the cost of liquidity: results from a natural experimentfncitt/files/cost of liquidity.pdfthe cost...

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.

References

[1] Amihud, Y., Mendelson, H., 1980. Dealership markets: market-makingwith inventory. Journal of Financial Economics 8, 31-53.

[2] Bessembinder, H., Seguin, P., 1992. Futures Trading Activity and StockPrice Volatility. The Journal of Finance 47, 2015-2034.

[3] Bloom�eld, R., O�Hara, M., Saar, G., 2005. The �make or take�decisionin an electronic market: evidence on the evolution of liquidity. Journalof Financial Economics 75, 165-199.

[4] Bollen, N., Smith, T., Whaley, R., 2004. Modeling the bid/ask spread:measuring the inventory-holding premium. Journal of Financial Eco-nomics 72, 97-141.

[5] Copeland, T., Galai, D., 1983. Information E¤ects on the Bid-AskSpread, Journal of Finance, 38, 1457-69.

[6] Chordia, T., Roll, R., Subrahmanyam, A., 2002. Order imbalance, liq-uidity, and market returns. Journal of Financial Economics 65, 111-130.

18

[7] Foucault T., Kadan, O., Kandel, E. 2005. Limit order book as a marketfor liquidity. Review of Financial Studies 18, 1171-1218.

[8] George, T., Kaul, G., Nimalendran, M., 1991. Estimation of the bid-askspread and its components: a new approach. The Review of FinancialStudies 4, 623-656.

[9] Glosten, L., Harris, L., 1988. Estimating the components of the bid-askspread. Journal of Financial Economics 21, 123-142.

[10] Grossman, S. J., Miller, M. H., 1988. Liquidity and market structure.The Journal of Finance 43, 617-633.

[11] Hansch, O., Naik, N., Viswanathan, S., 1998. Do inventories matter indealership markets: evidence from the London Stock Exchange. Journalof Finance 53, 1623-1656.

[12] Hasbrouck, J., 1988. Trades, quotes, inventories and information. Jour-nal of Financial Economics 22, 229-252.

[13] Hasbrouck, J., 2002. Stalking the �e¢ cient price�in market microstruc-ture speci�cations: an overview. Journal of Financial Markets 5, 329�339.

[14] Hasbrouck, J., 2007. Empirical Market Microstructure: The Institu-tions, Economics, and Econometrics of Securities Trading. Oxford Uni-versity Press, US.

[15] Hasbrouck, J., So�anos, G., 1993. The trades of market makers: anempirical analysis of NYSE specialists. The Journal of Finance 48, 1565-1593.

[16] Hsiao, C., 2003. Analysis of Panel Data. Cambrige University Press,New York.

[17] Hendershott, T., Jones, C. M., Menkveld, A. J., 2009. Does algorithmictrading improve liquidity? Unpublished working paper.

[18] Ho, T., Stoll, H., 1983. The dynamics of dealer markets under compe-tition. Journal of Finance 38, 1053-1074.

[19] Huang, R. D., Stoll, H. R., 1997. The components of the bid-ask spread:a general approach. Review of Financial Studies 10, 995-1034.

[20] Kaniel, R., Liu, H., 2006. So What Orders Do Informed Traders Use?Journal of Business 79, 1867-1913.

[21] Madhavan, A., Richardson, M., Roomans, M., 1997. Why do securityprices change? A transaction-level analysis of NYSE stocks. Review ofFinancial Studies 10, 1035-1064.

19

[22] Madhavan, A., Smidt, S., 1993. An analysis of changes in specialistinventories and quotations. The Journal of Finance 48, 1595-1628.

[23] O�Hara, M., Old�eld, G. S., 1986. The microeconomics of market mak-ing. The Journal of Financial and Quantitative Analysis 21, 361-376.

[24] Petersen, O. P., 2009. Estimating standard errors in �nance panel datasets: comparing approaches. The Review of Financial Studies 22, 435-480.

[25] Reiss. P. C., Werner, I. M., 1998. Does risk sharing motivate interdealertrading? Journal of Finance 53, 1657�1703.

[26] Stein, J., 1987. Informational externalities and welfare-reducing specu-lation. Journal of Political Economy 95, 1123-1145.

[27] Stoll, H., 1978. The supply of dealer services in securities markets.Journal of Finance 33, 1133-1151.

[28] Stoll, H. R., 1989, Inferring the components of the bid-ask spread: The-ory and empirical tests. Journal of Finance 44, 115-134.

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


01

-0.019 0.02


10

-0.037 0.12


11

-0.106 <.01

USindex = 0 Sunday = 0 Imbalance βI00

0.025 0.35


0.017 0.65

Usindex = 1 Sunday = 0 Imbalance βI10

0.045 0.37


0.061 0.56

USindex = 0 Dealer = D1

0.017 0.54


0.010 0.61

Usindex = 1 Dealer = D1

0.024 0.81


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


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


00

-0.002 0.78


01

0.012 0.25


10

-0.023 <.01


11

-0.097 <.01


-0.005 0.83


0.005 0.91


-0.013 0.61


0.018 0.85


0.041 0.49


0.036 0.55


0.065 0.24


0.384 <.01


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


σ2

01 0.039 <.01 0.039 <.01


σ2

10 0.094 <.01 0.093 <.01


σ2

11 0.570 <.01 0.469 <.01

Fit Statistics

-2 Log Likelihood 1,414.8 1,290.7


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


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


00

-0.001 0.01


01

-0.000 0.33


10

-0.002 <.01


11

-0.018 <.01


0.008 0.02


0.005 0.12


-0.000 0.99


0.019 0.63


0.006 0.86


0.011 0.75


0.139 <.01


-0.051 0.10

26

Table 5: Intraday Spreads (Continued)

Model 1 Model 2


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


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 = 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 = 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


Fit Statistics

-2 Log Likelihood 2,795.0 2,618.0


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


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


00

-0.002 0.69


01

0.016 0.06


10

-0.016 <.01


11

-0.080 <.01


-0.047 0.14


-0.031 0.59


0.004 0.85


0.043 0.47


0.154 0.00


0.014 0.78


0.264 <.01


-0.066 0.16


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


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


016 0.039 <.01 0.039 <.01


106 0.094 <.01 0.093 <.01


116 0.570 <.01 0.466 <.01

USindex = 0 Sunday = 0 2008 BLB σ2

00B 0.115 <.01 0.115 <.01


01B 0.051 <.01 0.050 <.01


10B 0.182 <.01 0.183 <.01


11B 0.432 <.01 0.411 <.01

USindex = 0 Sunday = 0 2008 ALB σ2

00A 0.026 <.01 0.026 <.01


01A 0.026 <.01 0.026 <.01


10A 0.509 <.01 0.517 <.01


11A 0.964 <.01 0.891 <.01

Fit Statistics

-2 Log Likelihood 5,724.7 5,130.1


the cost of liquidity: results from a natural experimentfncitt/files/cost of liquidity.pdfthe cost...

Documents