Trades outside the quotes: Reporting delay, trading option, or trade size?

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Journal of Financial Economics 79 (2006) 615–653

0304-405X/$

doi:10.1016/j

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Trades outside the quotes: Reporting delay,trading option, or trade size?$

Hans R. Stoll�, Christoph Schenzler

Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37203, USA

Received 8 July 2004; received in revised form 27 February 2005; accepted 9 March 2005

Available online 7 October 2005

Abstract

In the period 1993 through 2002 examined in this study, quoted and effective spreads declined

substantially on Nasdaq and to a lesser degree on the NYSE. At the same time, however, trades

outside the quotes increased dramatically on Nasdaq. Because investors would prefer to trade at the

quotes rather than outside the quotes, we examine why trades outside the quotes are observed. We

focus on how the continuous market mechanism itself influences the outcome of orders and the

reporting of trades, and we conclude that slippage exists in the market mechanism. Outside-trades

occur on Nasdaq, first, because of delays in reporting trades, second, because the ability of dealers to

delay execution of trades creates a look-back option, which when exercised results in outside-trades,

and third, because large trades can take place at prices outside the quotes. Outside-trades are rarely

observed on the NYSE because the market is more centralized. While the pattern of trading on the

NYSE is not inconsistent with the presence of a look-back option, our tests provide no direct

evidence that specialists are exercising such an option.

r 2005 Elsevier B.V. All rights reserved.

JEL classification: G14; G24

Keywords: Market structure; Trading costs; Look-back trading option

- see front matter r 2005 Elsevier B.V. All rights reserved.

.jfineco.2005.03.006

Stoll acknowledges research support from the Financial Markets Research Center and the Dean’s

ulty Research at the Owen Graduate School of Management. We gratefully acknowledge the helpful

an anonymous referee, of Kumar Venkataraman, and of seminar participants at Southern Methodist

niversity of Notre Dame, New York University, and Vanderbilt University.

nding author. Tel.: +1615 322 3674; fax: +1 615 343 7177.

dress: [email protected] (H.R. Stoll).

www.elsevier.com/locate/jfec

ARTICLE IN PRESSH.R. Stoll, C. Schenzler / Journal of Financial Economics 79 (2006) 615–653616

1. Introduction

Microstructure theories identify several factors that influence trading costs: theinventory risk incurred by the dealer who supplies liquidity, the expected loss to informedtraders, the out-of-pocket costs of handling and clearing trades, and the monopoly rentsthat a dealer might be able to extract.1 The theories typically assume that the marketmechanism works flawlessly: that quotes are updated quickly, that orders are handledimmediately, and that trades are reported without delay. However, the market mechanismmight not work flawlessly. Quotes might be updated slowly, orders perhaps are nothandled immediately, and trades might be reported with delay. The way in which themarket mechanism operates can affect trading costs because the information traders haveand the speed with which they trade are affected.We examine a relatively neglected issue: how the operation of the market mechanism

influences the outcome of orders and the reporting of trades. We analyze publicly availabledata on quotes and trade prices to make inferences about the nature and quality of theunderlying market mechanism that produces the observed data. The fact that tradesfrequently take place outside the quotes suggests slippage in the market mechanism, forevery investor would prefer to trade at the quote rather than outside the quote. To put itanother way, consider an investor who places a market order to buy five hundred shares ofa stock at the ask price of $20. Two minutes later he is notified that he bought at $20.03and that the current ask is $19.98. He wonders why he did not buy at $20, or even $19.98.There appears to be slippage in the system. We investigate the sources of this slippage.The focus of this paper is on the sources of trades outside the quotes, i.e. outside-trades.

On the one hand, outside-trades could be random occurrences unrelated to the marketmechanism. On the other hand, they could result from slippage in the market mechanism.We investigate three features of the market mechanism that are potential sources of tradesoutside the quotes. First, outside-trades could be a reporting phenomenon arising from theinaccurate time alignment of trades and quotes. Second, outside-trades could reflect theability of dealers to exploit a trading option by delaying execution of incoming marketorders. We describe this option, which we term the look-back trading option, and developan empirical test to determine if it is present. We find evidence that there is a look-backoption and that the exercise of this option causes outside-trades to be observed. Third,outside-trades could reflect the execution of large trades outside the quotes. We findevidence that this is the case. In summary, we conclude that the observed outside-trades aremore than a reporting phenomenon. The difference between Nasdaq, where outside-tradesare observed, and the NYSE, where outside-trades are infrequent, reflects the difference inmarket structures. On Nasdaq each dealer operates as a separate market center. On theother hand, trading is centralized and trade-throughs are prohibited by rule on the NYSE.Hence outside-trades are rarely observed on the NYSE. But we cannot ignore thepossibility that a look-back trading option exists for the NYSE specialist that isunobservable in public data.Prior research has examined the mechanism for opening or closing a market, but little

research deals with slippage in the continuous trading mechanism, which is the focus of

1The inventory model is developed in Stoll (1978a), the adverse selection model, in Glosten and Milgrom (1985).

Early empirical evidence on the sources of spreads is in Tinic (1972) and Stoll (1978b). Alternative measures of

trading costs are compared in Stoll (2000).

ARTICLE IN PRESSH.R. Stoll, C. Schenzler / Journal of Financial Economics 79 (2006) 615–653 617

this paper. Amihud andMendelson (1987) and Stoll and Whaley (1990) examine the openingmechanism and show that there is more volatility than at other times. The closingmechanism is studied by Stoll and Whaley (1987), Harris (1989), Cushing and Madhavan(2000), and others. An extensive literature exists on dealer versus auction marketmechanisms, but that literature assumes that the two systems, while different, are workingwithout slippage, (see, e.g., Madhavan, 1992; Christie and Schultz, 1994; Huang and Stoll,1996). Similarly, trading via the limit order book has been examined by Biais, et al. (1995) onthe assumption the book is operating smoothly. The work of Copeland and Galai (1983)may be viewed as an analysis of an imperfect market mechanism in which the inability toadjust quickly limit prices creates a free trading option. In this study, we posit a new tradingoption, the look-back trading option, which exists because of flexibility given to dealers bythe market mechanism. Our work is related to Ready (1999), who shows how the delay intrading when the specialist attempts to improve prices gives the specialist valuable discretion.Other relevant prior research deals with empirical issues in measuring market quality. Recentpapers on this subject include Bessembinder (2003) and Bacidore et al. (2003).

In Section 2 of this study we describe the trend in market quality over the period January1, 1993 to December 31, 2001, as measured by the quoted half-spread and the effectivehalf-spread. The quoted half-spread is half the difference between the ask and bid price.The effective half-spread is the absolute difference between the trade price and the quotemidpoint. If a trade takes place inside the spread (that is, the price is improved), theeffective half-spread is less than the quoted half-spread. We find that market quality asmeasured by the quoted and effective spreads improved significantly in the nine-yearperiod from 1993 to 2001. The improvement has been particularly dramatic on Nasdaqwhere spreads fell by more than 80%. At the same time as spreads fell, the relation betweenthe quoted and effective spreads changed dramatically on Nasdaq. As quoted spreadsdeclined on Nasdaq, effective spreads began to exceed quoted spreads, particularly forlarge actively traded stocks, so much so that by 1999 the average daily effective spreadalmost always exceeds the average daily quoted spread. No such trend is observed forNYSE stocks, even though NYSE spreads, for the most part, are smaller than Nasdaqspreads.

In Section 3, we discuss in detail two potential sources of outside-trades: delayed trade-reporting and the look-back trading option. In Section 4, we provide evidence on tradingdelays and the look-back option. The analysis in Sections 2–4 is based on Trade and Quote(TAQ) data. Section 5 considers Nastraq data, which contain the execution time as well asthe report time of trades. These data allow a clearer test of the reporting delay hypothesis.In addition, Nastraq data permit an analysis of outside-trades in SelectNet and the SmallOrder Execution System (SOES), two electronic trading systems on Nasdaq. We findevidence of outside-trades based on execution times. In Section 6, we provide an estimateof the value of the look-back option based on the volatility of quotes in a 30-s interval. Weconclude that the option is valuable primarily for the highest volume stocks. In Section 7we find that Nasdaq outside-trades are most frequent in the case of large trades, yet theyare frequent as well for the smallest trade sizes. In Section 8, we analyze the trend in theRoll implied spread. This measure, which does not depend as much on the propersequencing of trades and quotes, tracks the effective spread more closely than the quotedspread. This result implies that effective spreads and the associated outside-trades moreaccurately reflect trading costs than does the quoted spread. Conclusions and implicationsare presented in Section 9.


This study bears on current policy issues. The Securities and Exchange Commission(SEC) has proposed that the trade-through rule, which currently applies to exchange-listedstocks, be modified and be applied to Nasdaq stocks (see U.S. Securities and ExchangeCommission, 2004). The modified rule would allow investors to trade through slow manualmarkets by an amount to be established by rule. An alternative approach would be toeliminate the trade-through rule altogether and encourage improvements in the marketmechanism. In a well-functioning market mechanism, investors’ self-interest and brokers’best execution obligations limit the frequency and magnitude of trade-throughs.

2. The trend in quoted and effective spreads

In this section we measure the market quality of Nasdaq and the NYSE as reflected inthe quoted and effective spreads. Spreads in the post-1993 period have declineddramatically as a result of regulatory action and technological improvements, while, atthe same time, the relation between the quoted and effective spreads has changed onNasdaq.

2.1. Quoted and effective spreads

Data to measure the trend in quoted and effective spreads are from the TAQ databasecompiled by the NYSE. For each stock-day, the average quoted half-spread and theaverage effective half-spread are calculated. The quoted half-spread, S, is defined as

S ¼A� B

2, (1)

where A is the lowest ask price and B is the highest bid price. We often simply refer to thequoted half-spread as the quoted spread. On the NYSE, the best quote could be that of alimit order or of the specialist. We do not include quotes disseminated by other markets.On Nasdaq, the best quote is constructed from the highest bid and lowest ask displayed bythe market makers in the stock. The SEC’s order handling rules, implemented in January1997, require market makers to display customer limit orders, with the consequence that inrecent years Nasdaq quotes also could represent public limit orders. Evidence on the effectof the order handling rules is in Barclay et al. (1999).The effective half-spread, E, is the absolute difference between the trade price and the

quote midpoint prior to the trade:

E ¼ jP�Mj, (2)

where P is the trade price and M ¼ ðAþ BÞ=2. We often refer to the effective half-spreadas the effective spread. For NYSE stocks, trades (unlike quotes) are those taking place onany exchange. We have followed the five-second rule recommended by Lee and Ready(1991), which is to link a trade to the quote with a recorded time five or more secondspreceding the recorded time of the trade.2 A number of recent papers examine this rule aswell as the related question of how to identify whether the buyer or seller was the activeparty. See Ellis et al. (2000), Finucane (2000), Lee and Radhakrishna (2000), Odders-White(2000), and Bessembinder (2003). Except for the opening trade for which there might not

2Later in this article, when analyzing more recent data for 1997 to 2002, we do not apply the five-second rule.


be a prior quote, the number of quotes is equal to the number of trades. The daily averagequoted and effective spreads are then averages of the quoted and effective spreadsassociated with each of these trades. In effect, we calculate average spreads weighted by thenumber of trades at each spread.

2.2. Trend in Microsoft versus IBM

To illustrate the trend in quoted and effective spreads, first consider Microsoft, a largeNasdaq stock, and IBM, a large NYSE stock. The trends in Microsoft’s average dailyquoted and effective half-spreads, plotted in Fig. 1, are dramatic. In the first three monthsof 1993, the quoted half-spread of Microsoft averages 16.8 cents. By the end of 2001, thequoted half-spread averages less than 1 cent. The effective half-spread also declined, butnot as much (from an average of 12.5 cents in the first three months of 1993 to an averageof 1.7 cents at the end of 2001). At the beginning of the nine year period, the averagequoted spread always exceeds the average effective spread; at the end of the period, theaverage quoted spread never exceeds the average effective spread.

There are roughly four steps in the decline of Microsoft’s quoted spreads between 1993and 2001. The first is the dramatic decline following a meeting of Nasdaq market makerson May 24, 1994 described in Christie et al. (1994). The quoted half-spread dropped bymore than half from more than 15 cents to about 7.5 cents. It remained at 7.5 cents untilJanuary 1997. The second step occurred in 1997. On January 20, 1997, the SEC’s orderhandling reforms were implemented. These rules, described in greater detail in Barclay etal. (1999), require limit orders and electronic communication network (ECN) quotes to bedisplayed and reduce the minimum quote size from one thousand shares to one hundredshares. These changes apply to 50 phase-in stocks, of which Microsoft is one. Other stocks,

May 24, 1994meeting

Order handling rulesand 1/16ths

February 1998

Decimals

Quoted half-spreadEffective half-spread

Cen

ts

0

2

4

6

8

10

12

14

16

18

20

Time

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Fig. 1. Microsoft’s average daily quoted and effective half-spread, 1993–2002.


phased in later that spring, continued to have minimum depth of one thousand shares.A further change occurred on June 2, 1997 when the tick size was reduced to one-sixteenth.These regulatory changes in the first half of 1997 reduced the quoted half-spread to about 5cents by mid-1997. A third, less discernable, drop occurred in February 1998 when thequoted half-spread fell below 4 cents. The fourth event was the adoption of penny priceincrements (completed on April 9, 2001 for Nasdaq stocks), which further reduced quotedspreads. Studies that examine the effect of decimalization include Nasdaq EconomicResearch (2001) and Chung et al. (2004).The effective half-spread also dropped dramatically to about 6.3 cents subsequent to the

May 1994 meeting, but it recovered and began to exceed the quoted half-spread by July1995. Effective spreads were large and highly variable until March 1996. Schultz (2000)reports that delays in reporting transactions data to the Securities Industry AutomationCorporation (SIAC) are the source of the large effective spreads at that time. But evenafter the reporting problems were corrected, effective spreads continued to exceed quotedspreads. In 1997, effective spreads declined when quoted spreads declined but less so. Sincemid 1997, effective spreads in Microsoft have consistently exceeded quoted spreads.The relation of effective and quoted spreads is not the same for IBM. Fig. 2 plots quoted

and effective spreads for IBM. In the first three months of 1993, the quoted half-spread ofIBM averages 7.8 cents. By the end of 2001, the quoted half-spread averages slightly lessthan 4 cents. The main discernable changes evident in Fig. 2 are the decline in spreads withthe move to sixteenth price increments in June 1997 and with the introduction of pennyprice increments (completed by January 29, 2001 for NYSE stocks). The effect ofsixteenths is documented in Bollen and Whaley (1998), Goldstein and Kavajecz (2000), andJones and Lipson (2001). The effect of decimalization is analyzed in Bacidore et al. (2003),

Quoted half-spreadEffective half-spread

Cen

ts

0

2

4

6

8

10

12

14

16

18

20

Time

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Fig. 2. IBM’s average daily quoted and effective half-spread, 1993–2002.


and in Jennings (2001). The difference in time trends between IBM and Microsoft are twofold: First, spreads for IBM did not start as high and did not fall as far as Microsoft.Second, the quoted spread of IBM always exceeds the effective spread of IBM, whereasthis is not true for Microsoft.

2.3. A broader sample

Most prior studies (Lee, 1993; Huang and Stoll, 1996) find the effective spread to besubstantially less than the quoted spread, in contrast to our results for Microsoft. Thisfinding is taken as an indication that market orders are able to achieve price improvementrelative to the quotes, although the exact mechanism by which such price improvement isachieved is not always clear. Ready (1999) shows that price improvement can be a mixedblessing for a resting limit order as the market maker improves the price in some cases(taking the incoming trade) but not in others (leaving the trade to the resting limit order).

To determine if the changing relation of quoted and effective spreads is specific toMicrosoft, consider the quoted and effective spreads for a broader sample of 60 stocksfrom each market. The 60 stocks are chosen each January from the top 25% of stocksranked by number of trades. We focus on the more actively traded stocks because only ifquotes change and transactions occur can slippage in the market mechanism be analyzed.The procedure is as follows. A stock in the Center for Research in Security Prices (CRSP)database is eligible if it is a domestic ordinary common stock the price of which never fellbelow $10 in January. Stocks are then ranked by the total number of trades in January,and the top 25% in each market (NYSE and Nasdaq) are retained. These stocks aredivided into three equal groups, and from each group, the 20 most active stocks (in termsof number of trades) are retained for analysis. The three groups are labeled high, medium,and low volume. Although all stocks are from the 25% most active stocks, we findsubstantial differences across the three volume categories.

The quote and trade data are taken from the TAQ database. The period of analysis isJanuary 4, 1993 to December 31, 2001 (except October 28, 1997 when trade time stampswere recorded incorrectly for Nasdaq stocks). Our data set contains all normaltransactions executed in any market between 9:30 a.m. and 4 p.m. (Those marked witha special code in the COND field were excluded). Trades that are marked as reported lateand out of sequence are excluded, as are trades with special settlement conditions. (Theanalysis of Porter and Weaver, 1998, is based on those trades, coded ‘‘z,’’ that are reportedlate and out of sequence. We exclude such trades from our analysis.) For each trade wealso retain the quote associated with the trade. In the initial analysis of the TAQ data inTable 1, we follow Lee and Ready (1991) and associate with the trade the quote time-stamped at least five seconds before the trade. Only quotes from the primary market inwhich the stock trades are used.

Table 1 provides annual summary data for average quoted half-spreads, averageeffective half-spreads, and the percentage of stock-days in each year in which the averageeffective half-spread exceeds the average quoted half-spread. Again the results are striking.As in the case of Microsoft, average effective spreads decline on Nasdaq, but averagequoted spreads decline even more. By 1997, the average effective spread exceeds theaverage quoted spread in the high-volume stocks, and by 1999, medium-volume stocksexhibit the same behavior. Most striking is the percentage of stock-days for which thedaily average effective spread exceeds the daily average quoted spread. In the case of the

ARTICLE IN PRESS

Table 1

Quoted and effective half-spreads, 1993–2001

Average values in cents of quoted half-spread and effective half-spread by year, by market and by trading

volume category. % Eff4Quoted is percent of stock-days for which the average daily effective half-spread exceeds

the average daily quoted half-spread. Average stock price in dollars.

1993 1994 1995 1996 1997 1998 1999 2000 2001

High-volume Nasdaq stocks

Quoted 13.72 11.77 9.66 9.12 5.89 4.26 5.14 4.02 1.48

Effective 10.19 8.82 8.47 8.70 6.72 4.73 7.46 7.46 3.01

% Eff4quoted 0.39 0.68 20.49 26.12 55.99 79.37 96.03 99.62 99.82

Stock price 38.32 35.66 48.00 45.21 47.38 45.01 77.49 72.04 31.13

High-volume NYSE stocks

Quoted 8.03 7.74 7.56 7.73 6.61 5.71 6.45 7.49 2.99

Effective 5.97 5.73 5.78 5.87 4.99 3.97 4.79 5.32 2.36

% Eff4quoted 0.16 0.34 0.22 0.16 0.53 0.22 0.71 1.33 2.72

Stock price 43.63 42.35 44.92 48.54 59.18 60.70 66.85 71.92 42.56

Medium-volume Nasdaq stocks

Quoted 20.23 19.25 17.79 14.39 13.57 9.10 7.90 9.40 2.96

Effective 15.08 13.69 13.42 11.27 11.66 8.28 8.57 12.13 3.81

% Eff4quoted 0.46 0.02 2.80 5.81 9.96 15.02 67.90 96.22 99.23

Stock price 24.97 24.98 28.6 20.98 27.84 26.73 44.25 56.57 25.26

Medium-volume NYSE stocks

Quoted 9.40 8.43 8.55 8.54 7.36 6.52 6.59 8.35 3.18

Effective 6.06 5.67 5.94 5.99 5.28 4.55 4.45 5.71 2.43

% Eff4quoted 0.20 0.32 0.28 0.10 0.16 0.18 0.18 0.28 0.85

Stock price 47.02 36.20 46.31 43.36 55.27 44.60 44.23 56.74 49.65

Low-volume Nasdaq stocks

Quoted 23.96 21.51 18.13 21.15 13.52 10.17 9.44 7.81 4.18

Effective 17.47 14.99 13.23 16.56 11.22 9.10 9.38 9.16 5.07

% Eff4quoted 0.46 0.12 1.75 6.30 6.36 11.76 42.10 86.78 96.78

Stock price 22.35 18.28 23.64 28.02 23.73 21.88 29.78 28.86 29.97

Low-volume NYSE stocks

Quoted 9.24 8.82 8.56 8.53 7.99 6.4 6.74 6.38 3.66

Effective 5.88 5.92 6.00 5.86 5.67 4.42 4.42 4.23 3.58

% Eff4quoted 0.18 0.20 0.22 0.18 0.20 0.08 0.02 0.06 0.36

Stock price 35.08 34.04 39.54 36.35 55.81 42.26 44.78 40.12 47.13

H.R. Stoll, C. Schenzler / Journal of Financial Economics 79 (2006) 615–653622

high-volume Nasdaq stocks, this percentage steadily increases from less than 1% in 1993to 96% in 1999. In other words, on almost every day, the average effective spread for theday exceeds the average quoted spread for the day. Similar, albeit less pronounced, trendsare observable for the medium- and low-volume Nasdaq stocks. The 1999 percentages are67.9% and 42.1%, respectively, but by 2001, all Nasdaq stocks behaved in the same way.No such trend is observable for NYSE stocks. The percentage of days in which theeffective spread exceeds the quoted spread is always less than 1% for NYSE stocks, exceptfor the high-volume NYSE stocks in 2000 and 2001. On the NYSE, both quoted andeffective spreads have declined.The evidence in Fig. 1 and Table 1 confirms the well-known decline in Nasdaq spreads

and the tremendous improvement in market quality there. Less well known is the increase


in outside-trades evident in Fig. 1 and Table 1. The increase in outside-trades on Nasdaq ispuzzling, first because it implies that better prices are foregone by investors and secondbecause the phenomenon is observed only on Nasdaq, not at the NYSE.

3. Causes of outside-trades

Outside-trades could be random and unrelated to the market mechanism. Alternativelyoutside-trades could be systematically related to features of the market mechanism. Weconsider three features. First, an outside-trade could result from an imperfect tradereporting system. If trades are reported with delay, they could appear to be outside thequotes even though they are not. Second, an outside-trade could reflect the ability ofdealers to create a free trading option out of a market order. We call this option a look-back trading option because, in holding the market order, the dealer creates an option tolook back and choose the best price at which to trade the market order. Third, an outside-trade could reflect a trade size that exceeds the quoted depth of the dealer. If the marketmechanism makes it cumbersome to trade at superior quotes of other dealers beforeexecuting the trade with the dealer of choice, an outside-trade results. We consider thereporting delay and look-back option explanations in this section and describe theempirical tests used to infer their presence. The empirical evidence is presented in Sections4 and 5. An estimate of the cost to customers of the dealer look-back option is provided inSection 6. The relation between trade size and outside-trades is examined in Section 7.

3.1. Reporting delays

The effective spread is subject to greater error than the quoted spread because itsconstruction requires a comparison of a trade price and a quote, two numbers reported ondifferent systems. The quoted spread and its associated time stamp are generally consideredto be accurate because the quote updates are highly automated and because market makershave an incentive to report accurately as their quotes are required to be firm under the SEC’sfirm quote rule. However, trade reports could be delayed for several reasons.

First, trade reports must often be entered manually. In particular, the reportingprocedure in a fragmented dealer market such as Nasdaq could result in greater delaysthan in a centralized market such as the NYSE. Nasdaq dealers are required to reporttrades within 90 s, but a 90-s delay could cause significant misalignment of trades andquotes in an active market with rapidly changing quotes.3 Even if reporting is timely,trades of different dealers might be reported out of proper sequence. Delays in reportingare likely to vary with dealers’ volume of trading, which affects their capacity to reporttrades.4

3NASD Rule 5430(a)(1) states: ‘‘Registered Reporting Nasdaq Market Makers and Registered Reporting ADF

Market Makers shall, within 90 s after execution, transmit last sale reports of transactions in designated securities

executed during normal market hours. Transactions not reported within 90 s after execution shall be designated as

late and such trade reports must include the time of execution.’’ See: http://nasd.complinet.com/nasd/display/

display.html?rbid=1189&record_id=1159003711&highlight=market+makers.4SEC Regulation 11Ac1-5, implemented in 2001, requires market centers to report execution quality based on a

comparison of the trade price to the quote at time of order arrival. While this provides useful information, there is

no guarantee that there is no delay in reporting the time of order arrival just as there is in the time of order

execution.

http://nasd.complinet.com/nasd/display/display.html?rbid=1189&record_id=1159003711&highlight=market+makers




ARTICLE IN PRESS

At-1

uptA

dntA

tP

Fig. 3. Effect of delayed reporting of a trade that took place at the ask price at time t�1 but is reported at time t.

Whether the trade is above or below the ask at time t depends on whether the ask increased to Aupt or

decreased to Adnt .


Second, dealers could have an incentive to report certain trades late. For example, adealer perhaps does not want to reveal the occurrence of a large trade and thus delays inreporting it.5

Third, delays could also arise at the level of the securities information processor (SIP).Nasdaq’s SIP is Nasdaq, and the NYSE’s SIP is SIAC. Each SIP receives and time-stampsdata and disseminates the data to the public through vendors. Researchers use the datacreated by the SIP. Large volume of computer traffic can cause delays in the processingand dissemination of trades and quotes by the SIP. The time stamp placed by the SIP couldtherefore lag the actual trade reporting time of the dealer. However, such delays shouldaffect quotes and trades equally. Our data are the TAQ data provided by the NYSE. Thesedata come from SIAC and include Nasdaq data. The process of transmitting data fromNasdaq to SIAC could introduce additional delays, presumably in both quotes and trades.Schultz (2000) reports problems with SIAC in 1995–1996.Consider now the pattern of quotes and transaction prices across two points in time, t�1

and t. For simplicity assume all transactions take place at the quotes, but that reporting oftrades is delayed one unit of time. Consider a transaction that takes place at the ask priceat time t�1, At�1, but is not reported until time t. Denote the reported transaction price asPt. Then

Pt ¼ At�1. (3)

Whether this price is outside the ask price at time t depends on how the ask price changesbetween t�1 and t. The possibilities are illustrated in Fig. 3. If the ask increases to A

upt , the

transaction price is inside the spread, not outside (unless the quote increase is so dramaticthat the trade price is below the new bid price). If the ask decreases to Adn

t , the trade price isabove the ask and outside the spread. If the change in the ask price is independent of wherethe trade at time t�1 took place (ask or bid), one would expect an equal number of tradesinside and outside the new quotes at time t. We know that the ask tends to be adjustedupward after trades at the ask to reflect the information conveyed by the trade andinventory considerations (see, for example, Huang and Stoll, 1994). This correlation

5Porter and Weaver (1998) analyze Nasdaq trades in 1990 that are marked as being reported late (code ‘‘z’’ in

TAQ). They argue that dealers delay reporting trades in order to manage the information associated with the

trade. We exclude ‘‘z’’ trades, but dealers might delay within the 90 s reporting requirement for the reasons cited

by Porter and Weaver.


between quote changes and transactions implies that late reporting is more likely to resultin trades inside the quotes than outside the quotes.

A similar analysis holds for transactions that take place at the bid at time t�1 but arenot reported until time t. In that case,

Pt ¼ Bt�1. (4)

If the bid increases, the transaction price is below the new bid and outside the spread. If thebid decreases, the transaction price is inside the spread (unless the quote decrease is sodramatic that the trade price is above the new ask price).

The presence of reporting delays leads to two empirical predictions regarding thefrequency of trades inside and outside the quotes. The first empirical prediction is that theprobability of an outside-trade depends on how the quote has changed.

Reporting delay prediction 1:

�
Ask side: (Prob. of outside-trade |DAsk40)o(Prob. of outside-trade |DAsko0). � Bid side: (Prob. of outside-trade |DBid40)4(Prob. of outside-trade |DBido0).
Reporting delay prediction 1 simply says that the probability of an outside-trade on theask side of the market is greater if the ask has just decreased than if the ask has justincreased. Similarly, an outside-trade on the bid side is more likely if the bid has justincreased than if the bid has just decreased.

Reporting delay prediction 2 relates to the relative frequency of outside-trades andinside-trades:

Reporting delay prediction 2:

�
Ask side: (Prob. of inside-trade |DAsk40) X (Prob. of outside-trade |DAsko0). � Bid side: (Prob. of inside-trade |DBido0) X (Prob. of outside-trade |DBid40).
To see what reporting delay prediction 2 says, consider the ask side. If a transaction takesplace at the ask at t�1 and is reported at time t, it appears inside the spread if the askincreases and outside the spread if the ask decreases. If the change in the ask price israndom, the probability of an inside-trade equals the probability of an outside-trade.However, the change in the ask is not entirely random because quotes tend to be adjustedupward after a trade at the ask. The result is that inside-trades are more likely thanoutside-trades as stated in reporting delay prediction 2.

3.2. Dealer look-back trading option

Dealers have an incentive to delay execution of incoming market orders. By holding amarket order, the dealer in effect creates a free trading option. If the price moves in favorof the dealer, the dealer executes the order at the original quote. If the price moves againstthe dealer, the order is executed at the new quote or is returned. Free trading options areusually thought to be given by limit orders, but a market order can also give away anoption if the dealer who receives the market order can delay its execution. For example,suppose Dealer A asks $30, which is the national best offer (NBO). A market order to buyarrives. Dealer A holds the order for 30 s. At that time, assume the NBO falls to 29.90because another dealer changes the quote. Dealer A sells to the buyer at 30, which is


outside the quote, and receives 10 cents more than the current NBO. Alternatively,suppose the NBO increases to 30.10. In that case the dealer executes the trade at 30.10 orsends the order back arguing that his original ask was not valid, as he was in the process ofchanging quotes.6 We call this option a look-back trading option because, by delaying thetrade, the dealer can look back to determine which quote should serve as the exercise priceof the option. The maturity of the look-back option is the length of time for which thedealer can delay execution of the market order.The look-back trading option is limited by regulation. The SEC’s firm quote rule requires

dealers to honor their quotes. However, exceptions are possible if a dealer is in the process ofchanging quotes. These exceptions are intended to protect dealers from active day-traderswho pick off dealers’ stale quotes. Dealers are also able to delay if they seek to improve theprice of an order. Similarly, a dealer who is not quoting at the inside quote but promises tomatch the best quote has some flexibility in determining the best quote to be matched. Theallowable delay is limited by the reporting delay and the transparency of the market. If thereare two minutes between order placement and trade report, there are two minutes in whichthe routing and execution of the trade are not transparent. In that two minute period, thelook-back option has value if there are at least two quotes. The more frequent the quotesand trades, the greater the opportunity to look back and choose the best quote for a trade.

3.2.1. Look-back versus classic option

The look-back trading option is different from the classic free trading option granted by alimit order or a dealer quote that is immediately accessible (see Copeland and Galai, 1983).The classic free option arises when the limit price or dealer quote cannot be readily adjustedand is subject to immediate execution. As an example, assume a limit order is asking $30. Ifthe limit order is not monitored continuously, it grants an option to the rest of the market.The option is exercised (a trader buys at $30 and the limit order is picked off) if newinformation justifies a price above $30. New information could include fundamental newsabout the security or information about order flow. A dealer can protect himself againstbeing picked off if he is able to delay an incoming transaction and change his quote to reflectthe new information. Probably the single most important reason for dealer opposition toautomatic execution is that automatic execution at a dealer’s quotes causes the dealer togrant the classic free trading option. The ability to delay execution enables the dealer to shiftfrom granting the classic option to taking the look-back option.

3.2.2. Empirical prediction of the look-back option

How will the dealer’s look-back option affect the relation between the trade price, Pt, and thequote at time t? Assume that trades are reported accurately and without delay, but that thedealer can delay execution of an incoming market order. Then, for transactions on the ask side,where the dealer is selling to an incoming market order, the transaction price, Pt, is given by7

Pt ¼ maxðAt�1;AtÞ. (5)

6Market orders would not give away a free trading option to dealers if execution were immediate and automatic

at dealers’ posted prices. However, immediate execution presents legitimate problems for dealers. Dealers could

face double jeopardy as several trades could take place at posted quotes before quotes can be changed.7Eq. (5) is a simplification in that the dealer is assumed to choose from the first and last quote when in fact more

quotes could be available. Later in this article, when the look-back option is valued, we take account of all

possible quotes in the option interval.


If the ask has fallen, the dealer tends to sell at the original ask, At�1, in which case an outside-trade would be observed. If the ask has risen, the trade would be at the new ask or the orderreturned, and no outside-trade would be observed. For trades on the bid side, where the dealer isbuying from an incoming market order, the transaction price is given by

Pt ¼ minðBt�1;BtÞ. (6)

Because the dealer is buying, he buys at the lowest bid price. An outside-trade is observedif the bid increases between t–1 and t, and a trade at the quotes will be observed if the biddecreases.

What are the empirical predictions of the dealer look-back trading option? The firstprediction is identical to reporting delay prediction 1. Outside-trades on the ask side aremore likely after the ask has decreased than if the ask has risen. Outside-trades on the bidside are more likely after the bid has increased than if the bid has decreased. However,prediction 2 is different. In the case of delayed reporting, the probability of observing atrade inside the quotes is equal to or greater than the probability of observing a tradeoutside the quotes. But in the case of the look-back option, trades inside the quotes shouldbe observed infrequently because the dealer exercises the look-back option to trade at thebest quote. The look-back predictions are as follows:

Look-back option prediction 1:

�
Ask side: (Prob. of outside-trade |DAsk40)o(Prob. of outside-trade |DAsko0). � Bid side: (Prob. of outside-trade |DBid40)4(Prob. of outside-trade |DBido0).
Look-back option prediction 2:

�
Ask side: (Prob. of inside-trade |DAsk40)o(Prob. of outside-trade |DAsko0). � Bid side: (Prob. of inside-trade |DBido0)o(Prob. of outside-trade |DBid40).
The look-back option prediction 1 is the same as in the case of reporting delay. Look-backprediction 2 differs from reporting delay prediction 2. Under the look-back option, thedealer has the option to trade at the current ask (bid) or the lagged ask (bid). He choosesthe higher (lower) of the two, with the result that the frequency of outside-trades exceedsthe frequency of inside-trades.

The look-back option benefits dealers, which would enable dealers to lower quotedspreads relative to what they would be without the option.

3.2.3. Quote-driven versus order-driven market

The observability of the look-back option requires frequent independent postings ofcurrent quotes. For example when a dealer chooses to sell to an incoming market buyorder according to Pt ¼ maxðAt�1;AtÞ, we must be able to observe At�1 and At to test forthe look-back option. In a dealer market such as Nasdaq, trading is driven by quoteupdates and incoming market orders tend to execute against dealer quotes. Dealers arequick to update quotes as they are supposed to be firm for their quotes. We can observedealers taking the look-back option if at least one dealer updates quotes while one or a fewdealers are slow to update as they seek to exercise the look-back option.

Observability of the look-back option is more difficult in the NYSE, which is an order-driven market combined with a specialist. On the NYSE, fewer quote updates occur and


hence quotes perhaps do not reflect current market conditions as rapidly as in a quote-driven market. Quote changes are posted when limit orders arrive or when the specialistenters quotes. However, the specialist can trade directly against incoming orders withoutre-quoting. A Nasdaq dealer can trade without re-quoting, but so long as some dealer is re-quoting, the researcher has data to make inferences about the look-back option.8

An example could be helpful to illustrate the issue. Let At�1 ¼ $20 represent the askprice at time t�1, and assume that a market buy order arrives and is held by the dealer for15 s. During these 15 s, the dealer learns about market conditions. For example, publicinformation could warrant a change in the price, or additional orders could arrive. If thepublic information is bad news or if the additional orders are sell orders, the dealer sells atAt�1 ¼ $20 because he knows he can cover the sale at a subsequent lower price. In a quote-driven market, one can infer that a trade at At�1 ¼ $20 is outside the ask because otherdealers enter quotes of At ¼ $19:95 to reflect the bad news. If, however, the publicinformation is good news or the additional orders are buy orders that cause dealers to raisequotes to At ¼ $20:05, the dealer sells at the new ask quote of $20.05.Consider now an order-driven market such as the NYSE. The main difference is that the

new quotes are not necessarily posted because there are not multiple dealers updating theirquotes. As in the quote-driven market, let At�1 ¼ $20 represent the specialist’s ask price attime t�1, and assume that a market buy order arrives and is held by the specialist for 15 s.In those 15 s, the specialist learns about market conditions. If the news is bad (or if sellorders arrive), the specialist sells to the buy order at $20 and covers at lower pricesresulting from the bad news (or the sell orders). The researcher’s problem is that a new askquote need not be posted by the specialist. Hence one can neither observe outside-tradesnor infer the presence of the look-back option. A second source of difference is that thequote on the NYSE is frequently made by the limit order book. The specialist has limitedincentive to enter quotes. In an order driven market, he can always trade with incomingorders by bettering the quote from the book. Suppose in the above example, the ask ofAt�1 ¼ $20 is by a limit sell order on the book. If, as above, the news is bad, and thespecialist wishes to sell to the incoming market buy order, he could do so by improving onthe ask, for example, by selling at $19.99. Assuming no re-quoting at time t, the quoteobserved by the researcher at time t is the same as at time t�1, namely At ¼ At�1 ¼ $20.The transaction appears as inside the quote. If the news is good, the specialist does not sellat $19.99. Instead the limit order sells at $20 to the incoming market buy order, and thetrade is at the quote.

4. Empirical evidence on trading delays and trading options

If the market mechanism works well, transactions would occur at or inside the currentquote and would be reported to occur at or inside the current quote. Alternatively, if themarket mechanism works poorly, as evidenced by reporting delays or the look-backoption, trades would be observed outside the quotes, and the frequency of outside-tradeswould be systematically related to the quote change. Thus to determine if the marketmechanism is flawed, we examine situations in which quotes change, for if quotes neverchange, trades are at the quotes even if there is a reporting delay or look-back option.

8An analysis of quote changes (available from the authors) indicates that changes in quoted prices are more

frequent on Nasdaq than on the NYSE.

ARTICLE IN PRESS

Table 2

Implications of the reporting delay and dealer look-back option for the trade price at time t and for the likelihood

of outside and inside trades conditional on quote change, classified by ask side or the bid side of the market

At ¼ ask price at time t and Bt ¼ bid price at time t.

Reporting delay theory Look-back option theory

Trades on the ask side

Trade price at t Pt ¼ At�1 Pt ¼ maxðAt�1;AtÞ

Ask decreases (AtoAt�1) Outside-trades Outside-trades

Ask increases (At4At�1) Inside-trades Few inside-trades

Trades on the bid side

Trade price at t Pt ¼ Bt�1 Pt ¼ minðBt�1;BtÞ

Bid increases (Bt4Bt�1) Outside-trades Outside-trades

Bid decreases (BtoBt�1) Inside-trades Few inside-trades

H.R. Stoll, C. Schenzler / Journal of Financial Economics 79 (2006) 615–653 629

We distinguish the reporting delay and look-back option hypotheses by examining therelative frequencies of outside-trades and inside-trades as related to the quote changes.Table 2 summarizes the implications of reporting delay and look-back option hypothesesfor the likelihood of outside-trades and inside-trades. The first row gives the value of thetransaction price under the two theories. The second and third rows give the implicationsfor outside-trades and inside-trades. For example, consider trades on the ask side. Thereporting delay theory implies that there are outside-trades if the ask decreases and inside-trades if the ask increases. If we observe that the frequency of outside-trades after the askincreases equals the frequency of inside-trades after the ask decreases, we would concludethat outside-trades are primarily the result of reporting delays. By contrast, the look-backoption implies outside-trades if the ask decreases, but few inside-trades otherwise. In thiscase, if we observe outside-trades after the ask decreases, but few inside-trades after the askincreases, we would conclude that the dealer look-back option was the source of outside-trades.

We use a contingency table to test if there are trading delays and if a look-back option ispresent. The analysis is conducted for Nasdaq and NYSE stocks in each of the threevolume categories for the month of May in the years 1997–2002. Each transaction isclassified as occurring on the ask side (above the quote midpoint), on the bid side (belowthe midpoint), or at the midpoint based on the quote at the time of the trade. The quote atthe time of the trade is the most recent quote at or before the time of the trade. The trade isfurther classified according to the change in the ask or bid since the quote preceding thecurrent quote by at least 30 s. The 30 s time frame is chosen to give enough time for thetrading option to have value, yet not so much time that the trade or trade reporting wouldbe delayed unreasonably. We focus first on May 1999 when outside-trades are first clearlyevident. The outcomes of that contingency classification for Nasdaq and NYSE stocks inMay 1999 are in Tables 3 and 4, respectively.

4.1. Nasdaq stocks

The Nasdaq stocks are categorized into six groups by volume and market side, and theresults are reported in Table 3. The data in Table 3 are consistent with the alternativehypotheses that there is a trading delay or a look-back trading option. Consider first the

ARTICLE IN PRESS

Table 3

Nasdaq stocks. Number and percent of inside-trades and outside-trades conditional on quote change, by volume

category and side of market, May 1999

Panel A

Ask side, Nasdaq 20 high-volume stocks Bid side, Nasdaq 20 high-volume stocks

D ask At quote Inside Outside Total D bid At quote Inside Outside Total

o0 417580 58351 230237 706168 o0 607779 84394 98954 791127

59.13 8.26 32.6 76.82 10.67 12.51

¼ 0 1134230 40401 90851 1265482 ¼ 0 943867 73595 86759 1104221

89.63 3.19 7.18 85.48 6.66 7.86

40 643665 92088 118122 853875 40 340524 80667 187211 608402

75.38 10.78 13.83 55.97 13.26 30.77

Total 2195475 190840 439210 2825525 Total 1892170 238656 372924 2503750

77.7 6.75 15.54 100 75.57 9.53 14.89 100

Panel B

Ask side, Nasdaq 20 medium-volume stocks Bid side, Nasdaq 20 medium-volume stocks


o0 14391 4149 8419 26959 o0 27097 13341 3660 44098

53.38 15.39 31.23 61.45 30.25 8.3

¼ 0 87761 8054 6084 101899 ¼ 0 89061 10744 5777 105582

86.13 7.9 5.97 84.35 10.18 5.47

40 31433 13511 3890 48834 40 16258 4974 8146 29378

64.37 27.67 7.97 55.34 16.93 27.73

Total 133585 25714 18393 177692 Total 132416 29059 17583 179058

75.18 14.47 10.35 100 73.95 16.23 9.82 100

Panel C

Ask side, Nasdaq 20 low-volume stocks Bid side, Nasdaq 20 low-volume stocks


o0 3649 1023 1488 6160 o0 7396 6079 803 14278

59.24 16.61 24.16 51.8 42.58 5.62

¼ 0 43416 4007 1629 49052 ¼ 0 41442 5588 2237 49267

88.51 8.17 3.32 84.12 11.34 4.54

40 6530 4986 596 12112 40 4161 1038 1517 6716

53.91 41.17 4.92 61.96 15.46 22.59

Total 53595 10016 3713 67324 Total 52999 12705 4557 70261

79.61 14.88 5.52 100 75.43 18.08 6.49 100


high-volume stocks. Frequent outside-trades are observed, particularly after the askdeclines (32.60% of the trades) and after the bid increases (30.77% of the trades). Theresults are the same for the medium- and low-volume stock categories. The fact that thereare frequent outside-trades when the ask has declined or the bid has increased is consistentwith both the reporting delay and look-back option hypotheses.We now distinguish the delay hypothesis from the look-back option hypothesis by

comparing the frequency of inside-trades and outside-trades. The delay hypothesispredicts that the frequency of inside-trades is approximately equal to the frequency of

ARTICLE IN PRESS

Table 4

NYSE stocks. Number and percent of inside-trades and outside-trades conditional on quote change, by volume

category and side of market, May 1999.

Panel A

Ask side, NYSE 20 high-volume stocks Bid side, NYSE 20 high-volume stocks


o0 60617 17382 678 78677 o0 28317 22407 73 50797

77.05 22.09 0.86 55.75 44.11 0.14

¼ 0 151582 27748 411 179741 ¼ 0 105601 21960 504 128065

84.33 15.44 0.23 82.46 17.15 0.39

40 33304 32840 95 66239 40 41216 12652 523 54391

50.28 49.58 0.14 75.78 23.26 0.96

Total 245503 77970 1184 324657 Total 175134 57019 1100 233253

75.62 24.02 0.36 100 75.08 24.45 0.47 100

Panel B

Ask side, NYSE 20 medium-volume stocks Bid side, NYSE 20 medium-volume stocks


o0 9097 2893 91 12081 o0 4919 5321 8 10248

75.3 23.95 0.75 48 51.92 0.08

¼ 0 52225 13549 203 65977 ¼ 0 43203 11639 159 55001

79.16 20.54 0.31 78.55 21.16 0.29

40 6279 6893 8 13180 40 8280 2250 71 10601

47.64 52.3 0.06 78.11 21.22 0.67

Total 67601 23335 302 91238 Total 56402 19210 238 75850

74.09 25.58 0.33 100 74.36 25.33 0.31 100

Panel C

Ask side, NYSE 20 low-volume stocks Bid side, NYSE 20 low-volume stocks


o0 4608 1740 40 6388 o0 3013 3227 4 6244

72.14 27.24 0.63 48.25 51.68 0.06

¼ 0 35219 10885 120 46224 ¼ 0 31492 9783 91 41366

76.19 23.55 0.26 76.13 23.65 0.22

40 3479 3874 1 7354 40 4316 1506 74 5896

47.31 52.68 0.01 73.2 25.54 1.26

Total 43306 16499 161 59966 Total 38821 14516 169 53506

72.22 27.51 0.27 100 72.55 27.13 0.32 100


outside-trades as implied by Fig. 3.9 In Table 3, the delay hypothesis implies that the twobolded cells in each panel are equal. The alternative look-back hypothesis implies thatoutside-trades exceed inside-trades. This is because, under the look-back option, the dealertrades at the maxðAt;At�1Þ, which implies that there would be no inside-trades. The resultsin Table 3 depend on the volume category. For the top-volume stocks, the pure delay

9Because the ask adjusts upward after a trade at the ask, one would expect trades above the current ask

(outside-trades) to be somewhat fewer than trades below the current ask.


hypothesis is rejected in favor of the look-back hypothesis. On the ask side only 10.78% ofthe trades after the ask increases are inside the ask, which is much less than the 32.6%outside-trades after the ask decreases.10 This is consistent with the dealer exercising anoption to trade at the most advantageous price. A corresponding result obtains on the bidside. After the bid increases, 30.77% of the trades are outside, whereas only 10.67% areinside after the bid decreases. The symmetry expected under the reporting delay hypothesisis not evident in the data for high volume Nasdaq stocks. Instead the asymmetric resultsconsistent with the dealer look-back trading option are clearly revealed in the data.A possible alternative explanation for the results is that trades are misclassified. The

possibility of trade misclassification exists if trade reports are delayed. For example, if theask increases, a trade reported late is below the current ask. If far enough below, the tradeappears to occur on the bid side instead of the ask side. The possibility of misclassificationweakens our ability to distinguish the reporting delay and look-back option because itaffects the number of inside trades. Trades that should be reported as inside the quotecould instead be reported as occurring on the other side of the quote. For example, inPanel A of Table 3, the proportion of trades inside the ask after the ask increases couldexceed 10.78% if some trades have been misclassified as occurring at the bid side.Similarly, the proportion inside the bid after the bid decreases could exceed 10.67% if sometrades were misclassified as occurring at the ask side.We believe that misclassification of the data does not invalidate our conclusions about

the existence of a look-back option. Misclassification occurs only if the ask increases (forthen late reported trades could appear to be on the bid side of the market) or if the biddecreases (for then late reported trades could appear to be on the ask side of the market). Ifthere were misclassification, one would therefore expect a greater number of trades to bereported on the ask side (bid side) after the ask decreased (bid increased), than if the askincreased (bid decreased). However, the relative number of observations is directlyopposite of what would be expected if trades were misclassified. In Panel A of Table 3, thenumber of observations after the ask increased (and there is the possibility of beingmisclassified as trading on the bid side) is 853,875 compared with 706,168 after the askdecreased (and there is no possibility of being misclassified as trading on the bid side).Similarly, the number of observations after the bid decreased is 791,127 compared with608,402 after the bid increased.Turn now to the empirical results for medium- and low-volume stocks in Panels B and C

of Table 3.11 In these cases, the existence of the look-back option is much less clear. For themedium-volume stocks the bolded proportions are approximately equal, while for low-volume stocks the proportions reverse; that is, trades inside the quotes are more frequentthan trades outside the quotes. There are several reasons that the look-back option is notclearly evident in the medium- and low-volume stocks. First, if volume is low, quoteupdates and trading are not sufficiently frequent to give value to an option that is subjectto regulatory oversight and that lasts less than 90 s. If a dealer holds a market order but noquote updates or trades occur, the dealer does not have the information needed todetermine if the look-back option is worth executing. Second, if quote updates are

10Statistical tests of the difference between inside and outside proportions for all years 1997–2002 are provided

in Tables 5 and 6.11‘‘Medium’’ and ‘‘low’’ are relative terms. All stocks are selected from the top 25% ranked on number of

transactions.


infrequent, the researcher perhaps does not have the information needed to infer that thelook-back option is exercised. Third, spreads are wider for medium- and low-volumestocks so that outside-trades are less frequent. For such stocks, the look-back option couldstill exist but is less likely to result in outside-trades. At the same time, inside-trades aremore frequent when spreads are wider. Fourth, price improvement could occur morefrequently in low-volume stocks where spreads are higher, consequently resulting in moreinside-trades.

4.2. NYSE stocks

The results for the NYSE in Table 4 are different from the Nasdaq results in Table 3.Inside-trades are common on the NYSE, while outside-trades are rare. In the case of thetop 20 stocks, 49.58% of the trades when the ask has increased are inside the ask.Similarly, 44.11% of the trades when the bid has decreased are inside the bid.Corresponding results hold for the medium- and low-volume stocks. However, there arefew outside-trades on the ask side (bid side) when the ask decreases (increases)—the figuresare 0.86% and 0.96%, respectively—which implies that the outside-trades are not theresult of random delays in reporting transactions. One would expect approximately equalproportions of inside-trades and outside-trades if there were random reporting delays.

The considerable difference in the results for the NYSE and Nasdaq reflects thedifference in market structure. On Nasdaq, dealers compete and post quotes that differfrom quotes of other dealers. As a consequence one can observe outside-trades of onedealer vis-a-vis the quotes of other dealers. On the NYSE, trading is centralized and thespecialist has control over the quotes he and the book disseminate. Consequently tradesoutside the quotes, which would be against price priority rules of the NYSE, are notobserved. Inferences about the presence of a look-back option for the specialist are thusalso difficult to make.

While there are almost no outside-trades on the NYSE, the data in Table 4 are notinconsistent with specialist behavior akin to that of Nasdaq dealers. The specialist has theoption to delay execution of an incoming market order and then determine if it shouldtrade against the standing quote, usually made by a limit order, or if it should trade againstthe specialist. In effect, the classic option could be exercised against limit orders, and thelook-back option could be exercised against market orders. An example in which both theclassic option and the look-back option are operating is the process of price improvement.Assume a market order to buy arrives. The specialist guarantees the current ask, which weassume is made by a limit order, and seeks to improve the price. The process of priceimprovement delays execution of the market order in the same way that it occurs in thelook-back option when the dealer delays execution. If the specialist observes that theunderlying price of the stock has fallen (a judgment he can make on the basis of order flowor new information), he sells to the incoming market order at a price slightly less than theask price (the specialist must trade at a better price to gain price priority). If a new quote isnot displayed to reflect the lower price, the trade is reported inside the spread, below thedisplayed ask. If there is information that the stock price has risen, the specialist allows themarket order to execute against the ask set by the limit order. (There is risk. If the limitorder is canceled, the specialist is obligated for the trade). In other words, the classic optiongranted by the limit order is exercised; the limit order is picked off. The transaction againstthe limit order is reported as inside the quote if the quote is updated. Alternatively if the


quote is not updated, the transaction is reported as occurring at the ask quote establishedby the limit order.The evidence for actively traded stocks in Table 4 is consistent with the presence of the

classic option and the look-back option for the specialist. Table 4 indicates that, on the askside, trades inside the quotes are particularly frequent when the ask increases (49.58%)and, on the bid side, trades inside the quotes are particularly frequent when the bid declines(44.11%). These transactions are consistent with the exercise of the classic option againstthe limit order combined with rapid re-quoting to reflect the new price. There are alsotrades inside the spread when the ask decreases (22.09%) and when the bid increases(23.26%). These transactions are consistent with the specialist trading against an incomingmarket order at a price superior to the quoted price of the limit order, combined with slowre-quoting. Here the specialist could be stepping in front of the limit order. The fact thatthe trade is inside the spread requires that the new quote (which is lower when the specialistsells to the incoming market order and higher when the specialist buys from the incomingmarket order) is slow to be posted. In other words, the inference that the specialist isexercising a look-back option requires that the observed quote at time t be stale, notreflecting the new information on which the specialist bases his trade. We cannot inferfrom our data whether the quote is stale.

4.3. Time trend

Technology and market structure change over time. Trading has become moreautomated. Markets reduced their tick size to 1/16 in 1997 and to pennies in 2001. Thesechanges can affect the frequency of outside-trades and the presence of the look-backtrading option. We now examine the pattern of conditional outside-trades and inside-trades for the years 1997 to 2002 for Nasdaq and the NYSE, respectively (see Tables 5 and6). For each stock-day we calculate the proportion inside and outside conditional on thestated movement in the quote. The daily proportions are then averaged over the stocks-days in the sample. Because there are 20 stocks and about 20 trading days in the month,the number of observations is approximately four hundred. If a stock-day contains notrades with the stated quote change, the stock-day is not analyzed. Based on theseobservations we carry out a t-test of the difference between the two outcomes.The results for Nasdaq are in Table 5. The rows corresponding to the bolded cells in

Table 3 are Rows 2 and 3 of Table 5, which are bolded.12 Under the dealer look-backoption, we expect the proportion in Row 2 to exceed that in Row 3, and we expect theproportion in Row 7 to exceed that in Row 10. For the high-volume Nasdaq stocks, this isthe case in every year except 2002. In that year we cannot reject the null that theproportions on the ask side are equal, but in every other case the null of equal proportionsis rejected at high levels of significance, which implies that dealers exercise the look-backoption. As was true in Table 3, the medium- and low-volume stocks behave differently.The results for the NYSE are in Table 6. The proportions for the NYSE are consistent

across years and across stock categories. In every year and stock category, there are fewoutside-trades, in marked contrast with Nasdaq. The pattern for the NYSE does not reflect

12The proportions in Tables 5 and 6 differ somewhat from the proportions in Tables 3 and 4, because in Tables

3 and 4 an overall proportion is calculated whereas in Tables 5 and 6 daily mean proportions are calculated for

each stock and averaged over all stock days. This procedure was adopted to carry out the t-test.

ARTICLE IN PRESS

Table 5

Nasdaq stocks. Average percentage of trades inside or outside the quote, conditional on an increase or decrease in

the quote, classified by the ask side and the bid side, by year, and by stock category. Results are for May of each

year.

1997 1998 1999 2000 2001 2002


Trades on ask side

1 Ask up, trade outside ask 1.02 3.45 9.80 13.43 27.09 11.80

2 Ask down, trade outside ask 19.41 24.54 28.10 27.84 32.68 19.99

3 Ask up, trade inside ask 6.77 9.93 10.97 9.67 10.02 19.20

4 Ask down, trade inside ask 1.57 3.49 6.45 5.68 8.20 15.58

5 T-value (row 2�row 3) 17.43 18.58 24.95 47.97 48.95 2.08

6 Number of stock-days 420 400 400 440 440 440

Trades on bid side

7 Bid up, trade outside bid 17.88 23.81 26.47 28.93 33.92 20.51

8 Bid down, trade outside bid 0.94 4.06 9.27 12.49 26.65 11.07

9 Bid up, trade inside bid 1.9 5.83 10.01 11.03 10.37 16.73

10 Bid down, trade inside bid 8.25 10.34 10.9 10.18 8.57 17.97

11 T-value (row 10�row 7) �12.87 �18.2 �24.19 �48.12 �54.04 �6.79



Trades on ask side





5 T-value (row 2�row 3) �9.9 �19.2 �6.27 0.2 4.92 �53.58


Trades on bid side





11 T-value (row 10�row 7) 11.11 21.12 9.13 �0.20 �2.68 55.96



Trades on ask side





5 T-value (row 2�row 3) �13.76 �17.27 �15.85 �14.06 �13.30 �62.59


Trades on bid side





11 T-value (row 10�row 7) 12.37 18.57 16.15 11.57 18.14 69.77



ARTICLE IN PRESS

Table 6

NYSE stocks. Average percentage of trades inside or outside the quote, conditional on an increase or decrease in

the quote, classified by the ask side and the bid side, by year, and by stock category. Results are for May of each

year.

1997 1998 1999 2000 2001 2002

High-volume NYSE stocks

Trades on ask side





5 T-value (row 2�row 3) �12.18 �48.48 �54.88 �49.25 �141.63 �106.38


Trades on bid side





11 T-value (row 10�row 7) 11.99 43.79 52.90 46.71 125.91 93.97


Medium-volume NYSE stocks

Trades on ask side





5 T-value (row 2�row 3) �15.97 �34.51 �51.09 �63.70 �96.12 �97.24


Trades on bid side





11 T-value (row 10�row 7) 13.78 29.09 49.04 54.83 85.63 79.81


Low-volume NYSE stocks

Trades on ask side





5 T-value (row 2�row 3) �11.11 �33.73 �48.44 �48.99 �93.96 �87.40


Trades on bid side





11 T-value (row 10�row 7) 10.35 31.39 45.55 46.35 87.55 84.52




delayed reporting of transactions, for if this were the case, one would observe outside-trades particularly after a decline in the ask or an increase in the bid (Row 2 and Row 7),but there are few outside-trades. The high proportion of inside-trades, particularly after anincrease in the ask (Row 3) or a decrease in the bid (Row 10), is consistent with exercisingthe classic trading option against limit orders on the book. There is little direct evidence ofa look-back option for the specialist, although Rows 4 and 9 are consistent with such anoption. The trades reported in Rows 4 and 9, which are inside the quotes, could occurwhen the specialist steps in front of a limit order on the basis of new information thatarrives while he holds a market order, combined with a delay in updating quotes to reflectthe new information. These trades result in price improvement relative to a quote thatcould be stale.

5. Time delays and look-back option in Nastraq data

We also analyze Nastraq transactions data for our sample of 60 Nasdaq stocks in 1999.Nastraq data are compiled by Nasdaq and contain additional information not available onTAQ. In particular, the Nastraq data contain the execution time as well as the report time,and they classify trades according to trading venue (SelectNet, Small Order ExecutionSystem (SOES), or other).

5.1. Time delays

If outside-trades reflected in the TAQ data are the result of reporting delays, outside-trades should vanish when calculated on the basis of Nastraq execution times (assumingthose execution times are accurate). Similarly, effective spreads should not exceed quotedspreads when the calculations are based on Nastraq execution times. Alternatively, ifoutside-trades are real, they are observed even when the execution time is the basis forcalculations. We calculate effective and quoted spreads and the percent of outside-tradesfor our sample of 60 stocks for all trades in 1999 based on Nastraq execution times andNastraq report times. Quotes and trades with execution times between 9:30 a.m. and 4 p.m.are retained for analysis. In matching a trade to a quote, we do not employ the five-secondrule. Instead we associate a trade with the quote just prior to the reported execution time ofthe trade. We delete trades without volume, trades with prices greater than 6 standarddeviations from the daily mean price, and trades with an effective spread in excess of fivedollars. We delete quotes that are locked or crossed, and quotes that diverge by more than6 standard deviations from the daily average bid or ask quote. Few observations areeliminated, and the results for the screened data are virtually identical to the results for theunscreened data. We delete approximately 2.5% of the trades for which the report timeprecedes the execution time.

The Nastraq data also make it possible to distinguish trades on SOES, on SelectNet, oron other systems. SOES is a system for small orders in which execution and reporting ofcustomer trades are automated. There is no reporting delay for trades in this system.SelectNet is an automated system connecting market participants. Once a trade isaccepted, execution and reporting are automatic and simultaneous. However, the timebetween receipt and acceptance of a trade creates delays and a possible look-back optionfor the dealer. The other category encompasses the majority of customer trades that arecarried out with market makers or on ECNs. While ECNs are totally automated, market


makers might not be fully automated. Hence there could be delay in reporting trades andthe possibility of a look-back option.Table 7 provides evidence on effective and quoted spreads and on outside-trades when

calculations are based on execution times and on report times. Several points emerge fromthe analysis in Table 7. First, even when calculations are based on execution time, outside-trades are substantial and effective spreads exceed quoted spreads. For example, in thehigh-volume other category, 11.87% of the trades are outside the quotes, and effectivespreads average 6.97 cents compared with quoted spreads of 5.35 cents. This findingimplies that outside-trades are not primarily the results of reporting delays but are a realphenomenon.Second, reporting delays increase outside-trades and raise effective spreads relative to

quoted spreads. For example, in the high-volume other category, outside-trades based onreport times are 13.83% of trades as compared with 11.87% when based on executiontime.13 Effective spreads are 8.18 cents compared with 6.97 cents when based on executiontime. Reporting delays matter, but the major source of outside-trades and effective spreadslarger than quoted spreads seems to come from transactions that are outside the spread, asreflected in the results based on execution time.Third, consider the results for SOES and SelectNet. SOES is an automated execution

system in which incoming market orders are executed at posted quotes. One would expectall trades to be at or inside the quotes. The fact that they are not is puzzling and suggeststhat some of the SOES trades are not executed at the national best bid or offer (NBBO).SelectNet provides for automated trade reporting, but execution of an incoming orderrequires the receiving market maker to accept the order. Once accepted, the execution timeand report time are identical. However, delays in accepting an incoming market ordercould cause the trade price to fall outside the quotes. Such a delay could reflect the freetrading option held by market makers who are able to delay execution to see how marketconditions change. Alternatively outside-trades in SelectNet could simply reflect largetrades that exceed the posted depth.The results are most clear in the case of high-volume stocks. Outside-trades are less

frequent in the case of medium- and low-volume stocks primarily because quoted spreadsare larger for these stocks, hence reducing the likelihood of trading outside the quotes.

5.2. Look-back option and Nasdaq trading venue

We now analyze the Nastraq data to determine if the look-back option is observable andif it varies by execution venue (SOES, SelectNet, and other). The contingency table for allstocks categorized by trading venue is in Table 8. There is evidence of the look-backoption. Consider, for example, the 112,363 other trades (22.92%) that took place above theask after the ask decreased. We infer that many of these trades could have been traded atthe new lower ask but were not because the dealer exercised the look-back option to tradeat the prior higher ask. The inference is based on a comparison with the proportion ofother trades that took place inside the ask after the ask increased (9.33%). If outside-trades

13The number of observations in the other category is slightly larger when report times are used than when

execution times are used. This is because the report time is later, which makes it easier to find a prior quote. For

the SOES and SelectNet sample the observations are the same because the report time and execution time are the

same.

ARTICLE IN PRESS

Table 7

Quoted and effective half-spreads, number of transactions, and average trade size, based on execution times as

reported to the NASD, 60 Nasdaq stocks, 1999

Averages and medians are calculated for each stock day. The table reports average values over a maximum of

5040 stock-days in each volume category. Trades in which report time preceded execution time are excluded.

Execution time Report time

Other SOES SelectNet Other SOES SelectNet

High-volume stocks

Quoted half-spread, cents

Average 5.35 5.50 5.40 5.37 5.44 5.40

Median 4.33 4.43 4.36 4.37 4.39 4.36

Effective half-spread, cents

Average 6.97 5.40 5.72 8.18 5.34 6.27

Median 4.54 4.17 4.16 4.59 4.12 4.22

Trades per stock-day

Average number 9170 1025 3007 9224 1025 3008

Average percent outside spread 11.87 3.58 11.03 13.83 4.01 11.87

Medium-volume stocks


Average 8.23 9.14 8.77 8.35 9.17 8.78

Median 6.90 8.08 7.45 7.02 8.12 7.47


Average 7.98 8.32 7.50 8.52 8.21 7.58

Median 6.00 7.14 5.70 6.03 7.01 5.70


Average number 610 104 393 616 104 393


Low-volume stocks


Average 9.96 10.84 10.65 10.14 10.94 10.68

Median 8.63 10.11 9.43 8.84 10.22 9.46


Average 8.92 9.54 8.20 9.18 9.45 8.21

Median 7.19 8.77 6.60 7.16 8.66 6.57


Average number 248 28 148 251 28 148



were purely the result of reporting delays, one would expect these proportions to be equal.The fact that they are not provides evidence of the look-back option. The correspondinginferences apply on the bid side where the proportions are 23.04% outside the bid after abid increase versus 9.96% inside the bid after a bid decrease. The proportions are similarfor the SelectNet system, indicating the presence of the look-back option on that system.While SelectNet is an automated routing system for sending orders, it is not an automaticexecution system. Hence the presence of the look-back option is possible. The proportionof outside-trades is much smaller in SOES but still greater than one would expect in anautomated execution system. Furthermore, the relative proportions are indicative of alook-back option, which suggests that some delays in executing trades could haveoccurred, possibly as trades queue up in the computer.

ARTICLE IN PRESS

Table 8

Frequency of inside-trades and outside-trades conditional on quote change, by trading venue and side of market

Nastraq data, 60 Nasdaq stocks, May 1999, Number of trades and row percent are reported.

Panel A

Ask side, other trading venue Bid side, other trading venue


o0 346978 30986 112363 490327 o0 414655 52278 58120 525053

70.76 6.32 22.92 78.97 9.96 11.07

¼ 0 861576 30937 47531 940044 ¼ 0 686968 52047 46918 785933

91.65 3.29 5.06 87.41 6.62 5.97

40 477107 56895 75959 609961 40 284416 45479 98755 428650

78.22 9.33 12.45 66.35 10.61 23.04

Total 1685661 118818 235853 2040332 Total 1386039 149804 203793 1739636

82.62 5.82 11.56 100 79.67 8.61 11.71 100

Panel B

Ask side, Selectnet Bid side, Selectnet


o0 56435 15125 22708 94268 o0 155554 27976 32447 215977

59.87 16.04 24.09 72.02 12.95 15.02

¼ 0 258470 15613 18742 292825 ¼ 0 254095 17911 21998 294004

88.27 5.33 6.4 86.43 6.09 7.48

40 152248 29440 30572 212260 40 52809 16458 21844 91111

71.73 13.87 14.4 57.96 18.06 23.98

Total 467153 60178 72022 599353 Total 462458 62345 76289 601092

77.94 10.04 12.02 100 76.94 10.37 12.69 100

Panel C

Ask side, SOES Bid side, SOES


o0 14978 1348 1792 18118 o0 104016 2020 3475 109511

82.67 7.44 9.89 94.98 1.84 3.17

¼ 0 82318 525 1464 84307 ¼ 0 81189 523 1232 82944

97.64 0.62 1.74 97.88 0.63 1.49

40 112335 2311 4507 119153 40 17165 1298 1611 20074

94.28 1.94 3.78 85.51 6.47 8.03

Total 209631 4184 7763 221578 Total 202370 3841 6318 212529

94.61 1.89 3.5 100 95.22 1.81 2.97 100


6. Value of the dealer option

To this point we have provided evidence that a dealer look-back option exists. A naturalquestion is how much such an option might be worth. What is the value of the option givenup by customers to dealers when delays in executing orders are possible? In this section weprovide an estimate of the look-back option’s value to the dealer based on data for May ofeach year from 1997 to 2002. We take two approaches to valuing the dealer option: thehypothetical realized option gain approach and the ex ante option model approach.


6.1. Hypothetical realized value of the dealer option

One can estimate the value of the dealer option by estimating the average realized gainfrom optimally exercising the option. We assume that the option lasts 30 s and consider allthe quotes in that interval. Consider the ask side and let At�1 represent the ask quote at thebeginning of the period when the market buy order is submitted. Let At represent the askquote at the end of the 30 s period when the transaction is reported. Let AI

t represent the setof ask quotes between the first and last quote in the interval.14 Let Pt represent the priceat which the dealer would trade if a market order arrived at t�1. The dealer chooses Pt

such that

Pt ¼ maxðAt�1;AIt ;AtÞ. (7)

The gain, G, is

Gt ¼ Pt � At, (8)

where Pt is given by Eq. (7). If the maximum ask were the end-of-period price (At), thetransaction would take place at Pt ¼ At, and the gain would be zero. If the maximum askwere the beginning of period price, the transaction would take place at Pt ¼ At�1, and thegain would be positive. Similarly if the maximum ask were between the beginning andending points, the gain would also be positive. When the gain is positive, the transactionprice is above the ask price at the time the trade is reported, which causes the trade to beoutside the quote.

The transaction price and gain are calculated in a symmetric manner for trades on thebid side. The transaction price for trades on the bid side is

Pt ¼ minðBt�1;BIt ;BtÞ. (9)

And the gain is

Gt ¼ Bt � Pt. (10)

On the bid side, a gain arises if the final bid exceeds the bid at which the market order sold.In this case the trade is reported outside the quote.

We calculate the average of hypothetical dealer gains for the ask side and bid side forMay of each year from 1997 to 2002. The gain is hypothetical in the sense that the gain isnot based on actual transactions that took place. Instead, the gain is based on quotes atwhich trades might have taken place. The overall dollar gain also depends on the frequencywith which market orders arrive. If no market order arrives, no gain is possible for thedealer.

Our estimates of the dealer look-back option value proceed in two steps. First, the pershare option value is estimated conditional on a trade. These values are in Row 1 of Tables9 and 10. The per share option value depends on the frequency and size of quote changes inthe 30-s interval. Second, we estimate the dollar value of the dealer option based onassumptions about the probability that market orders arrive for which the dealer option isavailable. The dollar option value per stock-day is in Row 4 of Tables 9 and 10.

14Operationally the set of quotes in a given 30 s interval is determined as follows. Each day is divided into 781

30-s intervals. At�1 is the first quote update in the interval. If no quote update is encountered, the last prior quote

is used. At is the first quote in the next 30 s interval. If no quote update is encountered, the last prior quote is used.

ARTICLE IN PRESS

Table 9

Hypothetical realized gain from exercising the dealer look-back option

Ask side of the market. In Row 1 is the average gain per share from exercising the 30-s look-back option. In

Row 2 is the percentage of 30-s intervals with gains for the dealer. The number of shares traded in trade sizes of

less than five thousand shares is in Row 3. The dollar gain per stock-day in Row 4 is the per share gain (Row 1)

times the number of shares in trades of less than five thousand shares (Row 3) times 0.15, the fraction of shares

traded as market orders. Data are for May of each year.

1997 1998 1999 2000 2001 2002


1. Average gain in cents per share 0.84 0.83 4.52 3.51 1.76 1.70

2. Percent of gains 40 6.68 11.22 28.87 31.72 46.10 57.16

3. Daily share volume o5000 (thousands) 3512 3511 6879 11235 16643 15263

4. Average gain per stock-day in dollars 4425 4371 46640 59152 43938 38921



2. Percent of gains 40 1.26 4.25 8.79 14.95 30.64 34.01





2. Percent of gains 40 0.95 2.83 4.14 7.39 20.26 24.51




Consider now the results for the ask side in Table 9. (The results for the bid side in Table10 correspond.) The average per share exercise value of the 30-s look-back option is smallin 1997 (0.84 cents per share for high-volume stocks), peaks in 1999 (4.52 cents per sharefor high-volume stocks), and then declines (to 1.70 cents per share in 2002). The averageoption value depends on the number of intervals in which the gain is positive. For example,if quotes do not change, there is no gain. In 1997 only 6.68% of the intervals had gains inexcess of zero, which implies relatively little volatility in quotes in that year. By 2002,57.16% of the intervals had positive gains, which reflects the increased volatility of quotes.Second, the option value depends on the size of the gain conditional on being positive. In1997, gains are large because the minimum tick size is $0.125. However, the number ofpositive gains is small because quote changes are infrequent. By 2001, when Nasdaq hadmoved to penny price increments, the size of gains is much smaller but the number ofpositive gains is much larger because quote changes are more frequent.The option values are considerably smaller for the medium- and low-volume stocks than

for the high-volume stocks. The difference reflects the fact that quote changes are muchless frequent for the less active stocks. If quotes do not change, the dealer has no option.Thus in the peak option year of 1999, the medium-volume stocks’ option values average1.2 cents per share and the low-volume stocks’ option value average 0.58 cents per share,substantially less than the 4.52 cents for the high-volume stocks. The fraction of intervalswith positive gains in 1999 is 28.87% for high-volume stocks, 8.79% for medium-volumestocks, and 4.14% for low-volume stocks.We next estimate the dealer gain per stock-day. This gain, given in Row 4, depends on

the per share gain in Row 1 and the volume of trading subject to the option. We assume

ARTICLE IN PRESS

Table 10

Hypothetical realized gain from exercising the dealer look-back option

Bid side of the market. In Row 1 is the average gain per share from exercising the 30-s look-back option. In

Row 2 is the percentage of 30-s intervals with gains for the dealer. The number of shares traded in trade sizes of

less than five thousand shares is in Row 3. The dollar gain per stock-day in Row 4 is the per share gain (Row 1)

times the number of shares in trades of less than five thousand shares (Row 3) times 0.15, the fraction of shares

traded as market orders. Data are for May of each year.

1997 1998 1999 2000 2001 2002



2. Percent of gains 40 6.96 10.61 27.45 29.32 43.03 54.48





2. Percent of gains 40 1.4 4.19 8.81 14.42 30.39 32.85





2. Percent of gains 40 1.12 2.63 4.31 7.07 20.36 23.43




that large orders of five thousand shares or more are from sophisticated investors whoprotect themselves against the option. The daily share volume in trade sizes of less than fivethousand shares is given in Row 3. We further assume that 15% of this share volume is inthe form of market orders subject to the option. The 15% estimate is based on data inAppendix D of a report by the U.S. Securities and Exchange Commission’s Office ofEconomic Analysis (2001), ‘‘Report on the Comparison of Order Executions AcrossEquity Market Structures’’ (January 8, 2001). That report, based on trade data for June of2000, indicates that market orders on Nasdaq constitute 23.5% of shares traded. Weassume that some market orders are not subject to the look-back option and reduce thisnumber to 15%. The total gain per stock per day in Row 4 is then the per share gain(Row 1) times the number of shares in trades of less than five thousand shares (Row 3)times 0.15.

On the ask side, the estimated gain per stock-day is $4,425 in 1997 for the high-volumestocks, rises to $59,152 in 2000 and falls to $38,921 in 2002. In other words, in 2000, theestimated value of the option to dealers in the high-volume stocks was about $59,000 perstock-day on the ask side. On the bid side, the estimated value (Table 10) is $55,782 perstock-day, a total of about $115,000 per stock-day or about $28,750,000 in a year with 250trading days.15 The value peaks in 2000 because in that year quote changes were more

15For simplicity we report in the tables the same volume of trading on the ask and bid sides. In the long run, this

must be the case. We simply report the average of ask side and bid side volume. In our calculations we also assume

that the dealer participates on the opposite side of all trades. With the growth of ECNs in recent years, dealer

participation has undoubtedly declined.


frequent than in earlier years and were larger than in later years. With the arrival of pennyincrements, the size of dealer gains declines, albeit their frequency increases.The option values of the stocks classified as medium- and low-volume are substantially

less than the value for the high-volume category. This is because of the lesser frequencywith which quotes changed and the lesser frequency of trading. The look-back optionvalue is likely to be economically significant only for the most active Nasdaq stocks.Our estimates are subject to considerable error, but they do indicate the potential

magnitude of the look-back option. The option value on a per share basis is of the samemagnitude as the quoted spread in recent years. The presence of the option could allowdealers to lower their quoted spreads, knowing that they can make some gains on theoption.

6.2. Ex ante option model value of the dealer look-back option

An alternative approach to valuing the dealer look-back option is to apply the look-back option pricing formula. (The formula was derived by Goldman et al., 1979 and can befound in Hull, 2003, p. 441). The important inputs to the formula are the return standarddeviation in the 30-s interval and the stock price. (Of lesser importance is the risk-free rate.)The third row in each panel of Table 11 provides estimates of the per share look-backoption value, based on the average quote midpoint in the first row, the 30-s standarddeviation of returns calculated from the data and reported in the second row,16 and a risk-free rate of 10% per year. For comparison purposes, we also supply the Black–Scholesvalue in the fourth row of each panel. That value assumes that the option exercise price isthe initial quote in the interval, not the best quote in the interval.The dealer look-back option values reported in Row 3 are larger than those based on

realized values in Tables 9 and 10, although the pattern over time and across stockcategories is roughly similar. In 1999, the look back option for high-volume stocks isvalued at 8.35 cents per share in comparison to the realized value in that year of 4.52 centsper share for trades on the ask side. By 2002, look-back option model values have fallen asdid realized values, but the difference across the volume categories is eliminated, which isnot the case for the realized values. In 2002, the model based values for the three volumecategories are 2.77 cents, 2.78 cents, and 2.68 cents. We prefer to rely on the realized valuesreported in Tables 9 and 10 because the assumptions underlying the option models(normality and continuous prices) are unlikely to be met.In summary, we have shown that the potential value of the dealer look-back option is

significant, particularly for the highest volume stocks. But our estimates are just that,estimates. The value of the dealer option is limited by regulation and by trading strategiesof investors. The firm quote rule requires quotes to be honored and limits the flexibility ofthe dealer. Traders also adopt strategies to limit the dealer’s flexibility, such as cancelingorders that are not executed within a very short interval (say, ten seconds). Consequentlythe decline in the value of the dealer option in recent years is probably greater than Tables9 and 10 indicate.

16The standard deviation is calculated for 30-s returns for each stock-day and averaged over all stock-days in

each volume category and year. The standard deviation reflects trading noise as well as the fundamental volatility

normally used in valuing stock options.

ARTICLE IN PRESS

Table 11

Value of dealer option based on look-back option model

Average stock price is average quote midpoint in May of each year. 30-s standard deviation of quotes is

calculated from 30-s proportional quote changes each day averaged over all stock days. Look-back option value is

the option to sell at the maximum or buy at the minimum based on the quote midpoint, 30-s standard deviation,

and riskless rate of 10% per year. Black–Scholes value is the corresponding value of a European option calculated

by the Black–Scholes equation.

1997 1998 1999 2000 2001 2002


Average quote midpoint in dollars 48.76 45.23 80.52 65.75 34.41 26.69

30-s standard deviation of quotes, in percent 0.11 0.08 0.13 0.15 0.12 0.13

Look–back option value in cents per share 4.28 2.89 8.35 7.87 3.30 2.77

Black–Scholes value in cents per share 2.14 1.44 4.18 3.93 1.65 1.38




Look-back option value in cents per share 1.97 3.29 4.72 7.46 3.41 2.78





Look-back option value in cents per share 1.90 2.43 3.47 4.86 3.57 2.68



7. Trade size and outside-trades

Our analysis thus far has focused on reporting delays and the look-back option asexplanations of outside-trades. We turn now to large trades as a possible explanation. Atrade price could be outside the quote because the trade exceeds the posted depth of adealer. For example, an institution could agree to buy 20 thousand shares from aparticular dealer at a price of $20.15, even while the NBBO is $20.00 bid and $20.10offered, without trading at the $20.10 offers of other dealers. While this perhaps is notoptimal, no trade-through rule on Nasdaq exists, that would require a dealer to take outbetter prices of other dealers, even if the better prices are by limit orders. The dealer couldtake out better prices on behalf of the institution, usually using the SelectNet System tosend an offer to trade but is not required to do so. A dealer could choose not to clear betterprices if he believes doing so will take time and will reveal his trading position. The dealerhandling the large trade is required by the Manning Rule to execute any sell limit ordersthe dealer holds at prices lower than $20.15.

Related to trade size is the practice of markup pricing on Nasdaq. While individualcustomers have always been charged commissions on Nasdaq trades, institutionalcustomers typically pay no commission. Instead dealers would resell stock at a markup.Such a markup can cause the trade price to be outside the quotes. For example, aninstitution could give a ‘‘not-held’’ order to a particular dealer to buy 25 thousand shares.The dealer buys the shares as principal for an average price of $20.10. He then sells theshares to the institution for $20.13, a markup of 3 cents. The markup is in lieu of acommission. The trade at $20.13 appears on the tape and will be outside the NBBO. When


inside quotes become narrow, trade-throughs of inside quotes are more likely to beobserved. At the end of 2001 some Nasdaq market makers began to charge a separatecommission to institutions and to eliminate the markup.Because of the structure of the Nasdaq market, in which each dealer, each ECN, and the

Nasdaq execution systems (SOES, SelectNet) are separate market centers, outside-tradesof large trades are more likely to be observed in Nasdaq stocks than in NYSE-listed stocks.(SuperMontage, the successor to SOES and SelectNet, was launched on October 14, 2002).This is because the NBBO is based on all markets whereas trades occur on a specificmarket. Trading in NYSE-listed stocks is concentrated on the NYSE and hence thepossibility for outside-trades is less. The practice of mark up pricing is also unique to theNasdaq market. On the NYSE, commissions are charged.Table 12 provides average percentage outside-trades by trade size in May of the years

1999 through 2002 for the 60 Nasdaq and 60 NYSE stocks in our sample. As expected,large trades on Nasdaq frequently execute outside the quotes. For example, in 2002,39.61% of all Nasdaq trades between five thousand and ten thousand shares trade outsidethe NBBO. Perhaps more interesting is that substantial numbers of outside-trades areobserved for even the smallest trade sizes. In 2002, 8.43% of Nasdaq trades of one hundredor fewer shares are outside the quotes, and in 2001, the figure is 17.86%. Given that thenumber of trades in the smaller size categories exceeds greatly the number of trades in thelarger size categories, most trades are outside the quotes for reasons other than trade size.By contrast to Nasdaq, the NYSE reports virtually no outside-trades. For trades under

five thousand shares, outside-trades never exceed 1%. The maximum fraction of outside-trades is 6.21% in 2002 in the largest size category. The difference between the NYSE andNasdaq reflects the more centralized trading system of the NYSE. In the future, one couldexpect an increase in outside-trades on the NYSE as exchange markets fragment andtrades on other markets trade through quotes on the NYSE.Fig. 4 splits the Nasdaq data into the three volume categories. The relation between

outside-trades and trade size is the same for the three categories of stocks except that thelevel of outside-trades is greatest for the high volume stocks and lowest for the low-volumestocks. The year-by-year results are also similar with 2001 exhibiting the largest fraction ofoutside-trades.One implication of these trade size results is not unexpected. Large trades are more likely

to be outside the quotes than small trades. What is noteworthy is that small trades on

Table 12

Percentage of trades outside quotes by trade size, market, and year

The data are every trade in May of each year for 60 Nasdaq and 60 NYSE stocks. The overall percentage of

outside-trades is the average across stock-days of the daily percentage of outside-trades.

Trade size 1999 2000 2001 2002

Nasdaq NYSE Nasdaq NYSE Nasdaq NYSE Nasdaq NYSE

100 7.89 0.11 11.74 0.16 17.86 0.41 8.43 0.38

101–500 7.62 0.15 11.12 0.15 17.30 0.46 9.26 0.43

501–1000 8.02 0.17 11.76 0.16 20.02 0.55 10.44 0.49

1001–5000 14.52 0.28 18.70 0.26 29.64 0.87 18.14 0.82

5001–10,000 25.74 0.75 34.60 0.69 53.88 2.05 39.61 2.13

410,000 32.00 2.98 42.63 3.25 67.83 5.71 54.19 6.21

ARTICLE IN PRESS

0

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100 101-500 501-1000 1001-5000 5001-10000 >10000

Trade size

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ut-

trad

es

100 101-500 501-1000 1001-5000 5001-10000 >10000

Trade size

100 101-500 501-1000 1001-5000 5001-10000 >10000

Trade size

Per

cen

t o

ut-

trad

esP

erce

nt

ou

t-tr

ades

(C)

(B)

(A)

Fig. 4. Outside-trade percentage in Nasdaq stocks by trade size, year, and volume category: (A) outside-trades:

high-volume Nasdaq stocks; (B) outside-trades: medium-volume Nasdaq stocks; (C) outside-trades: low-volume

Nasdaq stocks.


Nasdaq are traded outside the quotes frequently, which points to the reporting delay andlook-back option findings discussed earlier. A second noteworthy observation is the cleardifference in outside-trades in all size categories between the NYSE and Nasdaq, which


reflects the fact that the NYSE is a centralized auction market whereas Nasdaq is adispersed dealer market.

8. Trends in the Roll trading cost measure

As shown in Table 1, Nasdaq quoted spreads declined dramatically relative to effectivespreads in the period from 1993 to 2001. Which measure is correct? Did execution costsdecline as much as implied by quoted spreads or are the effective spreads a better measureof actual execution costs? Interpretation of effective spreads is problematic as this paperpoints out because timing issues could introduce error. One approach to assessing thetrend in execution costs is to use a measure that does not depend on the time alignment ofquotes and trades. The Roll (1984) measure for inferring the spread depends only on thesequence of transaction prices.The Roll measure of the implied half-spread is calculated as

Roll half � spread ¼ffiffiffiffiffiffiffiffiffiffiffi

�covp

, (11)

where cov is the serial covariance of trade-by-trade price changes averaged over all stock-days in a given year and volume group.17 In other words, for each stock-day, the serialcovariance of transaction price changes is calculated and averaged over all days in the yearand all stocks in the volume group. Before averaging each day’s covariance estimates, wecensor the data for any case in which the day’s serial covariance estimate is more than4 standard deviations from the mean of the daily serial covariance in the year. Values ofthe Roll half-spread are presented in Table 13. Like quoted and effective spreads (reportedin Table 1), Roll spreads decline over time. The relation among the three is easier to see inPanels A–F in Fig. 5.The trend in the Roll spread mirrors the secular downward trend in quoted and effective

spreads. It also reflects the higher spreads in the bubble years 1999 and 2000. The highertrading costs in those years are particularly clear for the high-volume stocks. For Nasdaqstocks the trend in the Roll spread matches the effective spread more closely than thequoted spread. If we accept the Roll spread as the measure of trading costs, this suggeststhat effective spreads also represent true trading costs and are not a reflection of areporting delay. Quoted spreads declined more than effective and Roll spreads, whichimplies that they now understate trading costs, while, at the beginning of the nine-yearperiod, they overstated trading costs.For the NYSE, the trend in the Roll spread matches that in the quoted and effective

spreads. Further, the relation among the three measures is relatively stable over the nineyears (with the exception of the low-volume sample in 2001, when the effective and quotedspreads are equal). Competition on Nasdaq appears to have driven the quoted spreadlower than the effective spread at which trades tend to occur. This has not happened on theNYSE.

17As recommended by Harris (1990), we take the average of the covariance before applying the Roll

transformation to avoid the Jensen inequality bias.

ARTICLE IN PRESS

Table 13

Roll half-spread, 1993–2001. Average values in cents by year, by market, and by trading volume category

The Roll half-spread is calculated asffiffiffiffiffiffiffiffiffiffiffi

�covp

, where cov is the average serial covariance of 30-s price changes.

The serial covariance is estimated for each stock-day and then averaged over all stock-days in each year and stock

category.

1993 1994 1995 1996 1997 1998 1999 2000 2001

High-volume Nasdaq 10.85 9.36 7.97 7.94 6.14 4.67 12.8 13.18 3.02

High-volume NYSE 5.39 5.28 5.17 5.15 4.66 3.76 4.35 5.41 2.64

Medium-volume Nasdaq 16.82 13.56 13.76 11.1 10.9 7.77 9.14 17.57 3.71

Medium-volume NYSE 5.22 4.9 4.9 4.71 4.12 3.42 3.53 4.75 2.09

Low-volume Nasdaq 19.54 15.65 13.87 15.75 10.46 9.07 8.56 9.53 4.68

Low-volume NYSE 5.02 4.82 4.75 4.47 3.95 3.15 3.04 2.99 2.01


9. Conclusion and implications

Given the shrinking quoted spread on Nasdaq, it is perhaps not surprising that tradesoutside the quotes have become more common. The large quoted spreads in 1993 and 1994hide a great deal. Since then, as quotes have declined, outside-trades have increased. Weshow that three features of the market mechanism give rise to outside-trades. First,reporting delays can cause trades to appear to be outside the quotes even though theywere not.

Second, we find evidence of a dealer look-back trading option that can cause outside-trades of the type observed on Nasdaq. The look-back option probably also exists on theNYSE but is more difficult to observe. The look-back option is held by the dealer whodelays execution of incoming market orders and creates an option to trade at the originalquote when the order first arrived or at the best quote after the order has been held. Thelook-back option is different from the classic option granted by a stale limit order that failsto adjust its price to reflect new information. We find that the dealer look-back option iscostly to the customer and valuable to the dealer primarily in the most actively tradedstocks.

Third, we find evidence of outside-trades because large trades exceed the posted depth ofdealers. Because there is no trade-through rule on Nasdaq, large trades can be executed byone dealer at prices that trade through the quotes of other dealers. Customers could prefera trade-through to the alternative of breaking up the block.

One of the puzzles in market structure is the reluctance of markets to adopt automatedtrading. While routing of orders is automatic, the final step of executing a transactiontypically involves human intervention and delay. Dealers defend that delay as necessary toprotect them against being picked off by day-traders. We show in this paper that this delaygives the dealer a look-back option that is beneficial to the dealer. The effect of the look-back option is to produce slippage in the market mechanism and a reduction in the qualityof execution of market orders.

As trading becomes more automated, slippage in the market mechanism is reduced. Weanticipate a decline in outside-trades resulting from reporting delays (because tradereporting is instantaneous) and a decline in the look-back option (because orders areelectronically executed immediately on arrival). Certain trades could still trade outside thequotes. For example, customers could send orders to a market with an inferior quote,

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024

68

10

121416

1 2 3 4 5 6 7 8 9

Year

0123456789

1 2 3 4 5 6 7 8 9

Year

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9

Year

Quoted half-spread

Effective half-spread

Roll half-spread

(C)

(B)

(A)

Fig. 5. Quoted, effective and Roll half-spreads, in cents, by volume group, exchange and year (1993–2001): (A)

high-volume Nasdaq stocks; (B) high-volume NYSE stocks; (C) medium-volume Nasdaq stocks; (D) medium-

volume NYSE stocks; (E) low-volume Nasdaq stocks; (F) low-volume NYSE stocks.


which has lower fees or better service. Large orders that require negotiation and are notexecuted automatically could be traded outside the quotes.Current SEC rules prohibit trade-throughs in exchange traded stocks and impose

linkages requiring orders from markets that do not have the best quote to be sent to themarket with the best quotes. At the same time, trade-throughs have been permitted inNasdaq stocks. Under the SEC’s proposed Regulation NMS, a uniform trade-through rulewould be implemented that would prohibit trade-throughs of other markets unless the

ARTICLE IN PRESS

0123456789

10

1 2 3 4 5 6 7 8 9

Year

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Year

0123456789

10

1 2 3 4 5 6 7 8 9

Year

Quoted half-spread

Effective half-spread

Roll half-spread

(D)

(E)

(F)

Fig. 5. (Continued)


other markets are slow to adjust their quotes.18 An alternative to a regulatory trade-through prohibition is to make a trade-through rule unnecessary by making markets moreefficient. Because it is in the investor’s interest to trade at the best price (also taking

18Seconds count. The SEC proposal notes that the trade-through rule would not apply to trades within a second

of a quote change. This would in principle leave room for a one-second look-back option, but we do not believe

this option would have much value. See US Securities and Exchange Commission (2004).


account of convenience and speed), trade-throughs can be reduced by eliminatingreporting delays, by eliminating the dealer’s look-back option, and by assuring that largetrades are able to clear other markets quickly and automatically. Markets should beencouraged to make their quotes executable without delay. If that is the case, customerswill send orders to the best market, markets will be linked, and outside-trades will beinfrequent.

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Documents

Trades outside the quotes: Reporting delay, trading option, or trade size?