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Faculty of Business and Law School of Accounting, Economics and Finance
Financial Econometrics Series
SWP 2015/06
New Empirical Evidence on the Bid-Ask Spread
P.K. Narayan, S. Mishra, S. Narayan
The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.
New Empirical Evidence on the Bid-Ask Spread
Paresh Kumar Narayan, Centre for Economics and Financial Econometrics Research, Deakin Business School, Deakin University, Melbourne, Australia. Email:
Sagarika Mishra, Department of Finance, Deakin Business School, Deakin University, Melbourne, Australia. Email: [email protected]
Seema Narayan, School of Marketing, Economics, and Finance, Royal Melbourne Institute of Technology. Melbourne, Australia. Email: [email protected]
ABSTRACT
In this paper, we model the determinants of spread for 734 firms listed on the NYSE
over the period 1 January 1998 to 31 December 2008. We propose a panel data model of the
determinants of spread. There are four main messages emerging from our work. We find a
statistically significant effect of volume on spread inconsistent with the work of Johnson
(2000). On price, we find mixed results, consistent with the literature. On the effect of price
volatility on spread, our results are completely the opposite of the cross-sectional literature but
sides with the relatively recent work of Chordia et al. (2001). We allow for persistence of spread
as a determinant of spread and find significant evidence of spread persistence across all 16
sectors. Finally, we examine size effects and find statistically strong evidence of size effects
based on the relationship between price and spread, persistence and spread, and volatility and
spread.
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1. Introduction
The goal of this paper is to examine the dynamic relationship between the bid-ask
spread and stock characteristics. There are several unique features of our empirical analysis.
First, we propose an empirical framework for the determinants of the bid-ask spread that
explicitly treats spread persistence as having a role in determining spread, apart from modelling
the effects of stock characteristics. Second, our empirical framework establishes a panel data
approach, which provides a relatively rich characterisation of the data and the ensuing
empirical relationship between spread and stock characteristics compared to cross-sectional
studies. Third, we show particular concern with respect to the problem of heterogeneity in
driving the results from our proposed model. In total, we have 734 firms. They belong to
different sectors. They, thus, are characterised by different market and cost structures. The
inherent heterogeneity of firms implies that the impact of stock characteristics on spread may
differ depending on the sector to which a firm belongs. This demands a sector-level analysis
of the determinants of spread. We respond to the issue of heterogeneity by constructing panels
that are as homogenous as possible by using two approaches: (1) we divide stocks into 16
different panels (namely agriculture, banking, electricity, chemical, computer, energy,
engineering, financial, food, general services, manufacturing, medical, real estate, supply,
textiles, and transport); and (2) we divide stocks into five different sizes, based on market
capitalisation. Moreover, in the next section we provide an empirical motivation for why one
should pay particular attention to the issue of heterogeneity when modelling firm behaviour.
Our empirical analysis is based on daily data that spans the period 1 January 1998 to
31 December 2008 and includes 734 firms listed on the NYSE. Specifically, we test four
hypotheses: (1) that spread is persistent; (2) that volume affects spread; (3) that stock price
affects spread; and (4) that price volatility affects spread. To examine these hypotheses, we
propose a panel data model of the determinants of spread.
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Our empirical results are somewhat different from the literature. First, unlike the extant
literature, which has found that volume has a statistically significant and negative effect on
spread, we find a positive relationship between volume and spread. While this finding is
inconsistent with a recent theoretical model developed by Johnson (2008) which contends that
volume has zero effects on spread, it is consistent with the theoretical works of Brock and
Kleidon (1992) and Easley and O’Hara (1992). Second, unlike the extant literature, which has
found that price volatility has a statistically significant and positive effect on spread, our results
for all sectors reveal a statistically significant and negative impact of volatility, consistent with
the proposal of Chordia et al. (2001). Our results on the impact of price, however, are consistent
with the extant literature, in that we find mixed results—for some sectors the impact of price
on spread is positive while for others it is negative. When we examine spread persistence, we
find significant evidence of persistence for all sectors—lagged spread predicts current spread.
The magnitude of persistence varies by sector though. Finally, we find strong evidence of size
effects. With respect to the impact of persistence, price and volatility, we find that these
variables impact spread differently for small sized firms compared to large sized firms.
We organise the rest of the paper as follows. In section 2, we provide a motivation for
the proposed research idea. In section 3, we propose an empirical model for the determinants
of spread. In section 4, we discuss the data, hypotheses, and results. A robustness test is
undertaken in section 5, while, in section 6, we compare our findings with those from the
literature and provide some explanations for the conflicting results. In the final section, we
provide some concluding remarks.
2. Motivation
2.1. Existing models
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There are two classes of statistical models on the bid-ask spread. The first class of
models relates to spread components. These models have been used for several purposes. While
it is impossible to provide a survey of all the studies here, some of the relatively more influential
works are as follows. Affleck-Graves et al. (1994) and Lin et al. (1995) develop a model to
compare dealer and auction markets. Huang and Stoll (1997) develop a trade indicator model
which identifies the spread’s three components, namely order processing, adverse information,
and the inventory holding cost.
The second class of models, to which our proposed model belongs, is the determinants
of the bid-ask spread. To better place the novelty of our work, we provide a more detailed
diagnosis of the key influential models in this literature.
The main features of these regression models can be summarised as follows. First, there
is no standard and specific functional form for the regression model. Almost all studies have
used a different specification. For example, some studies (see, inter alia, Harris, 1994) have
used a non-log linear specification while others have used a log-linear and a mixed log-linear
specification (see, for instance, Hamilton, 1978; Demsetz, 1968). Second, there is no consensus
on the explanatory variables used to model the determinants of spread. A range of variables
have been used, including various proxies. While for some variables, such as volume, price
and volatility, there is a theoretical motivation for their inclusion; for others, such as the number
of financial institutions, there is lack of a theoretical motivation.
The third feature is that these studies are almost exclusively on the US market; Canada
is an exception. Fourth, there is no consensus on the effect of volume, price and volatility on
spread. In the main there are tensions between findings from the cross-section models versus
time series models. For example, the cross-sectional models find that volume has a negative
effect on spread. The time series studies, although scarce, find a positive effect (see Lee et al.
1993), consistent with the theoretical postulates of Brock and Kleidon (1992) and Easley and
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O’Hara (1992). Similarly, there is no consensus on the effect of price on spread; some studies
(Tinic, 1972; Benston and Hagerman, 1978; Table 5) report a positive effect of price on spread,
consistent with the Demsetz (1968) hypothesis, others (Stoll, 2000; Brockman and Chung,
2003; Table 5) report a negative association.
Fifth, there are limited time series or panel data studies; they are mainly cross-sectional
studies. Thus, limited attempts have been made to capture any dynamic relationship between
spread and stock characteristics. More specifically, Lee et al. (1993) and Chordia et al. (2001)
show particular preference for time series studies of the determinants of spread. They argue
that time series models have been ignored, and when they estimate time series models of the
determinants of spread, they find different results from those obtained by cross-sectional
studies. A common feature of these studies is that the core determinants of spreads are the
same. We go a step further and combine cross-sectional and time series dimensions of the data,
and propose a panel data model of the determinants of spread.
2.2. Main contributions
There are essentially three main contributions of this study. First, unlike the studies
alluded to earlier, we propose a spread determinants model that perceives spread persistence as
having a role in the determinants of spread. We do so because past spread will contain at least
some information useful to predict spread. Persistence in financial variables has been
extensively documented in the literature; see, inter alia, Bollerslev and Engle (1993).
Subsequently, persistence is now well-accepted in the financial economics literature. Using
this literature and empirical evidence as a motivation, we construct a spread determinants
model that explicitly treats spread persistence as a predictor of spread. It follows that our
proposed model, which captures the dynamic relationship between spread and stock
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characteristics, presented in section 3, offers a new avenue for analysing the determinants of
spread within a panel data framework.
The second contribution is that this literature, thus far, has not considered the
determinants of spread at the sectoral level. This matters because firms are heterogeneous. The
market structures are different for firms belonging to different sectors. For example, market
structures of firms belonging to the energy and transport sectors are different from those that
belong to the chemical and medical sectors; see also Chun et al. (2008) for an analysis of firm-
specific performance. Firm heterogeneity has also been documented by the momentum profits
literature (see Daniel and Titman, 2006) which has shown that firms with high market-to-book
ratios produce greater momentum profits. Sagi and Seasholes (2007) show that momentum
strategies in high revenue volatile firms, low cost firms, and high market-to-book firms all
produce greater profits compared to traditional strategies. Moreover, in a sector-based analysis
of returns and oil price relationship, Narayan and Sharma (2011) show that sector-based firms
are heterogeneous. It follows that treating all stocks as a panel will make the results susceptible
to heterogeneity bias; that is, there may be a few firms dominating the results on the
determinants of spread.
To provide insights on possible heterogeneity of sectors, we examine the mean of log
price and log volume by sector. The mean price and volume varies by sector. We also read the
coefficient of variation by sector. For both price and volume, we find that volatility varies by
sector. Similarly, to see whether such disparities exist in the various firm sizes, in Table 1, we
report statistics on mean price and volume and their respective coefficient of variation. Again,
we find that the mean price and volume varies by size. Similarly, the volatility of the two
variables changes with firm size. We also test whether the mean price between pairs of sectors
are equal to zero. Except for pairs formed when using the agricultural sector, we reject the null
that mean price between pairs of sectors are equal to zero. The null is rejected at the 10% level
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or better for 105 out of 120 pairs. Similar results are found when we test whether the mean of
trading volume between pairs of sectors are equal to zero.
INSERT TABLE 1
To obviate this type of heterogeneity bias requires making a relatively more
homogenous panel.1 One way we do this is by constructing sector-based panels. We, thus, form
16 different panels; namely, agriculture, banking, electricity, chemical, computer, energy,
engineering, financial, food, general services, manufacturing, medical, real estate, supply,
textiles, and transport. This classification is based on the Global Industry Classification
Standard, following the work of Narayan and Sharma (2011). A second way we address
homogeneity is by organising stocks according to size, based on market capitalisation. Using
this strategy, we form five categories of firms, ranging from the smallest to the largest. We then
estimate the panel determinants of spread by sector and firm size.
Third, our proposed model of the determinants of spread is established on a panel data
framework. There are very few studies which use a panel data model. This specification is
relatively rich (compared to the extant literature), in that we are able to capture the dynamic
effects and information present in a longer time series (10 years of daily data) across a wide
range of firms, which ranges from as little as four and six firms in the case of agriculture and
textiles sectors, respectively, to 73, 86, 89, and 90 firms in the case of banking, financial,
manufacturing, and electricity sectors, respectively. It follows that a panel data approach to
modelling the determinants of spread, because it has a rich data characterisation, is likely to
produce results which would be free from the criticism of small sample size—a common
criticism generally associated with the extant literature.
1 A similar argument regarding homogenous panels is made by Narayan et al. (2011) who categorised 120 countries into various panels, keeping the panels as homogeneous as possible.
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A panel data model picks up information about spread, prices, volume, and volatility at
the firm-level; by comparison a time-series approach would have simply ignored information
inherent in firms. Moreover, a cross-section approach would have taken information from
across firms but would have ignored firm-specific information overtime. A panel data model
does not ignore information, neither from across firms nor from overtime. In our view,
therefore, if the intention is, as is the case with our research question, to extract information
from firms’ overtime, a panel data model is just ideal.
3. Model
In this section, we propose a simple model of the bid-ask spread2 that treats spread
persistence as a predictor of spread. The main motivation for considering the one period lagged
bid-ask spread as a determinant of bid-ask spread has roots in the idea that bid-ask spread itself
is likely to be persistent. This would imply that shocks that impact bid-ask spread actually stays
with the spread variable for some time, suggesting that whatever has happened to spread in the
past should matter to spread today.
Therefore, in the spirit of an autoregression type specification, the model allows for
spread persistence. Given the fact that 𝐿𝐿𝑖𝑖,𝑡𝑡 is stationary, we estimate:
𝐿𝐿𝑖𝑖,𝑡𝑡 − 𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏 = 𝛽𝛽𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏 + 𝛿𝛿𝛿𝛿𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝑖𝑖 + 𝜖𝜖𝑖𝑖,𝑡𝑡 (1)
where (𝐿𝐿𝑖𝑖,𝑡𝑡 − 𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏) is the difference in the bid-ask spread of stock 𝑖𝑖 between time 𝑡𝑡 and (𝑡𝑡 −
𝜏𝜏), 𝛿𝛿𝑖𝑖,𝑡𝑡 is a vector of variables that affect the spread position of stock 𝑖𝑖 , 𝜂𝜂𝑖𝑖 is stock specific
2 Our measure of the bid-ask spread is the dollar bid-ask spread (DBA). We use DBA since the bulk of the literature uses DBA; hence, our approach aids comparison of results with the literature. We also estimate the model by using relative bid-ask spread (RBA). To obtain RBA, we simply divide the DBA with the bid-ask mid-point; for a similar approach, see Roll and Subrahmanyam (2010). The results are only slightly different from those obtained by using DBA. Hence, to conserve space, we only report the results from the DBA. Additional results are obviously available upon request.
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effect, and 𝜖𝜖𝑖𝑖,𝑡𝑡 is an error term. If 𝛽𝛽 is statistically significant then it implies that spread is
persistent. We can re-write Equation (1) as follows:
𝐿𝐿𝑖𝑖,𝑡𝑡 = 𝛽𝛽�𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏 + 𝛿𝛿𝛿𝛿𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝑖𝑖 + 𝜖𝜖𝑖𝑖,𝑡𝑡 (2)
where 𝛽𝛽� = (1 + 𝛽𝛽). Equation (2) is dynamic by construction. It can be estimated using fixed
effects, but there will be a potential bias (Nickell, 1981). Moreover, by taking the first
difference, we can remove individual specific effects and estimate the above equation by
generalised method of moments (GMM); however, GMM also suffers from bias (Hahn et al.,
2001) and, more significantly, from weak instrumentation problems (Kruiniger, 2000; Hahn et
al., 2001). Phillips and Sul (2003) show that the bias persists even when T is large. Phillips and
Sul (2007) propose a bias correction method for the dynamic coefficients and the coefficients
of exogenous variables.
If we estimate Equation (2) when 𝛿𝛿 = 0 then the bias correction method is fairly straight
forward. When we include exogenous variables, the bias can also be removed fairly easily.
First, we estimate Equation (3) using fixed effects3:
𝐿𝐿𝑖𝑖,𝑡𝑡 = 𝛽𝛽�𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏 + 𝜂𝜂𝑖𝑖 + 𝜖𝜖𝑖𝑖,𝑡𝑡 (3)
Following Nickell (1981), the bias for 𝛽𝛽�̂ is given by:
plim𝑁𝑁→∞
�𝛽𝛽�̂ − 𝛽𝛽�� = 𝐺𝐺�𝛽𝛽�,𝑇𝑇� = −1�1 + 𝛽𝛽��𝑇𝑇−1 + 𝑂𝑂(𝑇𝑇−2) (4)
For large T, we can ignore the second term. Following Phillips and Sul (2007), the bias
can be corrected by:
𝛽𝛽�̂𝑀𝑀𝑀𝑀𝑀𝑀 = 𝑚𝑚−1(𝛽𝛽�̂) (5)
3 We have done the Hausman (1978) test, using our panel data model, based on which the null hypothesis of a random effects model is comfortably rejected at the 1% level for both sector and size based panels.
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where 𝑚𝑚−1 is the inverse of the function (𝐺𝐺 + 𝛽𝛽�), which can be computed by direct numerical
calculation. We first estimate Equation (3) and estimate 𝛽𝛽�̂𝑀𝑀𝑀𝑀𝑀𝑀 and then we estimate the
following model using fixed effects:
𝐿𝐿𝑖𝑖,𝑡𝑡 –𝛽𝛽�̂𝑀𝑀𝑀𝑀𝑀𝑀 𝐿𝐿𝑖𝑖,𝑡𝑡−𝜏𝜏 = 𝜂𝜂𝑖𝑖 + 𝛿𝛿𝛿𝛿𝑖𝑖,𝑡𝑡 + 𝜖𝜖𝑖𝑖,𝑡𝑡 (6)
A final note relates to the lag of the dependent variable—that is, the measure of persistence.
The optimal lag length can be chosen by applying any lag length selection criteria, such as the
Schwarz Information Criterion (SIC) or the Bayesian Information Criterion (BIC). In our
empirical application, we use the BIC.4
4. Data, Hypothesis, and Results
4.1. Data and basic features
We use daily data spanning the period 1 January 1998 to 31 December 2008 for 734
US firms listed on the NYSE. All data is obtained from the Centre for Research in Security
Prices. While the NYSE has several thousand firms listed, consistent time series daily data over
the period 1998 to 2008 was only available for 734 firms following our filtering process, which
was: (a) exclude all stocks that are priced at less than $5; (b) exclude all stocks that are priced
greater than $500; and (c) exclude all stocks which had four consecutive days of missing values.
Approaches (a) and (b) ensure that results are not influenced by unduly high and low priced
stocks.
Four variables are used; namely, average daily bid-ask spread, average daily trading
volume, average daily share price, and daily share price volatility. Following German and Klass
(GK, 1980), we compute average daily volatility as:
4 Indeed at the suggestion of the Editor of this journal we estimated a model with four lags of all variables. As expected, spread is highly persistent; that is, in all 16 sectors almost all lags of spread are statistically significant. In 11/16 sectors, lagged prices are significant, and in 2/16 and 4/16 sectors lagged trading volume and price volatility are statistically significant.
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𝐺𝐺𝐺𝐺 = 0.5[𝑙𝑙𝑙𝑙(𝐻𝐻𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝐿𝐿𝐻𝐻)]2 − [2𝑙𝑙𝑙𝑙2 − 1][𝑙𝑙𝑙𝑙(𝐶𝐶𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝑂𝑂𝐻𝐻)]2 (7)
Here, HP, LP, CP, and OP represent high price, low price, closing price, and opening
price, respectively.
An important pre-requisite for the estimation of our proposed model is that all variables
need to be stationary. Given our panel data framework, as shown in Equation (1), a first step
entails ascertaining that all variables are panel stationary. To achieve this objective, we apply
the Im et al. (IPS, 2003) panel unit root test. The application proceeds as follows. The test
considers a sample of 𝑁𝑁 groups (which in our case is the number of stocks in each panel)
observed over 𝑇𝑇 time periods (which in our case is from 1 January 1998 to 31 December 2008).
IPS then, drawing on the conventional augmented Dickey and Fuller (1981) regression for a
unit root in a time series, augment the regression with a subscript 𝑖𝑖 as follows:
∆𝑦𝑦𝑖𝑖,𝑡𝑡 = 𝛼𝛼𝑖𝑖 + 𝜋𝜋𝑖𝑖𝑡𝑡 + 𝛽𝛽𝑖𝑖𝑦𝑦𝑖𝑖,𝑡𝑡−1 + ∑ 𝜌𝜌𝑖𝑖,𝑗𝑗𝑘𝑘𝑗𝑗=1 ∆𝑦𝑦𝑖𝑖,𝑡𝑡−𝑗𝑗 + 𝜀𝜀𝑖𝑖,𝑡𝑡 (8)
Here, 𝑦𝑦 denotes the time series under consideration, ∆ is the first difference operator, 𝜀𝜀
is a white noise disturbance term with variance 𝜎𝜎2, and the ∆𝑦𝑦𝑖𝑖,𝑡𝑡−𝑗𝑗 terms on the right-hand side
of Equation (8) ensure a white noise disturbance term. The null hypothesis of a unit root in the
panel is defined as: 𝐻𝐻0:𝛽𝛽𝑖𝑖 = 0, for all 𝑖𝑖. The alternative hypothesis is that all series are
stationary processes: 𝐻𝐻1: 𝛽𝛽𝑖𝑖 < 0, 𝑖𝑖 = 1,2, … ,𝑁𝑁1,𝛽𝛽𝑖𝑖 = 0, 𝑖𝑖 = 𝑁𝑁1 + 1,𝑁𝑁2 + 2, … ,𝑁𝑁.
This formulation of the alternative hypothesis allows for 𝛽𝛽𝑖𝑖 to differ across groups, and
is more general than the homogenous alternative hypothesis, namely 𝛽𝛽𝑖𝑖 = 𝛽𝛽 < 0 for all 𝑖𝑖 (IPS
2003). To test the hypothesis, IPS (2003) propose a standardized t-bar statistic, which we use
here.
The results from the IPS test, not reported here to conserve space, suggest that we can
reject the panel unit root null hypothesis. Thus, we conclude that spread, price, volume, and
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volatility are panel stationary for all 16 panels.5 Results on size based panels are similar. The
test statistics are all smaller than the 1 percent level critical value for all the four variables for
all the five size panels, rendering all variables stationary in size based panels. The implication
of these findings is that we can now estimate Equation (1) since the pre-requisite that all
variables are panel stationary is satisfied.
4.2. Hypothesis 1: that lagged spread predicts spread
The ability of past firm spread to predict current firm spread is an important
consideration given that a certain level of spread is necessary for securities to be traded in
quantities required in a timely fashion without any price discount (see also Hasbrouck, 1991).
Before we begin to estimate panel data models, we estimate time series regression
models for each firm. Essentially, we regress spread on lagged spread, volume, price, and
volatility for each of the firms. We find that in 100 percent of cases—that is for all the 734
firms, lagged spread has a statistically significant negative effect on current bid-ask spread at
the 5 percent level of significance. This provides strong evidence of spread persistence on the
NYSE.
Next we consider the panel results of the effect of lagged spread on current spread.6
The results are reported in Table 2. We find that lagged spread is statistically significant at the
1 percent level for all sectors. This implies that spread is persistent and it helps explain current
5 One advantage of panel data models is that they allow a rich characterisation of data. This richness comes from two sources: the cross-sectional (N) dimension, which in our case is the firm, and the time-series (T) dimension, which is the length of time in our sample. From an econometric point of view, it implies that the power to reject the unit root null (and therefore accepting that the variable is stationary) increases substantially with panel data compared to time series data. Therefore, it is little surprising that while time-series unit root models fail to reject the unit root null for stock prices, panels of stocks when subjected to panel unit roots do in some cases reject the unit root null (see, for example, Narayan, 2008). While generally, apart from stock prices, panel data unit root models have not been fitted to other financial variables, such as those that we consider, the same logic of power increase can be used to explain the rejection of the unit root null for other variables in our data set. 6 Autocorrelation is a feature of our dataset. To account for this, we have used the Driscoll and Kraay (1998) standard errors.
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spread for all 16 sectors. However, we notice significant disparities in the coefficients of the
lagged spread variable. Two observations are worth making regarding this: (1) the coefficient
in absolute values ranges from as low as 0.22 in the case of the food sector to as high as 0.85
in the case of the chemical sector; and (2) in five sectors (banking, chemical, engineering,
financial, and general services), the persistence coefficient is greater than 0.5, implying
relatively higher spread persistence for these five sectors.
The size-based evidence of the persistence of spread is presented in Table 3. We find
that persistence exists regardless of size. This implies that past spread is useful predictor of
current spread even for the different sizes of stocks.
INSERT TABLES 2 and 3
4.3. Hypothesis 2: that volume explains spread
Copeland and Galai (1983) propose a compelling model that links trading volume to
bid-ask spread. According to their model, the impact of trading volume on bid-ask spread can
be either negative or positive depending on the probability of information available to the next
trader. Their model works as follows. If the probability is higher for thinly traded stocks, and
assuming that the transaction size is constant, there will be a negative association between
trading volume and bid-ask spread. On the other hand, Copeland and Galai show that the
probability may increase if more information is associated with the size of the transaction. In
this case, assuming that the number of transactions is held constant, trading volume will exert
a positive effect on bid-ask spread.
The inventory theory, meanwhile, posits a negative relationship between volume and
spread. The amount of inventory held by a dealer is a key determinant of the dealer’s cost.
Required inventory is a positive function of volume, although the positive relationship is not
proportional. Thus, as argued by Benston and Hagerman (1978), because dealer’s hold less
inventory per transaction, the spread would decline as volume increases.
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Tinic and West (1972) also provide a detailed insight into the plausible relationship
between volume and spread. Their main idea is that temporal imbalances in the inflow of orders
dictate dealer participation in trading activities. It follows that, as clearly explained by West
and Tinic (1971), the probability that there will be an imbalance is inversely related to time
rate of transactions. Put differently, a higher trading volume is associated with smaller
disparities and discontinuities in the inflow of buy and sell orders, which Tinic and West (1972:
p.1709) perceive as ‘giving the market a self-equating’ quality.
Finally, in a recent contribution contrary to Copeland and Galai (1983), Benston and
Hagerman (1978) and Tinic and West (1972), Johnson (2008) argues that there is no real effect
of volume on liquidity. The key features of the Johnson model are: (a) it’s a frictionless model
of stochastically participating agents, where agents trade assets, quantify trading demands, and
establish liquidity, leading to the evolution of joint behaviour of liquidity and volume; and (b)
agents arrivals and departures ensure trade demand. The central argument for the lack of
relationship between volume and liquidity is that ‘volume responds symmetrically to arrivals
and departures whereas liquidity responds antisymmetrically’ Johnson (2008: p. 395).
From the aforementioned discussion of the relationship between volume and spread, on
theoretical grounds there is no consensus. We begin our empirical investigation with 734 time
series regressions—that is, for each firm, we estimate the effect of volume on spread. The
results from this regression analysis are presented in Figure 1. The percentage of times volume
has a statistically significant positive and negative effects on spread are plotted in Figure 1.
The following features of this result are of interest. We discover that out of 734 firms, for 13.7
percent volume has a statistically significant positive effect on spread, while for 12.3 percent
of firms volume exerts a statistically significant negative effect on spread. This result implies
two things: (1) the percentage of statistically significant relationships are small—only 26
14
percent; and (2) there is almost an even split of the statistically significant results in terms of
its sign.
INSERT FIGURE 1
The panel data results on the effect of volume on spread for each of the 16 sectors are
presented in column 5 of Table 2. We also find that for all sectors volume has a statistically
significant effect on spread.
4.4. Hypothesis 3: that price explains spread
The classical paper by Demsetz (1968), which essentially pioneered the work on the
determinants of spread, was the first to propose the link between price and spread. Demsetz
(1968) argued that a positive relationship exists between spread and price on the grounds that
spread would increase in proportion to an increase in the price so as to equalize the cost of
transacting per dollar exchanged. This will be the case because in the absence of equalisation
of the cost of transacting, Demsetz (1968: 45) contends that those submitting limit orders will
profit by narrowing spreads on those securities for which spread per dollar exchanged is larger.
In contrasting work produced by McInish and Wood (1992) and Stoll (1978), an inverse
relationship between price and spread is observed. McInish and Wood (1992) attribute their
finding to the resulting economies of scale in trading. It follows that when prices are high, the
dollar value of transaction rises. The resultant is: dealers required bid-ask price is reduced to
cover their costs.
Based on time series regression models, out of the 734 firms, we find that price has a
statistically significant positive effect on spread for a very small 12.6 percent of firms. A
summarised result organised by sector for cases of statistically significant effect of price on
spread is provided in Figure 2. Some key features of the time series regression results are: (a)
we notice that in four sectors (agriculture, financial, real estate, and textiles) at least 20 percent
15
of firms experience a statistically significant positive effect of price on spread, and (b) for
another five sectors (banking, electricity, chemical, general services, and medical) at least 10
percent of firms experience a statistically significant positive effect of price on spread.
INSERT FIGURE 2
Next we examine the panel data regression model. The results are reported in column
4 of Table 2. We find that price has a statistically significant positive effect for firms belonging
to six of the 16 sectors; these sectors are agriculture, energy, engineering, manufacturing,
textiles, and transport. So, in sum, we can claim that for around six sectors, there is evidence
that price positively affects spread on the NYSE. For firms belonging to banking, electricity,
computer, financial, food, medical, real estate, and supply there is a statistically significant
negative effect of price on spread. For two sectors (general services and chemical), there are
no statistically significant relationship between price and spread. It follows that we find mixed
results on the effect of price on spread.
Finally, we consider whether the impact of price on spread is size-dependent. We find
two main results with respect to size. First, except for the middle-size firms, where, as predicted
by Demsetz (1968), price has a statistically significant positive effect on spread, for all other
firm sizes price has a statistically significant negative effect on spread, consistent with the
McInish and Wood (1992) and Stoll (1978). Second, while the impact of price on spread is
statistically significant and negative for both small and large sized firms, the effect of price is
larger in the case of large sized firms compared to small sized firms. Our findings, thus, suggest
that the price-spread relationship on the NYSE is dictated by firm size.
4.5. Hypothesis 4: that volatility explains spread
Tinic and West (1972) argue for a positive effect of volatility on spread because higher
price variability leads to greater risk associated with the performance of the dealership
16
functions. They, however, warn against a pre-determined expectation of this positive relation
by observing that ‘we should not try to predict the sign of this coefficient since it might be
possible for the influence of price volatility to be negligible if a dealer could diversity his
operations sufficiently’ (p.1710).
On the other hand, a negative relationship between volatility and spread is also possible
as explained by Chordia et al. (2001, p.519), who essentially contend that: “It appears that
sluggish trading following recent volatility allows dealers to reduce inventory imbalances,
which then prompts them to reduce spreads”.
Before we consider the effect of stock price volatility on spread for panels of firms, we
estimate time series regression models for each of the firms. From this, we compute the
percentage of times volatility has a positive effect and the percentage of times volatility has a
negative effect on spread for each of the sectors. The summary of the results on the statistical
significance of this relationship at the 5 percent level are plotted in Figure 3.
INSERT FIGURE 3
There are three main features of the time series results. First, we find that for 38.7
percent of 734 firms volatility has a statistically significant negative effect on spread. For only
a small 6.8 percent of firms volatility has a positive effect on spread. Second, as indicated by
Figure 3, except for the agricultural sector, in all sectors the negative effect of volatility on
spread dominates the relationship. Third, as outlined earlier, the main motivation of this study
was the concern that because firms are heterogeneous, the impact of stock characteristics will
most likely have different effects on spread for each firm depending on the sector to which they
belong to. Figure 3 proves this. For many sectors, firms experience negligible negative
relationship between volatility and spread. In fact, in three sectors, namely computer, general
services, and textiles, there is no evidence of a negative effect of volatility on spread. For
17
sectors, such as food, transport, chemical, electricity, and supply, the negative effect of
volatility on spread is relatively small.
The results from the fixed effect panel data model of the effect of volatility on spread
for each of the 16 sector-based panels are reported in the last column of Table 2. The main
findings are as follows. First, we find that the relationship between volatility and spread is
negative. In 12 of the 16 sectors, the relationship is statistically significant: at the 5 percent
level for financial, manufacturing, and real estate sectors; at the 10 percent level for the supply
sector; and at the 1 percent level for the rest of the sectors. The sectors for which the
relationship is statistically insignificant are banking, computer, general services, and medical.
Next we consider whether there are size effects when it comes to the relationship
between volatility and spread. The size effects are reported in Table 3. Two findings stand out.
First, the relationship between volatility and spread is negative and statistically significant.
Second, volatility affects spread regardless of size, although the magnitude of the effect
declines with size. In other words, there is evidence that for small firms’ volatility has a larger
effect on spread compared to large firms. For instance, the magnitude of the effect declines
from -5.7 in the case of the smallest sized firms to -0.5 in the case of the largest sized firms.
INSERT TABLE 3
5. Are our findings robust?
Our finding that is most inconsistent with the literature is on the effect of volatility on
spread. However, at the outset it should be noted that generally on the determinants of spread,
the results are different from cross-sectional models compared to time series models.
Theoretically, no distinction is based between cross-sectional and time series models giving
the impression that the expected signs on the effects of the determinants of spread should hold
regardless of the type of empirical model. From an empirical point of view, however, because
the setup of a cross-sectional model is completely different from a time-series regression model
18
in that while a cross-sectional model depends on information across firms while a time-series
model depends on information over time, the expected signs could well be different. At least
this possibility, from an empirical perspective, needs to be entertained. This has been shown,
in the case of trading volume by Lee et al. (1993) and in the case of volatility by Chordia et al.
(2001). In fact, so far, our findings on the relationship between volatility and spread are
consistent with Chordia et al. (2001). However, given the lack of consensus on the impact of
volatility on spread, we see it essential to investigate this relationship further. To proceed along
these lines, it is fair to say that one limitation of our investigation of the effect of volatility on
spread has been our use of only one proxy for volatility. To ascertain that volatility has a
negative effect on spread regardless of the measure used, we use three additional measures of
volatility as follows:
1. 𝑉𝑉1 = ln(𝐻𝐻𝐻𝐻) − ln (𝐿𝐿𝐻𝐻) -- a measure proposed by Gallant et al. (1999) and Alizadeh et
al. (2002);
2. 𝑉𝑉2 = 0.361[𝑙𝑙𝑙𝑙(𝐻𝐻𝐻𝐻/𝐿𝐿𝐻𝐻)]2-- a measure proposed by Parkinson (1980); and
3. A measure proposed by Rogers and Satchel (1991) and Rogers et al. (1994), which has
the following form:
𝑉𝑉3 = [𝑙𝑙𝑙𝑙(𝐻𝐻𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝑂𝑂𝐻𝐻)][𝑙𝑙𝑙𝑙(𝐻𝐻𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝐶𝐶𝐻𝐻)]
+ [𝑙𝑙𝑙𝑙(𝐿𝐿𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝑂𝑂𝐻𝐻)][𝑙𝑙𝑙𝑙(𝐿𝐿𝐻𝐻) − 𝑙𝑙𝑙𝑙(𝐶𝐶𝐻𝐻)]
For V1, V2, and V3, HP, LP, OP, CP, and ln, denote high price, low price, opening
price, closing price, and natural logarithm, respectively.
Here, to conserve space, we only report results relating to the effect of volatility on
spread. The rest of the results, including graphs that plot the percentage of firms which have a
statistically significant negative relationship between volatility and spread based on the V1,
V2, and V3 measures of volatility, are available upon request. The panel data regression model
19
(Equation 6) is estimated in turn by using V1, V2, and V3 as proxies for volatility. The panel
data regression model is estimated for 16 panel-based sectors. Based on V1, 10 of the 16 sectors
have at least 50 percent of firms having a statistically significant negative effect of volatility
on spread. Based on the V2 measure, for 10 of the 16 sectors, at least 40 percent of firms
experience a statistically significant negative effect of volatility on spread. Similar evidence is
found based on the V3 measure: approximately 41 percent of firms experience a statistically
significant negative relationship between volatility and spread, while only 7.3 percent of firms
experience a positive relationship between volatility and spread.
In sum, then, based on firms at the sectoral level, evidence suggests a statistically
significant negative effect of volatility on spread. For the three measures of volatility, the
percentage of firms that have a statistically significant negative relationship ranges from 41
percent (V3) to 58 percent (V1).
We also estimate the spread determinants model with the three additional proxies for
volatility by size, and plot the results for the volatility-spread nexus are plotted (Figures
available upon request) for measures V1, V2, and V3. All three measures of volatility reveal
that firms regardless of their size experience statistically significant negative relationship
between volatility and spread.
Finally, we estimate the panel data regression model of the determinants of spread by
taking each of the three proxies for volatility. To conserve space, we do not report the results
for all coefficients of the model (price, volume, volatility, and persistence), we only report the
coefficients of the volatility variable. The results on price, volume, and persistence are
consistent across all proxies. The results on the effect of V1, V2, and V3 on spread are reported
in Table 4. Based on all three proxies for volatility, except for computer and medical, all sectors
experience a statistically significant and negative relationship between volatility and spread. In
sum, based on V1 and V2 proxies, firms in 14 out of the 16 sectors experience a statistically
20
significant negative relationship. And, based on the V3 proxy, firms in 11 out of 16 sectors
experience a negative relationship.
INSERT TABLE 4
In Table 5, we report the results on the effect of volatility on spread by size. Again, as
we found previously, all three proxies for volatility have a statistically significant negative
effect on spread regardless of size.
These results, for individual firms as well as for panels of firms based on sectors,
confirm that the statistically significant negative relationship between volatility and spread is
not dependent on the proxy for volatility. We use four proxies for volatility and find similar
results.
INSERT TABLE 5
We conclude this section with an analysis of whether the 2007 global financial crisis
actually has implications for the results that we have reported so far. To test this, we simply
re-run the determinants of spreads by excluding the period of the global financial crisis. In
other words, we re-estimate the spread determinants model for the period 1 January 1998 to 31
December 2006. The results are not reported here to conserve space and because they do not
add anything new to what we have already found; however, all results are available upon
request. The results are robust to the global financial crisis. The main results as reported over
the full sample period hold: lag spread and volatility have a statistically significant and negative
effect on the spread while volume has a statistically significant and positive effect on spread.
Price, as before, has a statistically significant positive effect on spread of some sectors and a
statistically significant and negative effect for other sectors. The size-based results are also
robust to the global financial crisis. Lag spread and share price volatility have statistically
significant and negative effect while volume across all sizes has a statistically significant and
positive effect on the spread.
21
6. Our Findings and the Literature
6.1. Overview
Before we compare our results with those from the extant literature, the key differences
between our work and that of the literature needs to be noted, and taken into consideration in
interpreting the results. The first difference between our study and that of the literature is in
terms of sample size. The literature has used cross-sectional data while we have used time
series (10 years of daily data covering 734 stocks) and extensive panel datasets, which have
observations ranging from around 11,000 to around 250,000. Hence, compared to the literature
our results are based on a significantly large sample size. Second, our study covers the most
recent period. Our sample size, covering 1998 to 2008, is over 12 years more recent compared
to the most recent influential study on this subject by Wei and Zheng (2010). It follows that
because of the relatively large sample size and more recent data, our study is likely to produce
different results. Such a possibility has already been demonstrated by Lee et al. (1993) and
Chordia et al. (2001) with respect to spread-volume and spread-volatility relationships,
respectively.
6.2. Volume
Our results regarding the effect of volume on spread is different from most of the
literature including the work of Johnson (2008) whose theoretical model sees no role of volume
in determining spread. Our results are however consistent with the works of Copeland and
Galai (1983), Brock and Kleidon (1992) and Easley and O’Hara (1992).
Generally, the empirical literature has documented that trading volume has a
statistically significant negative effect on spread. This finding has been consistent with those
suggested by Copeland and Galai (1983) that a higher probability of access to information for
22
traders for thinly traded stocks, when the transaction size is constant, can dictate a negative
association between volume and spread. This statistical relationship has been given credence
by the inventory theory and the work of Benston and Hagerman (1978), who contend that,
because dealers hold fewer inventories per transaction, spread would decline as volume
increases.
However, Tinic and West (1972) propose a temporal imbalance in the inflow of orders
hypothesis to explain the negative association between volume and spread. Our results
challenge these theoretical advances. We found a statistically significant positive effect for all
the 16 sectors. This positive association seems to be consistent with the Copeland and Galai
(1983) theory, which states that the probability of information access may increase if the source
of information is the transaction size.
6.3. Price
The literature has found mixed results on the impact of price on spread. Nine studies
have found a statistically significant positive relationship while five studies have found a
statistically significant negative effect of price on spread. That prices have a statistically
significant positive effect on spread is motivated by the work of Demsetz (1968). The positive
relationship results as spread per share tends to increase in proportion to an increase in the price
per share. This relationship will eventuate so as to equalise the cost of transacting per dollar
exchanged. We find this to be the case for firms belonging to agriculture, energy,
manufacturing, textiles, and transport, consistent with the findings from Tinic (1972), Benston
and Hagerman (1978), Demsetz (1968), Tinic and West (1972, 1974), Hamilton (1978), and
Stoll (1978).
On the other hand, Demsetz (1968) argues that if spread per share does not increase in
proportion to an increase in price per share, those submitting limit orders can, by narrowing
23
spreads on those securities for which spread per dollar exchanged is larger, make profits.
Moreover, McInish and Wood (1992) argue that the negative association between spread and
price is due to economies of scale in trading, such that when prices are high, the dollar value
of transaction rises. Thus, dealers required bid-ask price is reduced to cover their costs. From
our study, this type of behaviour seems to be prevalent in firms belonging to banking,
electricity, computer, financial, food, medical, real estate, and supply sectors. For firms
belonging to these sectors, we find a statistically significant negative effect of price on spread.
Our finding of a negative association is also consistent with the relatively more recent studies,
such as Harris (1994), Stoll (2000), Wei and Zheng (2010), and Brockman and Chung (2003).
In explaining the possible negative relationship, Brockman and Chung (2003: 930) contend
that it is likely to be due to a fixed cost component of the spread—that is, there is less variation
in market making costs than prices.
For firms belonging to sectors where we discovered a negative relationship between
price and spread, there are some interesting statistical features as well compared to firms which
experienced a positive relationship between spread and price. Of particular relevance here is
the skewness statistic. A number of studies, for instance, have shown that portfolio selection
can be affected by the skewness of returns; see, inter alia, Simkowitz and Beedles (1978), and
Chunhachinda et al. (1997). Essentially, these studies show that the low diversification of
portfolios is a result of the preference for positive skewness by investors. When we examine
the average return skewness for those sectors where the relationship between spread and price
is positive and compare it with those sectors for which the relationship is negative, we find a
significant difference. For those sectors having a positive relationship between spread and
price, we find a positive average skewness of 1.5, while for those firms having a negative
relationship the average skewness is almost double at 2.9.
24
When we consider average skewness statistics for other variables, again significant
disparity between the two groups of sectors are noticed: for sectors with a positive association,
the skewness statistics for volume (6.9) and volatility (112.2) are much lower than for those
sectors with negative association—volume (10.5) and volatility (164.9). Finally, the spread
skewness is found to be negative – -22.8 for sectors where price-spread is positively related
versus -6.2 for the sectors where price-spread is negatively related. As argued by Chunhachinda
et al. (1997), skewness is an important consideration in portfolio selection because ‘the
incorporation of skewness into the investor’s portfolio decision causes a major change in the
construction of the optimal portfolio.
6.4. Volatility
Empirical studies based on cross-sectional models have confirmed a statistically
significant positive effect of volatility on spread on the grounds proposed by Tinic and West
(1972) that higher price variability induces greater risks with dealership functions. However,
results from time series studies are different. Chordia et al. (2001), for instance, finds a negative
relationship between market volatility and spread. Our results are completely the opposite of
the Tinic and West theory, but consistent with Chordia et al. (2001), who attribute this negative
association to possible sluggish trading following recent volatility, prompting dealers to reduce
inventory imbalances, which, as a result, lead to a reduction in spreads.
6.5. Size-based evidence
Of the variables we use to proxy stock characteristics, we find that lagged spread
(persistence), price, and volatility exert size effects. We find that persistence declines with firm
size—small sized firms have higher persistence than the largest sized firms. The effect of price
on spread is relatively small for the smallest sized firms compared to the largest sized firms.
And, volatility has the largest effect on small sized firms and the least effect on the two largest
25
sized firms. From these results, it is clear that there are size effects of stock
characteristics (except for trading volume, which has zero effects on spread regardless
of size) in determining spread. Our finding is, thus, consistent with the broader literature
that has documented size effects in financial economics.
In a stream of studies (see Banz, 1981) size effects were documented.
Essentially, these studies found that small firms earn higher risk-adjusted returns
compared to large firms listed on the NYSE and AMEX markets. There have been other
studies which have found features unique to small firms, which may explain the
different behaviour of small firms compared to large firms. For instance, Froot et al.
(1993) and Vickery (2008) argue that small firms engage in risk management because
they are financially constrained; and Petersen and Rajan (1995) find that small firms
pay higher interest rates and are unable to maximize advantages from early-payment
discounts on trade credit.
7. Concluding Remarks
In this paper, we analyse the determinants of spread using a panel data empirical model
that specifically allows for spread persistence to explain the determinants of spread. Our
emphasis is on analysing how key stock characteristics, namely trading volume, stock price,
and volatility impact spread. Our empirical analysis is based on 734 firms listed on the NYSE
over the period 1 January 1998 to 31 December 2008. To ensure that our panel data model is
as homogenous as possible, we divide the total number of firms into 16 different panels. We
also consider the role of stock characteristics on spread by dividing firms into different sizes,
from smallest to largest.
There are four main messages emerging from our work. First, we find, inconsistent with
Johnson (2008) but consistent with Copeland and Galai (1983) theory that trading volume has
26
a statistically significant and positive effect on spread. Copeland and Galai (1983) argue that
the probability of information access may increase if the source of information is the
transaction size.
On price, we find mixed results, consistent with the literature. With respect to the
negative relationship, this turns out in support of the fixed cost component of the spread idea—
that is, there is less variation in market making costs than prices. Second, on the effect of
volatility on spread, our results are completely the opposite of the cross-sectional literature but
sides with the relatively recent work of Chordia et al. (2001) who attribute this negative
association to possible sluggish trading following recent volatility, prompting dealers to reduce
inventory imbalances. Third, we allow for persistence of spread as a determinant of spread and
find significant evidence of spread persistence across all 16 sectors. Fourth, we examine size
effects and find strong evidence of size effects based on the relationship between price and
spread, persistence and spread, and volatility and spread. In sum, small sized firms are impacted
differently by these stock characteristic variables compared to large sized firms.
27
REFERENCES
Affleck-Graves, J., Hegde, S., and Miller, R., (1994) Trading mechanisms and the components
of the bid-ask spread, Journal of Finance, 49, 1471-1488.
Alizadeh, S., Brandt, M.W., Diebold, F.X., (2002) Range-based estimation of stochastic
volatility models. The Journal of Finance, 57, 1047-1091.
Banz, R.W., (1981), The relationship between return and market value of common stocks,
Journal of Financial Economics, 9, 3-18.
Benston, G.J., and Hagerman, R.L., (1974) Determinants of bid-asked spreads in the over-the-
counter market, Journal of Financial Economics, 1, 353-364.
Benston, G.J., and Hagerman, R.L., (1978) Risk, volume and spread, Financial Analysts
Journal, 34, 46-49.
Bollerslev, T., Engle, R.F., (1993) Common persistence in conditional variances,
Econometrica, 61, 167-186.
Brockman, P., and Chung, D.Y., (2003) Investor protection and firm liquidity, The Journal of
Finance, 58, 921-937.
Brock, W.A., and Kleidon, A.W., (1992) Periodic market closure and trading volume, Journal
of Economic Dynamics and Control, 16, 451-489.
Chordia, T., Roll, R., and Subrahmanyam, A., (2001) Market liquidity and trading activity,
Journal of Finance, LVI, 501-530.
Chordia, T., Goyal, A., and Tong, Q., (2011) Pairwise correlations,
http://ssrn.com/abstract=1785390.
Chunhachinda, P., Dandapani, K., Hamid, S., Prakash, A.J., (1997) Portfolio selection and
skewness: Evidence from international stock markets, Journal of Banking and Finance, 21,
143-167.
28
Chun, H., Kim, J-W., Morck, R., and Yeung, B., (2008) Creative destruction and firm-
specific performance heterogeneity, Journal of Financial Economics, 89, 109-135.
Copeland, T.E., and Galai, D., (1983) Information effects on the bid-ask spread, The Journal
of Finance, 38, 1457-1469.
Daniel, K., and Titman, S., (2006) Market reactions to tangible and intangible information,
Journal of Finance, 61, 1605-1643.
Demsetz, H., (1968) The cost of transacting, Quarterly Review of Economics, 82, 33-53.
Dickey, D.A., and Fuller, W.A., (1981) Likelihood ratio statistics for autoregressive time series
with a unit root, Econometrica, 49, 1057-1072.
Driscoll, J.C., and Kraay, A.C., (1998) Consistent covariance matrix estimation with spatially
dependent panel data, Review of Economics and Statistics, 80, 549-560.
Easley, D., and O’Hara, M., (1992) Time and the process of security price adjustment, Journal
of Finance, 47, 577-605.
Frijns, B., Gilbert, A., and Tourani-Rad, A., (2008) Insider trading, regulation, and the
components of the bid-ask spread, Journal of Financial Research, XXXI, 225-246.
Froot, K.; D. Scharfstein; and J. Stein, (1993) Risk management: coordinating corporate
investment and financing policies, Journal of Finance, 48, 1629-1657.
Gallant, A.R., Hsu, C.T., Tauchen, G., (1999) Using daily range data to calibrate volatility
diffusions and extract the forward integrated variance, The Review of Economics and
Statistics, 81, 617-631.
Garman, M., and Klass, M., (1980) On the estimation of security price volatilities from
historical data, Journal of Business, 53, 67-78.
George, T.J., Kaul, G., and Nimalendran, M., (1991) Estimation of the bid-ask spread and its
components: A new approach, The Review of Financial Studies, 4, 623-656.
29
Glosten, L.R., and Harris, L.E., (1988), Estimating the components of the bid-ask spread,
Journal of Financial Economics, 21, 123-142.
Hamilton, J., L., (1976) Competition, scale economies, and transaction cost in the stock market,
Journal of Financial and Quantitative Analysis, 11, 779-802.
Hamilton, J., L., (1978) Marketplace organisation and marketability: NASDAQ, the stock
exchange, and the national market system, Journal of Finance, 33, 487-503.
Hahn, J., Hausman, J., Kuersteiner, G., (2001) Bias corrected instrumental variables estimation
for dynamic panel models with fixed effects, MIT working paper.
Harris, L.E., (1994) Minimum price variations, discrete bid-ask spreads and quotation sizes,
Review of Financial Studies, 7, 149-178.
Hasbrouck, J., (1988) Trades, quotes, inventories and information, Journal of Financial
Economics, 22, 229-252.
Hasbrouck, J., (1991) Measuring the information content of stock trades, Journal of Finance,
46, 179-207.
Hausman, J.A., (1978) Specification tests in econometrics, Econometrica, 46, 1251-1271.
Huang, R.D., and Stoll, H.R., (1994) Market microstructure and stock return predictions, The
Review of Financial Studies, 7, 179-213.
Huang, R.D., and Stoll, H.R., (1997) The components of the bid-ask spread: A general
approach, The Review of Financial Studies, 10, 995-1034.
Im, K.S., Pesaran, M.H., and Shin, Y., (2003) Testing for unit roots in heterogeneous Panels,
Journal of Econometrics, 115, 53-74.
Jegadeesh, N., and Titman, S., (1995) Short-horizon return reversals and the bid-ask spread,
Journal of Financial Intermediation, 4, 116-132.
Johnson, T.C., (2008) Volume, liquidity, and liquidity risk, Journal of Financial Economics,
87, 388-417.
30
Kruiniger, H., (2000) GMM estimation of dynamic panel data models with persistent data,
Mimeo, Queen Mary, University of London.
Lee, C.M.C., Mucklow, B., and Ready, M.J., (1993) Spreads, depths, and the impact of
earnings information: An intraday analysis, Review of Financial Studies, 6, 345-374.
Lin, J-C., Sanger, G.C., and Booth, G.G., (1995) Trade size and components of the bid-ask
spread, The Review of Financial Studies, 8, 1153-1183.
Madhavan, A., and Smidt, S., (1991) A Bayesian model of intraday specialist pricing, Journal
of Financial Economics, 30, 99-134.
Menyah, K., and Paudyal, K., (1996) The determinants and dynamics of bid-ask spreads on the
London Stock Exchange, Journal of Financial Research, XIX, 377-394.
Menyah, K., and Paudyal, K., (2000) The components of bid-ask spreads on the London Stock
Exchange, Journal of Banking and Finance, 24, 1767-1785.
Narayan, P.K., (2008) Do shocks to G7 stock prices have a permanent effect? Evidence from
panel unit root tests with structural change, Mathematics and Computers in Simulation, 77,
369-373.
Narayan, P.K., and Sharma, S., (2011) New evidence on oil price and firm returns, Journal of
Banking and Finance, 35, 3253-3262.
Narayan, P.K., Mishra, S., and Narayan, S., (2011) Do market capitalisation and stocks traded
converge? New global evidence, Journal of Banking and Finance, 35, 2771-2781.
Nickell, S., (1981) Biases in dynamic models with fixed effects, Econometrica, 49, 1417-1426.
Parkinson M., (1980) The extreme value method for estimating the variance of the rate of
return, Journal of Business, 53, 61-65.
Petersen, M., and R. Rajan, (1995) The effect of credit market competition on firm-creditor
relationships. Quarterly Journal of Economics, 110, 407-443.
31
Phillips, P. C. B. and Sul, D., (2003) Dynamic panel estimation and homogeneity testing under
cross section dependence, The Econometrics Journal, 6, 217–260.
Phillips, P. C. B. and Sul, D., (2007) Bias in dynamic panel estimation with fixed effects,
incidental trends and cross section dependence, Journal of Econometrics, 137, 162–188.
Rogers, L.C.G., Satchell, S.E., (1991) Estimating variance from high, low, and closing prices,
Analysis of Applied Probability, 1, 50-512.
Rogers, L.C.G., Satchell, S.E., Yoon, Y., (1994) Estimating the volatility of stock prices: a
comparison of methods that use high and low prices, Applied financial Economics 4, 241-247.
Roll, R., and Subrahmanyam, A., (2010) Liquidity skewness, Journal of Banking and
Finance, 34, 2562-2571.
Sagi, J.S., and Seasholes, M.S., (2007) Firm-specific attributes and the cross-section of
momentum, Journal of Financial Economics, 84, 389-434.
Simkowitz, M.A., Beedles, W.L., (1978) Diversification in a three-moment world, Journal of
Financial and Quantitative Analysis, 13, 927-941.
Stoll, H.R., (1978) The pricing of security dealer services: An empirical study of NASDAQ
stocks, Journal of Finance, 33, 1153-1172.
Stoll, H.R., (1989) Inferring the components of the bid-ask spread: Theory and empirical tests,
Journal of Finance, 44, 115-134.
Stoll, H.R., (1978a) The supply of dealer services in securities markets, Journal of Finance, 33,
1133-1151.
Stoll, H.R., (1978b) The pricing of security dealer services: An empirical study of Nasdaq
stocks, Journal of Finance, 33, 1153-1172.
Stoll, H.R., (2000) Presidential address: Friction, Journal of Finance, 55, 1479-1514.
Tinic, S.M., (1972) The economics of liquidity services, Quarterly Journal of Economics, 86,
79-97.
32
Tinic, S.M., and West, R.R., (1972) Competition and the pricing of dealer service in the over-
the-counter stock market, Journal of Quantitative and Financial Analysis, 7, 1707-1727.
Tinic, S.M., and West, R.R., (1974) Marketability of common stocks in Canada and the USA:
A comparison of Agent versus dealer dominated markets, Journal of Finance, 29, 729-746.
Vickery, J., (2008) How and why do small firms manage interest rate risk?, Journal of Financial
Economics, 87, 446-470.
Wei, J., and Zheng, J., (2010) Trading activity and bid-ask spreads of individual equity
options, Journal of Banking and Finance, 34, 2897-2916.
West, R.R., and Tinic, S.M., (1971) The economics of the stock market, Praeger Publishers,
New York.
33
Figure 1: Summary of time series regressions: % of firms with statistically significant
positive and negative effects of volume on spread
The figure below plots the percentage of firms having statistically significant positive
and negative effects of volume on spread for 16 sectors. These results are based
on time-series regressions performed for each firm by sector. The sample size for
each sector covers the period 1 January 1998 to 31 December 2008.
0
10
20
30
40
50
60
volume+ Volume-
34
Figure 2: Summary of time series regressions: % of firms with positive and
statistically significant effect of price on spread
The figure below plots the percentage of firms having statistically significant positive
effect of price on spread for 16 sectors. These results are based on time-series
regressions by firm for each sector. The sample size for each sector covers the
period 1 January 1998 to 31 December 2008.
0
5
10
15
20
25
30
35
Figure 3: Summary of time series regressions: % of firms with statistically
significant positive and negative effects of volatility on spread
The figure below plots the percentage of firms having statistically significant positive
and negative effect of volatility on spread for 16 sectors. These results are based
on time-series regressions for each firm by sector. The sample size for each
sector covers the period 1 January 1998 to 31 December 2008.
0
10
20
30
40
50
60
70
Volatility+ Volatility-
36
Table 1: Mean and coefficient of variation of log price and log volume
This table below provides mean and coefficient of variation for log price and log
volume of stocks that belong to five different sizes. The size classification is based
on firms’ market capitalisation. Size 1 represents stocks having lowest market
capitalisation and size 5 represents stocks having the largest market capitalisation.
The sample period is from 1 January 1998 to 31 December 2008.
Size Mean Coefficient of variation Price Volume Price Volume Size 1 3.541 11.406 0.255 1.437 Size 2 3.679 12.267 0.148 0.728 Size 3 3.742 13.009 0.307 0.631 Size 4 3.757 13.939 -0.693 0.392 Size 5 3.852 15.592 -0.693 0.668
37
Table 2: Results for the determinants of spread by sector
This table provides the panel fixed effect regression results for 16 different sector-
based panels. The dependent variable is the bid-ask spread. The explanatory variables
are lagged spread, price, volume, and volatility. P-values are provided in parenthesis.
*** and ** denote significance at 1% and 5% level, respectively. The sample
period covers from 1 January 1998 to 31 December 2008.
Sector Intercept Lagged Spread
Price Volume Volatility
Agriculture -0.197**
* (0.000)
-0.384**
* (0.000)
0.002*** (0.000)
0.0000000158*** (0.000)
-61.295**
* (0.000)
Banking 0.059***
(0.000)
-0.567**
* (0.000)
-0.004*** (0.000)
0.0000000003**
* (0.000)
-2.211*** (0.000)
Electricity -0.033**
* (0.000)
-0.307**
* (0.000)
-0.0006*** (0.000) 0.0000000003**
* (0.000)
-1.309*** (0.000)
Chemical -0.069**
* (0.000)
-0.848**
* (0.000)
-0.003 (0.678)
0.0000000251**
* (0.000)
-5.19*** (0.000)
Computer 0.048***
(0.000)
-0.352**
* (0.000)
-0.002** (0.000)
0.0000000010**
* (0.000)
-0.069 (0.544)
Energy -0.101**
* (0.000)
-0.326**
* (0.000)
0.0004*** (0.000)
0.0000000039**
* (0.000)
-4.445*** (0.000)
Engineering -0.147**
* (0.000)
-0.499**
* (0.000)
0.0008*** (0.000)
0.0000000101**
* (0.000)
-5.693*** (0.000)
38
Financial -0.064**
* (0.000)
-0.523**
* (0.000)
-0.002*** (0.000)
0.0000000064**
* (0.000)
-1.906*** (0.000)
Food -0.039**
* (0.000)
-0.223**
* (0.000)
-0.0004*** (0.000) 0.0000000041**
* (0.000)
-9.221*** (0.000)
General services
-0.405**
* (0.000)
-0.636**
* (0.000)
0.004 (0.000)
0.0000000055**
* (0.000)
-6.668 (0.333)
Manufacturing
-0.080**
* (0.000)
-0.338**
* (0.000)
0.0002*** (0.000)
0.0000000014**
* (0.000)
-1.156** (0.001)
Medical -0.032**
* (0.000)
-0.239**
* (0.000)
-0.0005*** (0.000) 0.0000000018**
* (0.000)
-0.082 (0.899)
Real estate -0.130**
* (0.000)
-0.498**
* (0.000)
-0.001*** (0.000)
0.0000000191**
* (0.000)
-8.649** (0.035)
Supply -0.045**
* (0.000)
-0.264**
* (0.000)
-0.00009**
* (0.000)
0.0000000005**
* (0.000)
-0.122** (0.042)
Textiles -0.083**
* (0.000)
-0.336**
* (0.000)
0.0004*** (0.000)
0.0000000090**
* (0.000)
-8.689*** (0.000)
Transport -0.075**
* (0.000)
-0.282**
* (0.000)
0.000*** (0.0003)
0.0000000117**
* (0.000)
-14.869**
* (0.000)
39
Table 3: Results for the determinants of spread by size
This table provides the panel fixed effect regression results for 5 different sizes of
stocks. The dependent variable is the bid-ask spread. The explanatory variables are
lagged spread, price, volume, and volatility. P-values are provided in parenthesis.
*** and ** denote significance at 1% and 5% level, respectively. The sample
period covers from 1 January 1998 to 31 December 2008.
Sector Intercept Lagged Spread
Price Volume Volatility
Size 1 -0.148*** (0.000)
-0.535*** (0.000)
-0.0007*** (0.000)
0.0000000547*** (0.000)
-5.748*** (0.000)
Size 2 -0.017*** (0.000)
-0.472*** (0.000)
-0.002*** (0.000)
0.0000000468***
(0.000)
-14.469*** (0.000)
Size 3 -0.223*** (0.000)
-0.645*** (0.000)
0.001*** (0.000) 0.0000000285***
(0.000)
-0.503 (0.144)
Size 4 -0.046*** (0.000)
-0.230*** (0.000)
-0.0006*** (0.001)
0.0000000053***
(0.000)
-3.399*** (0.000)
Size 5 -0.018*** (0.000)
-0.343*** (0.000)
-0.001*** (0.000) 0.0000000006***
(0.000)
-0.468*** (0.000)
40
Table 4: Results on the effect of different proxies of volatility on spread by sector
This table provides the panel fixed effect regression results on the effect of volatility
on spread for 16 different sector-based panels. The dependent variable is the bid-
ask spread. The explanatory variables are lagged spread, price, volume, and volatility,
but results are only reported for volatility. P-values are provided in parenthesis. ***
and ** denote significance at 1% and 5% level, respectively. The sample period
covers from 1 January 1998 to 31 December 2008.
Sector V1 V2 V3 Agriculture -2.341***
(0.000) -66.213*** (0.000)
-61.355*** (0.000)
Banking -0.768*** (0.000)
-0.682*** (0.000)
-0.258*** (0.000)
Electricity -0.542*** (0.000)
-2.045*** (0.000)
-0.049*** (0.000)
Chemical -1.129*** (0.000)
-7.072*** (0.000)
-0.307*** (0.000)
Computer -0.069 (0.544)
-0.163 (0.299)
0.003 (0.955)
Energy -0.527*** (0.000)
-6.419*** (0.000)
-0.031*** (0.000)
Engineering -4.307*** (0.000)
-2.036*** (0.000)
-0.108*** (0.000)
Financial -0.789*** (0.000)
-2.863*** (0.000)
-0.007 (0.341)
Food -0.871*** (0.000)
-10.87*** (0.000)
-0.069*** (0.000)
General services -1.477*** (0.000)
-10.85*** (0.000)
-4.140 (0.519)
Manufacturing -0.461*** (0.000)
-1.806*** (0.000)
-0.310*** (0.000)
Medical -0.030 (0.479)
-0.097 (0.886)
-0.144 (0.755)
Real estate -1.769*** (0.000)
-8.007*** (0.000)
-0.239 (0.255)
Supply -0.363** (0.000)
-0.257** (0.000)
-0.100** (0.000)
Textiles -0.625*** (0.000)
-9.555*** (0.000)
-0.070*** (0.012)
41
Transport -0.720*** (0.000)
-15.165*** (0.000)
-0.140*** (0.000)
42
Table 5: Results based on the determinants of spread based on daily data for
different sizes of stocks.
This table provides the panel fixed effect regression results for 5 different sizes of
stocks. The dependent variable is the bid-ask spread. The explanatory variables are
lagged spread, price, volume, and volatility. P-values are provided in parenthesis.
*** and ** denote significance at 1% and 5% level, respectively. The sample
period covers from 1 January 1998 to 31 December 2008.
Sector V1 V2 V3 Size 1 -3.918***
(0.000) -2.256*** (0.000)
-0.230*** (0.000)
Size 2 -1.500*** (0.000)
-17.083*** (0.000)
-0.138*** (0.000)
Size 3 -1.023*** (0.000)
-1.011*** (0.000)
-0.133*** (0.000)
Size 4 -0.699*** (0.000)
-4.552*** (0.000)
-0.081*** (0.000)
Size 5 -1.002*** (0.000)
-0.840*** (0.000)
-0.063*** (0.000)
43