Decimal Trading and Market Impact
Sugato Chakravarty
Purdue University, West Lafayette, IN 47907
Tel: (765) 494 6427
E-mail: [email protected]
Robert A. Wood
University of Memphis, Memphis, TN 38152
Tel: (901) 755-8322
E-mail: [email protected]
Stephen P. Harris
Bridge Information Systems
Tel: (314) 468-8292
Version 3.02: January 10, 2002
Abstract
Using high-frequency data and a carefully constructed 1-1 matched sample of control (non
decimal) stocks, we isolate the effects of decimalization for a sample of NYSE-listed common
stocks trading in decimals. We find that both quoted and effective bid-ask spreads and depths
have declined significantly following decimalization. Both trades and trading volume have
declined significantly in all trade size, as well as in all stock size, categories. Stock return
volatilities display an initial increase but a decline over the longer term – probably as traders
become more comfortable in their new milieu. Finally, although there is some evidence of
increased presence among regional stock exchanges in the wake of decimalization, the NYSE
still appears to be very much in the lead in all categories. Our results have important research
and policy implications.
JEL classification:
Keywords: decimalization, bid/ask spread, trading, stock exchange
Acknowledgements: Please direct all comments to either Chakravarty or Wood. We thank Robert
Battalio, Tarun Chordia, Bill Christie, Mike Cooper, Amy Edwards, Gene Finn, Michael Goldstein, Robert
Jennings, Ananth Madhavan, Tim McCormick, Eric Sirri, George Sofianos, Robert Wood Jr., and Robert
Van Ness, for comments on earlier drafts, and to the seminar participants in the 14th annual Financial
Markets Research Center conference at Vanderbilt, and, especially, Ingrid Werner, for her comments.
Wonil Hwang and Dan Zhou provided research assistance in an earlier draft and Jang-Chul Kim
provided exceptional research assistance during the revision of this paper. Stephen P. Harris of Bridge
Information Systems also provided some of the Bridge data at the initial stages of the project. We retain
all downside responsibilities while claiming all (residual) upside credit.
Decimal Trading and Market Impact
Abstract
Using high-frequency data and a carefully constructed 1-1 matched sample of control (non
decimal) stocks, we isolate the effects of decimalization for a sample of NYSE-listed common
stocks trading in decimals. We find that both quoted and effective bid-ask spreads and depths
have declined significantly following decimalization. Both trades and trading volume have
declined significantly in all trade size, as well as in all stock size, categories. Stock return
volatilities display an initial increase but a decline over the longer term – probably as traders
become more comfortable in their new milieu. Finally, although there is some evidence of
increased presence among regional stock exchanges in the wake of decimalization, the NYSE
still appears to be very much in the lead in all categories. Our results have important research
and policy implications.
JEL classification:
Keywords: decimalization, bid/ask spread, trading, stock exchange
“The theory is straightforward: As prices are quoted in smaller and
smaller increments, there are more opportunities and less costs for
dealers and investors to improve the bid or offer on a security. As more
competitive bidding ensues, naturally the spread becomes smaller. And
this means better, more efficient prices for investors.”
Arthur Levitt, Chairman SEC.
March, 2000.
1.
Introduction
Between August 28, 2000, and January 29, 2001, the New York Stock Exchange (NYSE),
through a series of incremental steps, began trading and quoting all its listed securities in
increments of a penny.1 Decimalization had finally arrived in Wall Street! A two-hundred-year
tradition of trading in fractions was history. We use this act of decimalization in the NYSE as a
natural experiment to determine its effect on variables related to market liquidity.
According to the NYSE, the reduction in minimum price increment to sixteenths, in June
1997, was but an interim step in a move toward the decimalization of prices and price
increments (Jones and Lipson (2001)). And while it is tempting to think of decimalization as
merely a continuation in the process of tick size reduction, it is actually much more than just
that. While the move to sixteenths resulted in a doubling of the price points or “ticks”, the
move to decimals (from sixteenths) resulted in a six-fold increase in ticks. Also, a unique, and
potentially dangerous, aspect of decimalization is that for as little as 1 cent per share (as
compared to about 6.25 cents a share under sixteenths), intermediaries can step in front of
public limit orders in what amounts to “front running.” If the stock heads down after this
purchase, these investors could simply sell to the public limit orders and be none the worse for
it. It is, therefore, conceivable that the supply of liquidity from the investing public in the form
of public limit orders may dry up as a result. It can also be easier for institutional investors to
jump in front of the queue with limit orders, supplying liquidity rather than demanding it
(thereby acting as pseudo-dealers) and, in the process, earning the spread rather than paying it.
The NYSE's board approved conversion to decimal pricing in June 1997 with the goal of
making prices more easily comprehensible by investors, reducing spreads and bringing the
1
Specifically, the NYSE lowered the minimum tick size to a penny for seven securities on August 28, 2000, 57
more securities on September 25, 2000, and an additional 94 securities on December 5, 2000. All remaining
securities began trading in decimals on January 29, 2001.
1
United States into conformity with international practices. Market liquidity is of paramount
importance to both suppliers and demanders of capital as well as regulators entrusted with the
mandate of maintaining a fair and orderly market. Other related benefits of decimalization
include savings for investors through narrower spreads and easily understood numbers. While
there is little debate that prices are easily understood under the decimal system where one does
not have to pause momentarily and wonder if 5/8 is greater than 9/16, for example, whether or
not this has actually impacted market liquidity (and its various facets) is an empirical issue and
is a focus of the current paper.
The fact that the NYSE converted to decimal pricing via a phased, pilot program allows
us to form a matched, non-decimal control sample. We use the matched securities to control for
market effects that might occur coincidentally with the decimalization of the pilot securities’
prices. In addition, we use the decimal-pilot securities as a control sample when trading in the
matched (non-decimal) securities was decimalized on January 29, 2001, by examining the
behavior of both groups of stocks up to March 30, 2001. Our final decimal sample of 79
common stocks (out of 158 total securities included in the decimal pilot) is arrived at after
filtering out all non-common stocks (like preferred stocks, closed end funds, ADRs, etc.) and
ensuring certain minimum price and trading conditions are satisfied. These filters are
incorporated to minimize confounding effects and are detailed later. The 79 common stocks
from the decimal pilot are denoted “decimal stocks,” while the 79 corresponding (non-decimal)
stocks created by matching each decimal stock to are labeled “control stocks”. We then use tickby-tick (TAQ) data for these stocks to investigate the impact of decimal trading on the various
facets of market liquidity. Our investigation period comprises three distinct periods
surrounding the decimal pilot in the NYSE: (1) a pre-decimal period (before any NYSE stock
was trading in decimals); (2) a decimal-trial period (when only securities in the NYSE’s decimal
pilot were trading in decimals); and (3) an all-decimal period (when all NYSE stocks were
trading in decimals).
Including the latter period enables us to study the long-term effects of
decimalization on the stocks in our sample.
Our main results can be summarized as follows. We find that both bid and ask quote
increments of 5 cents or less appear to be used actively by the market, and that both the quoted
and effective bid-ask spreads and depths have declined significantly, following decimalization.
We find that both trades and trading volume have declined significantly in all trade size
2
categories as well as in all stock size categories.
Stock return volatilities display an initial
increase but a decline over the longer term – probably as traders become more comfortable in
their new milieu. Although there is some evidence to suggest increased activity among the
regional stock exchanges with regard to bid-ask quote adjustment frequencies, autoquotes2 and
BBO times, in the wake of decimalization, the evidence is not strong and the NYSE appears to
be still very much in the lead in all these categories.
Our results have important policy implications as the debate continues over the
judiciousness of decimalization. The fact that quote increments of five cents or less appear to be
used actively following decimalization may imply the fact that minimum prices increments of
$1/8 or $1/16 may have represented barriers to price competition.
Furthermore, the
proponents of decimalization argue that decimals allow for more efficient price discovery
without adversely affecting the supply of liquidity. Opponents claim that decimals will result
in less liquid, high volatility markets. Our results, however, provide a mixed verdict on the
issue of liquidity and volatility. Overall, the results suggest that we have moved to a new phase
in security transactions – one in which participants will have to learn new rules to play the
game effectively. Whether or not they do so, will determine, in large part, the success of
decimalization in keeping prices efficient and markets liquid.
At the very least, information
about the available supply and demand schedule outside the BBO will be have to be made
available to market participants. Interestingly, the NYSE has already started publicly providing
information on the depth of the limit order book.3
The current research falls into a large body of research on tick-size reductions. And
despite such efforts – both theoretical and empirical, its appropriateness remains an open
question.4 Most relevant to our work, however, is a complementary research by Chakravarty,
2
Autoquote is a bid ask quote generated automatically by computers in regional exchanges positioned
just outside the prevailing highest price to buy and the lowest price to sell (otherwise known as the best
bid and offer or BBO). The presence of autoquotes usually mean that the regional specialists are willing
to be market participants for orders but not by paying as aggressive a price as the BBO.
3
Specifically, the NYSE, beginning March 19, 2001, started disseminating “depth indications” on eight of its stocks.
Its purpose is to show investors that there is a meaningful number of shares of a given stock available beyond the
best price being bid and offered for the stock (WSJ, March 15, 2001, C1). This has now been expanded to all
NYSE-listed securities.
4Examples
of theoretical research include Grossman and Miller (1988), Brown, Laux and Schachter (1991),
Hart (1993), Chordia and Subrahmanyam (1995), Peake (1995), Bernhardt and Hughson (1996), Kandel
and Marx (1996), Cordella and Foucault (1996), O’Connell (1997), Harris (1994, 1997), Seppi (1997), and
3
Panchapagesan and Wood (2001) that examines institutional trade execution costs around
decimalization in the NYSE using proprietary data and finds no evidence of increased trade
execution costs following decimalization. An important implication of their study is that the
available supply and demand of shares outside the best bid and offer prices remains
undiminished. Our results, combined with those of Chakravarty, Panchapagesan and Wood,
should allay the fears of regulators, academics and practitioners, who are afraid that
decimalization may have decreased liquidity in the NYSE.
2.
Data and Methodology
2.1
The Sample Stocks
The stocks in the decimal pilot were chosen based on several criteria developed by the
NYSE, along with a securities-industry committee. These criteria include stocks having varying
levels of daily trading activity, that trade on multiple exchanges, are part of an index, are
underlying issues for multiply listed options; and may have corporate action pending. To avoid
introducing confounding effects, we eliminate all preferred and convertible preferred stocks,
closed end funds, ADRs, stocks with abnormally low average daily trading volume and stocks
with no trading in at least one day over the study period. We also exclude all common stocks
below $5 and above $150, and those stocks in the decimal pilot that moved from Nasdaq to
NYSE during the period of the study. Our final sample comprises 79 NYSE-listed common
stocks selected for trading in decimals under the three phases of the decimal pilot.
2.2
Selection of Control Stocks
Investigating the impact of decimalization on the pilot stocks after (relative to before) the
event is valid under the assumption that the market remains constant over the entire
examination period. In the presence of market trends, however, it is impossible to tell if an
effect is due to decimalization or due to market trends. One way to isolate the effect of
decimalization, independent of market trends, is to examine a matching sample of stocks,
identical to the control stocks in every way, except that they do not trade in decimals.
Anshuman and Kalay (1998). Examples of empirical research include Crack (1994), Ahn, Cao and Choe
(1996), Bacidore (1997), Bessembinder (1997), Huson, Kim and Mehrotra (1997), Porter and Weaver (1997)
and Ahn, Cao and Choe (1998), Ronen and Weaver (1998), Bollen and Whaley (1998), Ricker (1998),
Goldstein and Kavajecz (2000), Jones and Lipson (2001)).
4
Accordingly, the control stocks are selected from the NYSE stocks with the same industry codes
and security types (e.g. common stock) as the particular decimal stock. The precise control
stock is now chosen to minimize the expression, Σk (cjk - cik)2/[(cjk +c i k)/2], where cik (cjk) is the
decimal (matched) stock measurement of characteristic k. Characteristics controlled include
stock price, equity market capitalization, and trading volume. In addition to minimizing the
sum, no single element of the summation is allowed to exceed unity. Bacidore et al. (2001) use a
similar approach to select their control sample. It should be noted, however, that we go beyond
them by employing an optimization model that simultaneously considers all possible (decimalcontrol) pairs, and selects only those pairs that minimize the overall distances. Further details
of the procedure are provided in McInish and Wood (1986). The appendix provides a listing
(and other details) of each decimal stock in our sample and the corresponding matched control
stock.
We obtain tick-by-tick transaction and quote data for each stock in our decimal
and control stock sample over the three distinct periods of study: October 2, 2000, to
January 26, 2001 (the decimal-trial period, when only some chosen stocks in the NYSE were
trading in decimals, with the remaining stocks trading in sixteenths);5 January 29, 2001 – March
30, 2001 (the all-decimal period, when all NYSE stocks were trading in decimals); and April 1,
2000 – June 30, 2000 (the pre-decimal period, when no NYSE stocks were trading in decimals but,
rather, trading in sixteenths).
3.
Decimalization and Bid and Ask Quotes
The quote data, used below, is extensively error filtered and all quotes with missing
values, with negative and zero spreads, and with quoted spreads greater than $2, are
eliminated. This removes less than 1% of the quotes.6
The corresponding transactions prices
5
We choose the start date of the decimal-trial period from October 2 -- i.e., week 6 onwards, relative to
the start of Phase I decimal pilot in August 28, 2000 -- to provide enough time for market participants to
have found an equilibrium trading pattern, since private communications with professional traders
confirm that significant “learning” took place in the first few weeks of commencement of the decimal
pilot as traders freely experimented with the new system.
6
The comparison of trades and quotes also requires that data from CTA and CQS be merged by time.
For various technical reasons (see Blume and Goldstein (1997), Hasbrouck and Soesbee (1992)), not only
can the time stamps be in error, but also the very sequencing of trades in the same stock can be wrong.
We considered using the Blume and Goldstein (1997) formula to adjust our quote time stamps the same
5
are also examined (and filtered) for potential errors. We begin our investigation by providing,
in the following section, some metrics related to bid-ask quotes, based on the NYSE-listed
decimal and control stocks in our sample, over the three distinct periods of study. These
metrics are of interest to practitioners and regulators as an indicator of the overall health of the
equity markets.
3.1
BBO quotes and quote change characteristics
There exists, at any point in time, a set of bid and ask quotes that represent the highest
price to buy and the lowest price to sell. This is known as the best bid and offer (BBO). In a
continuous auction market, such as the NYSE, a specialist posts quotes in stocks, comprising of
a combination of own interest as well as the interest of the public limit orders competing
directly with the specialist. Such competition can also come from the regional stock exchanges,
posting quotes simultaneously in those stocks. In short, BBOs are generated by public limit
orders originating both in the primary market as well in the regional stock exchanges, and
dictate which exchange at any point in time has the best bid and offer quotes. The fraction of
time that any particular exchange has the BBO is an indication of its dominance in terms of a
supplying liquidity as well as price discovery – arguably the two most important roles of a
modern financial exchange.
We begin by investigating the fraction of total trading time that a BBO is in effect across
the regional exchanges for decimal and control stocks over all three periods of interest. We find
that NYSE dominates the BBO times in both decimal and control stocks over all three periods.
Thus, for example, over the pre-decimal period, NYSE had about 95% of the BBO times for both
decimal and control stocks; about 94% and 96% of the BBO times for decimal and control stocks
over the decimal-trial period; and about 94% of the BBO times for both decimal and control
stocks over the all-decimal period. Thus, the dominance of the NYSE, in this regard, is clear.
Next, we move on to investigate the frequency of changes in the BBOs. The purpose is
to see if all penny increments are being hit after decimalization or if the BBO quote changes are
trading day. But the quote adjustment algorithm Blume and Goldstein develop is based upon 10-year old
data contained in the NYSE TORQ database. Extensive improvements in trade recording systems have
been implemented in the intervening years and there is currently a sense that adjusting quote time
stamps is no longer appropriate.
6
loading up only on certain penny increments. Specifically, we sum the number of times the best
prevailing bid (ask) changes by 1 cent, 2 cents, and so on, for all the decimal and control stocks
in our sample and over the decimal-trial and all-decimal periods.
Over the decimal-trial period, we find that while about 25% (40%) of quote changes in
control (decimal) stocks occur at 1/16ths (6 cents or less) and 52% (76%) at 1/8ths (12 cents or
less), and only about 6% of the changes in decimal stocks occur at one penny. Over the alldecimal period, in comparison, 36% (34%) of quote changes in control (decimal) stocks occur at
6 cents or less and 70% (68%) at 12 cents or less, and only about 5% of the changes in both
decimal stock and control stocks occur at one penny. Thus, while quote increments of less than
6 cents appear to be used actively by the market in decimal stocks, the evidence is by no means
overwhelming. Also, over time, the relative frequency of using quote increments of 6 cents or
less appears to have diminished significantly. This evidence flies in the face of those who
believe that a minimum tick size of $1/16 may have represented a significant barrier to price
competition, which would be ameliorated with decimal pricing.
Given the reasonable use of increments of 5 cents or less in the BBOs noted above, a
related question to investigate is which regional exchanges are responsible for this narrowing of
the BBOs. Specifically, we examine 1-5 cents quote changes (at the best bid and at the best ask)
classified by the regional exchanges quoting them over both decimal-trial and all-decimal
periods. Not surprisingly, we find that the NYSE has by far the greatest number of 1-5 cent
changes, while the NASDAQ is competitive in all five-cent categories. Overall, it appears that
even though the regional exchanges are actively contending for quote changes, the NYSE is still
leading the way.
We now turn to the issue of dynamic quote behavior addressed by various researchers
both in the context of increased fragmentation of U.S. equity orders and in the context of price
discovery (see, for example, Garbade and Silber (1979), Shapiro (1993) and Hasbrouck (1995)).
The NYSE and the regional exchanges are electronically linked and all trades and quotes are
disseminated by a central transmission authority (the Consolidated Tape Association (CTA)).
Although the regional exchanges sometimes establish the BBO, frequently they will choose to
extract themselves from active quote competition in listed stocks by programming a computer
to intercept all NYSE/AMEX quotes and immediately generate a new quote of their own by
adding a delta to the ask and subtracting a delta from the bid, with 100 shares bid and 100
7
shares offered (the bid and ask depths). The mechanism(s) by which the regional quotes default
to the BBOs, widened by a small arbitrary amount, are known as “autoquotes”. Thus, an
autoquote is effectively a non-quote whereby regional specialists signal that they are willing to
supply liquidity but not at the best prices. Trades occur on the regional exchanges during
periods of autoquoting, but those trades must match (or improve upon) the existing BBO. Our
algorithm identifies an autoquote as any regional or third-market quote that brackets the
existing NYSE or AMEX quote.
With the advent of decimalization it is reasonable to anticipate a change in the pattern of
posting of quotes off the BBO by serious liquidity providers wising to earn more than a 1-2 cent
spread. With the relatively thin book that naturally results from tighter spreads, significant
buy/sell programs could easily march up/down the book and hit limit orders away from the
minimum tick size.
We examine the percentage of time the NYSE-listed decimal and control stocks are
autoquoted, over the three periods of interest, in the various regional exchanges. Specifically,
we compute a simple percentage of all autoquotes from a given regional over all quotes
from the regionals and the NYSE. While tests reveal (results not presented formally) that the
percentage of autoquoting is statistically similar between decimal and control stocks in the predecimal period, autoquoting increased significantly over the decimal-trial period in decimal
stocks, relative to control stocks, in most regional exchanges. Specifically, Cincinnati, Pacific
and Chicago, among the regionals, appear to have the highest increases of autoquoting in
decimal stocks. This increase in autoquoting is perhaps an indication of the uncertainty felt by
these regionals in their effort toward efficient price discovery and their role as liquidity
suppliers in a post-decimal world.
3.2
Quoted and Effective bid/ask spreads
A traditional measure of market liquidity has been the quoted bid-ask spread capturing
the ex ante transactions cost. Petersen and Fialkowski (1994) and others have, however, argued
for a related measure, the effective spread7, which measures the ex post transaction cost,
contending that the quoted bid-ask spread is no longer an accurate measure of transaction costs
when trades are executed inside the prevailing quoted spread.
7
Effective spread is formally defined as twice the absolute difference between the transaction rice and the
midpoint of the prevailing best bid and ask (BBO) prices.
8
We begin our investigation into spreads by examining, in Table 1A, the distribution of
all quoted spreads originating from the national and regional exchanges in terms of odd and
even ticks for decimal and control stocks, over both the decimal-trial and all-decimal periods.
Over the decimal-trial period, the decimal stocks are almost even split between even and odd
ticks in every exchange, while the control stock spreads, over the same period, appear to be
overwhelmingly on even ticks. Recalling that the control stocks over this period were trading in
sixteenths, the implication is that the smallest possible spread in those stocks was $2/16 or $1/8.
Interestingly, over the all-decimal period, when all stocks were trading in decimals, the quotes
for both the decimal and control stocks originating in the regionals were almost evenly divided
into even and odd ticks. The exceptions were the NYSE (NASDAQ), which shows significantly
more odd (even) ticks in all stocks. Thus, for example, about 61% (45%) of all ticks from the
NASDAQ (NYSE) appear to be at even ticks.
Table 1B refines the examination of quoted spreads by investigating the distribution of
only the BBO spreads (in cents) for decimal and control stocks over the decimal-trial and alldecimal periods. Decimal stocks display a higher frequency of spreads at six cents or less
relative to the control stocks (51% versus 42%) over the decimal-trial period. Decimal stocks
continue to display a greater dispersion even at spreads of 25 cents (or below). In examining
the performance of decimal stocks over the all-decimal period, we see that the spread
dispersion at 12 cents or below declines, while it improves at 13 cents or above, both relative to
the decimal-trial period. Interestingly, the dispersion of the control stock spreads shows a
marked improvement over the all-decimal period relative to the decimal-trial period when they
were trading in sixteenths. Thus, for example, about 42% (52%) of the spreads in control stocks
were at 6 cents or below over the decimal-trial (all-decimal) period. Furthermore, 73% (78%) of
the spreads in control stocks were at 12 cents or below over the decimal-trial (all-decimal)
period.
Overall, it should be comforting to the supporters of decimal pricing that quote
increments of 5 cents or less appear to be used actively by the market in a post-decimal world.
Tables 2 and 3 provide information on the quoted and the effective bid/ask spreads, in
cents, on the NYSE-listed decimal stocks and the corresponding control stocks over all three
periods considered in the study – the pre-decimal, decimal-trial and all-decimal periods. Both
the quoted and effective bid/ask spreads are calculated on the basis of the best bid and offer
(BBO) quotes available at the time of trade. Thus, autoquotes, which simply bracket an existing
9
BBO, are automatically eliminated from consideration. We compute spreads of stock portfolios
formed on the basis of the average daily dollar volume of trade of stocks over the pre-decimal
period. Stocks in portfolio 1 (5) comprise the smallest (largest) dollar volume stocks. The
reported spreads in Table 2 (and in Panel A of Table 3) for each dollar volume portfolio are
computed by weighting, for a given stock within a given day, by the time each spread is
outstanding, and weighted across stocks, by their daily average pre-decimal dollar trading
volume.
Table 2 reveals that the decrease (over the decimal-trial period) in quoted spreads for
decimal stocks is significant across all five dollar volume portfolios, and ranges from 26% to
36%, while the (dollar-volume weighted) average decline over all portfolios is about 35%. The
corresponding decline in the control stock portfolios ranges from a 2% to 16%, with an overall
average decline of about 16%.
Thus, decimalization appears to have significantly reduced
quoted spreads, in comparison to control stocks. On continuing our examination over the alldecimal period we find that quoted spreads in the decimal stocks have increased a little only in
the smallest size portfolio. In the remaining portfolios, the quoted spreads continue to trend
downwards.
To isolate the effect of decimalization on the quoted spreads of decimals stocks, the net
difference in quoted spreads in decimal stocks is calculated as the difference between the daily
average quoted spread of each decimal stock and its paired control stock in a particular size
rank. For each portfolio, the average of these differences over each (pre-decimal, decimal-trial
and all-decimal) period is then computed. The average of the differences, (trial - pre) and (all pre), within each portfolio, is reported in Table 2. These reveal that decimalization itself may
have resulted in quoted spreads declining by an average of about 2.2 cents. The last column of
Table 2 confirms that the difference in quoted spreads between decimal and control stocks is
statistically insignificant over the all-decimal period, which is what we would expect if the
control stocks are similar to the decimal stocks and both groups are trading in decimals. The
last column, therefore, serves as a robustness check of the efficacy of our control stock selection.
Table 3 Panel A reports the effective spreads of portfolios, once again classified by their
average daily pre-decimal dollar volume. The reduction in effective spreads in decimal stocks
ranges from 19% (portfolio 5) to 30% (portfolio 1). Not surprisingly, the greatest reductions
occur in the lower dollar volume portfolios, which, as Table 2 indicates, have relatively wider
10
quoted spreads. The overall (dollar volume weighted average) decrease is about 16%. The
control portfolios also show a decline in effective spreads in almost all portfolio size categories
with an overall (dollar volume weighted average) decrease of about 13%. Furthermore, the
trend of declining effective spreads continues over the all-decimal period – especially in the
higher dollar volume portfolios. To isolate the effect of decimalization on the effective spreads
of decimal stocks, the net difference variable is reported. Only portfolios 2 and 4 show a
significant decline while the rest are insignificantly different from zero.
To get a sense of the relationship between effective spreads and trade size, we further
compute the effective spreads corresponding to trades in each of five trade size categories: all
trades less than 500 shares (small trades), all trades between 500 and 999 shares (medium1
trades), all trades between 1,000 and 4,999 shares (medium2 trades), all trades between 5000 and
9999 shares (medium3 trades), and all trades of 10000 shares or greater (large trades). Table 3
panel B presents the average effective spreads in each trade size category, for decimal and
control stocks, over the three periods of study.
We see that while the spreads in each trade size category are statistically similar between
decimal and control stocks over the pre-decimal period, there are significant declines in
effective spreads in almost every trade size category in decimal stocks (relative to control
stocks) over the decimal-trial period. Specifically, the spread decreases monotonically from 33%
in small trades to about 15% in large trades. In contrast, the decline is much more muted in
control stocks over the same period. The net difference variable indicates that decimalization
itself has resulted in reduction of effective spreads ranging from 2.8 to 3.1 cents in all but the
largest trade size category. For large size trades, however, the net difference variable is not
statistically significant at the 10% level, indicating no significant effective spread change
ascribable to decimalization itself.
On following the path of effective spreads over the all-decimal period, we see a
continuation in the downward trend in all trade size categories. This provides further support
of improving liquidity in asset markets in the wake of decimalization.
In sum, decimalization appears to have significantly reduced both quoted and effective
spreads in all but the largest size stocks and that this decline continues significantly beyond the
start of the decimal pilot, indicating that the decline is not just a temporary phenomenon. Our
conclusion holds even after accounting for effects other than decimalization, through the net
11
difference variable, and are consistent with those reported in Goldstein and Kavajecz (2000) and
Jones and Lipson (2001) following the conversion to sixteenths. Decimalization appears to have
also enabled relatively smaller size trades to obtain better prices and execute deeper inside the
quoted spreads, compared to relatively larger trades.
3.3
Changes in bid and ask depths
Following Harris (1990), it is now widely accepted that a complete characterization of
market liquidity encompasses both the bid/ask spreads and the corresponding bid and ask
depths. When liquidity is defined along these two dimensions, it is entirely likely that a
reduction in liquidity could occur through a reduction in the bid and/or ask depth even though
the bid/ask spread itself remains unchanged. Having examined spreads in the prior section,
we now turn to the depths to see if, collectively, we could say anything conclusive about market
liquidity following decimalization.
From a theoretical standpoint, it is reasonable to expect that quoted depths will decline,
the closer a bid or offer is to the “true” price, consistent with the shape of the supply-demand
curves. Further, the likelihood of a quote becoming stale increases as the spread narrows, so the
option cost implicit in quotes will increase correspondingly.8 Table 4 provides information on
depths of the decimal and control stocks over the three distinct periods of interest, where depth is
reported as the average of the bid and ask depths, in 100-share units. As in the case of spreads,
we report depths based on the five portfolios (1-5) formed on the basis of the average daily dollar
volume of trade of the sample stocks over the pre-decimal period. Consistent with the spread
table, the reported depths in Table 4 for each dollar volume portfolio are computed by averaging
across stocks in a portfolio, by their daily average dollar trading volume over the pre-decimal
period.
We see that depths decreased significantly during the decimal-trial, relative to predecimal, period. The average decline in decimal stocks over the decimal-trial period is about
8
Consider, for example, a stock trading at 20 - 20 1/8 where a trader has posted a limit order to sell at 20
1/8. If the quote then jumps to 20 1/4 - 20 3/8 while the limit order is left unchanged, one could buy the
stale limit order at 20 1/8 and immediately resell it at 20 1/4 ("picking it off"). With decimal trading, if a
stock is quoted at 20 - 20.01, a 20.01 sell limit order could be picked off with a much smaller upward
spread movement. Thus, the likelihood of the option being exercised against the limit-order provider is
greater with decimal trading, but the expected value of the payoff price is smaller. The net effect of these
two counteracting forces is indeterminate but could discourage the placement of limit orders in a decimal
environment.
12
69%. Not surprisingly, the decline is the greatest (least) in the more active (less active) higher
(lower) dollar volume stock portfolios. As the Table indicates, the prevailing depths in the
lowest dollar volume portfolio are the smallest to begin with. There is, thus, less room for
improvement in the smallest stocks. In contrast, the control stock portfolios, over the same
period, show an overall increase in depths (by about 14%). Once again, the net difference
variable isolates the impact of decimalization on the depths of decimal stocks following
decimalization. From here, we see that decimalization itself has lead to a reduction in depth of
about 9,742 shares. This trend of declining depths over the decimal-trial period continues into
the all-decimal period especially in the lower dollar volume stocks. Also, the difference in
depth between the decimal stocks and control stocks is statistically insignificant over the alldecimal period, which is what we would expect given that these are two matched groups of
stocks trading in decimals.
In summary, after controlling for market trends (other than decimalization), there
appears to be a significant decline in depth at the BBO and that this decline continues long after
the commencement of the decimal pilot – especially for the relatively less active stocks.
Goldstein and Kavajecz (2000) report an average quote depth decline of about 48% following
conversion to sixteenths. While a decline in quoted and effective spreads indicates an increase
in market liquidity, a simultaneous decrease in the corresponding depths (i.e., the
corresponding order sizes that these improved quotes are valid for) implies a drop in liquidity.
The overall effect of decimalization on market liquidity is therefore uncertain.
4.
Decimalization and Transaction-related Variables
4.1
Trades and trading volume
An issue of interest to regulators and practitioners is the relative behavior of institutions
compared to individual investors. It is generally perceived that institutions are “smart” or
informed traders while individuals are uninformed investors.
Evidence that institutional
investors are more likely to use larger size trades than individuals, appears in Chakravarty
(2001). Support that large trades are more likely to be from informed traders than small trades
comes from Easley and O’Hara (1987). To investigate the relative activity of large (informed)
trades versus small (uninformed) trades around decimalization, we investigate the frequency of
trades and trading volume in the five trade size categories described earlier: small, medium1,
13
medium2, medium3 and large.
Table 5 reports results both for decimal and control stocks over the usual three periods
of interest. Panel A presents the average daily trading volume results classified by trade size;
panel B provides the corresponding daily average trade frequency statistics.
From Table 5, we see a decrease in average daily trades and trading volume in all trade
size categories among decimal stocks in the decimal-trial period. The control stocks display the
same pattern and a similar magnitude of decline.
On tracking the trade and trading volume
pattern through the all-decimal period, we see a further decline in both in all trade size
categories. To isolate the effects of decimalization, we report the net difference in trade volume
(or trade frequency) in decimal stocks, calculated, in the usual way, as the difference between
the daily average volume (or trade frequency) of each decimal stock and its paired control stock
in a particular trade size category. These numbers indicate that decimalization has led to a
significant decrease in trades and trading volume in medium trades. There is evidence that the
frequency of large trades has also declined following decimalization.
4.2
Volatility
In this section we examine volatility in decimal and control stocks. If the risk of trading
in decimal stocks has increased significantly (relative to the control stocks) following
decimalization, we would expect a greater price impact (or higher volatility) for a trade of a
given size in decimal stocks.
To study volatility, we use the same five (quintile) portfolios of decimal and control
stocks separately, based on the average daily dollar trading volume over the pre-decimal
period. We form a minute-by-minute return series for the stocks within these portfolios, where
each return is weighted by its corresponding share volume. Portfolio returns are then formed
by weighting each stock in a portfolio by its pre-decimal average daily dollar volume.
Overnight returns are discarded. Volatility for portfolio returns is calculated daily and the
average volatility across days is reported.
Table 6 reveals a clear pattern of increase in volatility across all decimal stock portfolios
over the decimal-trial period.
This increase is small in the smallest dollar volume portfolio,
becomes larger in the intermediate size portfolios and declines for the largest portfolio. In
contrast, the control stocks display a universal decline in volatility over the same period.
As
always, the net difference variable attempts to isolate the effects of decimalization on decimal
14
stocks. The results indicate that decimalization has led to a significant increase in volatility in
all but the smallest portfolio.
On following the path of volatility in the two groups of stocks over the all-decimal
period, we find a significant decline in volatility in both groups of stocks relative to the decimaltrial period.
This might indicate a reduction in decimal-related risk in the market as
participants “learn” the new trading environment.
4.3
Runs and Reversals in Price Adjustments
We continue with our theme of investigating differential risks of trading in stocks
following decimalization. Specifically, there has been concern amongst practitioners in Wall
Street that decimal pricing may lead to more runs in price and less price reversals, thereby
exposing the limit orders of individual investors to greater stale price risks, which may, in turn,
leave them at the mercy of being picked off by professional investors. Thus, for example, an
investor could easily step in front (by a penny) of a standing limit order in a rising market or
sell into a standing limit order in a falling market (see also footnote 8). In either situation, the
liquidity supplier would be faced with losses in her position. If this situation leads some limit
order traders to avoid submitting such orders, the overall liquidity and depth of the markets are
in jeopardy. Brown and Holden (1999) model “mispricing” risk of limit orders and show how
market adjusted (or smart) limit orders can mitigate this risk.
To examine the issue of price runs versus reversals, we define a simple metric to
measure such phenomena.
Specifically, we examine the prevailing BBO quote midpoint
sequence and define an increase in quote midpoint by +1 and a decrease by –1. A simple run of
length 1 is defined as (+1+1) or a (-1-1). Similarly, a run of length 2 is defined as (+1+1+1) or (-11-1), and so on. A reversal is defined very simply as triples of BBO quote changes, where the
direction of the quote midpoint is reversed, as in (+1-1+1) or (-1+1-1).
It provides us with a
simple but intuitive framework to study the issue.9
Table 7 Panel A documents quote reversals, both in terms of the frequency of quote
reversals and the corresponding percentage of all non-zero quote changes, among decimal and
control stocks, over the three periods of study. While the frequency of quote reversals between
decimal and control stocks over the pre-decimal period is statistically similar (10.8% and 10.7%,
9
For robustness, we replicated our work using changes in transaction prices in place of quote midpoint
changes and obtained qualitatively similar results.
15
respectively), about 12% (10%) of all non-zero quote changes were reversals in the decimal
(control) stock sample over the decimal-trial period. This difference is statistically distinct at
reasonable levels of significance.
Thus, quotes appear to be reversed more frequently in
decimal stocks following decimalization. Interestingly, the percentage reversal in both decimal
and control stocks over the all-decimal period have increased even more (about 13% for both
groups of stocks). Thus, there appears to be significantly greater percentage of quote reversals
following decimalization in the NYSE. The implication is that there appears to be less risk from
stale prices in a post-decimal world.
Panel B provides the frequency (and the corresponding cumulative percentage) of runs
in quote adjustments between decimal and control stocks over the three distinct periods.
While the pre-decimal run length frequency at run lengths up to 25 are statistically similar
between the decimal and control stocks, we find statistically significantly greater run lengths
among decimal stocks relative to control stocks over the decimal-trial period.
Further, the
cumulative frequency at every run length continues to increase over the all-decimal (relative to
decimal-trial) period.
In summary, our results indicate, on one hand, more frequent quote reversals (i.e., lower
stale price risk), and on the other hand, significant increases in quote trends (i.e., higher stale
price risk) in the decimal-trial period, continuing on through the all-decimal period. The overall
effect on stale price risk, faced by the liquidity supplying limit order traders, is therefore
uncertain.
5.
Concluding Discussion
Even though it is tempting to think of decimalization as just another decrease in
minimum tick size, it is, in reality, much more than just that. The mantra is that the minimum
tick must make it an economic cost for someone to step up in front of another liquidity supplier.
While this was true even up to the conversion to sixteenths, it may not be true anymore -- where
it takes just one penny to step ahead of a standing limit order. And if it is almost costless to step
ahead, as one fund manager puts it, “……mutual funds may stop using limit orders and simply pay
fees to brokers to buy and sell at the prevailing market price. Most stocks already are traded that way on
the nation's exchanges.” With this backdrop -- and using tick-by-tick transaction and quote data
over three distinct periods related to before, during and after decimalization in the NYSE -- we
16
study the impact of decimalization on some of the common metrics of market liquidity, price
and order competition and the impact of regional versus the national exchanges. To isolate the
effects of decimalization, by ensuring that our results are not influenced by market trends over
the decimal period, we carefully construct a sample of control stocks matched 1:1 with each
decimal stock in our sample.
We find mixed evidence related to market liquidity following decimalization.
Specifically, while both the quoted and effective bid/ask spreads show significant decline, and
continue to decline in a decimal-trial world, the corresponding bid and ask depths also display
a similar significant downward trend over the same period. Thus, while better prices now exist
to buy and sell, the quantities that can be purchased or sold at those improved prices are also
fewer. Our finding of significantly smaller spreads following decimalization bodes well for
retail traders trading smaller size trades.
We find that both trades and trading volume have
declined significantly in all trade size categories as well as in all stock size categories. Stock
return volatilities show an increase in the short term but a decrease in the long term. This may
imply a degree of comfort experienced by market participants, as they learn to navigate their
way around in the new environment.
Although we find some increased activity among the regional stock exchanges in terms
of bid/ask quote adjustment frequencies, BBO times, and percentage of autoquotes, the
evidence is not strong and there is no evidence to suggest that the market share of transactions
executed by the regionals has increased, as a result. The NYSE appears to be still leading the
way in terms of 1-5 cent changes in bids and offers among all exchanges as well as in (dollar)
transactional volume. Finally, using a simple metric to capture runs and reversals in bid/ask
quotes, we find mixed evidence on stale price risk among stocks in a decimal-trial world.
Specifically, we find more frequent quote reversals, and simultaneously a significant increase in
quote trends in the market following decimalization.
One implication of our research is that retail investors are probably paying less to
transact in a decimal world. These are investors whose trade sizes do not usually exceed the
prevailing bid or ask sizes quoted at the improved (or tighter) prices.
What it does for
institutional investors’ trading costs is unclear since these trades are typically large and require
significant inroads into the limit order book and/or the presence of other suppliers of liquidity
– typically in the upstairs market. Institutional trades are also distinct in that they require
17
multiple trades, sometimes spanning days, to complete.
In that regard, Chakravarty,
Panchapagesan and Wood (2001) examine institutional execution costs around decimalization
in the NYSE using a large sample of institutional trades.
They find no increase in trade
execution costs in institutional trades after decimalization. An implication of their study is that
the available supply and demand of shares outside the best bid and offer prices remains
undiminished. Our results, combined with those of Chakravarty, Panchapagesan and Wood,
should be of some comfort to regulators who are under pressure from some professional
10
investors and academics to roll back decimalization and, instead, move to nickel ticks.
10
See “Decimal Move Brings Points Of Contention From Traders,” (Wall Street Journal, February 12, 2001, p.
C1) and “Deals & Deal Makers: Grasso Says NYSE Must Stick to Penny As Trade Increment,” ((Wall Street
Journal, March 22, 2001, p. C18).
18
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19
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21
Table 1A. Distribution of Odd and Even Tick Bid/Ask Spreads Among Regional Exchanges
The sample comprises of selected NYSE-listed common stocks included in the Decimal Pilot, and their corresponding NYSElisted matched control stocks over the decimal-trial and all-decimal periods. The cumulative percentages presented here are
computed from all (not just the BBOs) bid and ask quotes originating from the various exchanges. Only quoted spreads of up
to a dollar are considered for this table. Well over 95% of all quoted spreads are within a dollar.
Decimal-Trial Period
(October 2, 2000 -- January 26, 2001)
Decimal Stocks
All-Decimal Period
(January 29, 2001 - March 30, 2001)
Control Stocks
Decimal Stocks
Control Stocks
Exchanges
Boston
ticks
Even-ticks
Odd-ticks
Cum %
Cum %
Cum %
Cum %
52.69%
100.00%
100.00%
100.00%
51.45%
100.00%
51.43%
100.00%
Cincinnati
Even-ticks
Odd-ticks
54.12%
100.00%
100.00%
100.00%
52.26%
100.00%
53.45%
100.00%
Chicago
Even-ticks
Odd-ticks
52.78%
100.00%
99.97%
100.00%
52.31%
100.00%
52.51%
100.00%
NYSE
Even-ticks
Odd-ticks
46.33%
100.00%
99.99%
100.00%
45.28%
100.00%
44.27%
100.00%
Pacific
Even-ticks
Odd-ticks
50.52%
100.00%
100.00%
100.00%
52.63%
100.00%
50.87%
100.00%
Nasdaq
Even-ticks
Odd-ticks
51.44%
100.00%
99.97%
100.00%
60.54%
100.00%
59.91%
100.00%
Philadelphia Even-ticks
Odd-ticks
52.75%
100.00%
100.00%
100.00%
51.07%
100.00%
51.07%
100.00%
22
Table 1B. Distribution of BBO Quoted Spreads of NYSE-listed Decimal and Control Stocks
The sample comprises of selected NYSE-listed common stocks included in the Decimal Pilot, and their
corresponding NYSE-listed control stocks over the decimal-trial and all-decimal periods. The quoted bid/ask
spreads are denominated in cents and the cumulative percentages are computed from the best bid and ask
(BBO) prices in the various exchanges. Only quoted spreads of up to a dollar are considered for this table.
About 99.9% of all quoted BBO spreads are within a dollar.
Quoted Spread
Cents
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Decimal-Trial Period
(October 2, 2000 -- January 26, 2001)
Decimal Stocks
Control Stocks
Cum%
Cum%
11.86%
21.81%
29.46%
36.58%
44.89%
51.26%
56.47%
60.46%
64.43%
70.02%
73.03%
75.33%
77.45%
79.63%
82.59%
84.09%
85.22%
86.35%
87.71%
89.84%
90.81%
91.47%
92.12%
92.93%
94.25%
94.83%
95.17%
95.52%
95.91%
96.54%
96.83%
97.02%
97.21%
97.42%
97.74%
97.89%
98.02%
98.14%
100.00%
0.00%
0.00%
0.00%
0.00%
0.00%
42.35%
42.35%
42.35%
42.35%
42.36%
42.36%
72.59%
72.59%
72.59%
72.60%
72.60%
72.60%
86.49%
86.49%
86.49%
86.49%
86.49%
86.50%
86.50%
94.04%
94.04%
94.04%
94.04%
94.04%
94.05%
96.82%
96.82%
96.82%
96.82%
96.82%
96.82%
98.43%
98.43%
100.00%
23
All-Decimal Period
(January 29, 2001 -- March 30, 2001)
Decimal Stocks
Control Stocks
Cum%
Cum%
10.50%
19.72%
27.29%
34.59%
42.73%
49.15%
54.23%
58.77%
63.37%
69.13%
72.62%
75.14%
77.49%
80.00%
82.96%
84.62%
85.93%
87.23%
88.75%
90.80%
91.84%
92.56%
93.27%
94.11%
95.15%
95.66%
96.02%
96.38%
96.80%
97.35%
97.58%
97.76%
97.93%
98.14%
98.39%
98.51%
98.62%
98.73%
100.00%
10.97%
21.37%
29.63%
37.38%
45.48%
52.18%
57.44%
62.08%
66.72%
72.29%
75.80%
78.33%
80.66%
83.06%
85.89%
87.38%
88.54%
89.67%
90.93%
92.64%
93.39%
93.97%
94.53%
95.19%
96.02%
96.41%
96.68%
96.96%
97.28%
97.71%
97.91%
98.06%
98.21%
98.39%
98.59%
98.71%
98.80%
98.89%
100.00%
Table 2. Quoted Spreads of NYSE-listed Decimal and Control Stocks
The sample comprises of selected NYSE-listed common stocks included in the Decimal Pilot, and their corresponding NYSE-listed control stocks.
The three periods considered for the study are the pre-decimal, decimal-trial and all-decimal periods. All stocks in the sample are classified into
portfolios based on average daily dollar trading volume computed over the pre-decimal period. Portfolio 1 consists of the smallest dollar volume
stocks and portfolio 5 consists of the largest dollar volume stocks. The average quoted bid/ask spreads are denominated in cents. The quoted
spreads are computed from the best bid and ask prices (BBO) in the various exchanges. The spreads are weighted intra-day and across days by the
transaction volume, and across stocks by the daily average pre-decimal dollar trading volume. For each given portfolio, the reported spreads are
weighted intraday by time outstanding and across stocks by pre-decimal dollar trading volume. The net difference in quoted spreads in decimal
stocks is calculated as the difference between the daily average quoted spread of each decimal stock and its paired control stock in a particular size
rank. The average of these differences over each size rank and over each of the three periods are then computed. The table reports the net
differences (trial – pre) and (all – pre). T-tests (of equality of means) are performed to see if these differences, in decimal stocks in each size portfolio,
are statistically distinct from zero.
Net
Net
Pre-decimal Period Decimal-Trial Period All-decimal Period
Difference
Difference
(April 1, 2000 -- June (October 2, 2000 –
(January 29, 2001 -% Change % Change % Change % Change
in
in
30, 2000)
January 26, 2001)
March 30, 2001)
Quoted
Quoted
(trial –
(trial –
Spreads
pre)
pre)
(all – pre) (all – pre) Spreads
(trial –
pre)
Portfolio
Size Rank
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
1
2
3
4
5
17.51
16.65
16.13
12.65
12.16
16.33
16.33
16.46
12.00
12.35
12.76
12.25
10.49
8.13
8.10
15.7
16.07
14.03
11.47
10.43
13.41
11.89
10.26
7.20
7.32
Dollar
Volume
Weighted
Average
11.46
11.69
7.43
9.84
7.07
Decimal Control Decimal Control
(all – pre)
Cents
Cents
Decimal
Stocks
Stocks
Stock
Stocks
Stock
Decimal
Stocks
13.87
13.56
10.10
7.23
6.59
-27.13%
-26.43%
-34.97%
-35.73%
-33.39%
-3.86%
-1.59%
-14.76%
-4.42%
-15.55%
-23.42%
-28.59%
-36.39%
-43.08%
-39.80%
-15.06%
-16.96%
-38.64%
-39.75%
-46.64%
-4.12***
-4.15**
-3.37**
-4.00***
-2.14
-1.64
-2.00
0.33
-0.69
0.92
6.2
-35.17%
-15.83%
-4.85%
-36.99%
-2.18*
1.10
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
24
Table 3. Effective Spreads of NYSE-listed Decimal and Control Stocks
The sample comprises of selected NYSE-listed common stocks included in the Decimal Pilot, and their corresponding NYSE-listed control stocks. The three
periods considered for the study are the pre-decimal, decimal-trial and all-decimal periods. For Panel A, all stocks in the sample are classified into portfolios
based on average daily dollar trading volume computed over the pre-decimal period. Portfolio 1 consists of the smallest dollar volume stocks and portfolio 5
consists of the largest dollar volume stocks. The average effective bid/ask spreads are denominated in cents. The effective spread is calculated as twice the
absolute difference between the transaction price and the midpoint of the prevailing BBO. In panel A, for a given portfolio, the effective spreads are weighted
intra-day and across days by the transaction volume, and across stocks by their average daily pre-decimal dollar trading volume. In panel B, the effective
spreads are calculated on the basis of trade size categories as indicated. The net difference in effective spreads in decimal stocks is calculated as the difference
between the daily average quoted spread of each decimal stock and its paired control stock in a particular size rank. The average of these differences over each
size rank and over each of the three periods are then computed The table reports the difference of these net differences (trial – pre) and (all – pre). In panel B,
the corresponding net differences are calculated (and reported) based on trade size categories. T-tests are performed to see if these differences, in decimal stocks
in each size portfolio (or trade size category), are statistically distinct from zero.
Panel A: Effective Bid/ask Spreads of stock portfolios classified by of dollar volume
Pre-decimal Period Decimal-trial Period
(April 1, 2000 -- June (October 2, 2000 –
30, 2000)
January 26, 2001)
All-decimal Period
(January 29, 2001 March 30, 2001)
% Change
(trial – pre)
Portfolio Decimal
Size Rank Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Net Difference Net Difference
in
in
Quoted
Quoted
(trial – pre) (all – pre) (all – pre)
Spreads
Spreads
% Change
Control
% Change % Change
(trial – pre )
(all – pre )
Cents
Cents
Decimal Control
Stocks
Stock
Stocks
Stock
Decimal Stocks
Decimal Stocks
1
2
3
4
5
14.20
15.20
13.10
11.41
12.05
14.84
13.69
13.58
10.64
12.14
9.88
10.59
10.10
8.29
9.74
12.06
14.03
12.03
10.47
10.59
11.09
10.76
9.04
7.05
8.12
10.43
12.86
9.12
7.48
7.28
-30.42%
-30.33%
-22.90%
-27.34%
-19.17%
-18.73%
2.48%
-11.41%
-1.60%
-12.77%
-21.90%
-29.21%
-30.99%
-38.21%
-32.61%
-29.72%
-6.06%
-32.84%
-29.70%
-40.03%
-1.54
-4.95***
-0.82
-2.94**
-0.77
1.30
-3.61
0.11
-1.19
0.93
Dollar
Volume
Weighted
Average
12.42
11.75
10.41
10.23
8.11
7.14
-16.18%
-12.94%
-34.70%
-39.23%
-0.50
0.30
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
25
Table 3 continued.
Panel B: Effective Bid/Ask Spreads by Trade Size
Pre-decimal Period Decimal-trial Period All-decimal Period
Net
Net
Difference Difference
(October 2, 2000 –
(July, 2000)
(January 29, 2001 -% Change % Change % Change % Change
in
in
January 26, 2001)
March 30, 2001)
(trial –
(trial –
Quoted
Quoted
Spreads
pre)
pre)
(all – pre) (all – pre) Spreads
Portfolio
Size Rank
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stock
Decimal
Stocks
Control
Stock
(trial –
pre)
Cents
Decimal
Stocks
<500
500-999
1,000-4,999
5,000-9,999
>=10,000
10.26
11.11
12.47
13.13
15.08
9.72
10.80
11.86
12.05
16.43
6.83
7.74
9.06
10.36
12.75
9.09
10.12
11.47
12.33
12.76
6.41
7.44
8.76
10.53
11.35
6.59
7.55
8.57
11.63
11.55
-33.43%
-30.33%
-27.35%
-21.10%
-15.45%
-6.48%
-6.30%
-3.29%
2.32%
-22.34%
-37.52%
-33.03%
-29.75%
-19.80%
-24.73%
-32.20%
-30.09%
-27.74%
-3.49%
-29.70%
-2.81***
-2.69***
-3.03***
-3.08***
0.76
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
26
(all –
pre)
Cents
Decimal
Stocks
-0.73
-0.42
-0.43
-2.16
0.30
Table 4. Depth Changes of NYSE-listed Decimal and Control Stocks
Depth is defined as the average of the bid and ask depths and is expressed in round lots of 100-shares. The sample comprises of selected NYSE-listed
common stocks included in the Decimal Pilot, and their corresponding NYSE-listed control stocks. The three periods considered for the study are the predecimal, decimal-trial and all-decimal periods. The bid and ask depths correspond to the sizes corresponding to the prevailing best bids and offers (BBO)
and represent round lots of 100 shares. The net difference in depths in decimal stocks is calculated as the difference between the daily average depth of
each decimal stock and its paired control stock in a particular size rank. The average of these differences over each size rank and over each of the three
periods are then computed. The table reports the difference of these net differences (trial – pre) and (all – pre). T-tests are performed to see if these
differences, in decimal stocks in each size portfolio, are statistically distinct from zero.
P re -d ecim al P e riod D ecim a l-trial P eriod
(A p ril 1 , 20 00 -- Ju n e
(O ctob e r 2 , 20 00 –
3 0 , 2 00 0)
Ja n u ary 26 , 2 00 1)
A ll-d e cim al P eriod
(Jan u a ry 2 9, 20 01 -M a rc h 30 , 20 01 )
P ortfolio
S iz e R a n k
D ec im a l
S toc k s
C on trol
S tock s
D e cim al
S tock s
C on trol
S tock s
D ec im a l
S toc k s
C on trol
S tock s
1
2
3
4
5
22 .3 3
74 .3 0
45 .7 4
75 .7 5
10 3.8 2
18 .66
79 .32
68 .04
80 .67
1 56 .09
2 1.74
2 0.73
2 1.13
3 3.30
3 3.03
2 8.4 2
10 6.2 8
7 9.2 3
8 8.1 5
19 6.3 6
15 .5 7
17 .8 4
20 .5 1
34 .8 0
34 .5 7
D olla r
V olu m e
W eigh te d
A ve rage
11 3.3 6
1 35 .13
35 .3
15 4.4 8
37 .0 1
N et
N et
D iffere nc e D iffer ence
% C h a n ge % C h a n ge % C h an ge % C h an ge
in
in
(tria l –
(trial –
D epths
D epths
p re)
p re)
(all – p re ) (all – p re )
(tria l –
pre )
(a ll –
pre)
D e cim a l
S tock s
C on trol
S tock
D ecim a l
S toc k s
C on trol
S toc k
D ecim al
Stock s
D ecim a l
Stock s
16 .80
30 .59
29 .11
30 .10
43 .05
-2 .6 4%
-7 2.1 0%
-5 3.8 0%
-5 6.0 4%
-6 8.1 9%
5 2.3 0%
3 3.9 9%
1 6.4 5%
9 .27 %
2 5.8 0%
-30 .27 %
-75 .99 %
-55 .16 %
-54 .06 %
-66 .70 %
-9.9 7%
-6 1.43 %
-5 7.22 %
-6 2.69 %
-7 2.42 %
-1 0.3 5
-8 0.5 3
-35 .8 0 **
-49 .9 2 **
-11 1.0 5**
-4 .91
-7.73 **
1 3.7 1
9 .6 3
4 3.8 0
40 .11
-6 8.8 6%
1 4.3 2%
-67 .35 %
-7 0.32 %
-97 .4 2 **
1 8.6 6
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
27
Table 5. Trade Frequency and Trading Volume in NYSE-listed Decimal and Control Stocks.
The sample comprises of selected NYSE-listed common stocks included in the Decimal Pilot, and their corresponding NYSE-listed control stocks. The
three periods considered for the study are the pre-decimal, decimal-trial and all-decimal periods. Panel A presents the average daily trading volume
results classified by trade size, and panel B provides the corresponding daily average trade frequency statistics. The average daily volume numbers
are represented in round lots (100-share units). The net difference in trade volume (or trade frequency) in decimal stocks is calculated as the
difference between the daily average volume (or trade frequency) of each decimal stock and its paired control stock in a particular trade size category.
The average of these differences over each trade size category and over each of the three periods is then computed. The table reports the difference of
these net differences (trial – pre) and (all – pre). T-tests are performed to see if these differences, in decimal stocks in each trade size category, are
statistically distinct from zero.
Panel A: Trading Volume
Pre-decimal Period Decimal-trial Period
(April 1, 2000 -- June (October 2, 2000 –
30, 2000)
January 26, 2001)
All-decimal Period
Net
Net
Difference Difference
(January 29, 2001 -% Change % Change % Change % Change
in
in
March 30, 2001)
(trial –
(trial –
Trade
Trade
Volume
pre)
pre)
(all – pre) (all – pre) Volume
Portfolio
Size Rank
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
<500
500-999
1,000-4,999
5,000-9,999
>=10,000
1735
1722
7565
4327
16057
1245
1395
6338
3677
14519
892
925
3732
1874
8406
659
758
3372
1940
8448
539
616
2482
1291
5396
474
557
2300
1199
4442
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
28
Decimal Control Decimal Control
Stocks
-49%
-46%
-51%
-57%
-48%
Stock
-47%
-46%
-47%
-47%
-42%
Stocks
-69%
-64%
-67%
-70%
-66%
Stock
(trial –
pre )
in round
lots
Decimal
Stocks
(all –
pre)
in round
lots
Decimal
Stocks
-62%
-257
-425.05*
-60%
-160
-268
-64% -867.43* -1044.61*
-67% -715.36*** -557.11*
-69%
-1581
-585
Panel B: Trade Frequency
Pre-decimal Period Decimal-trial Period
(April 1, 2000 -- June (October 2, 2000 –
30, 2000)
January 26, 2001)
All-decimal Period
Net
Net
Difference Difference
(January 29, 2001 -% Change % Change % Change % Change
in
in
March 30, 2001)
(trial –
(trial –
Trade
Trade
pre)
pre)
(all – pre) (all – pre) Frequence Frequence
Portfolio
Size Rank
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
Decimal
Stocks
Control
Stocks
<500
500-999
1,000-4,999
5,000-9,999
>=10,000
951
288
417
70
64
649
230
341
59
55
472
151
206
30
30
341
123
180
31
30
280
100
135
20
20
245
89
122
19
17
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
29
Decimal Control Decimal Control
(trial –
pre )
(all –
pre)
Decimal
Stocks
-266.56*
-48
-63.65*
-8.99*
-6
Stocks
Stock
Stocks
Stock
Decimal
Stocks
-50%
-47%
-51%
-57%
-53%
-47%
-46%
-47%
-48%
-46%
-71%
-65%
-68%
-71%
-68%
-62%
-61%
-64%
-68%
-69%
-170.71*
-30
-51.10*
-11.81***
-8.39*
Table 6. Return Volatility in NYSE-listed Decimal and Control Stocks.
Volatility before and after decimalization is presented for five portfolios formed from the selected NYSE-listed common stocks in the decimal pilot
and the matched sample of control stocks. The three periods considered for the study are the pre-decimal, decimal-trial and all-decimal periods.
The portfolios are formed based on average daily dollar trading volume size quintiles over the pre-decimal period. Portfolio 1 (5) has the smallest
(largest) dollar trading volume stocks. A minute-by-minute return index is calculated for each portfolio with overnight returns excluded, where
each return is weighted by its trading volume. Volatility is calculated as the standard deviation of the intra-day return series of these portfolios.
For each portfolio, the net difference in volatility in decimal stocks is calculated as the difference between the daily average volatility of each decimal
stock and its paired control stock. The average of these differences over each trade size category and over each of the three periods is then
computed. The table reports the difference of these net differences (trial – pre) and (all – pre). T-tests are performed to see if these differences -- in
decimal stocks, in each portfolio -- are statistically distinct from zero.
Pre-decimal Period Decimal-trial Period
(April 1, 2000 -- June (October 2, 2000 –
30, 2000)
January 26, 2001)
Portfolio Decimal
Size Rank Stocks
1
2
3
4
5
0.49%
0.67%
0.73%
0.65%
0.97%
Control
Stocks
0.48%
0.73%
0.80%
0.73%
0.93%
Decimal
Stocks
0.49%
0.82%
1.31%
0.85%
1.06%
Control
Stocks
0.45%
0.63%
0.64%
0.56%
0.92%
All-decimal Period
Net
Net
Difference Difference
(January 29, 2001 -% Change % Change % Change % Change
in
in
March 30, 2001)
(trial –
(trial –
Return
Return
pre)
pre)
(all – pre) (all – pre) Volatility Volatility
Decimal
Stocks
0.35%
0.57%
0.60%
0.60%
0.76%
Control
Stocks
0.38%
0.50%
0.57%
0.52%
0.86%
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
30
Decimal Control Decimal Control
(trial –
pre)
(all –
pre)
Decimal
Stocks
-0.0007**
0.0011**
0.0015***
0.0014***
0.0027***
Stocks
Stock
Stocks
Stock
Decimal
Stocks
0.00%
22.39%
79.45%
30.77%
9.28%
-6.25%
-13.70%
-20.00%
-23.29%
-1.08%
-28.57%
-14.93%
-17.81%
-7.69%
-21.65%
-20.83%
-31.51%
-28.75%
-28.77%
-7.53%
0.0003
0.0023***
0.0077***
0.0037***
0.0011**
Table 7. Runs and Reversals in BBO Quote Midpoints in NYSE-listed Decimal and Control Stocks.
This table examines reversals and runs for selected NYSE-listed common stocks in the decimal pilot and their matched sample of control stocks, over
the pre-decimal, decimal-trial and all-decimal periods. Runs and reversals are defined in the text and are computed based on the prevailing BBO
midpoint. T-tests (of equality of means) are performed between decimal and control stocks for (trial – pre) and (all – pre) periods.
Panel A. Quote Reversals
Pre-decimal Period
(April 1, 2000 -- June 30, 2000)
Decimal Stocks
Total
number of
quote
reversals
Quote
Reversals
6,252
% of all
non-zero
quote
changes
10.76%
Control Stocks
Total
number of
quote
reversals
5,350
% of all
non-zero
quote
changes
10.66%
Decimal-trial Period
(October 2, 2000 – January 26, 2001)
Decimal Stocks
Total
number of
quote
reversals
5,791
% of all
non-zero
quote
changes
11.97%
Control Stocks
Total
number of
quote
reversals
3,228
% of all
non-zero
quote
changes
10.48%
All-decimal Period
(January 29, 2001 -- March 30, 2001)
Decimal Stocks
Total
number of
quote
reversals
% of all
non-zero
quote
changes
Total
number of
quote
reversals
% of all
non-zero
quote
changes
8,701
12.81%
7862
12.59%
T-Tests
t-statistic
Decimal
Trial - Pre All - Pre
5.63***
7.65***
Control
Trial - Pre All - Pre
-1.06
5.90***
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
31
Control Stocks
Table 7 continued
Panel B: Quote Runs
Run Length
Pre-decimal Period
(April 1, 2000 -- June 30, 2000)
Decimal Stocks
Control Stocks
Cumulative
1
2
3
4
5
6
7
8
9
10
15
20
25
percentage
Number
1.6%
115362
2.3%
49430
2.6%
23272
2.8%
12452
2.9%
7021
3.0%
4061
3.0%
2494
3.0%
1547
3.0%
976
3.0%
593
3.0%
1089
3.0%
158
3.0%
34
Number
100,601
43,568
20,442
10,619
5,904
3,336
1,972
1,247
779
484
820
135
17
Cumulative
percentage
1.6%
2.2%
2.5%
2.7%
2.8%
2.9%
2.9%
2.9%
2.9%
2.9%
2.9%
2.9%
2.9%
Decimal-trial Period
(October 2, 2000 – January 26, 2001)
Decimal Stocks
Control Stocks
Number
93,745
40,620
22,051
12,354
7,454
4,512
3,026
1,930
1,305
883
1,769
338
83
Cumulative
percentage
1.6%
2.3%
2.7%
2.9%
3.1%
3.1%
3.2%
3.2%
3.2%
3.3%
3.3%
3.3%
3.3%
Number
65,593
27,416
12,272
6,061
3,292
1,850
1,044
636
410
217
403
53
10
Cumulative
percentage
1.6%
2.3%
2.6%
2.7%
2.8%
2.8%
2.9%
2.9%
2.9%
2.9%
2.9%
2.9%
2.9%
All-decimal Period
(January 29, 2001 -- March 30, 2001)
Decimal Stocks
Control Stocks
Number
150,863
66,489
34,022
19,104
11,345
6,824
4,342
2,789
1,820
1,164
2,235
355
70
T-Tests
t-statistic
Decimal
Trial - Pre
All - Pre
7.35***
15.79***
Control
Trial - Pre All - Pre
-0.85
16.67***
*** p-value ≤ 0.01, ** 0.01 < p-value ≤ 0.05, * 0.05 < p-value ≤ 0.10
32
Cumulative
percentage
1.8%
2.7%
3.1%
3.3%
3.5%
3.5%
3.6%
3.6%
3.6%
3.7%
3.7%
3.7%
3.7%
Number
138,438
61,051
31,184
17,088
10,016
5,947
3,619
2,431
1,564
1,043
714
443
293
Cumulative
percentage
1.8%
2.6%
3.1%
3.3%
3.4%
3.5%
3.5%
3.6%
3.6%
3.6%
3.6%
3.6%
3.6%
Appendix
We provide summary statistics for each decimal stock in our sample and its matched control stock.
Share price is the average share price over the pre-decimal period (defined in the text). Volatility is
the standard deviation of the bid-ask spread midpoints over the pre-decimal period and expressed as
a percentage. Share volume is the total shares transacted over the pre-decimal period. Market
capitalization is also calculated over the pre-decimal period.
decimal
stock
ABX
ACR
AHP
AOL
APC
ASF
ASH
ATW
AXM
BBC
BEN
BLC
BN
BVF
CBU
CGI
CI
CL
CPQ
DCX
DLX
DON
DTF
ESA
FDS
FDX
FUN
GDI
GLT
GMH
GT
GTW
H
HAR
HUG
KF
Decimal stocks
share
volume
(millions
of
volatility
shares) price ($)
(%)
market
cap
(Billons
of
dollars)
paired
control
stock
103.31
1.821
232.827
865.236
115.879
9.461
16.294
4.926
0.975
34.736
32.021
16.945
3.772
26.893
0.42
2.071
50.055
106.959
947.645
34.063
16.964
0.495
0.8
7.094
6.847
75.068
3.267
1.332
5.128
249.197
74.264
109.886
13.907
4.986
4.424
14.294
6.626
0.118
74.724
136.039
5.569
0.697
2.44
0.75
0.05
0.82
7.917
1.743
0.467
3.077
0.161
0.978
14.397
32.723
44.334
59.694
1.877
0.073
0.11
0.825
0.912
11.411
1.009
0.28
0.44
14.7
3.474
17.942
2.425
1.018
0.41
0.711
KEY
TNM
WFC
PFE
AZA
SRT
FLR
CKH
TEA
OMX
BBT
BC
MLS
BOW
TAI
CPJ
DOX
BK
MO
VIA
AMB
MAL
BSD
GRL
PME
ABS
CTR
LNN
WAB
TER
RDC
FDC
TGH
E
ALN
OTE
17.895
6.511
56.603
56.589
46.3
51.097
34.603
57.342
9.343
5.624
31.549
16.489
19.054
47.756
22.808
28.072
85.118
57.197
27.374
58.058
25.287
13.567
12.989
8.751
27.134
37.462
19.361
18.065
10.988
97.659
26.665
53.777
40.365
61.165
17.675
12.93
0.9596
0.9906
2.1281
4.6093
6.3594
9.0003
1.2673
6.9504
0.4032
0.4139
1.5373
0.5114
0.4618
3.6156
0.4678
1.1008
6.1823
2.1504
1.1841
4.6359
0.6722
0.9151
0.4087
0.7427
2.6458
1.8669
0.4792
0.7677
0.7299
9.3569
2.2245
3.7677
6.6188
2.8314
1.5544
0.8316
33
Control stocks
share
volume
(millions
of
volatility
shares) price ($)
(%)
market
cap
(Billons
of
dollars)
83.359
1.927
262.768
713.297
89.64
6.485
19.319
3.756
0.743
30.639
31.552
19.697
3.85
29.561
0.268
3.088
50.606
122.304
675.184
15.492
11.766
0.53
1.061
7.092
5.27
76.276
2.665
1.103
4.735
161.231
69.672
100.676
17.519
4.036
4.583
13.806
8.406
0.107
66.287
160.469
4.93
0.846
2.421
0.67
0.044
0.663
9.264
1.636
0.447
2.543
0.139
0.767
15.69
33.004
56.1
62.361
1.891
0.068
0.092
0.701
0.954
13.787
0.779
0.225
0.519
13.563
2.812
19.9
1.734
0.896
0.454
0.711
19.302
7.603
42.338
43.328
47.852
58.768
33.135
57.356
9.424
5.525
27.562
18.749
18.118
51.942
21.976
26.385
68.29
44.61
24.68
59.711
22.487
13.642
12.637
8.362
28.274
33.909
19.215
18.724
11.167
90.762
29.281
49.599
44.301
51.886
16.042
12.425
1.206
0.9107
2.0515
2.5238
5.4143
8.3827
1.5558
8.5981
0.3932
0.3181
1.5096
0.7696
0.5812
3.2861
0.5336
1.0892
7.2727
2.4064
2.36
6.208
0.6656
0.8042
0.4088
0.8116
2.6411
1.969
0.579
0.8515
0.6807
11.0448
1.7043
3.7628
6.1251
2.828
1.3595
0.7114
Appendix -- continued
decimal
stock
KSM
LE
LMT
LSI
LSS
LUV
MAD
MAT
MCK
MDC
MI
MLM
MMR
MPR
MWY
N
NHL
NSS
POM
PTZ
RBK
RCL
S
SFD
SGY
SLR
STT
SWM
SYK
TBC
TM
TMO
TRC
VAL
VFC
VIG
VTS
WLV
WSO
ZTR
share
volume
(millions
of
volatility
shares) price ($)
(%)
0.659
10.155
0.3288
19.266
39.836
9.0205
98.283
23.986
1.8449
289.077
57.969
7.5614
8.447
47.071
3.2544
87.46
20.588
0.9552
2.478
8.293
0.8143
195.404
12.615
1.1706
81.147
19.038
1.7293
1.281
18.318
0.9882
10.527
48.398
2.9588
11.597
48.808
3.978
6.84
14.29
1.8214
0.756
9.142
0.3027
13.896
7.888
1.7389
30.056
16.642
0.9936
2.901
27.573
0.5719
9.808
17.463
1.8295
24.579
24.384
1.8965
1.639
39.89
0.5552
30.366
15.03
1.9227
47.024
22.42
2.4831
117.05
36.739
2.6614
7.798
23.62
2.7565
6.95
54.827
5.1406
281.586
38.61
4.8205
53.356
104.626
6.3287
3.037
14.119
0.7441
23.771
53.729
16.1397
0.839
11.542
0.8754
1.294
96.45
5.9787
30.769
19.393
0.9665
0.569
22.424
0.8542
8.602
35.747
1.431
18.209
27.099
1.991
0.555
8.226
0.696
12.423
25.281
1.9745
2.474
15.713
1.3245
1.997
13.162
1.2765
11.057
6.628
0.1665
market
cap
(Billons
of
dollars)
0.11
1.397
8.997
19.016
1.108
9.906
0.073
5.067
5.871
0.404
5.252
2.065
0.245
0.057
0.42
3.005
0.831
0.387
2.915
0.328
0.721
4.226
11.443
1.34
1.014
23.925
16.31
0.198
7.617
0.09
0.63
3.235
0.29
1.6
2.837
0.041
0.705
0.182
0.292
0.614
34
paired
control
stock
MFI
IBI
BSX
TMX
PCP
BNI
AGL
KM
EIX
OCQ
MGA
RDN
MNC
CSI
GEN
NFB
SUS
SKO
DNY
CHE
FBN
CF
ELN
LUX
FS
GPS
CSC
TWK
RHI
UNO
NVO
PLD
DEL
GAS
VVI
ISH
CEC
EWF
BKE
PIM
share
volume
(millions
of
volatility
shares) price ($)
(%)
0.689
10.03
0.3023
27.488
35.478
10.6135
108.849
24.169
2.1211
177.712
55.05
5.1988
10.432
44.504
3.5716
91.016
24.086
1.0407
1.949
7.626
0.9044
203.49
8.09
0.7295
73.201
19.719
1.6198
1.117
18.758
0.8553
10.101
47.494
2.8928
12.858
52.089
3.4563
6.385
15.215
2.0297
0.588
8.988
0.3234
16.374
8.917
1.6654
37.836
16.563
0.8293
3.212
30.505
0.5453
11.404
18.391
1.6266
23.59
23.193
1.6171
1.387
29.38
0.788
23.417
17.682
2.0988
55.398
21.929
1.7228
108.614
42.529
2.7345
5.194
23.388
2.7984
8.682
55.741
5.2643
244.823
36.243
5.1277
66.575
83.358
7.0252
2.634
14.348
0.8008
32.057
51.394
12.2536
1.012
11.09
0.8497
0.816
77.977
6.2152
26.868
20.457
0.8494
0.582
21.617
0.7026
8.742
34.426
1.2809
15.245
26.523
1.8233
0.25
8.162
0.6195
10.548
26.825
1.9368
2.308
15.409
1.2105
2.491
12.878
1.4022
11.887
5.986
0.1523
market
cap
(Billons
of
dollars)
0.13
1.578
8.788
19.992
1.003
10.253
0.078
4.073
6.342
0.307
3.386
1.875
0.308
0.082
0.33
2.954
0.854
0.503
2.707
0.297
0.84
4.712
12.055
1.262
0.65
33.385
12.657
0.238
4.673
0.121
0.474
3.339
0.272
1.559
2.405
0.052
0.712
0.191
0.29
0.607