The Cost of Liquidity:Results from a Natural Experiment1
Eugene KandelSchool of Business Administrationand Department of EconomicsHebrew University and CEPR,[email protected]
and
Isabel Tkatch2
Department of FinanceJ. Mack Robinson College of Business
Georgia State [email protected]
This Version: November 2009
1We thank Reza Mahani and seminar participants at the University of Arizonafor helpful comments. We also thank the Tel Aviv Stock Exchange for providingus with the data and we gratefully acknowledge �nancial support from the KruegerCenter for Financial Research.
2Corresponding author.
Abstract
Tel Aviv Stock Exchange is the only market open on Sundays and tradesETNs on local and US indices. We use this feature to estimate the causalrelation between the inventory cost and the bid-ask spread. We comparespreads on the most liquid indices on Sundays and other days using di¤erences-in-di¤erences approach to estimate the inventory component of the spreadwithout making structural assumptions. We show that on Sundays the bidask spread in the US ETNs more than doubles relative to the rest of theweek, indicating that inventory cost is an economically signi�cant transac-tion cost. The same e¤ect is found during the weekday morning hours whenthe Israeli market is open, but the European markets are still closed - theinventory component can reach as high as 80% of the spread during sometime intervals. No such e¤ects are observed in the Israeli indices.
JEL classi�cation: G10, G12, G15.Key words: Inventory, Liquidity, Limit order book, ETF.
1 Introduction
We use a unique feature of the Tel Aviv Stock Exchange (TASE) to es-
timate the causal relation between the cost of inventory and the bid-ask
spread. TASE is the only market in the world that is open on Sundays,
and which trades Exchange Traded Notes (ETNs) on domestic and foreign
indices throughout the week.1 The ETN market is organized as an elec-
tronic limit order book, where the issuers of ETNs implicitly act as market
makers providing additional liquidity. All ETN liquidity providers, includ-
ing issuers, can hedge their exposure to ETNs on Israeli indices throughout
the week, however, they cannot hedge their exposure to ETNs on foreign
indices on Sunday and holidays.2 This implies that the cost of carrying in-
ventory of foreign ETNs on Sundays is much higher than during the rest of
the week, while there is no corresponding di¤erence for the domestic ETNs.
We use this natural experiment to estimate the e¤ect of inventory costs on
the spread in ETN markets. We �nd that on Sundays and holidays the
bid ask spread in foreign ETNs more than doubles relative to the rest of
the week, indicating that inventory holding cost imposes a large transaction
cost. The same e¤ect is found during the weekday morning hours, when the
Israeli market is open but the European markets are still closed. No e¤ects
are found in the Israeli ETNs.
Our methodological approach is completely di¤erent from those used in
previous studies of the e¤ect of inventory costs on the spread, which fall into
two broad categories: studies that estimate spread components, and those
1Exchange Traded Notes (ETNs) are similar to Exchange Traded Funds (ETFs), exceptthat they are structured as bonds, and the issuer is obligated to follow the index ratherthan to make the best e¤ort. The di¤erence is due to the Israeli regulatory environmentand as far as we can tell has no bearing on the issue we study.
2Hereafter we will use the terms US / foreign ETNs and Israeli / domestic ETNs toshorten for ETNs on US indices and ETNs on Israeli Indices.
1
that relate spreads to the actual inventory of the dealer. Empirical papers in
the �rst category (e.g. Glosten and Harris 1988, Hasbrouck 1988, Stoll 1989,
George, Kaul and Nimalendran 1991, Huang and Stoll 1997, Madhavan,
Richardson and Roomans 1997, Bollen, Smith and Whaley 2004) impose
strong assumptions on the order arrival and the fundamental price processes
to separate the variation in the bid-ask spread associated with inventory
control considerations from that associated with adverse selection and from
the order processing costs (see Hasbrouck 2002). The common approach is
to model the price process as the sum of transitory and permanent changes:
transitory price changes are attributed to inventory control, while permanent
ones are attributed to information.3 Most studies �nd that inventory costs
constitute a small proportion of the spread.
The second category includes papers that use data of market makers on
various exchanges (e.g. Hasbrouck and So�anos 1993, Madhavan and Smidt
1993, Hansh, Naik, and Vishwanathan 1998, and Reiss and Werner 1998),
and show that dealers hold large inventories, which deviate from their target
levels over long periods of time. The inventory positions are endogenous, and
so is the spread, which requires instruments to determine causality. Some try
to address this problem (e.g. Reiss and Werner 1998), but the identi�cation
relies on similarly strong structural assumptions about the price and order
arrival processes.
Our approach does not impose any structural assumptions, and does
not make use of the dealers�endogenous inventory levels. Instead, we focus
3Huang and Stoll (1997) is an interesting example of the e¤ect of the structural as-sumption on the estimated e¤ects. Their two-way decomposition of the spread impliesthat inventory and adverse selection together account for 11% of the spread. Yet, theresult is di¤erent in a three-way decomposition, which that requires additional structuralassumptions needed to separate the adverse selection component from the inventory com-ponent. Now, the inventory component is estimated as 29% of the spread and the adverseselection is 10%.
2
on changes in the inventory holding cost due to an exogenous shock which
prevents hedging positions on Sundays, as opposed to any other day of
the week. This allows us to establish a causal relation between inventory
management costs and the bid-ask spread and to estimate the magnitude
of this e¤ect in a clean way. To the best of our knowledge, this is the
�rst study in which the inventory e¤ect is estimated without making any
structural assumptions about the order �ow and price processes. We also
�nd a larger inventory cost component of the bid ask spread than previously
estimated.
Our �ndings suggest that in order to reduce the cost of liquidity, it is
important to allow the suppliers of liquidity to hedge their positions and
control their inventory exposure. Derivative markets, as well as trading
venues for designated market makers, are important for ensuring the low
cost of liquidity in the main (spot) security markets.4
The paper is organized as follows. Section 2 presents the data and the
empirical hypotheses. Section 3 presents the results and Section 4 concludes.
2 Hypotheses and Data
In this section we describe the speci�c features of the Tel Aviv Stock Ex-
change (TASE) that allow us to estimate the e¤ect of the inventory cost
4Our study is tangentially related to the literature on the relation between derivativesand spot markets. Facilitating e¢ cient risk sharing is the main argument supporting newderivatives markets, yet, the bene�ts of an increased speculative activity associated withthem are controversial (for example, see the theoretical discussion in Stein, 1987, and theempirical analyses in Bessembinder and Seguin, 1992). In our data, we cannot determinewhich traders provide liquidity. They could be better diversi�ed (Stoll, 1978), informed(Bloom�eld et al., 2005), speculators (Grossman and Miller, 1988) or patient traders(Foucault et al., 2005). Even though we can not test how any one of the trader typesa¤ects liquidity, we are able to show that when liquidity providers can hedge againstinventory risks the costs of liquidity provision decreases, depth increases, spreads arenarrow and the traded volume is high.
3
on the spread and establish a causal relation; we postulate the empirical
hypotheses and describe the data.
2.1 TASE Features and Empirical Hypotheses
TASE equity market operates quite similarly to Paris Euronext and Milan
Exchange. Trading starts with a call auction, followed by a continuous phase
and culminates with a closing phase. The day starts with an empty order
book at 8:30 AM, when traders start submitting limit and market orders.
At a random time between 9:45AM and 9:50AM all the submitted orders
are crossed, using an auction mechanism with time and price priority rules,
and the continuous trading phase begins. The continuous phase is a limit
order book, with designated market makers in some securities. All traders
observe the best three prices and quantities on each side. Traders may post
either market or limit orders, and those are executed according to price and
time priority rules. The closing phase begins at 4:55 PM; during our sample
period it was a simple crossing of traders�market orders that were executed
at the closing price. All unexecuted orders are cancelled at the end of the
trading day and the next day starts, again, with an empty book. Equities,
bonds, index options, futures contracts and ETNs are all traded on the same
TASE platform, with some minor di¤erences in hours, minimum order size
and tick size.
Since their inception, ETNs gained popularity in Israel as an inexpensive
tool for retail and institutional investors to get exposure to local and foreign
indices. We focus on three institutions that dominate the market with a
large number of o¤erings of ETNs on Israeli and US indices.5 The issuers
serve as informal market makers and supply liquidity for their ETNs along
5We chose ETNs on the major US indices, since they are much more liquid in Israelthan ETNs on other foreign indices.
4
with other market participants.
We utilize a speci�c feature in the TASE trading schedule that is driven
by the Jewish calendar, according to which Israeli markets and institutions
are closed on Fridays, but open on Sundays. This means that between Mon-
day and Thursday market makers and other liquidity suppliers can fully
hedge their open positions in foreign indices in the European futures mar-
kets. They do not use the US markets due to time di¤erences - US markets
open shortly before the Israeli markets close. European markets are closed
on Sunday, thus liquidity providers in US ETNs must carry the risk until the
next day, making the inventory cost on Sundays much higher than during
the rest of the week. Since the Israeli stock market is open on Sunday, no
such problem arises for Israeli ETNs.6
These features, combined with the implications of Grossman and Miller
(1988) and with the standard inventory models (e.g. Stoll 1978, Amihud
and Mendelson 1980, Ho and Stoll 1983, and O�Hara and Old�eld 1986)
allow us to postulate the following empirical hypotheses. Since carrying
inventory on Sundays is more expensive, liquidity providers will demand
a higher premium. The same intuition applies to intraday spreads, since
European futures markets open two hours later than the Israeli market,
which leads to the �rst hypothesis.
H1: Daily (Hourly) average bid ask spreads in ETNs on foreign indices,
during the days (hours) when European futures markets are closed are higher
than the spreads during the days (hours) when these markets are open. There
is no similar prediction for ETNs on Israeli indices.
Stoll (1989) suggests that the trading volume is inversely related to the
inventory holding period and, therefore, a¤ects the dealer�s ability to return6Bollen, Smith and Whaley (2004) show that the availability of options reduces inven-
tory costs on NASDAQ, since dealers may use them to hedg their inventory position.
5
to his preferred inventory level. We expect the e¤ect of trading volume to
be more pronounced for US ETNs on Sundays.
H2: The e¤ect of trading volume on the daily average bid ask spread
during the days when European futures markets are closed is higher than
the same e¤ect during the days when these markets are open. There is no
similar prediction for ETNs on Israeli indices.
Chordia, Roll and Subrahmanyam (2002) �nd that higher order imbal-
ances tend to increase spreads. When liquidity providers can hedge their
exposure this e¤ect should be rather small, but it should manifest itself
mostly when hedging is not available.
H3: The e¤ect of order imbalances on the daily average bid ask spread
during the days when European futures markets are closed is higher than
the same e¤ect during the days when these markets are open. There is no
similar prediction for ETNs on Israeli indices.
Finally, we use additional data for the year of 2008 (before and after
Lehman Brothers �led for bankruptcy) and compare the spreads to those
in 2006. The additional data presents one more natural experiment which
allows us to test the e¤ect of an exogenous shock to price volatility on the
cost of inventory and, through the inventory channel, on the bid-ask spread.
Our design allows for separation between the e¤ect of volatility on the spread
through the free option channel suggested by Copeland and Galai (1983),
and the e¤ect of volatility on the spread through the inventory channel
suggested by Stoll (1978) and O�Hara and Old�leld (1986).7 In periods of
high volatility we expect spreads to be wider due to an increase in the cost
7Note that in Stoll(1978) and O�Hara and Old�eld (1986) price volatility a¤ects thespread because it increases the probability of loss due to an adverse price change after thetrade in which inventory was acquired (inventory e¤ect). In Copeland and Galai (1983)price volatility a¤ects the spread because it increases the probability of loss due to anadverse price change before the trade (free option / picking o¤ e¤ect).
6
of inventory.
H4: The inventory component of the spread for US ETNs on Sundays
(described in Hypothesis H1) increases in the volatility of the price process.
When price volatility is low (in 2006) we expect the inventory component to
be small; when price volatility is high (in the second period of 2008, after
Lehman Brothers �led for bankruptcy) we expect the inventory component to
be large.
2.2 Sample and Descriptive Statistics
We have chosen a sample period of one year: January 1 to December 31, 2006.
During this period there were no drastic events a¤ecting the TASE market,
and there were no signi�cant regulatory changes. Our methodology relies on
di¤erences between days of the week thus, which requires a relatively long
sample period. We chose 14 most liquid ETNs and obtain quotes, orders
and transactions data on all the above mentioned ETNs from TASE. We
restrict our sample to the three largest issuers, each of whom has ETNs on
both Israeli and US indices. In Table 1 we present summary statistics for
the sample of ETNs, and it is evident that there is a similar pattern for all
issuers: ETNs on the Israeli indices have higher daily volumes and lower
spreads.
As stated above, we are interested in comparisons of the percentage
quoted bid-ask spread across two regimes: on days/hours when the European
futures exchanges are closed (Sundays and European holidays, as well as
the morning hours of regular weekdays) versus other trading days/hours.
Unlike the US ETNs, the Israeli ETNs are not predicted to exhibit signi�cant
di¤erences under the two regimes.8 In Table 2 we present summary statistics
8We will shorten the description of ETNs and use the terms US/foreign ETNs andIsraeli/domestic ETNs.
7
for Israeli and US ETNs and the two regimes. The bid ask spread for
Israeli ETNs is practically una¤ected by Sundays (0.11% versus 0.13%),
while the spread for US ETNs is more than doubled (0.40% versus 0.94%).
The spreads for US ETNs are higher on any day of the week, which may
result from FX exposure risk, lower liquidity and higher cost of hedging
abroad. It is clear that the Sunday e¤ect on Israeli ETNs is trivial while the
e¤ect on US ETNs is large.
It is evident that other variables are also a¤ected by the type of the
ETN and by holidays. The average daily trading volume, which proxies
for liquidity, is higher for Israeli ETNs and it decreases much more for US
ETNs on Sundays. We also de�ne a measure of order imbalance as the net
buy-side order volume scaled by the total order volume for the day. This
measure ranges from minus one to one, and assumes the extreme values if
all the orders are either sell side (-1) or buy-side orders (+1). Since we are
interested in the imbalance for orders that demand liquidity, we consider only
market orders in this calculation.9 Order imbalance is on average negative
and, on average, it is more extreme for Israeli ETNs. For US ETNs on
Sundays, we observe the lowest average imbalance.
Lastly, we show that there is intense competition among liquidity providers
on TASE. The daily order volume is about 1,000 times higher than the
traded volume, and practically all of that volume is limit orders (supply of
liquidity). Market orders, which constitute about 35% of the order �ow for
the most liquid stocks traded on TASE, constitute only 2% of the ETNs�
daily order �ow. This is what we expect to see in a market with high fre-
quency computerized trading, in which traders make money as voluntary
9We will use the term market order to describe both market and marketable limitorders, since market orders per se are almost never used on TASE. A marketable limitorder is a de�ned as limit buy (sell) order priced at or above the best ask (bid).
8
suppliers of liquidity. Hendershott et al. (2009) show that this phenom-
ena contributed to the decrease in spreads on the NYSE. Even though the
trading and order volumes for US ETNs Sundays are low relative to other
trading day, we still �nd 94% limit order in the order �ow, which suggests
an intense competition among liquidity suppliers.
3 Results
We start by modeling the daily average bid-ask spread. Then, we investi-
gate a more detailed intraday version of the data, in which the dependent
variable is the average bid-ask spread measured for �ve 90 minutes time
intervals during the day. We use two di¤erent estimation approaches: a
regression model with clustered (robust) standard errors and a mixed linear
model approach.10 The disadvantage of mixed linear models is the assump-
tion of normality,11 but it has one major advantage. We are able to ex-
plicitly model a speci�c variance-covariance structure, which contributed to
our understanding of inventories and spreads beyond the control for possible
correlations and heteroskedasticity.
3.1 The Daily Average Bid-Ask Spread
The daily panel data regression is designed for a simple di¤erences-in-di¤erences
analysis: we are interested in the change in spreads for Israeli ETNs versus
the change in spreads for US ETNs due to an exogenous shock: whether the
trading day is Sunday (Sundays / holidays) or not. The exogenous shock to
the dealer�s ability to hedge against inventory risk, and therefore the DID
10For discussion of clustered standard errors see Petersen (2009). For discussion ofmixed linear model see Hsiao (2003).11The normality assumption should not be a problem for our dependent variable since
we model the average spread.
9
estimate, captures the e¤ect of inventory on the bid-ask spread.
Let us de�ne the notations. The time-weighted average percentage-
spread is denoted by yst, which is observed for ETN s on day t (s = 1; :::; 14,
t = 1; :::; 248).12 We estimate the model
yst = �ij + xst�
ij + "st;
where i takes the value of one (or USIndexs = 1) if ETN s is on one of the US
indices, and zero if the ETN is on an Israeli index. Similarly, j takes the value
of one (or Sundayt = 1) if the European markets are open on date t (Sun-
day or holiday), and zero otherwise. The superscript ij identi�es four sets of
parameters, one for each combination of the binary variables USIndexs and
Sundayt. We estimate four intercepts (�00; �01; �10; �11) and four vectors of
slope coe¢ cients (�00; �01; �10; �11), to allow for variation in the e¤ects of the
explanatory variables on the spreads, for the Israeli and US ETNs, on Sun-
days and on other trading days. The vector of explanatory variables is the
same for all ETNs and regimes ij, xst= [LogV olumst; Imbalancest; D1st; D2st].
We denote by LogV olumst the log of daily trading volume for ETN s on
day t. Imbalancest is the absolute value of net buy-side market order �ow
scaled by the total market order volume for for ETN s on day t. We also
use dealer / issuer �xed e¤ects (D1st and D2st) and cluster the standard
errors by ETN and date.
Estimation results are presented in Table 3. Model 1 uses only four
intercepts, which are the conditional means of the spread for various cat-
egories: weekdays versus Sundays, and Israeli versus US ETNs.13 At the
12We have spread data for 248 days, but the orders and transactions data is missing forthe week of January 22 - January 26. Therefore, we include 248 days in all analyses of thespread, but only 243 day in the analyses involving trading volume and order imbalances.13Note that the speci�cation of an intercept for every one of the four combinations
of USIndexs, and Sundayt is standard for Generalized Linear Models (GLM), and it is
10
bottom of the table we present the estimates of di¤erences and di¤erences-
in-di¤erences across various categories. First, the spreads of US ETNs are
always signi�cantly higher than those of Israeli ETNs, which is not surpris-
ing as the former involve higher processing and hedging costs. The di¤erence
between the spread on Israeli ETNs on weekdays and Sundays is not statis-
tically signi�cant (0.113% versus 0.127%) as there are no di¤erences in the
inventory costs. The spread of US ETNs is more than doubled on Sundays
relative to other trading days (0.404% versus 0.943%) and the di¤erence
is highly statistically signi�cant. The DID estimate is large (0.526%) and
highly signi�cant. This implies that the inventory component of the bid-ask
spread is over 55% , which is higher than what was traditionally found in
the empirical studies.
Model 2 controls for other explanatory variables: trading volume, order
imbalances and dealer e¤ects, which implies that the intercepts are no longer
simple conditional means. Yet, the implied inventory component still range
between 51% and 59% across dealers. The coe¢ cients on the explanatory
variables are in line with our expectations: the trading volume has a negative
and signi�cant e¤ect on the spread, while the e¤ect of order imbalances is
positive but insigni�cant. We test the DID contrasts for those two variables
and show that trading volume and order imbalances have stronger e¤ects
when traders cannot hedge inventory risk: the contrast of trading volume is
negative and statistically signi�cant while the order imbalances contrast is
positive but insigni�cant.
When presented with the predictions of theoretical models of inventory
equivalent to the speci�cation yst = �+ �1 � USIndexs + �2 � Sundayt + �3 � USIndexs �Sundayt+"st, in which �00 = �, �01 = �+�1, �10 = �+�2 and �11 = �+�1+�2+�3. Wechoose to structure the equation that way to simplify the interpretation of the parameters,interaction terms and DID tests.
11
control, dealers tend to dismiss them as an oversimpli�cation (see Hasbrouck,
2007). We suspect that they do not constantly adjust the spread in response
to inventory changes since they are able to hedge those risks. When hedging
is not possible spreads become more sensitive to inventory changes and thus
to order imbalances.
The estimation approach used above is standard for panel data, but it
does allow for an explicit estimation of a more complex variance-covariance
structure. As the variance of spreads may be of interest to regulators and
other investors, we estimate a similar model of daily spreads using the mixed
linear e¤ects approach with repeated observations. this way we account for
possible correlation and obtain estimates of the variance covariance structure
under various regimes. Speci�cally, we estimate the model
yst = �ij + xst�
ij + s + �t + "st;
in which the �xed part �ij + xst�ij remains the same as before. We add
s and �t, ETN and date random e¤ects to control for correlated standard
errors instead of clustering. We also control for possible heteroskedasticity
by estimating four di¤erent variances, one for each combination of USIndexs
and Sundayt.
The results presented in Table 3 are similar to those presented before
for the �xed e¤ects and the DID tests. To check whether heteroskedasticity
adds explanatory power to the model we compare the likelihood of our model
to that of restricted models, which assume either two variances (determined
by categories of USIndexs) or a single variance parameter. Both likelihood
ratio tests are signi�cant, indicating that the chosen structures contributes
to the explanatory power of our model.14 The heteroskedasticity result14Estimation results of the restricted models are not presented in the paper. They are
available upon request.
12
has an appealing intuitive explanation and it extends our understanding
of the e¤ect of inventory risk. If a trader demands liquidity in US ETNs
and arrives to the market on Sunday, not only the expected spread is wide
relative to other trading days (0.952% versus 0.412%) but there is also more
uncertainty about the spread, as implied by the higher variance (0.570 versus
0.094). We expect to see higher price volatility for US ETNs on Sunday, not
only because the average spread is wide but because the range of spread
realizations is also wide.
Lastly, the variance result remains in Model 2, where we control for
trading volume and order imbalances, which rules them out as explanations
of this phenomena. We suspect that properties of the limit order book,
beyond the best bid and ask prices, are driving the heteroskedasticity result:
the distance to the next price level and depth. When we observe small
variances in cases such as Israeli ETNs on Sundays, we �nd that the depth
at the best quote is high and the distance between the best and the next
quote is small. When we observe large variances in cases such as US ETNs
on Sundays, we �nd that depth at the best quote is low and the distance
between the best and the next quote is large. This implies that an order
that will not have any e¤ect on the spread for Israeli ETNs will increase the
spread for US ETNs, which leads to higher variance. Since we only model
the inside spread rather than the whole book, it is important to allow for
heteroskedasticity to control for such di¤erences.
The daily data clearly indicates that we cannot reject the causal rela-
tion between the exogenous shock to inventory cost and the spread that is
statistically and economically signi�cant. We now proceed to the intraday
analyses.
13
3.2 The Intraday Spread
We calculate the time weighted percentage bid-ask spread for every 90
minutes interval during the continuous trading phase, and obtain �ve in-
traday spread observations rather than one daily average for every ETN
and trading day in our sample. To account for the additional complexity of
the data, we extend the speci�cation of the mixed model described above
and estimate
ystk = �ijk + xstk�
ij + s + �t + "stk:
As before, i takes the value of one if ETN s is on one of the US indices,
and zero if the ETN is on an Israeli index; j takes the value of one if the
European markets are open on date t and zero otherwise. The new index
k (or the variable Daytime) takes the values of one through �ve according
to the time interval
Daytime =
8>>>><>>>>:1 between 09:45 - 11:152 between 11:15 - 12:453 between 12:45 - 14:154 between 14:15 - 15:455 between 15:45 - 17:15
:
The superscript ij identi�es four sets of slope coe¢ cients (�00; �01; �10; �11),
one for each combination of the binary variables USIndexs and Sundayt.
As for the intercepts, we now use the superscript ijk to identify 20 para-
meters (�001; :::; �005; �011; :::; �115), one for each combination of USIndexs,
Sundayt and Daytime (3-way interaction). The explanatory variables are
the same as before calculated for every 90 minutes interval rather than
on a daily basis. As before, we add s and �t, ETN and date random
e¤ects to control for correlated standard errors. We control for possible
heteroskedasticity by estimating 20 di¤erent variances, one for each combi-
nation of USIndexs, Sundayt and Daytime, and four autocorrelations of
the intraday spreads, one for each combination of USIndexs and Sundayt.
14
Results are presented in Table 5. First, we observe a clear U-shaped
intraday pattern for Israeli ETN spreads and an inverted J-shaped pattern
for US ETNs. Second, US ETN spreads are much wider, especially in the
�rst hour of the day when the European futures markets are closed due
to time di¤erences between Europe and Israel. Third, as before, Sunday
spreads for Israeli ETNs are no di¤erent than spreads during the rest of the
week, but the spreads for US ETNs are much wider on Sundays. The DID
estimates, for the second through �fth time intervals, range between 0.470%
and 0.619% and. In relative terms, it implies an inventory component of 60%
to 78%. In the �rst time interval we get the lowest estimate (0.466% which
is 31% of the spread), but in this case the inventory e¤ect is underestimated
since hedging is not available for US ETNs on the �rst time interval of
any trading day. This is also supported by the positive DID estimates of
the �rst and second time intervals, which are positive and signi�cant. This
implies that the expectation to be able to hedge in the next time interval
decreases the spreads for US ETNs on weekdays, but not to their levels in
the second time interval when hedging is actually possible. Again, these
�ndings indicate that the e¤ect of the inventory cost can be larger than
previously documented.
Controlling for dealer e¤ects, trading volume and order imbalances dur-
ing the time interval does not change our results. Both volume and imbal-
ances have the correct signs and the e¤ect of volume is even signi�cant, but
the variables don�t contribute much to the explanatory power of the model.
In fact Model 2 implies an even higher inventory component than Model 1.
In Table 5, we extend the number of groups from four that we used in the
daily model to twenty: four for every time interval. We allow for intraday
variation in the variance of the spread and assume that the intraday spreads
15
may be autocorrelated (follow an ARH(1) process).15 Similar to the daily
model in Table 4, we �nd that the inventory cost a¤ects not only the average
spread, but also its volatility. First, the volatility of the spread for US ETNs
is higher than that of Israeli ETNs. Second, there is another di¤erence in
the intraday patterns between the local and US ETNs: while the volatility is
much higher towards the end of the day in the Israeli ETNs on all days, the
highest volatility for the US ETNs is during the �rst time interval, and it is
much higher on Sundays. Third, the di¤erences in spread volatility between
Sundays and the rest of the week for the Israeli ETNs are negligible, while
they are very large for the US ETNs. As we showed for the daily spreads,
the increased cost of inventory control has a strong independent e¤ect on
the variances of intraday spreads.
3.3 The E¤ect of Price Volatility
In this section we introduce one more exogenous shock to test the volatility
hypothesis. The model is similar to that described for average daily bid
ask spreads, but now we simultaneously estimate the intercepts for three
time periods: 2006, 2008 before Lehman Brothers �led for bankruptcy (Jan-
uary, 1 - September, 15) and 2008 after Lehman Brothers �les for bank-
ruptcy. Estimation results are presented in Table 6. Model 1 uses only
twelve intercepts (four for every period), which are the conditional means
of the spread for various categories: weekdays versus Sundays, and Israeli
versus US ETNs. At the bottom of the table we present the estimates of
di¤erences-in-di¤erences (DID) and di¤erences-in-di¤erences-in-di¤erences
(DIDID) across categories.
15ARH(1) is a heterogenous AR(1) process. In our case, we get 5 variance parameters(one for every daytime category) and one autocorrelation parameter. Likelihood ratiotests indicate that the ARH(1) speci�cation signi�cantly increases the explanatory powerof the model.
16
First, it is clear that spreads for all ETNs on all trading days are rela-
tively low in 2006 and they increase to the highest level in the second period
of 2008. This e¤ect may be attributed to the high levels of uncertainty and
price volatility during the �nancial crisis, but we are interested in the causal
e¤ect of volatility on the cost of inventory and therefore on the spread rather
than a general relation between price volatility and spreads. We start with
the �rst three DID tests, which are similar to those we presented in Tables
3 and 4 and imply a signi�cant inventory cost in every one of the three time
intervals. Yet, the test of a causal volatility e¤ect comes from a comparison
of the inventory component over time. Since price volatility increases from
a relatively low level in 2006 to a higher level in the �rst period of 2008
and its highest level in the second period of 2008, we expect the inventory
component to increase as well. Comparing the three inventory components,
we get a signi�cant increases as a result of the rise in price volatility (0.741-
0.526=0.215 and 1.129-0.741=0.388), which supports our fourth hypothesis.
In this test we establish a causal relation between the price volatility and the
cost of inventory, which leads to a statistically and economically signi�cant
increase in the bid ask spread.
4 Conclusions
In this paper we use the fact that Tel Aviv Stock Exchange is open on
Sundays to estimate the causal relation between the inventory cost and the
bid-ask spread. We compare spreads on the most liquid ETNs on the ma-
jor Israeli and US indices, on Sunday and other days, using di¤erences-in-
di¤erences approach. This allows us to avoid making structural assumptions
to estimate the inventory component of the spread. We show that on Sun-
days and other European holidays the bid ask spread in the US ETNs more
17
than doubles relative to the rest of the week, indicating that inventory cost
is an economically signi�cant transaction cost. The same e¤ect is found
during the weekday morning hours when the Israeli market is open, but the
European markets are still closed - the inventory component can reach as
high as 80% of the spread during some intraday time intervals. No such
e¤ect is observed in the Israeli indices. Finally, we show that the e¤ect of
the trading volume on the spread is much more pronounced in foreign in-
dices on Sunday than on other days or on the Israeli indices. The e¤ect of
buying/selling pressure on the spread is positive but insigni�cant. The e¤ect
of price volatility on the inventory component of the spread is economically
and statistically signi�cant.
This study shows that inventory control consideration can have large
e¤ects on the trading costs. Market designers and regulators should make
sure that liquidity providers can hedge their inventory risk to reduce the
costs of liquidity provision.
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20
21
Table 1: Sample of ETNs
Summary statistics for the sample of 14 most liquid ETNs traded on TASE. The sample period is from January 1, 2006 to December 31, 2006 with the exception of the last two ETNs, which started trading on February 9 and February 2 respectively. We report the issuer, index and index country, average bid-ask spread and the mean daily NIS volume for every ETN. There are 248 trading days in 2006 but transactions and orders data is missing for 5 trading days (January 22 to January 26). Any calculation involving trading and order volume will exclude the observations for those days.
Number of Avg. Price* Avg. Bid-Ask Daily Trading
Issuer (Dealer) Index Country Trading Days (NIS)** Spread Volume (NIS)**
Excellence TA100 Israel 248 85.3 0.10% 8,783,466
Excellence TA25 Israel 248 84.4 0.08% 21,121,451
Excellence SP500 US 248 58.4 0.22% 3,857,287
Excellence NASDQ100 US 248 73.1 0.21% 5,013,806
Excellence DJ30 US 248 50.9 0.52% 618,422
Excellence Russell2000 US 248 32.7 0.50% 1,152,598
CLAL Finance TA100 Israel 248 8.6 0.18% 3,075,061
CLAL Finance TA25 Israel 248 8.4 0.09% 10,999,631
CLAL Finance SP500 US 248 58.4 0.74% 596,337
CLAL Finance NASDQ100 US 248 16.2 0.44% 562,095
TACHLIT TA100 Israel 248 85.9 0.16% 3,637,179
TACHLIT TA25 Israel 248 8.4 0.09% 7,967,820
TACHLIT SP500 US 224 58.3 0.67% 661,398
TACHLIT NASDQ100 US 219 36.5 0.89% 611,715
* The tick size is {0.001 if price < NIS 10; 0.01 if NIS 10≤ price< NIS 100; 0.1 if NIS 100≤ price< NIS 1000; 1 if price > NIS 1,000}
** In 2006 the exchange rate was about NIS 4.5 to $US 1.
22
Table 2: Descriptive Statistics
Descriptive statistics for the sample of 14 most liquid ETNs traded on TASE. The sample period is from January 1, 2006 to December
31, 2006. We present the median, mean and standard deviation for the spread, order imbalance measure, trading volume and order
volume. All distribution statistics are presented by Index country (Israel / US) and for two regimes (Sunday / Weekday).
Percentage Spread # of Obs. Median Mean STD
Israel Weekday 1,176 0.07% 0.11% 0.23%
Sunday 312 0.07% 0.13% 0.25%
US Weekday 1,526 0.31% 0.40% 0.38%
Sunday 405 0.68% 0.94% 0.82%
Order Imbalance Measure
Israel Weekday 1,152 -0.102 -0.077 0.405
Sunday 306 -0.074 -0.108 0.401
US Weekday 1,502 -0.026 -0.053 0.658
Sunday 399 0.000 -0.032 0.597
Daily Trading Volume (1,000 NIS)
Israel Weekday 1,152 5,298 9,794 13,378
Sunday 306 4,549 7,270 9,577
US Weekday 1,502 564 1,993 3,898
Sunday 399 123 392 623
Daily Order Volume (1,000 NIS)
Israel Weekday 1,152 6,922,351 9,693,085 11,099,233
Sunday 306 6,433,447 9,577,979 12,083,183
US Weekday 1,502 537,151 1,010,417 1,277,976
Sunday 399 5,985 12,694 25,103
Daily Limit Order Volume / Total Order Volume
Israel Weekday 1,152 99.71% 99.34% 1.44%
Sunday 306 99.73% 99.32% 1.64%
US Weekday 1,502 99.56% 98.51% 3.93%
Sunday 399 94.04% 86.94% 18.45%
Daily Trading Volume / Daily Order Volume
Israel Weekday 1,152 0.12% 0.46% 1.24%
Sunday 306 0.10% 0.49% 1.45%
US Weekday 1,502 0.15% 0.90% 3.19%
Sunday 399 4.50% 11.23% 17.68%
Daily Trading Volume / Market Order Volume
Israel Weekday 1,152 49.56% 53.08% 30.35%
Sunday 306 46.19% 50.95% 32.31%
US Weekday 1,502 60.60% 65.34% 118.04%
Sunday 399 96.60% 95.88% 67.62%
23
Table 3: Daily Bid-Ask Spreads I
Table 3 reports the results of a panel data regression model for the average daily bid-ask spread. The model is estimated using least
squares approach and the standard errors are clustered by ETN and date. Model 1 uses only four intercepts, which are the
conditional means of the spread for various categories: weekdays versus Sundays, and Israeli versus US ETNs. Model 2 uses four
intercepts and controls for other explanatory variables: trading volume, order imbalances and dealer effects. The section Hypothesis
Tests reports estimates and tests of the DID contrasts.
Model 1 Model 2
Effects Notation Estimate P_Value Estimate P_Value
USindex = 0 Sunday = 0 μ00 0.113 <.01 0.361 <.01
USindex = 0 Sunday = 1 μ01 0.127 <.01 0.406 0.01
USindex = 1 Sunday = 0 μ10 0.404 <.01 0.776 0.03
USindex = 1 Sunday = 1 μ11 0.943 <.01 2.011 <.01
USindex = 0 Sunday = 0 Log Volume βV
00
-0.017 0.02
USindex = 0 Sunday = 1 Log Volume βV
01
-0.019 0.02
USindex = 1 Sunday = 0 Log Volume βV
10
-0.037 0.12
USindex = 1 Sunday = 1 Log Volume βV
11
-0.106 <.01
USindex = 0 Sunday = 0 Imbalance βI00
0.025 0.35
USindex = 0 Sunday = 1 Imbalance βI01
0.017 0.65
Usindex = 1 Sunday = 0 Imbalance βI10
0.045 0.37
USindex = 1 Sunday = 1 Imbalance βI11
0.061 0.56
USindex = 0 Dealer = D1
0.017 0.54
USindex = 0 Dealer = D2
0.010 0.61
Usindex = 1 Dealer = D1
0.024 0.81
USindex = 1 Dealer = D2
0.311 <.01
Hypothesis Tests Estimate P_Value Estimate P_Value
1. H0: (μ01 – μ00) = 0 0.013 0.56 0.044 0.73
2. H0: (μ11 – μ10) = 0 0.540 <.01 1.235 0.02
3. H0: (μ11 – μ10) – (μ01 – μ00) = 0 0.526 <.01 1.190 0.02
4. H0: (βV
11 – βV
10) – (βV
01 – βV
00) = 0
-0.067 0.05
5. H0: (βI11 – β
I10) – (β
I01 – β
I00) = 0
0.024 0.83
Fit Statistics
Adjusted R2
0.52 0.62
Number of Observations 3,419 3,359
24
Table 4: Daily Bid-Ask Spreads II
Table 4 reports the estimation results of as a mixed linear model of the average daily bid-ask spread. Model 1 uses only four
intercepts, which are the conditional means of the spread for various categories: weekdays versus Sundays, and Israeli versus US
ETNs. Model 2 uses four intercepts and controls for other explanatory variables: trading volume, order imbalances and dealer
effects. The section Hypothesis Tests reports estimates and test of the DID contrasts. The section Variance-Covariance reports the
random effects and estimates of the variances for four categories: weekdays versus Sundays, and Israeli versus US ETNs.
Model 1 Model 2
Effects Notation Estimate P_Value Estimate P_Value
USindex = 0 Sunday = 0 μ00 0.113 0.07 0.112 0.26
USindex = 0 Sunday = 1 μ01 0.127 0.05 -0.089 0.61
USindex = 1 Sunday = 0 μ10 0.412 <.01 0.612 <.01
USindex = 1 Sunday = 1 μ11 0.952 <.01 1.905 <.01
USindex = 0 Sunday = 0 Log Volume βV
00
-0.002 0.78
USindex = 0 Sunday = 1 Log Volume βV
01
0.012 0.25
USindex = 1 Sunday = 0 Log Volume βV
10
-0.023 <.01
USindex = 1 Sunday = 1 Log Volume βV
11
-0.097 <.01
USindex = 0 Sunday = 0 Imbalance βI00
-0.005 0.83
USindex = 0 Sunday = 1 Imbalance βI01
0.005 0.91
USindex = 1 Sunday = 0 Imbalance βI10
-0.013 0.61
USindex = 1 Sunday = 1 Imbalance βI11
0.018 0.85
USindex = 0 Dealer = D1
0.041 0.49
USindex = 0 Dealer = D2
0.036 0.55
Usindex = 1 Dealer = D1
0.065 0.24
USindex = 1 Dealer = D2
0.384 <.01
Hypothesis Tests Estimate P_Value Estimate P_Value
1. H0: (μ01 – μ00) = 0 0.013 0.58 -0.201 0.25
2. H0: (μ11 – μ10) = 0 0.540 <.01 1.293 <.01
3. H0: (μ11 – μ10) – (μ01 – μ00) = 0 0.527 <.01 1.494 <.01
4. H0: (βV
11 – βV
10) – (βV
01 – βV
00) = 0
-0.087 <.01
5. H0: (βI11 – β
I10) – (β
I01 – β
I00) = 0
0.020 0.86
Variance-Covariance Notation Estimate P_Value Estimate P_Value
ETN RE
σ2
ETN 0.023 <.01 0.003 0.01
Date RE
σ2
Date 0.017 <.01 0.018 <.01
USindex = 0 Sunday = 0
σ2
00 0.036 <.01 0.037 <.01
USindex = 0 Sunday = 1
σ2
01 0.039 <.01 0.039 <.01
USindex = 1 Sunday = 0
σ2
10 0.094 <.01 0.093 <.01
USindex = 1 Sunday = 1
σ2
11 0.570 <.01 0.469 <.01
Fit Statistics
-2 Log Likelihood 1,414.8 1,290.7
Number of Observations 3,419 3,359
25
Table 5: Intraday Spreads
Table 5 reports the estimation results of as a mixed linear model of the average bid-ask spread calculated for five 90 minutes
intervals during the day. Model 1 uses 20 intercepts, which are the conditional means of the spread for various categories: time
interval (1-5), weekdays / Sundays and Israeli / US ETN. Model 2 uses 20 intercepts and controls for other explanatory variables:
trading volume, order imbalances and dealer effects. The section Hypothesis Tests reports estimates and test of the DID contrasts.
The section Variance-Covariance reports the random effects and estimates of the variances for 20 categories: time intervals (1-5),
weekdays / Sundays and Israeli / US ETN, as well as intraday autocorrelations.
Model 1 Model 2
Effects Notation Estimate P_Value Estimate P_Value
USindex = 0 Sunday = 0 09:45 - 11:15 μ001 0.138 <.01 0.146 <.01
USindex = 0 Sunday = 0 11:15 - 12:45 μ002 0.060 0.03 0.066 0.01
USindex = 0 Sunday = 0 12:45 - 14:15 μ003 0.064 0.02 0.069 0.01
USindex = 0 Sunday = 0 14:15 - 15:45 μ004 0.110 <.01 0.116 <.01
USindex = 0 Sunday = 0 15:45 - 17:15 μ005 0.156 <.01 0.157 <.01
USindex = 0 Sunday = 1 09:45 - 11:15 μ011 0.131 <.01 0.127 <.01
USindex = 0 Sunday = 1 11:15 - 12:45 μ012 0.060 0.03 0.056 0.03
USindex = 0 Sunday = 1 12:45 - 14:15 μ013 0.057 0.04 0.052 0.04
USindex = 0 Sunday = 1 14:15 - 15:45 μ014 0.141 <.01 0.138 <.01
USindex = 0 Sunday = 1 15:45 - 17:15 μ015 0.192 <.01 0.175 <.01
USindex = 1 Sunday = 0 09:45 - 11:15 μ101 1.066 <.01 1.074 <.01
USindex = 1 Sunday = 0 11:15 - 12:45 μ102 0.183 <.01 0.183 <.01
USindex = 1 Sunday = 0 12:45 - 14:15 μ103 0.166 <.01 0.165 <.01
USindex = 1 Sunday = 0 14:15 - 15:45 μ104 0.235 <.01 0.234 <.01
USindex = 1 Sunday = 0 15:45 - 17:15 μ105 0.271 <.01 0.266 <.01
USindex = 1 Sunday = 1 09:45 - 11:15 μ111 1.525 <.01 1.650 <.01
USindex = 1 Sunday = 1 11:15 - 12:45 μ112 0.802 <.01 0.909 <.01
USindex = 1 Sunday = 1 12:45 - 14:15 μ113 0.713 <.01 0.812 <.01
USindex = 1 Sunday = 1 14:15 - 15:45 μ114 0.788 <.01 0.880 <.01
USindex = 1 Sunday = 1 15:45 - 17:15 μ115 0.777 <.01 0.871 <.01
USindex = 0 Sunday = 0 Log Volume βV
00
-0.001 0.01
USindex = 0 Sunday = 1 Log Volume βV
01
-0.000 0.33
USindex = 1 Sunday = 0 Log Volume βV
10
-0.002 <.01
USindex = 1 Sunday = 1 Log Volume βV
11
-0.018 <.01
USindex = 0 Sunday = 0 Imbalance βI00
0.008 0.02
USindex = 0 Sunday = 1 Imbalance βI01
0.005 0.12
USindex = 1 Sunday = 0 Imbalance βI10
-0.000 0.99
USindex = 1 Sunday = 1 Imbalance βI11
0.019 0.63
USindex = 0 Dealer = D1
0.006 0.86
USindex = 0 Dealer = D2
0.011 0.75
Usindex = 1 Dealer = D1
0.139 <.01
USindex = 1 Dealer = D2
-0.051 0.10
26
Table 5: Intraday Spreads (Continued)
Model 1 Model 2
Hypothesis Tests Estimate P_Value Estimate P_Value
1. H0: (μ111 – μ101) – (μ011 – μ001) = 0 0.466 <.01 0.594 <.01
2. H0: (μ112 – μ102) – (μ012 – μ002) = 0 0.619 <.01 0.736 <.01
3. H0: (μ113 – μ103) – (μ013 – μ003) = 0 0.553 <.01 0.664 <.01
4. H0: (μ114 – μ104) – (μ014 – μ004) = 0 0.522 <.01 0.623 <.01
5. H0: (μ115 – μ105) – (μ015 – μ005) = 0 0.4670 <.01 0.587 <.01
6. H0: (1) – (5) simultaneously
<.01 0.142 0.03
7. H0: [(μ112 – μ102) – (μ012 – μ002)] - [(μ111 – μ101) – (μ011 – μ001)] = 0 0.153 0.02
0.03
8. H0: (βV
11 – βV
10) – (βV
01 – βV
00) = 0
-0.017 <.01
9. H0: (βI11 – β
I10) – (β
I01 – β
I00) = 0
0.022 0.58
Variance-Covariance Notation Estimate P_Value Estimate P_Value
ETN RE
σ2
ETN 0.004 <.01 0.001 0.01
Date RE
σ2
Date 0.001 <.01 0.001 <.01
USindex = 0 Sunday = 0 09:45 - 11:15 σ2
001 0.010 <.01 0.010 <.01
USindex = 0 Sunday = 0 11:15 - 12:45 σ2
002 0.002 <.01 0.002 <.01
USindex = 0 Sunday = 0 12:45 - 14:15 σ2
003 0.043 <.01 0.044 <.01
USindex = 0 Sunday = 0 14:15 - 15:45 σ2
004 0.243 <.01 0.248 <.01
USindex = 0 Sunday = 0 15:45 - 17:15 σ2
005 0.135 <.01 0.129 <.01
USindex = 0 Sunday = 0 ARH(1) ρ00 0.202 <.01 0.202 <.01
USindex = 0 Sunday = 1 09:45 - 11:15 σ2
011 0.008 <.01 0.008 <.01
USindex = 0 Sunday = 1 11:15 - 12:45 σ2
012 0.001 <.01 0.001 <.01
USindex = 0 Sunday = 1 12:45 - 14:15 σ2
013 0.001 <.01 0.001 <.01
USindex = 0 Sunday = 1 14:15 - 15:45 σ2
014 0.379 <.01 0.386 <.01
USindex = 0 Sunday = 1 15:45 - 17:15 σ2
015 0.124 <.01 0.097 <.01
USindex = 0 Sunday = 1 ARH(1) ρ10 0.490 <.01 0.494 <.01
USindex = 1 Sunday = 0 09:45 - 11:15 σ2
101 1.518 <.01 1.534 <.01
USindex = 1 Sunday = 0 11:15 - 12:45 σ2
102 0.035 <.01 0.035 <.01
USindex = 1 Sunday = 0 12:45 - 14:15 σ2
103 0.011 <.01 0.011 <.01
USindex = 1 Sunday = 0 14:15 - 15:45 σ2
104 0.459 <.01 0.464 <.01
USindex = 1 Sunday = 0 15:45 - 17:15 σ2
105 0.118 <.01 0.110 <.01
USindex = 1 Sunday = 0 ARH(1) ρ10 0.343 <.01 0.345 <.01
USindex = 1 Sunday = 1 09:45 - 11:15 σ2
111 2.468 <.01 2.351 <.01
USindex = 1 Sunday = 1 11:15 - 12:45 σ2
112 0.662 <.01 0.606 <.01
USindex = 1 Sunday = 1 12:45 - 14:15 σ2
113 0.435 <.01 0.392 <.01
USindex = 1 Sunday = 1 14:15 - 15:45 σ2
114 0.952 <.01 0.909 <.01
USindex = 1 Sunday = 1 15:45 - 17:15 σ2
115 0.692 <.01 0.631 <.01
USindex = 1 Sunday = 1 ARH(1) ρ11 0.722 <.01 0.694 <.01
Fit Statistics
-2 Log Likelihood 2,795.0 2,618.0
Number of Observations 16,699 16,401
27
Table 6: Volatility and the Daily Bid-Ask Spreads
Table 6 reports the estimation results of as a mixed linear model of the average daily bid-ask spread. Model 1 uses only twelve
intercepts, four intercepts for each one of the three time periods: the year of 2006, the first part of 2008 (before Lehman Brothers
filed for bankruptcy in September 15, 2008) and the second part of 2008 (after Lehman Brothers filed for bankruptcy). We estimate
the conditional means of the spread, in every time period, for various categories: weekdays versus Sundays, and Israeli versus US
ETNs. Model 2 uses twelve intercepts and controls for other explanatory variables: trading volume, order imbalances and dealer
effects. The section Hypothesis Tests reports estimates and test of the DID and DIDID contrasts. The section Variance-Covariance
reports the random effects and estimates of the variances for twelve categories: weekdays versus Sundays, and Israeli versus US
ETNs in every one of the three time periods described above.
Model 1 Model 2
Effects Notation Estimate P_Value Estimate P_Value
USindex = 0 Sunday = 0 2006 μ006 0.113 0.07 0.089 0.43
USindex = 0 Sunday = 1 2006 μ016 0.127 0.05 -0.170 0.27
USindex = 1 Sunday = 0 2006 μ106 0.413 <.01 0.565 <.01
USindex = 1 Sunday = 1 2006 μ116 0.953 <.01 1.774 <.01
USindex = 0 Sunday = 0 2008 BLB μ00B 0.231 <.01 0.208 0.02
USindex = 0 Sunday = 1 2008 BLB μ01B 0.186 <.01 -0.117 0.41
USindex = 1 Sunday = 0 2008 BLB μ10B 0.417 <.01 0.569 <.01
USindex = 1 Sunday = 1 2008 BLB μ11B 1.113 <.01 1.837 <.01
USindex = 0 Sunday = 0 2008 ALB μ00A 0.282 0.10 0.259 0.15
USindex = 0 Sunday = 1 2008 ALB μ01A 0.294 0.09 -0.015 0.94
USindex = 1 Sunday = 0 2008 ALB μ10A 0.707 <.01 0.857 <.01
USindex = 1 Sunday = 1 2008 ALB μ11A 1.847 <.01 2.606 <.01
USindex = 0 Sunday = 0 Log Volume βV
00
-0.002 0.69
USindex = 0 Sunday = 1 Log Volume βV
01
0.016 0.06
USindex = 1 Sunday = 0 Log Volume βV
10
-0.016 <.01
USindex = 1 Sunday = 1 Log Volume βV
11
-0.080 <.01
USindex = 0 Sunday = 0 Imbalance βI00
-0.047 0.14
USindex = 0 Sunday = 1 Imbalance βI01
-0.031 0.59
USindex = 1 Sunday = 0 Imbalance βI10
0.004 0.85
USindex = 1 Sunday = 1 Imbalance βI11
0.043 0.47
USindex = 0 Dealer = D1
0.154 0.00
USindex = 0 Dealer = D2
0.014 0.78
Usindex = 1 Dealer = D1
0.264 <.01
USindex = 1 Dealer = D2
-0.066 0.16
Hypothesis Tests Estimate P_Value Estimate P_Value
1. H0: (μ116 – μ106) – (μ016 – μ006) = 0 0.527 <.01 1.469 <.01
2. H0: (μ11B – μ10B) – (μ01B – μ00B) = 0 0.741 <.01 1.593 <.01
3. H0: (μ11A – μ10A) – (μ01A – μ00A) = 0 1.129 <.01 2.022 <.01
4. H0: [(μ11B – μ10B) – (μ01B – μ00B)] – [(μ116 – μ106) – (μ016 – μ006)] = 0 0.214 <.01 0.125 0.04
5. H0: [(μ11A – μ10A) – (μ01A – μ00A)] – [(μ11B – μ10B) – (μ01B – μ00B)] = 0 0.388 <.01 0.429 <.01
4. H0: (βV
11 – βV
10) – (βV
01 – βV
00) = 0
-0.082 <.01
5. H0: (βI11 – β
I10) – (β
I01 – β
I00) = 0
0.023 0.80
28
Table 6: Volatility and the Daily Bid-Ask Spreads (Continued)
Model 1 Model 2
Variance-Covariance Notation Estimate P_Value Estimate P_Value
ETN RE
2006 σ2
ETN,6 0.023 <.01 0.037 <.01
ETN RE
2008 BLB σ
2ETN,B 0.021 <.01 0.002 0.08
ETN RE
2008 ALB σ
2ETN,A 0.172 <.01 0.153 <.01
Date RE
2006 σ2
Date,6 0.017 <.01 0.018 <.01
Date RE
2008 BLB σ2
Date,B 0.046 <.01 0.046 <.01
Date RE
2008 ALB σ2
Date,A 0.018 <.01 0.018 <.01
USindex = 0 Sunday = 0 2006 σ2
006 0.036 <.01 0.037 <.01
USindex = 0 Sunday = 1 2006 σ2
016 0.039 <.01 0.039 <.01
USindex = 1 Sunday = 0 2006 σ2
106 0.094 <.01 0.093 <.01
USindex = 1 Sunday = 1 2006 σ2
116 0.570 <.01 0.466 <.01
USindex = 0 Sunday = 0 2008 BLB σ2
00B 0.115 <.01 0.115 <.01
USindex = 0 Sunday = 1 2008 BLB σ2
01B 0.051 <.01 0.050 <.01
USindex = 1 Sunday = 0 2008 BLB σ2
10B 0.182 <.01 0.183 <.01
USindex = 1 Sunday = 1 2008 BLB σ2
11B 0.432 <.01 0.411 <.01
USindex = 0 Sunday = 0 2008 ALB σ2
00A 0.026 <.01 0.026 <.01
USindex = 0 Sunday = 1 2008 ALB σ2
01A 0.026 <.01 0.026 <.01
USindex = 1 Sunday = 0 2008 ALB σ2
10A 0.509 <.01 0.517 <.01
USindex = 1 Sunday = 1 2008 ALB σ2
11A 0.964 <.01 0.891 <.01
Fit Statistics
-2 Log Likelihood 5,724.7 5,130.1
Number of Observations 6,849 6,789