spread is two times larger, (7) the dollar price impact is two times larger, (8) the majority of order

1 The national best bid (offer) is the highest bid (lowest offer) across all U.S. exchanges and market makers.


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routing decisions are different, and (9) performance is biased in favor of some exchanges and against

others. These distortions are so massive that standard microstructure techniques essentially fail.

Next we examine what to do about it. One possibility is purchasing a different database. The most

popular database for academic market microstructure research in U.S. equities is the New York Stock

Exchange (NYSE)s Monthly Trade And Quote (MTAQ) database. It provides intraday trade and quote

data time-stamped to the second. For a three to four-times larger price,2 the NYSE also sells the Daily

Trade And Quote (DTAQ) database. DTAQ is identical to MTAQ, except for four things: (1) it adds a file

containing the official NBBO quotes from the Securities Industries Processors (SIPs),3 (2) all trades,

quotes, and NBBO quotes are time-stamped to the millisecond(i.e., 1/1,000th of a second), (3) there are

additional quote condition fields, and (4) each days data can be downloaded the next day as opposed to a

monthly cycle for MTAQ. We use the official SIPs NBBO quotes from DTAQ as our benchmark. Our

empirical results show that this benchmark is credible as it yields a much lower frequency of crossed

markets and outside the NBBO trades than any of the methods we test.

We test fourteen different methods for matching trades to quotes based on different combinations

of two alternative quote sources (DTAQ Quotes and MTAQ Quotes), three clean-up techniques, and three

quote timing techniques. One clean-up technique, the Withdrawn Quotes Technique, treats zeros or

missing values in individual quotes as withdrawn quotes, meaning that momentarily there is no

outstanding quote for that specific exchange or market maker. A second clean-up technique, the NBBO

Crossed and Locked Technique, is to exclude observations when the NBBO is crossed or locked (e.g.,

when National Best Bid from BATS National Best Offer from Direct Edge X), not just when a given

exchange or market maker is crossed or locked (e.g., when NYSE Bid NYSE Offer). A third clean-up

2 Specifically, there is no academic price for DTAQ. So academic researchers who want to use DTAQ must pay itscommercial price, which is three to four-times the academic price of MTAQ. For pricing details, seewww.nyxdata.com/Data-Products/Daily-TAQ or the Wharton Research Data Services (WRDS) website.3 There are two SIPs. The Consolidated Tape Association (CTA) covers all Tape A (NYSE-listed) and Tape B(AMEX and regional) securities and the Unlisted Trading Privileges (UTP) Committee covers all Tape C(NASDAQ) securities.


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technique is the Duration Limit Control (DLC) Technique as proposed by Jain, Upson, and Wood (2008),

which drops all quotes older than a one minute duration when computing the NBBO.

One quote timing technique is Prior Second as recommended by Henker and Wang (2006), which

matches a trade to the NBBO quotes that are in-force in the prior second. A second quote timing

technique is Same Second as recommended by Bessembinder (2003) and Peterson and Sirri (2003), which

matches a trade to the NBBO quotes that are in-force during the same second. We introduce a third quote

timing technique that we call Interpolated Time. It uses the ordering of trades and quotes within a second

to make an educated guess about what millisecond the events occurred and then to match each trade at the

inferred millisecond to the NBBO quotes that are inferred to have been in-force in the prior millisecond.

Our sample is 99 randomly selected firms4 from April 1st, 2008 to June 30th, 2008. This period is

prior to the severe phase of the financial crisis which started in mid-September 2008. 5 We obtain 34

million trades and 351 million quotes.

We conclude that the first best solution is to use DTAQ NBBO, because this is the only way to

avoid major distortions on most performance criteria. If a researcher is financially constrained to using

only MTAQ data, then the second best solution is use both the Withdrawn Quotes and NBBO Crossed

and Locked Techniques (e.g., treat zeros or missing values in quotes as withdrawn quotes and exclude the

remaining NBBO crossed and locked observations) and use Interpolated Time as the quote timing

technique. Each of these three techniques independently contributes to reducing distortion on most


distortion.

A recent paper by Jain, Upson, and Wood (2008) is closest to our paper. They address the

problem of cancelled quotes and propose DLC to mitigate this issue.6

They test DLC based on 1, 5, 10,

4 A 100th randomly selected firm was lost because of an error in the spelling of a ticker symbol in the DTAQdatabase. Specifically, Benihana Inc., symbol BNHNA, is incorrectly listed as BNHN A in DTAQ for the datesof our analysis.5 During our sample period, the Volatility Index (VIX) ranged from 19 to 25, which is the same range that it hadbeen in for the prior twelve months. During the severe phase of the financial crisis from mid-September 2008 toDecember 2008, the VIX ranged from 55 to 80.


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and 20 minute durations. They find a significant benefit of using DLC and that a 1 minute duration

performs best. Compared to Jain, Upson, and Wood (2008), we analyze three clean-up techniques, two

quote data sources, and three quote timing techniques. We find that DLC does betterthan no clean-up

technique and adding DLC to a single other clean-up technique does betterthan that single other clean-up

technique alone. However, adding DLC to a single other clean-up technique does worse than two other

clean-up techniques without DLC and adding DLC to two other clean-up techniques does worse than two

other clean-up techniques without DLC.Thus, we conclude that both other clean-up techniques should be

used and DLC should not be.

Looking to the future, we consider what happens when the trading process accelerates into

microseconds (10-6 seconds) in the 2010s and into nanoseconds (10-9 seconds) in the 2020s. We find that

the speed of light barrier causes a breakdown of the Newtonian concept of a single, absolute NBBO for

all economic agents in all locations. As a replacement, we propose an Einsteinian concept of a Relative

Best Bid and Offer (RBBO) that is different for each market center.

The paper is organized as follows. Section 2 describes the institutional setting. Section 3 explains

the research design. Section 4 describes our performance criteria. Section 5 describes the data. Section 6

presents our results. Section 7 examines the economic significance of the results. Section 8 discusses the

ultimate breakdown of the NBBO and our proposed replacement concept of RBBOs. Section 9 concludes.

2. The Institutional Setting

Figure 1 illustrates the information flows in Tape A (NYSE-listed) and Tape B (AMEX and

regional) securities. On the left-side we see that there are N market centers, where a market center is

defined as an exchange, market maker, or broker-dealer. For convenience, we designate theth

N market

center as the NYSE. Each market center has a matching engine that arranges trades by matching and/or

recording matches of liquidity-demanding orders with liquidity-supplying orders and/or dealers and that

updates quotes as appropriate. Trades and quotes from each market center are sent to the Consolidate

6 They also proposed a second method, Forward Activity Control on Entry (FACE), where future quote activity isexamined to identify likely cancelled quotes and remove them. Our paper does not test the FACE method.


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Tape Association (CTA), which is the SIP for Tapes A and B. Operating out of a data center in Brooklyn,

the CTAs Consolidated Quotation System (CQS) integrates the quotes from all market centers and

computes the NBBO. Operating out of a data center in lower Manhattan, the CTAs Consolidated Tape

System (CTS) integrates the trades from all market centers. At the moment that the corresponding

information is processed by each of the two systems an official timestamp is added, which is recorded to

the millisecond. From there, the integrated quotes, NBBO, and integrated trades are broadcast by IP

Multicast back to all of the Market Centers, including the NYSE. Finally, the NYSE warehouses the CQS

and CTS data feeds into the DTAQ and MTAQ databases.

The process works in an analogous manner for Tape C (NASDAQ) securities. The substitutions

are: (1) UTP Committee replaces CTA, (2) UTP Quote Data Feed replaces Consolidate Quote System,

and (3) UTP Trade Data Feed replaces the Consolidated Trade System.

3. Research Design

We analyze fourteen methods for matching trades to quotes and compare these methods to two

benchmarks. We define distortion as the absolute value of the difference in outcomes produced by one of

these methods versus the corresponding benchmark. These methods use one of two quote data sources:

the DTAQ Quote file and the MTAQ Quote file. The DTAQ (MTAQ) Quote file is used to calculate the

NBBO across all exchanges and all market makers for any given millisecond (second). When using the

DTAQ Quote file, a trade at millisecond mmm is matched to the calculated NBBO quotes that are in-force

one millisecond earlier at mm(m-1). When using the MTAQ Quote file, a trade at second ss is matched to

the calculated NBBO quotes that are in-force one second earlier at s(s-1). Our benchmark #1 uses the

DTAQ NBBO file, which is the official consolidated record from the SIPs, directly without modification.

We match a trade at millisecond mmm to the DTAQ NBBO quotes that are in-force one millisecond

earlier at mm(m-1). If there are multiple quote updates from a given exchange or market maker within a

given millisecond (second), then the last quote update within that millisecond (second) is what is

considered to be in-force from that exchange or market maker.


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We also test three clean-up techniques. One clean-up technique, the Withdrawn Quotes

Technique, treats zeros and missing values in quotes as withdrawn quotes, rather than the common

practice of treating them as errors. Relatively frequently, the MTAQ Quotes file shows a zero or a

missing value as the bid price, ask price, bid depth, or ask depth. A common interpretation is that this is

an error in the database and this observation is thrown away. In this case, the previously established bid-

ask quote by that exchange or market maker is still considered to be valid. However, the TAQ 3 Users

Guide (2008), page 26 suggests that a zero as the bid price, ask price, bid depth, or ask depth represents

an exchange or market maker withdrawing their previously established quote. Under this interpretation,

momentarily, there is no quote for that exchange or market maker. The absence of a quote for that

exchange or market maker lasts until a new quote is made by that exchange or market maker. Correct

recognition of withdrawn quotes avoids the use of old, stale quotes that might easily generate apparent

crossed or locked markets.

A second clean-up technique, the NBBO Crossed and Locked Technique, excludes observations

where the calculated NBBO is crossed or locked. To be clear, under all methods we throw away

observations where the bid of one exchange or market maker is greater than or equal to the ask of the

same exchange or market maker (e.g., when NYSE Bid NYSE Ask or, for market maker TRIM, when

TRIM Bid TRIM Ask)7. But this clean-up technique goes a step further and throws away observations

when the national best bid from any exchange or market maker is greater than or equal to the national best

offer from any exchange or market maker (e.g., when National Best Bid from BATS National Best

Offer from Direct Edge X or, for market maker FLOW, when National Best Bid from FLOW National

Best Offer from NYSE ARCA). The rational for excluding NBBO locked and crossed markets is that this

is a temporary state which does not make economic sense and would otherwise contaminate the

computation of cost of trading measures. Our benchmark #2 uses quotes from the DTAQ NBBO file and

implements the NBBO Crossed and Locked Technique on it.

7 However, when both the Withdrawn Quotes and NBBO Crossed and Locked Techniques are used, then if anobservation is crossed because the bid > 0 and the ask = 0, we assume the bid is valid and the ask has beenwithdrawn.


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A third clean-up technique, the DLC Technique, is DLC with a one minute duration. This

technique drops all quotes older than a one minute duration when computing the NBBO. The idea is that

recent quotes are very likely to still be in-force. By contrast, older quotes run an increasing risk of

cancellation and are more likely to be further away from current values. This technique admittedly throws

away some older quotes that are still valid, but it limits the likelihood and potential size of cancelled

quote contamination.

When using the MTAQ Quote file, we also test three quote timing techniques: (1) Prior Second,

(2) Same Second, and (3) Interpolated Time. Prior Second matches a trade at second ss to the calculated

NBBO quotes that are in-force in thepriorsecond s(s-1). Same Second matches a trade at second ss to the

calculated NBBO quotes that are in-force during the same second ss.

We introduce a new quote timing method that we call Interpolated Time. Suppose that the

MTAQ dataset lists I trades and J quotes as occurring in second ss. We do not know what millisecond

those trades or quotes occurred at, but we do know the order of the trades and the order of the quotes in

MTAQ. Interpolated time takes advantage of that ordering to make an educated guess about what

millisecond each event happened at through a process of simple interpolation. Specifically, we assume a

priory that trades and quotes are each uniformly distributed over the second. Based on this assumption,

the ith trade in the second ss is assigned an interpolated trade time of

2 11, 2, , .

2

iss i I

I

(1)

This formula assigns a time gap of 1I of a second between each trade, a time gap of 1

2I of a second

from the beginning of the second to the first trade, and a time gap of 1

2I of a second from the last trade

to the end of the second. Similarly, thejth quote in the second ss is assigned an interpolated quote time of

2 11, 2, , .

2

jss j J

J

(2)


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Similarly, this formula assigns a time gap of 1J of a second between each quote, a time gap of 1

2J of a

second from the beginning of the second to the first quote, and a time gap of 1

2J of a second from the

last quote to the end of the second. The jth quote is presumed to have occurred at the interpolated quote

time and the usual NBBO computation across all exchanges and all market makers is updated at that time.

The ith trade is presumed to have occurred at the interpolated trade time and is matched to the NBBO

quotes that were in-force one millisecond earlier.

Figure 2 provides an example of Interpolated Time when there are 4I trades and 5J

quotes in second ss. Applying equation (1), the four trades are assigned interpolated trade times of

1

,8ss

3

,8ss

5

, and8ss

7

.8ss Applying equation (2), the five quotes are assigned interpolated

quote times of1

,10

ss

3,

10ss

5,

10ss

7, and

10ss

9.

10ss Consider the third trade. It is

presumed to have occurred at the interpolated trade time of5

.6258

ss ss and it is matched to the

NBBO presumed to be in-force one millisecond earlier at .624.ss The time .624ss is after the third

quotes interpolated quote time of 5 .50010

ss ss , but before the fourth quotes interpolated quote time

of7

.700.10

ss ss Thus, the third trade is matched to the NBBO presumed to be in-force at .624ss as

computed from the third quote and all earlier quotes, but excluding the fourth and fifth quote.

Table 1 summarizes the fourteen different methods that we analyze.


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Table 1 Summary of Methods

MethodQuote

Data SourceWithdrawn

QuotesNBBO Crossed

and LockedQuote Timing

TechniquesDuration Limited

Control (DLC)1 DTAQ Quotes No No -- No2 MTAQ Quotes No No Prior Second No3 DTAQ Quotes Yes No -- No4 MTAQ Quotes Yes No Prior Second No5 DTAQ Quotes No Yes -- No6 MTAQ Quotes No Yes Prior Second No7 DTAQ Quotes Yes Yes -- No8 MTAQ Quotes Yes Yes Prior Second No9 MTAQ Quotes Yes Yes Same Second No10 MTAQ Quotes Yes Yes Interpolated Time No11 MTAQ Quotes No No Prior Second Yes12 MTAQ Quotes Yes No Prior Second Yes13 MTAQ Quotes No Yes Prior Second Yes14 MTAQ Quotes Yes Yes Prior Second Yes

4. Performance Criteria

The performance criteria that we study are standard measures of market quality in market

microstructure. Specifically, we study measures of trade location, quoted spread, effective spread,

realized spread, price impact, depth, and absolute order imbalance.

Our first performance criteria evaluate trade location, or the percentage of trades that are At,

Inside, and Outside the NBBO and that occur when a market is experiencing the economically

nonsensical conditions of being Crossed or Locked. The thk trade at price kP is consideredAt the NBBO

when k kP A or k kP B , where kA is the National Best Ask and kB is the National Best Bid assigned

to the thk trade by a particular method. A trade is consideredInside the NBBO when k k kA P B and

Outside the NBBO when k kP A or k kP B . The more that a particular method misaligns trades and

quotes, then the apparent percentage of trades Outside the NBBO will be elevated and so we will focus on

this metric, rather than At or Inside the NBBO. A market is Crossed, when the National Best Ask is

strictly less than the National Best Bidk k

A B and the market isLockedwhen the National Best Ask is

equal to the National Best Bidk k

A B . A Crossed market is a more severe condition than a Locked


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market, because the former presents an arbitrage opportunity, whereas the latter does not. Thus, we focus

on the frequency of a Crossed market.

Our second performance criteria evaluate the quoted and effective spread. For a given time

interval s , the dollar and percent quoted spread are defined as

s s sDollar Quoted Spread A B , (3)

s ss

s

A BPercent Quoted Spread

M

, (4)

where sA is the National Best Ask and sB is the National Best Bid assigned to time interval s by a

particular method and sM is the midpoint, which is the averageof sB and sA . Aggregating over thesample period, a stocks Dollar (Percent) Quoted Spread is the time-weighted average of Dollar

(Percent) Quoted Spreads computed over all time intervals. For a given stock, the dollar and percent

effective spread on the thk trade is defined as

2k k kDollar Effective Spread P M , (5)2

k kkk

P MPercent Effective Spread

M

, (6)

where kM is the midpoint of the NBBO quotes assigned to theth

k trade by a particular method.

Aggregating over the sample period, a stocks Dollar (Percent) Effective Spread is the dollar-volume-

weighted average ofDollar (Percent) Effective Spreadkcomputed over all trades.

Our third performance criteria consider the realized spread and price impact. The dollar realized

spread is the temporary component of the dollar effective spread. For a given stock, the dollar realized

spread on theth

k trade is defined as

52k k k k Dollar Realized Spread D P M , (7)whereDk is an indicator variable that equals +1 if the thk trade is a buy and -1 if the thk trade is a selland 5kM is the midpoint five-minutes after the midpoint kM . Aggregating over the sample period, a


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stocks Dollar Realized Spread is the dollar-volume-weighted average of the Dollar Realized Spreadk

computed over all trades. The dollar price impact is the permanent component of the dollar effective

spread. For a given stock, the dollar price impact on theth

k trade is defined as

52k k k k Dollar Price Impact D M M . (8)Aggregating over the sample period, the Dollar Price Impactis the dollar-volume-weighted average of

Dollar PriceImpactkcomputed over all trades.

There are three popular trade-typing conventions for determining whether a given trade is a

liquidity-demander buy or liquidity-demander sell, which in turn determines whetherk

D is +1 or -1.

Under the Lee and Ready (1991) (LR) convention, a trade is a buy whenk k

P M , a sell whenk k

P M ,

and the tick test is used whenk k

P M . The tick test specifies that a trade is a buy (sell) if the most

recent prior trade at a different price was at a lower (higher) price than .kP Under the Ellis, Michaely and

OHara 2000 (EMO) convention, a trade is a buy whenk k

P A , a sell when k kP B , and the tick test is

used otherwise. Under the Chakrabarty, Li, Nguyen, and Van Ness 2006 (CLNV) convention, a trade is a

buy when 0.3 0.7 ,k k k k P B A A , a sell when ,0.7 0.3k k k k P B B A , and the tick test is used

otherwise. So we consider three versions of dollar realized spread and three versions of dollar price

impact based on these three trade-typing conventions.

Our fourth performance criteria evaluate dollar and share bid and ask depth. The dollar (share)

ask depth is the dollar (share) amount available at the best ask quote from the exchange or market maker

with the largest size quoted at that price. In the benchmark DTAQ NBBO, depth is also the largest size

based on price priority and then size priority. The dollar (share) bid depth is computed analogously.

Our final performance criterion is absolute order imbalance. It is defined as

Buys SellsAbsolute Order Imbalance

Buys Sells

, (9)


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whereBuys and Sells are the number of buys and number of sells, respectively, in the sample period based

on a particular method. Easley, Engle, OHara, and Wu (2008) and Kaul, Lei, and Stoffman (2008) show

that absolute order imbalance is an alternative measure of the probability of informed trading, in the spirit

of PIN. Absolute Order Imbalance has two advantages over PIN. It can be computed over relatively short

periods of time and it does not have the convergence problems that are often encountered when

computing PIN.

Now that we have specified our performance criteria, we can be precise about what we mean by

the word distortion. It is defined as

m bDistortion V V . (10)

wherem

V is the value of a performance criterion produced by a method andb

V is the value of a

performance criterion produced by the corresponding benchmark.

5. Data

We use both the DTAQ and MTAQ datasets. Because of the high price of the DTAQ data, we

purchase a limited sample from April 1st, 2008 to June 30th, 2008. Since using the full dataset would

involve massive computations, we select a random sample of traded stocks. Following the methodology

of Hasbrouck (2009), a selected stock must meet five criteria to be eligible: (1) it must be a common

stock; (2) it must be present on the TAQ master file for the first and last date of the sample period; (3) it

must have a primary listing on the New York Stock Exchange, American Stock Exchange, or National

Association of Securities Dealers Automated Quotations (NASDAQ); (4) it cannot change primary

exchange, ticker symbol or its CUSIP code during the sample period; and (5) it must be listed in the

Center for Research in Security Prices (CRSP) database.

Starting with eligible firms, we divide them into 5 quintiles based on number of trades per day,

and then randomly select 20 firms from each quintile. Thus, we have a random sample of 99 traded

stocks, which results in 34 million trades and 351 million quotes over the sample period.


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We then apply the following screens to the trade and quote data. Only quotes/trades during

normal market hours (between 9:30AM and 4:00PM) are considered. For each exchange or market maker,

we delete cases where the bid of one exchange or market maker is greater than or equal to the ask of the

same exchange or market maker. If the quoted spread is greater than $5.00 and the bid (ask) price is less

(greater) than the previous midpoint - $2.50 (previous midpoint + $2.50) then the bid (ask) is not

considered. The quote condition must be normal, which excludes cases in which trading has been halted.8

We exclude bid (ask) quotes that have a bid (ask) prices or bid (ask) size that is equal to or less than zero

or are missing values.9 We calculate the NBBO across all exchanges and across all market makers for any

given millisecond (second).

6. Results

Table 2 reports trade locations, cost of trading measures, and depths so as to compare two quote

data sources: DTAQ Quotes file and MTAQ Quotes file, two clean-up techniques: (1) Withdrawn Quotes,

(2) NBBO Crossed and Locked, and three quote timing techniques: (1) Prior Second, (2) Same Second,

and (3) Interpolated Time.

Panel A reports the trade location. Column (1) presents Benchmark #1 using the DTAQ NBBO

file directly without modification (i.e., including observations when the NBBO is crossed and locked). In

this case, the frequency of Outside the NBBO is 3.7%. Columns (2)-(3) present the case when no clean-up

technique is used. We find a huge increase to 20.6% under DTAQ Quotes, an even larger increase to

26.5% under MTAQ Quotes, and both are statistically significantly different from benchmark #1 at the

1% level. Similarly, the frequency of Crossed NBBO goes from 0.5% under Benchmark #1, way up to

16.1% under DTAQ Quotes, further up to 18.4% under MTAQ Quotes, and both differences are

significant. On the one hand, this verifies the credibility of benchmark #1 as it has a much lower

8 For the DTAQ data, we exclude quotes having the following quote condition: A,B,H,O,R,W. For the MTAQ data,we exclude quotes having the following quote condition (mode): 4, 7, 9, 11, 13, 14, 15, 19, 20, 27, 28.9 We alter this screen in the Withdrawn Quotes Technique; see footnote 7.


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frequency of Outside the NBBO and Crossed NBBO than the other methods. On the other hand, there are

huge distortions under both DTAQ Quotes and MTAQ Quotes.10

Columns (4)-(5) show results for the Withdrawn Quotes Technique. This cuts in half the DTAQ

distortion (Outside is 11.3%; Crossed is 8.1%) and reduces the MTAQ distortion by one-third or more

(Outside is 17.6%; Crossed is 9.9%), but all differences are still significant.

Column (6) presents Benchmark #2 using the DTAQ NBBO file and the NBBO Crossed and

Locked Technique. In this case, the frequency of Outside the NBBO is 3.2%. Columns (7)-(8) show

results for the NBBO Crossed and Locked Technique. This greatly reduces the DTAQ distortion (Outside

is 8.0%) and cuts in half the MTAQ distortion (Outside is 13.6%), but the differences are still significant.

Of course, NBBO crossed and locked is zero percent in this case.

Columns (9)-(12) use both clean-up techniques: Withdrawn Quotes and excluding the remaining

NBBO Crossed and Locked observations. When both clean-up techniques are combined with the

millisecondtimestamp of DTAQ Quotes in column (9), the distortion is very small (Outside is 4.8%), but

is still significant. When both clean-up techniques are combined with the second timestamp of MTAQ

Quotes in column (10), the distortion is reduced (Outside is 10.5%), but is still statistically and

economically significant. The sizable difference between columns (9) and (10) shows that the issue of

millisecond vs. second timestamps is an important and independent cause of distortion, even net of

addressing withdrawn quotes and cancelled quotes. Columns (11) and (12) show that the choice of quote

timing techniques can reduce distortion further, even net of using both clean-up techniques (Outside is

7.5% under Prior Second and 5.6% under Interpolated Time). Of course, NBBO crossed and locked is

zero percent in this case.

An important advantage of using both techniques is that it throws away only about half as many

observations as the single technique. Specifically, using just the single NBBO Crossed and Locked

10 These results are robust under alternative quote timing techniques. In unreported results, there is still a hugedistortion under MTAQ Quotes with no clean-up techniques when combined with Same Second or InterpolatedTime. Specifically, under Same Second, Outside is 25.3% and Crossed is 20.7%. Under Interpolated Time, Outsideis 22.7% and Crossed is 21.1%.


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Technique of excluding all NBBO crossed and locked observations throws away 19.7% of DTAQ or

21.4% of MTAQ observations (see the sum of crossed and locked in columns 2 and 3). However, using

two clean-up techniques together only throws away the remaining NBBO crossed and locked

observations after withdrawn quotes have been accounted for. Thus, when both techniques are used

together only half as many observations are thrown away (specifically, 10.5% of DTAQ or 11.6% of

MTAQ see the sum of crossed and locked in columns 4 and 5).

Panel B reports quoted and effective spreads. Columns (1)-(3) show the dollar quoted spread

going from 7.59 under Benchmark #1, way down to 2.87 under DTAQ Quotes, further down to 2.01

under MTAQ Quotes, and both differences are significant.11 Intuitively, these large distortions are related

to the frequency of negative quoted spreads under crossed markets and zero quoted spreads under locked

markets. The dollar effective spread goes from 5.62 under Benchmark #1, up to 12.64 under DTAQ

Quotes, up to 12.86 under MTAQ Quotes, and both differences are significant. It is very troubling that

the dollar effective spread more than doubles in size under both DTAQ Quotes and MTAQ Quotes. These

huge distortions are very important results. The percentage of the time that the effective spread is greater

than the quoted spread goes from 8.0% under Benchmark #1, jumps to 27.0% under DTAQ Quotes,

increased further to 37.0% under MTAQ Quotes, and both differences are significant. Logically, these

huge upward distortions in the effective spread are generated in part by the large increases in frequency of

outside the NBBO trades. Again, these huge distortions are devastating.

Columns (4)-(5) show that the DTAQ distortion is cut in half (Dollar Quoted Spread is 5.13;

Dollar Effective Spread is 7.85) and the MTAQ distortion is cut by more than half (Dollar Quoted

Spread is 4.77; Dollar Effective Spread is 8.62). The Withdrawn Quotes Technique is an effective way

to remove half or more of this kind of distortion.

11 Throughout Tables 2 and 3, the percent quoted spread follows a qualitatively similar pattern to the dollar quotedspread and the percent effective spread follows a qualitatively similar pattern to the dollar effective spread. Thus, weonly discuss the dollar quoted and effective spread patterns, but we incorporate the percentage quoted and effectivespreads patterns by analogy.


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Columns (6)-(8) show that the dollar quoted spread stays relatively flat going from 7.65 under

Benchmark #2, to 7.80 under DTAQ Quotes, to 7.62 under MTAQ Quotes, and the differences are not

significant. This confirms the prior intuition that the distortion in dollar and percentage quoted spreads

was mainly due to the increased frequency of NBBO crossed and locked markets. Thus, throwing out

NBBO crossed and locked markets appears to fix quoted spreads, which do not depend on matching

trades and quotes.

However, effective spreads are a different story, because they do depend on matching trades and

quotes. Under the NBBO Crossed and Locked Technique, the dollar effective spread goes from 5.66

under Benchmark #2, up to 14.00 under DTAQ Quotes, to 13.62 under MTAQ Quotes, and the

differences are significant. Huge distortions remain. Further, the percentage of time that the effective

spread is greater than the quoted spread goes from 9.0% under Benchmark #2, jumps to 17.1% under

DTAQ Quotes, jumps again to 35.0% under MTAQ Quotes, and the differences are significant.

Columns (9)-(12) show the dollar quoted spread staying relatively flat going from 7.65 under

Benchmark #2, to 7.58 under DTAQ Quotes, to 7.57, 7.57, and 7.67 under MTAQ with the three

quote timing techniques. Thus, both techniques completely fix the quoted spread.

Again, effective spreads are a different story. The dollar effective spread goes from 5.66 under

Benchmark #2, to 5.88 under DTAQ Quotes, to 6.44, 5.78, and 5.87 under MTAQ with the three

quote timing techniques, and the differences are significant. This represents a large reduction in distortion

compared to using no clean-up technique, but the distortion is still too high. The percentage of time that

the effective spread is greater than the quoted spread goes from 9.0% under Benchmark #2, to 12.0%

under DTAQ Quotes, and to 30.0%, 14.6%, and 10.8% under MTAQ with the three quote timing

techniques, and the differences are significant. In summary, both techniques combined remove a large

proportion of the distortion of effective spreads, but a meaningful amount of distortion remains.

Panel C reports realized spread and price impact under three trade-typing conventions: (1) Lee

and Ready 1991 (LR), (2) Ellis, Michaely and OHara 2000 (EMO), and (3) Chakrabarty, Li, Nguyen,

and Van Ness 2006 (CLNV). Columns (1)-(3) show the dollar realized spread based on all three trade


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typing conventions, increases 30%-60% under DTAQ Quotes, 100%-200% under MTAQ Quotes, and all

differences are significant. These are huge distortions relative to the size of the dollar realized spread

itself. The dollar price impact based on all three trade typing conventions, increases 80%-160% under

DTAQ Quotes, 80%-140% under MTAQ Quotes, and all differences are significant. Again, these are

huge distortions relative to the size of the dollar price impact. The percent realized spread and percent

price impact comparisons yield slightly smaller percentage increases, but nonetheless show huge

distortions under both DTAQ Quotes and MTAQ Quotes.

Columns (4)-(5) show a reduction in distortion of the realized spread and price impact. Columns

(6)-(8) show a further reduction in distortion. Columns (9)-(12) show even more reduction in distortion

under DTAQ Quotes and under MTAQ with Prior Second, but an increase in distortion under MTAQ

with Interpolated Time and even more distortion under DTAQ with Same Second.12 Excluding the Same

Second and Interpolated Time cases, both techniques remove the majority of the distortion of realized

spread and price impact, but meaningful distortion remains.

Panel D reports depth measures. Columns (1)-(3) show the dollar ask depth in thousands going

from $13.9 under Benchmark #1, down slightly to $13.5 under DTAQ Quotes, and up slightly to $13.6

under MTAQ Quotes, where the DTAQ difference is significant, but the MTAQ difference is not. A

similar, very flat pattern holds in columns (4)-(5), (6)-(8), and (9)-(12). A similar, very flat pattern holds

for dollar bid depth, share ask depth, and share bid depth. Across all four depth measures in columns (2)-

(3), the average distortion as a percentage of benchmark depth is 3.6%. The comparable figure for

columns (9)-(12) is 1.3%. Overall, the depth distortions are relatively minimal.

Here is a summary of Table 2 regarding quote data source and clean-up techniques. When no

clean-up technique is used, both DTAQ Quotes and MTAQ Quotes show huge distortions in outside the

NBBO, crossed NBBO, dollar and percentage quoted spread, dollar and percentage effective spread,

percent of time dollar effective spread is greater than dollar quoted spread, dollar and percentage realized

12 The differences in Dollar Realized Spread and Price Impact across the three different quote timing techniques are

primarily due to incorrect trade classifications (see Table 4) as they impactDk the buy/sell indicator for thethk

trade.


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spread, and dollar and percentage price impact. The single Withdrawn Quotes Technique fixes the dollar

and percent quoted spread and partially reduces other distortions, but large distortions remain. The single

NBBO Crossed and Locked Technique reduces distortions further, but large distortions remain. The two

techniques combined fixes the dollar and percent quoted spread and further reduces other distortions, but

meaningful distortions remain. We conclude that the first best solution is to use DTAQ NBBO, because

this is the only way to avoid major distortions on most performance criteria. We conclude that the second

best solution among the six methods utilizing MTAQ Quotes (columns 3, 5, 8, 10, 11, and 12) is the two

clean-up techniques combined, because this goes the furthest towards mitigating the distortions on most

performance criteria.13

Here is a summary of Table 2 regarding quote timing techniques in the particular case of using

MTAQ Quotes and two clean-up techniques (columns 10, 11, and 12). Interpolated Time greatly reduces

distortions in outside the NBBO, Interpolated Time slightly improves the dollar and percentage quoted

spread, Same Second and Interpolated Time meaningfully reduce distortions in dollar and percentage

effective spread, Interpolated Time greatly reduces distortions in percent of time dollar effective spread is

greater than dollar quoted spread, Prior Second does the best in dollar and percentage realized spread,

Prior Second does the best in dollar and percentage price impact, and none of the quote timing

alternatives makes much difference with dollar and share depth. We conclude that when using MTAQ

Quotes and two clean-up techniques (columns 10, 11, and 12), the best quote timing technique is

Interpolated Time, because it yields the greatest benefit on the greatest number of performance criteria.

Overall, if a researcher is financially constrained to using only MTAQ data, then the second best

solution is to use two clean-up techniques (Withdrawn Quotes and exclude the remaining NBBO Crossed

and Locked) and use Interpolated Time as the quote timing technique. Each of these three techniques

independently contributes to reducing distortion on most performance criteria and the combination of all

three goes the furthest distance possible in reducing distortion. Since each technique makes a significant

13 Similarly, we conclude that among the four methods involving DTAQ Quotes (columns 2, 4, 7, and 9), the best isthe two clean-up techniques combined, because this goes the furthest towards mitigating the distortions on mostcriteria.


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and independent contribution to reducing the distortion, we conclude that each of the three corresponding

issues (cancelled quotes, withdrawn quotes, and millisecond versus second timestamps) is a significant

and independent source of distortion.

Table 3 examines the robustness of the results in Table 2 by examining trade frequency quintiles.

Panel A breaks out the percentage of trades that are outside the NBBO by quintiles based on the number

of trades per day, where quintile 1 is the lowest and quintile 5 is the highest. Within each of the twelve

columns, the percentage outside the NBBO is relatively similar across trade frequency quintiles. Panel B

breaks out the percentage of time that the NBBO is crossed by trade frequency quintiles. Again, within

each of the twelve columns, the percentage crossed is relatively similar across trade frequency quintiles.

Looking across the columns, the pattern of less distortion as more clean-up techniques are used is

qualitatively similar to Table 2.

Panel C breaks out dollar quoted spread by trade frequency quintiles. Columns (2)-(3) show that

distortion increases monotonically in trade frequency, leading to negative spreads in high quintiles.

Columns (4)-(5) show less distortion in each quintile than columns (2)-(3), but the distortions are still

large. Columns (7)-(8) show relatively little distortion in any quintile. Columns (9)-(12) show generally

less distortion in each quintile than columns (7)-(8). Across columns, the pattern of less distortion as more

clean-up techniques are used is qualitatively similar to Table 2.

Panel D breaks out dollar effective spread by trade frequency quintiles. In columns (2)-(3), the

distortions are huge for all quintiles. For example in quintile 1, the dollar effective spread goes from

17.50 under Benchmark #1, nearly doubles to 32.80 under DTAQ Quotes, and remains high at 29.80

under MTAQ Quotes. At the other extreme in quintile 5, the dollar effective spread goes from 1.90

under Benchmark #1, more than quintuples to 10.30 under DTAQ Quotes, and increases to 10.60 under

MTAQ Quotes. Columns (4)-(5) show that the quintile 1 distortion is greatly reduced, but that the

distortion in quintiles 2 5 is still large. Columns (7)-(8) show an enormous distortion in quintile 1 and a

more moderate, but still important distortion in quintiles 2 5. Columns (9)-(12) have less distortion in


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each quintile than any other set of columns, but there is still meaningful distortion in each quintile. Again,

the pattern of less distortion as more clean-up techniques are used is qualitatively similar to Table 2.

Panel E breaks out the dollar ask depth by trade frequency quintiles. There is some variability

across quintiles, but generally the distortions are quite modest. Across all four depth measures in columns

(2)-(3), the average distortion as a percentage of benchmark depth is 3.8%. The comparable figure for

columns (9)-(12) is 1.8%. Thus, the overall pattern of relatively minimal distortions is qualitatively

similar to Table 2.

To summarize Table 3, within each column the distortions of outside the NBBO and crossed

NBBO are relatively similar by trade frequency. Within each column, the distortions of dollar quoted

spread and dollar effective spread are generally increasing in trade frequency. Across columns, the

patterns are qualitatively similar to Table 2. Thus the conclusions that we drew from Table 2, that the first

best solution is to use DTAQ NBBO and that the second best solution involving MTAQ Quotes is to use

two clean-up techniques and Interpolated Time, are found in Table 3 to be robust by trade frequency.

We further explore the second best solution in Table 4. Panel A reports on the accuracy of trade

classification of different methods compared to DTAQ NBBO under three trade-typing conventions: LR,

EMO, and CLNV. For example, in column (2) each trade is classified as a buy or a sell using MTAQ

Quote and no clean-up procedure under the LR convention and this is compared with the buy or sell

classification using Benchmark #1 under the LR convention. When the two classifications match, the

trade is reported as Correctly Classified LR. When DTAQ NBBO says it is a buy (sell) and MTAQ

says it is a sell (buy), then the trade is reported as Buy Misclassified as a Sell - LR (Sell Misclassified

as a Buy - LR). The percentage of trades that are correctly classified is 88.3% under LR, 91.8% under

EMO, and 90.2% under CLNV, and all three are significantly less than 100.0%. Interestingly, the

misclassifications are close to evenly balanced under all three techniques. For example under LR, 5.8% of

trades are buys misclassified as sells and 6.0% are sells misclassified as buys. The same close balance

holds under the other two trade-typing conventions.


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Columns (4)-(6) repeat this exercise when trade typing is done under MTAQ Quote with both

clean-up techniques and is compared to trade typing done under Benchmark #2. Using both clean-up

techniques with either Prior Second or Interpolated Time (columns 4 and 6) yield a higher percentage of

correct classifications under all three conventions than using no clean-up technique (column 2). Prior

Second and Interpolated Time perform about the same, with Prior Second doing slightly better on LR,

Interpolated Time doing slightly better under EMO, and both tying under CLNV. Again, we see that

misclassifications are close to evenly balanced under all three quote-timing techniques and under all three

trade-classification techniques.

Panel B reports absolute order imbalance, which as discussed in Section 3, is an increasingly

popular measure of the probability of informed trading. Column (2) reports absolute order imbalances

under MTAQ with no clean-up technique that are very close to benchmark #1 under all three trade-typing

conventions. Is it possible that the even balance of misclassifications reported above roughly offset errors

and thus we find very little distortion in absolute order imbalance.

Columns (4)-(6) report absolute order imbalances under MTAQ with both clean-up techniques

that are a little bit higher than those reported under benchmark #2 under all three trade-typing

conventions. Among the three quote timing techniques, Interpolated Time has the least distortion and is

relatively close to benchmark #2. Again, the even balance of misclassification reported above may be a

key factor in the small amount of distortion here. In summary, the second best solution of using both

clean-up techniques and Interpolated Time is tied for the least amount of buy-sell misclassification and

leads to the least amount of distortion in absolute order imbalance.

Table 5 reports trade locations, cost of trading measures, and depths shown with and without

Duration Limited Control (DLC) under eight methods that match trades with MTAQ Quotes and use Prior

Second. For columns (2)-(5), the reference benchmark is benchmark #1 in column (1), which is the

DTAQ NBBO file including NBBO crossed and locked.

The first comparison is between column (3) with DLC and column (2) without DLC, where both

methods have no other clean-up techniques. Compared to column (2), column (3) has much less distortion


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in Outside the NBBO, Crossed NBBO, dollar quoted spread, dollar effective spread, percent of time that

dollar effective spread is greater than dollar quoted spread, dollar realized spread under all three

conventions (LR, EMO, and CLNV), and dollar price impact under all three conventions (LR, EMO, and

CLNV) and there is very little difference in dollar and share depth. Thus, DLC helps reduce distortion

across-the-board when no other clean-up techniques are used.

The second comparison is between column (5) with DLC and column (4) without DLC, where

both methods use a single other clean-up technique: Withdrawn Quotes. Compared to column (4), column

(5) has less distortion in Outside the NBBO, Crossed NBBO, dollar quoted spread, dollar effective

spread, percent of time that dollar effective spread is greater than dollar quoted spread, dollar realized

spread under all three conventions (LR, EMO, and CLNV), and dollar price impact under all three

conventions (LR, EMO, and CLNV) and there is very little difference in dollar and share depth. Thus,

DLC helps reduce distortion when a single other clean-up technique (Withdrawn Quotes) is used.

For columns (7)-(10), the reference benchmark is benchmark #2 in column (6), which is the

DTAQ NBBO file using the NBBO Crossed and Locked technique. The third comparison is between

column (8) with DLC and column (7) without DLC, where both methods use a single other clean-up

technique: NBBO Crossed and Locked. Compared to column (7), column (8) has less distortion in

Outside the NBBO, by construction zero Crossed NBBO, more distortion in dollar quoted spread, less

distortion in dollar effective spread, percent of time that dollar effective spread is greater than dollar

quoted spread, dollar realized spread under all three conventions (LR, EMO, and CLNV), and dollar price

impact under all three conventions (LR, EMO, and CLNV), and there is very little difference in dollar and

share depth. Thus, DLC helps reduce distortion in most cases when a single other clean-up technique

(NBBO Crossed and Locked) is used.

The fourth comparison is between column (5) combining the Withdrawn Quotes and DLC

techniques and column (9) combining two other clean-up techniques without DLC. Compared to column

(9), column (5) has more distortion in Outside the NBBO, Crossed NBBO, dollar quoted spread, dollar

effective spread, percent of time that dollar effective spread is greater than dollar quoted spread, dollar


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price impact under all three conventions (LR, EMO, and CLNV), and dollar realized spread under all

three conventions (LR, EMO, and CLNV) and there is very little difference in dollar and share depth.

Thus combining Withdrawn Quotes and DLC increases distortion across-the-board compared to using

two other clean-up techniques without DLC.

The fifth comparison is between column (8) combining the NBBO Crossed and Locked and DLC

techniques and column (9) combining two other clean-up techniques without DLC. Compared to column

(9), column (8) has nearly the same distortion in Outside the NBBO, by construction zero Crossed

NBBO, about the same distortion in dollar quoted spread, increased distortion in dollar effective spread,

percent of time that dollar effective spread is greater than dollar quoted spread, dollar price impact under

all three conventions (LR, EMO, and CLNV), and dollar realized spread under all three conventions (LR,

EMO, and CLNV) and there is very little difference in dollar and share depth. Thus combining the NBBO

Crossed and Locked and DLC techniques increases distortion in nearly all cases compared to using two

other clean-up techniques without DLC.

The sixth comparison is between column (10) with DLC and column (9) without DLC, where

both methods have two other clean-up techniques. Compared to column (9), column (10) has slightly less

distortion in Outside the NBBO, by construction zero Crossed NBBO, much more distortion in dollar

quoted spread and dollar effective spread, very little difference in dollar realized spread under all three

conventions (LR, EMO, and CLNV), less distortion in percent of time that dollar effective spread is

greater than dollar quoted spread, and dollar price impact under all three conventions (LR, EMO, and

CLNV), and very little difference in dollar and share depth. Thus, DLC meaningfully increases distortion

in the critical cases of quoted spread and effective spread and has modest or no benefit on other

performance criteria when two other clean-up techniques are used.14

To summarize Table 5, we find that DLC does betterthan no clean-up technique and adding DLC

to a single other clean-up technique does betterthan that single other clean-up technique alone. However,

14 In unreported results, we find qualitatively similar results when performing the same test (i.e., testing two otherclean-up techniques with and without DLC) under Same Second and Interpolated Time quote timing techniques.


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adding DLC to a single other clean-up technique does worse than two other clean-up techniques without

DLC and adding DLC to two other clean-up techniques does worse than two other clean-up techniques

without DLC.We conclude that two other clean-up techniques should be used and DLC should not be.

7. Economic Significance

This section explores the economic significance of different methods of computing the NBBO for

realistic research questions. We imagine a skeptical reader acknowledging that effective spread, realized

spread, price impact, etc. more than double when using MTAQ Quotes with no clean-up techniques

compared to DTAQ NBBO, but asking whether these distortions really make a difference. In other words,

perhaps the absolute dollar amount of these performance criteria are scaled up, but conceivably relative

comparisons across stocks, across exchanges, etc. might be unchanged.

To examine the economic significance of different methods on a relative basis, we consider a

highly relevant question faced by all brokers and/or security traders, where should I route my order?

During our sample period, investors could route their orders to nine stock exchanges: Chicago Board

Options Exchange (CBOE), Chicago Stock Exchange (CHX), International Securities Exchange (ISE),

National Association of Security Dealers (NASD) Alternative Display Facility (ADF) and Trade

Reporting Facility (TRF),15

National Association of Security Dealers Automatic Quotation (NASDAQ),

National Stock Exchange (NSX), NYSE including the American Stock Exchange (AMEX), NYSE

Archipelago (NYSE ARCA), and the Philadelphia Stock Exchange (PHLX). Following the methodology

of Boehmer, Jennings, and Wei (2007), we compute the dollar effective spread for each stock-day for

both DTAQ NBBO and MTAQ Quotes under four different methods. Then for each stock-day, we rank

each stock exchange from 1 to 9. A rank of 1 is the lowest dollar effective spread, which is most likely to

attract orders, whereas a rank of 9 is the highest dollar effective spread, which is least likely to attract

orders. So our question is, on what percentage of the stock-days will these relative rankings change based

on different methods of calculating the NBBO?

15 This catch-all category that in the sample period included BATS, Direct Edge A and X, and dark pool trades.


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Table 6 reports the difference in dollar effective spread rankings between MTAQ Quotes and

DTAQ NBBO. Panel A reports the difference in rankings under MTAQ Quotes when no clean-up

technique is used and the quote timing technique is Prior Second. Looking in the Average column, we see

that the rankings agree (the difference is 0) on only 46.0% of stock-days. Conversely, the rankings differ

the majority (54.0%) of the time. For example, the difference +1 means that MTAQ yields a one rank

higher number (i.e., one rank worse performance) 13.6% of the time. Looking at the bottom two rows, we

see that MTAQ gives the CBOE a lower rank number (better performance) 41.0% of the time and a

higher rank number (worse performance) 12.5% of the time. More often than not, MTAQ makes some

exchanges (e.g., CBOE, CHX, NYSE, etc.) appear to perform better and other exchanges (e.g., ISE,

NASDAQ, NYSE ARCA, etc.) appear to perform worse.

Panels B, C, and D report the difference in rankings under MTAQ Quotes when both clean-up

techniques are used and the quote timing technique is Prior Second (Panel B), Same Second (Panel C),

and Interpolated Time (Panel D). On average, the rankings agree 51.2% (Prior Second), 49.7% (Same

Second), and 58.1% (Interpolated Time) of the time. The increase in the frequency of rankings agreement

provides additional support for the second best solution of using both clean-up techniques (Panels B, C,

and D) and using Interpolated Time (Panel D) as the quote timing technique.

We conclude that different methods of computing the NBBO yield economically significant

differences. With no clean-up techniques, the majority of order routing decisions are different and

performance is biased in favor of some exchanges and against others. The use of both clean-up techniques

and Interpolated Time reduces the distortion in routing decisions and exchange performance, but

meaningful distortion remains. The only way to completely avoid distortion is to go with the first best

solution of using the DTAQ NBBO file.

8. The Ultimate Breakdown of the NBBO

Hasbrouck and Saar (2010) provide evidence that some traders are responding to market events in

milliseconds. Specifically, they find that after a quote either improves or deteriorates, there is a peak in

the hazard rate 2-to-3 milliseconds later for limit order submission, limit order cancellation, and execution


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at the updated quoted price. In other words, current trading algorithms are able to observe the market

event, process the information, and take action in about 2-to-3 milliseconds.

There is every reason to believe that response times will get faster in the decades ahead. Moore

(1965) (Moores Law) and other similar formulations have found evidence that over the past half

century there has been an exponential increase in computing power (as measured by CPU speed per

dollar, memory capacity per dollar, hard disk capacity per dollar, etc.) and an exponential increase in

network power (as measured by internet backbone bandwidth, wireless network speeds, network latency,

etc.). This has fueled a competitive arms race by proprietary trading firms to continually reduce

network latency and increase processing speed in order to leapfrog the competition (see Aldridge 2009).

Projecting these trends into the future, response times will likely accelerate into microseconds (10-6

seconds) in the 2010s and into nanoseconds (10-9 seconds) in the 2020s.

As response times accelerate, we predict that the fundamental legal and economic concept of the

NBBO will ultimately breakdown. In 1905, Albert Einstein published his theory of special relativity,

which assumes that all observers in inertial frames of reference will measure the speed of light to be the

same irrespective of their motion relative to each other. Special relativity has the implication that no

physical entity can travel faster than the speed of light.

Consider a trading algorithm co-located with the servers of the CSX and a second trading

algorithm co-located with the servers of the NYSE. Suppose for a particular security that at 9:47:25.000

both locations observe that the best ask is $47.10 and the best bid is $47.00. Then one millisecond later at

9:47:25.001, the trading algorithm in Chicago submits a limit sell at $47.09, which improves the CSX ask

price. Then one millisecond later at 9:47:25.002 the trading algorithm in New York submits a market buy

to the NYSE. Chicago and New York are 790 miles apart, or equivalently, 4.3 light-milliseconds apart. At

9:47:25.002, it is physically impossible for the matching engine on the NYSE to be aware of the

improved CSX ask price, so the market buy is executed at the unimproved NYSE ask price of $47.10.

This example illustrates that the Newtonian concept of a single, absolute NBBO for all economic agents

in all locations breaks down under sufficiently fast trading.


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As a replacement for the NBBO, we propose an Einsteinian concept of a Relative Best Bid and

Offer (RBBO) that is different for each market center, where a market center is defined as an exchange,

market maker, or broker-dealer. The RBBO for a given market center matching engine is based on local

information in real time and remote information with various lag times. Suppose that market center i is

one ofNmarket centers in the U.S. Letij

be the total time to communicate an event on market center j

to market center i, including any time required to process the information. Let ,Bid j t and

,Offer j t be the bid and offer of market centerj at time t. We propose that the Relative Best Bid and

Offer for market center i at time tis

1 2

1 2

1, , 2, , , , ,, ,

1, , 2, , , ,

i i iN

i i iN

Max Bid t Bid t Bid N tRBBO i t

Min Offer t Offer t Offer N t

(11)

where the local lag timeii

is either zero or is much smaller than any other lag time. In the example

above, the RBBO on the CSX at 9:47:25.002 is given by RBBO(CSX, 9:47:25.002) = {$47.00, $47.09},

which differs from the RBBO on the NYSE at the same millisecond given by RBBO(NYSE, 9:47:25.002)

= {$47.00, $47.10}.

9. Conclusion

We address three NBBO issues: (1) millisecond versus second timestamps, (2) withdrawn quotes,

and (3) cancelled quotes. We find that each of these three issues is a significant and independent source of

distortion in standard measures of market quality. The distortions are so massive that standard

microstructure techniques essentially fail. We test fourteen different methods for matching trades and

quotes based on different combinations of three clean-up techniques, two alternative quote sources, and

three quote timing techniques. We conclude that the first best solution is to use the NBBO file in the

Daily Trade And Quote (DTAQ) database, because this is the only way to avoid major distortions on

most performance criteria. If a researcher is financially constrained to using only Monthly Trade And

Quote (MTAQ) database, then the second best solution is to use two clean-up techniques (Withdrawn


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Quotes and exclude the remaining NBBO Crossed and Locked) and use Interpolated Time as the quote

timing technique. Each of these three techniques independently contributes to reducing distortion on most


distortion. Looking to the future, we anticipate the ultimate demise of the NBBO and propose to replace it

with a Relative Best Bid and Offer (RBBO) that is different for each market center.


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References

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Chordia, T., Roll, R., Subrahmanyam, A., 2010, Recent Trends in Trading Activity, working paper,

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Easley, D., de Prado, M., OHara, M, 2011, Flow toxicity and volatility in a high frequency world,working paper, Cornell University.

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Finucane, T., 2000. A direct test of methods for inferring trade direction from intra-day data.Journal of

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Hendershott, T., Moulton, P., 2011, Automation, Speed, and Stock Market Quality, Journal ofFinancial Markets 14, 568-604.

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Riordan, R., Storkenmaier, A., 2008, Optical Illusions: The effects of exchange system latency onliquidity, working paper, University of Karlsruhe.

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...

Figure1.InformationflowsinTapeA(NYSElisted)andTapeB(AMEXandregional)securities.

IntegratedQuotes

and

NBBO

ConsolidatedTapeAssociation

MarketCenter1MatchingEngine

ConsolidatedTapeSystem

QuotesTrades

Quotes

Quotes

Trades

Trades

MarketCenter2MatchingEngine

IntegratedTrades

DTAQinMillisecondsMTAQinSeconds

MarketCenterNMatchingEngine

=NYSE

IntegratedQuotes,NBBO,andIntegratedTradesinMilliseconds

ConsolidatedQuotationSystem


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T1 T2 T3 T4

Q1 Q2 Q3 Q4 Q5

ss1

10

1

8

3

10

3

8

5

10

5

8

7

10

7

8

9

10

s(s+1)

Figure 2. How Interpolated Time Assigns 4I Trades and 5J Quotes Over A Second.


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Table 3

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Bench-

mark #1:

DTAQ

NBBO File

Bench-

mark #2:

DTAQ

NBBO File

Including

NBBO

Crossed

& Locked

DTAQ

Quotes;

Prior

Millisec.

MTAQ

Quotes;

Prior

Second

DTAQ

Quotes;

Prior

Millisec.

MTAQ

Quotes;

Prior

Second

& NBBO

Crossed

& Locked

Technique

DTAQ

Quotes;

Prior

Millisec.

MTAQ

Quotes;

Prior

Second

DTAQ

Quotes;

Prior

Millisec.

MTAQ

Quotes;

Prior

Second

MTAQ

Quotes;

Same

Second

MTAQ

Quotes;

Interpo-

lated Time

Panel A: Outside the NBBO

# of Trades 1 (Low) 3.0% 22.7% 26.9% 13.3% 17.6% 2.6% 1 6.0 % 19 .8 % 8 .4 % 1 2.5 % 1 0.2 % 9 .3 %

# of Trades 2 3.3% 19.7% 25.2% 12.8% 18.5% 3.0% 8.6% 13.1% 4.9% 9.7% 7.1% 5.7%

# of Trades 3 3.5% 19.0% 25.0% 10.1% 15.5% 3.1% 5.7% 10.5% 3.3% 8.1% 5.5% 3.9%

# of Trades 4 3.8% 21.4% 28.9% 10.4% 19.1% 3.3% 5.2% 11.6% 3.6% 10.2% 6.6% 4.4%

# of Trades 5 (High) 4.9% 20.1% 26.2% 10.0% 17.5% 3.9% 4.7% 12.9% 4.0% 12.1% 8.0% 4.7%

Panel B: Crossed NBBO

# of Trades 1 (Low) 0.3% 9.7% 1 1.0% 6.3% 7.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

# of Trades 2 0.4% 14.5% 17.3% 10.1% 12.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

# of Trades 3 0.5% 1 6.3 % 20 .0 % 8 .5% 1 0.4 % 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

# of Trades 4 0.5% 2 0.5 % 24 .2 % 8 .7% 1 2.5 % 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

# of Trades 5 (High) 0.7% 19.4% 19.2% 7.2% 7.4% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Panel C: Dollar Quoted Spread

# of Trades 1 (Low) 23.77 21.50 20.10 21.80 21.19 24.12 23.96 23.00 23.41 23.33 23.33 23.58

# of Trades 2 4.30 1.80 1.10 2.37 2.03 4.30 4.48 4.50 4.46 4 .47 4 .4 7 4 .5 4

# of Trades 3 3.80 0 .8 0 -0 .1 0 2 .20 1.8 3 3.77 4.05 4.07 3.83 3.85 3.85 3.89# of Trades 4 3.60 -3 .00 -4.50 0 .68 -0 .44 3.57 3.86 3.88 3.63 3.66 3.66 3.71

# of Trades 5 (High) 2.40 -6.80 -6.60 -1.43 -0.80 2.45 2.59 2.58 2.49 2.47 2.47 2.51

Panel D: Dollar Effective Spread

# of Trades 1 (Low) 17.50 32.80 29.80 18.56 19.68 17.61 57.99 54.02 18.40 19.24 17.93 18.40

# of Trades 2 3.40 5.70 6.60 5.10 5.81 3.42 3.97 4.46 3.58 4.04 3.51 3.54

# of Trades 3 2.70 5.40 6.50 4.17 4.88 2.74 2.90 3.39 2.80 3.21 2.76 2.77

# of Trades 4 2.50 8 .8 0 1 0.6 0 5 .44 6.9 1 2.54 2.79 3.35 2.59 3.15 2.58 2.60

# of Trades 5 (High) 1.90 10.30 10.60 5 .90 5 .74 1.93 2.11 2.69 1.98 2.54 2.08 2.00

Panel E: Depth Measures (000's)

# of Trades 1 (Low) $4.67 $4.23 $4.29 $4.70 $4.73 $4.69 $4.30 $4.35 $4.74 $ 4.7 9 $ 4.7 9 $ 4.7 9

# of Trades 2 $6.62 $6.55 $7.06 $6.61 $6.72 $6.62 $6.49 $6.76 $6.62 $ 6.7 2 $ 6.7 2 $ 6.7 3

# of Trades 3 $8.56 $8.37 $8.25 $8.79 $8.81 $8.56 $8.55 $8.52 $8.69 $8.69 $8.69 $8.72

# of Trades 4 $14.15 $14.07 $14.19 $14.41 $14.43 $14.16 $14.34 $14.33 $14.41 $14.37 $14.37 $14.39

# of Trades 5 (High) $34.96 $33.91 $33.83 $35.77 $35.77 $35.11 $35.42 $35.32 $35.87 $35.92 $35.92 $36.04

Comparison by Trade Frequency Quintiles

No Clean-Up

Techniques

One Clean-Up

Technique:

Withdrawn

Quotes

One Clean-Up

Technique:

NBBO Crossed

and Locked

Two Clean-Up Techniques:

Withdrawn Quotes and

Exclude Remaining NBBO

Crossed & Locked

Trade locations, cost of trading measures, and depths are shown under ten methods to calculate the NBBO and under two NBBO benchmarks. Two clean-

up techniques are tested: (1) Withdrawn Quotes, which treat zeros and missing values in quotes as withdrawn quotes and (2) NBBO Crossed and Locked,

which excludes these observations. Two quote data sources are tested: the Daily Trade And Quote (DTAQ) Quotes file and the Monthly Trade And

Quote (MTAQ) Quotes file. Three MTAQ quote-timing techniques are test ed: Prior Second , Same Second, and Interpolated Time. Benchmark #1 is the

DTAQ NBBO file including NBBO crossed and locked. Benchmark #2 is the same, but using the NBBO Cross ed and Locked technique. The s ample spans

April - June 2008 inclus ive and cons ists of 99 randomly selected stocks, resulting in 33,735,796 trades. Bold numbers are statistically different from the

corresponding benchmark at the 1% level.


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Table 4

(1) (2) (3) (4) (5) (6)

Benchmark

#1: DTAQ

NBBO File

Including

NBBO

MTAQ Quote

File Us ing

No Clean-Up

Techniques

Benchmark

#2: DTAQ

NBBO File

& NBBO

Crossed

Crossed& Locked

PriorSecond

& LockedTechnique

PriorSecond

SameSecond

InterpolatedTime

Panel A: Trade Classification Compared to the DTAQ NBBO File Benchmark

Correctly Classified - LR 88.3% 90.4% 83.7% 90.2%

Buy Misclassified as a Sell - LR 5.8% 5.0% 8.9% 5.5%

Sell Misclassified as a Buy - LR 6.0% 4.6% 7.4% 4.4%

Correctly Classified - EMO 91.8% 92.8% 88.9% 93.1%

Buy Misclassified as a Sell - EMO 4.1% 3.7% 5.8% 3.6%

Sell Misclassified as a Buy - EMO 4.1% 3.5% 5.3% 3.3%

Correctly Classified - CLNV 90.2% 91.9% 87.0% 91.9%

Buy Misclass ified as a Sell - CLNV 4.8% 4.1% 6.8% 4.3%

Sell Misclassified as a Buy - CLNV 5.0% 4.0% 6.2% 3.8%

Panel B: Absolute Order Imbalance

Absolute Order Imbalance: LR 12.6% 12.6% 12.7% 14.0% 14.7% 13.8%

Absolute Order Imbalance: EMO 10.9% 11.2% 11.0% 12.2% 11.3% 11.3%

Absolute Order Imbalance: CLNV 12.2% 12.0% 12.3% 13.2% 12.8% 12.7%

Trade Classification and Absolute Order ImbalanceTrade classification and absolute order imbalance are shown under four methods that calculate the NBBO using

the Monthly Trade And Quote (MTAQ) Quotes file and under two NBBO benchmarks. In one treatment, no clean-

up techniques are used. In another treatment, both clean-up techniques are used. Three quote timing techniques

are considered: (1) Prior Second, (2) Same Second, and (3) Interpolated Time. Benchmark #1 is the DTAQ NBBOfile including NBBO crossed and locked. Benchmark #2 is the same, but using the NBBO Crossed and Locked

technique. The sample spans April - June 2008 inclusive and cons ists of 99 randomly selected stocks, resulting in

33,735,796 trades. In Panel A, bold numbers for Correctly Classified indicate statist ically different from 100% and

bold numbers for Buy Misclass ified as a Sell and Sell Misclass ified as a Buy indicate stat istically different from

0%. In Panel B, bold numbers are statistically different from the corresponding benchmark at the 1% level.

MTAQ Quote File Using

Two Clean-Up Techniques :

Withdrawn Quotes and

Exclude Remaining NBBO

Crossed & Locked


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Table 5

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Bench-mark

#1: DTAQ

NBBO File

Including

NBBO

Benchmark

#2: DTAQ

NBBO File

& NBBO

Crossed

Crossed

& Locked

No

DLC

Plus

DLC

No

DLC

Plus

DLC

& Locked

Technique

No

DLC

Plus

DLC

No

DLC

Plus

DLC

Panel A: Trade Location

At the NBBO 68.9% 61.0% 66.8% 67.8% 68.6% 69.0% 70.6% 70.9% 73.0% 71.5%

Inside the NBBO 27.4% 12.6% 17.0% 14.6% 17.8% 27.8% 15.8% 18.6% 16.5% 19.1%

Outside the NBBO 3.7% 26.5% 16.2% 17.6% 13.6% 3.2% 13 .6% 10.5% 10.5% 9.3%

Locked NBBO 1.7% 3.0% 1.7% 1.7% 1.7% 0.0% 0.0% 0.0% 0.0% 0.0%

Crossed NBBO 0.5% 18.4% 7.4% 9.9% 5.1% 0.0% 0.0% 0.0% 0.0% 0.0%

Panel B: Quoted and Effective Spreads

Dollar Quoted Spread 7.59 2.01 7.80 4.77 8.18 7.65 7.62 9.87 7.57 9.90

Percent Quoted Spread 0.405% 0.211% 0.500% 0.3% 0.509% 0.405% 0.395% 0.575% 0.400% 0.589%

Dollar Effective Spread 5.62 12.86 10.43 8 .62 8 .21 5.66 13.62 8.92 6.44 7.06

Percent Effective Spread 0.323% 0.501% 0.461% 0.441% 0.457% 0.323% 0.387% 0.401% 0.365% 0.420%

Time %: $ Eff Spd > $ Quo Spd 8.4% 37.0% 31.0% 34.6% 28.5% 9.0% 35.0% 22.0% 30.0% 21.0%

Panel C: Realized Spread and Permanent Price Impact

Dollar Realized Spread : LR 1.76 3.51 3.19 3.02 2.97 1.76 3.45 3.15 2.96 2.95

Dollar Realized Spread: EMO 0.92 2.73 2.28 2.25 2.07 0.92 2.51 2.16 2.10 1.98

Dollar Realized Spread: CLNV 1.58 3.33 2.99 2.88 2.82 1.58 3.22 2.93 2.79 2.79

Dollar Price Impact: LR 3.87 9.35 7.16 5.56 5.17 3.87 10.11 5.61 3.37 3.99

Dollar Price Impact: EMO 4.50 7.92 6.07 6.11 5.88 4.50 3.82 4.43 3.98 4.77

Dollar Price Impact : CLNV 4.02 9.48 7.23 5.65 5.29 4.02 10.28 5.69 3.49 4.13

Panel D: Depth Measures

Dollar Ask Depth (000's) $13.9 $13.6 $13.6 $14.2 $13.9 $13.9 $13.9 $13.8 $14.2 $14.0

Dollar Bid Depth (000's) $13.8 $13.3 $13.7 $13.6 $13.6 $13.8 $13.7 $13.8 $13.9 $13.9

Share Ask Depth 552 534 534 564 546 553 547 541 562 548

Share Bid Depth 557 532 545 537 536 559 545 547 556 548

Two Techniques:

Withdrawn

Quotes and

NBBO Crossed

and Locked

The Impact of Adding Duration Limited Control To Other Clean-Up Techniques

Trade locations, cost of trading measures, and depths are shown with and without Duration Limited Control (DLC) under eight methods that

calculate the NBBO and under two NBBO benchmarks. The eight methods to calculate the NBBO use the Monthly Trade and Quote (MTAQ)

Quotes file and the Prior Second quote timing technique. Two methods have no

breakdown of standard microstructre techniques, jacobsen, 2011

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