SPECIAL SECTION: ‘FINANCIAL MARKET ENGINEERING’
INTRODUCTION
The rapid growth of electronic
markets in the securities industry
has increased the competition
among market centres and reshaped
the industry organizational structure. Market centres compete for
order flow by offering lower transaction costs and/or improved
execution quality. One of the most
widely used variables for measuring
execution quality and transaction
costs is the effective spread.1
Accurately
measuring
effective
spreads has implications for all
market participants – market centres, investors and regulators.2 The
effective spread is estimated by
matching the trades to a benchmark
quote by an algorithm. The most
widely used algorithm in estimating
effective spread is the 5-second rule
proposed by Lee and Ready (1991),
which matches trades with quotes
that time-stamped at least 5 seconds
before the trade report.3 The objective of this paper is to examine the
measurement issues in estimating
effective spreads. In particular, we
study the sensitivity of effective
spread estimates to various trade–
quote matching algorithms. We
propose a criterion to determine an
optimal algorithm and evaluate its
performance in the time period of
1993 to 2000.
Although the Lee and Ready 5second rule was originally developed
specifically for the particular trade
and quote dissemination procedures
of the NYSE at a particular point in
time, it has been widely applied in
the literature and in more recent
sample periods and to NASDAQ
stocks.4 Several studies examine
the potential bias of applying the
existing trade–quote matching algorithms to recent data and NASDAQ
stocks, and urge caution of measuring effective spreads. Bessembinder
(2003) shows that effective spread
estimates can change significantly
when trades are matched with different quotes. Madhavan et al.
(2003) find bias in the 5-second
rule in estimating effective spreads
employing the TAQ and the ITG
Inc’s proprietary data. Ellis et al.
(2000b), Peterson and Sirri (2003)
and Werner (2002) show that Lee
and Ready’s 5-second rule can overestimate effective spreads over the
actual effective spreads using NYSE’s
System Order Data (SOD) and
Audit Trail Data (CAUD) data.
Vergote (2005) shows that Lee and
Ready’s 5-second rule is too rigid to
be applied to all NYSE stocks.
We use two publicly available
transaction level datasets, TAQ and
Nastraq, to conduct the in-depth
analysis of effective spread estimation
in this study.5 During our sample
b
s
t
r
a
c
t
We find that effective spread estimates are
sensitive to trade–quote matching algorithms. In particular, Lee and Ready’s 5second algorithm can overestimate effective
spreads for active stocks. The sensitivities
can be particularly important for stocks in
which a significant amount of trading
occurs electronically. We develop a criterion
to determine the optimal algorithm and
demonstrate that it provides consistent and
appropriate estimates. We demonstrate that
a simple algorithm of matching trades with
contemporaneous quotes provides good
estimates of effective spreads during our
sample period. We also document that using
trade execution times, instead of report
times, to match trades with quotes can
reduce effective spread estimates by 0.24
cents, or about 3%, for active stocks.
Keywords: trade–quote matching algorithm,
effective spread, execution cost
A
u
t
h
o
r
s
Michael S. Piwowar
([email protected]) is a Financial
Economist at the US Securities and
Exchange Commission. The Securities
and Exchange Commission, as a matter
of policy, disclaims responsibility for any
private publication or statement by any
of its employees. The views expressed
herein are those of the author and do not
necessarily reflect the views of the
Commission or of the author’s
colleagues upon the staff of the
Commission. Both authors’ research
focuses on market microstructure.
Li Wei
([email protected]) is a Senior Economist
at the New York Stock Exchange. The
opinions expressed in this paper do not
necessarily reflect those of the members
or directors of the NYSE.
DOI: 10.1080/10196780600643803
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
MICHAEL S. PIWOWAR AND LI WEI
A
Copyright ß 2006 Electronic Markets
Volume 16 (2): 112-129. www.electronicmarkets.org
The Sensitivity of Effective Spread Estimates
to Trade–Quote Matching Algorithms
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Electronic Markets Vol. 16 No 2
period covering 1993 to 2000, NASDAQ changed
from an OTC dealer market with traditional market
makers to an increasingly electronic marketplace with a
plethora of electronic trading venues, order routing
algorithms, and automatic execution mechanisms.
Examining the sensitivity issue using both NASDAQ
and NYSE data serves two purposes: it helps us to
understand electronic market better; it also highlights
the difference between the electronic market and the
traditional exchange and its impact on measuring market
quality. The sensitivity issue of effective spread measurement is particularly related to electronic markets where
trading is active and/or quotes are updated frequently.6
In markets where quote updates are not frequent, such
as the LSE in 1990s, effective spread estimates can be
insensitive to various matching algorithms.7
Our findings are intuitive and practical. Consistent
with the increase in the amount of trades being executed
on electronic markets, we find that estimates of effective
spread are more sensitive to trade–quote matching
algorithms for NASDAQ stocks in recent sample
periods. The average dollar effective spread estimates
for the most liquid stocks from using a 5-second
algorithm are 4 cents or 36% higher than those from
using a 0-second algorithm in 1999. In contrast, the
difference was only 0.52 cents or 2% in 1993. The
effective spread estimates increase monotonically with
longer delays of matched quotes. For the most liquid
NASDAQ stocks, the average effective spread estimate
reaches nearly 30 cents when a 15-second algorithm is
applied. This is about 3.4 times larger than the 8.8-cent
effective spread estimate obtained from a 0-second
algorithm. It is clear that using the existing algorithms
of the 5-second or longer delays can significantly
overestimate effective spreads.
We use the fact that small-size orders often receive
price improvement, and are executed within the spreads
in the US equity markets to determine and justify the
optimal algorithm in estimating effective spreads. The
optimal matching algorithm can be affected by many
factors, such as tick size, speed of execution, frequency
of quote updating, institutional details in trade reporting, and etc. Because trading activities and system
characteristics of quote dissemination and trade reporting have experienced significant changes in the past few
years in the US equity markets, it is reasonable to expect
the optimal algorithm to change over time.8 We argue
that the criterion for the optimal trade–quote matching
algorithm should minimize the number of small-size
trades executed outside of quotes, since the average
quoted depths are larger than these order sizes during
our sample period for NASDAQ stocks.
Overall, we find that the average optimal algorithm is
between 1 and 2 seconds for our sample stocks during
our investigation period, with a median equal to 1
second.9 The outside ratio associated with the optimal
algorithm ranges from 3.4% to 6.7% across our five
113
NASDAQ sub-groups. Our results are consistent with
the more recent findings of Vergote (2005). With a
completely different methodology, the authors find
similar results to our study using pre- and post-decimal
data. Of particular interest to empirical researchers, we
find that a simple algorithm of matching trades with
contemporaneous quotes (a ‘0-second rule’) provides
satisfactory accuracy, with a 2% or less estimation
difference compared to the optimal algorithm results.
We also document that using trade execution times,
provided in Nastraq data, can reduce effective spread
estimates by 0.24 cent or 3% for liquid stocks.
We conduct a number of robustness checks. These
checks examine whether different choices for the cut-off
point for small-size trades, the trade-direction classification rule, and the procedures to match the NYSE and
NASDAQ stocks, would affect our overall results. Our
results are robust to all of these issues, as detailed in the
Results section. Finally, we suggest caution in interpreting our results. Our study should be viewed as a piece of
evidence showing the complicated nature of measuring
effective spreads. One should not regard our results as
the ultimate rules in matching trades with quotes. The
optimal algorithm, as we point out, is a function of the
institutional details of trade execution, trade reporting,
and quote updates. It also relates to the sample period,
characteristics of sample stocks, and market under
examination. As a result, one should have caution in
interpreting our results and application to his/her
research.
The remainder of the paper is organized as follows.
The next section introduces institutional details and our
criterion for determining the optimal trade–quote
algorithm. We then develop testable hypotheses and
describes the data and sample. We follow with results
and robustness checks, and we end with a concluding
section.
INSTITUTIONAL DETAILS AND DETERMINATION OF
THE OPTIMAL ALGORITHM
Trade reporting and quote dissemination on NASDAQ
Arbitrarily matching trades with quotes can yield biases
in estimating effective spreads if trade and quote time
stamps are not synchronized. Non-synchronization
between trades and quotes happens due to handling of
trades and quotes.10 Even with fully automatic and
electronic order processing and trade reporting, nonsynchronization can also happen if trade report and
quote dissemination systems function separately and are
not fully integrated. System capacity and order processing ability may cause temporary delays in trade
reporting and quote updating during heavy volume
periods.11 In this section, we provide an overview of
NASDAQ trade reporting and quote dissemination
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
114
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
procedures as of the end of our sample period, and
discuss how institutional features translate into time
stamps contained in Nastraq and TAQ data sets.
Nastraq time stamps for trades and quotes originated
from the NASDAQ Quotation Dissemination Service
(NQDS) and the Trade Dissemination Service (NTDS).
Compared to Nastraq, the sources of trade and quote
time stamps in TAQ have changed over time.12 From
March 1997 to the end of our sample period, the TAQ
time stamps for NASDAQ issues came from the NQDS
and the NTDS, the same sources of time stamps in
Nastraq.
Market makers were the primary source for execution
services for NASDAQ stocks during our sample period.13 Small-size orders were often automatically executed in NASDAQ, while trading for large-size orders
remains manual and often involved direct contact and
negotiation with market makers.14 For manually executed trades, NASDAQ market makers were required to
report all transactions within 90 seconds of executions.
In addition to market makers, the Small Order
Execution System (SOES) and SelectNet were two most
widely used electronic execution systems on NASDAQ
during our sample period.15 Trades executed on SOES
and SelectNet were recorded electronically and time
stamped at the execution. SOES automatically executed
public orders less than or equal to 1,000 shares against
inside quotes posted by NASDAQ market makers.16
SOES was used primarily by day traders, commonly
referred to ‘SOES Bandits’.17 SelectNet was used
primarily by NASDAQ market makers to trade with
each other.18
Both TAQ and Nastraq provide trade and quote
information for NASDAQ issues. Several differences
exist between these two data sources. Nastraq trade files
contain unrounded transaction sizes and prices, while
TAQ trade files contain only rounded sizes (down to the
nearest 100 shares) and rounded prices (up to the
nearest $1/16 at the end of our sample period). Second,
Nastraq trade data indicates execution venues for each
trade, while TAQ does not. Third, Nastraq provides
trade execution times in addition to trade report times,
while TAQ only contains trade report times.19 Since
Nastraq and TAQ share the same sources for trade and
quote time stamps for NASDAQ issues, one might
expect that the optimal trade–quote matching algorithms should be the same for these two data sets. It is an
empirical issue whether the optimal matching algorithms
are data-specific.
Determination of the optimal trade–quote matching
algorithm
Without the true execution time or a direct link between
trade report and execution times, the determination of
an optimal algorithm becomes an issue.20 It requires
institutional knowledge to develop an appropriate rule of
matching. Lee and Ready’s 5-second algorithm uses the
fact of trade late reporting on the NYSE in the late
1980s.
The execution quality on NASDAQ improved significantly during the late 1990s.21 Small-size retail
orders sometimes received price improvement, and were
executed within the spreads. It is reasonable to expect
that the ratio for small-size trades executed outside of
inside quotes should be small, especially when markets
have depth. Therefore, our criterion for the optimal
algorithm is to minimize the frequency of small-size
trades that occur outside of the NBBO (National Best
Bid and Offer) quotes.
The percentage of small-size orders executed outside
of best quotes, which we refer to as the outside ratio,
reflects a market’s execution quality.22 The NASD’s
Firm Quote rule required NASDAQ marker makers to
execute all customers’ orders at their quoted prices up to
their quoted size. In our sample period, both the mean
and median quoted depths on NASDAQ were 2,500
shares or greater for large-cap stocks and 1,000 shares
for median- and small-cap stocks. In such market
conditions, small-size trades, such as 1,000 shares or
less, should not be executed outside of inside quotes.23
In addition, 30% of small-size trades were executed on
the SOES and SelectNet in our sample period. SOES
operated like an electronic limit order book that honours
strict price-time priority, and SOES trades often
occurred at quotes. SelectNet had electronic functions
that allowed trading parties to send counter offers and
negotiate for incoming orders, and small-size orders
were often filled inside of quotes.
Our criterion, developed based on NASDAQ stocks,
can also apply to the NYSE stocks. Studies, such as
Bessembinder and Kaufman (1997), Blume and
Goldstein (1997), Huang and Stoll (1997) and
Werner (2002) document that the NYSE provided
better execution quality than NASDAQ, and small-size
market orders often received price improvements on the
NYSE trading floor. Our empirical evidence indicates
that the NYSE provided more depth than NASDAQ.
For example, the mean quoted depth on the NYSE was
3,000+ shares for large stocks, and 2,000 shares for
medium- and small-cap stocks, all larger than NASDAQ
depths. Therefore, small-size trades with less than 1,000
shares should not have been executed outside of inside
market if quote depths were larger than order sizes on
the NYSE.
We choose 1,000 shares as a benchmark for small-size
trades to be consistent with NASDAQ’s practice that the
SOES could only execute orders with 1,000 shares or
less. As a robustness check, we later re-examine our
benchmark for small-size orders and reduce 1,000 to
500 shares, and discuss whether our benchmark affects
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Electronic Markets Vol. 16 No 2
115
our conclusions. We compute the dollar and relative
effective spread as:
quotes would provide a satisfying accuracy in estimating
effective spreads. This leads to our second hypothesis:
Dollar Effective Spread52 * I * (Trade Price – Midpoint of Ask and
Bid)
Relative Effective Spread5Dollar Effective Spread/Quote
Midpoint
Hypothesis 2: 0-second algorithm5optimal algorithm for
NASDAQ stocks
where I is the indicator variable for trade direction.
We use the quote rule to classify trade directions:
trades above bid–ask mid-points are classified as buys
with I equal to ‘+1’ and trades below the midpoints are
classified as sells with I equal to ‘21.’24 Our results
would remain the same if we use Lee and Ready’s hybrid
rule, which states that trades occurring above or below
the prevailing quote midpoint are classified using the
quote rule and trades occurring at the midpoint are
classified using the tick rule. Lee and Radhakrishna
(2000) use the NYSE TORQ data to document that Lee
and Ready’s rule has high degree of accuracy for trades
that can be unambiguously classified (no-stopped and
non-crosses trades).25 In the robust check, we further
discuss the trading classification rules, such as Ellis iet al.
(2000b).
We use executions of small order to estimate the
optimal trade–quote matching algorithm. Besides our
approach, Vergote (2005) proposes an alternative
method using quote revisions around trades to estimate
the appropriate adjustment rule for trade and quote
matching. Even different in nature, our study and
Vergote (2005) find very similar evidence suggesting
that the optimal rule is time and stock varying and the 2second rule should be used to replace Lee and Ready’s
5-second rule.
HYPOTHESES, SAMPLE AND DATA
Hypotheses
We test five hypotheses related to the estimates of
effective spreads and the comparison of execution costs
between NASDAQ and NYSE.
Hypothesis 1: 5-second algorithm5the optimal algorithm for
NASDAQ stocks.
The above hypothesis is supported when the Nastraq
trade report times are systematically delayed relative to
the quote times by 5 seconds. It will be rejected if the
effective spread estimates from the 5-second algorithm
are significantly different from those based on the
optimal algorithm. Our criterion, minimizing the
number of small-size trades executed outside of inside
quotes, can yield various optimal delays for different
sample groups. We, therefore, wonder whether a simple
algorithm of matching trades with contemporaneous
Support for this hypothesis provides evidence that the
simple algorithm of matching trades with contemporaneous quotes can be applied to NASDAQ stocks in a
more recent sample period. The simple 0-second
algorithm would have obvious appeal for empirical
researchers. Additionally, the 0-second algorithm would
suggest that the quality of the more recent transaction
level data is improved, in the sense that trades and
quotes are more fully synchronized. This hypothesis is
rejected when the difference of estimates between the
two algorithms are significantly different.
The above two hypotheses evaluate the effective
spreads by using trade report times. One difference
between Nastraq and TAQ is that Nastraq contains trade
execution time stamps. We thus evaluate whether using
the execution time, instead of the report time, provides
different effective spread estimates. The third hypothesis
is:
Hypothesis 3: execution time5trade report time for estimating
effective spreads for NASDAQ stocks
This hypothesis is supported when the differences in
trade report time and trade execution time are small and
not significantly different.
Since researchers can use either TAQ or Nastraq to
estimate effective spreads for NASDAQ stocks, it is of
particular interest to examine whether effective spread
estimates are affected by the choice of database. Because
TAQ only includes trade report time stamps, we use
Nastraq trade report time stamps in the comparison.
Hypothesis 4: Nastraq5TAQ for effective spread estimates for
NASDAQ stocks
This hypothesis is supported when differences in the two
databases, most notably the price and size rounding in
TAQ and the trade report, do not affect the overall
estimation of effective spreads.
The previous four hypotheses are all constructed to
provide tests using only NASDAQ stocks. We now
consider whether the algorithm affects the comparison
of execution costs between NASDAQ and the NYSE.
Using our optimal delay algorithms for our sample of
NASDAQ stocks and a matched sample of NYSE stocks,
we compute the difference in effective spreads between
NASDAQ and the NYSE matched samples. We then
compare it to the results from the 5-second, the 10second, and the 20-second algorithms for the same
sample. The motivation for this hypothesis is to test the
extent to which the matching algorithm affects the
116
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
execution cost comparisons between NASDAQ and the
NYSE. Our final hypothesis is to test the equality of Diff
Optimal and Diff 5-second:
Diff
Diff
Optimal5Effective
Spread NASDAQ – Effective Spread NYSE
5Effective
Spread NASDAQ – Effective Spread NYSE
5-second
Hypothesis 5: Optimal algorithm55-second algorithm for NYSE –
NASDAQ difference
Since NASDAQ is a more electronic market, it is
possible that the electronic trading makes NASDAQ
stocks have different degrees of sensitivities to the trade–
quote algorithms compared with the NYSE stocks. If the
optimal and the 5-second algorithm yield similar
estimates, then the impact of electronic trading is
minimal.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Data and sample
Our study employs three data sets, CRSP, TAQ and
Nastraq. We use CRSP data as of 30 July 1999 to
construct, filter, classify, and match our sample firms.
We use Nastraq and TAQ data during 5–11 July 1999 to
estimate effective spreads.26 In constructing our
NASDAQ sample, we use the CRSP to identify all
NASDAQ-listed US common stocks with market
capitalization available as of 30 July 1999. We use
common filters to select our sample stocks. After all
filters, 920 NASDAQ NNM stocks and 34 NASDAQ
Small Caps remain in the sample pool.27 We sort the 920
NASDAQ NNM stocks and group them into four subsamples by market capitalization:
1.
2.
3.
4.
Very Large: $25 billion+ market capitalization;
Large: $1–25 billion market capitalization;
Medium: $250 million–$1 billion market capitalization; and
Small: $100–250 million market capitalization.
The ‘Very Large’ group consists of the ten largest stocks
on NASDAQ.28 We cut off our sample size of this group
at the top ten because market cap drops drastically after
that. In the next three groups, we randomly select 30
stocks from each of the ‘Large’, ‘Medium’, and ‘Small’
group.29 We make the 34 small cap stocks (the total
number of NASDAQ SmallCaps remaining after all
filters) as the fifth group, the ‘Micro.’ As a result, our
final NASDAQ sample includes 134 stocks, with 10, 30,
30, 30, and 34 in the ‘Very Large’, ‘Large’, ‘Medium’,
‘Small’, and ‘Micro’ sub-groups.30
Table 1 presents the sample summary statistics. We
report market capitalization, daily closing price, and
trade and quote information for each of the sub groups
of our NASDAQ sample. Several interesting points in
the table are worth mentioning. The market cap drops
drastically after Group 1. The Group 1 average market
cap is nearly 40 times Group 29s, and nearly 1,000 times
Groups 49s and 59s. Second, daily volatility, trade
number, and quote durations are decreasing with market
cap, too. Third, the most interesting finding in Table 1 is
that the quoted depths are larger than trade sizes for
every sub group, indicating that the market has larger
depth when compared to average trade sizes.
We construct the NYSE match sample as follows. For
each of the 100 NASDAQ NNM stocks in our sample,
we match it with a NYSE stock by market capitalization,
price level, volume volatility, and turnover as of 30 July
1999.31 We measure the following equally weighted
absolute percentage deviation for each of the NYSE
stocks
(s5volatility,
h5turnover,
N5NYSE,
T5NASDAQ):
McapN PriceN sN hN Deviation~1{
z
1{
z
1{
z
1{
MCapT PriceT sT hT Our matching criterion is to minimize the deviation. For
each NASDAQ stock, we choose the NYSE stock with
the smallest deviation without replacement.32 This
matching procedure yields 100 NYSE stocks.33 Note
that we do not find the NYSE matched samples for the
‘Micro’ stocks because most of them are below the
NYSE listing requirements. Studies that compare
liquidity and execution cost of different market mechanisms have all employed matching procedures to construct a matched sample to ensure ‘apples to apples’
comparisons.34 Our comparison is also subject to the
apple-to-apple issue. In the robustness check the results
section, we discuss the matching issue again and discuss
whether our results are affected if alternative matching
procedures are employed.
For the NASDAQ and the NYSE samples, we apply
the commonly used filters to minimize the number of
errors in the intraday data.35 Since we are not fully aware
of the institutional features of trade reporting and quote
disseminating in the five regional stock exchanges
(Chicago, Boston, Pacific, Cincinnati and Philadelphia),
we further delete the trades and quotes that originate
from them. Our final sample yields about 5 million trades
and about 2 million quotes in the second week (5–11
July) 1999. We use the second week of July in 2000 as a
robustness check, and the second week of each year
during 1993 and 1998 for the time series study.
In estimating effective spreads, we compute both
dollar spreads and relative spreads, which are computed
as the ratio between the dollar effective spreads and the
quote midpoints. In studying the sensitivity of effective
spreads to various trade–quote algorithms, we delay
quotes from 0 to 30 seconds in matching with trades.
We calculate the frequency of trades that occur outside
of the quotes, at the quotes, and inside the quotes for
each delayed algorithm. Among the trades that occur
inside the quotes, we also calculate the frequency of
trades that occur exactly at the quote midpoints.
Electronic Markets Vol. 16 No 2
117
Table 1. Sample statistics
Sample characteristics
Sample size (# of stocks)
Market capitalization ($ million)
Average daily closing price ($)
Daily volatility
Daily number of trades
Small-size trades
Medium-/large-size trades
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Daily share volume (1,000 shares)
Small-size trades
Medium-/large-size trades
Trade size (shares)
Mean
Median
Quoted spread (cents)
Quoted relative spread (bps)
Quoted depth (shares)
Quote duration (seconds)
Group 1
Very large
10
133,220.20
75.77
3.70%
Group 2
Large
Group 3
Medium
30
30
Group 4
Small
30
Group 5
Micro
34
3,411.50
48.66
4.90%
519.10
22.59
4.60%
177.20
14.46
5.50%
138.50
13.06
8.90%
18,019.17
1,643.25
2,751.26
153.96
259.52
36.73
265.77
41.05
503.24
55.85
7,015.75
7,587.75
930.51
515.69
109.05
163.73
115.67
134.89
212.91
147.25
742.71
300.00
497.79
200.00
920.75
400.00
816.51
500.00
644.21
500.00
7.51
10.94
2,546.81
18.11
18.69
42.07
1,003.31
37.02
17.60
84.75
954.98
243.86
15.73
114.97
954.33
242.01
15.33
124.35
979.61
165.99
Notes: This table shows the descriptive statistics for the 5 NASDAQ groups. Market capitalization, average daily closing price, and daily
volatility are obtained from the CRSP data set. Quoted depth, defined as the average of bid size and ask size on the inside market, is computed
using the TAQ data set. All remaining variables are obtained from the Nastraq data set. Quoted spread, relative spread, and depth are all timeweighted averages. A small-size trade is defined as a transaction of 1,000 shares or less, a medium-size trade is between 1,000 and 10,000
shares, and a large-size trade is above 10,000 shares. The investigation period is 5–11 July 1999, except for daily volatility, which is computed
from 1 January 1999 to 30 June 1999.
RESULTS
Table 2 reports the average outside ratios, inside ratios and
effective spreads (dollar and relative) for the most liquid
(‘Very large’) NASDAQ stocks and their matched NYSE
sample for 1993 and 1999 using various trade–quote
matching algorithms. Figures 1 and 2 plot the outside
ratios and the dollar effective spread estimates, respectively, for various trade–quote matching algorithms.
Table 2 together with Figures 1 and 2 indicate that the
sensitivity of effective spread estimates to matching
algorithms has gone up drastically from 1993 to 1999.
Panel A of Table 1 shows the outside ratios and effective
spread estimates for 1993 data are not very sensitive to
matching algorithms, even for NASDAQ samples. The
curves of the outside ratio and the effective spread are
flat in Panel A of both Figures 1 and 2, confirming the
results. The picture is different in 1999 when NASDAQ
moves to more electronic trading. NASDAQ stocks have
narrower effective spreads in 1999 (9 cents vs. 20 cents).
Second, NASDAQ effective spread estimates are more
sensitive to matching algorithms in 1999. As shown in
Panel B of both Figures 1 and 2, the slopes of the
outside ratio curve and the effective spread curves are
steeper in 1999. The increase in sensitivity happens not
only to NASDAQ stocks, but also slightly for the NYSE
samples but with smaller magnitude as shown in Table 2
and Figures 1 and 2. This is not surprising given the
difference between these two markets in respect of
electronic trading. The sensitivity of the outside ratios
and effective spread estimates has also dramatically
increased for less liquid NASDAQ stocks and their
NYSE matched samples.36
Motivated by our criterion that the optimal matching
algorithm should minimize the outside ratio for small
trades, we compute the optimal algorithm for each of
our sample stocks. The results are reported in Table 3.
The means of the optimal algorithms across our five
NASDAQ sub-groups are between 1.1 and 2.0 seconds,
and the medians are between 0 and 2 seconds. Under
the optimal algorithm, we find that the outside ratios
range from 3% to 8%; 80% of trades are executed at the
quotes; and the price improvement ratios are 7% to 21%.
In particular, we find that the percentage of trades that
are executed inside of quotes is relatively low, about 11%
to 17% across our sample groups.
The low percentage of inside-quote trades has
implications for our effective spread estimates if using
118
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
Table 2. Estimates of effective spreads for the most liquid NASDAQ stocks (group 1) and a matched sample of NYSE stocks
PANEL A: 1993
NASDAQ
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Delay
(seconds)
0
1
2
3
4
5
6
7
8
9
10
15
20
25
30
Outside
ratio (%)
Price IMPVT
ratio (%)
4.67
4.67
4.67
4.81
4.96
5.03
5.08
5.13
5.20
5.24
5.30
5.87
6.69
7.39
8.02
19.44
19.17
19.25
19.81
20.45
20.90
21.14
21.18
21.21
21.15
21.03
20.76
20.21
19.93
19.57
NYSE
Dollar effective Relative effective
spread (cents)
spread (bps)
19.56
19.66
19.69
19.70
19.69
19.68
19.70
19.77
19.82
19.92
20.00
20.49
21.15
21.64
22.08
Outside
ratio (%)
Price IMPVT
ratio (%)
5.08
5.09
5.12
5.09
5.10
5.06
5.06
5.07
5.07
5.11
5.18
5.38
5.55
5.78
5.98
26.23
26.22
26.16
26.12
25.99
25.89
25.83
25.57
25.50
25.24
25.04
24.11
23.64
23.48
23.12
46.21
46.41
46.48
46.47
46.37
46.30
46.31
46.47
46.56
46.78
46.95
47.99
49.40
50.42
51.36
Dollar effective Relative effective
spread (cents)
spread (bps)
11.25
11.24
11.24
11.23
11.23
11.24
11.24
11.28
11.28
11.31
11.35
11.52
11.63
11.69
11.82
24.71
24.72
24.65
24.61
24.60
24.61
24.64
24.71
24.71
24.77
24.84
25.13
25.35
25.42
25.65
PANEL B: 1999
NASDAQ
Delay
(seconds)
0
1
2
3
4
5
6
7
8
9
10
15
20
25
30
Outside
ratio (%)
Price IMPVT
ratio (%)
8.45
8.02
7.62
7.95
9.43
10.80
11.92
12.96
14.03
15.09
16.19
21.34
25.89
30.03
33.39
9.12
8.54
7.28
6.80
6.96
6.98
6.86
6.72
6.68
6.64
6.59
6.35
6.05
5.79
5.53
NYSE
Dollar effective Relative effective
spread (cents)
spread (bps)
8.35
8.39
8.50
8.63
8.80
8.99
9.18
9.39
9.61
9.83
10.07
11.32
12.60
13.85
15.04
11.62
11.69
11.84
11.99
12.18
12.38
12.59
12.81
13.03
13.26
13.51
14.81
16.15
17.48
18.73
Outside
ratio (%)
Price IMPVT
ratio (%)
5.67
5.59
5.57
5.70
5.89
5.97
6.10
6.26
6.48
6.70
6.95
8.61
10.39
12.35
14.10
36.62
35.48
34.92
34.46
33.98
33.62
33.37
33.17
33.00
32.78
32.55
31.68
30.99
30.21
29.55
Dollar effective Relative effective
spread (cents)
spread (bps)
8.53
8.66
8.71
8.76
8.83
8.87
8.93
8.95
9.00
9.06
9.12
9.46
9.90
10.44
10.95
10.55
10.71
10.77
10.85
10.93
11.00
11.07
11.11
11.18
11.26
11.34
11.76
12.30
12.92
13.51
Notes: This table reports the estimates of effective spreads, outside ratios, and price improvement ratios for the small-size trades (1,000
shares or less) of the most liquid (Group 15‘Very Large’) NASDAQ stocks and a matched sample of NYSE stocks obtained from using various
trade–quote matching algorithms. Effective spreads are reported in dollars and relative to the benchmark quote midpoint. The outside ratio
and price improvement ratio are defined as the percentage of trades that are classified as occurring outside and inside the benchmark quote,
respectively. Panel A presents the results for 1993, and Panel B presents the results for 1999. The 1993 NASDAQ sample does not include
Yahoo and WorldCom. The 1993 NYSE sample does not include AOL, Lucent, and UMG. The 1999 results for the NASDAQ sample are computed
using the Nastraq data set. All other results are computed using the TAQ data set.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Electronic Markets Vol. 16 No 2
119
Figure 1. Estimates of the outside ratio for the small-size trades of the most liquid NASDAQ sample and its matched NYSE sample by applying
different trade–quote matching algorithms. Notes: The outside ratio is defined as the percentage of small-size trades executed outside of the
benchmark quotes. Small-size trades are defined as transactions of 1,000 shares or less. Panel A presents the results for 1993, and Panel B for
1999. We use the TAQ data set to compute the 1993 results for both samples, and Nastraq and TAQ data sets for the 1999 NASDAQ and the
1999 NYSE samples. The investigation periods for all samples are the second week of July.
an alternative trade classification rule. Note that the Ellis
et al. (2000b) rule is only different from the quote rule
for those inside-quote trades. Since these inside-quote
trades are only a small part of our trade sample, our
results should not change materially if we change
our classification rule for trade direction. We will describe
this issue again in detail in the later part of the section.
Is the 5-second algorithm appropriate for NASDAQ
stocks in 1999 sample period? Is the 0-second
algorithm a better alternative?
We test Hypotheses 1 and 2 by comparing the effective
spread estimates from the 5-second and the 0-second
algorithm to that from the optimal. We find, as reported
in Table 4, that the 5-second dollar effective spreads are
0.5 cents, or about 6%, larger than that from the optimal
algorithm for the most liquid group. The numbers are
similar for the less liquid samples. The t-tests confirm
that the differences are statistically significant at the 5%
or better level, thus we reject Hypothesis 1, suggesting
the 5-second algorithm and the optimal algorithm yield
different estimates.
In comparing the 0-second to the optimal, we find
that all of the group differences are negative, implying
using contemporary quotes leads to smaller spread
estimates. The differences are statistically significant at
the 5% level for all groups, but none is significant
economically. The 0-second rule, for example, underestimates the spreads only by 0.16 cents, or about 2%,
for the most liquid NASDAQ stocks. Even though we
reject H2 on a purely statistical basis, given the appeal of
the simple algorithm and the low estimating error, the
0-second algorithm can be used in recent sample periods
without inducing an economically significant bias.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
120
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
Figure 2. Estimates of dollar effective spreads for small-size trades of the most liquid NASDAQ sample and its matched NYSE sample by
applying different trade–quote matching algorithms. Notes: Small-size trades are defined as transactions of 1,000 shares or less. Panel A
presents the results for 1993, and Panel B for 1999. We use the TAQ data set to compute the 1993 results for both samples, and Nastraq and
TAQ data sets for the 1999 NASDAQ and the 1999 NYSE samples. The investigation periods for all samples are the second week of July.
Do the trade execution time stamps in Nastraq
provide more accurate effective spread estimates than
the trade report time stamps?
The trade execution time stamp is unique to Nastraq
data. Hypothesis 3 tests whether the execution time has
value in estimating effective spreads for NASDAQ
stocks.37 In testing Hypothesis 3, we delete 7% of the
trades that have no execution time, and another 1% that
have inconsistent execution times, such that the execution times are zero or later than trade report times.
Among these deleted trades, over 99.5% of them are
dealer transactions. We compare effective spread estimates from report and execution times, and report the
results in Table 5.
Panel A of Table 5 demonstrates that using execution
time can yield lower effective spread estimates than using
report time. The differences range from 0.08 cents to
0.38 cents across sample groups with varied statistical
significance. Panel B shows that the lower effective
spread estimates from execution time are associated with
lower outside ratios, and the differences are all significant at the 5% or better levels. Thus, we reject
Hypothesis 3. On a relative basis, the improvements of
the effective spread estimates and the outside ratios are
stronger for liquid NASDAQ stocks, which also show
that the matching algorithm has a larger impact on
electronic markets.
Do TAQ and Nastraq yield the same estimates of
execution quality?
In testing Hypothesis 4, whether TAQ yields the same
estimates as Nastraq, we replicate the optimal algorithm
calculation for the TAQ data. We report the results in
Table 6.
The Nastraq vs. TAQ results are mixed. For the most
liquid NASDAQ stocks, the effective spread estimates
Electronic Markets Vol. 16 No 2
121
Table 3. Trade–quote optimal matching algorithms and trade categories
PANEL A: OPTIMAL TRADE DELAY
Delay in seconds
Group
N
Mean
Std dev
Minimum
Median
Maximum
Very large
Large
Medium
Small
Micro
10
30
30
30
34
2.00
1.93
1.20
1.13
1.41
0.00
1.51
1.81
1.80
1.79
2
0
0
0
0
2
2
1
0
1
2
8
8
8
7
PANEL B: TRADE CATEGORIES
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Percent of Trades Executed
Group
N
Outside of quotes (%)
At bid or ask (%)
Inside of quotes (5)
Very large
Large
Medium
Small
Micro
10
30
30
30
34
7.61
6.44
4.23
3.33
5.72
85.10
76.84
74.55
76.99
76.05
7.28
16.73
21.21
19.68
18.22
Notes: This table shows the optimal trade–quote matching algorithms for the 5 NASDAQ sub-samples. The reported numbers are averages
across stocks in each sub-sample. The criterion for the optimal algorithm is to minimize the outside ratio of small-size trades. The outside ratio
is defined as the percentage of trades that are classified as occurring outside the benchmark quote. Small-size trades are defined as
transactions of 1,000 shares or less. The reported numbers are averages computed across each sub-sample. The investigation period is 5–1 July
1999.
from Nastraq are 0.12 cents, or 1.4%, lower than that
from the TAQ. However, for the other four groups the
differences are statistically insignificant. Overall, we
cannot reject Hypothesis 4 regarding the equality of
TAQ and Nastraq in terms of effective spread estimates.
Nevertheless, it is noteworthy that the TAQ optimal
algorithms have longer delays than the Nastraq ones.
For the most liquid sample, the TAQ optimal algorithm
is 3 seconds compared to 2 seconds for Nastraq. This
provides additional evidence that electronically executed
orders are associated with reduced time lags in reporting
and updating.
across these two markets.38 For the most liquid group,
the differences change from negative (NASDAQ has
lower effective spreads) to positive (NYSE has lower
effective spreads), but the differences are statistically
insignificant. For the other four groups, the NASDAQ
effective spread estimates are statistically larger than the
NYSE.
Overall, our results imply that assessing execution
costs, over time and across markets, requires extreme
caution in choosing the trade–quote algorithms.
Time series evidence
Comparing execution costs between NASDAQ and the
NYSE using various algorithms
Does the trade–quote algorithm affect the comparison
of execution costs between the NYSE and NASDAQ?
Table 7 presents the results. We compare effective spread
estimates from various algorithms ranging from 0 to 5
seconds for each of NASDAQ groups with its NYSE
matching sample. It shows that longer delays of
matching algorithm cause larger spread differences
Having established that the sensitivity of effective
spreads increased during our sample period, we now
investigate the changes of the optimal algorithm and the
validity of our criterion in determining the optimal
algorithm in a time series study. We span our study from
1993, the earliest sample period we can have, to 1999.
We select the second week of July in each sample year as
our investigation period. For each of the NYSE sample
groups and the top 4 NASDAQ groups, we compute the
outside ratio and the effective spread by using various
122
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
Table 4. Estimates of dollar effective spreads using four different trade–quote matching algorithms
PANEL A: EFFECTIVE SPREADS ESTIMATES
Trade–Quote Matching Algorithms
Group
N
Optimal
0-Second
5-Second
10-Second
Very large
Large
Medium
Small
Micro
10
30
30
30
34
8.50
16.36
14.92
13.27
13.76
8.35
15.96
14.75
13.07
13.52
8.99
17.24
15.93
14.09
14.42
10.07
18.31
16.45
14.58
14.97
PANEL B: TEST OF EQUALITY OF MEANS
Difference of Dollar Effective Spread ($0.01)
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
0-Second – Optimal
5-Second – Optimal
10-Second – Optimal
Group
N
Difference
(p-value)
Difference
(p-value)
Difference
(p-value)
Very large
Large
Medium
Small
Micro
10
30
30
30
34
20.16
20.40
20.18
20.19
20.25
(0.00)
(0.00)
(0.00)
(0.01)
(0.00)
0.49
0.88
1.01
0.82
0.66
(0.02)
(0.00)
(0.00)
(0.00)
(0.00)
1.57
1.95
1.53
1.31
1.20
(0.01)
(0.00)
(0.00)
(0.00)
(0.00)
Notes: This table shows the group mean estimates of dollar effective spreads for small-size trades of all NASDAQ sub-samples using four
different trade-quote matching algorithms. Small-size trades are defined as transactions of 1,000 shares or less. Panel A reports the dollar
effective spreads computed from the optimal, the contemporaneous (0-second), the Lee and Ready 5-second, and the 10-second delay
algorithms. Panel B reports the difference between the mean estimates, with the t-test results.44 The numbers in parentheses are p-values.
The investigation period is 5–11 July 1999.
trade–quote matching algorithms using the TAQ data.39
Table 8 presents our results for the most liquid (‘Very
Large’) NASDAQ stocks and the matched NYSE sample
from 1993 through 1999 using 6 trade-quote matching
algorithms.
In Table 8, we report the outside ratio in Panel A, the
dollar effective spread in Panel B, and the difference of
the dollar effective spread in Panel C. For the most
liquid NYSE and NASDAQ stocks, the outside ratio and
the dollar effective spread become larger if increasing the
delay when matching trades with quotes. In particular,
the increases of the outside ratios and the effective
spreads are accelerated in more recent sample periods for
both the NYSE and NASDAQ stocks, even though the
trend is clearer for the NASDAQ sample. This finding is
consistent with the evidence in Figure 1 and further
confirms the electronic market impact. Panel C
shows that the NASDAQ-NYSE spread differences are
declining over time. The differences are also sensitive to
the matching algorithm during 1993 to 1999 with
larger extent in more recent sample periods.
If we use our criterion in 1993 to determine the
optimal algorithm, we obtain the exact same algorithm,
the 5-second, for the NYSE stocks as Lee and Ready
(1991). This is because the outside ratio is the smallest,
5.06%, for the NYSE stocks among all 6 algorithms. The
evidence suggests that our criterion is consistent with
the NYSE institutional details and the methodology
used in Lee and Ready (1991). During 1994 to 1999,
our criterion has suggested an optimal algorithm closer
to but different than the 5-second rule. For example, we
find the optimal algorithms are between 2 and 4 seconds
during 1994 to 1999. However, we confirm that
different algorithms have limited impact on the effective
spread estimates for the NYSE stocks based on the
evidence in Panel B in Table 8. For NASDAQ stocks, the
impact exists with increasing extent in more recent
sample periods, especially after 1996.
The time series study confirms our previous evidence
showing that choosing the optimal algorithm has
important implications in studying market quality in
more recent sample periods.
Electronic Markets Vol. 16 No 2
123
Table 5. Comparisons of the estimates of dollar effective spread and outside ratios using trade report time stamps and trade execution
time stamps
PANEL A: MEAN DOLLAR EFFECTIVE SPREADS (cents)
Nastraq Time Stamp
(T1)
Group
N
Very large
Large
Medium
Small
Micro
10
30
30
30
34
Report time
8.50
16.36
14.92
13.27
13.76
(T2)
Execution time
8.26
15.98
14.84
13.19
13.54
(T2–T1)
Difference
(p-value)
20.24
20.38
20.08
20.08
20.23
(0.00)
(0.00)
(0.40)
(0.14)
(0.01)
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
PANEL B: PERCENT OF TRADES EXECUTED OUTSIDE OF THE QUOTES (%)
Nastraq Time Stamp
(T1)
Group
N
Very large
Large
Medium
Small
Micro
10
30
30
30
34
Report time (%)
7.61
6.44
4.23
3.33
5.72
(T2)
Execution time (%)
6.81
6.00
3.99
3.12
5.31
(T2–T1)
Difference (%)
(p-value)
20.81
20.43
20.24
20.21
20.41
(0.00)
(0.00)
(0.04)
(0.04)
(0.00)
Notes: This table reports the optimal delay algorithm estimates of dollar effective spread and the outside ratio for small-size trades computed
using Nastraq trade report time stamps (T1) and trade execution time stamps (T2) for all NASDAQ groups. Small-size trades are defined as
transactions of 1,000 shares or less. The outside ratio is defined as the percentage of trades that are classified as occurring outside the
benchmark quote. We also report the difference of the estimates from two time stamps and t-test results. The numbers in parentheses are pvalues. The investigation period is 5–11 July 1999.
Robustness checks
Does the choice of the 1,000-share cut off for small-size
trades affect our results? We replicate our examination by
only including trades that are less than 500 shares. We
re-calculate all the variables, and re-test our five
hypotheses. The final results are similar to the reported
results presented in the paper, except that the estimates
of effective spreads and the outside ratio are slightly
smaller.40
Second, do the trade direction classification rules
affect our results? Our study implicitly uses the quote
rule to infer trade directions. Many studies examine the
trade classification rule and evaluate the hybrid rule in
Lee and Ready (1991).41 Our results remain the same
when we use the Lee and Ready (1991) hybrid rule,
since the directions of trades executed at quote
midpoints do not have any effects in calculating effective
spreads. Ellis et al. (2000b) propose another hybrid rule
(EMO), trades occurring at bids or asks are classified
using the quote rule and all other trades are classified
using the tick test, and find that this new hybrid rule
provides better classification for trade directions, as do
Peterson and Sirri (2003). We replace the quote rule
with EMO rule, and find that our results do not
qualitatively change. This is not surprising for two
reasons. First, the new rule only affects trades that are
executed inside quotes. Table 3 shows that only a small
percentage of trades, about 11–17%, are inside quotes
but not at quote midpoints across sample groups.
Second, Ellis et al. (2000b) report that the new hybrid
rule has a marginal contribution of trade direction
classification, less than 1% improvement as reported in
their paper.42
Does the matching procedure affect our NYSE–
NASDAQ comparison? We choose two alternative
stock-matching procedures between NASDAQ and the
NYSE stocks to confirm that our results are not driven
124
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
Table 6. Comparisons of the estimates of dollar effective spreads and the outside ratios using Nastraq and TAQ
PANEL A: EFFECTIVE SPREADS
Effective spreads ($0.01)
Optimal algorithm (seconds)
Mean
(TAQ - Nastraq)
Group
N
Nastraq
TAQ
Nastraq
TAQ
Difference
(p-value)
Very large
Large
Medium
Small
Micro
10
30
30
30
34
2.00
1.93
1.20
1.13
1.41
3.00
2.43
1.43
0.90
1.47
8.50
16.36
14.92
13.27
13.76
8.62
16.21
14.75
13.18
13.60
0.12
20.15
20.17
20.09
20.17
(0.08)
(0.31)
(0.46)
(0.61)
(0.36)
PANEL B: PERCENT OF TRADES EXECUTED OUTSIDE OF THE QUOTES
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Outside ratio (%)
Optimal algorithm (seconds)
Mean
(TAQ - Nastraq)
Group
N
Nastraq
TAQ
Nastraq (%)
TAQ (%)
Difference (%)
(p-value)
Very large
Large
Medium
Small
Micro
10
30
30
30
34
2.00
1.93
1.20
1.13
1.41
3.00
2.43
1.43
0.90
1.47
7.61
6.44
4.23
3.33
5.72
10.17
7.98
7.39
6.61
8.86
2.56
1.54
3.16
3.28
3.13
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
Notes: This table reports the optimal matching algorithms, the estimates of effective spreads, and the outside ratios for small-size trades for
all NASDAQ sub-samples using Nastraq and TAQ data sets. Small-size trades are defined as transactions of 1,000 shares or less. The outside
ratio is defined as the percentage of trades that are classified as occurring outside the benchmark quote. Panel A reports the dollar effective
spreads and its difference between TAQ and Nastraq. Panel B reports the outside ratio and its difference between TAQ and Nastraq. The
numbers in parentheses are p-values. The investigation period in this study is 5–11 July 1999.
by a particular matched sample. First, we match by
market capitalization only, as used by Bessembinder
(1999, 2003). Second, we match stocks by market
capitalization and price. We replicate our comparison
study, and find that our main conclusion does not
change.
Are our results robust if a different sample period is
used? We re-do our study using 4–11 June 2000, and
keep our sample stocks unchanged.43 The new results
show that our basic conclusions regarding the sensitivity,
the trade execution time, and the difference of TAQ and
Nastraq do not change.
In addition, we obtain three interesting findings. First,
the average optimal algorithms in 2000 have dropped
slightly compared to 1999 for the same sample groups.
For example, for the most liquid groups, the mean
optimal algorithm reduces from 1.2 seconds in 1999 to
1.0 second in 2000. Slightly different reductions, about
0.1–0.5 second, happen to less liquid groups. Second,
the sensitivity of effective spread estimates to matching
algorithm becomes stronger. For the most liquid group,
the 5-second rule overestimates the dollar effective
spread by 4.72 cents, which is over 50% of the dollar
effective spreads from the optimal algorithm. The
difference between the 0-second and the optimal
reduces to 0.05 cents for the most liquid sample, and
about 0.05–0.2 cents for all other groups.
Third, the trade execution time gives better estimates
of effective spreads. In the 2000 data, the differences of
effective spread estimates by using execution time and
report time go up compared to that in the 1999 data.
For the most liquid NASDAQ stocks, for example, the
difference has gone up from 0.44 cents to 0.57 cents,
which is 6.42% of the effective spread estimated using
trade reporting time. The evidence again suggests that
electronic trading has made the non-synchronization
problem between trades and quotes mitigated in more
recent sample periods. We conjecture that the optimal
algorithm will converge to 0 seconds. Indeed, in many
recent studies, such as Bennett and Wei (2006),
Hendershott and Jones (2005), Moulton and Wei
(2005), among others, use contemporaneous quotes.
Electronic Markets Vol. 16 No 2
125
Table 7. Estimates of effective spreads for NASDAQ groups and their matched NYSE samples
Outside ratio (%)
Dollar effective spreads ($0.01)
DELAY
NASDAQ
NYSE
NASDAQ
NYSE
Very large (n510)
0
1
2
3
4
5
8.45
8.02
7.61
7.95
9.43
10.80
5.67
5.59
5.57
5.70
5.89
5.97
8.35
8.39
8.50
8.63
8.80
8.99
8.53
8.66
8.71
8.76
8.82
8.87
20.18
20.27
20.21
20.13
20.02
0.11
Large (n530)
0
1
2
3
4
5
7.09
6.81
6.57
6.99
8.16
9.10
4.40
4.39
4.50
4.68
4.88
5.11
15.96
16.09
16.46
16.76
17.01
17.24
8.49
8.58
8.65
8.70
8.75
8.81
7.47
7.50
7.81
8.06
8.25
8.42
Medium (n530)
0
1
2
3
4
5
4.55
4.49
4.56
5.01
5.69
6.10
7.29
7.29
7.48
7.72
7.87
8.08
14.75
14.85
15.26
15.57
15.74
15.93
9.03
9.14
9.18
9.22
9.25
9.29
Small (n534)
0
1
2
3
4
5
3.51
3.49
3.49
3.99
4.53
4.87
8.60
8.73
8.93
9.10
9.29
9.41
13.07
13.19
13.54
13.83
13.96
14.09
8.44
8.53
8.58
8.60
8.63
8.67
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
GROUP
Relative effective spreads (bps)
Difference
NASDAQ
NYSE
Difference
11.62
11.69
11.84
11.99
12.18
12.38
10.55
10.70
10.77
10.84
10.93
11.00
1.07
0.99
1.06
1.14
1.25
1.38
35.41
35.71
36.55
37.20
37.67
38.09
22.33
22.59
22.76
22.87
22.99
23.15
13.08
13.12
13.79
14.34
14.68
14.94
5.72
5.71
6.08
6.35
6.49
6.65
72.41
72.99
74.95
76.40
77.10
77.87
56.09
56.80
57.08
57.27
57.50
57.62
16.31
16.18
17.86
19.13
19.60
20.25
4.64
4.66
4.96
5.23
5.33
5.42
95.53
96.39
98.98
101.13
102.20
102.97
89.97
90.98
91.56
91.68
91.98
92.33
5.56
5.41
7.42
9.44
10.21
10.64
1
2
Notes: 1. Bold indicates that the t-test of the cross-sectional mean differences are equal to zero is significant at 1% level.
2. Italics indicates that the t-test of the cross-sectional mean differences are equal to zero is significant at 5–10% level.
This table reports the estimates of dollar effective spreads and relative effective spreads for four NASDAQ groups and their NYSE matched
counterparts. The relative effective spread is defined as the dollar effective spread divided by the quote midpoint. The results for the NASDAQ
and the NYSE stocks are computed using the Nastraq and the TAQ data sets, respectively. The investigation period is 5–11 July 1999.
CONCLUSIONS
Which quote should be matched with a particular trade
when estimating the effective spread? This paper
develops a criterion to determine the optimal trade–
quote matching algorithm and shows that the criterion
works well during our 1993–2000 data sample period.
We find that the sensitivity of effective spread estimates
to the trade–quote matching algorithms increased
drastically during that period. Using existing trade–
quote algorithms that apply 5-second or longer delays in
trade–quote matching can induce large and significant
biases in effective spread estimates, particular for markets
with electronic trading.
We argue that the optimal matching algorithm should
minimize the percentage of small-size trades executed
outside of inside market quotes. We estimate the optimal
matching algorithm using the July 1999 data from the
Nastraq and TAQ databases. We find that the average
optimal matching algorithms are between 1 to 2 seconds,
far less than the existing 5 or 14 seconds delay that
pervious studies have used in estimating effective spreads.
We find that the effective spread estimates obtained
from the 5-second algorithm are significantly different
from the results obtained from the optimal algorithm,
both statistically and economically. The 5-second algorithm overestimates the effective spreads for almost all
stocks in our sample. In particular, the overestimation is
as high as 3.16 cents or 36% for the most liquid stocks.
The evidence suggests that using the existing 5-second
rule to estimate effective spreads in recent sample
periods is not justified.
We propose a simple algorithm of matching trades
with contemporaneous quotes, although not strictly
optimal, provides satisfactory effective spread estimates.
Compared to the results from the optimal algorithm, the
126
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
Table 8. 1993–99 results for the most liquid NASDAQ stocks (Group 1) and matched NYSE samples
1993
1994
1995
1996
1997
1998
1999
PANEL A: MEAN OUTSIDE RATIOS
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
DELAY
NASDAQ
NYSE
0
1
2
3
4
5
4.67
4.67
4.67
4.81
4.96
5.03
5.08
5.09
5.12
5.09
5.10
5.06
3.51
3.49
3.48
3.51
3.69
3.84
0
1
2
3
4
5
NASDAQ
19.56
19.66
19.69
19.70
19.69
19.68
NYSE
11.25
11.24
11.24
11.22
11.23
11.24
NASDAQ
14.42
14.48
14.53
14.54
14.54
14.53
0
1
2
3
4
5
NASDAQ NYSE
8.31
8.41
8.46
8.48
8.46
8.45
NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE
4.44
4.41
4.41
4.44
4.45
4.46
8.62
8.56
8.49
8.60
9.05
9.68
PANEL B: MEAN
NYSE NASDAQ
11.60 16.88
11.63 16.95
11.63 17.04
11.63 17.12
11.65 17.24
11.64 17.39
6.03
6.00
5.97
5.97
5.96
5.98
7.12
7.03
7.10
7.91
9.49
10.45
5.32
5.33
5.34
5.34
5.34
5.38
8.98
10.90
12.09
12.92
13.75
14.49
4.71
4.62
4.58
4.53
4.58
4.65
9.89
9.42
8.95
8.68
9.63
11.08
5.56
5.44
5.35
5.29
5.35
5.43
8.45
8.02
7.61
7.95
9.43
10.80
5.67
5.59
5.57
5.70
5.89
5.97
DOLLAR EFFECTIVE SPREAD ESTIMATES ($0.01)
NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE
12.44 15.88 11.47 11.23
8.27
9.04
8.15
8.35
8.53
12.44 16.06 11.51 11.57
8.28
9.08
8.17
8.39
8.66
12.43 16.20 11.51 11.81
8.30
9.16
8.19
8.50
8.71
12.45 16.41 11.53 12.02
8.31
9.28
8.21
8.63
8.76
12.44 16.67 11.55 12.23
8.33
9.51
8.24
8.80
8.82
12.45 16.87 11.58 12.42
8.34
9.77
8.28
8.99
8.87
PANEL C: DIFFERENCES IN MEAN DOLLAR EFFECTIVE SPREAD ESTIMATES ($0.01)
NASDAQ NASDAQ NASDAQ NASDAQ NASDAQ NYSE
NYSE
NYSE
NYSE
NYSE
2.82
4.44
4.41
2.96
0.90
2.85
4.51
4.55
3.28
0.91
2.90
4.61
4.69
3.51
0.97
2.91
4.67
4.88
3.71
1.08
2.90
4.80
5.12
3.90
1.27
2.89
4.95
5.28
4.09
1.48
NASDAQ NYSE
20.18
20.27
20.21
20.13
20.02
0.11
Notes: 1. Bold indicates that the t-test of the cross-sectional mean differences are equal to zero is significant at 1% level.
2. Italics indicates that the t-test of the cross-sectional mean differences are equal to zero is significant at 5–10% level.
This table reports the outside ratios and the estimates of dollar effective spreads for four NASDAQ groups and their NYSE matched
counterparts. The results for the NASDAQ stocks are computed using the TAQ database for 1993–98 and the Nastraq database for 1999. The
results for the NYSE stocks are computed using the TAQ database for 1993–99. The investigation periods are the first week of trading in July
of the various years. Numbers in bold represent the optimal delay for each group in each year.
difference is between 0.16 and 0.40 cents or 1% to 2%.
Although this difference is statistically significant, is not
economically meaningful. The findings imply that
empirical researchers can employ the simple algorithm
to estimate effective spreads during our sample period
without incurring economically significant bias.
Moreover, we show that trade execution time has
value in estimating effective spreads. We also find that
the sensitivity of effective spreads is increasing over time
for both NYSE and NASDAQ stocks. This effect is
stronger for NASDAQ stocks, which is not surprising
given the dramatic increase in electronic order execution
over the sample period. Finally, we urge caution for
researchers in interpreting our results. Our study should
not be viewed as a universal rule in measuring and
studying execution costs. The optimal algorithm in our
study is developed based on a specific sample and
investigation period, and the results are both stock and
time sensitive.
The proliferation of electronic trading venues over the
past few years has led to significant changes in the speed
of order interaction and execution, as well as the
dissemination of pre-trade and post-trade information
to market participants. Many of them are continuing to
improve the quality of the many services that our
securities markets provide. New methods must be
developed to study and evaluate them appropriately.
Our study highlights the difference between electronic
markets and traditional exchanges and the impact of
such a difference on estimating market quality over a
particularly interesting and important period of time in
the development of equity market structure.
Electronic Markets Vol. 16 No 2
ACKNOWLEDGEMENTS
This research was started while both authors were faculty
members at Iowa State University. We thank Cynthia
Campbell, Rick Carter, Arnold Cowan, Rick Dark,
Ananth Madhavan, Tim McCormick, Elizabeth
Odders-White, Mark Peterson, Jeffrey Smith, James
Weston, Kumar Venkataraman, and participants of
seminars at Iowa State, the 2002 FMA, and the 2002
EFMA. Any errors are entirely the authors’ own.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
Notes
1. Effective spread is defined as the signed (positive for buyerinitiated order and negative for seller-initiated order) difference
between trade price and bid-ask midpoint.
2. A study ‘Report on the Comparison of Order Executions
Across Equity Market Structures’ by the US Securities and
Exchange Commission (SEC) used effective spreads to study
execution quality of retail orders on NYSE and NASDAQ. A
more recent study by the US Government Accountability
Office (GAO) has used effective spreads to investigate trading
cost for retail and institutional investors since the
implementation of decimal pricing in 2001. Beginning June
2001, Securities Exchange Act Rule 11Ac1-5 (recently
amended as Securities Exchange Act Regulation NMS Rule
605) requires all equity market centres to publish their effective
spreads along with other measures of execution quality.
3. Bessembinder (1997) uses a 20-second algorithm in the
1994 transaction-level data to examine the trading cost on
NASDAQ. Blume and Goldstein (1997) report a median delay
of 16 seconds between trade execution and reporting. Weston
(2000) employs a 10-second algorithm in 1996–97 transaction
level data to investigate the impact of market reforms on
NASDAQ market liquidity. Barclay et al. (2003) use a 2second algorithm when matching trades to quotes in more
recent NASDAQ data.
4. Lee and Ready caution that the 5-second algorithm is
sample period-specific, with a different pattern found when
they used the NYSE data from late 1987. Hasbrouck et al.
(1993) report that the median trade report delay in the
Consolidated Trade System on the NYSE was 14 seconds in
1990. Studies, such as Bessembinder (1997), Huang and Stoll
(1996), Weston (2000) among others, use the Lee and Ready’s
5-second rule.
5. The most widely used transaction level databases for
academic research are TAQ (for NYSE, AMEX, and NASDAQ
stocks beginning in 1993).44 Nastraq provides trades and
quotes for NASDAQ stocks beginning in 1999.
6. During our sample period of July 1999, the ten largest
NASDAQ stocks have an average of 20,000 trades and 4,000
quote updates per day, which translates into trade occurring
every 1 second and quotes being updated every 5 seconds.
Under such conditions, a mismatch of trades and quotes could
lead to a bias equal to one tick ($1/16 or 6.25 cents) in
effective spread estimates. This potential bias is large and
economically significant when compared to the estimated
127
effective spread published by the SEC (2001), which reports
that the average effective spreads of retail order flows for
frequently traded stocks and small-cap stocks on the US equity
market are about 8 cents and 15 cents, respectively.
7. Chang et al. (2000) report that the average time of quote
duration was almost 60 minutes for the FTSE stocks on the
LSE, and that quotes on the London Stock Exchange (LSE)
were only revised 5 to 10 times a day on average during the
1995–96 period and as a result, using a 5-second, a 15-second,
or even a 5-minute algorithm would probably make little
difference in estimating effective spreads on the LSE.
8. The January 2001 issue of the NYSE newsletter ‘The
Exchange’ reported that the NYSE had doubled its system
processing capacity since 1995. During the year 2000,
messages per second, or ‘MPS’ (the number of orders, reports,
cancellations and other messages that the NYSE receives each
second) reached 578, compared to about 250 in 1995.
9. As a comparison, Ellis et al. (2000b) find the median delay
between trades and quotes was 14 seconds for NASDAQ
stocks using 1996–97 data.
10. In the early 1990s, trades originating on the NYSE floor
were reported by specialist clerks who entered the trade
information using computer keyboards.
11. During the stock market crash in October 1989, for
example, it was documented that the extremely active trading
caused delays in both trade reporting and quote updating.
12. Before March 1996, the time stamps for NASDAQ issues
in TAQ originated from the NYSE’s Information Generation
System (IGS). During March 1996 to October 1996, the time
stamps for NASDAQ issues in TAQ came from the SIACoperated Consolidated Quote System (CQS) and the
Consolidated Trade System (CTS). The accuracy of NASDAQ
trade and quote time stamps during the transition period from
1993 through 1997 might have been affected by changes in
data sources. Schultz (2000) reports that existing matching
algorithms worked poorly and led to severe bias in estimating
effective spreads for NASDAQ stocks when using the TAQ
database for 1995 and 1996. We suspect that the nonsynchronization between trade and quote time stamps during
the transition period might partly cause this problem.
13. NASDAQ market makers executed around 65% of total
NASDAQ dollar volume, 64% share volume, and 71% trades
for our sample stocks in the second week of July 1999.
14. In private conversations with NASDAQ market makers, we
learned that market makers often execute orders up to 3,000
shares in their automated proprietary execution systems.
15. There were two less frequently used electronic trading
systems on NASDAQ: the Advanced Computerized Execution
System (ACES) and the Computer Assisted Execution System
(CAES). ACES was used by market makers to execute order
flow from order entry firms. CAES linked the third market and
the Intermarket Trading System (ITS) and automatically
executed market orders against third market makers who used
the CQS service to disseminate quotes for the NYSE and Amex
issues.
16. In 2000, the SOES became SuperSOES, and the share
limit increased to 99,999.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
128
Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates
17. See Harris and Schultz (1997, 1998). After SuperSOES
and SuperMontage, this has changed.
18. Smith (2000) reports that 70% of SelectNet volume in
1998 was due to interdealer trading. NASDAQ does not have
SelectNet anymore on SuperMontage.
19. In our sample, over 92% trades in Nastraq contain both
trade report times and trade execution times.
20. In fact, Bacidore et al. (1999) point out that other time
stamps involved in the execution process for a typical NYSE
market order, such as order enter time and order display time,
might also be the appropriate time stamp to use in certain
situations.
21. See Christie and Schultz (1994), and Christie et al.
(1994), Chung and Van Ness (2001), Schultz (2000),
Weston (2000) among others.
22. The outside ratio has been used in Bessembinder (2003)
and Schultz (2000) and other studies in assessing the market
execution quality on the NYSE and NASDAQ.
23. Order flow preferencing was widely practiced on
NASDAQ, especially for small-size retail order flows in our
sample period. Huang and Stoll (1996) point out that all
orders for NASDAQ stocks were preferenced. According to the
NASD rules for preferenced order flows, NASDAQ market
makers were required to match market best bid or ask in
executing any preferenced order flows regardless of their order
sizes.
24. Three basic trade classification rules are widely used in
academic research: trade rule, quote rule, and hybrid rules. The
tick rule classifies a trade as a buy if the most recent price
change is an uptick and a sell if the most recent price change is
a downtick. Trades occurring above the prevailing quote
midpoint are classified as buys in the quote rule, trades
occurring below the midpoint are classified as sells, and trades
occurring at the midpoint are unclassified. Lee and Ready
(1991) introduce a hybrid rule: trades occurring above or
below the prevailing quote midpoint are classified using the
quote rule and trades occurring at the midpoint are classified
using the tick test. Ellis et al. (2000b) propose an alternative
hybrid rule: trades occurring at the bid or ask are classified
using the quote rule and all other trades are classified using the
tick test.
25. Bertin et al. (2004) also use the NYSE TORQ data to
compare trade classification algorithms.
26. When we started the project on November 2000, 5–11
July 1999 was the only Nastraq data we had.
27. We exclude foreign stocks, REITs, closed end funds, and
unit shares. This procedure yields 4,401 stocks with 3,489
NASDAQ NNM (NASDAQ National Market) stocks and 912
NASDAQ SmallCap stocks. We then exclude stocks if they ever
have less than 20 trades per day or their transaction prices are
less than $5 during our sample periods. After these filters,
1,252 stocks (1,209 NASDAQ NNM stocks and 43 NASDAQ
SmallCap stocks) remain. We also require each of our
NASDAQ sample stocks have at least a 12-month trading
history as of June 1999 and delete all stocks that are IPOs in
the last 12 months. We do this because studies have shown that
return volatility and trading activity during the first few months
after the IPOs are high and unstable. See Ellis et al. (2000a, b)
and SEC (2001).
28. The largest stock in this group is Microsoft Corporation
with a market cap of about $441 billion as of 30 July 1999,
while the smallest in this group is Yahoo! with a market cap of
about $27 billion.
29. Within each market cap category, we select the first 30
stocks with rankings including the number ‘3,’ such as the 3rd,
the 13th, and so on and so forth.
30. We have a slightly larger number of stocks, 34, in the
micro group than the other three groups. This is the total
number of NASDAQ Small Cap stocks that have been passed
our filters. Company names and ticker symbols for each stock
in our sample are available from the authors upon request.
31. The variable Turnover directly comes from the CRSP data.
It is defined as a ratio of the daily share trading volume to the
total outstanding shares.
32. We start with the stock with a larger capitalization.
33. Detailed descriptions of each NASDAQ stock and its
NYSE matched counterpart, as well as summary statistics of
matching variables for the four sub-groups, are available from
the authors upon request.
34. See Bessembinder and Kaufman (1997), Huang and Stoll
(1996), Venkataraman (2001), Weston (2000) and SEC
(2001).
35. We exclude the following trades and quotes: trades that
happen outside of the normal trading hours (9:30 a.m. to 4:00
p.m.); trades that are coded out of time sequence, or coded as
non-standard settlement; trades with price changes over 10%
from previous trade prices; trades that are reported late; trades
with sizes larger than 1,000 shares; quotes outside of normal
trading hours (9:30 a.m. to 4:00 p.m.); quotes if the spreads
are greater than $5 or greater than 10% of quote midpoints;
quotes if ‘locked’ (spread5$0) or ‘crossed’ (spread,$0) the
market; bid (ask) quotes with changes over 10% from previous
bid (ask).
36. These results are available upon request.
37. A separate issue is whether order submission time and/or
order display time would improve effective spread estimates.
Unfortunately, without NASDAQ order data, we cannot test
this hypothesis.
38. The results for delays longer than 5 seconds are stronger,
and can be inferred from Figure 1 Panel B.
39. We drop the NASDAQ ‘Micro’ group because the trade
and quote data for most of the stocks in the group are not
available back to 1993.
40. The results for trades with 500 shares or less are not
reported in the paper, but they are available from the authors.
41. Ellis et al. (2000b), Finucane (2000), Odders-White
(2000) and Werner (2002).
42. The success rate for the new rule is 81.9% versus 81.0% for
the Lee and Ready rule.
43. We choose the second week of June 2000 to match up
with the SEC (2001) study, which uses 5–11 June data to
study and compare the trading cost between the NYSE and
NASDAQ.
Electronic Markets Vol. 16 No 2
44. The results for relative effective spreads, defined as the
dollar effective spread divided by the quote midpoint, are
similar to the results reported above.
Downloaded By: [Schmelich, Volker] At: 11:32 24 March 2010
References
Bacidore, J., Ross, K. and Sofianos, G. (1999) ‘Quantifying
Best Execution at the New York Stock Exchange: Market
Orders’, NYSE working paper, 99–05.
Barclay, M., Hendershott, T. and McCormick, T. (2003)
‘Competition Among Trading Venues: Information and
Trading on Electronic Communications Networks’, Journal
of Finance 58: 2637–65.
Bennett, P. and Wei, L. (2006) ‘Market Structure,
Fragmentation, and Market Quality’, Journal of Financial
Markets 9(1): 49–78.
Bertin, W., Michayluk, D. and Prather, L. (2004) ‘Updating
Traditional Trade Direction Algorithms with Liquidity
Motivation), working paper, University of Technology
Sydney.
Bessembinder, H. (1997) ‘The Degree of Price Resolution and
Equity Trading Costs’, Journal Of Financial Economics 45:
9–34.
Bessembinder, H. (1999) ‘Trade Execution Costs on NASDAQ
and the NYSE: A Post-Reform Comparison’, Journal of
Financial and Quantitative Analysis 34: 387–408.
Bessembinder, H. (2003) ‘Issues in Assessing Trade Execution
Costs’, Journal of Financial Markets 6: 233–57.
Bessembinder, H. and Kaufman, H. M. (1997) ‘A CrossExchange Comparison of Execution Costs and Information
Flow for NYSE-listed Stocks’, Journal of Financial
Economics 46: 293–319.
Blume, M. E. and Goldstein, M. A. (1997) ‘Quotes, Order
Flow, and Price Discovery’, Journal of Finance 52: 221–44.
Chang, R. P., Liu, C. and Rhee, S. G. (2000) ‘Is the London
Market Competitive? A Study of Trading Behavior of
London Market Makers’, working paper, University of
Hawaii.
Christie, W. G. and Schultz, P. H. (1994) ‘Why Do NASDAQ
Market Makers Avoid Odd-Eighth Quotes?’, Journal of
Finance 49: 1813–40.
Christie, W. G., Harris, J. H. and Schultz, P. H. (1994) ‘Why
Did NASDAQ Market Makers Stop Avoiding Odd-Eighth
Quotes?’, Journal of Finance 49: 1841–60.
Chung, K. and Van Ness, R. (2001) ‘Order Handling Rules,
Tick Size, and the Intraday Pattern of Bid-ask Spread for
NASDAQ Stocks’, Journal of Financial Markets 4: 143–61.
Ellis, K., Michaely, R. and O’Hara, M. (2000a) ‘When the
Underwriter is the Market Maker: An Examination of
Trading in the IPO Aftermarket’, Journal of Finance 55:
1039–74.
Ellis, K., Michaely, R. and O’Hara, M. (2000b) ‘The Accuracy
of Trade Classification Rules: Evidence from NASDAQ’,
Journal of Financial and Quantitative Analysis 35: 529–51.
Finucane, T. (2000) ‘A Direct Test of Methods for Inferring
Trade Direction from Intra-day Data’, Journal of Financial
and Quantitative Analysis 35: 553–76.
129
Harris, J. H. and Schultz, P. H. (1997) ‘The Importance of
Firm Quotes and Rapid Executions: Evidence from the
January 1994 SOES Rules Change’, Journal of Financial
Economics 45: 135–66.
Harris, J. H. and Schultz, P. H. (1998) ‘The Trading Profits of
SOES Bandits’, Journal of Financial Economics 50: 39–62.
Hasbrouck, J., Sofianos, G. and Sosebee, D. (1993) ‘New York
Stock Exchange Systems and Trading Procedures’, NYSE
working paper, 93–01.
Hendershott, T. and Jones, C. (2005) ‘Island Goes Dark:
Transparency, Fragmentation, and Regulation’, Review of
Financial Studies 18: 743–93.
Huang, R. D. and Stoll, H. R. (1996) ‘Dealer Versus Auction
Markets’, Journal of Financial Economics 41: 313–57.
Huang, R. D. and Stoll, H. R. (1997) ‘The Components of the
Bid-ask Spread: A General Approach’, Review of Financial
Studies 10: 995–1034.
Lee, C. and Radhakrishna, B. (2000) ‘Inferring Investor
Behavior: Evidence from TORQ Data’, Journal of
Financial Markets 3: 83–111.
Lee, C. and Ready, M. (1991) ‘Inferring Trade Direction from
Intra-day Data’, Journal of Finance 46: 733–46.
Madhavan, A., Ming, K., Straser, V. and Wang, Y. (2003)
‘How Effective Are Effective Spreads? An Evaluation of
Trade Side Classification Algorithms’, working paper, ITG
Inc.
Moulton, P. and Wei, L. (2005) ‘A Tale of Two Time Zones,
Cross-Listed Stock Liquidity and the Availability of
Substitutes’, working paper, New York Stock Exchange.
Odders-White, E. (2000) ‘On the Occurrence and
Consequences of Inaccurate Trade Classification’, Journal
of Financial Markets 3: 259–86.
Peterson, M. and Sirri, E. (2003) ‘Evaluation of the Biases in
Execution Cost Estimation Using Trade and Quote Data’,
Journal of Financial Markets 6: 259–80.
Schultz, P. (2000) ‘Regulatory and Legal Pressures and the
Costs of NASDAQ Trading’, Review of Financial Studies
13: 917–57.
Smith, J. (2000) ‘The Role of Quotes in Attracting Orders on
the NASDAQ Interdealer Market’, working paper,
NASDAQ.
SEC (US Securities and Exchange Commission) (2001)
‘Report on the Comparison of Order Executions Across
Equity Market Structures’.
Venkataraman, K. (2001) ‘Automated Versus Floor Trading:
An Analysis of Execution Costs on the Paris and the New
York Exchanges’, Journal of Finance 56: 1445–85.
Vergote, O. (2005) ‘How to Match Trades and Quotes for
NYSE Stocks?’, working paper, Katholeike Universiteit
Leuven.
Weston, J. P. (2000) ‘Competition on the NASDAQ and the
Impact of Recent Market Reforms’, Journal of Finance 55:
2565–98.
Werner, I. (2002) ‘NYSE Order Flow, Spread, and
Information’, working paper, Ohio State University.