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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National Best Bid and Offer (NBBO) quotes.We address three NBBO issues: (1) millisecond versus second timestamps, (2) withdrawn quotes, and (3)cancelled quotes.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
performance criteria and the combination of all three goes the furthest distance possible in reducing
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
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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References
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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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Saar, G., Westbrook, H., 2011, Low-Latency Trading, working paper, Cornell University.
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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