The Sensitivity of Effective Spread Estimates to Trade Quote Matching Algorithms

Transcription

1 SPECIAL SECTION: FINANCIAL MARKET ENGINEERING The Sensitivity of Effective Spread Estimates to Trade Quote Matching Algorithms MICHAEL S. PIWOWAR AND LI WEI 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 Although the Lee and Ready 5- second 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 A 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 5- second 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 (piwowarm@sec.gov) 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 (lwei@nyse.com) 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. Copyright ß 2006 Electronic Markets Volume 16 (2): DOI: /

2 Electronic Markets Vol. 16 No 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 In contrast, the difference was only 0.52 cents or 2% in 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 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

3 114 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

4 Electronic Markets Vol. 16 No our conclusions. We compute the dollar and relative effective spread as: Dollar Effective Spread52*I * (Trade Price Midpoint of Ask and Bid) Relative Effective Spread5Dollar Effective Spread/Quote Midpoint 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 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 2- second 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 quotes would provide a satisfying accuracy in estimating effective spreads. This leads to our second hypothesis: Hypothesis 2: 0-second algorithm5optimal algorithm for NASDAQ stocks 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 10- second, 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

5 116 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 Optimal 5Effective Spread NASDAQ Effective Spread NYSE Diff 5-second 5Effective Spread NASDAQ Effective Spread NYSE 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. 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 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. Very Large: $25 billion+ market capitalization; 2. Large: $1 25 billion market capitalization; 3. Medium: $250 million $1 billion market capitalization; and 4. Small: $ 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 We measure the following equally weighted absolute percentage deviation for each of the NYSE stocks (s5volatility, h5turnover, N5NYSE, T5NASDAQ): Deviation~ 1{ Mcap N MCap T z 1{ Price N Price T z 1{ s N s T z 1{ h N h T 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) 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.

6 Electronic Markets Vol. 16 No Table 1. Sample statistics Sample characteristics Group 1 Very large Group 2 Large Group 3 Medium Group 4 Small Group 5 Micro Sample size (# of stocks) Market capitalization ($ million) 133, , Average daily closing price ($) Daily volatility 3.70% 4.90% 4.60% 5.50% 8.90% Daily number of trades Small-size trades 18, , Medium-/large-size trades 1, Daily share volume (1,000 shares) Small-size trades 7, Medium-/large-size trades 7, Trade size (shares) Mean Median Quoted spread (cents) Quoted relative spread (bps) Quoted depth (shares) 2, , Quote duration (seconds) 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 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 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 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 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

7 118 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 NYSE Delay (seconds) Outside ratio (%) Price IMPVT ratio (%) Dollar effective spread (cents) Relative effective spread (bps) Outside ratio (%) Price IMPVT ratio (%) Dollar effective spread (cents) Relative effective spread (bps) Delay (seconds) Outside ratio (%) Price IMPVT ratio (%) NASDAQ Dollar effective spread (cents) PANEL B: 1999 Relative effective spread (bps) Outside ratio (%) Price IMPVT ratio (%) NYSE Dollar effective spread (cents) Relative effective spread (bps) 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 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.

8 Electronic Markets Vol. 16 No 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 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.

9 120 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 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

10 Electronic Markets Vol. 16 No 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 PANEL B: TRADE CATEGORIES Percent of Trades Executed Group N Outside of quotes (%) At bid or ask (%) Inside of quotes (5) Very large Large Medium Small Micro 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 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 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

11 122 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 PANEL B: TEST OF EQUALITY OF MEANS Difference of Dollar Effective Spread ($0.01) 0-Second Optimal 5-Second Optimal 10-Second Optimal Group N 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. Difference (p-value) Difference (p-value) Difference (p-value) Very large (0.00) 0.49 (0.02) 1.57 (0.01) Large (0.00) 0.88 (0.00) 1.95 (0.00) Medium (0.00) 1.01 (0.00) 1.53 (0.00) Small (0.01) 0.82 (0.00) 1.31 (0.00) Micro (0.00) 0.66 (0.00) 1.20 (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 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 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 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.

12 Electronic Markets Vol. 16 No 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) (T2) (T2 T1) Group N Report time Execution time Difference (p-value) Very large (0.00) Large (0.00) Medium (0.40) Small (0.14) Micro (0.01) PANEL B: PERCENT OF TRADES EXECUTED OUTSIDE OF THE QUOTES (%) Group Robustness checks N Nastraq Time Stamp 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 (T1) (T2) (T2 T1) Report time (%) Execution time (%) Difference (%) (p-value) Very large (0.00) Large (0.00) Medium (0.04) Small (0.04) Micro (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 p- values. The investigation period is 5 11 July (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

13 124 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 (0.08) Large (0.31) Medium (0.46) Small (0.61) Micro (0.36) PANEL B: PERCENT OF TRADES EXECUTED OUTSIDE OF THE QUOTES Outside ratio (%) Group N Optimal algorithm (seconds) 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 Slightly different reductions, about second, happen to less liquid groups. Second, the sensitivity of effective spread estimates to matching algorithm becomes stronger. For the most liquid group, Mean (TAQ - Nastraq) Nastraq TAQ Nastraq (%) TAQ (%) Difference (%) (p-value) Very large (0.00) Large (0.00) Medium (0.00) Small (0.00) Micro (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 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 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.

14 Electronic Markets Vol. 16 No Table 7. Estimates of effective spreads for NASDAQ groups and their matched NYSE samples Outside ratio (%) Dollar effective spreads ($0.01) Relative effective spreads (bps) GROUP DELAY NASDAQ NYSE NASDAQ NYSE Difference NASDAQ NYSE Difference Very large (n510) Large (n530) Medium (n530) Small (n534) 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 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 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

15 126 Michael S. Piwowar and Li Wei & The Sensitivity of Effective Spread Estimates Table results for the most liquid NASDAQ stocks (Group 1) and matched NYSE samples PANEL A: MEAN OUTSIDE RATIOS DELAY NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE PANEL B: MEAN DOLLAR EFFECTIVE SPREAD ESTIMATES ($0.01) NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE NASDAQ NYSE PANEL C: DIFFERENCES IN MEAN DOLLAR EFFECTIVE SPREAD ESTIMATES ($0.01) NASDAQ - NYSE NASDAQ - NYSE NASDAQ - NYSE NASDAQ - NYSE NASDAQ - NYSE NASDAQ - NYSE NASDAQ - NYSE 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 and the Nastraq database for The results for the NYSE stocks are computed using the TAQ database for 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.

16 Electronic Markets Vol. 16 No 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. 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 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 transaction level data to investigate the impact of market reforms on NASDAQ market liquidity. Barclay et al. (2003) use a 2- second 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 Hasbrouck et al. (1993) report that the median trade report delay in the Consolidated Trade System on the NYSE was 14 seconds in 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 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 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 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 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 As a comparison, Ellis et al. (2000b) find the median delay between trades and quotes was 14 seconds for NASDAQ stocks using 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 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 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.

17 128 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 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.

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