Can Global Stock Liquidity Be Measured?*
Kingsley Fong
University of New South Wales
Craig W. Holden
Indiana University
Charles A. Trzcinka**
Indiana University
February 2010
Abstract
A growing literature uses percent cost or cost per volume liquidity proxies constructed from daily stock data
to conduct research in international asset pricing, international corporate finance, and international market
microstructure. Relatively little is known about how well these proxies are related to transactions costs in the
global setting. We compare these proxies to actual transaction costs using the microstructure data in the
Reuters Datascope Tick History dataset by the Securities Industry Research Centre of Asia-Pacific. Our
sample contains 8.1 billion trades and 12.2 billion quotes representing 16,096 firms on 41 exchanges around
the world from 1996 to 2007. We evaluate nine percent cost proxies (including two new ones) relative to four
percent cost benchmarks: percent effective spread, percent quoted spread, percent realized spread, and
percent price impact. We examine twelve cost per volume proxies (including two new ones) relative to a cost
per volume benchmark: the slope of the price function “lambda.” We test three dimensions: (1) higher
average cross-sectional correlation with the benchmarks, (2) higher portfolio correlation with the
benchmarks, or (3) lower prediction error relative to the benchmarks. We find that a new measure, FHT, is
the best proxy for percent effective spread, percent quoted spread, and percent realized spread. We find that
FHT is the best proxy for percent price impact, but is only moderately-well correlated with it and does not
capture the correct scale. We find that LOT Mixed Impact, Zeros Impact, and Zeros2 Impact are the best
proxies for lambda, but they are only moderately-well correlated with it and do not capture the correct scale.
JEL classification:
C15, G12, G20.
Keywords: Liquidity, transaction costs, effective spread, price impact, asset pricing.
* We thank seminar participants at Hong Kong University, Hong Kong University of Science and
Technology, Indiana University, Michigan State University, University of New South Wales, University of
Sydney Microstructure Meeting, and University of Technology, Sydney. We are solely responsible for any
errors.
** Corresponding author: Charles A. Trzcinka, Kelley School of Business, Indiana University, 1309 E. Tenth
St., Bloomington, IN 47405-1701. Tel.: + 1-812-855-9908; fax: + 1-812-855-5875: email address: ctrzcink@
indiana.edu
1
1. Introduction
A rapidly growing literature uses percent cost or cost per volume liquidity proxies
constructed from daily stock data to conduct research in international asset pricing,1 international
corporate finance,2 and international market microstructure.3 For example, Bekaert, Harvey, and
Lundblad (2007) use the proportion of zero returns as a percent cost proxy to test the relationship
between liquidity cost and asset pricing in 19 emerging markets. Karolyi, Lee and Van Dijk,
(2008) use the Amihud (2002) measure as a cost per volume proxy to analyze the commonality patterns
of cost per volume liquidity, returns, and turnover across 40 countries. Lang, Lins, and Maffett (2007)
use the proportion of zero returns to examine the relationship between earnings smoothing,
governance, and liquidity cost in 21 countries. Levine and Schmukler (2006) use both the proportion
of zero returns and the Amihud measure to examine the relationship between home market liquidity and
cross-listed trading across 31 home countries.
Despite the widespread use of various percent cost and cost per volume liquidity proxies in
international research, relatively little is known about how well these proxies are related to actual
transactions costs in the global setting. To fill this gap in the literature, we compare these proxies
to actual transaction costs using the Reuters Datascope Tick History (RDTH) dataset by the
Securities Industry Research Centre of Asia-Pacific (SIRCA), which contains more than a
decade of global intraday Reuters data. Our sample contains 8.1 billion trades and 12.2 billion
quotes representing 16,096 firms on 41 exchanges around the world from 1996 to 2007. We
evaluate nine percent cost proxies (including two new ones that we introduce) relative to four percent cost
benchmarks: percent effective spread, percent quoted spread, percent realized spread, and percent price
1
See Jain, Xia, and Wu (2004), Stahel (2005), Liang and Wei (2006), Lee (2006), Griffin, Kelly, and Nardari
(2007), and Bekaert, Harvey, and Lundbland (2007).
2
See Bailey, Karolyi, and Salva, (2005), LaFond, Lang, and Skaife (2007) and Lang, Lins, and Maffett (2009).
3
See Jain (2005), Levine and Schmukler (2006), Henkel, Jain, and Lundblad (2008), Henkel (2008), Karolyi, Lee,
and van Dijk (2008), and DeNicolo and Ivaschenko (2009).
1
impact. We examine twelve cost per volume proxies (including two new ones that we introduce) relative
to a cost per volume benchmark: the slope of the price function “lambda.” In each case, we test three
performance dimensions: (1) higher average cross-sectional correlation with the benchmarks, (2)
higher portfolio correlation with the benchmarks, or (3) lower prediction error relative to the
benchmarks. We find that global stock liquidity can be measured using percent cost and cost per volume
liquidity proxies and we identify the best proxies in each case.
Percent cost and cost per volume liquidity proxies provide an enormous advantage for
international research by spanning a large cross-section of countries over a long time-series. The
daily stock data from which they are constructed are available from various vendors. For example,
Thompson Financial’s DataStream provides daily stock data on tens of thousands of stocks from 64
countries. Their daily stock price data, from which percent cost proxies are computed, goes back to the
1980’s for 12 countries, back to the 1970’s for 16 additional countries, and back to the 1960’s for 2 more
countries. Their daily stock volume data, which is a required variable to compute cost per volume proxies,
goes back to the 1990’s for 19 countries, back to the 1980’s for 23 additional countries, and back to the
1970’s for 2 more countries.
Three studies test the performance of available percent cost and cost per volume liquidity
proxies using U.S. data. Lesmond, Ogden, and Trzcinka (1999) test how three annual percent cost
proxies are related to the annual quoted spread as computed from daily closing quoted spreads in
U.S. data. Hasbrouck (2009) tests how three annual percent cost proxies and one annual cost per
volume proxy are related to the benchmarks: percent effective spread and the slope of the price
function lambda as computed from high-frequency U.S. trade and quote data. Goyenko, Holden,
and Trzcinka (2009) test how nine annual and monthly percent cost proxies are related to the
annual and monthly percent cost benchmarks: percent effective spread and percent realized
spread as computed from high-frequency U.S. trade and quote data. Goyenko, Holden, and
2
Trzcinka also test how twelve annual and monthly cost per volume proxies are related to the
annual and monthly benchmarks: the slope of the price function lambda and percent price impact
as computed from high-frequency U.S. trade and quote data.
Lesmond (2005) tests how three quarterly percent cost proxies and two quarterly cost per
volume proxies are related to average daily spreads in 23 emerging markets. In contrast, we test
nine percent cost proxies and twelve cost per volume proxies computed on a monthly basis
against five benchmarks computed from intraday trade and quote data. We run these tests for 41
exchanges in both developed and emerging countries. Our benchmarks are more precise
measures of transactions costs because they are computed from high frequency data rather than
end of day spreads.
We can safely assert that the international literature has generally not been mistaken in
using Zeros and the LOT measures as proxies for percent effective spread, percent quoted spread,
percent realized spread, or percent price impact around the world. However, we show that a new proxy,
which is a simplification of the LOT measure, performs significantly better. Further, we show that the
Amihud measure is only moderately-well correlated with lambda (the slope of the price function)
around the world and does not capture the correct scale. However, we show that other proxies perform
somewhat better than Amihud.
We find that a new measure that we introduce, FHT, is the best and most consistent proxy for
percent effective spread, percent quoted spread, and percent realized spread. We find FHT is the best
proxy for percent price impact, but is only moderately-well correlated with it and does not capture the
correct scale. We find that LOT Mixed Impact, Zeros Impact, and Zeros2 Impact are the best proxies for
lambda, but they are only moderately-well correlated with it and do not capture the correct scale.
The paper is organized as follows. Section 2 explains the high-frequency percent cost and
cost per volume benchmarks. Section 3 explains the low-frequency percent cost proxies. Section
3
4 explains the low-frequency cost per volume proxies. Section 5 describes the dataset and
methodology used. Section 6 presents our empirical results. Section 7 concludes. An online
appendix with 20 additional tables is available at www.kelley.iu.edu/cholden/fhtappendix.pdf.
2. High Frequency Percent Cost and Cost Per Volume Benchmarks
We analyze four high frequency percent cost benchmarks. Our first percent cost
benchmark is percent effective spread. For a given stock, the percent effective spread on the k th
trade is defined as
Percent Effective Spread k  2  ln  Pk   ln  M k  ,
(1)
where Pk is the price of the k th trade and M k is the midpoint of the consolidated BBO
prevailing at the time of the k th trade. Aggregating over month i, a stock’s Percent
Effective Spread i is the dollar-volume-weighted average of Percent Effective Spread k computed
over all trades in month i.
Our second percent cost benchmark is percent quoted spread. For a given time interval s ,
the percent quoted spread is defined as
Percent Quoted Spread s  ( Ask s  Bid s ) / (( Ask s  Bid s ) / 2),
(2)
where Asks is the best ask quote Bids is the best bid quote in that time interval. Over month i, the
stock’s Percent Quoted Spreadi is the time-weighted average of the time interval values during
the month.
Our third percent cost benchmark is realized spread, which is the temporary component
of the percent effective spread. For a given stock, the percent realized spread on the k th trade is
defined as
Percent Realized Spreadk  2  ln( Pk )  ln( M k 5 ) ,
(3)
4
where M(k+5) is the midpoint five-minutes after the k th trade. Aggregating over month i, a stock’s
Percent Realized Spreadi is the dollar-volume-weighted average of Percent Realized Spreadk
computed over all trades in month i.
Our fourth percent cost benchmark is percent price impact, which is the percent change in
quote midpoint caused by a trade. For a given stock, the percent price impact on the k th trade is
defined as
Percent Price Impactk  2  ln(M k 5 )  ln( M k ) ,
(4)
where Mk+5 is the midpoint of the consolidated BBO prevailing five minutes after the kth
trade, and Mk is the midpoint prevailing at the time of the kth trade. For a given stock aggregated
over a month i, the Percent Price Impacti is the dollar-volume-weighted average of Percent Price
Impactk computed over all trades in month i.
We also analyze a cost per volume benchmark,  , which is the slope of the price
function. We follow Hasbrouck (2009) and calculate  as the slope coefficient of the regression
rn    Sn  un ,
(5)
where, for the nth five-minute period, rn is the stock return, S n =  k Sign  vkn  vkn is the
signed square-root dollar volume , vkn is the signed dollar volume of the k th trade in the nth fiveminute period, and un is the error term.
3. Low Frequency Percent Cost Proxies
Nine low frequency percent cost proxies are explained below. For each measure, we
require that the measure always produces a numerical result. If a measure cannot be computed
we substitute a default value.
5
3.1. Roll
Roll (1984) develops an estimator of the effective spread based on the serial covariance
of the change in price as follows. Let Vt be the unobservable fundamental value of the stock on
day t . Assume that it evolves as
Vt  Vt 1  et ,
(6)
where et is the mean-zero, serially uncorrelated public information shock on day t .
Next, let Pt be the last observed trade price on day t . Assume it is determined by
Pt  Vt  12 SQt ,
(7)
where S is the effective spread and Qt is a buy/sell indicator for the last trade that equals 1 for
a buy and 1 for a sell. Assume that Qt is equally likely to be 1 or 1 , is serially
uncorrelated, and is independent of et . Taking the first difference of Eq. (7) and combining it
with Eq. (6) yields
Pt  12 S Q t et
(8)
where  is the change operator. Given this setup, Roll shows that the serial covariance is
Cov  Pt , Pt 1   14 S 2
(9)
S  2 Cov  Pt , Pt 1  .
(10)
or equivalently
When the sample serial covariance is positive, the formula above is undefined and so we
substitute a default numerical value of zero. We therefore use a modified version of the Roll
estimator:
6
 2 Cov  Pt , Pt 1 
Roll  
0

When Cov  Pt , Pt 1   0
When Cov  Pt , Pt 1   0
.
(11)
3.2. Extended Roll
Holden (2009) extends the Roll model by developing a more precise version of Roll.
Individual stock returns, that are adjusted for splits and dividends, can be decomposed into three parts:
(1) systematic value innovations generated by the market, (2) idiosyncratic value innovations generated
by the firm, and (3) bid -ask bounce. From a “signal extraction” perspective, the bid-ask bounce is the
signal to be extracted and the systematic value innovations and idiosyncratic value innovations are both
noise terms. It is useful to remove the systematic value innovations, because the residuals that are left
have a higher signal-to-noise ratio.
The empirical procedure is to perform a “market model” regression
art  rf      rmt  rf   zt ,
(12)
where art is the adjusted return on date t which accounts for splits and dividends, rf is the daily riskfree
rate,  and  are the regression coefficients, rmt is the value-weighted market return on date t , and zt
is the regression residual. Then use the residual to compute the idiosyncratic adjusted price change Pt *
as
Pt *  zt  Pt 1 .
(13)
where Pt 1 is the unadjusted price on date t  1 .
The Extended Roll model uses zero when the serial covariance is positive as follows
 2 Cov  P* , P* 
t
t 1

Extended Roll  
P

0

when Cov  Pt* , Pt*1   0
(14)
when Cov  Pt * , Pt*1   0.
3.3. Effective Tick
7
Holden (2009) and Goyenko, Holden, and Trzcinka (2009) jointly develop a proxy of the
effective spread based on observable price clustering as follows. Let St be the realization of the
effective spread at the closing trade of day t . Assume that the realization of the spread
corresponding to the closing trade of day is randomly drawn from a set of possible spreads
s j , j  1, 2,  , J
(ordered from smallest to largest) with corresponding probabilities
 j , j  1, 2,  , J . For example on a $ 18 price grid, St is modeled as having a probability  1 of
s1  $ 18 spread,  2 of s2  $ 14 spread,  3 of s3  $ 12 spread, and  4 of s4  $1 spread.
Let N j be the number of trades on prices corresponding to the j th spread
 j  1, 2,, J 
using only positive-volume days in the month. In the $ 18 price grid example (where J  4 ), N1
through N 4 are the number of trades on odd
number of trades on odd
1
2
1
8
prices, the number of trades on odd
1
4
prices, the
prices, and the number of trades on whole dollar prices, respectively.
Let F j be the probabilities of trades on prices corresponding to the j th spread
 j  1, 2,, J  . These empirical probabilities are computed as
Fj 
Nj
for j  1, 2, , J .
J
N
j 1
(15)
j
Let U j be the unconstrained probability of the
j th spread
 j  1, 2,, J  .
The
unconstrained probability of the effective spread is
 2 Fj

U j  2 Fj  Fj 1
 F F
j 1
 j
j 1
j  2,3, , J  1 .
(16)
j  J.
The effective tick model directly assumes price clustering (i.e., a higher frequency on
rounder increments). However, in small samples it is possible that reverse price clustering may
8
be realized (i.e., a lower frequency on rounder increments), which could cause an unconstrained
probability to go above 1 or below 0. Let ˆ j be the constrained probability of the jth spread
 j  1, 2,, J  . It is computed in order from smallest to largest as follows
 Min  Max U j , 0 ,1



ˆ
j 1
j 


 Min  Max U j , 0 ,1   ˆk 

k 1


j 1
j  2,3,  , J .
(17)
Finally, the effective tick measure is simply a probability-weighted average of each
effective spread size divided by Pi , the average price in time interval i
J
Effective Tick 
 ˆ s
j
j 1
Pi
j
.
(18)
4.5. Zeros
Lesmond, Ogden, and Trzcinka (1999) introduce the proportion of days with zero returns
as a proxy for liquidity. Two key arguments support this measure. First, stocks with lower
liquidity are more likely to have zero volume days and thus are more likely to have zero-return
days. Second, stocks with higher transaction costs have less private information acquisition
(because it is more difficult to overcome higher transaction costs), and thus, even on positive
volume days, they are more likely to have no-information-revelation, zero-return days.
Lesmond, Ogden, and Trzcinka define the proportion of days with zero returns as
Zeros = (# of days with zero returns)/T,
(19)
where T is the number trading days in a month. An alternative version of this measure, Zeros2, is
defined as
Zeros2 = (# of positive volume days with zero return)/T.
(20)
4.6. LOT
9
Lesmond, Ogden, and Trzcinka (1999) develop an estimator of the effective spread based
on the idea that stocks with larger transaction costs pose a larger hurdle for potential traders
(both informed and liquidity traders). Thus, a larger segment of potential true returns are
incorporated into zero returns.
The LOT model assumes that the unobserved “true return” R*jt of a stock j on day t is
given by
R*jt   j Rmt   jt ,
(21)
where  j is the sensitivity of stock j to the market return Rmt on day t and  jt is a public
information shock on day t. They assume that  jt is normally distributed with mean zero and
variance  2j . Let 1 j  0 be the percent transaction cost of selling stock j and  2 j  0 be the
percent transaction cost of buying stock j. Then the observed return R jt on a stock j is given by
R jt  R*jt  1 j
when R*jt  1 j
R jt  R*jt
R jt  R*jt   2 j
when 1 j  R*jt   2 j
when  2 j  R*jt .
(22)
The LOT liquidity measure is simply the difference between the percent buying cost and
the percent selling cost:
LOT   j 2   j1.
(23)
Lesmond, Ogden, and Trzcinka develop the following maximum likelihood estimator of
the model’s parameters:
10
L 1 j ,  2 j ,  j ,  j | R jt , Rmt 

1
 R  1 j   j Rmt 
n  jt

 j 
j

1
     j Rmt
  N  2 j
j
0 
 

 1 j   j Rmt
  N 
j



 
 
(24)
 R   2 j   j Rmt 
n  jt

j
2 j


S .T .  j1  0,  j 2  0,  j  0,  j  0,

where N 

1
is the cumulative normal distribution.
A key issue for LOT is the definition of the three regions over which the estimation is
done. The original LOT (1999) measure, now called LOT Mixed, distinguishes the three regions
based on both the X-variable and the Y-variable (region 0 is R jt  0 , region 1 is R jt  0 and
Rmt  0 , and region 2 is R jt  0 and Rmt  0 ). Goyenko, Holden, and Trzcinka (2009) developed
a new version of the measure, which they called LOT Y-split, that breaks out the three regions
based on the Y-variable (region 0 is R jt  0 , region 1 is R jt  0 , and region 2 is R jt  0 ).
4.7. FHT
This paper develops a new estimator of the effective spread, which is a simplification of
the LOT Mixed and Y-split measures. First, it assumes that transaction costs are symmetric. Let
S 2 be the percent transaction cost of buying a stock and S 2 be the percent transaction cost
of selling the same stock. Substituting this assumption into equation (22) and suppressing the
subscripts, the observed return R on an individual stock is given by
R  R*  S 2 when R*   S 2
R  R*
R  R*  S 2
when  S 2  R*  S 2
when S 2  R* .
(25)
11
Note that observed return is zero in the middle region where  S 2  R*  S 2 .
Secondly, the new estimator simplifies LOT by focusing on the return distribution of an
individual stock and providing no role for the market portfolio. Specifically, the unobserved
“true return” R* of an individual stock on a single day is assumed to be normally distributed
with mean zero and variance  2 . Thus, the theoretical probability of a zero return is given by
 S
N
 2

 S 
 N
.

 2 
(26)
The empirically observed frequency of a zero return is given by the measure Zeros. Let
z  Zeros. Equating the theoretical probability of a zero return to the empirically-observed
frequency of a zero return, we obtain
 S
N
 2

 S 
N
z

 2 
(27)
By the symmetry of the cumulative normal distribution, equation (27) can be rewritten as

  z

(28)
 1+z 
FHT  S  2 N 1 
,
 2 
(29)
 S
N
 2
 
 S
  1  N 
 
 2
Solving for S, we obtain
where N 1 

is the inverse function of the cumulative normal distribution. The FHT measure is
a simple, analytic measure that can be computed with a single line of SAS code.4
4.8. FHT2
This paper develops a second new estimator of the effective spread, which takes a
slightly more involved approach to simplifying the LOT Mixed and Y-split measures. Like FHT
4
Specifically: Sigma=Std(Returns); Zeros=ZeroReturnDays/TotalDays; FHT = 2*Sigma*Probit((1+Zeros)/2); Run;
If the daily mean return is not negligible, simply add mean(Returns) to FHT.
12
it assumes that the “true return” R*jt of a stock j on day t is normally distributed with mean zero
and variance  2j . Thus, the theoretical probability that the observed return is zero and the true


return is positive R*  0 is
  1
N  2  .
  2
(30)
Similarly, the theoretical probability that the observed return is zero and the true return is


negative R*  0 is
1
 
 N  1 .
2
 
(31)
Unlike FHT, the new measure doesn’t impose symmetry of buy and sell transaction costs.
Instead, it empirically identifies asymmetric costs by distinguishing between zero returns that
take place when the market return is positive vs. negative. Define the percentage of days with
zero returns on positive market return days PZ as
 # of zero returns on positive market return days

PZ  Min 
, 0.49  ,
# of open-exchange days in the month


(32)
where the cap at 0.49 is required for numerical reasons that will be explained below. Similarly,
define the percentage of days with zero returns on negative market return days NZ as
 # of zero returns on negative market return days

NZ  Min 
, 0.49  ,
# of open-exchange days in the month


(33)
where the cap at 0.49 is also required for numerical reasons that will be explained below.
Equating the theoretical probability of a positive true return and zero observed return to
its empirically-observed counterpart, we obtain
  1
N  2    PZ .
  2
(34)
13
Similarly, equating the theoretical probability of a negative true return and zero observed
return to its empirically-observed counterpart, we obtain
1
 
 N  1   NZ .
2
 
(35)
Solving for  2 , we obtain
1
2


 2   N 1   PZ  .
(36)
Notice that in the limit as PZ  12 ,  2  . To avoid this problem, a cap is imposed of
PZ  0.49 , which implies a large maximum value of  2  2.32 . Solving for 1 , we obtain
1
2


1   N 1   NZ  .
(37)
In the limit as NZ  12 , 1  . To avoid this problem, a cap is imposed of NZ  0.49 , which
implies a large minimum value of 1  2.32 . Combining these results, we obtain the new
measure

1

1

FHT 2   2  1    N 1   PZ   N 1   NZ   .
2

2


(38)
5. Low Frequency Cost Per Volume Proxies
Next, we explain twelve low-frequency cost per volume proxies. As before, we require
that each measure always produce a numerical result.
5.1. Amihud
Amihud (2002) develops a cost per volume measure that captures the “daily price
response associated with one dollar of trading volume.” Specifically, he uses the ratio

rt

Illiquidity  Average 
,
 Volumet 
(39)
14
where rt is the stock return on day t and Volumet is the currency value of volume on day t
expressed in units of local currency. The average is calculated over all positive-volume days,
since the ratio is undefined for zero-volume days.
5.2. Extended Amihud Proxies
Goyenko, Holden, and Trzcinka (2009) develop a new class of cost per volume proxies
by extending the Amihud measure. They decompose the total return in the numerator of the
Amihud model into a liquidity component and a non-liquidity component. By assumption, the
non-liquidity component is independent of the liquidity component and can be eliminated as
being unrelated to the variable of interest. The remaining numerator value can be approximated
by any percent cost proxy over month i and the average daily currency value of volume in units
of local currency over the same time interval as follows
Extended Amihud Proxy i =
Percent Cost Proxyi
.
Average Daily Currency Volumei
(40)
The equation above defines a class of cost per volume proxies depending on which
percent cost proxy is used. For example, one member of this class uses the Roll measure for
month i as follows:
Roll Impact i 
Rolli
.
Average Daily Currency Volumei
(41)
We test nine versions of this class of cost per volume measures based on nine different
percent cost proxies. The nine measures we test are: Roll Impact, Extended Roll Impact,
Effective Tick Impact, LOT Mixed Impact, LOT Y-split Impact, Zeros Impact, Zeros2 Impact,
FHT Impact, and FHT2 Impact.
5.3. Pastor and Stambaugh
15
Pastor and Stambaugh (2003) develop a measure of cost per volume called Gamma by
running the regression
rte1     rt   Gamma  sign  rte  Volumet    t
(42)
where rt e is the stock’s excess return above the value-weighted market return on day t and
Volumet is the currency value of volume on day t expressed in units of local currency.
Intuitively, Gamma measures the reverse of the previous day’s order flow shock. Gamma should
have a negative sign. The larger the absolute value of Gamma, the larger the implied price
impact.
5.4. Amivest Liquidity
The Amivest Liquidity ratio is a volume per cost measure
 Volumet
Liquidity  Average 
rt


 .

(43)
The average is calculated over all non zero-return days, since the ratio is undefined for zero
return days. A larger value of Liquidity implies a lower cost per volume. This measure has been
used by Cooper, Groth, and Avera (1985), Amihud, Mendelson, and Lauterback (1997), and
Berkman and Eleswarapu (1998) and others.
6. Data
To compute our benchmarks (effective spread, realized spread, quoted spread, percent
price impact, and lambda), we use data from the Reuters Datascope Tick History (RDTH)
supplied by the Securities Industry Research Centre of Asia-Pacific (SIRCA). The RDTH is a
commercial product launched in June 2006 and its subscribers include central banks, investment
16
banks, hedge funds, brokerages, and regulators.5 RDTH provides millisecond-time-stamped tick
data since January 1996 of over 5 million equity instruments worldwide. RDTH data is sourced
from the Reuters IDN (Integrated Data Network) which obtains the feeds directly from the
exchanges.
We verified the quality of RDTH by double-checking its Finland data against the Nordic
Security Depository, which is the central clearing agency for all trading in Finland. It includes
the complete, official trading records of all trading in securities listed on the Helsinki Stock
Exchange. The random checks we performed showed the trades agree so that if a trade of 200
shares at $10 shows in the RDTH database, we will see a purchase of 200 shares at $10 and a
corresponding sale of 200 shares in the Depository data.
Our non-U.S. dataset covers 39 countries, including 20 developed countries and 19
emerging countries. These countries are selected on the basis of Reuters intraday and Datastream
daily price, volume and market capitalization data availability. We analyze the leading exchange
by volume in each country, plus two exchanges in Japan (the Tokyo Stock Exchange and the
Osaka Securities Exchange) and two exchanges in China (the Shanghai Stock Exchange and
Shenzhen Stock Exchange). Altogether we analyze 41 exchanges. We select all firms listed on
those 41 exchanges at any time from 1996 to 2007. We impose two activity filters on each stockmonth in order to have reliable and consistent proxy estimates. We require that a stock have at
least five positive-volume days in the month. And we require that a stock have at least five nonzero return days in the month. Our final sample has 8,178,077,962 trades and 12,255,684,751
quotes. We compute the percent cost benchmarks and proxies and cost per volume benchmarks
5
Prior to July 10, 2009, the same underlying tick history data has been supplied by SIRCA to academics subscribers
via the interface called Taqtic, which is a more restricted version of the commercial RDTH. Taqtic was
decommissioned on July 17, 2009. For more information on the RDTH which is the current platform for academic
and
commercial
users
to
access
the
global
tick
history,
see
http://about.reuters.com/productinfo/tickhistory/material/DataScopeTickHistoryBrochure_260707.pdf.
17
and proxies for 16,096 firms in 1,193,909 stock-months. For the proxies that require a market we
use the local value-weighted market portfolio.
Table 1 provides the mean of the monthly percent cost benchmarks and proxies. Panel A
is for developed markets and Panel B is for emerging markets. Each row represents a different
exchange. For example, looking at the first row, the country is Australia and the exchange code
is AX, which stands for the Australian Stock Exchange. Panel C maps each exchange code into
the full name of the exchange. Table 2 provides the mean of the monthly cost per volume
benchmarks and proxies. Again, Panel A is for developed markets and Panel B is for emerging
markets.
7. Results
7.1. The Spread Results
Tables 3 – 6 report monthly percent cost proxies compared with percent cost benchmarks
(percent effective spread, percent quoted spread, and percent realized spread). Tables 3, 4, and 5
each report on one of three performance dimensions (average cross-sectional correlation, timeseries correlation, and average root mean squared error) and Table 6 reports breakouts by size
and turnover quintiles.
Turning to Table 3, the performance criterion is the average cross-sectional correlation
between the percent cost proxy and the percent cost benchmark based on individual firms. This is
computed in the spirit of Fama and MacBeth (1973) by: (1) calculating for each month the crosssectional correlation across all firms on a given exchange, and then (2) calculating the average
correlation value over all months available for that exchange.
Panel A reports each percent cost proxy compared to percent effective spread in
developed countries and Panel B compares to percent effective spread in emerging countries. A
18
solid box is placed around the highest correlation in the row. A dashed box is placed around
correlations that are statistically indistinguishable from the highest correlation in the row at the
5% level.6 In the first row for the Australian Stock Exchange (AX), the new proxy FHT has the
highest average cross-sectional correlation with percent effective spread at 0.620 and the other
new proxy FHT2 is statistically indistinguishable from the highest correlation at 0.619. All of the
rest of the correlations in the first row are statistically lower than the highest correlation.
Boldfaced correlations are statistically different from zero at the 5% level.7 Nearly all
correlations in the table are statistically different from zero.
There is considerable variation from exchange-to-exchange. In Panel A, the correlations
range from .305 for Luxembourg to .822 for Ireland. The large majority exchanges have best
correlations in the 0.50’s and 0.60’s. In Panel B, the large majority exchanges also have best
correlations in the 0.40’s, 0.50’s, and 0.60’s.
However, both Chinese exchanges seem to be outliers. The best correlation on the
Shanghai Stock Exchange (SS) is 0.078 and the best on the Shenzhen Stock Exchange is 0.114.
None of the percent cost proxies do well on these two exchanges and a few correlations are even
negative. It is not clear why these two exchanges are so different. For a subset of firms, China
has a system of “A shares” that can only be traded by domestic investors and “B shares” that can
6
In Tables 3, 6-7, 10, and 13, we test whether the cross-sectional correlations are different between proxies on the
same row by t-tests on the time-series of correlations in the spirit of Fama-MacBeth. Specifically, we calculate the
cross-sectional correlation of each proxy for each month and then regress the correlations of one proxy on the
correlations of another proxy. We assume that the time series of correlations of each proxy is i.i.d. over time, and
test if the regression intercept is zero and the slope is one. Standard errors are adjusted for autocorrelation with a
Newey-West correction using four lags.
7
We test all correlations in Tables 3, 4, 6-8, 10-11, and 13 to see if they are statistically different from zero and
highlight the correlations that are significant in boldface. For an estimated correlation  , Swinscow (1997, Ch. 11)
gives the appropriate test statistic as
t 
where
D2
,
1 2
D is the sample size.
19
only be traded by foreigner investors. We report the “A share” only results, but we verified that
the inclusion of “B shares” leads to very similar results.
Looking at both Panels A and B, we see that FHT and FHT2 either have a solid box
(being the winner) or a dashed box (being insignificantly different from the winner) for nearly all
exchanges. On average across all 21 exchanges in developed countries, FHT and FHT2 tie with
an average cross-sectional correlation of 0.558. On average across all 20 exchanges in emerging
countries, FHT has an average cross-sectional correlation of 0.438 and FHT2 has a correlation of
0.437. For nearly all exchanges, the average cross-sectional correlations for FHT and FHT2 are
much higher than the correlations for any other proxy. FHT and FHT2 dominate the effective
spread comparisons.
Panel C reports each percent cost proxy is compared to percent quoted spread. In Panel
C, FHT2 has the best correlation for average developed at 0.656 and FHT is insignificantly
different at 0.655. For average emerging FHT and FHT2 tie at 0.499. In both cases, the FHT and
FHT2 correlations are much higher than the correlations for any other proxy. An online appendix
with 20 additional tables is available at www.kelley.iu.edu/cholden/fhtappendix.pdf. In online
Appendix Table 1, the percent quoted spread results by exchange are qualitatively similar to the
percent effective spread results by exchange in Panels A and B. For nearly all exchanges, the
average cross-sectional correlations for FHT and FHT2 are much higher than the correlations for
any other proxy.
Panel D reports each percent cost proxy is compared to percent realized spread. Again,
FHT and FHT2 have the highest correlations for both average developed and average emerging.
Again, they are much higher than the correlations for any other proxy. In online Appendix Table
2, the percent realized spread results by exchange show that, for nearly all exchanges, the
20
average cross-sectional correlations for FHT and FHT2 are much higher than the correlations for
any other proxy. To summarize Table 3, FHT and FHT2 do a good job of capturing percent
effective spread, percent quoted spread, and percent realized spread and they dominate all other
proxies.
We conducted a comparison of the distribution of the maximum correlation in each row of the
developed exchanges with the distribution of the maximum correlation in each row of the emerging
exchanges. The developed exchanges stochastically dominated the emerging exchanges. The x percentile
of the twenty-one developed market’s highest correlation is always higher than the same percentile for the
twenty emerging markets. This is true for the effective spread results reported in table 3 and the timeweighted quote and realized spread results reported in Appendix Tables 1 and 2. The later tables show
stronger correlations than in Table 3 and the developed markets are more dominant. This suggests that
proxies are stronger for firm level data in developed markets.
Next, we form equally-weighted portfolios across all stocks on a given exchange for
month i. Then, we compute a portfolio percent cost proxy in month i by taking the average of
that percent cost proxy over all stocks on a given exchange in month i. Table 4 reports the timeseries correlation between each portfolio percent cost proxy and the portfolio percent cost
benchmarks. A solid box identifies the highest correlation in the row and a dashed box indicates
correlations that are statistically indistinguishable from the highest correlation in the row at the
5% level.8 Boldfaced correlations are statistically different from zero at the 5% level.
Panel A reports each portfolio percent cost proxy compared to portfolio percent effective
spread in developed countries and Panel B compares to portfolio percent effective spread in
emerging countries. In these two panels, there is huge variation in the best time-series correlation
values. In Luxembourg, the best time-series correlation is only 0.023 and it is not significantly
8
In Tables 4, 8, and 11, we test whether time-series correlations are statistically different from each other using
Fisher’s Z-test.
21
different from zero! By contrast, in Indonesia the best time-series correlation is 0.975. Six
proxies are frequently the best or insignificantly different from the best. Specifically, FHT is the
best or insignificantly different from the best on 32 exchanges. The same is true for FHT2 on 30
exchanges, Roll on 19 exchanges, LOT Mixed on 18 exchanges, Zeros on 17 exchanges, and
LOT Y on 16 exchanges. For all of the developed countries, FHT was the best with an average
time-series correlation of 0.475. For all of the emerging countries, Effective Tick was the best
with an average time-series correlation of 0.580. FHT was close behind with an average timeseries correlation of 0.570.
Panel C reports each percent cost proxy is compared to percent quoted spread. FHT has
the best correlation for average developed at 0.640 and FHT2 is close at 0.635. FHT has the best
correlation for average emerging at 0.634 and Effective Tick is close at 0.633.
Panel D reports each percent cost proxy is compared to percent realized spread. FHT has
the best correlation for average developed at 0.481 and FHT2 is close at 0.476. FHT has the best
correlation for average emerging at 0.572.
Comparing the distribution of the maximum correlation in each row for the developed markets
versus the emerging markets does not show the clear results of Table 3. The emerging markets are often
but not always , stochastically dominant. To summarize Table 4, FHT and FHT2 do a good job of
capturing percent effective spread with Roll, LOT Mixed, Zeros, and LOT Y close behind. FHT
does a good job of capturing percent quoted spread and percent realized spread with FHT2 close
behind.
Table 5 reports the average root mean squared error (RMSE) between each percent cost
proxy and percent cost benchmarks based on individual firms. The root mean squared error is
calculated every month for a given exchange and then averaged over all sample months. A solid
box identifies the lowest RMSE in the row and a dashed box indicates RMSEs that are tatistically
22
indistinguishable from the lowest RMSE in the row.9 Boldfaced RMSEs are statistically
significant at the 5% level.10
Panel A reports each percent cost proxy compared to percent effective spread in
developed countries and Panel B compares to percent effective spread in emerging countries.
Strikingly, very few of the RMSEs are statistically significant (boldfaced). In other words, most
proxies lack explanatory power regarding the level of percent effective spread. FHT is
statistically significant on 22 exchanges, followed by FHT2 on 19 exchanges, and then the next
best is Roll on 5 exchanges. FHT has the lowest average RMSE on 26 exchanges. For average
developed, FHT was the best with an average RMSE of 0.0374, which was much lower than any
other proxy. For average emerging, FHT was the best with an average RMSE of 0.0448, which
was much lower than any other proxy.
Panel C reports each percent cost proxy is compared to percent quoted spread. FHT was
the best for both average developed and average emerging. In online Appendix Table 5, FHT
was the best on 26 exchanges. Panel D reports each percent cost proxy is compared to percent
realized spread. Again, FHT was the best for both average developed and average emerging. In
online Appendix Table 6, FHT was the best on 29 exchanges.
Summarizing Table 5, FHT is the only proxy that is regularly capturing the level of
percent effective spread, percent quoted spread, and percent realized spread. Compared to other
proxies, it is very dominant.
9
In Tables 5-6, 9, 12, and 13, we test whether RMSEs are statistically different from each other using a paired t-test.
In Tables 5-6, 9, 12, and 13, we test whether RMSEs are statistically significant using the U-statistic developed by
Theil (1966). Here, if U2 = 1, then the proxy has zero predictive power (i.e., it is no better at predicting the
benchmark than the sample mean). If U2 = 0, then the proxy perfectly predicts the benchmark. We test if U2 is
significantly less than 1 based on an F distribution where the number of degrees of freedom for both the numerator
and the denominator is the sample size.
10
23
To examine the robustness of our results, Table 6 breaks out the comparison of percent
cost proxies to percent effective spread by country type (developed vs. emerging), turnover, and
size.11 Panel A reports the average cross-sectional correlation for stocks in developing countries
broken out into turnover subsamples and Panel B reports the same for stocks in emerging
countries broken out by turnover. In both panels, average cross-sectional correlations are
generally higher in high turnover stocks and lower in low turnover stocks. FHT is the best in 7 of
the 10 subsamples with correlations in the 0.50’s and 0.60’s in most cases.
Panel C reports the average RMSE for stocks in developing countries broken out into size
subsamples and Panel D reports the same for stocks in emerging countries broken out by size. In
both panels, very few RMSEs are statistically significant. Average RMSEs are generally lower
for large stocks and higher for small stocks. FHT is the best in 7 of the 10 subsamples. Effective
Tick is best in 4 subsamples.
To summarize Table 6, FHT dominates compared to other proxies. Its correlation with
percent effective spread is strong and robust by turnover and size subsamples, but its explanatory
power in capturing the level of percent effective spread is quite modest.
To summarize Tables 3 – 6, the new measure FHT is the best and most consistent proxy
for percent effective spread, percent quoted spread, and percent realized spread. FHT ties for the
best in Table 3, leads Table 4, heavily dominates Table 5, and strongly leads Table 6. FHT
produces high correlations and low RMSEs on nearly all exchanges and in nearly all subsamples.
Its explanatory power in capturing the level of percent effective spread is modest, but is far
greater than any other proxy.
11
The turnover of stock j in month i is defined as the share volume of stock j in month i divided by the number of
shares outstanding of stock j in month i. Size is market capitalization.
24
Online Appendix Table 7 contains additional results based on the same U.S. data used by
Goyenko, Holden, and Trzcinka (2009) and by Holden (2009). Their sample spans 1993-2005
inclusive. It consists of 400 randomly selected stocks with annual replacement of stocks that
don’t survive resulting in 62,100 firm-months. The online appendix table compares the proxies
in this paper plus the Holden proxy from Holden (2009) and the Gibbs proxy from Hasbrook
(2004).12 FHT has the highest correlation at 0.748 for the pooled time-series, cross-sectional
correlations between the proxies and percent effective spread computed from TAQ. Extended
Roll has the highest correlation at 0.955 for the time-series correlations based on equallyweighted portfolios. FHT is not far behind at 0.932. , FHT is the lowest average RMSE at
0.0283. This excellent showing for FHT means that researchers can be confident of the
performance of FHT on U.S. data, as well as non-U.S. data.
An interesting aside is to compare the Zeros vs. the LOT proxies vs. FHT. All of these
proxies are fundamentally driven by the frequency of zero returns. Prior research13 has
established and this paper confirms that LOT Mixed and LOT Y-split have greater explanatory
power for effective spread than Zeros itself. But the source of the LOT proxy advantage has been
hard to pin down, since the LOT proxies do multiple things as the same time. Specifically, the
LOT proxies have three likelihood function regions, impose the limited dependent variable
functional form, and use the market portfolio as part of the estimation. We find that FHT has
greater explanatory power for effective spread than either the LOT proxies or Zeros. Since the
FHT proxy focuses on the zero return region of the three LOT regions, it is clear that the zero
return region is the key source of extra explanatory power. Since FHT throws away the other two
12
We do not compare the Holden or Gibbs proxies in this paper because both proxies are very numerically
intensive, which would make them infeasible to compute on a scale as large as we are analyzing.
13
Specifically, Lesmond, Ogden, and Trzcinka (1999), Lesmond (2005), Goyenko, Holden, and Trzcinka (2009),
and Holden (2009).
25
regions, drops the limited dependent variable functional form, and drops the market portfolio, it
is clear that none of these items were essential to the success of the LOT proxies. Indeed, these
items most likely added noise, since FHT gains extra explanatory power when they are dropped.
The use of market returns in FHT2 occasionally improves performance on a specific
exchange over FHT. It is possible that a different market index may improve the performance of
FHT2. It is unlikely that a different likelihood function will improve the performance of LOT
Mixed or LOT-Y split. Finally, zeros are clearly dominated but are still a significant correlate
with effective spreads. It is not surprising that the many studies using them find significant
results. The findings of Tables 3 – 6 suggest that the results will be stronger with FHT.
7.2. The Percent Price Impact Results
Tables 7 – 9 report nine percent cost proxies and three cost per volume proxies (Amihud,
Pastor and Stambaugh, and Amivest)14 compared with the percent cost benchmark: percent price
impact. Tables 7, 8, and 9 each report on one of three performance dimensions.
Table 7 reports the average cross-sectional correlation between each proxy and percent
price impact based on individual firms. Panel A reports for developed countries and Panel B for
emerging countries. In both panels, the best correlations are typically in the 0.30’s, 0.40’s, or
0.50’s. Portugal (LS) is the only exchange where the best correlation is not significantly different
from zero. FHT is the best on 19 exchanges and LOT Mixed is the best on 15 exchanges. For
Average Developed, the best correlation is 0.322 by FHT. For Average Emerging, the best
correlation is 0.319 by FHT. To summarize Table 7, FHT and LOT Mixed do moderately-well at
capturing percent price impact.
14
We tested all cost per volume proxies compared with percent price impact (see online Appendix Tables 18, 19,
and 20). We found that they performed much worse than the percent cost proxies. Indeed, the best correlations using
percent cost proxies are typically twice as large as the best correlation using cost per volume proxies.
26
Table 8 reports the time-series correlation between each portfolio proxy and the portfolio
percent price impact. Panel A reports for developed countries and Panel B for emerging
countries. In both panels, the best correlations are typically in the 0.50’s or 0.60’s. Several
exchanges have very high correlations, such as Japan (T) at 0.864, Sweden (ST) at 0.837, and the
U.K. (L) at 0.801. FHT has the best correlation on 11 exchanges and Roll has the best on 7
exchanges. For Average Developed, the best correlation is 0.456 by Effective Tick with FHT,
FHT2, and Zeros in the leadership group. For Average Emerging, the best correlation is 0.510 by
FHT with Effective Tick, FHT2, and Zeros in the leadership group. To summarize Table 8, FHT
leads, but Roll, Effective Tick, FHT2, and Zeros also do well at capturing percent price impact.
Table 9 reports the average RMSE between each proxy and percent price impact based on
individual firms. Panel A reports for developed countries and Panel B for emerging countries.
None of the RMSEs are statistically significant (i.e., none are bold-faced). Therefore, none of the
price impact proxies does a good job capturing the level of percent price impact.
To summarize Tables 7 – 9, we find FHT is the best proxy for percent price impact.
However, it is only moderately-well correlated with percent price impact and does not capture
the correct scale.
7.3. The Lambda Results
Tables 10 – 13 report monthly cost per volume proxies compared with the benchmark
lambda (the slope of the price function). Tables 10, 11, and 12 each report on one of three
performance dimensions and Table 13 reports breakouts by size and turnover quintiles.
Table 10 reports the average cross-sectional correlation between the cost per volume
proxy and lambda based on individual firms. Panel A reports for developed countries and Panel
B for emerging countries. In both panels, the best correlations are relatively low – typically in the
27
0.30’s or 0.40’s. LOT Mixed Impact is the best on 14 exchanges and Zeros Impact is the best on
12 exchanges. For Average Developed, the best correlation is 0.360 by LOT Mixed Impact. For
Average Emerging, the best correlation is 0.355 also by LOT Mixed Impact. To summarize
Table 10, LOT Mixed Impact does moderately-well at capturing lambda.
Similar to Table 8, we form equally-weighted portfolios across all stocks on a given
exchange for month i. Then, a portfolio cost per volume proxy in month i is computed by taking
the average of that cost per volume proxy over all stocks on a given exchange in month i. Table
11 reports the time-series correlation between each portfolio cost per volume proxy and the
portfolio lambda benchmark. Panel A reports for developed countries and Panel B for emerging
countries. In both panels, the best correlations are typically in the 0.30’s or 0.40’s. Several
exchanges have very high correlations, such as the UK (L) at 0.839, China Shanghai (SS) at
0.802, and China Shenzhen (SZ) at 0.820. Zeros2 Impact has the best results on 9 exchanges and
Amihud has the best results on 8 exchanges. For Average Developed, the best correlation is
0.319 by Zeros2 Impact. For Average Emerging, the best correlation is 0.310 by FHT Impact. To
summarize Table 11, Zeros2 Impact does moderately-well at capturing lambda.
Table 12 reports the average RMSE between each cost per volume proxy and the Lambda
benchmark based on individual firms. As before, the RMSE is calculated every month for a
given exchange and then averaged over all sample months. Panel A reports for developed
countries and Panel B for emerging countries. Nearly all of the RMSEs are statistically
insignificant. Only two proxies are significant on one exchange. To summarize Table 12, nothing
captures the level of lambda.
Table 13 checks the robustness of our results by breaking out the comparison of cost per
volume proxies to lambda by country type, turnover, and size. Panel A reports the average cross-
28
sectional correlation for developing countries stratified by turnover and Panel B reports the same
for emerging countries stratified by turnover. In Panel A, the best correlations are typically in the
0.40’s and in the 0.10’s or 0.20’s in Panel B. Zeros Impact is the best on 8 out of 10 exchanges.
Panel C reports the average RMSE for developing countries stratified by size and Panel D
reports the same for emerging countries stratified by size. Again, none of the RMSEs are
statistically significant.
To summarize Tables 10 – 13, we find that LOT Mixed Impact, Zeros Impact, and
Zeros2 Impact are the best proxies for lambda. However, they are only moderately-well
correlated with Lambda and do not capture the correct scale.
8. Conclusion
We compare percent cost or cost per volume liquidity proxies constructed from daily
stock data to actual transaction costs using the Reuters Datascope Tick History dataset by the
Securities Industry Research Centre of Asia-Pacific, which contains more than a decade of global
intraday Reuters data. Our sample contains 8.1 billion trades and 12.2 billion quotes representing
16,096 firms on 41 exchanges around the world from 1996 to 2007. We evaluate the
performance of nine percent cost proxies (including two new ones that we introduce) relative to
four percent cost benchmarks: percent effective spread, percent quoted spread, percent realized
spread, and percent price impact. We evaluate the performance of twelve cost per volume
proxies (including two new ones that we introduce) relative to a cost per volume benchmark: the
slope of the price function lambda. In each case, we test three performance dimensions: (1)
higher average cross-sectional correlation with the benchmarks, (2) higher portfolio correlation
with the benchmarks, or (3) lower prediction error relative to the benchmarks.
29
We find that a new measure that we introduce, FHT, is the best proxy for percent
effective spread, percent quoted spread, and percent realized spread. We find FHT is the best
proxy for percent price impact, but is only moderately-well correlated with it and does not
capture the correct scale. We find that LOT Mixed Impact, Zeros Impact, and Zeros2 Impact are
the best proxies for lambda, but they are only moderately-well correlated with it and do not
capture the correct scale.
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Jain, P., 2005. Financial market design and the equity premium: Electronic versus floor
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Karolyi, A., Lee, K. and Van Dijk, M. 2008. Commonality in returns, liquidity, and turnover
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LaFond, R., Lang, M., and Skaife, H., 2007. Earnings smoothing, governance and liquidity:
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Technology.
Lang, M., Lins, K., and Maffett, M., 2009. Transparency, liquidity, and valuation: International
evidence. Unpublished working paper. University of North Carolina at Chapel Hill.
Lee, K., 2006. The world price of liquidity risk. Unpublished working paper. Ohio State
University.
Lesmond, D., 2005. Liquidity of emerging markets. Journal of Financial Economics 77, 411-452.
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Liang, S., Wei, K.C., 2006. Liquidity risk and expected returns around the world. Unpublished
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Stahel, C., 2005. Is there a global liquidity factor? Unpublished working paper. George Mason
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Swinscow, T., 1997. Statistics at Square One, 9th ed. BMJ Publishing Group, London.
31
Table 1
Mean of Monthly Percent Cost Benchmarks and Proxies
The percent cost benchmarks (percent effective spread, percent quoted spread, percent realized spread, and percent price impact) are calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐
months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. Percent Cost Benchmarks
% Effec‐ % Quot % Real % Exch. tive ed ized Price Country
Code Spread Spread Spread Impact
Panel A: Developed Markets
Australia
AX 0.039 0.047 0.041 0.023
Austria
VI 0.011 0.012 0.010 0.009
Belgium
BR 0.036 0.039 0.036 0.007
Canada
TO 0.033 0.037 0.032 0.025
Denmark
CO 0.032 0.022 0.032 0.006
France
PA 0.013 0.015 0.013 0.009
Finland
HE 0.023 0.023 0.024 0.005
Germany
F
0.019 0.031 0.019 0.009
Ireland
I
0.026 0.035 0.024 0.009
Italy
MI 0.008 0.009 0.009 0.006
Japan
T
0.009 0.013 0.011 0.010
Japan
OS 0.039 0.092 0.075 0.060
Luxembourg LU 0.018 0.016 0.018 0.001
Netherlands AS 0.013 0.014 0.013 0.010
New Zealand NZ 0.024 0.025 0.024 0.009
Norway
OL 0.028 0.031 0.028 0.010
Portugal
LS 0.017 0.019 0.017 0.010
Spain
MC 0.007 0.007 0.007 0.006
Sweden
ST 0.012 0.017 0.013 0.006
Switzerland
S
0.013 0.014 0.013 0.006
UK
L
0.032 0.041 0.031 0.005
Average Developed 0.022 0.027 0.023 0.011
0.030
0.009
0.202
0.029
0.014
0.012
0.017
0.021
0.023
0.062
0.014
0.019
0.013
0.013
0.013
0.017
0.017
0.013
0.014
0.012
0.009
0.027
0.002
0.000
0.126
0.001
0.000
0.111
0.000
0.002
0.001
0.184
0.000
0.001
0.002
0.001
0.000
0.001
0.009
0.005
0.000
0.000
0.001
0.021
0.053
0.003
0.022
0.031
0.012
0.003
0.014
0.011
0.029
0.004
0.011
0.024
0.003
0.008
0.035
0.020
0.017
0.004
0.009
0.003
0.006
0.015
0.108
0.018
0.094
0.072
0.041
0.024
0.044
0.053
0.090
0.029
0.028
0.069
0.036
0.029
0.059
0.090
0.043
0.024
0.030
0.027
0.063
0.051
0.105
0.008
0.089
0.043
0.028
0.013
0.032
0.027
0.077
0.012
0.013
0.051
0.024
0.016
0.048
0.087
0.031
0.011
0.014
0.015
0.067
0.039
0.040
0.005
0.038
0.024
0.014
0.007
0.016
0.015
0.024
0.007
0.008
0.025
0.014
0.009
0.022
0.018
0.015
0.006
0.009
0.009
0.022
0.017
0.042
0.005
0.041
0.025
0.015
0.007
0.017
0.016
0.025
0.007
0.009
0.026
0.015
0.009
0.024
0.019
0.016
0.006
0.009
0.009
0.023
0.017
0.316
0.101
0.233
0.204
0.269
0.105
0.226
0.168
0.238
0.080
0.131
0.337
0.290
0.118
0.359
0.254
0.234
0.093
0.149
0.179
0.317
0.209
0.194
0.073
0.147
0.131
0.134
0.083
0.121
0.108
0.136
0.065
0.100
0.165
0.134
0.090
0.256
0.139
0.182
0.089
0.114
0.105
0.257
0.134
1,431 90,733 1/96 12/07
65
4,081 6/96 12/07
138
6,935 2/96 12/07
391 29,874 1/96 12/07
153
6,958 1/09 12/07
480 34,331 1/96 12/07
136
9,868 5/96 12/07
511
8,042 1/96 12/07
31
2,296 6/00 12/07
227 19,174 1/98 12/07
2,199 252,645 1/96 12/07
238 28,066 1/96 12/07
12
601 1/99 4/07
108
9,032 1/96 12/07
111
6,408 1/96 12/07
142
9,306 1/96 12/07
31
935 1/96 12/07
109
9,242 1/96 12/07
259 13,119 4/96 12/07
185
7,886 1/96 12/07
1,553 68,866 1/96 12/07
8,510 618,398
Panel B: Emerging Markets
Argentina
BA 0.023
Brazil
SA 0.068
China
SS 0.004
China
SZ 0.004
Chile
SN 0.035
Greece
AT 0.018
Hong Kong
HK 0.026
India
BO 0.014
Indonesia
JK 0.046
Israel
TA 0.037
Korea
KS 0.011
Malaysia
KL 0.040
Mexico
MX 0.027
Philippines
PS 0.041
Poland
WA 0.041
Singapore
SI 0.028
South Africa
J
0.044
Taiwan
TW 0.006
Thailand
BK 0.025
Turkey
IS 0.012
Average Emerging 0.027
0.023
0.068
0.004
0.004
0.035
0.018
0.026
0.014
0.046
0.037
0.011
0.040
0.027
0.041
0.041
0.028
0.044
0.006
0.025
0.012
0.027
0.036
0.058
0.003
0.003
0.040
0.020
0.038
0.017
0.076
0.040
0.010
0.056
0.049
0.067
0.057
0.043
0.047
0.007
0.040
0.014
0.036
0.023
0.068
0.008
0.008
0.034
0.018
0.028
0.018
0.048
0.038
0.013
0.039
0.032
0.045
0.041
0.028
0.043
0.009
0.027
0.016
0.029
0.012
0.010
0.008
0.008
0.011
0.014
0.016
0.010
0.028
0.013
0.011
0.029
0.020
0.026
0.020
0.017
0.020
0.007
0.015
0.012
0.015
0.012
0.023
0.011
0.011
0.007
0.025
0.023
0.016
0.038
0.011
0.013
0.042
0.011
0.028
0.021
0.027
0.020
0.010
0.022
0.109
0.024
0.001
0.002
0.000
0.000
0.000
0.031
0.002
0.001
0.002
0.001
0.000
0.002
0.001
0.004
0.001
0.001
0.002
0.000
0.001
0.369
0.021
0.029
0.013
0.003
0.003
0.007
0.010
0.027
0.003
0.062
0.007
0.003
0.072
0.011
0.054
0.015
0.051
0.036
0.007
0.018
0.017
0.022
0.144
0.072
0.019
0.018
0.051
0.038
0.074
0.028
0.158
0.044
0.025
0.170
0.052
0.132
0.083
0.090
0.090
0.024
0.071
0.065
0.072
0.051
0.083
0.008
0.008
0.067
0.025
0.065
0.011
0.146
0.030
0.009
0.135
0.047
0.131
0.067
0.070
0.076
0.009
0.054
0.035
0.056
73
5,292
175
2,578
788 80,214
527 35,660
136
4,819
275 25,524
854 81,798
918 52,160
309 24,183
491
5,209
695 33,267
26
1,376
91
4,393
213 14,541
118
6,164
452 33,001
235 20,469
668 68,106
444 38,140
178 31,784
7,666 568,678
0.036
0.058
0.003
0.003
0.040
0.020
0.038
0.017
0.076
0.040
0.010
0.056
0.049
0.067
0.057
0.043
0.047
0.007
0.040
0.014
0.036
0.023
0.068
0.008
0.008
0.034
0.018
0.028
0.018
0.048
0.038
0.013
0.039
0.032
0.045
0.041
0.028
0.043
0.009
0.027
0.016
0.029
0.012
0.010
0.008
0.008
0.011
0.014
0.016
0.010
0.028
0.013
0.011
0.029
0.020
0.026
0.020
0.017
0.020
0.007
0.015
0.012
0.015
Percent Cost Proxies
Extend‐ Effec‐
ed tive LOT LOT Stock‐ Start End Roll
Roll
Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Stocks Months Date Date
7/98
1/06
1/96
11/01
6/02
1/96
1/96
1/02
1/96
1/96
1/03
3/02
1/96
1/96
11/00
10/97
3/96
1/96
1/96
1/96
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
12/07
32
Table 1 Continued
Panel C. Exchange Code to Exchange Name
Developed Exch.
Country
Code Exchange Name
Australia
AX Australian Stock Exchange
Austria
VI Vienna Stock Exchange
Belgium
BR Brussels Stock Exchange
Canada
TO Toronto Stock Exchange
Denmark
CO Copenhagen Stock Exchange
France
PA Paris Stock Exchange
Finland
HE Helsinki Stock Exchange
Germany
F Frankfurt Stock Exchange
Ireland
I Irish Stock Exchange
Italy
MI Milan Stock Exchange
Japan
T Tokyo Stock Exchange
Japan
OS Osaka Stock Exchange
Luxembourg LU Luxembourg Stock Exchange
Netherland
AS AEX Stock Exchange
New Zealand NZ New Zealand Stock Exchange
Norway
OL Oslo Stock Exchange
Portugal
LS Lisbon Stock Exchange
Spain
MC Barcelona Stock Exch. (CATS)
Sweden
ST Stockholm Stock Exchange
Switzerland
S SWX Swiss Exchange
UK
L London Stock Exchange
Emerging
Country
Argentina
Brazil
China
China
Chile
Greece
Hong Kong
India
Indonesia
Israel
Korea
Malaysia
Mexico
Philippines
Poland
Singapore
South Africa
Taiwan
Thailand
Turkey
Exch
Code
BA
SA
SS
SZ
SN
AT
HK
BO
JK
TA
KS
KL
MX
PS
WA
SI
J
TW
BK
IS
Exchange Name
Buenos Aires Stock Exchange
Sao Paulo Stock Exchange
Shanghai Stock Exchange
Shenzhen Stock Exchange
Santiago Stock Exchange
Athens Stock Exchange
Hong Kong Stock Exchange
Bombay Stock Exchange
Jakarta Stock Exchange
Tel Aviv Stock Exchange
Korea Stock Exchange
Kuala Lumpur Stock Exchange
Mexican Stock Exchange
Phillipine Stock Exchange
Warsaw Stock Exchange
Singapore Stock Exchange
Johannesburg Stock Exchange
Taiwan Stock Exchange
Thailand Stock Exchange
Istanbul Stock Exchange
33
Table 2
Mean of Monthly Cost Per Volume Benchmarks and Proxies
The cost per volume benchmark (slope of the price function lambda) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All cost per volume proxies are calculated from daily stock price and volume data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,095,544 stock‐months from 16,096 firms. The means of all price impact benchmarks and proxies are multiplied by 1,000,000, except for the mean of Amivest which is divided by 1,000,000.
Cost/Volume Cost Per Volume Proxies
Benchmark
Slope of the Price Exch. Function Country
Code
Lambda
Panel A: Developed Markets
Australia
AX
110.3
Austria
VI
14.9
Belgium
BR
46.9
Canada
TO
135.7
Denmark
CO
6.1
France
PA
36.2
Finland
HE
38.2
Germany
F
52.2
Ireland
I
34.5
Italy
MI
10.5
Japan
T
3.7
Japan
OS
17.7
Luxembourg LU
13.0
Netherlands AS
34.3
New Zealand NZ
59.2
Norway
OL
5.7
Portugal
LS
32.7
Spain
MC
7.0
Sweden
ST
4.2
Switzerland
S
6.1
UK
L
6.1
Average Developed
32.2
Panel B: Emerging Markets
Argentina
BA
36.1
Brazil
SA
42.0
China
SS
3.7
China
SZ
4.1
Chile
SN
0.5
Greece
AT
66.0
Hong Kong
HK
15.9
India
BO
7.0
Indonesia
JK
0.9
Israel
TA
15.2
Korea
KS
0.6
Malaysia
KL
156.1
Mexico
MX
11.4
Philippines
PS
38.5
Poland
WA
118.0
Singapore
SI
64.1
South Africa
J
4.3
Taiwan
TW
36.2
Thailand
BK
76.1
Turkey
IS
1.5
Average Emerging
34.9
Extend‐ Effec‐
Paster ed tive LOT LOT and Roll Roll Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Stam‐
Impact Impact Impact Impact Impact Impact Impact Impact Impact Amihud baugh Amivest
Stock‐
Months
3,161
379 6,141 14,861 16,812 5,501 5,898 30,938 11,824
165
6
111
447
321
170
167 3,732 1,878
305,319 421,473 155,038 531,653 700,867 233,198 252,461 360,887 196,189
3,725
257 4,097 10,647 8,399 3,948 4,136 19,284 8,440
111
5
116
419
361
149
162 2,083
547
590 2,127
259 1,512 1,045
546
562 6,384 3,321
1,078
37 1,128 3,867 3,382 1,491 1,581 18,142 5,565
2,214
559 2,028 5,906 4,784 2,282 2,425 20,661 8,060
11,226
271 10,990 13,985 11,945 13,104 13,750 43,410 14,713
674 1,703
123
637
412
227
235 2,855 1,251
3.4
0.1
4
10
7
4
4
47
23
16
1
22
68
58
26
26
278
101
508
79
128 1,337
924
536
555 10,841 4,242
1,297
39 1,604 5,153 4,844 2,019 2,327 9,798 5,576
1,051
70 2,852 5,543 5,549 2,136 2,304 21,853 10,443
87
6
137
245
236
122
130 1,224
362
6,928
729 5,317 23,031 22,984 8,763 9,810 62,918 21,382
100
29
53
270
177
93
97 1,481 1,266
54
2
55
176
134
66
69
712
261
172
8
65
523
415
194
204 2,921
982
5
1
12
58
95
21
22
214
128
16,118 20,370 9,061 29,540 37,322 13,076 14,139 29,555 14,122
4,005
‐20 1.22E+08
8,160
5 2.45E+04
47,780 ‐12,175 4.42E+05
12,481
‐150 1.21E+07
24,128
1 1.33E‐02
14,420
27 4.74E+06
13,374
15 1.42E+07
23,597
110 5.01E‐03
5,323 ‐1,386 8.47E‐02
1,646
0.4 8.58E+07
4,182
0.1 6.10E+04
8,400
0.4 2.83E‐03
57,806
10 1.45E‐04
6,903
‐70 2.70E‐01
2,709
34 1.72E+08
9,299
1 2.23E+05
15,079
‐941 2.59E‐01
1,074
3 3.64E‐01
4,961
0.1 9.18E‐02
27,868
3 3.83E‐03
1,096
‐4 5.03E+07
14,014
‐692 3.66E+05
90,733
4,081
6,935
29,874
6,958
34,331
9,868
8,042
2,296
19,174
252,645
28,066
601
9,032
6,408
9,306
935
9,242
13,119
7,886
68,866
618,398
5,004
‐15 3.66E+05
34,545
109 5.01E‐02
29
‐0.3 1.22E+07
38
‐0.3 4.90E+06
1,753 ‐0.03 3.87E+01
7,224
62 6.09E+06
1,922
8 1.02E+09
17,688
‐21 6.28E+04
5,224
‐0.1 2.48E‐01
14,773
7 1.41E‐02
4,970
0.01 3.22E‐02
8,583
181 1.93E+08
7,884
‐76 4.81E‐01
3,321
‐828 6.92E+07
34,353
326 1.89E‐02
1,562
32 3.56E+08
8,311 ‐1,587 6.86E+07
427
‐1 2.51E+08
14,611
‐1 5.30E+08
4,142
82 6.31E‐02
8,818
‐86 1.26E+08
5,292
2,578
82,704
35,660
4,819
25,524
22,298
52,160
24,183
5,209
33,267
1,376
4,393
14,541
6,164
33,001
20,469
68,106
38,140
31,784
511,668
547
1,935
2.1
2.15
0.8
1,523
312
1,008
4
387
0.3
4,640
174
4,865
6,094
2,644
1,632
9
325
12,246
1,918
50
280
0.05
0.05
0.1
1,117
38
65
0.5
31
0.004
178
21
94
460
170
284
1
35
45,332
2,408
1,756
1,879
1
1
1
1,146
431
912
6
260
0.1
6,309
290
3,578
4,786
5,645
3,488
9
220
1,682
1,620
6,302
7,673
4
3
8
3,463
504
3,349
19
1,749
0.4
18,779
1,051
12,228
16,021
10,588
8,910
33
1,230
5,013
4.8E+03
4,290
9,378
2
1
20
2,139
517
3,238
20
1,643
0.2
16,334
1,244
10,067
13,538
10,219
10,223
26
1,131
2,548
4,329
1,382
3,104
1
1
2
1,256
500
1,198
7
672
0.1
6,740
357
5,127
6,590
4,050
3,293
12
458
1,563
1,816
1,110
3,302
1
1
2
1,276
539
1,237
7
698
0.1
7,282
401
5,309
7,020
4,103
3,626
13
500
1,663
1,905
19,127 6,233
18,622 4,392
12
10
15
12
34
12
12,436 8,286
3,479 1,003
5,857 1,137
30
7
8,361 2,011
3
1
37,736 19,236
2,979
569
30,457 12,482
45,574 13,646
25,030 9,920
12,272 4,565
137
64
3,103
698
10,421 9,125
11,784 4,670
34
Table 3
Monthly Percent Cost Proxies Compared to Percent Cost Benchmarks: Average Cross‐Sectional Correlation
The percent cost benchmarks (percent effective spread, percent quoted spread, and percent realized spread) are calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Exch. Extended Effective LOT LOT Country
Code
Roll
Roll
Tick
Mixed
Y‐split
FHT
FHT2
Zeros
Zeros2 Months
Panel A: Compared to Percent Effective Spread in Developed Markets
Australia
AX
0.411
0.341
0.392
0.565
0.525
0.620
0.619
0.482
0.065
144
Austria
VI
0.262
0.149
0.273
0.523
0.523
0.566
0.562
0.483
0.341
139
Belgium
BR
0.680
0.405
0.739
0.803
0.790
0.813
0.810
0.490
0.366
143
Canada
TO
0.477
0.265
0.395
0.547
0.515
0.566
0.560
0.405
0.218
144
Denmark
CO
0.321
0.293
0.247
0.490
0.486
0.512
0.513
0.324
‐0.020
72
France
PA
0.339
0.204
0.316
0.529
0.498
0.542
0.542
0.471
0.318
144
Finland
HE
0.393
0.274
0.349
0.632
0.610
0.614
0.630
0.510
0.215
140
Germany
F
0.189
0.050
0.528
0.507
0.505
0.503
0.529
0.468
0.333
84
Ireland
I
0.677
0.364
0.548
0.365
0.315
0.822
0.817
0.610
0.258
91
Italy
MI
0.185
0.098
0.169
0.294
0.310
0.352
0.351
0.452
0.186
120
Japan
T
0.259
0.192
0.369
0.548
0.562
0.615
0.613
0.565
0.344
144
Japan
OS
0.183
0.147
0.183
0.327
0.345
0.395
0.391
0.271
0.050
144
Luxembourg LU
0.215
0.165
‐0.034
0.311
0.277
0.305
0.300
0.089
‐0.073
100
Netherlands AS
0.512
0.181
0.621
0.697
0.696
0.723
0.723
0.535
0.481
144
New Zealand NZ
0.373
0.396
0.394
0.612
0.596
0.639
0.635
0.402
0.080
125
Norway
OL
0.269
0.215
0.303
0.027
0.019
0.467
0.465
0.336
0.064
144
Portugal
LS
0.522
0.233
0.541
0.687
0.734
0.743
0.742
0.667
0.300
144
Spain
MC
0.188
0.056
0.327
0.400
0.423
0.465
0.470
0.497
0.488
144
Sweden
ST
0.251
0.189
0.295
0.468
0.471
0.484
0.484
0.363
0.070
76
Switzerland
S
0.225
0.131
0.239
0.448
0.441
0.456
0.458
0.368
‐0.045
138
UK
L
0.211
0.266
0.477
0.464
0.404
0.505
0.503
0.375
0.279
144
Average Developed 0.340
0.220
0.365
0.488
0.478
0.558
0.558
0.436
0.206
127
Panel B: Compared to Percent Effective Spread in Emerging Markets
Argentina
BA
0.143
0.257
0.231
0.471
0.522
Brazil
SA
0.324
0.352
0.276
0.527
0.500
China
SS
‐0.014
0.031
0.045
0.001
0.000
China
SZ
‐0.032
0.002
0.070
0.114
0.075
Chile
SN
0.221
0.237
0.167
0.369
0.379
Greece
AT
0.174
0.125
0.192
0.318
0.317
Hong Kong
HK
0.328
0.221
0.288
0.000
‐0.001
India
BO
0.306
0.202
0.475
0.493
0.430
Indonesia
JK
0.487
0.327
0.396
0.576
0.602
Israel
TA
0.157
0.305
0.146
0.402
0.397
Korea
KS
0.210
0.019
0.120
0.238
0.264
Malaysia
KL
0.305
0.231
0.143
0.454
0.465
Mexico
MX
0.259
0.276
0.346
0.499
0.488
Philippines
PS
0.329
0.339
0.295
0.551
0.574
Poland
WA
0.225
0.232
0.142
0.157
0.139
Singapore
SI
0.531
0.312
0.386
0.605
0.648
South Africa
J
0.459
0.385
0.427
0.591
0.598
Taiwan
TW
0.071
0.069
0.242
0.296
0.290
Thailand
BK
0.341
0.293
0.206
0.526
0.549
Turkey
IS
0.112
0.032
0.171
0.212
0.208
Average Emerging
0.247
0.212
0.238
0.370
0.372
0.558
0.549
0.069
0.076
0.436
0.351
0.451
0.524
0.654
0.422
0.277
0.482
0.527
0.604
0.389
0.659
0.631
0.314
0.571
0.222
0.438
0.530
0.547
0.069
0.075
0.440
0.352
0.454
0.517
0.656
0.412
0.279
0.479
0.525
0.606
0.392
0.656
0.631
0.318
0.576
0.227
0.437
0.521
0.554
0.078
0.082
0.357
0.324
0.413
0.514
0.447
0.343
0.310
0.267
0.482
0.442
0.345
0.496
0.396
0.279
0.478
0.208
0.367
0.114
0.178
0.066
0.082
0.102
0.146
‐0.036
0.158
0.036
0.016
0.121
‐0.266
0.167
‐0.143
‐0.059
0.140
0.086
0.182
‐0.181
0.182
0.055
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
Panel C: Compared to Percent Quoted Spread
Average Developed 0.373
0.266
0.405
Average Emerging
0.267
0.244
0.261
0.559
0.421
0.558
0.430
0.655
0.499
0.656
0.499
0.520
0.435
0.193
0.027
127
109
Panel D: Compared to Percent Realized Spread
Average Developed 0.345
0.241
0.358
Average Emerging
0.259
0.250
0.227
0.492
0.395
0.474
0.377
0.551
0.453
0.551
0.452
0.413
0.334
0.182
0.015
127
109
35
Table 4
Monthly Percent Cost Proxies Compared to Percent Cost Benchmarks: Portfolio Time‐Series Correlation
The percent cost benchmarks (percent effective spread, percent quoted spread, and percent realized spread) are calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Exch. Extended Effective LOT LOT Portfolio‐
Country
Code
Roll
Roll
Tick
Mixed
Y‐split
FHT
FHT2
Zeros
Zeros2 Months
Panel A: Compared to Portfolio Percent Effective Spread in Developed Markets
Australia
AX
0.373
0.309
0.632
0.455
0.104
0.580
0.554
0.403
‐0.057
144
Austria
VI
0.443
0.192
0.459
0.451
0.416
0.481
0.452
0.646
0.533
139
Belgium
BR
0.111
0.102
0.425
0.668
0.535
0.615
0.609
0.214
0.147
143
Canada
TO
0.868
0.559
0.811
0.620
0.430
0.638
0.605
0.166
0.334
144
Denmark
CO
0.036
‐0.007
0.049
0.032
0.059
0.052
0.035
0.134
0.064
72
France
PA
0.473
‐0.010
‐0.008
0.461
0.024
0.354
0.402
0.313
0.137
144
Finland
HE
0.266
0.107
0.283
0.193
0.137
0.216
0.209
0.268
0.200
140
Germany
F
0.425
0.416
0.567
0.406
0.707
0.776
0.747
0.517
0.294
84
Ireland
I
0.772
0.606
0.390
0.413
0.365
0.809
0.819
0.533
0.090
91
Italy
MI
0.234
0.226
0.532
0.285
0.300
0.305
0.305
0.621
0.365
120
Japan
T
0.763
0.638
0.751
0.812
0.777
0.781
0.780
0.554
0.397
144
Japan
OS
0.344
0.483
0.521
0.468
0.516
0.508
0.521
0.458
0.476
144
Luxembourg LU
0.007
‐0.082
0.023
‐0.004
‐0.020
0.003
0.001
‐0.057
‐0.177
100
Netherlands AS
0.812
0.557
0.771
0.877
0.819
0.880
0.864
0.756
0.669
144
New Zealand NZ
0.430
0.287
0.174
0.228
0.162
0.314
0.289
‐0.173
‐0.339
125
Norway
OL
0.468
0.402
0.298
‐0.170
‐0.065
0.284
0.284
‐0.011
‐0.288
144
Portugal
LS
0.113
0.013
0.229
0.468
0.399
0.454
0.451
0.443
‐0.173
144
Spain
MC
0.410
0.275
0.297
0.359
0.256
0.298
0.299
0.365
0.380
144
Sweden
ST
0.660
0.414
0.827
0.533
0.458
0.620
0.635
0.564
0.239
76
Switzerland
S
0.196
0.006
0.352
0.248
0.180
0.298
0.295
0.416
‐0.245
138
UK
L
0.611
0.626
0.374
0.704
0.376
0.704
0.693
0.116
‐0.150
144
Average Developed 0.420
0.291
0.417
0.405
0.330
0.475
0.469
0.345
0.138
127
Panel B: Compared to Portfolio Percent Effective Spread in Emerging Markets
Argentina
BA
0.486
0.679
0.620
0.410
0.462
0.825
Brazil
SA
0.735
0.545
0.571
0.757
0.266
0.815
China
SS
0.209
‐0.074
0.550
0.013
0.036
0.208
China
SZ
‐0.050
‐0.049
0.747
0.095
0.185
0.241
Chile
SN
0.220
‐0.059
‐0.021
0.046
0.022
0.064
Greece
AT
0.167
0.180
0.205
0.250
‐0.036
0.290
Hong Kong
HK
0.439
0.305
0.771
‐0.303
‐0.148
0.757
India
BO
0.914
0.726
0.957
0.868
0.891
0.925
Indonesia
JK
0.943
0.729
0.797
0.951
0.865
0.974
Israel
TA
0.196
0.283
0.344
0.331
0.252
0.271
Korea
KS
0.557
0.012
0.744
0.402
0.408
0.633
Malaysia
KL
0.772
‐0.040
0.690
0.437
0.774
0.681
Mexico
MX
0.349
0.281
0.511
0.372
0.402
0.347
Philippines
PS
0.500
0.111
0.619
0.739
0.279
0.803
Poland
WA
0.824
0.354
0.787
0.734
0.692
0.825
Singapore
SI
0.759
0.372
0.902
0.887
0.928
0.943
South Africa
J
0.244
0.252
0.118
0.209
0.158
0.208
Taiwan
TW ‐0.050
0.138
0.188
0.237
0.019
0.354
Thailand
BK
0.871
0.645
0.806
0.944
0.928
0.972
Turkey
IS
0.221
0.199
0.696
0.227
0.227
0.261
Average Emerging
0.465
0.279
0.580
0.430
0.380
0.570
‐0.400
0.812
0.200
0.234
0.050
0.319
0.758
0.949
0.975
0.267
0.582
0.687
0.361
0.807
0.828
0.888
0.203
0.348
0.972
0.279
0.506
0.248
0.831
0.005
0.272
0.035
0.264
0.657
0.814
0.542
0.672
0.180
0.800
0.564
0.334
0.834
0.780
‐0.070
0.343
0.528
‐0.094
0.427
‐0.219
0.331
0.247
0.513
0.018
0.122
0.336
0.918
0.560
0.040
0.316
0.580
0.161
‐0.627
0.346
0.523
‐0.207
0.333
‐0.435
‐0.114
0.187
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
Panel C: Compared to Portfolio Percent Quoted Spread
Average Developed 0.542
0.410
0.544
0.551
Average Emerging
0.488
0.312
0.633
0.475
0.444
0.396
0.640
0.634
0.635
0.566
0.493
0.481
0.192
0.198
125
109
Panel D: Compared to Portfolio Percent Realized Spread
Average Developed 0.414
0.291
0.408
0.411
Average Emerging
0.513
0.368
0.497
0.472
0.334
0.388
0.481
0.572
0.476
0.512
0.330
0.338
0.117
0.022
127
109
36
Table 5
Monthly Percent Cost Proxies Compared to Percent Cost Benchmarks: Average Root Mean Squared Error
The percent cost benchmarks (percent effective spread, percent quoted spread, and percent realized spread) are calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the lowest average root mean squared error (RMSE) in the row. Dashed boxes mean average RMSEs that are statistically indistinguishable from the lowest RMSE in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Exch. Extended Effective LOT LOT Country
Code
Roll
Roll
Tick
Mixed
Y‐split
FHT
FHT2
Zeros
Zeros2 Months
Panel A: Compared to Percent Effective Spread in Developed Markets
Australia
AX 0.0599
0.0705
0.0927
0.1668
0.6767
0.0567
0.0595
0.3551
0.2162
144
Austria
VI
0.0139
0.0149
0.0148
0.0239
0.0209
0.0139
0.0140
0.1496
0.1049
139
Belgium
BR
1.2090
0.9826
0.0666
0.1721
0.2338
0.0615
0.0677
0.2721
0.1807
143
Canada
TO 0.0480
0.0572
0.0645
0.1031
0.0808
0.0442
0.0457
0.2346
0.1575
144
Denmark
CO 0.1432
0.1483
0.1503
0.1720
0.1604
0.1399
0.1404
0.4140
0.2563
72
France
PA 0.0193
1.3862
0.0213
0.0374
0.0852
0.0208
0.0211
0.1486
0.1137
144
Finland
HE
0.0500
0.0542
0.0543
0.0861
0.0902
0.0493
0.0503
0.2708
0.1597
140
Germany
F
0.0300
0.0247
0.0247
0.0691
0.0463
0.0229
0.0240
0.1877
0.1139
84
Ireland
I
0.0275
0.0421
0.0523
0.1259
0.1238
0.0233
0.0248
0.2835
0.1541
91
Italy
MI
0.2468
0.8936
0.0150
0.0739
0.0475
0.0248
0.0257
0.1307
0.0972
120
Japan
T
0.0175
0.0133
0.0196
0.0373
0.0264
0.0112
0.0117
0.1869
0.1308
144
Japan
OS 0.0775
0.0770
0.0862
0.1160
0.1044
0.0754
0.0760
0.3733
0.1992
144
Luxembourg LU 0.0172
0.0230
0.0221
0.0306
0.0247
0.0166
0.0168
0.3049
0.1519
100
0.1463
0.1121
144
Netherlands AS
0.0170
0.0230
0.0181
0.0375
0.0327
0.0125
0.0134
New Zealand NZ 0.0259
0.0325
0.0556
0.0765
0.0738
0.0251
0.0267
0.3879
0.2753
125
Norway
OL
0.0534
0.0586
0.0660
0.2065
0.3042
0.0550
0.0557
0.3283
0.1876
144
Portugal
LS
0.0360
0.0754
0.0329
0.0545
0.0449
0.0221
0.0233
0.2618
0.1512
144
Spain
MC 0.0260
0.0260
0.0109
0.0509
0.0345
0.0171
0.0176
0.1472
0.1364
144
Sweden
ST
0.0285
0.0279
0.0290
0.0508
0.0378
0.0258
0.0262
0.1914
0.1421
76
Switzerland
S
0.0216
0.0244
0.0216
0.0448
0.0374
0.0196
0.0201
0.2406
0.1088
138
UK
L
0.0536
0.0573
0.0504
0.1017
0.2727
0.0480
0.0488
0.3689
0.3083
144
Average Developed 0.1058
0.1958
0.0461
0.0875
0.1219
0.0374
0.0385
0.2564
0.1647
127
Panel B: Compared to Percent Effective Spread in Emerging Markets
Argentina
BA 0.0297
0.0329
0.0515
0.2111
0.1037
Brazil
SA
0.1107
0.1223
0.1197
0.1214
0.3533
China
SS
0.0168
0.0068
0.0068
0.0589
0.0623
China
SZ
0.0144
0.0050
0.0058
0.0322
0.0256
Chile
SN 0.0894
0.0935
0.0933
0.1356
0.3078
Greece
AT
0.1001
0.2263
0.0292
0.0759
0.1779
Hong Kong
HK 0.0418
0.0462
0.0535
0.1334
0.4447
India
BO 0.0247
0.0257
0.0233
0.0484
0.0527
Indonesia
JK
0.0496
0.0652
0.0955
0.2030
0.2860
Israel
TA
0.0424
0.0436
0.0433
0.0702
0.0839
Korea
KS
0.0171
0.0142
0.0143
0.0369
0.0262
Malaysia
KL
0.0414
0.0510
0.0846
0.1978
0.1431
Mexico
MX 0.0409
0.0457
0.0459
0.0731
0.0868
Philippines
PS
0.0590
0.0799
0.0888
0.1794
0.3421
Poland
WA 0.1016
0.1103
0.1043
0.1579
0.1556
Singapore
SI
0.0325
0.0413
0.0846
0.1220
0.1041
South Africa
J
0.0889
0.1015
0.1041
0.1759
0.1852
Taiwan
TW 0.0138
0.0078
0.0116
0.0341
0.0384
Thailand
BK
0.0393
0.0425
0.0489
0.1039
0.1117
Turkey
IS
0.5697
2.6336
0.0248
0.1234
0.0862
Average Emerging
0.0762
0.1898
0.0567
0.1147
0.1589
0.0241
0.0996
0.0242
0.0104
0.0842
0.0343
0.0444
0.0224
0.0483
0.0503
0.0149
0.0502
0.0384
0.0484
0.1024
0.0328
0.0826
0.0118
0.0326
0.0398
0.0448
0.0283
0.0996
0.0255
0.0114
0.0845
0.0339
0.0465
0.0233
0.0535
0.0526
0.0155
0.0556
0.0389
0.0519
0.1023
0.0334
0.0849
0.0123
0.0343
0.0398
0.0464
0.3584
0.2626
0.0850
0.1008
0.4149
0.1470
0.3036
0.0875
0.4208
0.2042
0.1410
0.4273
0.3008
0.4233
0.2542
0.3452
0.3637
0.1313
0.3397
0.1783
0.2645
0.1749
0.1476
0.0465
0.0516
0.2389
0.1177
0.1800
0.0456
0.2835
0.0980
0.1046
0.3660
0.1115
0.2651
0.1726
0.2481
0.2311
0.1235
0.2090
0.1751
0.1696
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
Panel C: Compared to Percent Quoted Spread
Average Developed 0.1013
0.1946
0.0415
Average Emerging
0.0805
0.1980
0.0576
0.0774
0.1039
0.1131
0.1493
0.0308
0.0442
0.0316
0.0450
0.2448
0.2509
0.1569
0.1644
127
109
Panel D: Compared to Percent Realized Spread
Average Developed 0.1081
0.1980
0.0483
Average Emerging
0.0763
0.1911
0.0576
0.0892
0.1139
0.1235
0.1591
0.0395
0.0454
0.0407
0.0469
0.2560
0.2636
0.1661
0.1690
127
109
37
Table 6
Monthly Percent Cost Proxies Compared to Percent Effective Spread by Country Type, Turnover and Size
The percent cost benchmark (percent effective spread) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐
2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the highest correlation (lowest average root mean squared error = RMSE) in the row. Dashed boxes mean correlations (average RMSEs) that are statistically indistinguishable from the highest correlation (lowest average RMSE) in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Extended Effective LOT LOT Roll
Roll
Tick
Mixed Y‐split FHT FHT2 Zeros Zeros2 Months
Panel A: Average Cross‐sectional Correlation for Stocks in Developed Countries Stratified by Turnover
Subsample 1 (Smallest Turnover) 0.132 0.115
0.311
0.355 0.315 0.395 0.395 0.401 0.327
143
Subsample 2
0.348 0.226
0.453
0.490 0.461 0.553 0.551 0.461 0.340
143
Subsample 3
0.412 0.281
0.447
0.565 0.533 0.626 0.623 0.469 0.285
143
Subsample 4
0.391 0.310
0.397
0.547 0.529 0.610 0.607 0.453 0.187
143
Subsample 5 (Largest Turnover) 0.349 0.302
0.314
0.452 0.460 0.539 0.536 0.313 0.027
143
Panel B: Average Cross‐sectional Correlation for Stocks in Emerging Countries Stratified by Turnover
Subsample 1 (Smallest Turnover) 0.210 0.123
0.436
0.322 0.311 0.327 0.326 0.428 0.387
Subsample 2
0.249 0.147
0.414
0.314 0.300 0.423 0.420 0.411 0.360
Subsample 3
0.286 0.163
0.419
0.338 0.326 0.510 0.511 0.423 0.316
Subsample 4
0.363 0.237
0.377
0.398 0.398 0.581 0.579 0.420 0.202
Subsample 5 (Largest Turnover) 0.355 0.258
0.262
0.430 0.417 0.564 0.564 0.348 ‐0.074
143
143
143
143
143
Panel C: Average Root Mean Squared Error for Stocks in Developed Countries Stratified by Size
0.341 0.372
0.110
0.192 0.759 0.084 0.087 0.405
Subsample 1 (Smallest Size)
Subsample 2
0.086 0.897
0.061
0.094 0.120 0.055 0.056 0.309
Subsample 3
0.079 0.171
0.050
0.078 0.074 0.047 0.047 0.249
Subsample 4
0.067 0.118
0.045
0.070 0.067 0.045 0.046 0.189
Subsample 5 (Largest Size)
0.055 0.135
0.020
0.044 0.039 0.021 0.022 0.106
0.234
0.216
0.200
0.166
0.096
143
143
143
143
143
Panel D: Average Root Mean Squared Error for Stocks in Emerging Countries Stratified by Size
Subsample 1 (Smallest Size)
0.315 1.380
0.090
0.185 0.305 0.061 0.064 0.350
Subsample 2
0.126 0.396
0.051
0.126 0.151 0.044 0.046 0.288
Subsample 3
0.099 0.291
0.039
0.108 0.323 0.039 0.040 0.232
Subsample 4
0.062 0.164
0.024
0.088 0.154 0.028 0.029 0.182
Subsample 5 (Largest Size)
0.079 0.212
0.029
0.095 0.111 0.033 0.033 0.165
0.190
0.189
0.171
0.141
0.140
143
143
143
143
143
38
Table 7
Monthly Proxies Compared to Percent Price Impact: Average Cross‐Sectional Correlation
The percent cost benchmark (percent price impact) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies and three cost per volume proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Paster & Extended Effective LOT LOT Stam‐
Country Exchange Roll
Roll
Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Amihud baugh Amivest Months
Panel A: Compared to Percent Realized Spread in Developed Markets
Australia
AX 0.316
0.291
0.267 0.410 0.373 0.457 0.455 0.301 0.012
0.160 ‐0.005 ‐0.107 144
Austria
VI 0.166
0.175
0.134 0.367 0.294 0.326 0.319 0.144 0.070
0.345 ‐0.008 ‐0.267 139
Belgium
BR 0.058
0.031
0.029 0.070 0.037 0.061 0.062 0.025 0.026
0.052
0.037 ‐0.042 143
Canada
TO 0.435
0.284
0.357 0.494 0.454 0.508 0.502 0.349 0.160
0.278 ‐0.017 ‐0.179 144
Denmark
CO 0.267
0.285
0.242 0.404 0.348 0.406 0.404 0.211 ‐0.036
0.219
0.010 ‐0.124 72
France
PA 0.272
0.212
0.260 0.430 0.366 0.409 0.407 0.270 0.177
0.382
0.047 ‐0.131 144
Finland
HE 0.177
0.203
0.118 0.303 0.246 0.250 0.261 0.162 0.042
0.119 ‐0.064 ‐0.075 140
Germany
F 0.043
0.052
0.144 0.095 0.099 0.079 0.095 0.065 0.069
0.171
0.019 ‐0.157 84
Ireland
I 0.465
0.322
0.394 0.271 0.231 0.597 0.592 0.454 0.154
0.283 ‐0.027 ‐0.245 91
Italy
MI 0.169
0.153
0.141 0.295 0.234 0.266 0.264 0.264 0.076
0.318
0.021 ‐0.164 120
Japan
T 0.266
0.236
0.283 0.501 0.453 0.509 0.505 0.381 0.187
0.213
0.011 ‐0.153 144
Japan
OS 0.166
0.158
0.111 0.259 0.214 0.267 0.266 0.102 ‐0.046
0.071 ‐0.011 ‐0.019 144
Luxembourg
LU ‐0.016
‐0.023
‐0.005 ‐0.106 ‐0.082 ‐0.078 ‐0.081 ‐0.170 ‐0.016 ‐0.181 ‐0.020
0.155 100
Netherlands
AS 0.366
0.225
0.449 0.516 0.459 0.495 0.492 0.390 0.315
0.382
0.083 ‐0.232 144
New Zealand NZ 0.269
0.318
0.282 0.479 0.473 0.501 0.497 0.315 0.042
0.319 ‐0.016 ‐0.182 125
0.149
0.080 ‐0.131 144
Norway
OL 0.244
0.247
0.266 0.023 0.017 0.378 0.375 0.188 0.010
Portugal
LS 0.108
0.075
0.079 0.033 0.050 0.058 0.058 ‐0.044 0.190 ‐0.155
0.039
0.233 144
Spain
MC 0.211
0.091
0.339 0.426 0.391 0.437 0.441 0.361 0.345
0.340
0.045 ‐0.212 144
Sweden
ST 0.171
0.187
0.155 0.277 0.224 0.232 0.234 0.115 ‐0.052
0.160
0.002 ‐0.097 76
Switzerland
S 0.189
0.144
0.197 0.356 0.306 0.334 0.334 0.170 ‐0.051
0.323
0.003 ‐0.151 138
UK
L 0.213
0.218
0.130 0.257 0.171 0.271 0.266 0.039 ‐0.033
0.126 ‐0.010 ‐0.035 144
Average Developed 0.217
0.185
0.208 0.293 0.255 0.322 0.321 0.195 0.078
0.194
0.010 ‐0.110 127
Panel B: Compared to Percent Realized Spread in Emerging Markets
Argentina
BA 0.104
0.160
0.134 0.296 0.245 0.302
Brazil
SA 0.214
0.179
0.105 0.230 0.170 0.209
China
SS 0.086
0.250
0.014 0.001 0.000 0.238
China
SZ 0.081
0.268
0.037 0.333 0.230 0.236
Chile
SN 0.148
0.251
0.154 0.321 0.250 0.363
Greece
AT 0.124
0.117
0.164 0.279 0.220 0.261
Hong Kong
HK 0.341
0.288
0.212 ‐0.001 ‐0.003 0.436
India
BO 0.210
0.178
0.235 0.314 0.190 0.254
Indonesia
JK 0.344
0.256
0.314 0.435 0.422 0.503
Israel
TA 0.045
0.162
0.129 0.247 0.225 0.229
Korea
KS 0.246
0.200
0.068 0.363 0.225 0.249
Malaysia
KL 0.230
0.252
0.174 0.423 0.417 0.442
Mexico
MX 0.155
0.159
0.253 0.359 0.319 0.370
Philippines
PS 0.249
0.292
0.238 0.438 0.417 0.477
Poland
WA 0.160
0.187
0.104 0.093 0.082 0.223
0.258
0.284 0.471 0.477 0.509
Singapore
SI 0.412
South Africa
J 0.316
0.301
0.318 0.447 0.446 0.473
Taiwan
TW 0.016
0.203
0.015 0.231 0.073 0.093
Thailand
BK 0.251
0.222
0.138 0.325 0.292 0.340
Turkey
IS 0.080
0.106
0.079 0.272 0.169 0.176
Average Emerging 0.191
0.214
0.158 0.294 0.243 0.319
0.296
0.206
0.237
0.234
0.363
0.260
0.434
0.239
0.499
0.222
0.249
0.436
0.365
0.472
0.221
0.505
0.472
0.090
0.338
0.183
0.316
0.225
0.127
0.137
0.074
0.176
0.185
0.185
0.184
0.286
0.119
0.047
0.184
0.335
0.264
0.142
0.320
0.339
‐0.161
0.104
‐0.024
0.162
0.060
0.016
‐0.065
‐0.097
0.081
0.075
‐0.113
0.057
0.036
‐0.018
‐0.057
‐0.268
0.150
‐0.135
‐0.074
0.071
0.100
‐0.208
‐0.154
‐0.049
‐0.030
0.124
0.161
0.121
0.102
0.016
0.255
0.155
0.262
0.210
0.131
0.229
0.453
0.221
0.109
0.184
0.300
0.231
0.063
0.187
0.063
0.179
‐0.035
0.062
‐0.027
‐0.019
‐0.004
0.010
0.000
‐0.023
0.005
0.065
0.005
0.117
‐0.026
0.008
0.043
0.032
0.042
‐0.015
0.007
0.019
0.013
‐0.159
‐0.068
0.030
‐0.013
‐0.022
‐0.238
‐0.056
‐0.084
‐0.152
‐0.082
‐0.034
‐0.238
‐0.162
0.024
‐0.007
‐0.088
‐0.124
‐0.007
‐0.001
‐0.032
‐0.076
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
39
Table 8
Monthly Proxies Compared to Percent Price Impact: Portfolio Time‐Series Correlation
The percent cost benchmark (percent price impact) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies and three cost per volume proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Paster & Extended Effective LOT LOT Stam‐
Portfolio‐
Country Exchange Roll
Roll
Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Amihud baugh Amivest Months
Panel A: Compared to Portfolio Percent Realized Spread in Developed Markets
Australia
AX ‐0.129
0.038
0.565 0.391 0.101 0.444 0.417 0.636 0.303
0.509 ‐0.116
0.015
144
Austria
VI
0.268
‐0.099
0.635 0.326 0.296 0.353 0.322 0.586 0.421
0.658 0.025
0.053
139
Belgium
BR 0.083
0.352
0.054 0.124 0.083 0.205 0.209 0.102 0.047 ‐0.044 0.089
‐0.046
143
Canada
TO 0.853
0.538
0.788 0.626 0.455 0.646 0.624 0.159 0.278 0.702 ‐0.249 ‐0.020
144
Denmark
CO 0.675
0.585
0.701 0.726 0.662 0.773 0.745 0.535 0.431 ‐0.218 0.072
‐0.778
72
France
PA 0.722
0.053
0.576 0.368 ‐0.107 0.166 0.201 ‐0.074 ‐0.177 0.366 ‐0.012 ‐0.023
144
Finland
HE 0.662
0.530
0.590 0.685 0.536 0.728 0.717 0.635 0.224
0.704 0.045
0.149
140
Germany
F
0.306
0.364
0.509 0.317 0.519 0.595 0.560 0.178 0.129 0.316 ‐0.748 ‐0.162
84
Ireland
I
0.401
0.461
0.405 0.168 0.203 0.500 0.475 0.377 0.106
0.403 ‐0.100 ‐0.258
91
Italy
MI 0.205
0.190
0.345 0.244 0.232 0.232 0.232 0.384 0.115
0.242 ‐0.030
0.041
120
Japan
T
0.822
0.770
0.787 0.864 0.802 0.820 0.805 0.465 0.295 0.166
0.295
‐0.062
144
Japan
OS 0.184
0.401
0.440 0.360 0.407 0.397 0.428 0.370 0.422 0.155
0.054
‐0.379
144
Luxembourg LU 0.002
0.043
0.036 0.013 0.015 0.026 0.023 ‐0.007 ‐0.011 ‐0.032
0.037
0.054
100
Netherlands AS 0.774
0.563
0.781 0.847 0.748 0.828 0.815 0.700 0.599
0.811 ‐0.121 ‐0.691
144
New Zealand NZ ‐0.086
0.196
0.261 0.134 0.144 0.132 0.159 0.300 0.218
0.150 0.019
0.029
125
Norway
OL 0.740
0.630
0.532 ‐0.143 0.017 0.393 0.391 0.195 ‐0.292 0.311 ‐0.094 ‐0.099
144
Portugal
LS ‐0.037
‐0.037
0.063 0.179 0.243 0.259 0.259 0.011 ‐0.081
0.448 0.003
‐0.021
144
Spain
MC 0.345
0.192
0.139 0.273 0.147 0.171 0.175 ‐0.056 ‐0.059 0.156
0.029
‐0.505
144
Sweden
ST 0.691
0.538
0.837 0.548 0.431 0.614 0.622 0.438 0.003
0.797 ‐0.205 ‐0.755
76
Switzerland
S
0.130
0.001
0.265 0.349 0.304 0.383 0.401 0.360 ‐0.197
0.633 0.014
‐0.360
138
UK
L
0.801
0.682
0.261 0.704 0.425 0.734 0.713 0.344 ‐0.154 0.532
0.116
‐0.140
144
Average Developed 0.401
0.333
0.456 0.386 0.317 0.448 0.443 0.316 0.125 0.370 ‐0.042 ‐0.189
127
Panel B: Compared to Portfolio Percent Realized Spread in Emerging Markets
Argentina
BA 0.182
0.155
0.245 ‐0.215 0.085 0.304 0.316
Brazil
SA 0.492
0.263
0.267 0.409 ‐0.133 0.403 0.421
China
SS 0.472
0.594
0.171 0.037 0.062 0.262 0.266
China
SZ 0.317
0.536
0.070 0.636 0.463 0.476 0.475
Chile
SN 0.251
0.105
0.338 0.430 0.310 0.433 0.396
Greece
AT ‐0.003
‐0.007
‐0.052 0.029 ‐0.063 ‐0.081 ‐0.068
Hong Kong
HK 0.642
0.378
0.552 ‐0.287 ‐0.159 0.671 0.663
India
BO 0.763
0.660
0.806 0.753 0.742 0.781 0.797
Indonesia
JK
0.874
0.754
0.721 0.885 0.804 0.940 0.928
Israel
TA 0.053
0.054
0.306 0.132 0.099 0.112 0.104
Korea
KS 0.623
0.422
0.511 0.614 0.420 0.593 0.569
Malaysia
KL 0.772
0.047
0.682 0.448 0.724 0.718 0.715
Mexico
MX 0.336
0.223
0.528 0.286 0.282 0.288 0.305
Philippines
PS 0.480
0.065
0.509 0.710 0.108 0.780 0.779
Poland
WA 0.690
0.291
0.721 0.662 0.639 0.767 0.764
Singapore
SI
0.662
0.482
0.727 0.751 0.717 0.793 0.737
South Africa
J
0.319
0.415
0.593 0.621 0.467 0.674 0.639
Taiwan
TW 0.236
0.621
0.197 0.414 0.106 0.148 0.190
Thailand
BK 0.881
0.627
0.831 0.879 0.843 0.919 0.909
Turkey
IS
0.192
0.179
0.581 0.201 0.198 0.225 0.246
Average Emerging 0.462
0.343
0.465 0.420 0.336 0.510 0.508
0.039
0.346
‐0.044
0.129
0.274
‐0.401
0.163
0.645
0.372
0.281
‐0.377
0.652
0.535
‐0.059
0.707
0.488
0.384
‐0.484
0.420
‐0.227
0.192
‐0.168
‐0.016
‐0.456
‐0.561
0.068
‐0.393
‐0.053
0.728
0.528
‐0.117
‐0.226
0.478
0.192
‐0.727
0.240
0.302
0.070
‐0.470
‐0.337
‐0.249
‐0.058
0.319
0.438
‐0.115
0.045
0.342
0.028
‐0.203
0.822
0.372
‐0.091
0.352
0.322
0.260
0.220
0.717
0.480
0.586
‐0.075
0.694
0.579
0.305
0.066
0.135
‐0.006
0.063
‐0.193
‐0.043
0.191
‐0.195
‐0.042
0.557
0.274
0.051
0.039
‐0.040
0.273
‐0.012
‐0.065
0.044
‐0.107
0.012
0.050
0.043
‐0.296
‐0.043
‐0.043
‐0.092
0.045
‐0.002
0.116
‐0.321
‐0.060
‐0.030
‐0.064
0.277
‐0.029
‐0.578
0.019
‐0.058
0.043
‐0.086
‐0.743
‐0.095
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
40
Table 9
Monthly Proxies Compared to Percent Price Impact: Average Root Mean Squared Error
The percent cost benchmark (percent price impact) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All percent cost proxies and three cost per volume proxies are calculated from daily stock price data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,193,909 stock‐months from 16,096 firms. A solid box means the lowest average root mean squared error (RMSE) in the row. Dashed boxes mean average RMSEs that are statistically indistinguishable from the lowest RMSE in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Paster & Stam‐
Extended Effective LOT LOT Country Exchange Roll
Roll
Tick
Mixed Y‐split FHT FHT2 Zeros Zeros2 Amihud baugh Amivest Months
Panel A: Compared to Percent Realized Spread in Developed Markets
Australia
AX 0.0464 0.0416
0.0899 0.1732 0.6823 0.0540 0.0580 0.3660 0.2180 0.0434 0.0426 2.60E+15 144
Austria
VI 0.0138 0.0115
0.0121 0.0260 0.0210 0.0128 0.0128 0.1538 0.1084 0.0166 0.0115 1.34E+11 139
Belgium
BR 1.2278 0.9358
0.0727 0.2355 0.2978 0.1072 0.1156 0.3020 0.1954 0.1143 0.2794 2.94E+12 143
Canada
TO 0.0458 0.0446
0.0632 0.1094 0.0831 0.0409 0.0427 0.2429 0.1633 0.0536 0.0471 1.47E+14 144
Denmark
CO 0.0217 0.0103
0.0294 0.0741 0.0585 0.0222 0.0242 0.3497 0.1684 0.0461 0.0106 4.15E+04
72
France
PA 0.0159 1.3773
0.0137 0.0388 0.0835 0.0162 0.0167 0.1532 0.1166 0.0309 0.0127 5.89E+13 144
Finland
HE 0.0209 0.0076
0.0234 0.0698 0.0717 0.0246 0.0264 0.2622 0.1447 0.0264 0.0082 9.86E+13 140
Germany
F 0.0315 0.0185
0.0241 0.0753 0.0516 0.0274 0.0288 0.1943 0.1195 0.0409 0.0175 2.23E+05
84
Ireland
I 0.0369 0.0162
0.0570 0.1388 0.1339 0.0367 0.0399 0.3044 0.1673 0.0191 0.0268 1.67E+05
91
Italy
MI 0.2465 0.8916
0.0135 0.0749 0.0480 0.0241 0.0251 0.1335 0.0988 0.0094 0.0090 1.07E+15 120
Japan
T 0.0171 0.0128
0.0202 0.0378 0.0275 0.0119 0.0125 0.1881 0.1317 0.0217 0.0132 2.94E+12 144
Japan
OS 0.1070 0.1050
0.1150 0.1392 0.1301 0.1058 0.1059 0.3624 0.2108 0.1080 0.1057 7.93E+03 144
Luxembourg
LU 0.0173 0.0051
0.0081 0.0434 0.0318 0.0173 0.0180 0.3205 0.1639 0.0746 0.0020 2.24E+02 100
Netherlands
AS 0.0193 0.0155
0.0214 0.0468 0.0408 0.0178 0.0190 0.1518 0.1176 0.0213 0.0164 6.91E+05 144
New Zealand NZ 0.0218 0.0145
0.0625 0.0902 0.0855 0.0309 0.0331 0.4032 0.2882 0.0155 0.0154 9.66E+14 125
Norway
OL 0.0230 0.0145
0.0411 0.1959 0.2927 0.0303 0.0323 0.3326 0.1823 0.0255 0.0151 4.15E+12 144
Portugal
LS 0.0393 0.0559
0.0240 0.0723 0.0570 0.0268 0.0286 0.2829 0.1673 0.0487 0.0231 1.64E+05 144
Spain
MC 0.0258 0.0251
0.0103 0.0514 0.0348 0.0167 0.0173 0.1489 0.1381 0.0083 0.0075 1.13E+06 144
Sweden
ST 0.0210 0.0127
0.0201 0.0492 0.0354 0.0185 0.0192 0.1942 0.1421 0.0200 0.0129 3.00E+05
76
Switzerland
S 0.0205 0.0145
0.0143 0.0495 0.0390 0.0174 0.0179 0.2469 0.1129 0.0505 0.0135 6.10E+03 138
UK
L 0.0164 0.0082
0.0248 0.1180 0.2866 0.0387 0.0415 0.3968 0.3328 0.0095 0.0078 1.84E+15 144
Average Developed 0.0969 0.1733
0.0362 0.0909 0.1235 0.0333 0.0350 0.2614 0.1661 0.0383 0.0332 3.24E+14 127
Panel B: Compared to Percent Realized Spread in Emerging Markets
Argentina
BA 0.0211 0.0176
0.0525 0.2230 0.1145 0.0266
Brazil
SA 0.0466 0.0297
0.0526 0.1380 0.3737 0.0582
China
SS 0.0139 0.0081
0.0074 0.0568 0.0611 0.0229
China
SZ 0.0132 0.0085
0.0080 0.0299 0.0258 0.0114
Chile
SN 0.0246 0.0244
0.0311 0.1008 0.2761 0.0277
Greece
AT 0.0947 0.2182
0.0210 0.0756 0.1743 0.0274
Hong Kong
HK 0.0330 0.0269
0.0492 0.1326 0.4421 0.0404
India
BO 0.0231 0.0128
0.0168 0.0556 0.0566 0.0205
Indonesia
JK 0.0486 0.0379
0.1020 0.2254 0.3092 0.0634
Israel
TA 0.0220 0.0176
0.0195 0.0709 0.0807 0.0377
Korea
KS 0.0161 0.0128
0.0135 0.0359 0.0259 0.0141
Malaysia
KL 0.0400 0.0348
0.0842 0.2093 0.1552 0.0566
Mexico
MX 0.0349 0.0352
0.0403 0.0811 0.0943 0.0373
Philippines
PS 0.0483 0.0555
0.0899 0.1962 0.3604 0.0544
Poland
WA 0.0534 0.0498
0.0540 0.1423 0.1355 0.0567
Singapore
SI 0.0349 0.0233
0.0914 0.1373 0.1200 0.0431
South Africa
J 0.0464 0.0393
0.0743 0.1734 0.1811 0.0566
Taiwan
TW 0.0130 0.0070
0.0113 0.0341 0.0390 0.0117
Thailand
BK 0.0347 0.0227
0.0420 0.1181 0.1260 0.0370
Turkey
IS 0.5697 2.6336
0.0250 0.1229 0.0860 0.0397
Average Emerging 0.0616 0.1658
0.0443 0.1180 0.1619 0.0372
0.0211
0.0614
0.0242
0.0122
0.0299
0.0272
0.0435
0.0218
0.0703
0.0406
0.0147
0.0629
0.0387
0.0600
0.0582
0.0433
0.0614
0.0122
0.0407
0.0396
0.0392
0.3727
0.3211
0.0822
0.0987
0.4093
0.1502
0.3146
0.0975
0.4416
0.2248
0.1428
0.4388
0.3101
0.4424
0.2743
0.3586
0.3650
0.1321
0.3557
0.1786
0.2756
0.1841
0.1454
0.0443
0.0504
0.2198
0.1185
0.1836
0.0455
0.2955
0.0960
0.1055
0.3723
0.1135
0.2719
0.1497
0.2566
0.2176
0.1237
0.2113
0.1754
0.1690
0.0186
0.0949
0.0083
0.0084
0.0252
0.0299
0.0290
0.0548
0.0377
0.0340
0.0191
0.0425
0.0386
0.0420
0.0912
0.0230
0.0459
0.0083
0.0561
0.0244
0.0366
0.0181
0.0289
0.0083
0.0085
0.0248
0.0168
0.0240
0.0134
0.0392
0.0173
0.0132
0.0365
0.0355
0.0519
0.0517
0.0251
0.0597
0.0072
0.0214
0.0165
0.0259
2.22E+12
1.53E+05
2.50E+14
1.07E+14
3.09E+08
6.94E+13
2.22E+16
1.79E+12
6.34E+05
3.95E+04
9.51E+04
8.04E+14
1.42E+06
6.20E+14
5.45E+04
4.71E+15
7.93E+14
5.68E+15
7.19E+15
2.12E+05
2.12E+15
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
41
Table 10
Monthly Cost Per Volume Proxies Compared to Lambda: Average Cross‐Sectional Correlation
The cost per volume benchmark (slope of the price function lambda) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All cost per volume proxies are calculated from daily stock price and volume data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐
months with at least five positive‐volume days and five non‐zero return days. This results in 1,095,544 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Paster LOT Extended Effective LOT & Stam‐
Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Roll Exch. Roll Country
Code Impact Impact Impact Impact Impact Impact Impact Impact Impact Amihud baugh Amivest Months
Panel A: Developed Markets
Australia
AX 0.225
0.182
0.228 0.275 0.270 0.293 0.293 0.299 0.236 0.125 ‐0.008 ‐0.047
144
Austria
VI 0.336
0.330
0.361 0.425 0.373 0.384 0.385 0.301 0.292 0.331
0.018 ‐0.241
139
Belgium
BR 0.217
0.215
0.206 0.268 0.252 0.263 0.263 0.259 0.251 0.127
0.062 ‐0.092
143
Canada
TO 0.382
0.269
0.345 0.386 0.368 0.397 0.394 0.408 0.376 0.229 ‐0.001 ‐0.122
144
Denmark
CO 0.244
0.195
0.162 0.272 0.286 0.270 0.273 0.308 0.213 0.181 ‐0.031 ‐0.079
72
France
PA 0.467
0.316
0.374 0.542 0.481 0.508 0.505 0.473 0.434 0.406
0.107 ‐0.114
144
Finland
HE 0.143
0.120
0.159 0.227 0.198 0.204 0.205 0.250 0.171 0.237 ‐0.041 ‐0.064
140
Germany
F ‐0.076 ‐0.320
‐0.058 ‐0.042 ‐0.063 ‐0.191 ‐0.138 ‐0.160 ‐0.158 ‐0.093 0.129
0.115
84
Ireland
I
0.568
0.348
0.543 0.437 0.388 0.571 0.570 0.545 0.504 0.387
0.024 ‐0.269
91
Italy
MI 0.329
0.223
0.269 0.402 0.359 0.387 0.386 0.412 0.357 0.325
0.031 ‐0.144
120
Japan
T
0.348
0.254
0.287 0.432 0.393 0.423 0.420 0.416 0.373 0.153
0.043 ‐0.105
144
Japan
OS 0.265
0.206
0.213 0.354 0.329 0.354 0.357 0.333 0.284 0.117
0.020 ‐0.136
144
Netherlands AS 0.536
0.415
0.538 0.589 0.532 0.553 0.552 0.546 0.519 0.522
0.136 ‐0.266
144
New Zealand NZ 0.367
0.315
0.389 0.450 0.426 0.443 0.442 0.453 0.422 0.323
0.010 ‐0.167
125
Norway
OL 0.228
0.168
0.253 0.191 0.170 0.292 0.295 0.287 0.242 0.200
0.059 ‐0.078
144
Portugal
LS 0.166
0.213
0.236 0.268 0.269 0.262 0.265 0.231 0.285 0.093
0.082 ‐0.083
144
Spain
MC 0.574
0.311
0.509 0.641 0.554 0.596 0.595 0.557 0.563 0.489
0.090 ‐0.219
144
Sweden
ST 0.302
0.139
0.272 0.295 0.247 0.265 0.262 0.238 0.200 0.181
0.053 ‐0.110
76
0.158
0.081
0.103 0.203 0.178 0.192 0.190 0.159 0.085 0.150 ‐0.013 ‐0.063
138
Switzerland
S
UK
L
0.377
0.396
0.478 0.592 0.527 0.606 0.602 0.580 0.590 0.286
0.011 ‐0.142
144
Average Developed 0.308
0.219
0.293 0.360 0.327 0.354 0.356 0.345 0.312 0.238
0.039 ‐0.121
128
Panel B: Emerging Markets
Argentina
BA 0.277
Brazil
SA 0.094
China
SS 0.462
China
SZ 0.445
Chile
SN 0.179
Greece
AT 0.383
Hong Kong
HK 0.306
India
BO 0.234
Indonesia
JK 0.262
Israel
TA ‐0.001
Korea
KS 0.525
Malaysia
KL 0.518
Mexico
MX 0.321
Philippines
PS 0.187
Poland
WA 0.254
Singapore
SI 0.367
South Africa
J
0.289
Taiwan
TW 0.293
Thailand
BK 0.224
Turkey
IS 0.074
Average Emerging 0.285
0.274
0.072
0.374
0.330
0.135
0.291
0.262
0.190
0.240
0.139
0.377
0.446
0.357
0.165
0.204
0.249
0.216
0.324
0.171
0.075
0.245
0.270
0.062
0.404
0.420
0.109
0.478
0.272
0.209
0.236
0.247
0.253
0.603
0.479
0.175
0.188
0.303
0.273
0.304
0.169
0.107
0.278
0.400
0.110
0.276
0.548
0.189
0.546
0.254
0.312
0.344
0.315
0.494
0.682
0.549
0.251
0.264
0.405
0.344
0.419
0.259
0.131
0.355
0.361
0.111
0.125
0.380
0.184
0.480
0.181
0.303
0.319
0.282
0.404
0.619
0.546
0.249
0.224
0.396
0.336
0.338
0.260
0.110
0.310
0.393
0.110
0.340
0.434
0.195
0.502
0.398
0.312
0.343
0.292
0.449
0.636
0.550
0.257
0.286
0.422
0.345
0.373
0.270
0.122
0.351
0.389
0.110
0.340
0.429
0.198
0.508
0.397
0.314
0.343
0.292
0.447
0.645
0.549
0.257
0.288
0.420
0.342
0.377
0.271
0.121
0.352
0.378
0.070
0.389
0.406
0.215
0.538
0.376
0.312
0.349
0.289
0.415
0.628
0.541
0.237
0.295
0.441
0.357
0.341
0.293
0.092
0.348
0.341
0.054
0.383
0.386
0.160
0.500
0.268
0.201
0.213
0.241
0.379
0.543
0.468
0.182
0.185
0.335
0.321
0.300
0.210
0.076
0.287
0.177
0.149
0.555
0.419
0.033
0.364
0.113
0.239
0.198
0.220
0.442
0.518
0.312
0.054
0.217
0.314
0.191
0.193
0.179
0.039
0.246
‐0.019
0.095
‐0.126
‐0.113
0.026
0.040
0.009
‐0.051
0.045
0.021
0.032
0.113
0.033
0.007
0.079
0.020
0.021
‐0.026
0.025
0.024
0.013
‐0.205
‐0.060
‐0.359
‐0.401
0.039
‐0.209
‐0.053
‐0.019
‐0.074
‐0.131
‐0.178
‐0.316
‐0.099
0.012
‐0.067
‐0.096
‐0.088
‐0.150
‐0.053
‐0.079
‐0.129
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
42
Table 11
Monthly Cost Per Volume Proxies Compared to Lambda: Portfolio Time‐Series Correlation
The cost per volume benchmark (slope of the price function lambda) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All cost per volume proxies are calculated from daily stock price and volume data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐
months with at least five positive‐volume days and five non‐zero return days. This results in 1,095,544 stock‐months from 16,096 firms. A solid box means the highest correlation in the row. Dashed boxes mean correlations that are statistically indistinguishable from the highest correlation in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Paster LOT Extended Effective LOT & Stam‐
Portfolio‐
Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Roll Exch. Roll Country
Code Impact Impact Impact Impact Impact Impact Impact Impact Impact Amihud baugh Amivest Months
Panel A: Developed Markets
Australia
AX 0.458
0.389
0.422 0.390 0.182 0.400 0.403 0.419 0.431 0.238 ‐0.068 0.023
144
Austria
VI 0.330
0.032
0.354 0.384 0.291 0.346 0.333 0.518 0.577 0.521 ‐0.124 0.019
138
Belgium
BR ‐0.001 ‐0.023
0.261 0.291 0.239 0.256 0.295 0.242 0.277 0.104
0.208 ‐0.018
141
Canada
TO 0.183
0.050
0.181 0.172 0.122 0.167 0.162 0.131 0.157 0.228 ‐0.100 ‐0.042
144
Denmark
CO 0.375
0.348
0.300 0.396 0.266 0.293 0.257 0.313 0.365 ‐0.018 0.071 ‐0.377
72
France
PA 0.195 ‐0.001
0.259 0.184 0.123 0.160 0.157 0.127 0.180 0.167 ‐0.019 ‐0.018
144
Finland
HE ‐0.007 ‐0.036
0.008 ‐0.029 ‐0.026 ‐0.023 ‐0.019 ‐0.010 0.056 ‐0.035 ‐0.010 ‐0.009
140
Germany
F
0.235
0.135
0.252 0.288 0.336 0.295 0.293 0.401 0.434 0.333 ‐0.181 ‐0.313
81
Ireland
I
0.001
0.093
0.108 0.324 0.356 0.096 0.106 0.180 0.164 0.044 ‐0.034 ‐0.089
91
Italy
MI 0.289
0.262
0.400 0.447 0.432 0.419 0.413 0.558 0.579 0.452 ‐0.009 0.015
120
Japan
T
0.483
0.399
0.452 0.480 0.477 0.481 0.483 0.524 0.542 0.234
0.038 ‐0.053
144
Japan
OS 0.218
0.337
0.219 0.249 0.251 0.246 0.274 0.142 0.166 0.219
0.015 ‐0.279
144
Luxembourg LU 0.271
0.011
‐0.097 0.106 0.061 0.141 0.096 0.056 0.017 0.119
0.109 ‐0.370
18
Netherlands AS 0.578
0.571
0.628 0.456 0.419 0.454 0.428 0.690 0.698 0.763 ‐0.238 ‐0.580
144
New Zealand NZ 0.188 ‐0.046
0.086 0.139 0.101 0.182 0.161 0.260 0.360 0.122
0.099
0.231
87
Norway
OL 0.187
0.166
0.148 0.148 0.036 0.172 0.170 0.195 0.182 0.201 ‐0.117 ‐0.049
144
Portugal
LS 0.210 ‐0.017
0.312 0.111 0.133 0.134 0.139 0.180 0.255 0.091 ‐0.269 ‐0.199
133
Spain
MC ‐0.016 ‐0.120
0.449 ‐0.182 ‐0.196 ‐0.185 ‐0.189 ‐0.091 ‐0.111 ‐0.200 ‐0.115 ‐0.126
144
Sweden
ST 0.631
0.357
0.666 0.609 0.606 0.602 0.604 0.540 0.520 0.780
0.025 ‐0.692
76
Switzerland
S ‐0.058 ‐0.031
0.006 0.078 0.087 0.099 0.130 0.288 0.003 0.233
0.108 ‐0.144
138
UK
L
0.623
0.427
0.238 0.702 0.362 0.728 0.733 0.795 0.839 0.383
0.111 ‐0.137
144
Average Developed 0.256
0.157
0.269 0.273 0.222 0.260 0.259 0.308 0.319 0.237 ‐0.024 ‐0.153
121
Panel B: Emerging Markets
Argentina
BA 0.060
Brazil
SA ‐0.274
China
SS 0.667
China
SZ 0.704
Chile
SN 0.349
Greece
AT ‐0.038
Hong Kong
HK 0.714
India
BO 0.399
Indonesia
JK 0.398
Israel
TA 0.261
Korea
KS 0.538
Malaysia
KL 0.751
Mexico
MX 0.303
Philippines
PS 0.006
Poland
WA 0.477
Singapore
SI 0.425
South Africa
J
0.173
Taiwan
TW ‐0.064
Thailand
BK 0.436
Turkey
IS ‐0.145
Average Emerging 0.307
‐0.036
‐0.183
0.802
0.641
0.276
‐0.087
0.571
0.386
0.483
0.020
0.421
0.203
0.096
‐0.026
0.198
0.370
0.329
‐0.103
0.441
‐0.126
0.234
0.165
‐0.295
0.669
0.820
0.114
0.288
0.643
0.289
0.465
‐0.043
0.451
0.316
0.189
0.002
0.483
0.496
0.046
0.097
0.455
‐0.351
0.265
‐0.070
‐0.167
0.724
0.809
0.254
0.044
0.745
0.390
0.289
0.047
0.471
0.579
0.196
0.002
0.551
0.500
0.162
‐0.106
0.493
‐0.232
0.284
0.017
‐0.225
0.555
0.606
0.240
‐0.041
0.135
0.253
0.236
0.053
0.242
0.487
0.147
0.002
0.584
0.481
0.121
‐0.112
0.500
‐0.224
0.203
0.200
‐0.146
0.732
0.738
0.439
‐0.011
0.724
0.425
0.381
0.139
0.391
0.592
0.255
0.004
0.542
0.490
0.175
‐0.125
0.505
‐0.252
0.310
0.329
‐0.150
0.718
0.731
0.399
‐0.001
0.719
0.387
0.393
0.134
0.364
0.544
0.245
0.003
0.533
0.534
0.155
‐0.124
0.513
‐0.258
0.308
0.308
‐0.230
0.679
0.683
0.487
0.119
0.742
0.434
0.325
0.108
0.212
0.463
0.222
0.005
0.538
0.378
0.095
‐0.009
0.461
‐0.379
0.282
0.257 0.138
‐0.271 ‐0.351
0.653 0.775
0.695 0.591
0.426 0.163
0.289 0.050
0.728 ‐0.164
0.398 0.448
0.308 0.336
0.162 0.106
0.549 0.556
0.467 0.161
0.250 0.277
‐0.004 0.069
0.544 0.488
0.378 0.369
0.084 0.120
0.227 0.010
0.415 0.635
‐0.386 ‐0.352
0.308 0.221
‐0.018
‐0.049
‐0.499
‐0.586
‐0.078
‐0.021
0.239
‐0.372
0.099
0.174
0.281
‐0.294
‐0.110
‐0.011
0.379
‐0.053
0.014
0.044
‐0.206
‐0.035
‐0.055
‐0.011
‐0.229
0.067
0.136
‐0.069
0.035
0.017
‐0.016
‐0.079
‐0.135
‐0.414
‐0.065
0.278
‐0.031
‐0.411
‐0.016
‐0.023
0.127
‐0.109
0.509
‐0.022
113
24
134
74
67
144
144
72
144
36
51
70
144
144
86
123
142
144
144
144
107
43
Table 12
Monthly Cost Per Volume Proxies Compared to Lambda: Average Root Mean Squared Error
The cost per volume benchmark (slope of the price function lambda) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All cost per volume proxies are calculated from daily stock price and volume data for a sample stock‐
month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐
volume days and five non‐zero return days. This results in 1,095,544 stock‐months from 16,096 firms. A solid box means the lowest average root mean squared error (RMSE) in the row. Dashed boxes mean average RMSEs that are statistically indistinguishable from the lowest RMSE in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level.
Exch. Extended Effective LOT LOT Paster & Country
Code Roll
Roll
Tick
Mixed Y‐split
FHT
FHT2
Zeros Zeros2 Amihud Stam. Amivest Months
Panel A: Developed Markets
Australia
AX 0.00798 0.00141 0.01484 0.02870 0.03304 0.01046 0.01119 0.04840 0.02351 0.01475 0.00302 2.68E+15 144
Austria
VI
0.00029 0.00003 0.00032 0.00067 0.00044 0.00026 0.00025 0.00646 0.00395 0.01462 0.00011 1.37E+11 139
Belgium
BR 0.86944 2.91478 0.28405 0.89711 1.01380 0.37815 0.40091 0.41372 0.27365 0.04803 0.11080 3.27E+12 143
Canada
TO 0.01461 0.00197 0.01530 0.03619 0.03078 0.01394 0.01475 0.04765 0.02579 0.03848 0.00471 1.27E+14 144
Denmark
CO 0.00036 0.00005 0.00047 0.00116 0.00088 0.00040 0.00043 0.00403 0.00119 0.04395 0.00013 4.23E+04 72
France
PA 0.00215 0.02631 0.00166 0.00494 0.00443 0.00191 0.00198 0.01662 0.00951 0.03012 0.00073 5.89E+13 144
Finland
HE 0.00230 0.00032 0.00278 0.00655 0.00613 0.00284 0.00297 0.02274 0.01024 0.01865 0.00089 4.63E+13 140
Germany
F
0.00016 0.00005 0.00019 0.00018 0.00006 0.00006 0.00006 0.00075 0.00072 0.00083 0.00008 2.45E+05 84
Ireland
I
0.00914 0.00062 0.01276 0.01348 0.01030 0.00858 0.00902 0.02951 0.01756 0.00587 0.00186 1.81E+05 91
Italy
MI 0.00421 0.01439 0.00048 0.00218 0.00163 0.00088 0.00091 0.00792 0.00344 0.00402 0.00032 1.11E+15 120
Japan
T
0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00011 0.00008 0.01912 0.00005 2.99E+12 144
Japan
OS 0.00010 0.00009 0.00011 0.00013 0.00012 0.00010 0.00010 0.00029 0.00019 0.01781 0.00010 8.64E+03 144
Netherlands AS 0.00232 0.00012 0.00273 0.00722 0.00632 0.00266 0.00288 0.01356 0.01044 0.01232 0.00070 6.99E+05 144
New Zealand NZ 0.00191 0.00026 0.00463 0.00910 0.00888 0.00330 0.00366 0.02519 0.01527 0.00346 0.00108 1.45E+15 125
Norway
OL 0.00021 0.00004 0.00036 0.00050 0.00050 0.00026 0.00027 0.00192 0.00078 0.01587 0.00007 4.55E+12 144
Portugal
LS
0.00619 0.00146 0.00571 0.01333 0.00967 0.00534 0.00554 0.07633 0.04268 0.01660 0.00109 1.79E+05 144
Spain
MC 0.00038 0.00019 0.00024 0.00097 0.00072 0.00035 0.00037 0.00502 0.00398 0.00363 0.00011 1.13E+06 144
Sweden
ST
0.00014 0.00002 0.00013 0.00034 0.00028 0.00013 0.00014 0.00108 0.00042 0.00895 0.00005 4.07E+05 76
Switzerland
S
0.00034 0.00003 0.00017 0.00101 0.00074 0.00036 0.00038 0.00392 0.00149 0.05198 0.00012 6.21E+03 138
UK
L
0.00001 0.00001 0.00001 0.00003 0.00007 0.00001 0.00001 0.00007 0.00006 0.00186 0.00001 2.87E+14 144
Average Developed 0.04611 0.14811 0.01735 0.05119 0.05644 0.02150 0.02279 0.03627 0.02225 0.01855 0.00630 2.89E+14 128
Panel B: Emerging Markets
Argentina
BA 0.00085
Brazil
SA 0.00312
China
SS 0.000005
China
SZ
0.00001
Chile
SN 0.000004
Greece
AT 0.00644
Hong Kong
HK 0.00077
India
BO 0.00416
Indonesia
JK 0.000012
Israel
TA 0.00030
Korea
KS 1.62E‐06
Malaysia
KL
0.01057
Mexico
MX 0.00023
Philippines
PS 0.04523
Poland
WA 0.01445
Singapore
SI
0.00845
South Africa
J
0.00711
Taiwan
TW 0.00016
Thailand
BK 0.00128
Turkey
IS
0.11905
Average Emerging 0.01111
0.00013
0.00044
0.000004
0.000005
0.000003
0.00996
0.00017
0.00037
0.000008
0.00007
1.56E‐06
0.00067
0.00004
0.00084
0.00116
0.00106
0.00141
0.00015
0.00072
0.51966
0.02684
0.00331
0.00927
0.000004
0.000004
0.000005
0.00377
0.00095
0.00381
0.00002
0.00022
1.54E‐06
0.01477
0.00043
0.03102
0.02078
0.02067
0.00992
0.00017
0.00105
0.01020
0.00652
0.0
0.00928
0.00002
0.00001
0.00002
0.00969
0.00109
0.01165
0.00003
0.00097
2.13E‐06
0.04285
0.00098
0.10644
0.04242
0.03054
0.03104
0.00022
0.00288
0.02481
0.01613
0.00445
0.01196
0.00002
0.00001
0.00007
0.00633
0.00132
0.01314
0.00003
0.00068
1.84E‐06
0.03619
0.00088
0.08421
0.03938
0.03113
0.04304
0.00021
0.00247
0.01358
0.01445
0.00160
0.00400
0.000004
0.000004
0.00001
0.00358
0.00090
0.00374
0.000015
0.00038
1.49E‐06
0.01428
0.00037
0.04550
0.01491
0.01167
0.01230
0.00017
0.00129
0.00854
0.00616
0.00124
0.00412
0.000004
0.000004
0.00001
0.00368
0.00096
0.00383
0.00002
0.00039
1.52E‐06
0.01538
0.00042
0.04685
0.01533
0.01189
0.01333
0.00017
0.00139
0.00849
0.00638
0.01981
0.01930
0.00003
0.00006
0.00005
0.02868
0.00492
0.01614
0.00004
0.00510
1.33E‐05
0.07232
0.00350
0.27064
0.09589
0.05117
0.02906
0.00050
0.00533
0.05069
0.03366
0.00861
0.01742
0.00003
0.00005
0.00002
0.01797
0.00179
0.00454
0.00002
0.00289
4.95E‐06
0.03196
0.00106
0.11311
0.04792
0.02122
0.01783
0.00033
0.00168
0.03909
0.01638
0.00884
0.02413
0.00008
0.00017
0.00346
0.02436
0.01346
0.04700
0.01138
0.02239
1.85E‐02
0.02626
0.01065
0.01153
0.07025
0.00581
0.02078
0.00327
0.03522
0.02100
0.01892
0.00061
0.00104
0.00001
0.00001
0.000003
0.00162
0.00028
0.00134
0.000010
0.00025
1.62E‐06
0.00331
0.00011
0.01517
0.00421
0.00378
0.00230
0.00016
0.00090
0.00567
0.00204
2.31E+12
1.54E+05
2.50E+14
1.07E+14
3.30E+08
6.94E+13
2.28E+16
1.82E+12
6.56E+05
5.55E+04
9.52E+04
8.04E+14
1.51E+06
6.44E+14
5.54E+04
4.75E+15
8.10E+14
5.69E+15
7.33E+15
2.12E+05
2.16E+15
113
24
134
74
67
144
144
72
144
68
51
70
144
144
86
123
142
144
144
144
109
44
Table 13
Monthly Cost Per Volume Proxies Compared to Lambda by Country Type, Turnover and Size
The cost per volume benchmark (slope of the price function lambda) is calculated from every trade and corresponding BBO quote in the SIRCA TACTIC database for a sample stock‐month. All cost per volume proxies are calculated from daily stock price and volume data for a sample stock‐month. The sample spans 41 non‐U.S. exchanges around the world from 1996‐2007. It consists of all stock‐months with at least five positive‐volume days and five non‐zero return days. This results in 1,095,544 stock‐months from 16,096 firms. A solid box means the highest correlation (lowest average root mean squared error = RMSE) in the row. Dashed boxes mean correlations (average RMSEs) that are statistically indistinguishable from the highest correlation (lowest average RMSE) in the row at the 5% level. Bold‐faced numbers are statistically different from zero at the 5% level. Extended Effective LOT LOT Paster & Roll Roll Tick Mixed Y‐split FHT FHT2 Zeros Zeros2 Stam‐
Impact Impact Impact Impact Impact Impact Impact Impact Impact Amihud baugh Amivest Months
Panel A: Average Cross‐sectional Correlation for Stocks in Developed Countries Stratified by Turnover
Subsample 1 (Smallest Turnover) 0.363
0.265
0.391
0.434 0.396 0.422 0.418 0.447 0.429 0.087
0.016
‐0.068
144
Subsample 2
0.414
0.291
0.389
0.470 0.434 0.474 0.468 0.483 0.449 0.093
0.080
‐0.058
144
Subsample 3
0.351
0.261
0.332
0.398 0.365 0.404 0.401 0.432 0.387 0.103
0.021
‐0.054
144
Subsample 4
0.321
0.229
0.319
0.351 0.343 0.369 0.365 0.398 0.358 0.102
0.019
‐0.036
144
Subsample 5 (Largest Turnover) 0.234
0.157
0.257
0.274 0.267 0.271 0.270 0.287 0.239 0.103 ‐0.025
‐0.036
144
Panel B: Average Cross‐sectional Correlation for Stocks in Emerging Countries Stratified by Turnover
Subsample 1 (Smallest Turnover) 0.040
0.035
0.065
0.069 0.074 0.084 0.082 0.058
Subsample 2
0.122
0.110
0.123
0.143 0.118 0.158 0.156 0.144
Subsample 3
0.172
0.106
0.162
0.174 0.139 0.187 0.184 0.206
Subsample 4
0.185
0.128
0.174
0.216 0.201 0.228 0.228 0.243
Subsample 5 (Largest Turnover) 0.105
0.074
0.079
0.117 0.115 0.123 0.123 0.136
0.031
0.131
0.196
0.212
0.083
0.039
0.045
0.051
0.077
0.099
‐0.034
0.002
0.030
0.020
0.015
‐0.031
‐0.036
‐0.025
‐0.018
‐0.020
144
144
144
144
144
Panel C: Average Root Mean Squared Error for Stocks in Developed Countries Stratified by Size
Subsample 1 (Smallest Size)
0.24891 0.79478 0.09589 0.28046 0.31873 0.11663 0.12362
Subsample 2
0.00122 0.01625 0.00106 0.00203 0.00170 0.00081 0.00084
Subsample 3
0.00050 0.00097 0.00023 0.00076 0.00057 0.00028 0.00029
Subsample 4
0.00018 0.00016 0.00012 0.00034 0.00027 0.00014 0.00015
Subsample 5 (Largest Size)
0.00005 0.00008 0.00002 0.00007 0.00004 0.00003 0.00003
0.15672
0.00826
0.00377
0.00200
0.00039
0.09445
0.00447
0.00222
0.00124
0.00025
0.04243
0.02370
0.01775
0.01160
0.00480
0.03501
0.00036
0.00011
0.00007
0.00002
1.97E+14
1.75E+14
4.09E+14
4.2E+14
2.08E+15
144
144
144
144
144
Panel D: Average Root Mean Squared Error for Stocks in Emerging Countries Stratified by Size
Subsample 1 (Smallest Size)
0.11055 0.36518 0.03541 0.09671 0.08520 0.03927 0.04025
Subsample 2
0.01142 0.02735 0.00416 0.01036 0.00706 0.00366 0.00374
Subsample 3
0.00333 0.00747 0.00110 0.00313 0.00228 0.00110 0.00114
Subsample 4
0.00059 0.00136 0.00021 0.00074 0.00048 0.00024 0.00024
Subsample 5 (Largest Size)
0.00099 0.00401 0.00015 0.00074 0.00037 0.00018 0.00017
0.21152
0.02088
0.00893
0.00272
0.00162
0.10035
0.01314
0.00652
0.00189
0.00085
0.04731
0.02106
0.01346
0.00662
0.00397
0.01419
0.00167
0.00046
0.00010
0.00007
7.79E+14
5.4E+15
6.57E+15
8.44E+15
1.17E+16
144
144
144
144
144
45