Market Microstructure of the Pink Sheets

Nicolas P.B. Bollen†

Associate Professor of Management

and

William G. Christie

Frances Hampton Currey Professor of Management and Professor of Law

Owen Graduate School of Management

Vanderbilt University

401 21st Avenue South

Nashville, TN 37203

Current Version: July 17th, 2007

________________________________________________________________________†Research support from the Financial Markets Research Center at Vanderbilt University is gratefully acknowledged. The authors thank Carl Giangrasso from Pink Sheets for patiently answering our numerous questions about the Pink Sheets trading and quotation systems and Yim Cheung for assistance with the data. Paul Brockman, Craig Lewis, Hans Stoll, and seminar participants at Vanderbilt University, the University of Missouri, the University of Mississippi, and the University of Virginia provided helpful suggestions. Please address all correspondence to Nick Bollen at nick.bollen@owen.vanderbilt.edu.

Market Microstructure of the Pink Sheets

Abstract

We study the microstructure of the Pink Sheets and assess the ability of

existing theory to capture salient features of this relatively unstructured

and unregulated market. Clustering patterns in quotes, quoted spreads, and

trade prices indicate that market participants have endogenously selected

price-dependent tick sizes for different stocks. Clustering intensity varies

across stocks as a function of proxies for information availability.

Similarly, the bid-ask spread varies as a function of volatility and

liquidity. We design a tick size schedule for the Pink Sheets that conforms

to the clustering present in quotes, and track measures of market quality

after the market adopted the schedule in 2006. No evidence of

deterioration is found, suggesting that the market’s endogenously selected

tick sizes are robust.

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I. Introduction

The past ten years have witnessed substantial structural reform in U.S. equity

exchanges, including the SEC Order Handling Rules, implementation of decimal pricing,

and the Trade Protection Rule that emerged from Regulation NMS. The pace of activity

has stirred controversy, leading some to question the current balance between rules and

unfettered innovation.1 Against this backdrop of regulatory reform, apparent pump and

dump schemes using internet spam stand in sharp contrast. The popular press describes

the impact on companies whose stock is the subject of these schemes, as well as the

potential losses for investors who trade in response to the hype.2 Empirical studies by

Frieder and Zittrain (2007) and Böhme and Holz (2006) document significant price and

volume reactions, and discuss the need for additional regulation.

In this paper, we use the rise in stock spam as a point of departure to study the

market microstructure of the Pink Sheets, on which most of the stocks involved in pump

and dump activity are quoted and traded. More specifically, we consider the ability of

microstructure theory developed over the past several decades to help us understand

quoting and trading behavior on the Pink Sheets, as well as the extent to which a

relatively unmonitored market can function effectively. Until recently, trade and quote

data were not recorded electronically on the Pink Sheets, rendering empirical analysis

exceedingly difficult. For this reason, we remain relatively ignorant about the

microstructure of a market that has been described as the remaining vestige of the “wild,

wild west” of securities trading. Indeed, the Pink Sheets website (www.pinksheets.com)

warns investors directly:

Unlike those listed on NASDAQ and New York Stock Exchange, Pink

Sheets stocks are not required to meet listing standards. This means there

is a wide range in the quality of issuers that are traded in the Pink Sheets,

from major international conglomerates to very small companies

struggling to survive. Investors must be aware that good information is

simply is not available for many Pink Sheets traded companies and that

there are unscrupulous individuals that will attempt to defraud investors

through manipulative schemes in Pink Sheets stocks.

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We have been provided with all quote and trade data from the Pink Sheets Electronic

Quotation and Trading System for the period January 2004, the first month that such data

are available, through July 2006. The data permit us to test whether the economic forces

shaping some of the worlds most important stock exchanges also govern one of the least

understood markets in our financial system.

Angel et al. (2004) and Macy et al. (2004) also study the Pink Sheets market in

the context of comparing trading costs for firms moving to either the Over-The-Counter

Bulletin Board (OTCBB) or the Pink Sheets market. Both of these papers report large

declines in liquidity and increases in trading costs after stocks are delisted from the

NYSE or NASDAQ and trading resumes on either of the other markets. While these

studies provide an important first glimpse of the differences between the Pink Sheets and

the national markets, our access to over two full years of intraday trade and quote data for

all Pink Sheets stocks allow us to examine the microstructure of the Pink Sheets in richer

detail.

A defining feature of the Pink Sheets has been the presence of stocks with quoted

prices as low as $0.0001, and as a consequence, no officially mandated tick size. Our

empirical analysis is centered on this issue and consists of three parts. First, we examine

clustering on whole multiples of $0.0001 as a measure of the extent to which market

participants have endogenously selected an effective tick size. We find striking patterns

for both quotes and trade prices revealing that stocks are quoted and traded using

different increments as a function of stock price. Clustering in quotes and trade prices

likely reflects the need for market participants to reduce the 10,000 increments between

each dollar that are possible on the Pink Sheets. We also examine clustering on a stock-

by-stock basis to determine whether variation in stock attributes can explain variation in

clustering. Ball et al. (1985), for example, argue that the degree of clustering increases in

the difficulty in obtaining information about an asset. Consistent with the empirical

results in Ball et al. (1985) and Harris (1991), we find that clustering is more pronounced

for stocks with higher volatility and lower trading frequency. This result suggests that the

link between information economics and clustering in asset prices established in prior

literature also governs quotation and trade activity on the Pink Sheets.

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Second, we study whether the lack of an officially mandated tick size, and the

resulting clustering of quotes, result in uncompetitive quoted spreads. Indeed, Christie

and Schultz (1994) and Christie, Harris and Schultz (1994) show that when dealers

systematically avoid certain price points, spreads can be maintained artificially wide to

the detriment of investors. We estimate parameters of a standard model of the

determinants of bid-ask spreads based on dealer costs. The model has significant

explanatory power, in some cases roughly the same magnitude as that reported in existing

studies of bid-ask spreads for stocks traded on NASDAQ or the NYSE. The coefficients

on stock return volatility and inverse trading volume are positive and statistically

significant. These results indicate that spreads vary across stocks on the Pink Sheets in a

manner predicted by microstructure theory.

Third, we report the results of a carefully designed and implemented experiment

that imposed a tick size schedule on a subset of Pink Sheets stocks. The tick size schedule

was selected to conform to the pre-existing clustering endogenously generated by market

participants. We find no evidence that quotation and trading activity was negatively

affected by the imposition of the tick size schedule, except for the lowest-priced stocks

subject to the new tick sizes. A modification to the tick size schedule appears to have

remedied this problem. The results of this experiment show that in a market of stocks

with prices ranging from over $100 to less than $0.001, tick sizes can be introduced

without harming market quality when minimum increments vary with stock price. This

price-dependent tick size schedule should be of informative for the continuing debate

regarding the optimal tick size for the NYSE and NASDAQ.

The rest of the paper is organized as follows. Section II describes the regulatory

and trading environment for Pink Sheets stocks. Section III provides an overview of the

data. Section IV reports evidence of clustering with a fractal pattern among both quotes

and trades, and presents results on the degree of price improvement. Section IV also tests

whether cross-sectional variation in clustering can be explained by proxies for the

availability of information. Section V tests whether the economic determinants of spreads

identified in organized markets also plays a significant role among Pink Sheets issues.

The results of a tick size experiment are presented in Section VI. Section VII concludes

the paper.

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II. Regulatory and Trading Environment

The Pink Sheets market originated in 1904 and can be traced to the formation of

the National Quotation Bureau which was established as a quotation service for market

makers in OTC securities.3 A similar facility (yellow sheets) was formed for the

quotation of bonds. In August 1971, a broad range of OTC securities began to be quoted

on NASDAQ, with the smaller issues continuing to be quoted solely on the Pink Sheets.

An electronic quotation service was created in 1999 and provided real-time quotations via

the Internet in both the Pink and Yellow Sheet markets. The market then became more

easily accessible with the creation of the www.pinksheets.com website, which

dramatically increased the visibility of Pink Sheets issues. On June 2, 2003, Pink Sheets

introduced Pink Link which offered electronic order negotiation and execution

capabilities as a supplement to the routine use of telephone negotiations.

The Pink Sheets market offers issuers, market makers and investors a unique set

of rules and regulations in comparison to the organized markets. At its core, the Pink

Sheets is a forum for market makers to post quotes and execute trades. It is formally a

Securities Information Processor (SIP) and an Interdealer Quotation System. Issuers do

not list their securities, and pay no fees to Pink Sheets if their stock is quoted/traded on

their market. Thus, stocks on the Pink Sheets can not be thought of as ever having been

“listed” or “delisted”. They are quoted or not quoted.

One of the key features of the market that has significant implications for both

issuers and investors is that issuers do not need to register their securities with the

Securities and Exchange Commission (SEC), nor are they required to be current in their

reporting requirements.4 In fact, financial statements need not be audited. While the Pink

Sheets encourages issuers to publish current and audited statements so that investors have

the necessary confidence to actively trade their stock and create a liquid market, issuers

are under no obligation to do so. Stocks in all other markets, including the OTCBB which

is operated by NASDAQ, must abide by the registration requirement and be current in

their financial reporting obligations. The only times that issuers are required by federal

law to provide adequate current information (independent of where their stock is traded)

occurs under one of the following four situations: (a) when firms are initially quoted, (b)

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when officers or affiliates are buying or selling securities in the OTC market, (c) when

issuers are actively promoting the firm that could lead to an increase in trading volume,

or (d) when privately placed securities become eligible to trade in the OTC market.

Investors trade Pink Sheets stocks through registered brokers who then route the

order to a market maker quoting the particular issue. Interestingly, investors must accept

the liability for potential losses when trading penny stocks on the Pink Sheets market by

physically signing Schedule 15G, which highlights the risks of their investment and that

they understand their entire capital is at risk. The inherent risk of many Pink Sheets

stocks is reflected in the size of their bid-ask spreads. For most stocks on the organized

exchanges, percentage spreads are typically not much larger than 1% or 2%. However, in

thinly traded penny stocks, these percentage spreads may be far larger with Macey et al.

(2004) reporting percentage spreads of 51% for newly delisted companies that begin

trading on the Pink Sheets. As a consequence, investors can lose a substantial fraction of

their capital simply from trading costs, even if the value of a stock is unchanged between

transactions!

The rules and regulations for market markers are also distinctly different in the

Pink Sheets market relative to either the OTCBB or the NASDAQ market. First, unlike

NASDAQ, there need only be one market maker posting quotes in order for trading to

occur relative to the two market-maker rule in the other dealer markets. Market makers

wishing to quote a Pink Sheets security must first qualify under NASD rules as a

qualified participant. There are two primary means of satisfying this condition. The first

requires that the market maker satisfy NASD rule 15c2-11 by submitting Form 211 to

NASD Regulation at least three days before they wish to submit quotes in a particular

issue. The form essentially certifies that the market maker has in his or her possession

certain material documents regarding the firm’s financial situation (such as offering

circulars, latest 10k reports, or a laundry list of specific items). Certain exceptions are

also available that alleviate the need to file Form 211. These exceptions include (a)

issuers who are currently traded on an exchange or NASDAQ, (b) submitting an

unsolicited quote that represents a customer order and not the interest of the market

making firm, (c) having quoted the stock on the OTCBB for the previous 30 days or (d)

the issue being piggyback qualified. This last exception permits a market maker to post

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quotes as long as another market maker has been posting Pink Sheets quotes for a

minimum of 30 days. In addition, quotes must appear on at least 12 of these days with no

more than four consecutive days without a quote. Thus, due diligence by one market

maker is sufficient to allow others to post quotes as well. Finally, investors who place

orders with broker/dealers should not expect to see their orders reflected in the market

maker quotes since the Pink Sheets market is not subject to the Limit Order Display

requirements introduced in the Order Handling Rules.

Market makers are, however, still subject to the requirement that they be

registered with the SEC and are subject to the same NASD rules of conduct as market

makers in the OTCBB or NASDAQ market. The NASD monitors trading in the Pink

Sheets and market makers are expected to abide by a number of rules that apply to stocks

traded in the larger markets. For example, market makers who post open quotes must

honor their prices for a normal-sized order in that security. Thus, market makers must

comply with the firm-quote rule. In addition, market makers must search other markets

where the security is traded (such as the OTCBB) to ensure that the Pink Sheets price is

the best available in the market at the time of execution. They are also subject to the rule

requiring that trades be reported within 90 seconds of execution.

Stocks appear on the Pink Sheets for several reasons. Some stocks will be

quoted/traded on the Pink Sheets even if they are simultaneously quoted/traded on the

OTCBB or even NASDAQ or one of the organized exchanges. However, stocks that

trade almost exclusively on the Pink Sheets fall into four categories. The first include

securities that are economically distressed. They will have been delisted from NASDAQ

or an Exchange (examples include Enron and Adelphia Communications), or represent

equity that has been issued by a firm after resolving a bankruptcy filing. The second

represent Microcap issues that do not quality for listing in other markets and would

typically fall under the penny stock umbrella. The third include large foreign issuers

whose stock is listed in their home country but elect to trade via ADRs on the Pink Sheets

market (examples include Nestle, Roche Pharmaceuticals, Volkswagen, Heineken and

Nintendo). These stocks generally carry much higher prices and trading volume, and far

narrower percentage spreads. Bypassing NASDAQ and the Exchanges allows foreign

companies to avoid the expense of filing documents with the SEC and lessens their

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regulatory burdens (such as not preparing their financial statements according to GAAP).

A number of ADRs will be of high quality and could qualify for listing on the other

markets. Similarly, some issuers could potentially delist and trade on the Pink Sheets to

avoid the increased compliance costs associated with Sarbanes/Oxley. The fourth

includes companies that are very tightly held and trade very infrequently.

In keeping with the lack of regulatory oversight of the market, there are no

prescribed tick sizes for any of the issues, independent of their share price. Since penny

stocks are prevalent, trades can be executed in increments of $0.0001. There are

potentially 10,000 price points per dollar available for each issue, and it will be an

empirical matter to determine if or how the market invokes the negotiation hypothesis of

Harris (1991) to manage the determination of an appropriate tick size.

The Pink Sheets market follows NASDAQ and the exchanges by permitting

trading between 9:30 a.m. and 4:00 p.m., and quotations are posted between 7 a.m. and 5

p.m. The Pink Sheets market also follows NASDAQ’s holiday schedule.

III. Data

Trade and quote data from January 2004 through July 2006 were obtained directly

from Pink Sheets. The quote data are a complete record of quoting activity on the Pink

Sheets electronic quotation service. Quote records include ticker symbol, issuer name,

time to the nearest second, and dealer identity. There are five categories of quotes

indicated by Code. Code (1) indicates a dealer is updating a quote, either in price,

quantity, or from inactive to active status. Only active quotes are eligible for trade. Code

(2) indicates a dealer is posting a quote for a stock for which the dealer does not have an

outstanding quote, i.e. it is an addition. Code (3) indicates a dealer is canceling a quote

for a stock, i.e. it is a deletion. Code (4) is reserved for beginning-of-day quotes that are

recycled from the prior trading day. These are indications of interest only and are not

eligible for trade. Code (6) indicates that the quote is the inside quote for the market, i.e.

the highest bid or lowest offer. In order for an inside quote to be recognized, there must

be at least two dealers posting active quotes for a stock. Quotes are further characterized

by Type. Type (A) quotes are active, and include a price and quantity. Type (U) quotes

8

are indications of interest, and do not have prices listed. Type (OW) (offer wanted) and

(BW) (bid wanted) indicate that the dealer is actively seeking a counterparty.

There are 132,115,761 records in the quote files, associated with 22,323 unique

ticker symbols. We eliminate 829,552 records with blank ticker symbols. Of the

remainder, 21,437,979 are inside quotes active at both the bid and the ask, associated

with 6,819 unique ticker symbols. We focus on this subset because they contain more

information about the cost of trading than other quote codes. Of these, 54,707 are

eliminated for having an ask quote less than or equal to the bid quote. In our preliminary

analysis of clustering and spreads, we partition the data into several time periods around

the changes in tick size implemented in 2006. We summarize below the quotes from

January 2004 through October 2005 to describe the state of the market prior to the tick

size experiment.

Figure 1A shows the number of stocks as a function of their average midpoint

quote. To be counted, a stock must have at least one active inside quote on at least 10

trading days over the January 2004 to October 2005 period. Clearly, there are large

numbers of stocks across a wide range of prices: 519 stocks have an average midpoint

less than $0.01 whereas 332 have an average midpoint greater than $10. Figure 1B shows

the average number of quote updates per stock per day again as a function of their

average midpoint quote. Higher priced stocks are much more actively quoted. This result

suggests and foreshadows substantial differences across subsamples of Pink Sheets stocks

formed by stock price. As a consequence, our analysis of clustering and spreads is

conducted across price-based subsamples.

Figure 2 displays the quoted percentage spread averaged across all valid active

inside quotes in the January 2004 to October 2005 period in five minute intervals

between 7:00 a.m. and 7:00 p.m. for four different price categories. The spread falls

rapidly after the 9:30 a.m. opening and rises rapidly at the 4:00 p.m. close, suggesting

that quotes outside the trading day do not accurately reflect the cost of trading and merely

indicate presence in the marketplace. We thus eliminate quotes outside this period. For

comparison, McInish and Wood (1992) and Lee, Mucklow and Ready (1993) document a

U-shaped pattern in the percentage inside spread during the trading day for NYSE stocks,

9

while Chan, Christie and Schultz (1995) find that inside spreads remain relatively flat for

the first few hours after the open, and then decline during the remainder of the day. They

attribute the absence of a post-open decline in inside quoted spreads to the absence of

limit orders on NASDAQ during their sample. As described in the next section, the

majority of Pink Sheets stocks are characterized by extreme levels of illiquidity and

volatility, suggesting that investors would shy away from using limit orders. This may

explain why the spread is relatively flat during the trading day on the Pink Sheets, as

opposed to a U-shaped pattern.

The trade data are a complete list of transactions executed on the Pink Link

electronic negotiation and trade execution system. According to the Pink Sheets website,

approximately 25% of share volume in Pink Sheets stocks is conducted using Pink Link.

Trade records include ticker symbol, time to the nearest second, price, quantity, dealer

identity for buyer and seller, and an indicator for whether the trade is buyer or seller

initiated. There are 13,105,880 trades in the January 2004 through July 2006 period. Of

these, 271,550 are dropped because they are posted outside the 9:30 a.m. to 4:00 p.m.

trading day, and an additional 2,963 are dropped because their ticker symbols cannot be

matched to any quotes. A total of 12,831,367 trades involving 12,372 different stocks are

left for the analysis. Figure 3 displays the number of trades in 5-minute intervals

partitioned by trade price. Trading occurs with a clear U-shaped pattern that has been

well documented for the NYSE and NASDAQ by Lee, Mucklow and Ready (1993) and

Chan, Christie and Schultz (1995). The most actively traded stocks on the Pink Link

system are those in the $1 to $10 price range.

From this initial view of the data, we already observe a feature of regularity

associated with more structured markets: the familiar intraday patterns in trading volume

and bid-ask spreads previously documented on NASDAQ and the NYSE. This suggests

that there is an inherent commonality across markets, perhaps driven by information

flow, independent of market structure or regulatory environment.

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IV. Clustering

Prior to February 21, 2006, the Pink Sheets quotation and trading systems did not

have mandated tick sizes. The only limiting factor with regard to price points are the

number of digits available in the electronic systems, which are four after the decimal in

the quotation system and five after the decimal in the trading system, corresponding to

hundredths and thousandths of a penny! Academic studies provide two relevant

arguments for why the ability to price stocks in these small increments may not be

optimal. First, Brown, Laux, and Schacter (1991) and Harris (1991) note that the smaller

the tick size, the larger the number of possible prices at which to trade, thereby

complicating negotiation and presumably decreasing the average speed of execution.

Second, a smaller tick size may decrease market depth by reducing the profitability of

supplying liquidity, as implied by the model of Anshuman and Kalay (1998).

To determine the tick sizes that market participants actually use, we investigate

the degree of clustering in bid quotes and trade prices over the January 2004 to October

2005 period. Figure 4 shows the percentage of bid quotes with decimal components at

each of the 10,000 possible price points. In Panel A, all stocks are included, and two

features are apparent. First, there are large spikes at the whole nickels and dimes. Second,

there is a right-skewed distribution with a peak at zero. This combination suggests two

distributions are mixed, corresponding to clustering patterns for relatively low and high

priced stocks. This is illustrated in Panels B through D. Panel B shows that for stocks

above $10, there are virtually no quotes other than the whole nickels and dimes. The

largest category is at zero, i.e. approximately 8% of these quotes are on whole dollars.

The next highest is $0.50, followed by $0.25 and $0.75. Panel C shows that for stocks

between $1 and $10, the nickels and dimes still contain the bulk of the quotes, but other

price points are visible. For stocks below $1, in Panel D, the distribution is right skewed

with a peak at zero. This is due to the large number of stocks with prices close to zero.

We control for this by focusing in Panel E on only those price points below $0.10 and

further in Panel F for those price points below $0.01. When we do this, the same sort of

clustering is evident, just at a different scale.5 In sum, regardless of the stock price,

dealers select a specific price grid to eliminate price points, presumably to facilitate trade.

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Figure 5 shows the percentage of trade prices with decimal components at the

same 10,000 possible price points examined in Figure 4. Though trade prices can actually

extend one additional decimal place, less than 0.5% have a number other than zero in the

final digit and these are not depicted. Trade prices cluster in a similar fashion, but the

level of clustering is somewhat lower, especially for the low-priced stocks, evidence that

negotiation results in a finer price grid.

Table 1 summarizes the clustering evidence by listing the frequency with which

bid quotes and trade prices are whole multiples of $0.25, $0.10, $0.05, $0.01, $0.005, and

$0.0005. The impact of price level on the degree of clustering is evident. In Panel A, for

example, the frequency of whole nickel quotes falls from 96.9% for quotes above $10, to

62.6% for quotes between $1 and $10, then to 28.1% for stocks between $0.10 and $1. A

simple explanation for this is that observed prices, which tend to cluster, can be viewed

as the unobserved “true” value rounded to the nearest increment. As stock prices

decrease, the resulting pricing error is a larger percentage of the true value for a given

increment, hence a finer price grid is used. Panel B shows a similar pattern for trade

prices. In most cases, there is somewhat less clustering, suggesting that pre-trade

negotiation provides some degree of price improvement. To investigate, we extract all

trades with an active inside quote posted on the same day but prior to the trade. Then, we

compare the trade price to the most recent active inside quote. Table 2 shows the results.

Overall, 9.8% of buys and 9.3% of sells benefit from price improvement. When trades are

segregated by trade price, one category stands out: buys with trade price below $0.001.

For these trades, 28.3% occur at prices less than the prior ask quote.

The results above suggest that market participants have endogenously established

effective tick sizes by simply grouping stocks by price. Prior literature provides other

determinants of clustering, however, suggesting that a price-based tick size schedule may

not be optimal for all stocks. Ball et al. (1985) study the economics of the price grid and

argue that the amount of information publicly available about an asset dictates the degree

of clustering that takes place. They study clustering in gold prices over the period January

1975 through April 1981 and find that the degree of clustering is positively related to the

level of price and price volatility, and declines over their sample. The time trend is

attributed to an increase in the efficiency of the gold market resulting from an increase in

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the number of gold markets and derivative securities. Harris (1991) conducts a cross-

sectional analysis of clustering in stock prices and, as in Ball et al. (1985), finds a

positive relation between the degree of clustering, price level, and volatility. Furthermore,

he finds that clustering is lower for stocks with higher market capitalization and trade

frequency, which is consistent with the idea that finer price grids are chosen by market

participants when information is more readily available.

We study whether clustering varies cross-sectionally in the Pink Sheets stocks as

predicted by prior work by estimating parameters of the following specification:

(1) ( )1 2 3lni i i i iF Q TradeFrequencyα β β β σ ε= + + + +

where Fi is the frequency with which bid quotes for stock i cluster during the 9:30 a.m. to

4:00 p.m. trading day, Q is the average bid quote, TradeFrequency is the average

number of trades per day, and σ is return volatility. Following the price-dependency

shown above, we separate stocks into four categories based on the average trade price

over the January 2004 to October 2005 period. For each category, we select an

appropriate dependent variable F. For each stock above $10, we use the percentage of the

stock’s bid quotes that are whole multiples of $0.25. For stocks between $1 and $10, we

use the percentage of bid quotes that are whole multiples of $0.05. For stocks between

$0.10 and $1, we use the percentage of bid quotes that are whole multiples of $0.01, and

for stocks between $0.10 and $0.001, we use the percentage of bid quotes that are whole

multiples of $0.0005.

We included average bid quote Q to account for the positive relation between

clustering and price level. Even though we have segregated the stocks by price, there is

still wide variation in prices within these categories. We apply a logarithmic

transformation to control for the right-skewed distribution of prices. We include trade

frequency to proxy for the amount of information available for a stock and the return

volatility σ to capture the uncertainty about true value.6 We construct daily returns from

closing midpoint prices. If there are days without quotes, we compute the close-to-close

return using the next available closing midpoint.7

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Table 3 shows the results of OLS regressions. In all cases the adjusted R-squared

indicates good explanatory power, increasing from 36% for the highest-priced stocks to

65% for the lowest. In contrast, Harris (1991) reports an R-squared between 25% and

35%, though these results are not directly comparable since he studies a market with a

tick size of one-eighth and hence defines the dependent variable differently. Below each

coefficient is the corresponding two-sided p-value. All coefficients are statistically

significant at the 5% level, with the exception of the coefficient on volatility for the two

lowest price categories, and the signs are as predicted. Clustering is positively related to

price level and volatility, and negatively related to trade frequency. Below the p-value for

the intercept is the fitted value of the dependent variable computed at the cross-sectional

mean of each independent variable. Below the p-value for each independent variable is

the change in the fitted value when the variable is increased by one cross-sectional

standard deviation. In all cases, the price level is the most influential variable. The impact

of price ranges from 17% for the lowest-priced stocks to 8% for the next category. The

impact of trade frequency ranges from 3% to 7%, and the impact of volatility is 5% and

10% for the two categories with higher-priced stocks. These results indicate that the

economic determinants of clustering identified in earlier studies are present in the Pink

Sheets market as well – in addition to stock price, trading frequency and volatility also

are related to the tendency for market participants to use a given tick size when quoting

and trading stocks. Furthermore, these results suggest that when measuring the impact of

the tick size schedule by comparing market quality statistics of stocks on which the tick

size schedule is imposed to those on which it is not, we must control for variables such as

price, trading activity, and volatility.

Tables 4 and 5 list stock-level summary statistics of quotes and trades computed

over the January 2004 to October 2005 period. To be included, a stock must have at least

one active inside quote on at least 10 days in this period, as well as at least one trade on at

least 10 days. A total of 3,436 stocks meet these criteria. Table 4 shows that the median

stock has average midpoint of $0.21, bid-ask spread of 28.2%, and close-to-close

volatility 15.5%. These numbers are dramatically different from listed stocks. Note,

though, that when stocks are categorized by price in Table 4, the 332 stocks with average

midpoint above $10 resemble stocks traded on the NYSE or NASDAQ. These highest-

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priced stocks have a median bid-ask spread of 3.9% and close-to-close volatility of 2.3%.

Looking across the categories, spreads widen and volatility increases as prices fall. Table

5 confirms the inverse relation between price and volatility when volatility is measured

using closing trade prices. These patterns suggest that grouping stocks by price for the

purposes of assigning tick sizes implicitly controls for the other determinants of

clustering. According to the theory described above, high priced stocks, which generally

feature lower volatility and higher quotation activity, should have smaller tick sizes (on a

percentage basis) than low priced stocks.

As shown in Table 4, quoted bid-ask spreads are quite high in the Pink Sheets

market, especially for low-priced stocks. Figures 4 and 5 reveal a large degree of

clustering for quotes and trade prices. Does the clustering contribute to artificially wide

spreads? Or can standard models of market making explain variation in spreads across

stocks?

V. Determinants of the Bid-Ask Spread

Figure 6 plots the clustering of quoted spreads in the January 2004 through

October 2005 period. We drop a relatively small number of observations with spread

greater than $1. Clearly, quoted spreads cluster in the same way that individual quotes

and trade prices do, suggesting that clustering may keep spreads wider than necessary. To

determine the degree to which the observed spreads can be explained by economic

features of the market, we estimate parameters of a cross-sectional model of market

maker costs. Stoll (1978) argues that these costs fall into three categories: order-

processing costs, inventory-holding costs, and adverse selection costs. Order-processing

costs are those associated with providing the market making service including

administrative, technological, and labor costs. Inventory-holding costs refer to the risk a

market maker incurs while maintaining positions in stocks necessary for providing

liquidity to investors. Adverse selection costs are generated when a market maker trades

with investors that are better informed about the expected price movement of a particular

stock.

15

Prior research investigating the determinants of the spread uses a variety of

variables to proxy for inventory-holding costs and adverse information costs, including

the volatility of stock returns, the time between trades, and market capitalization. The

impact of the variables on spreads is usually estimated in a linear regression. See, for

example, Demsetz (1968), Tinic (1972), and Benston and Hagerman (1974) for some

early examples and Bollen et al. (2004) for a review. To examine the role of market

maker costs on spread determination, we estimate the parameters of the following

representative specification:

(2) 1 2 3 4i i i i i iSPRD InvTV MHI Pα β σ β β β ε= + + + + +

where SPRD is the quoted dollar bid-ask spread, σ is the volatility of close-to-close

returns, InvTV is the inverse of trading volume, MHI is the modified Herfindahl index,

and P is average trade price. Return volatility proxies for the inventory risk. As is

standard in the literature, we use the inverse of trading volume to proxy for order-

processing costs. The larger the trading volume, the smaller should be the cost per share

of stock since costs can be amortized over a larger quantity. We use the modified

Herfindahl index to proxy for the level of competition for a given stock. The standard

Herfindahl index is computed as:

(3) 2

1

NMj

j

VHI

TV=

⎛ ⎞= ⎜ ⎟

⎝ ⎠∑

Where HI is the Herfindahl index, NM is the number of market makers, Vj is the number

of shares traded by market maker j, and TV is the total number of shares traded by all

market makers. The modified Herfindahl index MHI is computed as:

(4) 11 1

HI NMMHINM

−=

−.

The advantage of the MHI is that it ranges from zero, for the case of perfect competition,

to one, for the case of a monopolist, and so has a more natural interpretation.

For each stock, we compute an equal-weighted quoted spread each day the stock

is quoted in August through October of 2005. We use only the active inside quotes. Then,

we record the median of these daily averages. This serves to mitigate the impact of

16

outliers. Several stocks had extremely wide quoted spreads the first few days they

appeared in the database, indicating possible data-entry error. We scale inverse trading

volume by 1,000 to keep the variables’ coefficient estimates in a tighter range.

Table 6 shows the results with all standard errors corrected for heteroskedasticity.

For the 178 stocks with average midpoint above $10, and sufficient data to be included in

the analysis, the adjusted R-squared is 98%, which is high compared to the results of

prior studies. Benston and Hagerman (1974), for example, report an R-squared of 75%.

The coefficients on volatility, trading volume, and competition are statistically significant

at the 5% level, indicating that inventory risk, order processing costs, and competition are

significant determinants of bid-ask spreads in the higher-priced stocks on the Pink Sheets

market. For the lower-priced subsamples, the adjusted R-squared deteriorates somewhat

to between 51% and 66%. All coefficients are positive, as expected, and are statistically

significant at the 5% level in almost all cases.

In summary, the quoted spreads on the Pink Sheets market conform very well to

their economic determinants for stocks above $10. Stocks with average trade price below

$10, however, which constitute a majority of the stocks quoted on the Pink Sheets,

feature spreads that are somewhat less-well explained by estimates of volatility, trading

volume, and competition. For these stocks, standard measures of inventory risk may not

capture all the relevant uncertainties, such as the potential for substantial information

asymmetries that may exist in tightly held securities or time variation in liquidity caused

by pump and dump schemes. Time series models of the duration between trades may

allow an estimate of this latter risk – we leave this exercise for future research.

VI. Tick Size Experiment

Our analysis of clustering in quotes, trade prices, and spreads suggest that market

participants have created some degree of order in the Pink Sheets – a market without any

centrally dictated tick size. Existing studies of the reduction of tick sizes on the NYSE

and NASDAQ provide several advantages and disadvantages of a mandated minimum

price impact that raise the question whether the Pink Sheets market can be improved by

more structure. One impetus for decimalization on the major exchanges was that eighths

17

artificially widened spreads on some stocks. In the Pink Sheets market, with some stocks

trading near $0.0001, even a one penny spread would obviously be inappropriate, hence

we must guard against imposing artificially wide spreads by choosing different tick sizes

for different price levels. Harris (1994), Angel (1997), and Seppi (1997) argue that a

significant tick size can improve liquidity by strengthening price priority in a limit order

book – an insignificant tick size eliminates the cost of jumping ahead of an existing order.

However, given the illiquidity of many Pink Sheets stocks documented above, it seems

unlikely that limit orders will ever be a significant source of liquidity regardless of the

tick size. Anshuman and Kalay (1998) point out that a significant tick size can improve

liquidity by ensuring dealers are adequately compensated for making a market in a stock.

However, the level of spreads already seems quite wide. Perhaps the adoption of a tick

size schedule will increase liquidity by making investors feel more comfortable using a

market that better resembles the major exchanges. This is an empirical question and one

that we can begin to address by examining changes in quotation and trade activity around

any change in tick size.

This rest of this section describes a unique experiment in which we designed a

tick size schedule for the Pink Sheets, and then documented changes in quotation and

trading activity that occurred subsequent to its adoption.

A. Background

Starting on February 21st, 2006, stocks with ticker symbols beginning with the

letters A through D were subject to an experimental tick size schedule. Different tick

sizes were assigned to subsets of stocks formed by price. The size of each tick was

chosen to limit the frequency with which the tick would be binding, based on clustering

evidence reported in Table 1, while still remaining economically meaningful. Quotes

above $1 were required to conform to a tick size of $0.01; Table 1 indicates that 99.3% of

quotes above $10, and 96.3% of quotes between $1 and $10, used this tick size between

January 2004 and October 2005. Similarly, quotes at or less than $1 but above $0.10

required a tick size of $0.005; quotes in this category used this tick size 94.6% of the

time. Quotes at or less than $0.10 but above $0.001 required a tick size of $0.0005;

18

quotes in this category used this tick size 79.7% of the time. Remaining quotes at or less

than $0.001 could use the original tick size of $0.0001. Bid quotes were rounded down to

the nearest increment and ask quotes were rounded up to the nearest increment if they

were submitted between increments.

Preliminary analysis, described below, confirmed anecdotal claims that market

quality for some stocks deteriorated, hence the tick size schedule was revised slightly on

June 16th, 2006. Stocks between $0.005 and $0.001 were moved to the lowest tick size

category. Then on July 11th, 2006, the tick size schedule was implemented for stocks with

ticker symbols beginning with the letters E through Z. Given these dates, our analysis

contains two sets of observation windows. The first set has a pre-period of November 1st,

2005 to February 17th, 2006. This is the period prior to the first implementation of the

experimental tick size. The post-period is February 27th, 2006 to June 15th, 2006. The

second set of windows has a pre-period of May 15th, 2006 to June 15th, 2006 and a post-

period of June 16th, 2006 to July 10th, 2006. These periods bracket the revision to the tick

size schedule.

B. Summary Statistics

Table 7 summarizes all active inside quotes posted in the first pre- and post-

periods to provide a background for the other results. Listed are the number of quotes

each period for the A – D and E – Z stocks, the number of stocks contributing quotes to

each category, as well as the percentage of the quotes that fall into three categories. “LT,”

“EQ,” and “GT,” indicate a quoted spread less than, equal to, or greater than the

experimental tick size corresponding to the bid quote. In the pre-period, for example,

6.4% of the quoted spreads for the A – D stocks were less than the experimental tick size.

In other words, for these quotes the tick size schedule would have been binding and

would have resulted in a widening of the spread. For the A – D stocks, 3.5% of the

quoted spreads equaled the tick size, and the remaining 90.1% of the quoted spreads were

wider than the tick size. The results for E – Z stocks are similar. This result suggests that

the tick size schedule should not affect the vast majority of quotes.

19

When the statistics are broken down by price category, several interesting facts

are revealed. For quotes with bid prices above $1, virtually none of the quoted spreads in

the pre-period are less than or equal to the experimental tick size of $0.01. This suggests

that dealers opted not to use intra-penny quotes even though they could have done so. For

stocks between $0.10 and $1, 24.8% of the A – D stocks have quotes less than the

experimental tick size of $0.005. In contrast only 3.0% of the E – Z stocks have quotes

less than $0.005. Unreported analysis reveals that almost all of the sub $0.005 spreads in

the A – D category involve three stocks, so we should not draw much inference from this

result. We split the next category of stocks – those between $0.001 and $0.10 – into two

categories for greater precision. For stocks between $0.005 and $0.10, 2.9% of the A – D

quotes and 8.4% of the E – Z quotes have quoted spreads less than the tick size of

$0.0005. However, for stocks between $0.001 and $0.005, 43.6% of the A – D quotes and

45.2% of the E – Z quotes have quoted spreads less than the tick size, which is again

$0.0005. The reason for this is that the tick size is a much larger fraction of stock price

for stocks between $0.001 and $0.005 – a minimum of 10% and a maximum of 50%.

Hence for these stocks we might expect the tick schedule to have the greatest impact.

The results for post-period differ in two important ways. First, for the A – D

stocks, by design none of the quoted spreads are less than the tick size. We can see from

the percentage of E – Z stocks with quoted spreads less than the tick size an estimate of

the proportion of A – D quoted spreads that are forced apart as a result of the tick size. By

far the largest proportion is again in the category of stocks with price between $0.001 and

$0.005, for which 62.8% of the quoted spreads for E – Z stocks are less than the

corresponding tick size. Second, most categories of stock show a substantial increase in

activity as measured by the number of inside active quotes. The increase in quotation

activity is consistent with the long-term positive growth of the Pink Sheets market as

illustrated in Figure 7. In Table 8, the notable exceptions are the A – D stocks with price

between $0.10 and $1, and those between $0.001 and $0.005, which suffered a decline in

quotation activity. This result suggests that these two categories may have been

negatively affected by the tick size schedule.

Table 8 shows the average percentage spread for the same categories of quotes

listed in Table 7. In the pre-period, the A – D stocks and E – Z stocks have the same

20

average percentage spread, about 7%, and both show modest declines in the post-period.

When the results are broken down by the size of the bid quote, however, the two

categories identified above show a marked increase. A – D stocks with price between

$0.10 and $1 shown an increase from 8.94% to 11.15%, whereas the E – Z stocks show a

decrease from 14.01% to 12.67%. A – D stocks with price between $0.001 and $0.005

appear to be most affected, however, and show an increase from 30.25% to 40.26%. In

contrast, The E – Z quotes in the same price category have spreads that decrease from

30.33% to 22.78%.

Also displayed in Table 8 are results from a subset of the A – D stocks for which

a matching E – Z stock can be found using summary statistics computed over January

2004 to October 2005. The matched sample is constructed in order to control for

systematic differences between A – D stocks and E – Z stocks that might affect the

degree of clustering and the subsequent change in spreads and other activity measures

following the implementation of the tick size.

The matching procedure is as follows. For every stock with at least one active

inside quote on at least 10 days in January 2004 to October 2005 and at least one trade on

at least 10 days, we compute the dollar trading volume, average trade price, return

volatility, and median percentage spread over the period. Then, for every A – D stock for

which these statistics can be computed, we construct a distance measure between it and

all E – Z stocks for which the statistics can be computed. The distance between stock i

and j, for example, is computed as:

(5) 24

, ,,

1

Distance i k j ki j

k k

x xσ=

−⎛ ⎞= ⎜ ⎟

⎝ ⎠∑

where k denotes a matching criterion, kσ is the cross-sectional standard deviation of the

criterion, and , , and i k j kx x are the values of criterion k for stocks i and j, respectively. The

E – Z stock with minimum distance is selected as the match for a given A – D stock.

Each E – Z stock can only be used to match one A – D stock.

21

The results listed in Table 8 for the matched stocks are qualitatively similar to the

full sample, suggesting that the widening of the spread for the A – D stocks with price

between $0.001 and $0.005 is a direct result of the tick size experiment.

C. Determinants of the Bid-Ask Spread

As shown above, A – D stocks with price between $0.001 and $0.005 appear to

suffer wider spreads as a result of the experimental tick size schedule imposed on

February 21st, 2006. To determine whether the increase in observed spreads can be

explained by changes in other economic features of the market, we estimate parameters

of the cross-sectional model of market maker costs used in Section V but supplemented

with an additional variable as follows:

(6) 1 2 3 4 5i i i i i i iSPRD InvTV MHI P Iα β σ β β β β ε= + + + + + +

where Ii is an indicator variable that equals one if stock i has ticker symbol beginning A –

D and zero otherwise.

Table 9 shows the results for the pre-period with all standard errors corrected for

heteroskedasticity. Results are displayed for five categories of stocks based on their

average trade price. The adjusted R-squared ranges from 24% for the stocks with price

less than or equal to $0.001 to 99% for the highest-priced stocks. The most robust

predictors appear to be volatility and inverse trading volume, which have positive

coefficient estimates in all cases, and which are significant at the 5% level for most price

categories. More importantly here, the coefficient on the indicator variable is

insignificant in all price categories, suggesting that there is no systematic difference

between the unexplained spreads of A – D stocks and E – Z stocks in the pre-period.

Table 10 shows the results of the same regressions with variables computed over the

post-period. For stocks with price between $0.001 and $0.005, the coefficient on the A –

D indicator is positive and statistically significant with a p-value of 4%. The coefficient

estimate is 0.0006, which corresponds to an abnormal percentage spread of as much as

60% for stocks with price right at 0.001. Thus, even after controlling for other

22

determinants of the bid-ask spread, it appears as though stocks in this price range are

adversely affected by the tick size.

Table 11 reports trading statistics for the matched sample of A – D and E – Z

stocks. Due to the large cross-sectional variation in trading activity, none of the

differences between categories is statistically significant. Consistent with complaints

from market participants, though, the only category which features a drop in the number

of trades per stock contains the A – D stocks with price between $0.001 and $0.005.

D. The Revised Tick Size Schedule

On June 16th, the Pink Sheets revised the tick size schedule by dropping the tick

size to $0.0001 for A – D stocks with quotes between $0.001 and $0.005. To measure the

impact of this change, we analyze quote activity and percentage spreads before and after

this date. Table 12 shows the results in a manner identical to Table 8 but with a new set

of event dates. As mentioned above, the pre-period is May 15th, 2006 to June 15th, 2006

and the post-period is June 16th, 2006 to July 10th, 2006. The most important category is

listed in Panel E. The quotes of A – D stocks have average percentage spread of 39% in

the pre-period compared to 18% for the E – Z stocks. After the switch, the A – D stocks

feature a decline to 29%, the same as the E – Z stocks.

Our results show that when tick sizes are introduced but allowed to vary with

stock price, then market quality indicators such as quoted spread and trade frequency

show no sign of deterioration and some evidence of improvement. Even in a relatively

unregulated and unstructured market, investors appear to respond to tick sizes as

predicted by prior research.

VII. Conclusions

Overall, our analyses reveal a remarkable degree of order on the Pink Sheets

before the tick size schedule was introduced. Market participants endogenously selected a

tick size schedule as reflected in aggregate clustering patterns of quotes and trade prices.

Stocks with comparable price levels exhibited different degrees of clustering as function

23

of their volatility and liquidity. Spreads also varied cross-sectionally with stock-specific

attributes related to dealer costs. These results illustrate the applicability of previously

developed microstructure theory to new markets.

Following the tick size schedule, quotation and trade activity continued to

increase, consistent with the Pink Sheets overall growth rate. This preliminary

examination of the new tick sizes indicates that in this market, and quite likely more

generally, it may be optimal to allow tick sizes to vary with stock price. We leave

analysis of long-term impacts for future research.

24

References

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Angel, J., J. Harris, V. Pauchapogesan, and I. Werner. “From Pink Slips to Pink Sheets: Liquidity and Shareholder Wealth Consequences of NASDAQ Delisting.” University of Connecticut, working paper (2004).

Anshuman, R., and A. Kalay. “Market Making with Discrete Prices.” Review of Financial Studies, 11 (1998), 81-109.

Ball, C. A., W. A. Torous, and A. E. Tschoegl. “The degree of Price Resolution: The Case of the Gold Market.” Journal of Futures Markets, 5 (1985), 29-43.

Benston, G., and R. Hagerman. “Determinants of bid-ask spreads in the over-the-counter market.” Journal of Financial Economics 1 (1974), 353-364.

Böhme, R. and T. Holz. “The Effect of Stock Spam on Financial Markets.” Technische Universität Dresden, working paper (2006).

Bollen, N., T. Smith, and R. Whaley. “Modeling the Bid/Ask Spread: Measuring the Inventory-Holding Premium.” Journal of Financial Economics, 72 (2004), 97-141.

Brown, S., P. Laux, and B. Schacter. “On the Existence of Optimal Tick Size.” Review of Futures Markets, 10 (1991), 50-72.

Chan, K.C., W. Christie, and P Schultz, “Market Structure and the Intraday Pattern of Bid-Ask Spreads for NASDAQ Securities.” Journal of Business 68 (1995), 35-60.

Christie, W., and P. Schultz, “Why do NASDAQ Market Makers Avoid Odd-Eighth Quotes?.” Journal of Finance 49 (2004), 1813-1840.

Christie, W., J. Harris and P. Schultz, “Why Did NASDAQ Market Makers Stop Avoiding Odd-Eighth Quotes? Journal of Finance 49 (2004), 1841-181860.

Demsetz, H. “The cost of transacting.” Quarterly Journal of Economics 82 (1968), 33-53.

Frieder, L. and J. Zittrain. “Spam Works: Evidence from Stock Touts and Corresponding Market Activity.” Purdue University, working paper (2007).

Harris, L. “Stock Price Clustering and Discreteness.” Review of Financial Studies, 4 (1991), 389-415.

Harris, L. “Minimum Price Variations, Discrete Bid-Ask Spreads, and Quotation Sizes.” Review of Financial Studies, 7 (1994), 149-178.

Lee, C., and B. Mucklow, and M. Ready. “Spreads, Depths, and the Impact of Earnings Information: An Intraday Analysis.” Review of Financial Studies 6 (1993), 345-374.

Macy, J., M. O’Hara and D. Pompilio. “Down and Out in the Stock Market: The Law and Finance of the Delisting Process.” Cornell University, working paper (2004).

Mandelbrot, B. B. “Stochastic Models for the Earth's Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands.” Proceedings of the National Academy of Sciences of the United States of America 72 (Oct. 1975), 3825-3828.

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McInish, T., and R. Wood. “An analysis of intraday pattern in bid/ask spreads for NYSE stocks.” Journal of Finance 47 (1992), 753-764.

Tinic, S. “The economics of liquidity services.” Quarterly Journal of Economics 86 (1972), 79-83.

Seppi, D. “Liquidity Provision with Limit Orders and a Strategic Specialist.” Review of Financial Studies, 10 (1997), 103-150.

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26

Table 1. Clustering Frequency Listed are the frequencies with which active inside bid quotes and trade prices posted from 9:30 a.m. to 4:00 p.m. on the Pink Sheets market over the period January 2004 – October 2005 are whole multiples of six fractions of a dollar: quarters (0.2500), dimes (0.1000), nickels (0.0500), pennies (0.0100), halves of a penny (0.005), and twentieths of a penny (0.0005). Frequencies are computed separately for four subsets of the quotes (trades) formed by the size of the bid quote Q (trade price P).

A. Bid Quotes

Fraction All Quotes Q > $10 $10 ≥ Q > $1 $1 ≥ Q > $0.10 $0.10 ≥ Q > $0.001

0.0005 94.8% 100.0% 100.0% 99.8% 79.7%

0.0050 85.0% 99.9% 99.2% 94.6%

0.0100 79.6% 99.3% 96.3% 82.4%

0.0500 60.0% 96.9% 62.6% 28.1%

0.1000 31.6% 51.3% 33.7%

0.2500 15.2% 25.5% 16.4%

B. Trade Prices

Fraction All Trades P > $10 $10 ≥ P > $1 $1 ≥ P > $0.10 $0.10 ≥ P > $0.001

0.0005 93.6% 100.0% 100.0% 99.9% 79.5%

0.0050 79.8% 100.0% 99.8% 90.4%

0.0100 72.1% 99.4% 97.8% 76.4%

0.0500 32.9% 88.6% 48.4% 22.7%

0.1000 18.2% 52.8% 26.8%

0.2500 8.5% 34.4% 12.0%

27

Table 2. Price Improvement Listed are the rates of price improvement for trades posted between 9:30 a.m. and 4:00 p.m. on the Pink Link trading system over the period January 2004 – October 2005. Only trades with an active quote at the bid and ask on the same day but before the time of the trade are considered. Buys are “Worse” if the trade price is above the last ask, “Improved” if the trade price is below the last ask, and “At Quote” if the trade price equals the last ask. Sells are “Worse” if the trade price is below the last bid, “Improved” if the trade price is above the last bid, and “At Quote” if the trade price equals the last bid. Results are categorized by trade price P.

A. All Trades # Trades Worse At Quote Improved Buys 1,161,117 1.6% 88.6% 9.8% Sells 1,197,955 1.9% 88.8% 9.3% B. P > $10 # Trades Worse At Quote Improved Buys 196,395 1.9% 90.0% 8.2% Sells 181,656 2.1% 88.2% 9.7% C. $10 ≥ P > $1 # Trades Worse At Quote Improved Buys 317,497 2.5% 85.7% 11.9% Sells 313,307 2.4% 85.2% 12.5% D. $1 ≥ P > $0.10 # Trades Worse At Quote Improved Buys 265,774 1.6% 88.8% 9.6% Sells 272,671 2.2% 87.9% 9.9% E. $0.10 ≥ P > $0.001 # Trades Worse At Quote Improved Buys 326,600 0.9% 93.3% 5.8% Sells 377,548 1.3% 92.7% 6.0% F. $0.001 ≥ P # Trades Worse At Quote Improved Buys 54,851 0.1% 71.6% 28.3% Sells 52,773 0.5% 89.8% 9.7%

28

Table 3. Determinants of Clustering Listed are results of the cross-sectional regression:

( )1 2 3lni i i i iF Q TradeFrequencyα β β β σ ε= + + + +

where Fi is the frequency with which bid quotes for stock i cluster during the 9:30 a.m. to 4:00 p.m. trading day, Q is the average bid quote, TradeFrequency is the average number of trades per day, and σ is return volatility based on closing midpoints. Data are from January 2004 to October 2005. The sample is split into four categories formed by average trade price P. For stocks with P > $10, F measures the frequency of bid quotes that are whole multiples of 0.25; for stocks with $10 ≥ P > $1, F measures the frequency of bid quotes that are whole multiples of 0.05; for stocks with $1 ≥ P > $0.10, F measures the frequency of bid quotes that are whole multiples of 0.01; and for stocks with $0.10 ≥ P > $0.001, F measures the frequency of bid quotes that are whole multiples of 0.0005. Listed are the adjusted R-squared, number of observations, and OLS coefficient estimates. Below each estimate is the two-sided p-value using heteroskedasticity-consistent standard errors. Below the standard error for α is the fitted frequency computed at the cross-sectional mean of each independent variable. Below the standard error for each β is the change in the fitted frequency when each independent variable is increased by one cross-sectional standard error.

P > $10 α β1 β2 β3

R2 0.3592 Estimate 0.0932 0.1207 -0.0035 2.4947 N 327 p-value 0.0228 0.0000 0.0000 0.0000

Delta 0.5690 0.1327 -0.0679 0.1025

$10 ≥ P > $1 α β1 β2 β3

R2 0.4378 Estimate 0.5703 0.1800 -0.0020 0.4632 N 696 p-value 0.0000 0.0000 0.0014 0.0000

Delta 0.7443 0.1539 -0.0626 0.0509

$1 ≥ P > $0.10 α β1 β2 β3

R2 0.3928 Estimate 1.0755 0.0879 -0.0013 -0.0098 N 1,137 p-value 0.0000 0.0000 0.0007 0.7521

Delta 0.9352 0.0779 -0.0317 -0.0012

$0.10 ≥ P > $0.001 α β1 β2 β3

R2 0.6453 Estimate 1.4205 0.1204 -0.0119 0.0425 N 1,217 p-value 0.0000 0.0000 0.0000 0.2333

Delta 0.8452 0.1663 -0.0746 0.0051

29

Table 4. Summary Statistics of Active inside Quotes Listed are summary statistics of active inside quotes posted between 9:30 a.m. and 4:00 p.m. on the Pink Sheets Electronic Quotation Service over the period January 2004 – October 2005. Only stocks with at least one active inside quote and one trade on at least 10 days in January 2004 – October 2005 are included. Listed are inter-quartile ranges of the average quoted midpoint, the average percentage quoted spread, the daily volatility of percentage returns, the number of days the stock has an active inside quote (#Qday), the average number of quote updates per day the stock is quoted, and the number of unique market makers participating at least once in the inside quote (NMM). Statistics are reported for All Stocks as well as for subsets organized by the stocks’ average quoted midpoint Q.

All Stocks N =3,436 25th 50th 75thAvg Price 0.03 0.21 1.30Avg % Spread 13.1% 28.2% 47.9%Volatility 8.6% 15.5% 23.3%# Qday 45 75 141Avg #Q/QDay 3 4 8NMM 9 13 19

Q > $10 $10 ≥ Q > $1 N = 332 25th 50th 75th N = 641 25th 50th 75thAvg Price 15.34 22.56 40.99 Avg Price 1.45 2.51 4.45Avg % Spread 1.4% 3.9% 8.0% Avg % Spread 5.8% 13.4% 27.5%Volatility 1.6% 2.3% 4.2% Volatility 4.1% 8.4% 14.4%# Qday 56 107 246 # Qday 44 85 174Avg #Q/QDay 3 5 25 Avg #Q/QDay 3 5 9NMM 7 11 22 NMM 9 13 19 $1 ≥ Q > $0.10 $0.10 ≥ Q N = 1,113 25th 50th 75th N = 1,350 25th 50th 75thAvg Price 0.17 0.29 0.51 Avg Price 0.0048 0.0180 0.0480Avg % Spread 17.8% 29.9% 46.1% Avg % Spread 26.2% 40.3% 60.2%Volatility 10.5% 15.4% 21.4% Volatility 15.4% 20.9% 28.8%# Qday 45 82 148 # Qday 45 65 112Avg #Q/QDay 3 5 8 Avg #Q/QDay 3 4 6NMM 9 14 20 NMM 9 12 18

30

Table 5. Summary Statistics of Trades Listed are summary statistics of trades posted between 9:30 a.m. and 4:00 p.m. on the Pink Link trading system over the period January 2004 – October 2005. Only stocks with at least one trade and one active inside quote on at least 10 days in January 2004 – October 2005 are included. Listed are inter-quartile ranges of the average trade price, the average trade size in dollars, the daily volatility of percentage returns, the number of days the stock has a trade (#Tday), the average number of trades per day the stock is traded, and the number of unique dealers participating at least once in a trade (NDLR). Statistics are reported for All Stocks as well as for subsets organized by the stocks’ average trade price P.

All Stocks N = 3,436 25th 50th 75thAvg Price 0.04 0.23 1.41Avg $ Trade 528 1,264 2,618Volatility 11.7% 21.9% 35.8%# TDays 23 52 123Avg #T/TDay 2 2 5NDLR 10 15 23

P > $10 $10 ≥ P > $1 N = 327 25th 50th 75th N = 696 25th 50th 75thAvg Price 15.99 23.00 41.10 Avg Price 1.44 2.27 4.23Avg $ Trade 8,412 14,265 21,622 Avg $ Trade 1,887 3,008 5,037Volatility 2.2% 3.5% 6.1% Volatility 6.2% 11.5% 19.8%# TDays 25 58 163 # TDays 27 66 148Avg #T/TDay 1 2 4 Avg #T/TDay 2 2 5NDLR 7 12 27 NDLR 10 15 24 $1 ≥ P > $0.10 $0.10 ≥ P N = 1,137 25th 50th 75th N = 1,276 25th 50th 75thAvg Price 0.17 0.29 0.54 Avg Price 0.0055 0.0213 0.0531Avg $ Trade 1,041 1,449 2,011 Avg $ Trade 148 368 616Volatility 14.9% 22.2% 33.5% Volatility 22.4% 32.6% 48.6%# TDays 27 62 125 # TDays 18 37 96Avg #T/TDay 2 2 4 Avg #T/TDay 2 3 5NDLR 11 16 24 NDLR 9 13 21

31

Table 6. Determinants of the Bid-ask Spread Listed are results of the cross-sectional regression:

1 2 3 4i i i i i iSPRD InvTV MHI Pα β σ β β β ε= + + + + +

where SPRD is the median daily average quoted bid-ask spread, σ is return volatility based on closing midpoints, InvTV is the inverse of trading volume, MHI is the modified Herfindahl index, and P is average trade price. Observations are computed for each stock quoted on the Pink Sheets Electronic Quotation Service and traded on the Pink Link trading system over the period August 1, 2005 through October 31, 2005. The sample is split into four categories formed by average trade price P. Listed are the adjusted R-squared, number of observations, and OLS coefficient estimates. Below each estimate is the two-sided p-value using heteroskedasticity-consistent standard errors.

All Stocks α β1 β2 β3 β4

R2 0.9814 Estimate -0.1978 0.1975 0.2973 1.3764 0.0030N 1,295 p-value 0.0003 0.1611 0.0000 0.0082 0.2642

P > $10 α β1 β2 β3 β4 R2 0.9846 Estimate -1.4017 15.0980 0.2974 10.7739 0.0029N 178 p-value 0.0006 0.0498 0.0000 0.0054 0.2629

$10 ≥ P > $1 α β1 β2 β3 β4 R2 0.6581 Estimate -0.3263 1.3105 0.4117 0.2839 0.0221N 279 p-value 0.0000 0.0000 0.0000 0.2637 0.0001

$1 ≥ P > $0.10 α β1 β2 β3 β4 R2 0.5287 Estimate -0.0557 0.1718 0.2848 0.1814 0.0430N 394 p-value 0.0000 0.0002 0.0000 0.0002 0.0217

$0.10 ≥ P α β1 β2 β3 β4 R2 0.5116 Estimate -0.0067 0.0256 0.0325 0.0081 0.2152N 444 p-value 0.0000 0.0001 0.0278 0.1445 0.0000

32

Table 7. Quoted Spreads and Tick Sizes Listed are summary statistics of active inside quotes posted between 9:30 a.m. and 4:00 p.m. on the Pink Sheets Electronic Quotation Service over the periods November 1, 2005 to February 17, 2006 (the “Pre-period”) and February 27, 2006 to June 15, 2006 (the “Post-period”). Listed are the number of quotes for each period and the percentage of quoted spreads that fall into three categories: “LT,” “EQ,” and “GT” indicate a quoted spread less than, equal to, or greater than the experimental tick size that was implemented on February 21, 2006 for stocks with ticker symbol beginning with letters A through D.

Pre-period Post-period Spread Relative to Tick Size Spread Relative to Tick SizeA. All Quotes # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 449,030 1,147 6.4% 3.5% 90.1% 615,216 1,141 0.0% 7.6% 92.4%E-Z 1,225,268 2,975 2.5% 3.6% 93.8% 1,618,687 3,038 3.9% 4.4% 91.7% Spread Relative to Tick Size Spread Relative to Tick SizeB. Bid > $1 # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 298,085 325 0.0% 1.6% 98.4% 449,753 359 0.0% 4.4% 95.6%E-Z 889,965 776 0.3% 2.4% 97.3% 1,126,074 876 0.0% 2.8% 97.2% Spread Relative to Tick Size Spread Relative to Tick SizeC. $1 ≥ Bid > $0.10 # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 94,277 336 24.8% 7.8% 67.4% 92,246 345 0.0% 18.8% 81.2%E-Z 156,337 879 3.0% 6.8% 90.2% 210,798 954 5.3% 8.2% 86.5% Spread Relative to Tick Size Spread Relative to Tick SizeD. $0.10 ≥ Bid > $0.005 # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 41,256 443 2.9% 2.2% 94.9% 57,483 457 0.0% 6.3% 93.7%E-Z 134,548 1,201 8.4% 3.1% 88.5% 214,138 1,264 10.6% 4.7% 84.7% Spread Relative to Tick Size Spread Relative to Tick SizeE. $0.005 ≥ Bid > $0.001 # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 9,842 204 43.6% 8.7% 47.7% 7,256 213 0.0% 31.8% 68.2%E-Z 26,804 599 45.2% 9.0% 45.8% 47,902 649 62.8% 6.3% 30.9% Spread Relative to Tick Size Spread Relative to Tick SizeF. $0.001 ≥ Bid # Quotes # Stocks LT EQ GT # Quotes # Stocks LT EQ GTA-D 5,570 215 0.0% 33.2% 66.8% 8,478 172 0.0% 43.9% 56.1%E-Z 17,614 610 0.0% 35.3% 64.7% 19,775 505 0.0% 41.4% 58.6%

33

Table 8. Quoted Spread Listed are summary statistics of active inside quotes posted between 9:30 a.m. and 4:00 p.m. on the Pink Sheets Electronic Quotation Service over the periods November 1, 2005 to February 17, 2006 (the “Pre-period”) and February 27, 2006 to June 15, 2006 (the “Post-period”). Listed are the number of quotes for each period and the average quoted spread. “Matched Stocks” include the subset of A – D stocks for which a matching E – Z stock was found using summary statistics computed over January 2004 – October 2005, as well as the matching E – Z stocks.

All Stocks Matched Stocks Pre-period Post-period Pre-period Post-period A. All Quotes # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 449,030 6.84% 615,216 6.22% 340,561 5.37% 366,804 5.51%E-Z 1,225,268 6.79% 1,618,687 6.55% 388,587 5.05% 422,319 5.31% B. Bid > $1 # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 298,085 2.09% 449,753 2.01% 248,866 1.61% 274,518 1.62%E-Z 889,965 1.68% 1,126,074 1.91% 299,521 1.34% 305,326 1.54% C. $1 ≥ Bid > $0.10 # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 94,277 8.94% 92,246 11.15% 51,041 9.61% 45,977 10.76%E-Z 156,337 14.01% 210,798 12.67% 42,073 12.53% 45,820 12.36% D. $0.10 ≥ Bid > $0.005 # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 41,256 23.00% 57,483 19.58% 29,917 19.10% 35,703 17.49%E-Z 134,548 20.41% 214,138 16.73% 35,320 18.77% 54,922 14.12% E. $0.005 ≥ Bid > $0.001 # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 9,842 30.25% 7,256 40.26% 7,561 25.63% 4,750 35.38%E-Z 26,804 30.33% 47,902 22.78% 8,054 24.92% 10,513 20.17% F. $0.001 ≥ Bid # Quotes % Spread # Quotes % Spread # Quotes % Spread # Quotes % SpreadA-D 5,570 64.41% 8,478 55.99% 3,176 54.41% 5,856 49.50%E-Z 17,614 61.27% 19,775 56.14% 3,619 46.80% 5,738 37.96%

34

Table 9. Determinants of the Bid-ask Spread in the Pre-period Listed are results of the cross-sectional regression:

1 2 3 4 5i i i i i i iSPRD InvTV MHI P Iα β σ β β β β ε= + + + + + +

where SPRD is the median daily average quoted bid-ask spread, σ is return volatility based on closing midpoints, InvTV is the inverse of trading volume, MHI is the modified Herfindahl index, P is average trade price, and I is an indicator variable that equals one if the stock has ticker symbol beginning with the letters A – D and zero otherwise. Observations are computed for each stock quoted on the Pink Sheets Electronic Quotation Service and traded on the Pink Link trading system over the period November 1, 2005 through February 17, 2006. The sample is split into five categories formed by average trade price P. Listed are the adjusted R-squared, number of observations, and OLS coefficient estimates. Below each estimate is the two-sided p-value using heteroskedasticity-consistent standard errors.

$1 < P α β1 β2 β3 β4 β5 R2 0.9850 Estimate -1.3591 5.2493 0.9364 0.2367 0.0054 -0.0585N 448 p-value 0.0000 0.0000 0.0000 0.9219 0.1123 0.8174

$0.10 < P ≤ $1 α β1 β2 β3 β4 β5 R2 0.4992 Estimate -0.0798 0.3114 0.3716 0.1790 0.0324 0.0018N 346 p-value 0.0000 0.0000 0.0000 0.0002 0.3003 0.7637

$0.005 < P ≤ $0.10 α β1 β2 β3 β4 β5 R2 0.5296 Estimate -0.0079 0.0327 0.0450 0.0127 0.1574 -0.0009N 293 p-value 0.0000 0.0000 0.0000 0.1187 0.0000 0.2080

$0.001 < P ≤ $0.005 α β1 β2 β3 β4 β5 R2 0.2639 Estimate -0.0009 0.0021 0.0056 0.0023 0.2581 0.0004N 65 p-value 0.0846 0.0093 0.1547 0.1731 0.0006 0.2286

P ≤ $0.001 α β1 β2 β3 β4 β5 R2 0.2376 Estimate 0.0001 0.0000 0.0048 0.0002 0.0746 0.0000N 38 p-value 0.0006 0.3252 0.0506 0.1473 0.0011 0.2944

35

Table 10. Determinants of the Bid-ask Spread in the Post-period Listed are results of the cross-sectional regression:

1 2 3 4 5i i i i i i iSPRD InvTV MHI P Iα β σ β β β β ε= + + + + + +

where SPRD is the median daily average quoted bid-ask spread, σ is return volatility based on closing midpoints, InvTV is the inverse of trading volume, MHI is the modified Herfindahl index, P is average trade price, and I is an indicator variable that equals one if the stock has ticker symbol beginning with the letters A – D and zero otherwise. Observations are computed for each stock quoted on the Pink Sheets Electronic Quotation Service and traded on the Pink Link trading system over the period February 27, 2006 through June 15, 2006. The sample is split into five categories formed by average trade price P. Listed are the adjusted R-squared, number of observations, and OLS coefficient estimates. Below each estimate is the two-sided p-value using heteroskedasticity-consistent standard errors.

$1 < P α β1 β2 β3 β4 β5 R2 0.9935 Estimate -0.3824 3.9987 0.4387 0.8332 0.0015 -0.1625N 439 p-value 0.0006 0.0003 0.0000 0.3461 0.6117 0.2153

$0.10 < P ≤ $1 α β1 β2 β3 β4 β5 R2 0.3987 Estimate -0.0584 0.2301 0.3142 0.1429 0.0301 -0.0007N 345 p-value 0.0000 0.0000 0.0000 0.0186 0.1231 0.8976

$0.005 < P ≤ $0.10 α β1 β2 β3 β4 β5 R2 0.4899 Estimate -0.0117 0.0474 0.0570 0.0176 0.1740 -0.0009N 302 p-value 0.0000 0.0000 0.0005 0.0187 0.0000 0.2299

$0.001 < P ≤ $0.005 α β1 β2 β3 β4 β5 R2 0.2502 Estimate -0.0007 0.0016 0.0116 0.0018 0.2337 0.0006N 62 p-value 0.0366 0.1389 0.0712 0.2228 0.0058 0.0328

P ≤ $0.001 α β1 β2 β3 β4 β5 R2 0.2846 Estimate 0.0001 0.0001 0.0110 0.0001 0.0408 0.0000N 42 p-value 0.3840 0.6144 0.0000 0.5130 0.0923 0.5813

36

Table 11. Trade Activity Listed are summary statistics of trades posted between 9:30 a.m. and 4:00 p.m. on the Pink Link trading system over the periods November 1, 2005 to February 17, 2006 (the “Pre-period”) and February 27, 2006 to June 15, 2006 (the “Post-period”). Listed are the number of stocks, the number of trades per stock, and the dollar volume in $000. Results are broken down by stocks with ticker symbols beginning with A – D and a matched sample with ticker symbols beginning with E – Z. Results are also listed for categories determined by the average trade price of each stock.

Pre-period Post-period A. All Stocks # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 388 66 398.2 388 94 582.7E-Z 404 79 502.0 404 91 577.2 B. P > $1 # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 131 89 976.9 135 96 1,124.8E-Z 126 150 1,460.1 124 118 1,613.2 C. $1 ≥ P > $0.10 # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 102 78 222.39 100 154 683.6E-Z 107 52 124.77 120 69 161.9 D. $0.10 ≥ P > $0.005 # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 101 45 32.4 104 48 38.5E-Z 118 42 36.7 110 68 78.7 E. $0.005 ≥ P > $0.001 # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 29 38 12.5 30 25 15.0E-Z 32 34 11.0 32 55 42.8 F. $0.001 ≥ P # Stocks # Trades $ Volume # Stocks # Trades $ VolumeA-D 25 23 8.7 19 134 75.2E-Z 21 67 37.9 18 243 204.4

37

Table 12. Quoted Spread Listed are summary statistics of active inside quotes posted between 9:30 a.m. and 4:00 p.m. on the Pink Sheets Electronic Quotation Service over the periods May 15, 2006 to June 15, 2006 (the “Pre-period”) and June 16, 2006 to July 10, 2006 (the “Post-period”). Listed are the number of quotes for each period and the average quoted spread. “Matched Stocks” include the subset of A – D stocks for which a matching E – Z stock was found using summary statistics computed over January 2004 – October 2005, as well as the matching E – Z stocks.

Pre-period Post-period A. All Quotes # Quotes % Spread # Quotes % Spread A-D 216,382 5.46% 124,119 6.49% E-Z 525,229 5.97% 336,199 6.82% B. Bid > $1 # Quotes % Spread # Quotes % Spread A-D 170,390 2.06% 96,018 2.25% E-Z 385,575 1.92% 241,323 1.99% C. $1 ≥ Bid > $0.10 # Quotes % Spread # Quotes % Spread A-D 22,889 12.27% 13,550 14.91% E-Z 56,286 13.84% 39,620 14.97% D. $0.10 ≥ Bid > $0.005 # Quotes % Spread # Quotes % Spread A-D 18,645 18.54% 10,693 23.39% E-Z 63,313 17.32% 45,029 18.59% E. $0.005 ≥ Bid > $0.001 # Quotes % Spread # Quotes % Spread A-D 2,207 38.91% 2,511 29.43% E-Z 16,395 18.13% 7,064 28.61% F. $0.001 ≥ Bid # Quotes % Spread # Quotes % Spread A-D 2,251 51.63% 1,347 47.43% E-Z 3,660 61.55% 3,163 57.43%

38

Figure 1. Number of Stocks and Quote Activity by Midpoint Displayed in Figure 1A are the numbers of stocks with at least one active inside quote and at least one trade posted between 9:30 a.m. and 4:00 p.m. on the Pink Sheets electronic system on at least 10 days over the January 2004 – October 2005 period. Displayed in Figure 1B are the average numbers of inside quote updates per stock per day. Results for each stock are categorized by the average midpoint price.

1A. # Stocks

1B. # Daily Updates

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0.00 < P ≤ 0.010.01 < P ≤ 0.050.05 < P ≤ 0.100.10 < P ≤ 0.150.15 < P ≤ 0.200.20 < P ≤ 0.250.25 < P ≤ 0.300.30 < P ≤ 0.350.35 < P ≤ 0.400.40 < P ≤ 0.450.45 < P ≤ 0.500.50 < P ≤ 0.550.55 < P ≤ 0.600.60 < P ≤ 0.650.65 < P ≤ 0.700.70 < P ≤ 0.750.75 < P ≤ 0.800.80 < P ≤ 0.850.85 < P ≤ 0.900.90 < P ≤ 0.950.95 < P ≤ 1.001.00 < P ≤ 2.002.00 < P ≤ 3.003.00 < P ≤ 4.004.00 < P ≤ 5.005.00 < P ≤ 6.006.00 < P ≤ 7.007.00 < P ≤ 8.008.00 < P ≤ 9.009.00 < P ≤ 10.00

10.00 < P ≤ 20.0020.00 < P ≤ 30.0030.00 < P ≤ 40.0040.00 < P ≤ 50.0050.00 < P ≤ 60.0060.00 < P ≤ 70.0070.00 < P ≤ 80.0080.00 < P ≤ 90.0090.00 < P ≤ 100.00

P > 100.00

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10.00 < P ≤ 20.0020.00 < P ≤ 30.0030.00 < P ≤ 40.0040.00 < P ≤ 50.0050.00 < P ≤ 60.0060.00 < P ≤ 70.0070.00 < P ≤ 80.0080.00 < P ≤ 90.0090.00 < P ≤ 100.00

P > 100.00

39

Figure 2. Average Quoted Spread Intraday Displayed is the average percentage quoted spread computed over five-minute intervals using all active inside quotes posted on the Pink Sheets electronic system January 2004 – October 2005. Results are split into four price categories based on each quotes bid-ask midpoint.

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Figure 3. Trading Frequency Intraday Displayed is the total number of trades executed over five-minute intervals on the Pink Link electronic system January 2004 – October 2005. Results are split into four price categories based on trade price.

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Figure 4. Histogram of Bid Quotes

Displayed are histograms of bid prices of active inside quotes posted from 9:30 a.m. to 4:00 p.m. on the Pink Sheets market over the period January 2004 – October 2005. Quotes with ask prices less than or equal to bid prices and quotes with bid or ask prices less than or equal to zero are excluded. Panels A though D show the percentage of quotes at each of the 10,000 possible decimal increments from 0.0000 to 0.9999. Panel A shows all quotes and panels B through D show subsets based on bid price. Panels E and F show the percentage of quotes at the 1,000 possible decimal increments from 0.0000 to 0.0999, and at the 100 possible increments from 0.0000 to 0.0099, respectively, for quotes with bid price less than or equal to $1.

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Figure 5. Histogram of Trade Prices

Displayed are histograms of trade prices posted from 9:30 a.m. to 4:00 p.m. on the Pink Sheets market over the period January 2004 – October 2005. Panels A though D show the percentage of trades at each of the 10,000 possible decimal increments from 0.0000 to 0.9999. Panel A shows all trades and panels B through D show subsets based on trade price. Panels E and F show the percentage of trades at the 1,000 possible decimal increments from 0.0000 to 0.0999, and at the 100 possible increments from 0.0000 to 0.0099, respectively, for trades with price less than or equal to $1.

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43

Figure 6. Histogram of Quoted Spreads

Displayed are histograms of quoted spreads of active inside quotes posted from 9:30 a.m. to 4:00 p.m. on the Pink Sheets market over the period January 2004 – October 2005. Quotes with ask prices less than or equal to bid prices and quotes with bid or ask prices less than or equal to zero are excluded. Panels A though D show the percentage of quoted spreads at each of the 10,000 possible decimal increments from 0.0000 to 0.9999. Panel A shows all quoted spreads and panels B through D show subsets based on bid price. Panels E and F show the percentage of quoted spreads at the 1,000 possible decimal increments from 0.0000 to 0.0999, and at the 100 possible increments from 0.0000 to 0.0099, respectively, for quoted spreads with bid price less than or equal to $1.

B. P > $10

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Figure 7. Number of Trades and Active Inside Quote Updates by Month Displayed are the number of trades and active inside quote updates posted to the Pink Sheets system by month over the period January 2004 through July 2006.

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45

Endnotes

1 See “Donaldson's flawed stock exchange rule: The SEC should deregulate trading, not make it harder,” Financial Times, 5 April, 2005, p.18, and “Life after Donaldson,” Wall Street Journal, 6 June 2005, p. A10. 2 See “Pump and dump” The Economist, 26 August 2006, p.59, and “Stock tips from spam aren’t just silly. They’re costly.” The New York Times, 10 September 2006, p.6. 3 Much of the information in this Section was obtained from the Pink Sheets web site www.pinksheets.com. 4 Section 12 of the 1934 Exchange Act requires that issuers register with the SEC and provide periodic information if (a) they are listed on a national securities exchange or (b) they have assets in excess of $10 million and more than 500 shareholders. The nature of the Pink Sheets market is such that neither of these criteria apply. The ADR’s that trade on the Pink Sheets are Level I, implying that the firms can not raise new capital but can apply for an exemption from the SEC reporting rule 12g3-2(b) by filing Form F-6. 5 Mandelbrot (1975) is often credited with first using the word “fractal” to define the property of self-similarity at different scales. 6 We do not have data on market capitalization and so rely on trade frequency as the sole proxy for information. 7 In a market with infrequent trading, the quotes may not carry the same information as a trade. However, for many Pink Sheets stocks the paucity of trades makes estimation of volatility from trade prices problematic. For robustness, we compute volatility using successive last trade prices. Results are qualitatively identical.