Tilburg University

Stock Market and Liquidity

Has liquidity increased after the start of the financial crisis?

Bachelor Thesis Finance

Rick van Delft

ANR: 921290

Supervisor:

Zorka Simon

17-05-2013

2

Index

Introduction ............................................................................................................................................. 3

What is the definition of Liquidity? ......................................................................................................... 6

The level of liquidity ........................................................................................................................ 6

Liquidity Risk .................................................................................................................................... 7

The characteristics of stock liquidity ................................................................................................... 8

How can liquidity be measured? ....................................................................................................... 10

The bid ask-spread ........................................................................................................................ 11

The ILLIQ-measure ......................................................................................................................... 11

The turnover ratio ......................................................................................................................... 12

What is the expected relationship between liquidity and the stock market? .................................. 13

What is the role of liquidity in a financial crisis? ............................................................................... 14

Empirical Evidence................................................................................................................................. 16

Data description ................................................................................................................................ 16

The Models ........................................................................................................................................ 16

The variables ..................................................................................................................................... 16

The Working Method ........................................................................................................................ 18

Empirical Results ................................................................................................................................... 21

Conclusion ............................................................................................................................................. 27

Bibliography ........................................................................................................................................... 29

Appendix 1: ............................................................................................................................................ 31

Amihud & Mendelson (1986) Asset Pricing and the Bid-Ask Spread ............................................ 31

Appendix 2 ............................................................................................................................................. 34

Datar, Naik, and Radcliffe (1998) Liquidity and Stock Returns: An Alternative Test..................... 34

Appendix 3: Results Turnover Rate Model ............................................................................................ 36

Appendix 4: Descriptive Statistics of the Turnover rate Model ............................................................ 39

Appendix 5: Results Relative Bid-ask spread Model ............................................................................. 40

Appendix 6: Descriptive Statistics of the Relative Bid-Ask spread model ............................................. 43

Appendix 7: Results Bid-ask spread Model ........................................................................................... 44

Appendix 8: Descriptive Statistics of the Bid-ask spread Model ........................................................... 47

Appendix 9: Descriptive statistics summary of the Bid-ask spread ...................................................... 48

3

Introduction

In times of financial instability, investors are more and more interested in the sources which

can affect their positions. There are several frictions in the market which can affect the

investor’s position. Liquidity is one of them. Within liquidity a distinction can be made

between the level of liquidity (which is asset specific) and the liquidity risk (which is the

systematic risk of an asset). The level of liquidity is an important aspect of affecting the assets

returns. Amihud and Mendelson (1986) state that: “liquidity, marketability or trading costs

are among the primary attributes of many investment plans and financial instruments”. A

simple definition of liquidity is the ability to sell or buy stocks at low cost without affecting

the price. (Pastor and Stambaugh (2003)) In the same paper they also refer to liquidity as a

source of systematic risk. Acharya and Pedersen (2005) suggest that there are differences in

the effect of the liquidity level and the liquidity risk. Because of the costs liquidity is seen as

an important factor and therefore interest in liquidity has increased. Gomber, Schweikert and

Theissen (2004) argue its importance because: “It affects the transaction costs for investors,

and it is a decisive factor in the competition for order flow among exchanges, and between

exchanges and proprietary trading systems.”

Many studies have investigated the relationship between liquidity and the stock market.

Amihud and Mendelson (1986) studied this relationship between the differences of securities

bid-ask price on their returns. The difference of the bid- and ask-price is called the spread.

They find that higher yields required on higher-spread stocks give an incentive to firms to

enlarge the liquidity of their stocks and thereby reducing their opportunity cost of capital. In

this way, increasing liquidity can make the firm more valuable. In a later study in 2002,

Amihud proposes there is a risk premium for stocks excess return. The simple clarification for

this is because a compensation risk is needed when an investor is exposed to some more risk.

However, he relates the risk premium also to illiquidity. Illiquidity is the opposite of liquidity,

thus the higher the spread, the more illiquid a stock is. So, the risk premium is not only

reflecting the higher risk, it is too a premium for stock illiquidity.

In the past few decades, many researchers have tried to describe the relationship between

liquidity and the stock market. They disagree strongly about the best measure of liquidity.

Kyle (1985) describes market liquidity as: “a slippery and elusive concept”. So, the factors of

market liquidity are already hard to define. To measure these factors is thus even harder.

However, many researches proxy liquidity by using the bid-ask spread. Another measure

4

often used is the turnover ratio. This ratio can be calculated on several ways which makes it

known as a measure where many adjustments can be made.

The aim of this study is to understand the relation between stocks and liquidity and the

changes in liquidity over the last 15 years. I will use this time frame in particular with respect

to the financial crisis. Amihud and Mendelson (1986) used data for the period 1961-1980.

Datar, Naik and Radcliffe (1998) used a sample in the period from July 1962 through

December 1991. To see whether the same relationship holds for a later period, I will use a

time-span from January 1997 to December 2012. I will use the same measures of liquidity as

described in the papers by Amihud and Mendelson (1986) and Datar et al (1998). I have

chosen for these measures because Amihud and Mendelson (1986) were the first researchers

with an empirical study about the relationship between liquidity and the stock market. They

used the differences between the bid-ask price, the spread, to measure liquidity. Datar et al

(1998) have studied the same relationship, though they used an alternative measure, the

turnover rate to proxy liquidity. The reason for using this paper is because Petersen and

Fialkowski (1994) concluded that the quoted spread is not a good proxy for the real

transaction costs for investors. Thereby, Amihud and Mendelson (1986) give a theoretical link

between the turnover rate and liquidity. So to test this relationship, I am going to use the

measure provided by Datar et al (1998).

The time-span I will use is of interest because of the financial crisis. Brunnermeier (2008)

studied some of the leading key factors which caused the financial crisis. He also includes

liquidity as one of the main causes of the financial crisis. He argues that in 2006, many

investors had put their money in illiquid assets. So they were exposed to liquidity risk, as

already explained by Amihud (2002). Brunnermeier (2008) and Brunnermeier and Pedersen

(2009) divided the concept of liquidity into market liquidity and funding liquidity. Through a

mechanism between these two drivers of liquidity, which later will be explained further, “a

relative small shock can cause liquidity to dry up suddenly and carry the potential for a full-

blown financial crisis”. [Brunnermeier (2008)]

5

The next chapter will summarize the most important papers about how liquidity is related to

the stock market. To start with, an explanation of liquidity will be giving. Later the theoretical

relationship between liquidity and the stock market will be illustrated. Further, liquidity in

times of a financial crisis will be described. In section 3, the research methodology is going to

be introduced. The result of the tests will be explained in section 4, whereas section 5 will

summarize the results and conclusions can be made.

6

What is the definition of Liquidity?

The level of liquidity

Liquidity has many interpretations. The simplest way is to define liquidity as trading an asset

which could be sold immediately without any costs. Kyle (1985) interprets liquidity as an

elusive concept of some characteristics of transactional markets which you can distinguish in:

tightness, depth and resiliency. He states that tightness refers to the difference between the

bid- and the ask-quotes. Normally for stocks, a bid-price is slightly below the equilibrium

price whereas the ask-price is higher than the equilibrium price. So if the market is tighter, the

difference (the spread) between the bid- and the ask-price is smaller and thus the market is

more liquid. Perfect liquidity could be reached when there is zero spread between the quotes.

This facet is most commonly used to describe liquidity. However, this measure is only useful

for trading with low volumes. Larger orders are facing price reactions within the trade, only

tightness as a measure will not be enough. Thereafter, Kyle uses another concept: depth. Kyle

explains depth as: “the size of an order flow innovation required to change prices a given

amount”. Basically, it is the amount of trades which can be made without affecting the quote.

Engle and Lange (1997, 2001) have explained depth and tightness in the figure (the market

reaction curve) below:

The amount of trading in relation to the depth is here graphically explained by the horizontal

line as well by the rising line. Low trading volumes do not have an effect on the price which

is explained by the flat line, whereas the price is rising when the volume of trading becomes

bigger. The other concept of liquidity is resilience. Resiliency ‘considers the speed of return

to the efficient price after a random deviation’. [Engle and Lange (1997)] Based on the figure

Source: Engle and Lange (1997)

7

above, it could be seen as the time it will need to go back to the equilibrium level. There is

one problem; the equilibrium level has to be estimated. The estimation is very difficult

because of all sorts of new information could become available in the market, so there is no

clear point of reference of an equilibrium. This could also be a reason why Kyle states that

‘market liquidity is a slippery and elusive concept’. Therefore, it is hard to measure liquidity.

Damoradan (2005) describes liquidity differently. As already said, a simple form of defining

liquidity is as trading an asset which could be sold immediately without any costs. The

definition given by Damoradan comes closer to this simple view. Whereas the Kyle’s

arguments are more related to the trading aspect and market microstructure, Damoradan’s

interpretation of liquidity comes closer to the cost of liquidity, namely:

“When you buy a stock, bond, real asset or a business, you sometimes face buyer’s remorse,

where you want to reverse your decision and sell what you just bought. The cost of illiquidity

is the cost of this remorse”.

Liquidity Risk

The given definition of liquidity has to do with the level of liquidity. Kyle’s definitions are

stock specific, namely what or how liquidity is priced at a transaction. Another distinction

about liquidity can be made with the systematic liquidity risk. The systematic liquidity risk is

argued by Pastor and Stambaugh (2003). They investigated the market wide liquidity and the

correlation of it with the pricing of assets. Acharya and Pedersen (2005) found empirical

evidence to distract the level of liquidity of liquidity risk. They even argue that: “liquidity risk

contributes on average about 1.1% annually to the difference in risk premium between stocks

with high expected illiquidity and low expected illiquidity”. Although, the whole analysis they

made was complicated though the collinearity they faced. This is because when securities are

illiquid, they tend to have also high liquidity risk. Pastor and Stambaugh (2003) identified that

if the market liquidity drops heavily, stocks returns are correlated in a negative way with

fixed-income returns. This seems valid with the ‘flight-to-quality’, which will be explained

later in the paragraph of the role of liquidity in the financial crisis. Due to the collinearity in

the study of Acharya and Pedersen (2005), it is difficult to distinguish the impact of the level

of liquidity as well as the liquidity risk. The collinearity exists because highly illiquid

securities often have high commonality in liquidity with the market liquidity, have a higher

sensitivity to market liquidity and to market returns. Thus, the relationship of all these types is

complicated to recognize. However, there is another type of risk which has to be mentioned

8

here, the relative return impact of liquidity. Because Acharya and Pedersen (2005) argue that

the effect of this risk appears to be small, this type of risk will not be explained here.

The characteristics of stock liquidity

The definition used in the previous paragraph by Damoradan is very broad. For a better

understanding and a better use in this paper, this definition has to be more specific to the

liquidity of stocks. This is because of the differences in liquidity between the various asset

classes. Amihud, Mendelson and Pedersen (2005) discuss several sources of illiquidity like:

exogenous transaction costs, demand pressure, inventory risk, search fractions, and private

information. The sources of illiquidity are here described as a friction of the capital market.

The friction is a price concession for the immediacy according to the approach of Demsetz

(1968).

Exogenous transaction costs are costs such as brokerage fees and transaction costs. When

someone is buying or selling stocks, for every trading transaction there will be transaction

costs charged. Due to the communication and information needed arising from the transfer of

a security, transaction costs are ever-present in markets because: “There may be a necessity to

inspect and measure goods to be transferred, draw up contracts, consult with lawyers or

other experts and transfer title.” [Stavins (1995)] These transaction costs occur because

investors are not trading to each other but they are trading with a dealer. These dealers, or

market makers, will charge the transaction costs in reflecting the bid- and ask-price. The

spread will cover these transaction costs. Brennan and Subrahmanyam (1995) found evidence

of increasing liquidity by activities of brokerage houses. The reason of the existence of these

market makers is because they bridge the time gaps between the time a buyer gets available

and at some point in time, a seller is available. [Amihud & Mendelson (1986)] These costs are

affecting the prices the traders receive or pay and are thus frictions in the capital market.

[Stoll (2000)] That is the reason why these costs are seen as sources of illiquidity.

Another source of illiquidity is demand pressure. Demand pressure could be viewed the same

as the concept of depth in the previous paragraph. If a large trade would move the price of a

stock, the stock is more illiquid. Large buying orders will raise the price, large selling orders

will change the price in the opposite way. Dufour and Engle (2000) have studied this

relationship and argue that: “Short time durations, and hence high trading activity, are

related to both larger quote revisions and stronger positive autocorrelations of trades.” The

9

price reaction could also be a reason for another source of illiquidity, private information.

Through private information, the market makers will have to increase the spread because of

the higher inventory risk they are exposed to. However, the sources of private information and

the inventory will be described later. Here, in the demand pressure the price impact is more

important. The price impact, or the price change, is a reflection of the liquidity of the stock

market. The larger the difference between the bid- ask-spread, the more illiquid the market is.

So, a price impact could make the spread larger. This has also to do with the position of the

market makers. They will trade in anticipation of trading the stocks later to another trader,

however they will be exposed to the risk of the price changes. Due to being exposed to the

risk while they are holding the stock in inventory, a compensation is needed which impose the

costs of the market makers. [Amihud et al, (2005)] These proceedings are however necessary

for a trading market. Besides the already described friction costs, the costs are also required

for the main building blocks of the trading market like trading systems and the legal

documentation. The terms ‘friction’ and ‘costs’ give it a negative view, but it positive because

it is necessary to alleviate the frictions and therefore costs are involved. In a result, the spread

will increase and thus the market will become more illiquid.

The source of inventory is already mentioned with the demand pressure source. The

relationship between price changes and high trading activity is previously described. Also in

times of ‘normal’ trading activity there is a risk where the market maker is exposed to. The

market makers have to wait for a buyer while they have some stocks in inventory, the waiting

time or the risk for holding inventory is also a cost for the market maker. Besides the times in

high and normal trading activity, when there is only low volume trading there will also

consists some inventory costs. There could be a situation where there is no buyer available,

then two actions can be taken into account: just wait or sell at the bid-price. Both options will

cost the market maker money. Waiting or holding the stocks will require a compensation for

having the inventory and sell the stocks at the bid-price will result in a loss because the

transaction costs cannot be charged.

The next source is search frictions. It consists of the opportunity costs for holding stocks

while there is not yet a buyer available. Also, if a buyer is vacant, negotiations can lead to a

price below the ask-price. There are huge differences in the costs of search frictions in the

various asset classes. Real-estate is more difficult to sell immediately or if you could sell it

quickly, the price you are receiving is going to be substantial lower. On the other hand, U.S.

Treasury bills/bonds are very easy to sell directly. You can sell the U.S. Treasury bills/bonds

10

right away at the exchange market, which is not the case with real-estate. Selling real-estate is

thereby even more costly because you probably need to find a buyer, so there are more direct

costs involved of this sort of trading. Even with stocks, there is some discrepancy. If you have

a small minority in a private company, you will not be able to sell your stocks quickly. The

demand for such minorities is smaller than it is for stocks from a large company traded on the

S&P 500, so selling your position is a more complex task.

Amihud et al. (2005) discussed also private information as a source of illiquidity. Within

private information, or asymmetric information, there are two types of information which

have to be identified: information about the fundamentals of the security and information

about the order flow of a certain security. Information about the fundamentals of the security

is related to the demand pressure. In times of high trading activity, investors may justify this

trading because they think the seller / buyer has some private information. Trading with a

counterparty with private information can be costly and thus result in a loss. Stoll (2000)

describes the existence of private information as an informational view of the spread. If an

investor is buying stocks at the ask-price, it seems the trader has some private information

justifying the higher price. On the other hand, if an investor is selling stocks at the bid-price, it

seems the trade has some private information justifying the lower price. “When the

information becomes known, informed traders gain at the expense of suppliers of immediacy.

The equilibrium spread must at least cover such losses’. [Stoll (2000)] Information about the

order flow of a certain security has also to deal with private information. Trading agencies can

make a gain if they know some other trader has to trade large volumes in the future which can

affect the prices.

How can liquidity be measured?

“A major problem in estimating the effect of liquidity on asset prices or returns is how to

measure liquidity since there is hardly a single measure that captures all of its aspects. In

addition, measures used in empirical studies are constrained by data availability.”[Amihud

et al (2005)] There are various ways to estimate the liquidity. However, any measure of

liquidity has some error. To prove this, Amihud et al (2005) describe three different

arguments: (i) all facets of liquidity cannot be measured with one single measure, (ii) an

empirically-derived measure does always have some error in relation to the true factor and (iii)

11

if there is not enough data available, the error will increase. Besides this finding, without any

estimate of the relationship between liquidity and the stock market cannot be described.

Further, Goyenko, Holden, and Trzcinka (2008) tested several measures of liquidity and they

concluded that: “we can safely assert that the literature has generally not been mistaken in

the assumption that liquidity proxies measure liquidity”. Thereafter, the most used proxies for

liquidity are explained here.

The bid ask-spread

As already described at the characteristics of the stock market liquidity, the bid-ask spread is a

well-known measure of liquidity. Amihud and Mendelson (1986) were the first who build a

model the described the relationship of the bid-ask spread on asset returns. Their model

“predicts that higher-spread assets yield higher expected returns, and that there is a clientele

effect whereby investors with longer holding periods select assets with higher spreads.” The

reason for using the bid-ask spread as a proxy for liquidity is because of the characteristics of

stock market liquidity are explained by the bid-ask spread. In their study, they use the relative

spread to test the relationship between stock returns, relative risk and spread. To calculate the

relative spread, they divided the dollar spread by the average of the bid- and ask-price at year

end. There are also critics for using the bid-ask spread. Peterson and Fialkowski (1994) argue

that the spread does not correspond to the actual transaction costs. Furthermore, the

availability of data over long periods of time on a monthly basis is hard to obtain. (Datar et al

(1998))

The ILLIQ-measure

In 2002, Amihud introduced a new measure of illiquidity. An advantage of this measure in

contrast to other measures is that this illiquidity measure uses data which is available over a

long period of time. The measure is based on the following formula:

is here the average ratio of the daily absolute return to the trading volume

on that day in dollars. is the return on a specific stock, i, on day d and at year y.

is calculated as the volume in dollars of stock I traded at day d at year y. deals

with the availability of data, it is the number of days for stock i at year y for which there is

information accessible. Amihud is also in this paper doubtful whether this single measure can

12

capture all facets of liquidity. However, with this new measure, he is able to give an intuitive

interpretation of the average daily association between a unit of volume and the price change.

This is also an advantage compared to the Amivest measure or liquidity ratio which is known

through the monthly published Liquidity Report by the Amivest Corporation. Amihud

introduced this measure to show the effect between illiquidity and stock returns with cross-

section and time-series effects taken into account.

The turnover ratio

Another measure used often in the cross-country empirical studies is the turnover. Levine and

Zervos (1998) use this to indicate liquidity in relation to the whole stock market development.

The turnover is a widely used proxy because of its simplicity. There are different turnover

measures, like the turnover rate and the turnover ratio. Levine and Zervos (1998) use a

turnover measure plus a valued traded measure to calculate the overall stock market liquidity.

The turnover they use can be calculated by the value of traded shares divided by the value of

the total number of shares outstanding in that period. A high number can be an indicator of

low transaction costs. They also use the Traded Value as a measure to reflect liquidity on an

economy wide basis. The value of the traded stocks divided by the GDP of a country is the

calculation after the earlier definition. It thus captures trading relative to the GDP. However in

comparison to the study of Levine and Zervos (1998), in this study there is no involvement of

different countries, so the Traded Value measure is not important here. The reason for

describing the study of Levine and Zervos (1998) at this juncture is to see the possibilities

around the turnover measure in relation to the turnover rate and the turnover ratio. Datar et al

(1998) use a stock turnover or turnover rate measure to interpret liquidity. This measure is

calculated by the number of shares traded divided by the number of share outstanding at some

period. At first sign, this measure does not have any relationship with the factors of liquidity.

The idea however behind this measure is based on Amihud and Mendelson (1986). In an

equilibrium state, investors with less liquid stocks tend to hold these stocks longer in their

portfolio. High trading activity with less liquid stocks can only be achieved at high costs.

Investors will reduce their trading frequency [Constantinides (1986)] or will hold their stocks

much longer. With these arguments, the relationship between the stock turnover and liquidity

is much brighter. A high stock turnover can be related to very liquid stocks, i.e. the

transaction costs are low. Fleming (2001) reasons nevertheless also the other way around. He

argues that high trading frequency can also be associated with high volatility and lower

liquidity. Basically, he is arguing that periods of poor liquidity consist in times of high and of

13

low trading volumes. According to Fleming (2001) the turnover rate is not a good measure of

liquidity because at the end the conclusion can be made up two-folded. Datar et al (1998)

have two reasons for using a different test to proxy for liquidity. The two reasons are: (1)

monthly data is hard to get over long periods of time, and (2) in a study by Peterson and

Fialkowski (1994), they argue that the bid-ask spread is covering too much of the transaction

costs. The reason given for this is: “When trades are executed inside the posted bid-ask

spread, the posted spread is no longer an accurate measure of transactions costs faced by

investors.” They found that the effective spread is smaller than the quoted spread, where the

effective spread consists of the transaction costs. So, another liquidity measure can do better.

Datar et al (1998) use the turnover rate of an asset to measure liquidity. When using the

turnover rate, different data is needed. Therefore, the earlier reason given to use an alternative

test is hereby answered with the necessity of other data. The data needed is easier to obtain

over long periods of time.

What is the expected relationship between liquidity and the stock market?

Suppose there are two firms, they are exactly identical with the exception of their stocks

which have different liquidity. Firm A has more liquid stocks whether Firm B is more illiquid.

Pastor and Stambaugh (2003) continue this example and estimate that investors would prefer

stocks of firm A in this situation. In their paper, they find that more illiquid stocks have

substantially higher returns. This is because investors require higher expected returns for

stocks which are costlier to trade. If an investor would have to liquidate stocks to raise cash,

he would chose to liquidate the more liquid stocks, because of the lower costs involved. Even

if this situation does not occur at some time for an investor, the idea behind this situation will

hold. So, a rational investor will only invest in more illiquid stock when he expects to have a

higher return. The difference in liquidity for stocks of firms A and B will thus be expressed at

the expected return by an investor. A rational investor will choose for stocks of firm A, unless

firm B’s expectations are better. Longstaff (2001) has also looked at this relationship,

however he used bonds to study the relationship between bonds and liquidity. The idea is on

the other hand the same. He also concluded a flight to liquidity which is in fact the same as

the estimate in the previous example. Of course there is a big difference between bonds and

stocks. The expectations of an already issued bond do not change. The market can change and

therefore bonds prices can also change. However, the absolute return at maturity will be the

14

same. Longstaff (2001) finds large liquidity premiums in Treasury bond prices, which can

raise the bond price as much as 10 to 15%. If this idea of ‘flight to liquidity’ holds as well at

the stock market, more illiquid stocks will be cheaper relative to more liquid stocks. This idea

can also be explained by the Capital Asset Pricing Model (CAPM). This model is widely

accepted model to calculate the required rate of return of a specific asset. This model of

Sharpe (1964), Lintner (1965) and Mossin (1966) is based on the following calculation:

. is the expected return, is the risk free rate and is

the difference between the expected return of the market minus the risk free rate. The factor

which is interesting here is the . The is the measure of the sensitivity of asseti to the

market risk. So, for a more illiquid stock, the will be higher in respect to a more liquid

stock. Because of this, the required rate of return of a specific asset needs to be higher.

What is the role of liquidity in a financial crisis?

There are many causes which led to the crisis, however they will not be explained here. In this

paper, I focus on the involvement of liquidity with the crisis. As previously stated in the

introduction, in relation to the financial crisis it is useful to split liquidity as a concept into:

funding liquidity and market liquidity. [Brunnermeier (2008), Brunnermeier and Pedersen

(2009)] Market liquidity itself can be divided into the three different types of risk as stated in

chapter 2: the level of liquidity, the market wide liquidity and the relative return impact of

liquidity. Funding liquidity is the ease with which investors can acquire funding. Examples of

funding liquidity are loans and credit lines. If funding liquidity is high, investors can very

easily obtain money, the market is said to be ‘awash with liquidity’. If funding liquidity is low,

investors can hardly get any funding. An important note about funding liquidity is the

funding amount relative to the underlying asset which can be borrowed. A leveraged investor

purchases an asset and uses this asset as collateral to borrow the amount against it. An

investor cannot borrow the entire price an asset costs.

15

So, there will be a difference, a haircut, which will be financed by the investor itself.

Normally, this is not a problem. Investors use short-term debt to finance this haircut because

short-term debt is cheaper than long-term debt. Yet, if the market for short-term debt dries up,

investors have a huge problem to finance the haircut. One solution is to sell some securities.

In 2006, Brunnermeier (2008) argues investors were having many illiquid securities.

Liquidating them is costly. With a huge supply of illiquid securities, the prices will drop.

Because only the haircut is financed by the investor itself, when asset prices drop the investor

is faced with a situation where his assets are worth less than the debt on the related asset.

To hold the same leverage ratio, the investor has to sell parts of his securities. This leads to

the loss spiral. Investors will have trouble to hold their position and will have the problems as

indicated in the figure. This can result in a crash of the stock market. In earlier crises, Chordia,

Sarkar and Subrahmanyan (2005) studied the relationship between liquidity and crisis. They

found evidence based on several crises that the spreads are generally higher. Diamond and

Dybvig (1983) also suggest that liquidity is higher during crises. There will be a higher

demand for more liquid securities because they are easier and cheaper to trade.

Source: Brunnermeier and Pedersen (2009)

16

Empirical Evidence

In this section, the following factors will be reviewed: the data, the variables, the models and

the empirical method.

Data description

The collection of data is based on information provided by Compustat and CRSP from WRDS.

The risk-free rate I used is provided by Fama & French. I used the S&P 500 index as a proxy

for the stock exchange market. The time-span will be from 1997 to 2012. Only companies

enlisted at the S&P 500 in 1997 as well as in 2012 are taken into account. So, from the 500

companies enlisted at the S&P 500, there remained 204 companies. The reason for excluding

the other companies is because there is not enough data available in relation to the whole

time-span. Thereby, by using this sample I do not have to deal with a changing composition

of the S&P 500 index. The sample is large enough to exclude the other companies so I have

now a large sample over a large period of time. Datar et al (1998) and Amihud and

Mendelson (1986) worked with monthly data. I have worked with monthly data as well.

The Models

Two models are going to be used to measure the relationship between liquidity and the stock

market. Both models are previously mentioned in the introduction, the models are based on

Amihud and Mendelson (1986) and Datar et al (1998). The measures from the individual

papers are described in the literature review. A detailed summary of the statistical

performances used in the papers is described in Appendix 1 and Appendix 2. I will refer to the

appendix for the explanation of the variables I used in the regression. In the Working Method

paragraph, I will explain what I did with the models and why.

The variables

The variables I will use are based on Amihud and Mendelson (1986) and Datar et al (1998).

As already stated in the data description, the data sources are Compustat and CRSP at WRDS.

17

Besides, I will give here a numeration of the variables as well as the way I requested /

managed to get the information.

- Bid price:

This is the bid price of stock i at the end of a specific month t

- Ask price:

This is the ask price of stock i at the end of a specific month t

- Bid-Ask spread:

This is the difference between the bid price and the ask price of stock i at the end of a

specific month t

- Relative Bid-ask spread:

It is the bid-ask spread divided by the average of the highest and the lowest price of a

specific month t

- Closing price:

This is the price of a stock i at the end of the month t

- Traded volume:

This is the number of stocks i traded in a specific month t

- Market capitalization:

This is the price of a share at the end of a month t multiplied with the total amount of

shares outstanding. (The shares outstanding were not available for 1997, so the shares

outstanding at 31/01/1998 are used as a measure for the shares outstanding in 1997)

- Turnover rate:

This liquidity measure is calculated by averaging the monthly trading volume (the average

takes into account the three previous months) and divide it by the number of shares

outstanding of that firm

- Firm size:

This is the natural log of the Market capitalization variable

- Firm beta:

This is the estimator of beta for a specific portfolio p which is later used as an estimator for

each individual firm within the specific portfolio p

- Risk-free rate:

This is the Risk-free rate which is downloaded at the website of Fama and French.

- Excess Return:

This is the absolute return on stock variable minus the Risk-free rate variable.

18

The calculation behind the excess return is explained here further because it involved a few

steps to come to the final number. The absolute return on a stock is calculated by using the

CAPM model, . The , the Risk-free rate, is downloaded. The

is calculated by the change of in the stock closing price in a month. The is calculated by the

covariance between the stock and the index divided by the variance of the S&P 500 index.

The covariance and the variance are calculated per company for the whole time-span. The

monthly changes in the S&P 500 are used whereby all 500 companies enlisted at that time are

involved. After multiplying the with the difference of the - the and then adding the

, the is made. The is thus the absolute return on stock here. Afterwards the excess

return can be easily calculated by the minus the . Of course, without adding the for

the , the excess return is already calculated. The reason for using the excess return in this

way comes from the paper by Amihud and Mendelson (1986). As could be found in the first

appendix, they also used the excess return measure. All other variables are also based on their

paper and on the paper by Datar et al (1998).

The Working Method

The data is first downloaded via Compustat and CRSP. The first step was the selection of the

companies. I included all companies which where enlisted at the S&P 500 on December 1996

and which were still enlisted on December 2012. Most variables were easily downloaded via

Compustat and CRSP. The risk-free rate was made available by Fama and French. Some

variables were not yet available at the given resources, so I had to compute them myself. The

variables which needed to be computed are the Bid-Ask spread, Market Capitalization,

Turnover rate, Firm size, Firm beta and the Excess Return. The computations are explained at

the previous page.

Because of the two different models I used, I will describe my working method in twofold.

First of all, I will describe the construction made by using the paper by Datar et al (1998).

I used the following regressions:

- (1) Excess return = α + β1 (Turnover rate) + ε

- (2) Excess return = α + β1 (Turnover rate) + β2 (Firm size) + ε

- (3) Excess return = α + β1 (Turnover rate) + β3 (Firm beta) + ε

- (4) Excess return = α + β1 (Turnover rate) + β2 (Firm size) + β3 (Firm beta) + ε

19

The reason for using these variables is derived from Datar et al (1998). I made the regressions

for every year, for three periods and for the whole sample. The three periods are 1997 -2002,

2003-2007, 2008-2012. The α is the constant and the other variables are the same as stated in

the variable overview. In total, I got 80 regressions. 20 regressions have only one regression

coefficient, 40 regressions have two regression coefficients and the other 20 regressions are

consisting of all three regression coefficients. Datar et al (1998) use a trimmed dataset for the

regression. They discard the lowest 1% and the highest 1%. They showed however later in

their paper that there is not an important difference in the results by using the complete

dataset or the trimmed dataset. That is the reason I will only use the complete dataset. Besides,

by comparing two different models, I will also have to use the same dataset so that is another

advantage of using the whole dataset. The expectations of the described models are more or

less the same for two out of the three variables. I expect small values for the determination

coefficient of the Firm size and the Firm beta. Datar et al (1998) used these variables as

control variables to account for large differences in size and in volatility. In their paper, they

did not find a large change of the magnitude of the slope coefficient. I expect a small

negative coefficient for the turnover rate in all the three models. This is because based on the

theoretical assumptions; in times of crisis the frequency of trading will be lower. Lower

trading frequencies will proxy for an increased level of liquidity in the stock market. The

usage of the variables in the models is consistent with the paper of Datar et al (1998). The

reason for using different regressions is to see whether reducing the control variables does

influence the models.

Now I will describe of how I used the model of Amihud and Mendelson (1986) to construct

another measure of liquidity. Amihud and Mendelson (1986) based their model on the relative

bid-ask spread. They also used the beta and the firm size as a control variable to test for the

effect for both variables on the stock returns. They found a negligible effect on both variables.

The size of the firm is also replaced by its natural logarithm to make non-linear effect

available. By using the logarithm, the data will be trimmed (which is also done in the model

of Datar et al (1998)). The regressions I used are similar to the regressions I used earlier for

Datar et al (1998). The big difference is of course the use of the relative bid-ask spread

instead of the turnover rate. A great advantage of working with the same data is that I will

have comparable results.

20

I used the following regressions:

- (1) Excess return = α + β1 (Relative Bid-ask Spread) + ε

- (2) Excess return = α + β1 (Relative Bid-ask Spread) + β2 (Firm size) + ε

- (3) Excess return = α + β1 (Relative Bid-ask Spread) + β3 (Firm beta) + ε

- (4) Excess return = α + β1 (Relative Bid-ask Spread) + β2 (Firm size) + β3 (Firm beta)

+ ε

As stated before, I used the same regressions for every year, for three periods and for the

whole sample. The three periods are 1997 -2002, 2003-2007, 2008-2012. The α is the constant

and the other variables are the same as stated in the variable overview. In total, I got 80

regressions. 20 regressions have only one regression coefficient, 40 regressions have two

regression coefficients and the other 20 regressions are consisting of all three regression

coefficients. The expectations of the described models using the relative bid-ask spread are

more or less identical with the reasoning given on the previous page for the models based on

Datar et al (1998). I expect small values for the determination coefficient of the Firm size and

the Firm beta. Like Datar et al (1998), Amihud and Mendelson (1986) used these variables as

control variables to account for large differences in size and in volatility. My expectations of

the determination coefficients for both control variables are a very small value. As stated at

the expectations of the turnover rate models, the magnitude of the slope coefficient will not

change much. I expect a small positive determination coefficient for the relative bid-ask

spread variable, which is based on the results in the paper by Amihud and Mendelson (1986).

The usage of the variables is consistent with the paper. The reason for using different

regressions is to see whether reducing the control variables does influence the models.

My hypothesis is: Liquidity has increased after the financial crisis of 2007.

21

Empirical Results

In this chapter I will show the results of the regressions I made in the previous chapter. I will

summarize and describe the most important or the most striking results. I will do this in the

same way as I did in the previous chapter, so I will start with the model with the turnover rate

based on Datar et al (1998).

I used the following regressions:

- (1) Excess return = α + β1 (Turnover rate) + ε

- (2) Excess return = α + β1 (Turnover rate) + β2 (Firm size) + ε

- (3) Excess return = α + β1 (Turnover rate) + β3 (Firm beta) + ε

- (4) Excess return = α + β1 (Turnover rate) + β2 (Firm size) + β3 (Firm beta) + ε

I used a linear regression to regress the mentioned formula. The results in appendix 3 show

that not all the regression coefficients are significant. In the column ‘Model’ the 1, 2, 3, and 4

indicate which model is used in the specific regression. For example, in the year 2007, the

turnover rate in model 4 is not significant.

# Year Model Constant Beta 1 Significant Beta 2 Significant Beta 3 Significant Adj R2

2007 1 -,031 -,035 Yes ,002

2007 2 -,146 -,026 Yes ,011 Yes ,006

2007 3 ,005 ,043 Yes -,051 Yes ,072

2007 4 -,159 ,059 No ,016 Yes -,053 Yes ,078 Table 1: Results 2007

In the table, the adjusted R2 is also shown. The adjusted R2 is a better measure than the normal

R2. The adjusted R2 also takes into account how many variables the model consists. The

purpose of the R2 and the adjusted R2 is to predict the future outcomes of the model. However,

in this example the adjusted R2 is very low. Model 4 in 2007 is only for 7,8% predicting future

outcomes which is a very low percentage. Below, a summarized table is given for a quick

overview of the results. The coefficient determinants for the variables ‘Firm Size’ and ‘firm

Beta’ are, as expected, very small in 2007. This is in line with the conclusions by Amihud and

Mendelson (1986) and Datar et al (1998).

In the following tables, a summary is given which consists information about the significance

of the coefficient determinants and a table is given with the averages of the specific

coefficient determinants.

22

The ‘Year’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 48 18 24 Average adjusted R2 = 0,0533

Number of significant betas and

which are positive

35 17 4 Min adjusted R2 = 0,000

Number of significant betas and

which are negative

13 1 20 Max adjusted R2 = 0,448

Number of non-significant betas and

which are positive

11 11 3

Number of non-significant betas and

which are negative

5 5 3

The ‘Period’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 11 7 8 Average adjusted R2 = 0,1169

Number of significant betas and

which are positive

11 5 0 Min adjusted R2 = 0,000

Number of significant betas and

which are negative

0 2 8 Max adjusted R2 = 0,296

Number of non-significant betas and

which are positive

4 1 0

Number of non-significant betas and

which are negative

1 0 0

Table 2: Coefficient determinations significance description

Averages

Constant -0,128175

Turnover rate 0,186860759

Firm size 0,020511628

Beta -0,048289474

Table 3: Coefficient determinants averages

Recording to Datar et al (1998), the expectation is that the turnover rate will have a negative

sign. Instead of this, in the summary above only 18 of the 80 regression coefficients of the

turnover rate are negative. Thereby, five of them are not significant. The turnover rate by

Datar et al (1998) is on average -0,04 whereby in my sample the average is 0,1869. Most of

the regression coefficients for the turnover rate are significant. I expected that liquidity has

23

increased after the financial crisis of 2007. There is a large difference in the results from

period 2 to period 3. The constant factor is decreased which can easily be explained by the

decrease of the returns at the stock markets after the start of the financial crisis. The

regression coefficient for the turnover rate is much larger than it is in the second period (from

0,015 to 0,783 in the third period, the 0,015 is not significant however). Basically, this implies

that high trading volume leads to higher excess returns. This is not in line with the theoretical

assumption and is also contradictionary to my hypothesis. Also the sign of the firm size

variable is different compared to the study of Datar et al (1998). Nevertheless, they found a

very small regression coefficient for the ‘Log of size’ as they call it. Here, I found an even

tinier regression coefficient with a positive sign. More important, the control variable does not

affect the slope much. Also the regression coefficient of the other control variable, the ‘Firm

Beta’, is very small. Like Datar et al (1998) the sign is negative. I found however a smaller

coefficients which implies that the does not change the slope much.

The second model I used was the model with the relative bid-ask spread based on Amihud

and Mendelson (1986). In the previous chapter I already described why I used almost the

same regressions in comparison to the model by Datar et al (1998).

I used the following regressions:

- (1) Excess return = α + β1 (Relative Bid-ask Spread) + ε

- (2) Excess return = α + β1 (Relative Bid-ask Spread) + β2 (Firm size) + ε

- (3) Excess return = α + β1 (Relative Bid-ask Spread) + β3 (Firm beta) + ε

- (4) Excess return = α + β1 (Relative Bid-ask Spread) + β2 (Firm size) + β3 (Firm beta)

+ ε

I used a linear regression to regress the mentioned formulas. The results in appendix 5 show

that not all the regression coefficients are significant. In total there are 160 regression

coefficients calculated, 101 of them are significant at a 5% level. Most of the Relative Bid-ask

spread regression coefficients are significant, 56 out of 80. The adjusted R2 is very low. On

average, only 3,9% can be predicted by using this model. The full-period regression has an

even lower adjusted R2 of 0,000. So by using the full-period regression, no future decisions

can be made based on the model. In the year-to-year regressions there is change visible in the

importance of the relative bid-ask spread. From 2007 until 2009 the regression coefficient for

the relative bid-ask spread is much higher than it is in the years before. This could be due to

the crisis. On the other hand, at the period until 2003, the regression coefficient was also

24

relative high in comparison to the years after that period. After 2003 and before 2007, the

regression coefficient was very low. The conclusion can thus be drawn that there is a change

in the level of liquidity in the market after the beginning of the credit crisis. After 2010 there

is a decrease of the regression coefficient noticeable in the first and the second model. Yet,

model 3 and model 4 in 2010 estimate a regression coefficient which is not negligible.

Definitely, after 2011 the regression coefficient of the relative bid-ask spread is low. The

adjusted R2’s of the models from 2011 onwards are however also extremely low. The adjusted

R2 of the fourth model every year is most of the time higher than it is at the other models at

the same year. This implies that the fourth model could be used best to predict future levels of

liquidity.

Next, another summary is given about the significance of the coefficient determinants.

The ‘Year’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 44 9 28 Average adjusted R2=0,03942

Number of significant betas and

which are positive

16 5 8 Min adjusted R2 = 0,000

Number of significant betas and

which are negative

28 4 20 Max adjusted R2 = 0,268

Number of non-significant betas and

which are positive

9 15 2

Number of non-significant betas and

which are negative

11 8 2

The ‘Period’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 12 2 6 Average adjusted R2 = 0,0051

Number of significant betas and

which are positive

4 0 2 Min adjusted R2 = 0,000

Number of significant betas and

which are negative

8 2 4 Max adjusted R2 = 0,018

Number of non-significant betas and

which are positive

2 4 0

Number of non-significant betas and

which are negative

2 2 2

Table 4: Coefficient determinations significance description

25

The following table shows the averages of the different determination coefficients.

Averages

Constant -0,030105263

Turnover rate -0,000513158

Firm size -0,004184211

Beta 0,032626667

Table 5: Coefficient determinants averages

Amihud and Mendelson (1986) used the relative bid-ask spread in their regressions. To see if

there are differences between using the relative bid-ask spread and the bid-ask spread itself, I

made new regressions. I changed the independent variable ‘relative bid-ask spread’ by the

‘bid-ask spread’. In appendixes 7, 8 and 9 the results of the regressions are described in the

tables. There are some big differences between the two variables in the outcomes of the

regressions. For example in year 2008, where I earlier described the high regression

coefficient for the relative bid-ask spread, the influence of the bid-ask spread is very low. This

is no exception based on the other years. In all years the regression coefficient of the bid-ask

spread is very small. Below, I summarized the results of the fourth model for the three models

for the second and the third period. The reason why I used these periods here is because

changes in liquidity before and after the crisis are easily visible.

Model by Datar et al (1998) --> Excess return = α + β1 (Turnover rate) + β2 (Firm size) + β3 (Firm

beta) + ε

2003-2007 y = - 0,082 + 0,015 x (Turnover Rate) - 0,008 x (Firm Size) - 0,01 x (Firm Beta)

2008-2012 y = -0,823 + 0,783 x (Turnover Rate) + 0,075 x (Firm Size) - 0,134 x (Firm Beta)

Model by Amihud and Mendelson (1986) --> Excess return = α + β1 (Relative bid-ask spread) + β2

(Firm size) + β3 (Firm beta) + ε

2003-2007

y = 0,055 + 0,127 x (Relative bid-ask spread) - 0,007 x (Firm Size) - 0,014 x (Firm

Beta)

2008-2012

y = -0,016 - 0,023 x (Relative bid-ask spread) - 0,001 x (Firm Size) + 0,038 x (Firm

Beta)

Adjusted model --> Excess return = α + β1 (Bid-ask spread) + β2 (Firm size) + β3 (Firm beta) + ε

2003-2007 y = 0,09 + 0,001 x (Bid-ask spread) - 0,009 x (Firm Size) - 0,01 x (Firm Beta)

2008-2012 y = -0,033 - 0,001 x (Bid-ask spread) + 0,001 x (Firm Size) + 0,035 x (Firm Beta) Table 6: Results different models for 2003-2007 and 2008-2012

The reason for showing only the fourth model is because these models are the most extensive

and are in line with the models based on Amihud and Mendelson (1986) and Datar et al

(1998).The empirical results show there is a change in liquidity over the years from the start

26

of the crisis. First of all, the constant is much lower in the second period that it is in the period

2003-2007. This seems to be valid because of the decreasing returns after the start of the crisis.

The coefficient determinants of the Firm Size and the Firm Beta are as expected. They all

have very small values, except for the coefficient determinant of the Firm Beta at the second

period for the model based on Datar et al (1998). The other factor, beginning with the

turnover rate, changed also a lot from 0.015 to 0.783 in the last period. However, this is not in

line with the theoretical assumption. Expected was a decrease in the turnover rate because a

lower turnover rate would increase the expected return. Here, a decrease in the returns is

involved with a higher turnover rate. The hypothesis has liquidity increased after the start of

the financial crisis, cannot be answered positively. There has been a change in liquidity,

however it seems to be decreased since the start of the crisis based on the model of Datar et al

(1998). Amihud and Mendelsons (1986) model gave a decrease in the relative bid-ask spread

regression coefficient. The change, from 0.127 to -0.023, is nevertheless also not in

accordance with the theoretical part. The assumption is that a high relative bid-ask spread

would give a higher expected return. The negative regression coefficient does not correspond

to the assumption because a higher relative bid-ask spread will give a more negative return

based on the regression.

27

Conclusion

The purpose of this study was to understand the relation between liquidity and the stock

market and how this changes due to the credit crisis of 2007. In the theoretical section of this

study, explained is what the role of liquidity is. Furthermore, the connection between liquidity

and the stock market is illustrated. Two models are used to check whether the theoretical

relation holds in practice. I did this by using a time-span from 1997 until 2012 while using the

models based on Amihud and Mendelson (1986) and Datar et al (1998). Amihud and

Mendelson (1986) built their model around the relative bid-ask spread, whereas Datar et al

(1998) used the turnover rate as the most important variable. The theoretical background for

the bid-ask spread illustrates a high level of liquidity when the bid-ask spread is small. The

thoughts behind the turnover rate are similar, when the turnover rate is high the liquidity is

high. A simple definition of liquidity is the ability to sell or buy stocks at low cost without

affecting the price. [Pastor and Stambaugh (2003)] A high turnover rate and a small bid-ask

spread are related with low costs and can thus be used as proxies for liquidity. Pastor and

Stambaugh (2003) argue that when liquidity is low, the expected return will have to be higher

because investors require more returns for stocks which are costlier to trade.

Due to the credit crisis it was expected that the constant factor would decrease in the last two

periods. From the results of the regressions the expectations holds indeed, it decreased from

-0.082 to -0.823 at the regression with the turnover rate. The theoretical background of the

regression coefficients from the turnover rate and the relative bid-ask spread however do not

correspond to the output of the regressions. Shown in the last table in the previous section, the

turnover rate is much higher in the period 2008-2012 than it is in 2003-2007. The regression

coefficient of the relative bid-ask spread in the period 2003-2007 is 0.127, in the period

thereafter the regression coefficient is -0.023. Also in the extra model with the absolute bid-

ask spread the regression coefficient is decreasing. Though, the values of the regression

coefficients in that model are so small that no conclusions can be made. My hypothesis has

liquidity increased after the start of the financial crisis cannot be proved by the results. A

change in the liquidity is visible but not in the direction as I expected it would be. A reason

for this can be that not every regression coefficient was significant. Furthermore another

possibility can be the usage of the turnover rate. The turnover rate is namely mostly used with

cross-sectional regressions whereas I used only linear regressions. However, the other models

also did not confirm my hypothesis.

28

The restrictions of this paper were most of all the time constraint. Because of this, I could

only use a sample based on companies enlisted at the S&P 500. Although the S&P 500 is a

widely used index, using more or other indices could also have given other results. Using all

of the companies enlisted at the S&P 500 would probably also give some other results. The

papers that I used most, Amihud and Mendelson (1986) and Datar et al (1998) used a larger

timeframe for their regressions. Based on that, I could also have used a larger data sample

with a longer timeframe. However due to the time constraint, I was not able to do that. Further

research could thus be done for other indices with a larger timeframe. It is possible that other

indices have a different reaction on the crisis to the relationship between liquidity and the

stock market.

29

Bibliography

Acharya, V., Pedersen, L. (2005) Asset pricing with liquidity risk. Journal of

Financial Economics 77, 375-410

Amihud, J. (2002) Illiquidity and stock returns, cross-section and time-series effects.

Journal of Financial Markets. 5, 31-56

Amihud, J., Mendelson, H., Pedersen, L. (2005) Liquidity and Asset Prices.

Foundations and Trends in Finance, Vol 1, No. 4, pp. 269-364

Amihud, J., and Mendelson, H. (1986) Asset Pricing and the Bid-Ask Spread. Journal

of Financial Economics. (17), 223-249

Brennan, Michael and Avanidhar Subrahmanyam, 1995a, Investment analysis and

price formation in securities markets, Journal of Financial Economics 38, 361-381.

Brunnermeier, M. (2008) Deciphering the Liquidity and Credit Crunch 2007-2008,

Journal of Economic Perspectives. Vol 23, No 1, 77-100

Brunnermeier, M., Pedersen, L. (2009) Market Liquidity and Funding Liquidity

Chirinko, R., Schaller, H, (1995) Why Does Liquidity Matter in Investment Equations.

Journal of Money, Credit and Banking. 27 (2), 527-548

Chordia, T., Subrahmanyam, A. & Anshuman, R. (2001) Trading activity and

expected stock returns. Journal of Financial Economics. 59, 3-32

Constantinides, G. (1986) Capital Market Equilibirum with Transaction Costs. Journal

of Policital Economy 94, 842-862

Cooper, S., Groth, J., Avera, W. (1985) Liquidity, exchange listing and common stock

performance. Journal of Economics and Business 37, 19-33

Dalgaard, R. (2009) Liquidity and Stock Returns: Evidence from Denmark

Damodaran, A., (2005) Marketability and Value Measuring the Illiquidity Discount

Datar, V. Naik, N., & Radcliffe, R. (1998) Liquidity and Stock Retruns, an alternative

test. Journal of Financial Markets (1) 203-219

Diamond, D. and Dybvig, P. (1983) Bank runs, deposit insurance, and liquidity.

Federal Reserve Bank of Minneapolis Quarterly Review

Dufour, A., Engle, R. (2000) Time and the Price Impact of a Trade, The Journal of

Finance, Vol 55, No 6, 2467-2498

Engel, R. Lange, J. (1997) Measuring, forecasting and Explaining Time Varying

Liquidity In The Stock Market

30

Engle, R., Lange, J. (2001) Predicting VNET A model of the dynamics of Market

Depth. Journal of Financial Markets 4 113-142

Gomber, P., Scheweikert, U. & Theissen, E. (2004) Zooming in on Liquidity,

University of Tuebingen

Goyenko, R., Holden, C., Trzcinka, C (2008) Do Liquidity Measures Measure

Liquidity

Kyle, A. (1985) Continuous Auctions and Insider Trading. Econometrica. 53 (6) 1315-

1335

Lesmond, D. (2002) Liquidity of Emerging Markets

Levine, R. (1997) Financial Development and Economic Growth Views and Agenda.

Journal of Economic Literature, Vol 35. No 2 688-726

Nieuwenburg, S. (2010) Liquidity and the Stock Market

Pastor, L., Stambaugh, R. (2003) Liquidity Risk and Expected Stock Returns. Journal

of Political Economy, Vol 111, no 3, 642-685

Petersen, M. A., and D. Fialkowski, 1994, "Posted versus Effective Spreads: Good

Prices or Bad Quotes?" Journal of Financial Economics 35 (3), 269-292.

Stavins, R.N. (1995), ‘Transaction Costs and Tradable Permits’, 29 Journal of

Environmental Economics and Management, 133-148.

Stoll, H., (2000) Friction. The Journal of Finance, Vol 55, No 4., 1479-1514

Subrahmanyam, A. (1991) Risk Aversion, Market Liquidity, and Price Efficiency. The

Review of Financial Studies, Vol 4, No. 3. 417-441

31

Appendix 1:

Amihud & Mendelson (1986) Asset Pricing and the Bid-Ask Spread

Amihud and Mendelson (1986) model the effect of the bid-ask spread on asset returns. Their

hypotheses are:

1) “ Expected asset return is an increasing function of illiquidity costs, and

2) The relationship is concave due to the clientele effect: in equilibrium, less liquid assets

are allocated to investors with longer holding periods, which mitigates the

compensation that they require for the costs of illiquidity.” [Amihud et al (2005)]

They find evidence for their predictions. The data they use consists of monthly security

returns by the CRSP. By the NYSE they collected the relative bid-ask spreads. The ratio of

the dollar spread to the stock price is the calculation made behind the relative bid-ask spreads

variables. The spread is calculated by the average of the beginning- and end-of-year quotes.

The data tests the relationship between the stock returns, the risk and the spread over the

period of 1961 to 1980. 49 portfolios are made every year by sorting the stocks on previous-

year relative spread. In the portfolio, the stocks are also sorted on the previously-estimated

beta. After forming the portfolio, the monthly return is calculated. The data is divided into

twenty overlapping periods of eleven years. The twenty periods consists of a five-year β

estimation period En, a five-year portfolio formation period Fn and a one-year cross-section

test period described by Tn. To give a better understanding, see the table below:

En Fn Tn

E1 = 1951-1955 F1 = 1956-1960 T1 = 1961

E2 = 1952-1956 F2 = 1957-1961 T2 = 1962

E5 = 1955-1959 F5 = 1960-1964 T5 = 1965

E10 = 1960-1964 F10 = 1965-1969 T10 = 1970

E20 = 1970-1974 F20 = 1975-1979 T20 = 1980

Table 7: Explanation different periods

As earlier stated, the En is used as the estimation of β. The following is formula determining

the β: Rejt = αj + βjR

emt + εjt, with t = 1, .., 60. The R

ejt and the R

emt corresponds to the excess

return of a month t on stock j and on the market, respectively. The βj is the beta estimator of

stock j. The Fn is formed to use it as a test for the portfolio, as an estimator of the beta and to

view the spread of a the portfolios.

32

The Tn is used as a test to see the relationship between Rept, βpn, and Spn. R

ept and Spn will be

explained later. βpn is the estimator of the relative risk of a certain portfolio p at the last year

of period n. The stocks were ranked by the spread and divided into seven sets. In these equal

sets, stocks were ranked by the β, calculated at En. These sets were also divided into seven

new groups. Ultimately, they formed 49 equal-sized portfolios. After that, approximately the

same formula as used by the En, is used: Rept = αp + βpR

emt + εpt, t = 1, .., 60, p = 1, .., 49. The

factor j changed into the factor p, which states the portfolio. The previously announced Spn is

the portfolio spread. It is calculated by averaging the spreads across the stocks in portfolio p,

of the last year of Fn. After this, 980(!) portfolios are made by a pair of (βpn, Spn). P can take

values from 1 to 49, whereas there are 20 n’s periods. To test the hypothesis, a covariance

analysis and pooling of cross-section and time-series data is used. With this test, they could

test differences across cross-section units and over time. To do this, they made two sets of

dummy variables. The first set has 48 dummy variables, if the portfolio is in group (i, j), DPi,j

= 1, and zero otherwise. In DPi,j, the i is the spread-group index and the j is the β-group index.

These two sets of variables allow for the test over cross-sectional differences. The next set is

used for testing the over time differences and consists of a 1 if DYn if it is in a specific year n,

and will get a zero if not. The formula from the pooled cross-section and time-series

regression will be:

The first summation needs to be explained further. To make available different slope

coefficients across spread groups, the Spn needed to be changed. The stated summation now

allowed for that. The bi coefficient measures the changes of stock returns to increase the

spread within a spread group i. The cij coefficient measures the gap between the mean return

on portfolio (i, j) and that of the portfolio with the highest spread and the highest β group,

which is portfolio (7, 7). Later on, a generalized least squares (GLS) estimation procedure was

started to reduce the cross-sectional heteroskedasticity. After using the formulas described

here, the results fully supported the hypothesis, so expected return is indeed an increasing and

concave function of the spread. [Amihud and Mendelson (1986)]

33

To see whether the effect of size matters, they also used the variable ‘size’ to test if the same

relationship holds and if there are differences. The variable is conducted as the firm’s equity

at the end of the year in dollars. By adding this variable, they did not find any effect of firm

size on stock returns. Even when using the size variable by its natural logarithm, there is no

reason to indicate that the earlier results found without the size variable, are different from the

results with the variable. Amihud and Mendelson (1986) argue: “in sum, our results on the

return-spread relation cannot be explained by a ‘size effect’ even if the latter exists.”

34

Appendix 2

Datar, Naik, and Radcliffe (1998) Liquidity and Stock Returns: An Alternative Test

The statistical background of the model by Datar et al (1998) is explained here in more detail.

The reason why they used an alternative test is explained in ’the turnover ratio’ paragraph,

which can be found on page 12.

To test the cross-sectional variation in stocks, Datar et al (1998) use the following

methodology:

Rit is the return at time t of a security i, xit consists of the turnover rate and some control

variables like: the firm size, the book to market ratio and the firm beta of a security i at time t.

is a term which includes the deviation of the realized return from the expected return. Nt is

the amount of securities used in month t.

Due to some statistical background information, the generalized least-squares (GLS)

methodology is used, which is also used by Amihud and Mendelson (1986). So to specify,

is calculated at the following manner:

where

Datar et al (1998) use a dataset which consists of data from July 31, 1962 through December

31, 1991. They use data of all non-financial firms on the NYSE and collect them via

COMPUSTAT and the Centre for Research in Security Prices (CRSP). COMPUSTAT is used

to calculate the book value whereas CRSP is used to collect the monthly returns. The monthly

returns are computed as a percentage change in the value of one dollar in stock i at time t. The

measure of liquidity, the turnover rate, is calculated by averaging the monthly trading volume

and divide it by the number of shares outstanding of that firm. The average monthly trading

volume consists of data from the three previous months. The final outcome is then presented

as a percentage. They exclude stocks if due to stock changes the number of stock outstanding

varies. Data will be excluded then for three months. Finally, the dataset is trimmed. They

discard the lowest and the highest 1% observations of the turnover rate to get rid of the

extreme realizations. To test whether liquidity effect are still persisting after controlling for

several well-known determinants of stock returns, the previously announced firm size, book-

35

to-market ratio and firm beta variables are added. The first two variables are constructed by

using the natural logarithm. In this way, the book-to-market ratio is the natural logarithm of

the book value to the market value for individual firms. The natural logarithm of the firm size

is the total market capitalization of a firm i, at the end of the previous month. The last variable,

the firm beta, is calculated at the same way as it is used by Amihud and Mendelson (1986).

To recall, portfolios are made and the beta of a certain portfolio is given to all the stocks

within the portfolio. To conclude, Datar et al (1998) “find that the stock returns are strongly

negatively related to their turnover rates confirming the notion that illiquid stocks provide

higher average returns. In general, we find that a drop of 1% in the turnover rate is

associated with a higher return of about 4.5 basis points per month, on average”.

36

Appendix 3: Results Turnover Rate Model

Below, the results of model 4 are shown. In model 4, ‘Excess Returns’ is the dependent

variable. The ‘turnover rate’ (= Beta 1), ‘firm size’ (= Beta 2) and ‘the Beta’ (= Beta 3) are

the independent variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 4 -,065 -,075 0 ,007 0 -,040 1 ,028

1998 4 -,328 ,262 1 ,031 1 -,039 1 ,029

1999 4 -,166 ,226 1 ,013 1 -,010 0 ,012

2000 4 ,029 ,043 0 ,000 0 -,086 1 ,049

2001 4 ,058 ,111 1 -,006 0 -,035 0 ,011

2002 4 -,123 ,044 0 ,013 1 -,044 1 ,019

2003 4 -,050 ,154 1 ,002 0 ,033 1 ,037

2004 4 -,003 ,159 1 ,000 0 -,009 1 ,018

2005 4 -,041 ,094 1 ,003 0 -,021 1 ,015

2006 4 -,012 ,030 0 ,001 0 -,033 1 ,025

2007 4 -,159 ,059 0 ,016 1 -,053 1 ,078

2008 4 -,255 ,052 1 ,029 1 -,115 1 ,097

2009 4 -,769 1,048 1 ,069 1 -,225 1 ,448

2010 4 -,053 -,034 1 ,004 0 ,037 1 ,017

2011 4 -,896 ,727 1 ,082 1 -,110 1 ,158

2012 4 -,118 ,099 1 ,010 1 ,006 0 ,020 Table 8: Results Turnover Rate Model 4

Below, the results of model 1 are shown. In model 1, ‘Excess Returns’ is the dependent

variable. The ‘turnover rate’ is the independent variable.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 1 -0,023 -0,165 1 0,009

1998 1 -0,044 0,16 1 0,007

1999 1 -0,045 0,198 1 0,01

2000 1 -0,036 -0,145 1 0,003

2001 1 -0,033 0,043 0 0

2002 1 -0,02 -0,061 0 0,001

2003 1 -0,008 0,221 1 0,021

2004 1 -0,015 0,139 1 0,017

2005 1 -0,026 0,05 1 0,003

2006 1 -0,026 -0,024 0 0

2007 1 -0,031 -0,035 1 0,002

2008 1 -0,027 -0,119 1 0,013

2009 1 -0,251 0,946 1 0,428

2010 1 0,015 0,006 0 0

2011 1 -0,122 0,54 1 0,11

2012 1 -0,006 0,094 1 0,018 Table 9: Results Turnover Rate Model 1

37

Below, the results of model 2 are shown. In model 2, ‘Excess Returns’ is the dependent

variable. The ‘turnover rate’ (= Beta 1) and the ‘firm size’ (= Beta 2) are the independent

variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 2 -0,06 -0,161 1 0,004 0 0,008

1998 2 -0,339 0,187 1 0,029 1 0,016

1999 2 -0,164 0,207 1 0,012 1 0,012

2000 2 0,079 -0,156 1 -0,011 0 0,004

2001 2 0,062 0,03 0 -0,009 0 0,001

2002 2 -0,14 -0,035 0 0,012 1 0,002

2003 2 -0,055 0,233 1 0,005 0 0,021

2004 2 0,004 0,136 1 -0,002 0 0,017

2005 2 -0,033 0,051 1 0,001 0 0,003

2006 2 -0,009 -0,026 0 -0,002 0 0

2007 2 -0,146 -0,026 1 0,011 1 0,006

2008 2 -0,323 -0,095 1 0,028 1 0,018

2009 2 -1,288 0,963 1 0,102 1 0,432

2010 2 -0,021 0,007 0 0,003 0 0

2011 2 -0,968 0,603 1 0,081 1 0,128

2012 2 -0,115 0,107 1 0,01 1 0,019 Table 10: Results Turnover Rate Model 2

Below, the results of model 3 are shown. In model 3, ‘Excess Returns’ is the dependent

variable. The ‘turnover rate’ (= Beta 1) and ‘the Beta’ (= Beta 3) are the independent

variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 3 0,009 -0,085 1 -0,04 1 0,028

1998 3 -0,015 0,23 1 -0,037 1 0,02

1999 3 -0,038 0,213 1 -0,008 0 0,011

2000 3 0,028 0,043 0 -0,086 1 0,049

2001 3 -0,007 -0,036 1 0,122 1 0,011

2002 3 0,013 -0,044 1 0,013 0 0,018

2003 3 -0,031 0,149 1 0,033 1 0,038

2004 3 -0,009 0,16 1 -0,009 1 0,019

2005 3 -0,011 0,09 1 -0,021 1 0,015

2006 3 -0,002 0,029 0 -0,033 1 0,025

2007 3 0,005 0,043 1 -0,051 1 0,072

2008 3 0,048 0,027 0 -0,114 1 0,091

2009 3 -0,054 1,041 1 -0,235 1 0,446

2010 3 -0,011 -0,036 1 0,037 1 0,017

2011 3 -0,043 0,663 1 -0,11 1 0,14

2012 3 -0,01 0,087 1 0,006 0 0,018 Table 11: Results Turnover Rate Model 3

38

Furthermore, I used the annual data to create three periods. The first period contains the years

1997 until 2002. The second period is from 2003 until 2007, and the third period contains the

other years so from 2008 up to and including 2012. I used the same models as describe above.

In the column ‘Model’ the 1, 2, 3, and 4 indicate which model is used in the specific

regression.

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2002 1 -,035 ,021 0 ,000

1997-2002 2 -,089 ,027 0 ,005 0 ,000

1997-2002 3 -,003 ,100 1 -,042 1 ,015

1997-2002 4 -,091 ,111 1 ,009 1 -,042 1 ,016

2003-2007 1 -,014 ,006 0 ,000

2003-2007 2 ,082 -,004 0 -,009 1 ,002

2003-2007 3 -,006 ,026 1 -,011 1 ,003

2003-2007 4 ,082 ,015 0 -,008 1 -,010 1 ,004

2008-2012 1 -,160 ,668 1 ,260

2008-2012 2 -1,020 ,700 1 ,083 1 ,271

2008-2012 3 -,047 ,758 1 -,139 1 ,287

2008-2012 4 -,823 ,783 1 ,075 1 -,134 1 ,296 Table 12: Results Turnover Rate Model for the different periods

All years put together provides the following results:

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2012 1 -,096 ,515 1 ,168

1997-2012 2 -,382 ,526 1 ,028 1 ,171

1997-2012 3 -,035 ,570 1 -,072 1 ,187

1997-2012 4 -,324 ,581 1 ,028 1 -,072 1 ,191 Table 13: Results Turnover Rate Model for all years

A remark has to be made about the coefficient determinant of the Firm Size (=Beta 2 in the

tables). Because of the unavailability of the shares outstanding for 1997, I estimated them

with the first known number of 1998. Thereby, the market capitalization variable and the later

computed Firm Size variable are containing an estimation of the shares outstanding in 1997.

Because of that, the Firm Size of 1997 is less reliable.

39

Appendix 4: Descriptive Statistics of the Turnover rate Model

1997 1998 1999 2000 2001 2002 2003 2004

Number 2030 2445 2448 2448 2448 2448 2448 2448

Mean excess

return

-,035348 -,030639 -,027422 -,050757 -,027927 -,027826 ,020455 ,001472

St. dev.

excess return

,1295065 ,1507677 ,1525591 ,1820372 ,1537592 ,1527895 ,1173302 ,0919638

Mean

turnover rate

,073559 ,084828 ,087350 ,101662 ,111134 ,123339 ,127541 ,119124

St. dev.

turnover rate

,0749939 ,0822388 ,0799062 ,0739029 ,0747149 ,0759479 ,0782106 ,0871602

Mean firm

size

10,077126 10,085526 10,132673 10,122040 10,136369 10,112932 10,111888 10,211322

St. dev. firm

size

,5017091 ,5027970 ,5486329 ,5972686 ,5555651 ,5325395 ,5308077 ,5010850

Mean bèta ,961059 ,967835 ,968145 ,968145 ,968145 ,968145 ,968145 ,968145

St. dev. bèta ,4813839 ,4850464 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298

2005 2006 2007 2008 2009 2010 2011 2012

Number 2448 2448 2448 2448 2448 2448 2448 2448

Mean excess

return -,019362 -,029658 -,036831 -,056386 ,055462 ,016261 ,000246 ,013191

St. dev.

excess return

,0851393 ,0928544 ,0857464 ,1769764 ,7576674 ,1144963 ,2810435 ,1064868

Mean

turnover rate

,129467 ,144561 ,177652 ,247627 323634 ,244357 ,225427 ,200257

St. dev.

turnover rate

,0990219 ,1148397 ,1303045 ,1710655 ,5242879 ,2270249 ,1729698 ,1521204

Mean firm

size 10,260940 10,306109 10,353559 10,247372 10,132893 10,243287 10,291308 10,299395

St. dev. firm

size

,4818542 ,4782089 ,4795845 ,5051933 ,5199151 ,4885113 ,4871618 , 4960652

Mean bèta ,968145 ,968145 ,968145 968145 ,967145 ,968145 ,968145 ,968145

St. dev. bèta ,4848298 ,4848298 ,4848298 ,4848298 ,4823961 ,4848298 ,4848298 ,4848298 Table 14: Descriptions Turnover Rate Model

40

Appendix 5: Results Relative Bid-ask spread Model

Below, the results of model 4 are shown. In model 4, ‘Excess Returns’ is the dependent

variable. The ‘Relative Bid-ask spread’ (= Beta 1), ‘firm size’ (= Beta 2) and ‘the Beta’ (=

Beta 3) are the independent variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 4 -0,057 -0,311 1 0,009 0 -0,033 1 0,046

1998 4 -0,261 0,038 0 0,025 1 -0,026 1 0,012

1999 4 -0,184 0,342 1 0,011 1 -0,011 0 0,027

2000 4 0,09 -0,247 1 -0,002 0 -0,07 1 0,063

2001 4 0,134 -0,202 1 -0,011 1 -0,015 1 0,023

2002 4 -0,007 -0,218 1 0,004 0 -0,028 1 0,04

2003 4 -0,07 0,341 1 0,002 0 0,025 1 0,06

2004 4 0,109 -0,003 0 -0,011 1 0,004 0 0,002

2005 4 0,012 0,039 0 -0,002 0 -0,015 1 0,006

2006 4 -0,01 0,071 0 0 0 -0,033 1 0,025

2007 4 -0,062 -0,233 1 0,009 0 -0,039 1 0,089

2008 4 0,185 -0,473 1 -0,009 0 -0,052 1 0,268

2009 4 -0,738 0,85 1 0,047 0 0,153 1 0,042

2010 4 -0,018 -0,221 1 0,002 0 0,042 1 0,026 2011 4 -0,254 0,161 1 0,025 1 -0,024 1 0,002 2012 4 0,014 -0,085 0 -0,001 0 0,022 1 0,006

Table 15: Results Relative Bid-ask spread Model 4

Below, the results of model 1 are shown. In model 1, ‘Excess Returns’ is the dependent

variable. The ‘Relative Bid-ask spread’ is the independent variable.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 1 0,014 -0,384 1 0,032

1998 1 -0,028 -0,014 0 0

1999 1 -0,08 0,32 1 0,025

2000 1 0,02 -0,351 1 0,031

2001 1 0,011 -0,225 1 0,02

2002 1 0,017 -0,259 1 0,033

2003 1 -0,029 0,404 1 0,052

2004 1 0,001 0,008 0 0

2005 1 -0,018 -0,009 0 0

2006 1 -0,026 -0,041 0 0

2007 1 0,001 -0,354 1 0,044

2008 1 0,057 -0,52 1 0,25

2009 1 -0,146 1,036 1 0,035

2010 1 0,026 -0,084 1 0,002 2011 1 -0,008 0,064 1 0 2012 1 0,012 0,015 0 0

Table 16: Results Relative Bid-ask spread Model 1

41

Below, the results of model 2 are shown. In model 2, ‘Excess Returns’ is the dependent

variable. The ‘Relative Bid-ask spread’ (= Beta 1) and the ‘firm size’ (= Beta 2) are the

independent variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 2 -0,067 -0,385 1 0,008 0 0,033

1998 2 -0,275 -0,007 0 0,024 1 0,006

1999 2 -0,183 0,323 1 0,01 0 0,026

2000 2 0,111 -0,351 1 -0,009 0 0,031

2001 2 0,129 -0,227 1 -0,012 1 0,022

2002 2 -0,03 -0,255 1 0,005 0 0,033

2003 2 -0,062 0,409 1 0,003 0 0,051

2004 2 0,109 -0,013 0 -0,01 1 0,002

2005 2 0,009 -0,015 0 -0,003 0 0

2006 2 -0,016 -0,042 0 0 0 0

2007 2 -0,072 -0,344 1 0,007 0 0,045

2008 2 0,125 -0,525 1 -0,007 0 0,25

2009 2 -0,531 1,084 1 0,037 0 0,035

2010 2 0,024 -0,084 1 0 0 0,002 2011 2 -0,272 0,097 1 0,025 1 0,001 2012 2 -0,067 -0,385 1 0,008 0 0,033

Table 17: Results Relative Bid-ask spread Model 2

Below, the results of model 3 are shown. In model 3, ‘Excess Returns’ is the dependent

variable. The ‘Relative Bid-ask spread’ (= Beta 1) and ‘the Beta’ (= Beta 3) are the

independent variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 3 0,036 -0,311 1 -0,033 1 0,045

1998 3 -0,01 0,03 0 -0,026 1 0,006

1999 3 -0,073 0,336 1 -0,01 0 0,025

2000 3 0,068 -0,247 1 -0,071 1 0,063

2001 3 0,021 -0,199 1 -0,015 1 0,022

2002 3 0,038 -0,222 1 -0,028 1 0,04

2003 3 -0,045 0,336 1 0,025 1 0,06

2004 3 -0,001 -0,003 0 0,003 0 0

2005 3 -0,009 0,044 0 -0,015 1 0,006

2006 3 -0,005 0,07 0 -0,033 1 0,025

2007 3 0,027 -0,246 1 -0,039 1 0,088

2008 3 0,096 -0,467 1 -0,052 1 0,268

2009 3 -0,243 0,796 1 0,149 1 0,042

2010 3 0,003 -0,224 1 0,042 1 0,027 2011 3 0,007 0,129 1 -0,024 1 0,001 2012 3 0,001 -0,082 0 0,022 1 0,007

Table 18: Results Relative Bid-ask spread Model 3

42

Furthermore, I used the annual data to create three periods. The first period contains the years

1997 until 2002. The second period is from 2003 until 2007, and the third period contains the

other years so from 2008 up to and including 2012. I used the same models as describe above.

In the column ‘Model’ the 1, 2, 3, and 4 indicate which model is used in the specific

regression.

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2002 1 -,005 -,169 1 ,010

1997-2002 2 -,037 -,168 1 ,003 0 ,010

1997-2002 3 ,016 -,124 1 -,030 1 ,018

1997-2002 4 -,030 -,122 1 ,005 0 -,030 1 ,018

2003-2007 1 -,023 ,097 1 ,003

2003-2007 2 ,052 ,084 1 -,007 1 ,004

2003-2007 3 -,013 ,140 1 -,014 1 ,007

2003-2007 4 ,055 ,127 1 -,007 1 -,014 1 ,008

2008-2012 1 ,000 ,031 0 ,000

2008-2012 2 ,030 ,028 0 -,003 0 ,000

2008-2012 3 -,025 -,024 0 ,036 1 ,001

2008-2012 4 -,016 -,023 0 -,001 0 ,038 1 ,002 Table 19: Results Relative Bid-ask spread Model for the different periods

All years put together provides the following results:

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2012 1 -,008 -,047 1 ,000

1997-2012 2 -,001 -,047 1 ,000 0 ,000

1997-2012 3 -,005 -,042 1 -,003 0 ,000

1997-2012 4 ,001 -,042 1 ,000 0 -,003 0 ,000 Table 20: Results Relative Bid-ask spread Model for all years

A remark has to be made about the coefficient determinant of the Firm Size (=Beta 2 in the

tables). Because of the unavailability of the shares outstanding for 1997, I estimated them

with the first known number of 1998. Thereby, the market capitalization variable and the later

computed Firm Size variable are containing an estimation of the shares outstanding in 1997.

Because of that, the Firm Size of 1997 is less reliable.

43

Appendix 6: Descriptive Statistics of the Relative Bid-Ask spread

model

1997 1998 1999 2000 2001 2002 2003 2004

Number 2030 2445 2448 2448 2448 2448 2448 2448

Mean excess

return

-,035348 -,030639 -,027422 -,050757 -,027927 -,027826 ,020455 ,001472

St. dev.

excess return

,129656 ,156376 ,164083 ,202955 ,171668 ,172194 ,123726 ,099048

Mean relative

bid-ask

spread

,0608583 ,0847626 ,0757141 ,0917262 ,0987654 ,1076472 ,0662542 ,0523693

St. dev.

relative bid-

ask spread

,0749939 ,0822388 ,0799062 ,0739029 ,0747149 ,0759479 ,0782106 ,0871602

Mean firm

size

10,077126 10,085526 10,132673 10,122040 10,136369 10,112932 10,111888 10,211322

St. dev. firm

size

,5017091 ,5027970 ,5486329 ,5972686 ,5555651 ,5325395 ,5308077 ,5010850

Mean bèta ,961059 ,967835 ,968145 ,968145 ,968145 ,968145 ,968145 ,968145

St. dev. bèta ,4813839 ,4850464 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298

2005 2006 2007 2008 2009 2010 2011 2012

Number 2448 2448 2448 2448 2448 2448 2448 2448

Mean excess

return -,019362 -,029658 -,036831 -,056386 ,055462 ,016261 ,000246 ,013191

St. dev.

excess return

,0851393 ,0928544 ,0857464 ,1769764 ,7576674 ,1144963 ,2810435 ,1064868

Mean relative

bid-ask

spread

,094122 ,097179 ,107170 ,218328 ,193380 ,121031 ,127606 ,100295

St. dev.

relative bid-

ask spread

,0448569 ,0495940 ,0511998 ,1704961 ,1380179 ,0659324 ,0773674 ,0531617

Mean firm

size 10,260940 10,306109 10,353559 10,247372 10,132893 10,243287 10,291308 10,299395

St. dev. firm

size

,4818542 ,4782089 ,4795845 ,5051933 ,5199151 ,4885113 ,4871618 , 4960652

Mean bèta ,968145 ,968145 ,968145 968145 ,967145 ,968145 ,968145 ,968145

St. dev. bèta ,4848298 ,4848298 ,4848298 ,4848298 ,4823961 ,4848298 ,4848298 ,4848298 Table 21: Descriptions Relative Bid-ask spread Model

44

Appendix 7: Results Bid-ask spread Model

Below, the results of model 4 are shown. In model 4, ‘Excess Returns’ is the dependent

variable. The ‘Bid-ask spread’ (= Beta 1), ‘firm size’ (= Beta 2) and ‘the Beta’ (= Beta 3) are

the independent variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 4 -0,106 0 0 0,011 0 -0,043 1 0,027

1998 4 -0,207 0,001 0 0,019 1 -0,028 1 0,013

1999 4 0,142 0,007 1 -0,021 1 -0,019 1 0,044

2000 4 0,106 0,002 1 -0,008 -0,09 1 0,052

2001 4 0,032 -0,005 1 0 0 -0,021 1 0,027

2002 4 -0,115 -0,004 1 0,015 1 -0,041 1 0,028

2003 4 0,051 0,003 1 -0,008 0 0,041 1 0,032

2004 4 -0,008 0,002 1 -0,01 1 0,002 0 0,004

2005 4 0,015 0,001 1 -0,003 0 -0,015 1 0,007

2006 4 -0,005 0,002 1 0 0 -0,032 1 0,03

2007 4 -0,12 0,001 1 0,012 1 -0,048 1 0,077

2008 4 -0,244 -0,006 1 0,033 1 -0,098 1 0,152

2009 4 -0,056 0,019 1 -0,022 0 0,243 1 0,033

2010 4 -0,08 0 0 0,007 0 0,029 1 0,014 2011 4 -0,168 0,002 0 0,017 0 -0,015 0 0,002 2012 4 -0,009 3,04E-05 0 0 0 0,017 1 0,005

Table 22: Results Bid-ask spread Model 4

Below, the results of model 1 are shown. In model 1, ‘Excess Returns’ is the dependent

variable. The ‘Bid-ask spread’ is the independent variable.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 1 -0,027 -0,001 0 0,001

1998 1 -0,041 0,001 1 0,002

1999 1 -0,073 0,006 1 0,038

2000 1 -0,045 0 0 0

2001 1 0,011 -0,006 1 0,024

2002 1 -0,004 -0,004 1 0,008

2003 1 0,009 0,003 1 0,003

2004 1 -0,006 0,002 1 0,002

2005 1 -0,024 0,001 0 0,001

2006 1 -0,037 0,002 1 0,003

2007 1 -0,041 0,001 1 0,001

2008 1 -0,001 -0,007 1 0,065

2009 1 -0,056 0,02 1 0,009

2010 1 0,013 0,001 0 0 2011 1 -0,013 0,002 1 0,001 2012 1 0,013 8,07E-05 0 0

Table 23: Results Bid-ask spread Model 1

45

Below, the results of model 2 are shown. In model 2, ‘Excess Returns’ is the dependent

variable. The ‘Bid-ask spread’ (= Beta 1) and the ‘firm size’ (= Beta 2) are the independent

variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 2 -0,179 -0,002 1 0,016 1 0,004

1998 2 -0,263 0 0 0,023 1 0,006

1999 2 0,116 0,006 1 -0,019 1 0,041

2000 2 0,021 0 0 -0,007 0 0

2001 2 0,011 -0,006 1 -5,92E-05 0 0,024

2002 2 -0,176 -0,004 1 0,017 1 0,011

2003 2 0,112 0,003 1 -0,01 1 0,004

2004 2 0,097 0,002 1 -0,01 1 0,005

2005 2 0 0,001 0 -0,002 0 0,001

2006 2 -0,034 0,002 1 0 0 0,003

2007 2 -0,168 0,001 0 0,012 1 0,006

2008 2 -0,463 -0,007 1 0,045 1 0,081

2009 2 0,686 0,021 1 -0,074 1 0,012

2010 2 -0,009 0,001 0 0,002 0 0 2011 2 -0,201 0,002 0 0,018 0 0,002 2012 2 0,037 0 0 -0,002 0 0

Table 24: Results Bid-ask spread Model 2

Below, the results of model 3 are shown. In model 3, ‘Excess Returns’ is the dependent

variable. The ‘Bid-ask spread’ (= Beta 1) and ‘the Beta’ (= Beta 3) are the independent

variables.

# Year Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997 3 0,006 7,93E-05 0 -0,044 1 0,026

1998 3 -0,019 0,002 1 -0,03 1 0,01

1999 3 -0,06 0,006 1 -0,018 1 0,04

2000 3 0,025 0,001 1 -0,09 1 0,051

2001 3 0,028 -0,005 1 -0,021 1 0,028

2002 3 0,036 -0,004 1 -0,042 1 0,026

2003 3 -0,03 0,002 1 0,042 1 0,032

2004 3 -0,008 0,002 1 0,002 0 0,002

2005 3 -0,011 0,001 1 -0,014 1 0,007

2006 3 -0,009 0,002 1 -0,032 1 0,031

2007 3 0,001 0,001 1 -0,048 1 0,073

2008 3 0,093 -0,006 1 -0,103 1 0,144

2009 3 -0,287 0,019 1 0,248 1 0,034

2010 3 -0,012 0 0 0,028 1 0,013 2011 3 0,003 0,002 1 -0,017 0 0,002 2012 3 -0,004 3,90E-05 0 0,017 0,005

Table 25: Results Bid-ask spread Model 3

46

Furthermore, I used the annual data to create three periods. The first period contains the years

1997 until 2002. The second period is from 2003 until 2007, and the third period contains the

other years so from 2008 up to and including 2012. I used the same models as describe above.

In the column ‘Model’ the 1, 2, 3, and 4 indicate which model is used in the specific

regression.

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2002 1 -,031 ,000 0 ,000

1997-2002 2 -,093 ,000 1 ,006 1 ,000

1997-2002 3 ,000 ,000 0 -,038 1 ,013

1997-2002 4 -,045 ,000 0 ,005 0 -,038 1 ,013

2003-2007 1 -,015 ,000 0 ,000

2003-2007 2 ,079 ,001 0 -,009 1 ,002

2003-2007 3 -,006 ,001 1 -,009 1 ,002

2003-2007 4 ,090 ,001 1 -,009 1 -,010 1 ,005

2008-2012 1 ,011 -,001 0 ,000

2008-2012 2 ,054 ,000 0 -,004 0 ,000

2008-2012 3 -,021 -,001 0 ,035 1 ,002

2008-2012 4 -,033 -,001 0 ,001 0 ,035 1 ,002 Table 26: Results Bid-ask spread Model for the different periods

All years put together provides the following results:

# Year Model Constant Beta 1 Sign Beta 2 Sign Beta 3 Sign Adj R2

1997-2012 1 -,009 ,000 1 ,000

1997-2012 2 -,034 -,001 1 ,002 0 ,000

1997-2012 3 -,005 ,000 1 -,004 0 ,000

1997-2012 4 -,027 ,000 1 ,002 0 -,004 0 ,000 Table 27: Results Bid-ask spread Model for all years

A remark has to be made about the coefficient determinant of the Firm Size (=Beta 2 in the

tables). Because of the unavailability of the shares outstanding for 1997, I estimated them

with the first known number of 1998. Thereby, the market capitalization variable and the later

computed Firm Size variable are containing an estimation of the shares outstanding in 1997.

Because of that, the Firm Size of 1997 is less reliable.

47

Appendix 8: Descriptive Statistics of the Bid-ask spread Model

1997 1998 1999 2000 2001 2002 2003 2004

Number 2030 2445 2448 2448 2448 2448 2448 2448

Mean excess

return

-,035348 -,030639 -,027422 -,050757 -,027927 -,027826 ,020455 ,001472

St. dev.

excess return

,1295065 ,1507677 ,1525591 ,1820372 ,1537592 ,1527895 ,1173302 ,0919638

Mean bid-ask

spread

7,020606 7,880439 8,297970 9,329773 6,731674 5,908470 4,177488 4,041602

St. dev. bid-

ask spread

4,5506545 4,9470979 5,4166575 7,7260586 4,1642685 3,5833211 2,3811956 2,4413139

Mean firm

size

10,077126 10,085526 10,132673 10,122040 10,136369 10,112932 10,111888 10,211322

St. dev. firm

size

,5017091 ,5027970 ,5486329 ,5972686 ,5555651 ,5325395 ,5308077 ,5010850

Mean bèta ,961059 ,967835 ,968145 ,968145 ,968145 ,968145 ,968145 ,968145

St. dev. bèta ,4813839 ,4850464 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298 ,4848298

2005 2006 2007 2008 2009 2010 2011 2012

Number 2448 2448 2448 2448 2448 2448 2448 2448

Mean excess

return -,019362 -,029658 -,036831 -,056386 ,055462 ,016261 ,000246 ,013191

St. dev.

excess return

,0851393 ,0928544 ,0857464 ,1769764 ,7576674 ,1144963 ,2810435 ,1064868

Mean bid-ask

spread

4,223237 4,676206 5,634657 8,267601 5,416888 4,698161 5,540420 4,673963

St. dev. bid-

ask spread

2,7266408 3,4554410 4,3187442 6,8222202 3,6838558 3,8944523 5,0911366 6,1370660

Mean firm

size 10,260940 10,306109 10,353559 10,247372 10,132893 10,243287 10,291308 10,299395

St. dev. firm

size

,4818542 ,4782089 ,4795845 ,5051933 ,5199151 ,4885113 ,4871618 , 4960652

Mean bèta ,968145 ,968145 ,968145 968145 ,967145 ,968145 ,968145 ,968145

St. dev. bèta ,4848298 ,4848298 ,4848298 ,4848298 ,4823961 ,4848298 ,4848298 ,4848298 Table 28: Descriptions Bid-ask spread Model

48

Appendix 9: Descriptive statistics summary of the Bid-ask spread

Table 29: Coefficient determinations significance description

The ‘Year’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 44 15 28 Average adjusted

R2=0,02233

Number of significant betas and which

are positive 31 9 8

Min adjusted R2 =

0,000

Number of significant betas and which

are negative 13 6 20

Max adjusted R2 =

0,152

Number of non-significant betas and

which are positive 19 9 2

Number of non-significant betas and

which are negative 1 7 2

The ‘Period’ regressions Beta 1 Beta 2 Beta 3

Number of significant betas 7 3 6 Average adjusted R

2 =

0,0024

Number of significant betas and which

are positive 6 1 6

Min adjusted R2 =

0,000

Number of significant betas and which

are negative 1 2 0

Max adjusted R2 =

0,013

Number of non-significant betas and

which are positive 6 4 0

Number of non-significant betas and

which are negative 3 1 2

Averages

Constant -0,023

Bid-ask spread 0,001102868

Firm size 0,00112352

Beta -0,006825

Table 30: Coefficient determinations averages