new evidence on the relation between stock liquidity and measures of trading activity

International Review of Financial Analysis 19 (2010) 181–192

Contents lists available at ScienceDirect

International Review of Financial Analysis

New evidence on the relation between stock liquidity and measures oftrading activity

Daniel Chai a, Robert Faff b,⁎, Philip Gharghori a

a Department of Accounting and Finance, Monash University, Clayton, Victoria 3800, Australiab UQ Business School, University of Queensland, St Lucia, Queensland, 4072, Australia

⁎ Corresponding author.E-mail address: [email protected] (R. Faff).

1057-5219/$ – see front matter © 2010 Elsevier Inc. Aldoi:10.1016/j.irfa.2010.02.005

a b s t r a c t
a r t i c l e i n f o
Article history:Received 19 February 2009Received in revised form 10 February 2010Accepted 28 February 2010Available online 11 March 2010

JEL classification:G10

Keywords:Stock liquidityTrading characteristicsAustralian evidence

The goal of this paper is to examine two empirical issues regarding stock liquidity: (1) to what degree aredifferent liquidity proxies correlated? and (2) how are different liquidity proxies related to stocks' tradingcharacteristics? Answers to these questions will help us better understand whether there are commonsources of liquidity. This has considerable implications for studying stock liquidity, since selecting anappropriate proxy for liquidity is an important issue in empirical research design. Using data from theAustralian equity market, our results confirm prior research that stocks' trading characteristics are importantdeterminants of liquidity. Though the relationships are generally consistent with expectations, some proxiesdo react differently to certain trading characteristics. This finding is consistent with the contention thatliquidity is a multifaceted concept and each alternative proxy may only capture a certain aspect of liquidity.

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© 2010 Elsevier Inc. All rights reserved.

1. Introduction

Liquidity has long been an important issue for securities traded infinancial markets. A certain level of liquidity is necessary for securitiesto be traded in the quantities required in a timely fashion without anyprice discount. What are the factors that influence stock liquidity?Early studies such as Tinic (1972), Benson and Hagerman (1974),Branch and Freed (1977) and Stoll (1978) investigate the influence ofboth stock and market characteristics on bid–ask spreads, which isoften used as a proxy for the trading cost of immediate transactions(Demsetz, 1968). Stock characteristics include stock price, tradingvolume, number of trades and return volatility. Market characteristicsinclude market structure and competition. Stoll (2000) and Chordia,Roll and Subrahmanyam (2000) extend the early studies by employ-ing various alternative proxies for liquidity. Similar to the previousstudies, stocks' trading characteristics such as stock price, tradingvolume and volatility are found to be important determinants of thespread and other liquidity proxies.

As with most of the finance literature, the role of stocks' tradingcharacteristics on liquidity has been focused on quote-drivenmarkets,namely, the NYSE, AMEX and Nasdaq. The purpose of this paper is tofill the gap in the literature with respect to order-driven systems byexamining the relationship between stock liquidity and stocks'trading characteristics in the order-driven market of Australia. The

Australian trading mechanism is different from that of the US marketprimarily because of the absence of market makers and the fact thatpublic limit orders provide liquidity to the market and establish thebid and ask prices. This market characteristic provides a moretransparent trading environment to market participants, as theyhave the ability to observe recent trades. In recent years, order-drivenand limited order book market structures have increased rapidlybecause of improvements in information technology and financialmarket deregulation. As noted in Brown and Zhang (1997), marketsthat allow limit orders tend to have a lower execution-price risk andhave a higher level of liquidity. The Australian market provides us theopportunity to examine the role of liquidity in financial marketsacross different stock exchange mechanisms.

In this paper, we extend the literature by employing six differentliquidity proxies constructed from low-frequency data. The proxies areproportional bid–ask spread, stock turnover, the illiquidity ratio fromAmihud (2002), the return reversal measure from Pastor andStambaugh (2003), the zero return measure (proportion of zero dailyreturns) from Lesmond, Ogden and Trzcinka (1999), and turnover-adjusted number of zero daily volumes from Liu (2006). These liquidityproxies are widely used in asset pricing research and each of themrepresents different liquidity dimensions and trading behaviour. Byexamining the relationships between these liquidity proxies and stocks'trading characteristics, the current research seeks to understand theextent to which there are common determinants of stock liquidity.Specifically, we ask howare these proxies related to eachother and howare they related to stocks' trading characteristics? Afinding that they arenot related in the same way will support the view that liquidity is a

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182 D. Chai et al. / International Review of Financial Analysis 19 (2010) 181–192

complex multidimensional concept. The results also help us tounderstand the trading aspects that a particular proxy is capturing.The efforts are significant as liquidity plays an important role in assetpricing, and the selection of liquidity proxies in a research designwouldhave considerable influence on empirical results. The aims of this paperare in the spirit of Stoll (2000), who asserts that understanding thesource of liquidity is important for asset pricing research.

When using these liquidity proxies, we have to be aware of theirlimitations. Liu (2006) notes that existing liquidity proxies have alimited ability to capture liquidity risk and theymight bepoormeasures,even in the particular dimension they intend to capture. Moreover,liquidity proxies constructed from high-frequency (microstructure)data are more precise than those created from low-frequency data(Hasbrouck, 2009). Recently, Goyenko, Holden and Trzcinka (2009)demonstrate that liquidity proxies constructed from low-frequencydata are comparable to high-frequency measures. Their results give ussome confidence on the use of the liquidity proxies employed in thecurrent study.

The remainder of the paper is organised as follows. Section 2presents the literature review and statement of hypotheses. We firstintroduce the liquidity proxies, then the theoretical background of therelationship between trading characteristics and liquidity. Section 3discusses the methodology and data sources. Section 4 presents theempirical results and Section 5 concludes.

2. Literature review and statement of hypotheses

2.1. Liquidity proxies

Kyle (1985, p.1316) points out that “market liquidity is a slipperyand elusive concept, in part because it encompasses a number oftransactional properties of markets. These include tightness, depth, andresiliency.” Tightness refers to the cost of transactions, such as the bid–ask spread. Depth represents the ability of the market to absorb a largequantity of trade without having a large impact on price. Resiliency isdefined as the speed with which the prices bounce back to equilibriumfollowing a large trade. Black (1971) earlier suggested anotherdimension of liquidity, immediacy, which represents the speed withwhich buy or sell orders can be executed. Liquidity proxies used in theliterature can therefore be classified into these four categories. Whilethese dimensions are to some degree overlapping, there is no singleliquidity proxy that fully captures all dimensions. This paper employs sixwidely used liquidity proxies that are computed on a monthly basisusing both daily and monthly price information. The proxies are stockturnover, the illiquidity ratio, the return reversal measure, proportionalspread, the zero return measure and turnover-adjusted number of zerodaily volumes. Each is discussed in turn below.

2.1.1. Stock turnoverStock turnover is the ratio of the number of shares traded to the

number of shares outstanding:

turnoveri;t = VOLi;t = sharei;t ð1Þ

where VOLi,t is the total trading volume for stock i in month t andsharei,t is the number of shares outstanding for stock i in month t.Volume data for each stock is collected on a daily basis, while data onthe number of shares outstanding is collected on a monthly basis.1

1 Our method of calculating stock turnover over a month is similar to that used inChan and Faff (2003) and Datar et al. (1998). An alternative specification of Eq. (1) isto use daily shares outstanding. However, these data are not readily available to usover our sample period. We calculated an alternative measure of stock turnover byaveraging the current and prior month's shares outstanding to assess the robustness ofour results. These unreported findings, which are available on request from theauthors, demonstrate that our inferences are robust to this alternative measure.

The reciprocal of turnover is often used to represent the averageholding period of securities (e.g. see Atkins and Dyl, 1997). Thesmaller the turnover rate, the longer the average holding period.According to the clientele effect of Amihud and Mendelson (1986),assets with higher spreads have relatively longer expected holdingperiods. Thus, turnover should be negatively related to spread andshould be positively related to liquidity. Datar et al. (1998) show thatstock returns are strongly negatively related to the turnover ratio. Incontrast, Lee and Swaminathan (2000) question the use of turnover asa liquidity proxy. They find some evidence that turnover is not highlycorrelated with firm size or the relative bid–ask spread. Further, theyshow that turnover is related to stocks' past performance — stocksthat are perceived to or have growth potential (growth stocks) have ahigher turnover rate than stocks that are relatively undervalued(value stocks). However, Chan and Faff (2003) find evidence againstthe value/growth argument. They find a strong negative relationshipbetween turnover and stock returns from 1990 to 1999 in theAustralian market. The significant relationship remains even aftercontrolling for size, book-to-market, beta and momentum.

2.1.2. Illiquidity ratioThe illiquidity ratio, proposed by Amihud (2002), is defined as the

daily absolute return of a stock divided by its trading volume onthat day. The monthly illiquidity ratio is obtained from the followingequation:

Illiquidi;t =1Di;t

∑Di;t

d=1jri;d;t j = vi;d;t ð2Þ

where ri,d,t is the absolute return for stock i on day d inmonth t, and vi,d,tis the trading volume inmillions of dollars for stock i on day d inmonth tand D is the number of daily observations for stock i in month t.

The illiquidity ratio captures the price movement associated withtrading volume or the price impact of the order flow. Stocks areregarded as illiquid (liquid) if small (large) trades cause high (small)price movement. The illiquidity ratio follows Kyle's (1985) concept ofliquidity, which examines the relationship between price movementand net order flow and is commonly known as price impact or Kyle's λ.Amihud (2002) demonstrates that the illiquidity ratio is positivelyrelated to stock returns in the cross-section. The illiquidity ratioovercomes the shortcoming of stock turnover in that it incorporatesprice movement.2 Hasbrouck (2009) compares various price impactmeasures constructed from daily and microstructure data. He findsthat the Amihud illiquidity ratio is most strongly correlated withmicrostructure-based price impact measures. Goyenko et al. (2009)also find that the Amihud measure does a good job in capturing priceimpact.

Similar to other liquiditymeasures, the illiquidity ratio also has somelimitations. As Grossman and Miller (1988) point out, the illiquidityratio is usually obtained based on averaged price changes and averagedtrading volume from the past. Therefore, it cannot answer the questionof how the stockprice is influencedby the suddenarrival of a large trade.Further, it cannot distinguish whether the price fluctuations are due tothe lack of liquidity or the arrival of new information. A stock mightexperience large price fluctuations not because it is illiquid but becausenew information arrives frequently. To make the liquidity proxiesconsistent,weflip the signof the illiquidity ratio so that it is ameasureofliquidity.

2 Assume that stock A and stock B have the same turnover ratio over the sameperiod, but stock A has a price movement of 3% and stock B has a price movement of6%. According to the turnover ratio, both stocks have the same level of liquidity.However, in reality stock A may be more liquid than stock B since for stock A, the samelevel of trading volume induces lower price movement.

183D. Chai et al. / International Review of Financial Analysis 19 (2010) 181–192

2.1.3. Return reversal measureThe return reversal measure, developed by Pastor and Stambaugh

(2003), captures the price changes associated with order flow.Following Pastor and Stambaugh (2003), the monthly return reversalmeasure for security i is obtained by running the following OLSregression:

rei;t + 1 = γ0 + γ1ri;t + λ½signðrei;tÞ × voli;t � + εi;t ð3Þ

where ri,t+1e is the excess return with respect to the value-weighted

market index return for firm i on day t+1, ri,t is the return for firm i onday t, sign(ri,te ) is the sign of the excess return with respect to thevalue-weighted market index return for firm i on day t, and voli,t is thetrading volume in millions of dollars for firm i on day t. The coefficientλ measures the expected return reversal for a given trading volume.

The return reversal measure is in line with the concept of the priceimpact (resiliency) dimension of liquidity. The basic idea in this modelis that an asset is considered liquid if it is able to absorb large amountsof trading quickly without a big change in its price. In a quote-drivenenvironment, the return reversal is a form of compensation to marketmakers for bearing higher risk when facing selling (buying) pressuresfrom liquidity or non-informational trades. Thus, lambda in Eq. (3)should be negative and larger in absolute value when liquidity is low.However, the absence of dealers on the Australian Securities Exchange(ASX) suggests that the return reversal effect may be less relevant,when compared to markets such as NYSE.

When using the return reversal measure, we have to be cautiousabout the role that volume can play in current and lagged returns.Llorente, Michaely, Saar, and Wang (2002) show that stocks accompa-nied with a high degree of information-motivated trades producemorevolume-related return continuations. This return continuation wouldweaken the volume-related return reversal. Recently, Goyenko et al.(2009) find that the return reversal measure has a low correlation withmicrostructure-based price impact measures and sometimes has thewrong sign. It is important to note that Pastor and Stambaugh (2003) donot apply the lambda directly for individual stocks, but use a portfolioapproach instead. Moreover, they employ data filtering rules that arelikely to reduce the occurrence of extreme values for their measure.Pastor and Stambaugh (2003) exclude stocks with less than 15 days ofreturn observations in a givenmonth. This criterion could exclude quitea few small firms in the Australian market. Therefore, we set a weakerrule that firms only need to have at least 10 return observations in agiven month.3

2.1.4. Proportional spreadThe proportional bid–ask spread for stock i in month t is given by:

pspreadi;t =1Di;t

∑Di;t

d=1ðpAi;d;t−pBi;d;tÞ= ð0:5pAi;d;t + 0:5pBi;d;tÞ ð4Þ

where pi,tA (pi,tB ) is the daily closing ask (bid) prices for stock i on day d

in month t and D is the number of daily observations for stock i inmonth t.

The proportional spread is a widely usedmeasure of asset liquidityin the literature. Early research focuses on quoted bid–ask spread(difference between the ask price and the bid price), which is a directmeasure of transaction costs. Microstructure theory decomposes thespread into two components. The first component allows marketmakers to generate revenue from order flow to cover inventory costsand order processing fees. The second is an adverse selectioncomponent, which arises because market makers are facing investors

3 This filtering rule does not affect our results. The results are robust when either 5or 15 return observations are the minimums imposed for inclusion. This will bediscussed further in Section 3.

who are better informed than they are. However, bid–ask spreads arenot special to quote-driven markets. Glosten (1994) shows that bid–ask spreads are positively associatedwith adverse selection costs in anorder-driven trading environment, suggesting that the bid–ask spreadrepresents the cost of supplying immediacy. This finding is supportedby Handa, Schwartz and Tiwari (1998) who claim that the bid–askspread is a natural property of an order-driven market becausemarket participants are willing to pay for price certainty.

Despite being a widely used liquidity proxy, the bid–ask spreadhas certain shortcomings. As noted in Grossman and Miller (1988),buying and selling do not appear simultaneously but are randomlyseparated in time. The transaction price may occur outside or withinthe bid and ask prices. This is because when buying securities, limitorder customers may be willing to pay more than the bid price tominimise the price risk associated with waiting. Therefore, the spreadcannot serve as a reliable measure of the trading cost. Brennan andSubrahmanyam (1996) also argue that the bid–ask spread is a noisymeasure for the same reason. Further, large price stocks normallyhave wider spreads, but this does not really mean that they areilliquid. The proportional spread overcomes the problem that quotedspread is an increasing function of stock price. For consistency, we flipthe sign of the proportional spread to make it a liquidity measure.

2.1.5. Zero return measureThe proportion of zero daily returns observed over the relevant

month is calculated as:

zeroi;t = zeroreturni;t = tradingdayi;t ð5Þ

where zeroreturni,t is the number of zero daily return days for stock i inmonth t, and tradingdayi,t is the number of trading days for stock i inmonth t.

Lesmond et al. (1999) argue that zero returns occur when thetransaction cost threshold is not exceeded for marginal traders whomay be informed or uninformed. For informed traders, they are likelyto reduce their desired trades or choose not to trade wheninformation is not sufficient to compensate the cost of transacting.Therefore, there will be no pricemovement from the previous day. Forliquidity traders, they will generally choose not to trade if liquidity islow and the transaction costs are high. As a result, price will alsoremain unchanged. Lesmond et al. (1999) show that the zero returnmeasure is negatively related with firm size and is positively relatedwith spread measures, which is consistent with the transaction costeffect on stock returns. Bekaert, Harvey and Lundblad (2007) find thatthe zero return measure is to some degree correlated with otherliquidity measures such as stock turnover and bid–ask spreads acrossemerging markets. They also find evidence that this measuresignificantly predicts future returns in emerging equity markets.

The zero returnmeasure is readily obtainable since it only requiresdaily stock price information. However, there are some limitationswith the zero return measure. As noted in Bekaert et al. (2007), dailyzero returns may occur because of a lack of information flow. Smallerstocks may automatically show a higher level of non-tradingcompared to larger stocks. Further, the zero return measure ignoresprice fluctuation within a day, and therefore, it cannot truly representthe trading behaviour of stocks. To convert the measure into aliquidity proxy, it is modified as 1−zeroi,t.

2.1.6. Turnover-adjusted number of zero daily volumesLiu (2006) proposes a new liquidity measure that aims to capture

multiple dimensions of liquidity and places a particular focus ontrading speed. The liquidity measure is defined as:

LMi;t = NoZVi;t +1= ðturnoveri;tÞ

Deflator

� �×

21NoTDt

ð6Þ


whereNoZVi,t is the number of zero daily trading volumes for stock i inmonth t; turnoveri,t is the stock turnover rate for stock i in month tobtained from Eq. (1); NoTDt is the total number of trading days in themarket in month t; and the deflator4 is set to 480,000 as suggested inLiu (2006). Volume data for each stock are collected on a daily basis.

NoZV serves as an indicator of liquidity — the lower the number ofzero daily trading volumes, the more frequent the trade and, thus, themore liquid the stock. It reflects the continuity of trading and potentialdelay in executing a trade (Liu, 2006). To some extent, the turnovercomponent captures the notion of how much quantity has beentraded. It acts as a tiebreaker when two stocks have the same numberof zero daily trading volumes. Therefore, stocks that LM classifies asmost liquid are those that are traded frequently and have largeturnover over the relevant month. Multiplication by the factor 21/NoTD standardizes the number of trading days in a month to 21 andtherefore, makes LM comparable over time.

In sum, LM uses the number of zero daily trading volumes toidentify the liquidity of stocks, and then it relies on turnover todistinguish between stocks that have the same level of liquidity asclassified by the number of zero daily volumes. The role of NoZV is alsosimilar to the number of zero daily returns in Lesmond et al. (1999).Therefore, LM also reflects the trading cost dimension of liquidity. Theturnover component in LM overcomes the potential size effect in thenumber of zero daily trading volumes. However, it has a short-coming similar to the turnover measure — it does not consider stockprice movement. For consistency, we flip the sign of LM so that it is ameasure of liquidity.

2.1.7. Summary of liquidity proxiesIn sum, each of the six liquidity proxies captures a different dimension

of liquidity. Proportional spread and the zero return measure can becategorised as measures of tightness since both proxies reflect tradingcosts. The illiquidity ratio represents the pricemovement associatedwithtrading volume and therefore, it is related to depth/price impact. Thereturn reversal measure captures resiliency. Finally, stock turnover andthe turnover-adjusted number of zero daily volumes represent immedi-acy because both proxies reflect trading speed and trading frequency.

There is no consensus on which is the superior liquidity proxy. It isalso important to note thatwhile they are all plausible liquidity proxies,each of them captures a particular element of liquidity and tradingbehaviour. For example, Stoll (2000)points out that spreads capture realfriction and price impact measures represent informational friction.Further, since our liquidity proxies are obtained from low-frequencydata instead of intraday data, they are likely to contain some noise.Nevertheless, as the liquidity proxies that we employ address the fourseparate dimensions of liquidity, they can help us to understand the rolethat liquidity plays in financial markets.

In the subsequent analysis, we refer to stock turnover asTURNOVER; the Amihud (2002) illiquid ratio as AMIHUD, the returnreversal measure as PS; proportional bid–ask spread as PBA; the zeromeasure as ZERO; and the turnover-adjusted number of zero dailyvolumes proposed by Liu (2006) as LM.

2.2. Determinants of liquidity

In this section, we briefly review the literature to provide a contextfor the current study. Stock liquidity can be measured by the tradingcost for an immediate transaction. Traders need a price concessionwhen buying the asset immediately and they can then sell the asset

4 The reciprocal of turnover produces a wide range of numbers that can be verylarge or very small, depending on the magnitude of the monthly turnover rate. Thedeflator is used to ensure that 0b [(1/xmonthturnover)/deflator]b1, so stocks that havethe same number of zero daily volumes (NoZV) can be further differentiated.

according to some optimal policy. Demsetz (1968) shows that thedifference between the bid and ask price (bid–ask spread) canrepresent the trading cost for such transactions. Under this view, thespread serves as a (inverse) proxy for stock liquidity. If the spread isimportant, it is essential to understand the sources of the spread. AfterDemsetz (1968), studies such as Tinic (1972), Benson and Hagerman(1974), Branch and Freed (1977), Stoll (1978) and Stoll and Whaley(1983) examine variables that could influence the spread. Thevariables can be divided into three categories: (1) variables thathave an effect on the cost of positioning for an individual security (i.e.trading characteristics), (2) variables associated with the structure ofthe institutions that provide liquidity (e.g. capitalisation of theportfolio and securities included in the portfolio), and (3) variablesthat have an influence on the profit margin of the specialists (e.g.market structure and competition). The empirical results show thatvariables related to stocks' trading characteristics are most influential.

Recent studies such as Chordia, Roll and Subrahmanyam (2000) andStoll (2000) extend early studies by employing different alternativeliquidity proxies. Using a cross-sectional regression approach, Chordiaet al. (2000) find that variables such as stock price, volatility and tradingvolume are related to the quoted spread, the proportional spread,quoteddepth, the effective spread and theproportional effective spread.Except stock price, the influence of volume and volatility are consistentthrough different liquidity proxies.

Stoll (2000) uses ten different liquidity proxies constructed frommicrostructure data to examine whether they are related in the sameway to stocks' trading characteristics. The purpose of his investigationis to understand the common sources of different liquidity measures.His sample includes stocks from both the NYSE/AMEX and Nasdaqover a three-month period from December 1997 to February 1998.The liquidity proxies include various spread measures, covariance ofprice changes, price impactmeasures, and the volatility at the openingof the market. He first demonstrates that liquidity measures thatcapture different dimensions of liquidity are not strongly correlated.He then performs cross-sectional regressions having differentliquidity proxies regressed on stock price, return variance, tradingvolume and number of trades. These trading characteristics arefound to be important determinants of liquidity. However, not everyliquidity proxy is related in the same way to the estimated charac-teristics. The results imply that liquidity is a multifaceted concept.Moreover, the influence of stock price on price impact measures isdifferent in the two markets. Stoll (2000) argues that this finding mayindicate that information is incorporated into stock prices differentlyin the two markets.

The underlying principle on the relationship between liquidity andstock characteristics is based on order execution and inventorycontrol (Stoll, 2000). Large trading volume reduces the risk of carryinginventory for a period of time, which should increase stock liquidity.Higher return volatility increases the risk of holding inventory, and itshould have a negative effect on stock liquidity. Stock price controlsthe effects of price discreteness and can be used as a proxy for risk, aslow price stocks tend to be riskier. The transaction costs of small sizefirms should also be higher than for large size firms (Stoll andWhaley,1983). Based on this reasoning, our testable hypotheses are:

Hypothesis 1a. Price per share is expected to be positively related toliquidity.

Hypothesis 1b. Trading volume is expected to be positively related toliquidity.

Hypothesis 1c. Return volatility is expected to be negatively relatedto liquidity.

We refer to price per share at the end of each month as PRICE;return volatility of daily stock returns in each month as VARIANCE;and trading volume (aggregated in each month) as VOLUME.

7 Weuse this rule for three reasons. First, the return reversalmeasure requires at least fourreturnobservationswithin amonth. Second,weneed about the samenumber of daily returnobservations in order to calculate the standard deviation (volatility) of a stock's return. Third,the liquidity proxies can be estimatedwith less noisewhen a certain number of observationsare required. However, as will be shown in Table 1, the filtering criteria skew our sampletowards larger firms. As a robustness check to ensure that our results are not influenced byfirm size, we impose a weaker restriction that stocks only need to have 5 valid returnobservations in a month. This would allow us to include more small firms. As a furtherrobustness check, we look at results in a sub-period (e.g. after year 1995) where the data


2.3. Other potential determinants

We incorporate two additional variables into our analysis —

absolute monthly stock return and the thin tradingmeasure proposedby Beedles, Dodd and Officer (1988).

Absolute monthly stock return (ABSR) can be treated as analternative measure of volatility and may be used as a measure ofinformation flow.5 The advantage of this measure is that it is simple tocalculate, particularly in comparison to conventional volatility mea-sures. Similar to volatility, ABSR should have a negative influence onliquidity. ABSR is measured as the absolute value of a stock's monthlyreturn.

Beedles et al. (1988) use the difference between the last pricedate and last trading date in a month to create a crude proxy forthe proportion of missing daily returns. Specifically, the measure isdefined as:

BEEDLES = f100−½100= ðn + 1Þ�g= 100 ð7Þ

where n is the difference in time (measured in days) between the lastprice date and last trading date in each month from the Centre forResearch in Finance database (CRIF). For example, if a stock is traded onthe last trading day of themonth, n=0 and BEEDLES=0 (0%)— that is,it is assumed that the stock traded every day. As another example, if thestock's last trade was on the second last trading day, n=1 andBEEDLES=0.5 (50%)— that is, it is assumed that the stock traded everysecond day.

Beedles et al. (1998) note that this measure is not an ideal proxyfor liquidity. It is possible that a stock has no difference between thelast price date and the last trading date in a month throughout itstrading history. Nevertheless, they find that small size portfolios havea larger proportion of daily missing returns, indicating that smallstocks are less liquid. Their results show that liquidity is a partialexplanation for the size effect. Since the BEEDLES measure aims tocapture the thin trading aspect of stock illiquidity, it should benegatively related with liquidity. Thus, out testable hypotheses forthese two variables are:

Hypothesis 1d. Absolute monthly return is expected to be negativelyrelated to liquidity.

Hypothesis 1e. Beedles' thin trading measure is expected to benegatively related to liquidity.

3. Data and methodology

3.1. Data sources and sample coverage

The analysis in this paper is carried out at the monthly level fromJanuary 1991 to September 2006. Thedata come from twomain sources.Daily stock information such as stock price, trading volume and thevalue-weighted market index are obtained from the Securities IndustryResearch Centre of Asia-Pacific (SIRCA). Month end bid and ask pricesare also obtained from SIRCA. Company information such as marketcapitalisation, number of shares outstanding and monthly stock returnis obtained from the Centre for Research in Finance (CRIF) database.

In the calculation of the liquidity proxies, a daily observation isexcluded if the stock did not trade on the current or previous day.6

5 The idea is similar to using the absolute value of daily stock returns to proxy daily returnvolatility (e.g. Duffee, 1995; Ding, Granger and Engle, 1993; Chordia, Shivakumar andSubrahmanyam, 2004).

6 As an alternative way to deal with the non-trading issue, we assign a zero return tothe current trading day if the stock did not trade on the previous day. The results arerobust and are available upon request from the authors.

Finally, a stock must have at least 10 valid return observations in agiven month.7 Panel A of Table 1 shows market capitalisations andcoverage of our sample versus the population in the CRIF database.From the table, on average, our sample covers more than 60% of totalstocks available from 1995 to 2005. The coverage is lower from 1991to 1994 with less than 40% coverage in 1991 and 1992. As expected,our data filtering rules have excluded quite a few small stocks.Compared with the CRIF sample, our minimum market capitalisationis higher and the median market capitalisation is more than double.Nevertheless, our sample is representative of the Australian marketgiven that, on average, it comprises more than 80% of the market'stotal capitalisation.

Month end bid and ask prices are not available for all stocks in oursample. In order to calculate the spread, we revert to a subset of stocksthat have bid–ask prices. Panel B of Table 1 shows the availability ofthe bid–ask spread data. Comparing the number of companies inPanel A and Panel B, the sample coverage is about 10 percentagepoints lower in the latter. In our empirical analysis, we use the samplepresented in Panel B of Table 1 only in spread related results.

3.2. Fama–MacBeth cross-sectional regressions

To examine whether trading characteristics are significant deter-minants of liquidity, following Stoll (2000), we run cross-sectionalregressions using monthly data according to:

Liquidityjt = α0t + ∑K

k=1βktTradingActivityjkt + εjt ð8Þ

where j=1,2,…,N; t=1,2,…,T; Liquidity is the liquidity proxy forstock j in month t; TradingActivity represents each trading charac-teristic variable such as stock price, volatility, and trading volume. Theresearch method involves three stages. In stage one, the dependentvariable (each liquidity proxy) and independent variables (tradingcharacteristics) required for the cross-sectional regression are con-structed. We then estimate different versions of Eq. (8) each monthfrom January 1991 to September 2006 in stage two. Following Stoll(2000) and Chordia et al. (2000), the regressions are estimated usingOLS. In stage three, we compute the average coefficient and variancefrom the time series of the cross-sectional regression coefficientsgenerated in stage two.

We follow the Fama and MacBeth (1973) methodology and applyequal weight to all slope coefficients in estimating the averagecoefficient.8 Chordia et al. (2000) note that the coefficients from theestimated regression are likely to be correlated across time if boththe dependent variable and independent variables are not returns.

coverage is higher. Similar results are obtained under different filtering rules. Other datafiltering criteria such as the impact of low price stocks or IPOs were also considered.Specifically, the influence of trading characteristics remain similar if we exclude stocks withpricebelow10centsor if stockswere IPOs for thecalendaryear. Theresults areavailable fromthe authors upon request.

8 We chose the Fama–MacBeth procedure over the pooled time-series cross-sectionapproach because the error terms in the pooled regression are likely to be cross-sectionally correlated over time (Cochrane, 2001). The standard error will be biasedwhen errors are correlated. Petersen (2009) refers to this as a time effect and theFama–MacBeth procedure is designed to address this effect.

Table 1Comparison ofmarket capitalisation and sample coverage. At the end of each year, we calculate summary statistics of stocks' market capitalisation in our sample and in the CRIF database.Min, median and mean are in $millions. Max and total market capitalisation are in $billions. Panel A (B) presents the results for the sample without (with) bid–ask spread data.

Market capitalisation — sample Market capitalisation — all stocks (CRIF) Coverage percentage

Year Number offirms

Min.($M)

Max.($B)

Median($M)

Mean($M)

Total($B)

Number offirms

Min.($M)

Max.($B)

Median($M)

Mean($M)

Total($B)

Number offirms

Marketcap.

Panel A: without bid–ask spread data1991 302 1.36 21.51 72.55 618.43 186.77 926 0.05 21.55 8.98 267.10 247.34 32.61 75.511992 328 1.08 21.52 80.23 595.38 195.28 893 0.02 27.29 10.75 301.45 269.19 36.73 72.541993 565 1.45 29.12 50.92 532.76 301.01 1008 0.05 29.12 19.57 367.81 370.75 56.05 81.191994 446 2.12 33.60 94.62 594.16 265.00 1099 0.17 33.60 19.13 309.39 340.02 40.58 77.941995 580 1.69 37.03 58.46 563.76 326.98 1105 0.46 37.03 20.56 358.75 396.42 52.49 82.481996 750 0.72 35.60 49.24 552.19 414.14 1125 0.47 35.60 26.04 411.39 462.82 66.67 89.481997 621 1.63 30.26 73.42 734.38 456.05 1145 0.31 30.26 23.12 445.97 510.64 54.24 89.311998 626 0.65 35.62 83.76 898.36 562.37 1128 0.31 35.62 21.56 532.53 600.70 55.50 93.621999 841 1.59 53.17 54.47 764.07 642.58 1207 0.68 53.17 31.37 583.23 703.96 69.68 91.282000 862 1.15 43.70 42.02 764.40 658.91 1315 0.95 54.03 24.16 564.93 742.88 65.55 88.702001 772 0.92 49.74 56.35 922.05 711.82 1290 0.04 49.74 21.75 579.93 748.11 59.84 95.152002 726 0.89 48.18 62.08 916.78 665.58 1307 0.17 48.18 20.35 528.18 690.34 55.55 96.412003 965 1.45 45.76 57.36 803.16 775.05 1358 0.16 45.76 29.93 618.56 840.01 71.06 92.272004 1119 1.05 54.95 59.00 879.47 984.13 1488 0.58 54.95 33.88 701.55 1043.90 75.20 94.272005 1112 1.94 81.67 71.84 1038.59 1154.91 1614 0.65 81.67 34.95 763.19 1231.79 68.90 93.76

Panel B: with bid–ask spread data1991 245 1.36 21.51 84.62 696.40 170.62 926 0.05 21.55 8.98 267.10 247.34 26.46 68.981992 268 1.08 21.52 91.28 654.79 175.48 893 0.02 27.29 10.75 301.45 269.19 30.01 65.191993 459 1.45 29.13 65.29 602.77 276.67 1008 0.05 29.12 19.57 367.81 370.75 45.54 74.621994 368 2.12 33.61 95.41 645.97 237.72 1099 0.17 33.60 19.13 309.39 340.02 33.48 69.911995 501 1.69 37.03 58.53 590.22 295.70 1105 0.46 37.03 20.56 358.75 396.42 45.34 74.591996 652 1.45 35.60 46.13 573.69 374.04 1125 0.47 35.60 26.04 411.39 462.82 57.96 80.821997 551 1.63 30.26 64.27 753.53 415.19 1145 0.31 30.26 23.12 445.97 510.64 48.12 81.311998 551 0.65 35.62 72.97 885.02 487.65 1128 0.31 35.62 21.56 532.53 600.70 48.85 81.181999 724 1.59 53.17 48.27 829.89 600.84 1207 0.68 53.17 31.37 583.23 703.96 59.98 85.352000 690 1.15 43.70 44.86 876.68 604.91 1315 0.95 54.03 24.16 564.93 742.88 52.47 81.432001 592 0.92 49.74 63.45 1047.32 620.01 1290 0.04 49.74 21.75 579.93 748.11 45.89 82.882002 544 0.89 48.18 67.86 1008.21 548.47 1307 0.17 48.18 20.35 528.18 690.34 41.62 79.452003 675 2.18 45.76 69.97 930.94 628.38 1358 0.16 45.76 29.93 618.56 840.01 49.71 74.812004 781 1.05 54.95 68.75 958.26 748.40 1488 0.58 54.95 33.88 701.55 1043.90 52.49 71.692005 774 2.53 81.67 79.24 1131.35 875.66 1614 0.65 81.67 34.95 763.19 1231.79 47.96 71.09


Cochrane (2001) also suggests that ignoring such correlation could havea large impact on the inferences made. Following Cochrane (2001), theadjusted standard error is obtained by multiplying the standard errorby

ffiffiffiffiffiffiffiffiffiffiffiffiffi1 + p

p=

ffiffiffiffiffiffiffiffiffiffi1−p

p, where p is the first-order auto-correlation of the

estimated coefficients across the sample period.

4. Empirical results

4.1. Descriptive statistics

4.1.1. Basic resultsPanel A of Table 2 reports the time-series average of the cross-

sectional statistics of the liquidity proxies and stocks' tradingcharacteristics. Recall that we flipped the sign of AMIHUD, LM andPBA to make them liquidity measures. Therefore, a negative sign forthe statistics (except standard deviation) is expected for AMIHUD, LMand PBA. Among the six liquidity proxies, AMIHUD exhibits the largeststandard deviation. PS has a wide range of values from positive tonegative. We expect the value of PS to be negative and larger inabsolute value when liquidity is low. This is due to the return reversaleffect — the greater the order flow the greater the change in thesubsequent expected return. TURNOVER, ZERO and PBA have a lowervariation compared to the other proxies.

The lowest priced stock in our sample is less than 10 cents, while thehighest is above 60 dollars. This suggests that our sample comprisesstocks across a wide range of the size spectrum. It is worth mentioningthat BEEDLES is zero in minimum, lower quartile, median and upperquartile. Recall that BEEDLES is calculated as the difference between the

last price date and the last trading date. This difference is, however, zerofor most of the stocks. Stocks are deemed to have serious non-synchronous trading problems if the difference is greater than zero. Thesummary statistics reflect the nature of the BEEDLES measure. Bothliquidity proxies and trading characteristic variables display consider-able positive skewness with the sample means exceeding the medians.Therefore, in our empirical analysis we take the logarithmic transfor-mation of PRICE and VOLUME. VARIANCE, ABSR and BEEDLES are nottransformed because they may be zero for some stocks.

4.1.2. Size groupsTo understand the distributions of the liquidity proxies and trading

characteristics further, we separate the sample into size groups. In eachmonth, stocks are first sorted based on their current month's marketcapitalisation and are then separated equally into three size groups.

Panels B, C and D of Table 2 report summary statistics for small,medium and large size firms, respectively. In general, small firms havethe lowest average price and the highest return volatility. The meanvalue of PBA, LM, AMIHUD and ZERO increases from the small firm tothe large firm sample, which indicates that small firms are less liquidcompared to medium-size and large firms. The mean value of PS doesnot exhibit a strong pattern across size groups. The small size grouphas the largest average TURNOVER and it decreases dramatically fromsmall to medium-size firms. The difference is smaller betweenmedium-size and large firms. This finding is in contrast to the resultson the other liquidity proxies and could be explained by the resultson VOLUME. On average, small and large firms have a higher mean,lower quartile, median and upper quartile VOLUME than medium-

Table 2Summary statistics. Mean, minimum, lower quartile, median, upper quartile, maximum and standard deviation are computed eachmonth cross-sectionally and then averaged acrosstime from January 1991 to September 2006. AMIHUD is the liquidity ratio from Amihud (2002). PS is the return reversal measure from Pastor and Stambaugh (2003). TURNOVER isthe stock turnover rate. ZERO is the zero return measure from Lesmond et al. (1999), but is modified as (1 — the proportion of zero daily returns). LM is the turnover-adjusted zerodaily volumes from Liu (2006). PBA is the proportional bid–ask spread. PRICE is stock price at the end of each month. VARIANCE is the variance of stock returns. VOLUME is theaggregate trading volume. BEEDLES is the thin tradingmeasure proposed by Beedles et al. (1988). ABSR is the absolute stockmonthly return. All the variables are computedmonthly.VOLUME ismeasured in $millions. VARIANCE is multiplied by 100. Stocks are sorted based on their current month's market capitalisation in eachmonth and then allocated into threeequal groups: small, medium and large. Panel A presents the results for the entire sample whereas Panels B, C and D present the results for the small firm, medium firm and large firmsample, respectively. The F-tests (Kruskal–Wallis (KW) tests) are based on the null hypothesis that the mean (median) values of indicated variables are equal across the three sizegroups. P-values are reported for both the F and KW tests in Panel E.

Mean Min Lower quartile Median quartile Upper quartile Max Standard deviation

Panel A: all firms sample(a) Liquidity proxies

AMIHUD −1.7954 −101.5758 −1.5021 −0.5063 −0.1393 −0.0013 5.7740PS 0.0017 −6.1719 −0.0341 0.0001 0.0349 7.1513 0.5337TURNOVER 0.0453 0.0001 0.0127 0.0253 0.0496 1.1577 0.0771ZERO 0.6953 0.0672 0.5782 0.7148 0.8339 0.9997 0.1825LM −1.6424 −9.5488 −2.8411 −0.4471 −0.0367 −0.0366 2.1404PBA −0.0380 −0.3280 −0.0518 −0.0273 −0.0139 −0.0010 0.0364

(b) Trading characteristicsPRICE 2.0738 0.0083 0.2160 0.7511 2.1586 65.9903 4.4142VARIANCE 0.3271 0.0006 0.0288 0.0889 0.2653 30.8573 1.6245VOLUME 9.2401 0.0215 0.9462 2.5707 7.6052 360.9786 23.471BEEDLES 0.0360 0.0000 0.0000 0.0000 0.0000 0.8961 0.1397ABSR 0.1207 0.0000 0.0308 0.0730 0.1510 2.1485 0.1689

Panel B: small firms sub-sample(a) Liquidity proxies



Panel C: medium-size firms sub-sample(a) Liquidity proxies



Panel D: Large firms sub-sample(a) Liquidity proxies



Panel E: P-values for tests of equality of means and medians

F-tests KW tests

(a) Liquidity proxiesAMIHUD 0.00** 0.00**PS 0.99 0.91TURNOVER 0.00** 0.00**

(continued on next page)

KW tests


Table 2 (continued)

Mean Min Lower quartile Median quartile Upper quartile Max Standard deviation

ZERO 0.00** 0.00**LM 0.00** 0.00**PBA 0.00** 0.00**

(b) Trading characteristicsPRICE 0.00** 0.00**VARIANCE 0.00** 0.00**VOLUME 0.00** 0.00**BEEDLES 0.00** NAABSR 0.00** 0.00**

** and * denote significance at the 1% and 5% levels, respectively.

Panel E: P-values for tests of equality of means and medians

F-tests KW tests

(a) Liquidity proxies


sized firms do. This suggests that small and large firms are tradedmore actively than medium-size firms are. Small firms generally havea lower total number of shares outstanding. As a result, high turnoverrates are observed among small firms. Since trading volume plays animportant role in estimating TURNOVER and PS, it is not surprising tosee a non-linear pattern across size groups. The relationship betweensize and TURNOVER is also similar to those found in prior Australianstudies such as Chan and Faff (2003). Chan and Faff (2003) find thatsize is not correlated with turnover.

To compare the difference in values formally, we conduct F-tests(Kruskal–Wallis (KW) tests) to examine whether the mean (median)values of an indicated variable are statistically different across thethree size groups. The p-values of these two tests are reported in PanelE. The null hypothesis of equal means (medians) is rejected for all theliquidity proxies except PS, which provides evidence that liquidityvaries across the size groups. Regarding trading characteristics, thereis also evidence that the mean and median values vary with firm size.On average, large firms have higher stock prices, larger tradingvolumes and lower return volatility. It should be noted that we cannotperform the KW tests on BEEDLES because it has zero median valuesin each of the size groups. In sum, results in Table 2 support the viewthat smaller firms are less liquid when compared to larger firms.

4.2. Correlations

In Table 3, we report the averagemonthly cross-sectional correlationsbetween the liquidity proxies and trading characteristics, covering theperiod 1991 to 2006. In Panel A, the correlations are shown for the fullsample. We expect that the correlations of liquidity proxies that capturesimilar trading behaviours would be stronger. Table 3 shows that thecorrelations between liquidity proxies are generally low in the cross-section except for LMwith PBA, ZEROwith LM, and ZEROwith PBA. BothZEROandPBA capture a similar dimension (tightness) of liquidity so theirhigher correlation is not surprising. The component of zero tradingvolumes in LM is also similar to the concept of ZERO so again, the highercorrelation is expected. These three liquidity proxies also exhibit strongcorrelations with SIZE.

Except for LM, both AMIHUD and TURNOVER have low correlationswith the other proxies. The weak correlation between AMIHUD andTURNOVER is similar to Sadka (2006), whofinds that stock turnover hasa low correlation with price impact measures and firm size in the USmarket, indicating that volume may not always be a good proxy forliquidity.9 PS is generally uncorrelatedwith the liquidity proxies used inour sample. This finding is also similar to Eckbo and Norli (2002) andGoyenko et al. (2009) in the US setting.10 Pastor and Stambaugh (2003)

9 Sadka (2006) finds that the cross-sectional correlation between both the Amihudilliquidity ratio and firm size with stock turnover is close to zero.10 For example, Eckbo and Norli (2002) find the average time-series correlationacross firms is 0.019 between PS and stock turnover and −0.023 between PS andproportional quoted spread.

report that the characteristic of their liquiditymeasure is sensitive to thespecification of themodel given in Eq. (3).11 Further, Panel A shows thatLM tends to have better correlations with all the other proxies. Thisfinding is consistent with the intuition that LM captures multipledimensions of liquidity (Liu, 2006).

Consistent with the findings in Table 2, though small in magnitude,there is anegative relationshipbetweenTURNOVERandSIZE. This resultis similar to Chan and Faff (2003), who find that there is no relationshipbetween stock turnover and size, and the correlation is −0.064 in thecross-section in the Australian market. VOLUME is positively relatedwith all liquidity proxies except for PS. As expected, PRICE is highlycorrelated with SIZE and VARIANCE is correlated with ABSR.

Table 2 suggests thatfirm size has some influence on the relationshipbetween liquidity and trading characteristics. Accordingly, we considerto what extent the correlations are impacted by different size groups.Panels B, C andD of Table 3 report the cross-sectional correlations for thesmall, medium-size and large firms, respectively. The correlations aregenerally consistent with the results in Panel A. Both AMIHUD andTURNOVER have stronger correlations with other liquidity proxies (andsize) in each size group. Comparing across the size groups, thecorrelations are stronger between liquidity proxies for larger firms.This result implies that large firms are priced more efficiently thanmedium-size and small firms. Moreover, theweak correlations betweenthe liquidity proxies observed in Panel A might be influenced by thepattern of tradingvolumeacross the size groups as shown in Table 2. Ourresults also suggest thatwhile these proxies all capture liquidity to someextent, they do not necessarily behave similarly because they capturedifferent dimensions of liquidity.

4.3. Regression results

4.3.1. Basic resultsTable 3 shows that the correlations among the employed liquidity

proxies are generally low suggesting that the cross-sectional behaviourof these proxies is quite divergent. In this section,we run cross-sectionalregressions to understand the sources of liquidity more fully. Theregression results are presented in Table 4. According to our hypotheses,we expect that stock price and trading volume (volatility) are positively(negatively) related with stock liquidity.12 From Table 4, except for PS,trading characteristics are significantly related with the liquidityproxies. Their influences are generally consistent with the hypothesesand their impacts are large and highly significant. The impact of thetrading characteristics on PBAand LM is consistentwith ourhypotheses.Firms with large prices, large trading volumes and low volatilities tend

11 Pastor and Stambaugh (2003) point out that one can consider 24 alternativespecifications of their model. For example, the dependent variable can be either theexcess or the total stock return. They report that the correlations between liquidityseries generated from different specifications are low.12 We do not include size in our regression analysis because it is highly correlatedwith stock price. Recall that we modified ZERO and flipped the sign of AMIHUD, LMand PBA to make them liquidity measures. The results are interpreted based on themodified liquidity proxies.

Table 3Correlation matrix of liquidity proxies and trading characteristics. AMIHUD is the liquidity ratio from Amihud (2002). PS is the return reversal measure from Pastor and Stambaugh(2003). TO is the stock turnover rate. ZERO is the zero return measure from Lesmond et al. (1999), but is modified as (1 — the proportion of zero daily returns). LM is the turnover-adjusted zero daily volumes from Liu (2006). PBA is the proportional bid–ask spread. The sign of AMIHUD, LM and PBA was flipped to make them represent liquidity. PRICE is stockprice at the end of each month. VARIANCE is the variance of daily stock returns. VOLUME is the aggregate trading volume. BEEDLES is the thin trading measure proposed by Beedleset al. (1988). ABSR is the absolute stock monthly return. All the variables are computed monthly. VOLUME is measured in $millions. PRICE, VOLUME and SIZE are logarithmictransformed. The correlations reported in the table are the time-series average of the monthly cross-sectional correlations. Stocks are sorted based on their current month's marketcapitalisation in each month and then allocated into three equal groups: small, medium and large. Panel A presents the correlations for the entire sample whereas Panels B, C and Dpresent the correlations for the small firm, medium firm and large firm sample, respectively.

AMIHUD PS TO ZERO LM PBA PRICE VARIANCE VOLUME SIZE ABSR BEEDLES

Panel A: all firms sampleAMIHUD 1PS −0.0313 1TO 0.0981 0.0003 1ZERO 0.0413 0.0082 0.0505 1LM 0.2793 0.0023 0.1017 0.3593 1PBA 0.1974 −0.0076 −0.0737 0.4170 0.5338 1PRICE 0.1534 −0.0116 −0.0449 0.3483 0.4272 0.6960 1VARIANCE −0.0967 0.0034 0.2487 −0.0762 −0.1740 −0.5365 −0.3837 1VOLUME 0.3558 0.0001 0.4331 0.2313 0.4761 0.1529 −0.1465 0.1050 1SIZE 0.1001 −0.0011 −0.2011 0.5047 0.4703 0.6851 0.8319 −0.3279 0.2689 1ABSR −0.0258 0.0063 0.3754 0.0171 −0.0822 −0.3038 −0.2791 0.3776 0.1306 −0.2869 1BEEDLES −0.0861 0.0022 −0.0328 −0.1430 −0.3635 −0.1987 −0.1357 0.0639 −0.1496 −0.1805 0.0086 1

Panel B: small firms sub-sampleAMIHUD 1PS −0.0084 1TO 0.1284 −0.0009 1ZERO −0.0848 0.0151 0.1566 1LM 0.2091 0.0036 0.2595 0.1417 1PBA 0.1884 −0.0074 0.0844 0.1907 0.3741 1PRICE −0.1495 0.0026 −0.0286 0.3123 −0.0006 0.4541 1VARIANCE −0.1142 0.0067 0.1813 0.0585 −0.0647 −0.4997 −0.3078 1VOLUME 0.3285 0.0004 0.5412 −0.0148 0.4658 −0.0072 −0.6127 0.2257 1SIZE 0.0630 0.0052 −0.1033 0.1618 0.2915 0.5092 0.4956 −0.2525 −0.0506 1ABSR −0.0070 0.0124 0.3183 0.1623 0.0442 −0.1837 −0.0685 0.3164 0.2122 −0.1067 1

Panel C: medium-size firms sub-sampleAMIHUD 1PS −0.0213 1TO 0.1745 0.0026 1ZERO −0.0143 0.0200 0.1805 1LM 0.3285 0.0135 0.2398 0.2241 1PBA 0.2114 −0.0121 0.1154 0.1571 0.3423 1PRICE −0.2305 0.0032 −0.1439 0.1781 −0.1744 0.4176 1VARIANCE −0.0193 0.0091 0.2881 0.1552 0.0380 −0.4110 −0.3342 1VOLUME 0.4075 0.0019 0.5957 0.1156 0.5261 0.0127 −0.6433 0.3053 1SIZE 0.0145 −0.0019 −0.1117 0.1280 0.1310 0.3774 0.4756 −0.2094 −0.0524 1ABSR 0.0388 0.0103 0.3753 0.2018 0.0972 −0.2000 −0.1589 0.4778 0.2934 −0.1156 1

Panel D: large firms sub-sampleAMIHUD 1PS −0.0274 1TO 0.2082 0.0031 1ZERO 0.1219 0.0009 0.2247 1LM 0.4511 −0.0010 0.2072 0.3034 1PBA 0.4558 0.0037 0.3259 0.4441 0.5446 1PRICE −0.1585 0.0045 −0.0560 0.3943 −0.0503 0.3584 1VARIANCE −0.1082 −0.0086 0.2129 0.0780 −0.0531 −0.3277 −0.2292 1VOLUME 0.4663 0.0053 0.5940 0.3452 0.5090 0.5527 −0.1719 0.0279 1SIZE 0.0554 0.0022 0.0906 0.4718 0.1623 0.4983 0.5647 −0.1786 0.4913 1ABSR −0.0351 −0.0076 0.2595 0.1135 −0.0039 −0.1575 −0.0974 0.4729 0.0585 −0.1088 1


to have higher PBA and LM. The result for PBA is also consistent withChordia et al. (2000), Stoll (2000) and Aitken and Frino (1996).

For ZERO, the sign of the coefficients is consistent with ourhypotheses except for VARIANCE and ABSR. Our results indicate thatstockswithhigher returnfluctuations tend tohavea lowerproportion ofzero daily returns (i.e. higher liquidity). In general, the price movementfor a stockwill be low if its proportion of zero daily returns is high and soourfindings are not surprising. ABSRhas the same influence since it is analternative measure of volatility. Moreover, firms with large prices andlarge trading volumes tend to have fewer zero daily returns.

The positive (negative) coefficient of VOLUME (VARIANCE) in theAMIHUD regressions indicates that price impacts are smaller for firmswith large volumes and they are larger when the volatility is high. Thisfinding is consistent with our hypotheses and Stoll (2000). The negativecoefficient of PRICE is puzzling. It indicates that the price movement

associated with trading volume is larger when the prices are large. Apossible explanation is as follows. In Table 2, we find some evidence thattrading volumes are higher for small and large firms (as opposed tomedium-size firms). If a large stock experiences a large price movement,given the same level of trading volume, it would have a larger priceimpact. Ourfinding is similar to that in Stoll (2000). Stoll (2000)finds thatfirms with large prices tend to have higher price impacts on the Nasdaq.He argues that this result may be influenced by the information that isincorporated into price.

TURNOVER displays a somewhat different cross-sectional patternthan the other liquidity measures. The results show that firms withsmaller prices and higher volatilities tend to have higher turnover rates.These results are not surprising given the findings in Table 2. Small firmshave higher TURNOVER than medium-size and large firms. Therelationship between TURNOVER and BEELDES may look odd at first

Table 4Fama–MacBeth cross-sectional regressions — full sample. Individual stock liquidity proxies are regressed cross-sectionally each month on the concurrent month's closing price(PRICE), the variance of daily returns for the concurrent month (VARIANCE), monthly aggregate dollar trading volume (VOLUME), monthly absolute stock return (ABSR) andBeedles' thin tradingmeasure (BEEDLES). PRICE and VOLUME are logarithmic transformed. AMIHUD is the liquidity ratio fromAmihud (2002). PS is the return reversal measure fromPastor and Stambaugh (2003). TURNOVER is the stock turnover rate. ZERO is the zero return measure from Lesmond et al. (1999), but is modified as (1— the proportion of zero dailyreturns). LM is the turnover-adjusted zero daily volumes from Liu (2006). PBA is the proportional bid–ask spread. The sign of AMIHUD, LM and PBA was flipped to make themrepresent liquidity. The coefficients are averaged across 189 trading months in the sample. T-statistics are adjusted for first-order auto-correlation and are reported in parenthesesbelow the coefficient estimates.

Intercept PRICE VARIANCE VOLUME ABSR BEEDLES Adj. R2

Hypothesised sign + − + − −

AMIHUD −20.2155(−38.14)**

−0.2955(−6.10)**

−158.1188(−8.44)**

2.9346(35.58)**

0.1612

−19.9357(−37.05)**

−0.4005(−8.86)**

−159.5008(−8.00)**

2.9145(34.76)**

−1.1611(−5.12)**

−1.1331(−5.74)**

0.1665

PS 0.0311(0.61)

0.0075(1.43)

0.8012(1.10)

−0.0050(−0.67)

0.0125

0.0299(0.59)

0.0087(1.46)

0.3065(0.41)

−0.0053(−0.69)

0.0376(1.97)*

0.0051(0.22)

0.0163

ZERO 0.1934(2.57)**

0.1626(7.21)**

4.7084(10.85)**

0.0817(7.73)**

0.3871

0.2019(2.83)**

0.1669(6.93)**

3.8426(9.31)**

0.0785(7.44)**

0.1445(19.04)**

−0.0302(−7.76)**

0.4005

TURNOVER −0.2445(−9.30)**

−0.0065(−3.93)**

2.6707(8.08)* *

0.0438(10.27)**

0.3897

−0.2340(−9.91)**

−0.0032(−1.79)

1.4173(6.21)**

0.0403(11.00)**

0.1258(14.79)**

0.0063(4.20)**

0.3413

LM −12.367(−40.29)**

1.1055(25.60)**

−37.3496(−11.80)**

1.7250(35.43)**

0.3799

−11.4635(−37.96)**

0.978(27.18)**

−34.5721(−11.18)**

1.6074(34.05)**

−0.2549(−4.36)**

−3.7646(−60.22)**

0.4506

PBA −0.1142(−33.69)**

0.0309(25.61)**

−2.7036(−11.57)**

0.0135(25.88)**

0.6536

−0.1100(−31.57)**

0.0296(25.00)**

−2.6774(−12.01)**

0.0131(24.40)**

−0.0135(−6.77)**

−0.0168(−9.91)**

0.6676


Table 5Fama–MacBeth cross-sectional regressions — small firm sample. Individual stock liquidityproxies are regressed cross-sectionally each month on the concurrent month's closing price(PRICE), the variance of daily returns for the concurrent month (VARIANCE), monthlyaggregatedollar tradingvolume(VOLUME)andmonthlyabsolute stock return (ABSR). PRICEand VOLUME are logarithmic transformed. AMIHUD is the liquidity ratio from Amihud(2002). PS is the return reversal measure from Pastor and Stambaugh (2003). TURNOVER isthe stock turnover rate. ZERO is the zero return measure from Lesmond et al. (1999), but ismodified as (1— the proportion of zero daily returns). LM is the turnover-adjusted zero dailyvolumes from Liu (2006). PBA is the proportional bid–ask spread. The sign of AMIHUD, LMand PBA was flipped to make them represent liquidity. The coefficients are averaged across189 trading months in the sample. T-statistics are adjusted for first-order auto-correlationand are reported in parentheses below the coefficient estimates.

Intercept PRICE VARIANCE VOLUME ABSR Adj. R2

Hypothesised sign + − + −

AMIHUD −26.5802(−26.96)**

0.4805(4.02)**

−156.7351(−7.98)**

4.0127(24.55)**

0.1760

−26.8475(−27.40)**

0.5101(4.32)**

−156.7451(−7.96)**

4.0822(25.18)**

−0.9152(−3.09)**

0.1783

PS −0.0005(−0.00)

0.0041(0.32)

0.6785(0.72)

0.0001(0.01)

0.0326

0.0004(0.00)

0.003(0.24)

0.3547(0.34)

−0.0007(−0.04)

0.0334(1.26)

0.0348

ZERO 0.2426(6.37)**

0.2168(7.06)**

4.5105(9.43)**

0.0827(15.32)**

0.2394

0.2709(6.65)**

0.2105(7.06)**

4.0334(8.31)**

0.0752(12.48)**

0.0975(12.42)**

0.2477

TURNOVER −0.7362(−16.89)**

0.1111(16.51)**

2.0877(7.75)**

0.1387(18.20)**

0.4847

−0.6913(−17.21)**

0.1012(16.51)**

1.5129(6.78)**

0.1288(18.53)**

0.0717(9.76)**

0.5131

LM −20.5198(−87.09)**

2.0748(43.03)**

−29.0121(−9.99)**

3.0781(79.30)**

0.3472

−21.2028(−92.66)**

2.2625(41.35)**

−22.8765(−8.54)**

3.2281(84.47)**

−0.6724(−7.73)**

0.374

PBA −0.2184(−30.60)**

0.0549(29.84)**

−2.6395(−12.88)**

0.0323(28.39)**

0.5310

−0.2275(−32.89)**

0.0564(30.76)**

−2.4560(−13.13)**

0.0345(30.86)**

−0.0265(−13.45)**

0.5516


Table 6Fama–MacBeth cross-sectional regressions — medium-size firm sample. Individual stockliquidity proxies are regressed cross-sectionally each month on the concurrent month'sclosing price (PRICE), the variance of daily returns for the concurrent month (VARIANCE),monthly aggregate dollar trading volume (VOLUME) and monthly absolute stock return(ABSR). PRICE and VOLUME are logarithmic transformed. AMIHUD is the liquidity ratio fromAmihud (2002). PS is the return reversal measure from Pastor and Stambaugh (2003).TURNOVER is the stock turnover rate. ZERO is the zero return measure from Lesmond et al.(1999), but is modified as (1 — the proportion of zero daily returns). LM is the turnover-adjustedzerodailyvolumes fromLiu (2006). PBA is theproportional bid–ask spread. The signof AMIHUD, LM and PBA was flipped to make them represent liquidity. The coefficients areaveraged across 189 trading months in the sample. T-statistics are adjusted for first-orderauto-correlation and are reported in parentheses below the coefficient estimates.



AMIHUD −21.1798(−30.83)**

0.1176(0.99)

−310.7806(−12.92)**

3.1992(28.81)**

0.1992

−21.519(−29.96)**

0.1427(1.14)

−306.9715(−11.62)**

3.2738(27.77)**

−1.2216(−2.67)**

0.2016

PS −0.0018(−0.03)

0.0133(1.74)

5.0375(2.46)*

−0.0004(−0.05)

0.0254

0.006(0.11)

0.0099(1.25)

4.4921(1.47)

−0.0021(−0.24)

0.0193(−0.45)

0.0281

ZERO 0.0873(3.87)**

0.1903(9.28)**

17.0387(11.74)**

0.096(29.80)**

0.2092

0.1165(4.76)**

0.1857(9.38)**

15.3763(10.92)**

0.0896(25.32)**

0.1183(10.85)**

0.2156

TURNOVER −0.4494(−10.10)**

0.0629(11.13)**

5.0269(8.79)**

0.0784(10.72)**

0.5093

−0.4191(−10.79)**

0.0571(12.11)**

3.3282(6.27)**

0.0727(11.58)**

0.0617(10.38)**

0.5387

LM −15.4610(−44.08)**

1.1357(35.50)**

−81.3121(−10.65)**

2.3011(41.60)**

0.3181

−15.8823(−48.32)**

1.2284(36.82)**

−70.7545(−9.40)**

2.3791(46.77)**

−0.3394(−2.92)**

0.3393

PBA −0.1240(−32.29)**

0.0281(37.76)**

−3.4188(−12.39)**

0.0163(25.77)**

0.4521

−0.1270(−31.85)**

0.0284(38.99)**

−3.1708(−11.97)**

0.0169(25.81)**

−0.0159(−8.46)**

0.4697



Table 7Fama–MacBeth cross-sectional regressions — large firm sample. Individual stock liquidityproxies are regressed cross-sectionally each month on the concurrent month's closing price(PRICE), the variance of daily returns for the concurrent month (VARIANCE), monthlyaggregatedollar tradingvolume(VOLUME)andmonthlyabsolute stock return (ABSR). PRICEand VOLUME are logarithmic transformed. AMIHUD is the liquidity ratio from Amihud(2002). PS is the return reversal measure from Pastor and Stambaugh (2003). TURNOVER isthe stock turnover rate. ZERO is the zero return measure from Lesmond et al. (1999), but ismodified as (1— the proportion of zero daily returns). LM is the turnover-adjusted zero dailyvolumes from Liu (2006). PBA is the proportional bid–ask spread. The sign of AMIHUD, LMand PBA was flipped to make them represent liquidity. The coefficients are averaged across189 trading months in the sample. T-statistics are adjusted for first-order auto-correlationand are reported in parentheses below the coefficient estimates.



AMIHUD −17.632(−25.77)**

−1.5249(−9.75)**

−1061.1613(−10.43)**

2.6711(24.13)**

0.2574

−17.5842(−26.43)**

−1.5511(−9.66)**

−1151.2270(−9.97)**

2.6696(24.55)**

−0.0608(−0.11)

0.2617

PS 0.0559(0.52)

0.0372(1.59)

18.0408(1.31)

−0.0123(−0.71)

0.0583

0.061(0.54)

0.0369(1.59)

21.901(1.10)

−0.0128(−0.72)

−0.0573(−0.49)

0.0634

ZERO 0.1199(2.33)*

0.1858(56.42)**

46.5322(11.58)**

0.0881(11.91)**

0.386

0.1166(2.31)*

0.1866(57.90)**

43.0804(8.84)**

0.0875(11.94)**

0.1285(8.63)**

0.3925

TURNOVER −0.1424(−11.14)**

0.0070(8.70)**

10.1079(7.58)**

0.0245(12.40)**

0.4295

−0.1402(−10.86)**

0.0068(7.46)**

7.0283(5.81)**

0.0237(12.34)**

0.0646(10.73)**

0.4699

LM −6.2956(−23.30)**

0.0904(5.01)**

−115.5866(−6.18)**

0.8804(21.41)**

0.2473

−6.3265(−22.24)**

0.0722(4.46)**

−120.3095(−6.23)**

0.8885(20.47)**

0.0669(0.57)

0.2699

PBA −0.0739(−21.42)**

0.0097(24.22)**

−4.5445(−8.26)**

0.0088(18.58)**

0.5721

−0.0736(−21.73)**

0.0097(23.91)**

−4.3551(−10.00)**

0.0088(18.76)**

−0.0054(−4.09)**

0.5775


13 Pastor and Stambaugh (2003) note that it is often the case that volume is highwhen liquidity is low. This is especially the case during periods of financial crisis orstress. The problem with using trading volume as a proxy for liquidity is also discussedin Chordia et al. (2002).


glance, but this relationship is also consistentwith thefindings in Table 2.Non-zero values of BEEDLES are mainly concentrated in small firms,which also have higher TURNOVER on average.

We find no relationship between PS and trading characteristics.This indicates that the sources of the return reversal measure are notrelated to stocks' trading characteristics. It is important to note thatPastor and Stambaugh (2003) did not assign their liquiditymeasure toindividual stocks. They argue that while their liquidity measure isimprecise for individual stocks, their market-wide liquidity measurebecomes more precise as the sample size increases. Therefore, wehave to be cautious about applying PS to individual stocks.

Stoll (2000) points out that if the relationships with stock character-istics are the same using different liquidity proxies, liquidity is simply aone-dimensional concept. If not, liquidity is a multifaceted concept. Ourresults support the notion that liquidity is multidimensional, and that itcan be viewed from different aspects of trading behaviour.

4.3.2. Robustness check: size groupsAs a robustness check, the influences of trading characteristics on

liquidity across the size groups are examined. The BEEDLESmeasure isexcluded because all stocks within a size group have zero values forBEEDLES in some months. Tables 5, 6 and 7 report regression resultsfor small, medium and large size firms, respectively. The results in thesize groups are similar to those found in the main analysis. Theinfluences of trading characteristics on ZERO, PBA and LM remainconsistent across the size groups. Trading characteristics continue toshow no explanatory power on PS.

PRICE becomes positively related with TURNOVER in the size groups,which is consistent with expectations. This indicates that stocks withhigher prices have higher turnover rates in each size category. Therelationship between PRICE and AMIHUD is consistent with ourhypothesis in the small size group. Stocks with lower prices tend tohave higher price impacts. The relationship between PRICE and AMIHUDdisappears in the medium-size group and becomes negative for largefirms. This indicates that the negative relationship between PRICE andAMIHUD observed in Table 4 may be driven by large size firms.

5. Conclusion

The role of liquidity in generating stock returns has been examined inthe Australian equity market (e.g. see Chan and Faff, 2003; Marshall andYoung, 2003). In this paper, we take a step further and examine therelationships between liquidity proxies and the influences of tradingcharacteristics on stock liquidity in the pure order-driven market ofAustralia. Prior studies that have examined similar research issuesmainlyfocus on liquidityproxies constructed frommicrostructuredata. There aremany situations inwhich little ornomicrostructuredata are available andin these cases, we have much less guidance on the best way to proceed.This gap in the literature motivates the current research to use liquidityproxies constructed from low-frequency data. In this paper, we examinethe relationshipbetween liquidity andstocks' trading characteristics, suchas price per share, return volatility and trading volume in the Australianmarket.Wemainly focus on trading characteristic variables because datafor these variables are relatively accessible, and they have been shown tobe important sources of liquidity.

Wefind that the correlations among the employed liquidity proxiesare low in the cross-section. This implies that they represent differentdimensions of liquidity and a certain type of trading behaviour. Stoll(2000) also notes that different liquidity measures need not becorrelated for similar reasons. Consistent with the literature, tradingcharacteristics are important determinants of liquidity. However, theirrelationships with stock turnover and the return reversal measureexhibit a somewhat different pattern than the other liquidity proxies.In particular, the return reversal measure does not depend on stocks'trading characteristics. This result suggests that the source of thereturn reversal measure is not related to stock characteristics that are

important for the other proxies. This also implies that the returnreversal effect is small in the Australian market. In addition, we findthat small and largefirms have a higher average volume thanmedium-size firms do. This suggests that tradingmay bemore focused on smalland large firms in Australia. However, we are not claiming that highertrading volume necessarily indicates higher liquidity.13 In addition,based on other liquidity proxies, small firms do not necessarily havehigher liquidity than medium-sized firms do.

Notably, we have been silent on the question of what is the “best”liquidity proxy. This research issue is beyond the scope of the currentstudy. However, as noted in Goyenko et al. (2009), the selection ofliquidity proxies in an empirical design depends on what exactly onewants to capture. Our results support their assertion, as liquidity ismultidimensional and can be captured by different measures of tradingactivity. The current study shows that through firm trading character-istics, we can better understand the sources of liquidity.

Acknowledgements

The helpful comments of an anonymous referee and the financialsupport provided by an ARC Linkage Grant (LP0453913) are gratefullyacknowledged.


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new evidence on the relation between stock liquidity and measures of trading activity

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