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How Slow is the NBBO?

A Comparison with Direct Exchange Feeds

†

Shengwei Ding

John Hanna

Terrence Hendershott

July 8, 2013

† Ding is an associate employed by Wells Fargo Securities, CA; Hanna was employed by Redline Trading

Systems during this project; Hendershott is at the University of California, Berkeley. Redline provided

technological support for the project. We thank Gideon Saar, two anonymous referees and the editor,

Michael Goldstein, for helpful comments.

How Slow is the NBBO?

A Comparison with Direct Exchange Feeds

Abstract

Investors with the most up-to-date information on market conditions make the best trading

decisions. This paper provides evidence on the benefits of proprietary data feeds from stock

exchanges over the regulated “public” consolidated data feeds. We measure the amount of

latency in the public data and the potential costs of using stale data. The costs stem from missing

out on the best prices which we measure by comparing the National Best Bid and Offer (NBBO)

available through the public Security Information Processors to a synthetic NBBO calculated

from proprietary exchange data feeds, both measured at the same data center. Price dislocations

between the NBBOs occur several times a second in very active stocks and typically last one to

two milliseconds. The short duration of dislocations makes their costs small for investors

infrequently trading, while the frequency of the dislocations makes them costly for frequent

traders. Higher security price, trading volume, and volatility are associated with dislocations.

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1. Introduction

Financial markets have evolved from manual, human-based, single venue floor trading to ultra-

fast, low-latency multi-venue, fully automated electronic trading. Regulators have continuously

updated rules to cope with the change. In the United States the Securities and Exchange

Commission’s regulatory objectives include maintaining fair, orderly, and efficient markets

(Macey and O’Hara (1999)). By examining the differences between publically provided market

data and data sold directly from the exchanges we provide empirical evidence on the

transparency and fairness of the U.S. equity markets.

1

Our results characterize the amount of

latency, the frequency and magnitude of price differences due to latency, and the potential costs

to investors arising from latency. We find that using public information imposes small costs for

investors trading infrequently. In contrast, active traders are at a substantial disadvantage if they

use the public data.

Latency in the public data reduces transparency to those investors viewing the public data as

opposed to the direct data feeds.

2

This difference in transparency is a source of unfairness across

investors. Foucault, Roell, and Sandas (2003) investigate how investors with slower data are

more likely to be picked off by investors constantly monitoring market conditions.

3

The latency

in market data that we study provides the simplest type of information that some investors

receive before others. Hirshleifer, Subrahmanyam, and Titman (1994) and Foucault, Hombert,

and Rosu (2013) explicitly model the strategy of a trader receiving information just ahead of

other investors. Ready (1999) and Stoll and Schenzler (2006) empirically examine how slower

traders’ orders provide a free trading option for those traders with lower latency. Easley,

Hendershott, and Ramadorai (2013) study an upgrade in the New York Stock Exchange’s trading

system which reduced the latency of off-floor traders. They find this reduction is relative latency

as compare to on-floor traders improved liquidity and raised stock prices.

The speed at which investors receive new information is a form of differential information across

investors. A number of theoretical models explore different aspect of informational asymmetry

related to the trading process. Easley, O’Hara, and Yang (2012) show that when exchanges

provide differential access to trade information liquidity is reduced, volatility is increased, and

prices are lowered. Cespa and Foucault (2013) show that reductions in insiders access to post-

trade information relative to outsiders may also increase prices by reducing the risk to outsiders.

1

We use public to refer to market data provided under Section 11A of the Exchange Act. What we refer to as proprietary data

typically includes more detailed data, e.g., limit orders not at the best price, and is not consolidated before distribution. Both data

feeds are available to any subscriber, but the proprietary data is significantly more expensive.

2

Data processing and transmission lead to latency in market data regardless of whether trading is fragmented or centralized.

Huang (2002), Barclay, Hendershott, and McCormick (2003), and Goldstein, Shkilko, Van Ness, and Van Ness (2008) study

competition among equity markets. Stoll (2001) posits that investors and brokers can virtually integrate markets together through

technology.

3

Moallemi and Saglam (2012) model another cost of latency for investor trying to capture the bid-ask spread by using limit

orders. Gai, Yao, and Ye (2012) examine how congestion due to order arrivals at NASDAQ can increase the latency in market

data.

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Empirically measuring informational differences across investors is difficult as investors’

information set is typically not observable. O’Hara, Yao, and Ye (2013) study the importance of

trades smaller than 100 shares in the price discovery process. These trades are not reported in the

public data, but are reported in markets’ proprietary data feeds. Our results complement O’Hara,

Yao, and Ye (2013) by quantifying another advantage for investors with access to proprietary

data feeds: lower latency in observing quotes.

Market Data and the NBBO

Broadly speaking, there are two different trading systems in the U.S.: registered exchanges and

alternative trading systems. The registered exchanges are required to provide the best bids and

offers to be included in the consolidated quotation system (CQS) and are also required to file any

rule changes with the SEC. The alternative trading systems includes electronic communication

networks (ECNs) and dark pools which do not provide best quotes to CQS, but are required to

match trades within an NBBO. In this study, we only deal with the quotation system based on

registered exchanges.

There are 13 equity exchanges in the U.S. The chart below shows the aggregate trading volume

of each exchange on May 9, 2012. The statistics in the chart from the BATS website

(http://batstrading.com/market_summary) shows that NASDAQ, NYSE, NYSE ARCA,

BATS BZX, and Direct Edge EDGX and EDGA accounts for more than 88% of total volumes

across all registered exchanges. This comparison does not include trades in so-called dark pools,

which were estimated to account for around 12% of the total trading volume in May 2012. The

proportion of quote data by exchange is similar to the fractions of trading volume in Figure 1.

Figure 1. Market share of trading volume for different exchanges on May 9, 2012

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With multiple exchanges trading stocks simultaneously, the question arises how it can be assured

that the submitted order is executed at the best bid and offer price across all exchanges. This

prompted the SEC to establish Regulation National Market System (Reg NMS) in 2007 to

protect fair access to the best price for investors, particularly retail investors. Based on Reg NMS,

exchanges are required to provide the quotes to the primary exchanges such as NYSE and

NASDAQ. The Security Information Processors, known as SIPs for NYSE and NASDAQ,

gather the data from all exchanges and publish their respective National Best Bid and Offer

(NBBO). Stock brokers are required by Reg NMS to execute the retail customer trades at the

NBBO or better.

For stocks listed on the NYSE, the SIP that provides the NBBO is the Consolidated Quotation

System (CQS) and the equivalent system for NASDAQ is called the UTP Quote Data Feed

(UQDF). In this study, we obtain the data through the NASDAQ SIP, which provides the NBBO

for all the NASDAQ listed stocks. The cost difference for the actual feed is $2-3K per month

with an additional $10-30K per month in infrastructure costs (10Gb fiber network, ticker plant,

co-location) the difference in cost will vary due to variations in performance requirements. For

most firms 50 nanoseconds is not enough to significantly impact their fill rates, but for modern

day market makers, 50 nanoseconds can make a significant difference when they are all

competing for queue position in an exchange matching engine.

Not all market participants have equal access to trade and quote information. Both physical

proximity to the exchange and the technology of the trading system contribute to the latency.

Secondly, gathering and processing data takes time and also causes delay. The NBBO from the

NASDAQ SIP may not be the fastest NBBO investors can obtain from the market. The delay is

significant to the extent that investors cannot get the optimal price if they have a large amount to

be traded. Also there are delays in trade execution that cause the shown best price to be no longer

available at the moment an order reaches the market. Thus there is uncertainty whether NBBO

prices can translate into trade prices. To mitigate such problems, trading via inter-market sweep

orders (ISO) and dark pools are allowed by the SEC to work around the NBBO requirement. ISO

is a trade execution method where an investor sends orders to multiple exchanges for immediate

execution, disregarding whether such a price is the best nationwide.

The potential of deriving the NBBO more quickly opens opportunities for companies such as

Redline Trading Systems to directly subscribe to different exchanges, allowing them to calculate

a faster NBBO compared to the SIP NBBO. Access to exchanges and fast calculation of NBBO

could generate profitable opportunities, but few have quantified the benefits as this study does.

Different market participants have different levels of interest in quantifying latency costs. For

traditional fund managers whose trading frequency is days or even longer, it is debatable whether

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they should directly pay attention to latency costs. For institutional investors who commonly

adopt algorithmic trading strategies, such as value weighted average price (VWAP) or time

weighted average price (TWAP), their reliance on third party algorithmic trading software often

makes them aware of the latency cost but not to the extent that they monitor it closely. For these

investors latency is relevant to the execution of their trades, but not to their asset allocation and

portfolio choices. High-frequency traders decide which stocks to buy and sell continuously in

real time, so the latest and most accurate information is crucial. To the extent that high-frequency

traders have an informational advantage over less well-informed investors, all traders and/or

their brokers must be aware of latency issues.

Having access to less up-to-date information complicates trading in a number of ways. Price and

execution become less certain because orders at particular prices may change between the time

of the last update and the time an order reaches the market. The longer the latency, the larger is

the uncertainty. This can be compounded when trading is fragmented across many markets.

Traders with access to more recent prices can also devise various strategies to profit from slower

investors. These strategies can range from picking off stale orders in public markets to taking

advantage of any stale prices utilized by dark pools. After characterizing the magnitude and

frequency of dislocations between the public SIP NBBO and the synthetic proprietary NBBO we

will return to the economic costs of these dislocations.

The paper proceeds with Section 2 introducing the technology used to capture the exchanges’

proprietary data feeds. Section 3 studies the latency between the public SIP and the proprietary

data feeds. Section 4 constructs a synthetic NBBO and compares it to the SIP data. Section 5

discusses and quantifies the economic costs of latency. Section 6 examines factors that affect

latency costs across days. Sections 3 through 6 illustrate the issues using data for Apple in May

2012. Section 7 examines how the costs of latency differ across securities. Finally, section 8

highlights some conclusions that can be drawn from this study.

2. Data Collection

The trading system we use is called the InRush

TM

Accelerator ticker plant from Redline Trading

Solutions. It is run on an IBM server with 24 CPUs. The server is co-located at Savvis NJ2

center provided by Savvis in Weehawken, NJ. Savvis is a leading provider of outsourced internet

infrastructure services and low latency connectivity to major financial exchanges. The NJ2

center is where BATS hosts its BZX and BYX exchanges. By co-locating our server with BATS

exchange, we obtain the lowest possible latency with BATS. Additional details of the data

collection are available in an appendix available online.

In addition to the BATS exchanges, our server is also connected to various other exchanges

directly (Direct Edge A/X, NASDAQ’s TotalView feed) as well as UTP. Ideally, the server

should connect with all 13 exchanges to obtain the lowest latency updates and consolidate quotes

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to generate its own NBBO. If all data feeds exist, the Redline system can generate a NBBO in

the same way as UTP with lower latency. Data from the exchanges and the SIP are given time

stamps at our server so discrepancies in the clocks at the different exchanges and the SIP do not

affect our measurement of latency.

For this study the server is directly connected with the following exchanges, two BATS

exchanges: BYX and BZX, and two Direct Edge exchanges: EDGA and EDGX, and NASDAQ.

In order to construct a NBBO including data from all exchanges, we combine the direct

exchange feeds with the other exchange components from the SIP(s). We focus on NASDAQ

listed stocks so we use UTP, the NASDAQ component of the SIP.

The Redline synthetic NBBO is constructed primarily with the following two rules,

- Use direct data feeds BATS, EDGE, and NASDAQ and the SIP top of book BBO for

other exchanges to build its our NBBO

- If BATS, EDGE, or NASDAQ has a new price better than current SIP price, update our

NBBO with the new price; If BATS, EDGE, or NASDAQ is alone at the SIP NBBO and

has a new price worse than current SIP price, update our NBBO with the new price

The NBBO generated by this approach is not perfect. For exchanges where the information

comes through the SIP, there is no benefit at all. Also, if some updates arrive with short delay

(direct feed) and other updates arrive with longer delay (SIP), the amount of time each update

stays on top of the book deviates from the real value. However, if more than 90% of the top of

book updates are from exchanges with direct feed, the Redline system can generate a synthetic

NBBO quite accurately with relative low latency.

3. Data Latency

To measure the magnitude of the latency between the public (SIP NBBO) and proprietary

(synthetic NBBO) data we initially focus on Apple (AAPL), which is one of the most important

stock for investors. The analysis in Sections 3-5 focuses on Apple on May 9, 2012. Section 6

provides evidence on Apple for the entire month of May. Section 7 studies additional securities

in May.

To provide background on Apple’s trading on May 9, Figure 2 shows the bid and ask prices for

Apple. Apple’s price rose between one and two percent from the opening price being of $563.70

to the closing price of $569.18. The average bid-ask spread is $0.1621, which is roughly three

basis points of Apple’s stock price, consistent with Apple being highly liquid.

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Figure 2. AAPL bid/ask price from NASDAQ SIP NBBO on May 9, 2012.

Examining how the bid and ask prices differ between the SIP NBBO and the synthetic NBBO

requires much higher time resolution than a daily graph can provide. To illustrate this effect,

Figure 3 graphs the bid and ask prices for the SIP NBBO from 9:31am to 9:32am with dots

marking when the synthetic bid and ask prices differs from the SIP. Differences appear multiple

times each second while clustering around price changes. This suggests the natural intuition that

a security’s volatility plays an important role in the value of more up-to-date price information.

Figure 3. AAPL NBBO from 9:31-9:32am on May 9, 2012. Dots are when the synthetic Redline

NBBO is updated before the SIP NBBO

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Figure 3 demonstrates that dislocations between the SIP NBBO and the synthetic NBBO occur

frequently, possibly several times a second. Figure 3 does not provide information about how

long those price dislocations last. Quote changes occur when a limit order improves the best

price or the depth at the best price is cancelled or executed against. The changes occur first in the

synthetic NBBO and then subsequently in the SIP NBBO. The latency between the two data

sources can be quantified by calculating the amount of time between the time stamps of the

NBBOs:

Figure 4 provides a histogram of the distribution of latency for Apple on May 9 by market

centers. The average latency on BATS is larger than those on EDGE and NASDAQ because the

Redline server is located just next to the BATS data center. Thus, the updates directly from

BATS arrive immediately on the direct data feeds. The feeds from NASDAQ and EDGE arrive

at the BATS data center with some delay due to the distances between the data centers, reducing

their latency relative to the SIP. The amount of time it takes for information to be routed between

market centers and the SIP determines latency in an absolute sense, but latency perceived by

market participants depends on their perspective, i.e., from which data center latency is measured.

On average across all exchanges, the latency is about 1.5 milliseconds. As a comparison, the

average time it takes to execute a market order is less than one fifth as large, roughly 300

microseconds. Therefore, brokers waiting for the NBBO information to decide what price and

which exchange to route market orders to can face significant disadvantages. The aggregate

distribution of latency is the weighted average across markets centers. The SEC’s 2010 concept

release on equity market structure wrote that latency at the SIPs themselves was about 5

milliseconds. Our latency measure which incorporates both latency at the SIPs and between the

SIPs and the markets suggests that latency has fallen over time.

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Figure 4. Histogram of latency on May 9, 2012 for BATS, Direct Edge and NASDAQ

*We excluded any Direct Edge results where the latency was less than 200 microseconds due to an issue known at the time regarding

price publication variances between Direct Edge feeds and the Direct Edge SIP updates*

4. Price Dislocations

The latency in Figure 4 demonstrates the delays in price information that investors receive in the

SIP NBBO. The magnitude of latency generated price dislocations is particularly meaningful to

investors. Figure 5 shows the price dislocations for Apple throughout the trading day on May 9.

Price dislocations occur at the bid almost 25 thousand times in the day and at the ask nearly 30

thousand times. There are 23,400 seconds during the 9:30am to 4:00pm trading day, so prices

dislocations occur more than twice per second on average.

Figure 5 reports the median price dislocation as being the tick size of $0.01. However, many

price dislocations are greater than $0.10 making the mean price dislocation 3.4 cents, more than

three times greater than the median. If an investor routes orders based on the stale SIP NBBO

then the investor can lose this amount on each share. Figure 4 shows that these dislocations are

short-lived at only several milliseconds. Therefore, while dislocations are costly and frequent,

their impact on infrequently trading investors can be quite small as prices are dislocated less than

one percent of the time.

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Figure 5. Price dislocations for Apple on May 9, 2012.

Figure 6 examines how price dislocations occur across exchanges at the ask (the bid looks

similar). Dislocations occur most often on NASDAQ and are slightly smaller there. As seen in

Figure 1, NASDAQ has the largest market share, something that is also true in Apple, so it is not

surprising that NASDAQ is where the differences appear most often.

Figure 6. Price Dislocations by Exchange for AAPL on May 9, 2012.

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5. The cost of latency

Up to this point we have illustrated the frequency and magnitude of the price dislocations

between the SIP NBBO and the synthetic NBBO using direct data feeds from the exchanges.

These price dislocations can impact investors in a number of ways depending on their trading

strategies. The simplest example would be an investor routing a market order to the exchange

with the best price at the SIP NBBO. In this case the frequency and durations of price

dislocations provide an estimate of how often the investor’s order could go to the wrong

exchange. Figure 5 shows that there 54,734 price dislocations for Apple on May 9 during the 6.5

hour trading day. This corresponds to 2.34 dislocations per second on average. Estimating that

dislocations last as long as the latency shown in Figure 4 of approximately 1.5 milliseconds

implies that for 3.51 milliseconds of each second the SIP NBBO and synthetic NBBO differ.

This could result in a buy or sell market order going to the wrong market roughly half that often:

0.175% of the time. Figure 5 shows that the average price dislocation is $0.034. Simply

multiplying this times the percentage of the time a dislocation occurs yields an expected price

dislocation of $0.006 per 100 shares for a market order entered randomly throughout the day.

Multiplying this dollar amount by Apple’s May 9 trading volume of 17,167,989 shares yields

$942, representing 0.001 of a basis point of dollar volume traded. This suggests that investors

randomly routing market orders are unlikely to face meaningful costs due to data latency.

While price dislocations have small effects on infrequently trading investors, investors that are

continuously in the market can be substantially disadvantaged. One example involves dark pools

that use the NBBO as a reference price at which orders are matched. If the NBBO is based on the

SIP and not the NBBO constructed from exchanges, then the dislocations illustrated in Figure 5

are incorporated in the trading prices at the dark pool. If a high-frequency trader monitors the

proprietary and SIP NBBOs the trader can enter a buy order when the synthetic NBBO is above

the SIP NBBO. If the trader initiating the trade in the dark pool at the SIP NBBO can exit the

position at the midpoint of the synthetic NBBO, a profit of half the price dislocation is realized.

That profit comes at the expense of the investor who had an order resting in the dark pool.

To illustrate the above logic we provide a simple example. Assume BATS updates AAPL bid

price from $530 to $531, and the ask price remains at $532. This changes the mid-price from

$531 to $531.5. In the first 1.5 milliseconds, slower traders are not aware of the price change. If

some such regular traders have placed an order to trade at mid-price in a dark pool, then a faster

trader can buy the stock at $531 in dark pool when the synthetic NBBO gets updated. After 1.5

milliseconds, the trader can sell it for $531.5 in the dark pool. In this case the trade gains 50% of

the price dislocation. Dark pools represent roughly 11% of trading volume, corresponding to

1,888,478 share of AAPL on May 9

th

. If half of the average dislocation of 0.034 cents is captured

on this volume then the fast trader would make a profit of $376,900 in a single stock on a single

day. While Apple is one of the highest-volume stocks and this almost certainly represents an

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upper bound on the profits of strategies based on latency, the dollar figure illustrates the possible

magnitude of profits and costs stemming from latency for traders continuously in the market.

The above calculations illustrate that latency costs can be very low for infrequently trading

investors, but that latency in data can be quite costly for very active investors. There are many

other possible costs of latency. For example, we have focused solely on price dislocations for

marketable orders. Adjusting limit orders with slow data can result in worse queue position

which reduces the likelihood of the order being filled. Having slower data also reduces the

accuracy of information on the quantities at the best prices which complicated filling larger

orders.

6. Price dislocations over time

May 9 is a single day so we next examine its representativeness by studying Apple on other days

in May 2012. In addition to each day’s number of dislocations, Figure 7 graphs AAPL’s intraday

volatility based on the percentage difference between each day’s high and low prices. The largest

number of dislocations is 81,279 on May 18. That day AAPL had its second highest intraday

volatility in the sample period of two percent and its highest daily trading volume of over 26

million shares (not shown). The three lowest number of dislocations occur on May 2, 10 and 25,

40,486, 35,264, and 41,467, respectively, which have the lowest intraday volatilities, 0.73%,

0.65%, and 0.66%, and trading volumes, 15, 12, and 12 million shares, respectively.

The number of dislocations and volatility clearly move together in Figure 7 and the correlation

between the two series is 0.71. This is not surprising as higher volatility implies more prices

changes and dislocations occur when the bid and ask prices change. Trading activity also

impacts the frequency of bid and ask changes. Trading volume and stock price volatility are

generally highly correlated and in the AAPL sample the daily correlation is 0.86. Hence, the

correlation between the number of dislocations and trading volume is also high.

The daily analysis shows that dislocations are greater when volatility and trading volume are

higher. If these same relations hold within each trading day, then the potential costs of latency

calculated in this paper represent a lower bound. For example, the costs calculated in Section 5

take daily averages of the number of dislocation, the average size of the dislocations, and trading

volume. If these are positively correlated as in Figure 7, then by Jensen’s inequality the average

of the number of dislocations times the size of the dislocation times the trading volume is larger

than the average of the number of dislocations times the average of the size of the dislocation

times the average of the trading volume.

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AAPL number of price dislocation and intraday volatility in May 2012

Number of Dislocations

AAPL Intraday Volatility

Figure 7. Price dislocations and intraday volatility for AAPL in May 2012.

7. Price dislocations across securities

While Apple is a very important stock for investors, its high price makes the tick size of one cent

small as a percentage of share price. Its finer pricing grid and rapid trading activity could both

lead to price discrepancies occurring quite often in Apple. To examine the differences across

various types of security we turn to data for 24 securities. The securities were selected to

represent a broad cross section of characteristics include share price, market capitalization, and

trading volume. Market capitalization, share price, volatility, trading volume, and number of

trades are taken from CRSP.

4

Volatility is measured as the percentage difference between the

day’s highest and lowest price. The number of securities is limited to ensure that the latency

measures do not arise from any congestion on the server collecting the data.

5

The sample period

is the 16 trading days from May 4 through May 25, 2012. This is a few days shorter than the

sample for Apple shown in Figure 7 because the first few days of May were used for testing and

data was not collected for all securities.

4

Two exchange traded funds, Powershares QQQ and Proshares Ultrapro Short QQQ, are included. Market capitalization is

reported in CRSP for these, but its meaning is less well defined for ETFs. The results are not sensitive removing these two

securities.

5

Queuing models demonstrate that as the server’s utilization increases latency in the server, as opposed to latency in the data

feeds themselves, nonlinearly. By keeping the number of securities small, the server’s average utilization was kept very low to

avoid congestion on the server from contributing to the latency measures.

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Table 1 provides information on how these securities vary in terms of characteristics and trading

activity. Each variable is measured daily and Table 1 reports the average across days in the

sample. Dislocations are measured by their number in thousands, their total value (number times

size) in thousands of dollars, and their average size in percentage of share price.

6

A Herfindahl

index is calculated daily using trading volume at each of the exchange codes in the NYSE’s

Trade and Quote (TAQ) database. While this is the best publically available data, it

underestimates the true fragmentation of trading as the trade report facilities aggregate trading

from a number of different trading venues. This possibly causes the variation in the Herfindahl to

be relatively small.

[Table 1 here]

Apple is the largest, highest price, and most actively traded security in our sample. Apple has

three times more dislocations than the next highest security, Amazon.com, but the average size

of these dislocations is only one basis point. The smallest firm is Cleantech Solutions with a

market capitalization of approximately $10 million and about one million dollars per day in

trading volume. Alexza is the lowest price stock at $0.41. These small, low priced securities have

only five and 50 dislocations per day, but these dislocations are large at 21 and 57 basis points.

The descriptive statistics in Table 1 suggest a number of interesting possible relations among

security characteristics and dislocations. To examine these more systematically Table 2 provides

pairwise correlations among the variables for the 384 security-day observations. The reciprocal

(inverse) of price is typically used because the tick size is fixed at one cent for securities priced

above one dollar and to mitigate the impact of high prices securities. As is often done the

logarithm of trading volume and market capitalization are taken. The correlations among the

security characteristics are not surprising: larger stocks are higher priced with lower volatility

and higher trading activity. Trading volume is negatively correlated with volatility because of the

negative cross-sectional relation between them. As suggested by Table 1 the number and value

of dislocations are highly correlated at 0.95. These two variables are negatively correlated with

the average percentage dislocation at -0.28 and -0.24, respectively. Security characteristics that

are positively correlated with the number of dislocations are generally negatively correlated with

the percentage average size of these dislocations.

[Table 2 here]

Table 2 calculates the correlations among the variables in Table 1 where observations across

firms are pooled. This mixes together cross-sectional and time-series correlations. The

correlation between volatility and the number of dislocations in Table 2 has the opposite sign as

6

For May 10, 2012 data on Arena Pharmaceuticals (ARNA) is missing from CRSP. For EDS on May 15 and CLNT on May 16

there are zero price dislocations.

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shown for Apple in Figure 7. The graphical correlation is purely times series while the pooled

correlation is both cross sectional and time series. To estimate the pairwise time-series relations

between the variables and the dislocation measures Table 3 estimates univariate regressions with

securities fixed effects for each of the three dislocation measures on the security characteristics.

Because trading volume and the number of trades have a 0.73 correlation we will focus only on

trading volume as the results for number of trades are similar. Because there are no stock splits in

our sample period and share price is incorporated in inverse price market capitalization is not

included. Therefore, the four security characteristics and three measures of dislocation lead to 12

separate regressions. Each coefficient in Table 3 is from estimation of a regression of the column

dislocation measure on the row security characteristic and security fixed effects. Hence, Table 3

corresponds to time series only correlations between the variables. Statistical significance is

calculated controlling for heteroskedasticity.

[Table 3 here]

Table 3 shows that the times-series correlations between the number of price dislocations and

volatility, trading volume, trading concentration, and lower price are all positive, as are the

correlations with the total value of those dislocations. The channels by which price, volatility,

and volume could lead to more dislocations are straightforward as all of these lead to more

frequent price changes and limit order book updates. That a higher trading concentration would

cause more dislocations is not obvious. A possibly explanation is that when dislocations are

more likely, investors choose to trade in the main market. The times series correlations with the

average size of dislocations have the same signs except for trading volume. Higher trading

volume is associated with more frequent, but smaller dislocations.

The correlations in Tables 2 and 3 are useful for assessing the relations between dislocations due

to latency and security characteristics. Table 2 shows nontrivial correlations among the security

characteristics which make understanding their marginal impact more difficult. For example,

market capitalization and trading volume have a correlation of 0.90 in Table 2. Table 4 conducts

panel regressions with and without security fixed effects of the dislocation measures regressed

on the security characteristics. The coefficient on inverse price is positive, although marginally

statistically significant when fixed effects are included. The coefficients on volatility are

generally positive, but statistically significant in less than half the specifications. The

coefficients on trading volume are positive for the frequency and value of dislocations and

negative for the size of dislocations.

[Table 4 here]

How Slow is the NBBO?

15

8. Conclusion

In this study we compare the NBBO from the public/regulated SIP and the NBBO from

proprietary data feeds from the exchanges. Price dislocations between the NBBOs occur several

times a second in Apple and typically last one to two milliseconds. The brevity of dislocations

mitigates costs for investors trading infrequently. However, the frequency of the dislocations

makes them costly for frequent traders. Higher security price, trading volume, and volatility are

associated with dislocations.

How well does current market data regulation meet its goals? This depends on many factors

including: (i) how much could further regulatory intervention possibly reduce the small costs for

infrequent traders? (ii) how much regulation is needed to protect frequent traders from possible

market power by exchanges in the pricing of their proprietary data? (iii) how inefficient is it for

all frequent traders to purchase the data from exchanges and then consolidate it? (iv) how

effective are the incentives for technological innovation by the more heavily regulated public

data providers?

How Slow is the NBBO?

16

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How Slow is the NBBO?

17

Table 1. Sample Descriptive Statistics. The daily sample extends from May 4 to 25, 2012 for 24 securities. Market capitalization is in billions of

dollars. Volatility is the percentage difference between the day’s highest and lowest prices. Trading volume is in millions of dollars. Number of

trades is in thousands. Dislocations are measured by their number in thousands, their total value (average number times average size) in thousands of

dollars, and their average size in percentage of share price.

Market

Share

Trading

Number of

# of Price

Value of

Average

Ticker

Capitalization

Price

Volatility

Volume

Trades

Herfindahl Dislocations

Dislocations

Dislocations

Symbol

Security Name

($B)

($)

(%)

($M)

(000)

Index

(000)

($000)

Size (%)

AAPL

Apple

522.68

558.98

1.32

10,741.29

138.04

0.23

60.78

1.90

0.01

ALXA

Alexza Pharmaceuticals

0.05

0.41

5.96

0.77

1.62

0.29

0.50

0.00

0.57

AMZN

Amazon.com

99.48

220.80

1.34

959.68

34.49

0.23

19.74

0.52

0.01

ARNA

Arena Pharmaceuticals

0.98

5.23

4.29

122.02

51.72

0.31

1.54

0.02

0.21

BRCD

Brocade Communications

2.27

4.96

2.13

33.13

18.33

0.20

0.05

0.00

0.21

CLNT

Cleantech Solutions

0.01

3.69

7.51

1.10

0.87

0.29

1.44

0.02

0.44

DNDN

Dendreon

1.32

8.57

3.42

60.34

29.77

0.23

0.82

0.01

0.13

EDS

Exceed

0.06

2.04

3.65

0.12

0.18

0.35

0.27

0.00

0.78

FSLR

First Solar

1.33

15.28

3.82

96.18

29.46

0.29

6.77

0.07

0.07

GPRO

Gen Probe

3.68

81.13

0.19

90.89

6.32

0.19

0.89

0.01

0.02

HOLX

Hologic

4.54

17.17

1.36

85.98

22.64

0.26

0.93

0.01

0.06

INTC

Intel

134.19

26.67

0.95

1,057.12

125.74

0.20

0.44

0.00

0.04

MDRX

Allscripts Healthcare

2.08

10.91

1.52

68.96

28.10

0.23

0.42

0.00

0.09

MNKD

Mannkind

0.31

1.84

2.91

2.99

4.34

0.30

0.03

0.00

0.58

PPHM

Peregrine Pharmaceuticals

0.05

0.50

4.66

0.41

1.20

0.31

1.01

0.00

0.54

QGEN

Qiagen

3.95

16.76

0.89

20.08

7.72

0.21

0.72

0.01

0.06

QQQ

Powershares QQQ Trust

30.85

63.17

0.85

4,014.79

120.99

0.18

1.48

0.01

0.02

RMBS

Rambus

0.49

4.46

2.04

3.50

4.03

0.27

0.17

0.00

0.23

SIRI

SIRIUS XM Radio

7.71

2.03

2.54

167.32

47.31

0.28

0.03

0.00

0.49

SOHU

Sohu.com

1.71

44.96

1.90

29.86

4.81

0.23

4.47

0.08

0.04

SQQQ

Proshares Trust

0.14

40.14

2.45

102.18

8.26

0.21

16.71

0.18

0.04

VVUS

Vivus

2.36

23.64

2.30

74.66

18.70

0.21

3.54

0.04

0.04

YRCW

YRC Worldwide

0.04

5.80

3.79

1.12

0.66

0.36

1.23

0.02

0.23

ZNGA

Zynga

1.68

7.65

4.58

169.74

53.87

0.28

1.41

0.01

0.13

How Slow is the NBBO?

18

Table 2. Correlations. The daily sample extends from May 4 to 25, 2012 for 24 securities. Inverse of share price is one divided by the share price.

Volatility is the percentage difference between the day’s highest and lowest prices. Trading volume is in dollars. Dislocations are measured by their

number, their total value (average number times average size) in dollars, and their average size in percent.

Market

Inverse of

Trading

Number of Herfindahl # of Price

Value of

Average

Capitalization Share Price Volatility

Volume

Trades

Index

Dislocations Dislocations Dislocation

Market Cap

1

Inverse Price

-0.16

1

Volatility

-0.20

0.39

1

Trading Volume

0.90

-0.17

-0.19

1

Trades

0.64

-0.28

-0.16

0.73

1

Herfindahl

-0.16

0.36

0.37

-0.18

-0.31

1

# of Dislocations

0.88

-0.18

-0.12

0.85

0.49

-0.14

1

Value of Dislocations

0.92

-0.16

-0.14

0.90

0.52

-0.11

0.97

1

Avg Dislocation

-0.25

0.63

0.45

-0.25

-0.35

0.55

-0.28

-0.24

1

How Slow is the NBBO?

19

Table 3. Pairwise Regressions with Security Fixed Effects. The daily sample extends

from May 4 to 25, 2012 for 24 securities. Regressions are conducted on each measure of

price dislocation for each independent variable, so the table reports coefficients for 12

different regressions. Each regression includes security fixed effects. Inverse of share

price (1/Price) is one divided by the share price. Volatility is the percentage difference

between the day’s highest and lowest prices. Trading volume is in millions of dollars.

Dislocations are measured by their number in thousands, their total value (average

number times average size) in thousands of dollars, and their average size in percent.

Statistical significance is calculated controlling for heteroskedasticity. ∗/∗∗ denote

significance at the 95%/99% level.

# of Price

Value of

Average

Size of

Dislocations

Dislocations Dislocations

1/Price

2.40**

0.07**

0.10**

(0.72)

(0.02)

(0.03)

Volatility

49.61

2.27**

2.31**

(27.82)

(0.81)

(0.50)

log(Trading Volume)

2.03**

0.03*

-0.06**

(0.57)

(0.01)

(0.01)

Herfindahl

40.77**

1.44**

0.68**

(10.73)

(0.33)

(0.19)

How Slow is the NBBO?

20

Table 4. Panel Regressions. The daily sample extends from May 4 to 25, 2012 for 24

securities. Regressions are conducted on each measure of price dislocation. Regressions

are performed with and without security fixed effects. Market capitalization is in billions

of dollars. Inverse of share price (1/Price) is one divided by the share price. Volatility is

the percentage difference between the day’s highest and lowest prices. Trading volume is

in millions of dollars. Dislocations are measured by their number in thousands, their total

value (average number times average size) in thousands of dollars, and their average size

in percent. Statistical significance is calculated controlling for heteroskedasticity. ∗/∗∗

denote significance at the 95%/99% level.

# of Price

Value of

Average Size of

Dislocations

Dislocations

Dislocations

log(Market Capitalization)

1.32

0.09**

0.03**

(0.80)

(0.02)

(0.01)

1/Price

2.40**

3.67

0.07**

0.09*

0.10**

0.40

(0.72)

(1.98)

(0.02)

(0.04)

(0.03)

(0.22)

Volatility

49.61

-6.54

2.27**

-0.10

2.31**

1.34*

(27.82)

(9.05)

(0.81)

(0.15)

(0.50)

(0.52)

log(Trading Volume)

2.03**

2.25**

0.03*

0.04**

-0.06**

-0.01

(0.57)

(0.49)

(0.01)

(0.01)

(0.01)

(0.01)

Herfindahl

40.77**

-3.83

1.44**

0.08

0.68**

0.06

(10.73)

(3.29)

(0.33)

(0.07)

(0.19)

(0.18)

Constant

-61.01**

-2.00**

0.46**

(11.35)

(0.36)

(0.09)

Fixed Effects

N

Y

N

Y

N

Y

Observations

383

383

383

383

381

381

R-squared

0.29

0.92

0.32

0.94

0.62

0.85