• No results found

The relative performance of different liquidity measures: Evidence from the Dutch market

N/A
N/A
Protected

Academic year: 2021

Share "The relative performance of different liquidity measures: Evidence from the Dutch market"

Copied!
55
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

1

The relative performance of different liquidity measures: Evidence from the Dutch

market

By Niko Levikari*

June 2016

Abstract

This study assesses whether liquidity risk is priced in the Dutch stock market and implements a horse race for a set of liquidity measures to test their relative performance in Amihud, Hameed, Kang, and Zhang (2015) framework. I argue liquidity risk is not captured by the Carhart’s (1997) four-factor model. The results are based on a sample of 237 companies over a period from January 1990 to December 2015. The results indicate most liquidity measures and weighting schemes are unable to capture the illiquidity premium left unexplained by the four factors. Secondly, illiquidity is priced when the IML factor is built using Amihud (2002) illiquidity measure and equal weighting scheme. This illiquidity premium is not due to January effect, however the results do not pass the Bonferroni approximation test. I conclude there is weak support for the inclusion of the IML factor to a four-factor model in the Dutch market.

Keywords: Asset pricing, liquidity measure, liquidity risk, risk factor, four-factor model.

(2)

2

1. Introduction

Well-known asset pricing models, such as the Carhart (1997) four-factor model, do not account for liquidity risk in the explanatory factors despite the growing body of literature suggesting liquidity risk to be counted for as an additional factor that is not captured by the other factors. The papers suggesting a liquidity risk related factor include Liu (2006), Amihud (2014) and Amihud, Hameed, Kang, and Zhang (2015). While authors such as Bessler and Kurmann (2014) argue that the liquidity factor and its dynamics are captured by the other factors in their model.

Despite the ongoing debate whether liquidity risk is captured by other factors, several papers show that liquidity risk significantly impacts the expected returns of both equities and fixed income securities. The early work of Amihud and Mendelson (1986) suggests that there is a positive relation between the illiquidity of an asset and the required return demanded by investors. As another example, Brennan and Subrahmanyam (1996) show a positive and statistically significant relation between the expected returns or return premium and their measure of illiquidity. Acharya and Pedersen (2005) show in their liquidity adjusted capital asset pricing model that the expected return of a security is impacted by its expected liquidity. In the case of US bonds, Amihud and Mendelson (1991) found a liquidity effect that meant less liquid notes had a higher yield to maturity than more liquid T-bills of the same maturity. While De Jong and Driessen (2012) found in their study liquidity risk to be reflected in the expected returns of corporate bonds with below investment grade US bonds having higher liquidity risk premium.

Several papers found liquidity risk to be important for expected returns in other markets than the US. Lee (2011) tested the LCAPM of Acharya and Pedersen (2005) and found liquidity to impact expected returns in international markets. Bekaert, Harvey, and Lundblad (2007) covered 19 developing markets across Latin America, Africa, Europe and Asia and show liquidity to be an important factor for expected returns. Amihud, Hameed, Kang, and Zhang (2015) found the illiquidity premium and risk adjusted liquidity return premium to be significant and positive in most of the developing and developed markets included in their sample with the effect being stronger in developing countries. In the Asian markets, Lam and Tam (2011) and Narayan and Zheng (2010) found liquidity risk to be priced in the Chinese and Hong Kong stock markets.

(3)

3 Given the various liquidity measures, this paper performs a horse race between different liquidity measures to analyse which of them performs the best in the Dutch equities market. The closest paper that compared the relative performance of several different liquidity proxies is by Houweling, Mentink, and Vorst (2005). They test nine different liquidity measures for euro corporate bonds. In the case of equities, the closest paper is by Amihud, Hameed, Kang, and Zhang (2015) who test another liquidity measure, dollar trading volume, as a part of their robustness tests to construct the liquidity-based portfolios and compare the results with those from using Amihud (2002) illiquidity measure.

Regarding the methodology, this study uses the framework of Amihud, Hameed, Kang, and Zhang (2015) to construct the illiquid-minus-liquid (IML) factor returns. The liquidity risk factor is built using several liquidity measures instead of a subjective choice between different measures. Since different liquidity measures are not comparable per se, the uniform framework allows for a better comparison of the performance of different liquidity measures at capturing the illiquidity related premium left unexplained by Carhart (1997) four factors in the Dutch market. To further improve the comparability of the results, the same time period and sample is used to construct each measure.

There are two main questions that this study aims to answer. Firstly, are systematic co-movements in liquidity priced in the Dutch stock market after controlling for other well-known risk factors? I test if shares with higher IML coefficient value have a higher return when controlled for other well-known risk factors. The second research question is which of the different liquidity measures performs the best at capturing the illiquidity related premium left unexplained by the four factors in the Dutch market?

In-line with the empirical results regarding IML factor by Amihud (2014) and Amihud, Hameed, Kang, and Zhang (2015), this study expects the IML premium to be positive and statistically and economically significant in the presence of the risk factors of the multifactor model. Similar to Amihud, Hameed, Kang, and Zhang (2015), I expect the risk-adjusted illiquidity premium to be positive and statistically significant for the best performing liquidity measure. Regarding the second research question, I expect some of the IML variants to perform better than the others.

These research questions are interesting as liquidity measures can be built in many ways. Some are computationally more demanding because they involve higher frequency data, while others involve several intermediate calculations. If several IML versions have positive risk-adjusted illiquidity premium and none of them performs relatively better, it would seem sensible for an asset manager to use the computationally easiest liquidity proxy to build the IML factor as the more complicated measures would not do better.

(4)

4 industry classifications, Worldscope industry grouping is used to group the sample companies according to major industries. When a classification is missing, Orbis database is used to check for the available industry classifications. Then I choose the closest matching industry group for that company from Worldscope. A set of filters is used to improve the quality of the sample. To limit survivorship bias, dead companies are included in the sample. The company status data (dead or active) comes from Datastream and the final sample consists of 78 active and 159 dead companies. Following Brückner, Lehmann, Schmidt, and Stehle (2015) companies that traded below 1 euro any time during their listing are classified as penny stocks and removed from the final sample. Only in a few exceptional cases a company is kept in the sample when the fall in the share price below 1 euro is temporary and it has subsequently recovered above this limit. Penny stocks are excluded to prevent the findings from being driven by highly volatile very low priced shares. Book values are needed to construct the high-minus-low (HML) factor of Fama and French (1993). Therefore companies included in the final sample need to have book values for the same months as the share price to form the M/P ratio. A couple of companies were removed due to this criterion as they did not have the M/P ratio available. Lastly, this study follows Christoffersen and Sarkissian (2009) and uses 36 months or 3 years of observations as the minimum for companies to be included in the sample.

There is weak evidence that share illiquidity is priced in the Dutch market when the IML factor is built using Amihud (2002) liquidity measure and equal weighting. The best performing Amihud (2002) liquidity measure and equally weighted show a positive and statistically significant monthly risk-adjusted excess returns of 0.3033 percent per month at 5 percent significance level. This is 3.7 percent on an annual basis. The mean equally weighted illiquidity premium for this measure is 0.96 percent annually. It is noteworthy that these figures are based on returns calculated from the price adjusted series of Datastream that ignore dividend yields. Thus the reported figures are biased downwards as they do not represent total returns. To counter a potential multiple comparisons problem, the Bonferroni approximation is calculated according to which the initial findings are no longer found significant. Regarding the second research question, I conclude that most of the liquidity measures and weighting schemes are incapable to capture illiquidity related premium left unexplained by the four factors. Despite the poor performance of the majority of the IML factors, there is quite a bit of common variation in the various IML factors according to the principal components analysis, as the first principal component counts for 54.25 percent of the total variance.

(5)

5 While the measure of Liu (2006) that claims to capture multiple dimensions liquidity does not appear to do so based on the results. Liu’s measure shows no correlation with the Amihud and Mendelson (1986) measure even though both measures are supposed to capture trading costs. Thirdly, this study produces the results on a less commonly used dataset and given the horse race testing of liquidity measures in this study, it is the first such for the Dutch stock market.

The remainder of this paper is organised in the following manner. In Section 2, I describe the relevant literature and Section 3 covers the formulation of the research questions. I present the methodology in Section 4, including the construction of the IML factor and the different liquidity measures. In Section 5, I explain the sample construction and provide the descriptive statistics. While Section 6 presents the results and robustness testing. I provide the conclusions and the summary of the thesis in Section 7.

2. Literature review

Liu (2006) defines liquidity for equities and other securities as the ability to transact large volumes of securities with a minimal price impact and with low transaction costs. Huberman and Halka (2001) add that while liquidity implies the speed and ease of transacting, it is not directly observable. I follow Liu (2006) and call different proxies for liquidity as liquidity measures and the risk of illiquidity as liquidity risk.

The lack of a direct measure for liquidity means researchers have used several proxies for liquidity to capture the impact of liquidity risk. These include the price impact of orders Kyle (1985), the relative bid-ask spread of Amihud and Mendelson (1986), stock turnover by Datar, Naik, and Radcliffe (1998), market depth by Chordia, Roll, and Subrahmanyam (2001), the illiquidity ratio of Amihud (2002), liquidity measure by Pastor and Sambaugh (2003), the liquidity adjusted capital asset pricing model of Acharya and Pedersen (2005) and the liquidity ratio of Liu (2006) among others. Most of these studies show there is a positive correlation between illiquidity and the expected returns of a given share. These findings provide support for treating liquidity risk as a systematic risk that cannot be diversified away as stated by Amihud and Mendelson (2015). I argue that liquidity risk factor should be included in multifactor models as an additional factor to explain security excess returns.

(6)

6 liquidity which are trading quantity, trading costs and a less researched dimension of liquidity referred to as trading speed. Given these different measures, which of them is the best at capturing the effects of liquidity. One of the earliest studies regarding liquidity risk is from Amihud and Mendelson (1986) who state that there is a positive relationship between liquidity and return. They argue that as an asset becomes more illiquid its expected return increases as investors adjust the price of that asset downwards to be compensated for the additional illiquidity related risks. Another early work by Brennan and Subrahmanyam (1996) looked at the price formation and the friction between privately informed and uninformed investors stating that informed investors generate illiquidity costs for the uninformed ones and the expected return should be higher for more illiquid assets. There are also a number of studies documenting the commonality in liquidity and that it varies over time such as Chordia, Roll, and Subrahmanyam (2000, 2001) and Hasbrouck and Seppi (2001) who found evidence of a common time varying factor when using bid-ask spread based proxies for liquidity. These findings point to liquidity being important for the expected returns and that its impact/influence varies over time.

The previous studies focused mainly on the US market. However, a number of papers focus on the relation between liquidity and expected returns for shares in international context and find liquidity to be important. The study by Bekaert, Harvey, and Lundblad (2007) looks at 19 developing markets across Latin America, Africa, Europe and Asia and concludes liquidity to be an important factor for expected returns. Amihud, Hameed, Kang, and Zhang (2015) made similar findings as they found both the illiquidity premium and risk-adjusted liquidity return premium to be positive and significant in most of the developing and developed markets in their sample. While Lee (2011) studied liquidity risk in 50 international markets using a liquidity adjusted capital asset pricing model and found liquidity risk to be priced separately from market risk. Brockman, Chung, and Perignon (2009) found in their study of 47 markets commonality in liquidity level when using bid-ask spread as their liquidity proxy. The study by Karolyi, Lee, and Van Dijk (2012) found illiquidity higher in their 40 sample countries when the stock market experienced higher volatility. Lastly, Vu, Chai, and Do (2015) researched the impact of systematic liquidity risk via LCAPM on Australian stock returns and found the liquidity risk to be priced and robust to various liquidity proxies. Martinez, Nieto, Rubio, and Tapia (2005) found liquidity risk to be priced in the Spanish equities. While Narayan and Zheng (2010) have similar results for the Chinese equity market and Lam and Tam (2011) for the Hong Kong stock market. The results indicate that liquidity is important across markets and its lack increases the expected returns of securities in a systematic manner. Based on these results, liquidity risk impacts securities in a systematic manner and cannot simply be diversified away.

(7)

7 corporate bonds in the US and the European market. Their results indicate that liquidity risk is priced in the expected returns of corporate bonds with the risk premium varying from 0.6 per cent in the case of US long term investment grade bonds to 1.5 per cent per annum in the case of below investment grade US bonds. Their findings for European bonds are in-line with the US findings and both the US and the European corporate bonds show exposure to liquidity risk. Acharya, Amihud, and Bharath (2013) use a regime switching model to study the impact of liquidity shocks to the US corporate bonds. Their findings indicate a time varying liquidity risk on corporate bonds with prices rising in the case of investment grade bonds and falling in the case of junk bonds when illiquidity increases. In case of illiquidity shocks the higher liquidity investment grade bonds are more sought after. These results suggest that liquidity risk is not confined to equities, instead it also influences other asset classes systematically.

There is a debate whether another factor for illiquidity is needed and not all researchers agree that liquidity risk represents a separate systematic risk factor. The argument against a separate liquidity risk factor is that liquidity risk is already captured by the existing factors in more commonly used models like the Carhart multifactor model. Bessler and Kurmann (2014) assume for the liquidity factor, that its dynamics are captured by the other factors in their model. Based on robustness tests that count for liquidity risk, Bessler and Kurmann (2014) report that liquidity risk is captured by their set of bank risk factors that excludes the liquidity risk factor even in crisis periods. Likewise, Fama and French (2015) do not report the findings of the multifactor model that includes the momentum factor of Carhart (1997) or a measure for the liquidity risk factor of Pastor and Stambaugh (2003) as these two factors have regression slopes close to zero and provide minimal effects on their model performance. This indicates that liquidity risk along with the momentum effect are captured by the other factors in their model.

3. Formulation of the research questions

This study is motivated by the work of Vu, Chai, and Do (2015), Amihud, Hameed, Kang, and Zhang (2015) and Amihud (2014) who consider liquidity risk as a source of systematic risk impacting all securities and thus should be represented by a risk factor. This is in the spirit of earlier publications such as Amihud and Mendelson (1986) and Pastor and Stambaugh (2003) among others. Since there are numerous liquidity measures, which one of them performs the best in a well-known Carhart four-factor model context for the Dutch equities?

(8)

8 The first question this study aims to answer is, whether systematic co-movements in liquidity are priced in the Dutch equities in the multifactor asset pricing model context? I will test if the shares with a higher IML coefficient have a higher return when controlled for other well-known risk factors. The second research question is, which of the different liquidity measures performs the best at capturing the illiquidity related premium left unexplained by the four factors in the Dutch market?

In-line with the empirical results regarding IML factor by Amihud (2014) and Amihud, Hameed, Kang, and Zhang (2015), I expect the IML premium to be positive and statistically and economically significant in the presence of the risk factors of the four-factor model. Regarding the second research question, I am expecting some of the IML variants to perform better and that some of the IML factors may even fail to capture illiquidity related premium. Likewise, I anticipate the risk-adjusted illiquidity premium to be positive and statistically significant for the best performing liquidity measure. Alternatively, it is possible that the liquidity risk is captured by the factors already included in the multifactor model and then the IML factor has insignificant risk-adjusted excess returns regardless of the liquidity measure used to construct the factor.

Amihud (2014) used the Carhart four-factor model when testing the IML liquidity factor for the US equities. While Amihud, Hameed, Kang, and Zhang (2015) found the IML liquidity factor to be positive and significant in several countries included in their sample when they used three global and regional Fama French (1993) factors. In the case of the Netherlands, Amihud, Hameed, Kang, and Zhang (2015) found a positive but not statistically significant illiquidity return premium. In both of these studies, the IML factor was constructed using Amihud (2002) illiquidity measure.

The research questions are interesting since one cannot compare the different liquidity measures per se because they have different units of measurement and reflect different dimensions of liquidity. By using a uniform framework to build the IML factor, the different liquidity measures are more comparable. This way it is possible to comment on how well the different liquidity measures and IML factors capture a liquidity risk premium and explain unexplained excess returns. Typically, the findings of different studies about liquidity measures are harder to compare as they are often done using samples that cover different markets and time periods. This study uses the Dutch market and the same time period between 1990 and 2015 when constructing each of the liquidity measures. This further improves the comparability of the results.

Since liquidity measures can be built in several manners with some being computationally more demanding than others, it is interesting to see if they provide similar results in a multifactor framework. If the results were similar, it would make sense for an asset manager to use the computationally easiest liquidity measure to build the IML factor as the more complicated proxies do not improve the results.

4. Methodology

4.1 The definition of a risk factor and the impact of weighting schemes

(9)

9 of average returns of the sample companies and will continue to explain them in the future. They are proxies for sensitivity to common risks that are undiversifiable. An example of such risk factors is liquidity risk, the focus of this study. The risk factors are important as they explain the average cross-sectional excess returns of stocks that are not explained by the excess market return of CAPM of Sharpe (1964) and Lintner (1965). These risk factors are built as zero investment portfolios where we go long on a portfolio that according to the theory should have a higher return for exposure to a given risk than a portfolio that has low exposure to this risk. Then we short the portfolio that has low exposure to this same risk. The portfolio that combines these portfolios x (long) minus y (short) then earns a return on the mimicking portfolio for a given risk factor. Factor loadings are the slope coefficients of risk factors in time series regressions. They represent the sensitivity of a given security to that systematic risk and can be positive or negative. One can think of the factor loadings as how much a given risk factor explains the dependent variable returns. The slope coefficient can also be thought of as the risk premium for a given systematic risk exposure that is different from the market risk premium. I can then say a given risk is priced or that a given risk factor is priced.

The weighting schemes used to construct risk factor mimicking portfolios are an important point. As Brückner, Lehmann, Schmidt, and Stehle (2015) highlight that while changes to the way factors are constructed are usually done to take into account country-specific settings, they can affect the types of stocks, returns and weighting schemes used in calculating portfolio returns and ultimately have an impact on the factors. As they mention these issues are not typically discussed by the factor providers or others. The graphs of Figure 1 in the appendix show that the choice of the weighting scheme has an impact on the performance of a given risk factor mimicking portfolio. Figure 1 graphs show that size effect no longer appears present in the Dutch equities given the poor performance of the SMB factor regardless of the weighting used. Evidence of the value effect is more mixed, based on value-weighted HML factor the value effect is still strong while the equally-weighted HML factor has performed particularly poorly at the end of the sample period. The momentum effect is very strong in the Dutch equities over the sample period regardless of the weighting scheme. Because of the impact a weighting scheme has, I perform the calculations using both equal and value weighting schemes for the risk factors. Even Amihud, Hameed, Kang, and Zhang (2015) test three weighting schemes to calculate the average monthly portfolio returns used to build their IML factor.

4.2 The liquidity risk factor

There are various liquidity measures that have been developed as stated by Liu (2006). As an example, we cannot take the relative bid-ask spread liquidity measure of Amihud and Mendelson (1986) and the turnover rate measure of Datar, Naik, and Radcliffe (1998) and compare the values of these two measures as they are expressed in different units of measurement.

(10)

10 Houweling, Mentink, and Vorst (2005) compared different liquidity measures in the euro denominated corporate bonds market. The closest study for equities that compared liquidity measures is by Amihud, Hameed, Kang, and Zhang (2015) who as a robustness test constructed the liquidity-based portfolios using dollar trading volume and compared the results with those from using Amihud (2002) illiquidity measure. However, to the best of my knowledge of the literature there have not been any other studies that extensively compare the performance of different liquidity measures for equities.

The liquidity risk factor (illiquid-minus-liquid) used here is created by Amihud (2014). I use the version of from the paper of Amihud, Hameed, Kang, and Zhang (2015). Once a given liquidity measure is calculated for the sample, the next step is to pre-sort the stocks based on their daily return volatility. Amihud, Hameed, Kang, and Zhang (2015) point out how the effects of liquidity and volatility can be mixed and because of this there should be a pre-sorting based on volatility before doing the liquidity measure sorting. I divide stocks into volatility terciles based on the daily return volatility of t-3 to t-1 months. In-line with Amihud, Hameed, Kang, and Zhang (2015) the stocks are then ranked within each tercile into quintiles based on a liquidity measure that was calculated over the same t-3 to t-1 months. The high illiquid quintile is then the sum of the top quintile portfolios across the three volatility terciles. Similarly, the low illiquid quintile is then the sum of the bottom quintile portfolios across the three volatility groupings. Amihud, Hameed, Kang, and Zhang (2015) call this a ranking by the liquidity measure that controls for volatility.

In accordance with Amihud, Hameed, Kang, and Zhang (2015) the return is then calculated for the high and low illiquid quintile portfolios in the months t+1, t+2 and t+3. The month t is skipped to avoid the impact of short-term reversals in returns when forming the factor similarly to calculating Carhart (1997) and Jageesh and Titman (1993) momentum factor WML. With delisted companies, the last return used is the one reported by Datastream. Following Liu (2006) the post de-listing monthly return is assumed zero for the remaining holding period.

(11)

11 Unlike Amihud, Hameed, Kang, and Zhang (2015) I do not remove the most illiquid 1 percent of the sample as the data quality has already been improved by excluding penny stocks, including dead companies and having a minimum number of observations per company as further elaborated in the sample construction section below. Further, different liquidity measures have their own filters to reduce the impact of extreme liquidity measure values. Amihud, Hameed, Kang, and Zhang (2015) delete the top 1 percent to ensure their results are not driven by extreme observations.

I am interested in the risk-adjusted excess return for the factor in the presence of common risk factors following Amihud, Hameed, Kang, and Zhang (2015). In the Equation 1 the intercept represents the risk-adjusted excess return when is regressed against the common risk factors. I follow Amihud (2014) and use as the common risk factors on the RHS Fama and French (1993) three factors and the Carhart (1997) version of momentum factor. I test if the risk-adjusted excess return, the intercept , is positive and both statistically and economically significant for some of the variants when controlling for the return of the four factors.

Unlike Amihud, Hameed, Kang, and Zhang (2015) I do not use the Fama French global and regional three factors on the RHS of Equation 1. As a support for my choice to use country-specific factors a paper by Moerman (2005) found that even in the euro area, country-specific three factor model outperformed the regional euro area version of the model. Similar results were earlier reported by Griffin (2002) for the US, the UK, Canada and Japan. As an acknowledgement of contradictory evidence, Brooks and Negro (2005) show opposite results according to which in a regional setting, country-specific factors can mostly be explained by regional factors. Since I focus on the Dutch market, I argue the country-specific factors are appropriate for this paper.

=

+ (

,

,

) +

+ ℎ

+

+

,

(1)

In the equation, the liquidity risk factor is constructed following Amihud, Hameed, Kang, and Zhang (2015), the represents the risk-adjusted excess return for the illiquidity factor. The factor , is the

value-weighted return on the market and is constructed using the companies in the sample instead of using an existing market index such as the AEX index. Here , represents the one-month risk-free rate.

The size factor represents the return on a portfolio of small stocks minus the return on large stocks. This factor is build following Fama and French (1993) paper where the sample is split to large and small companies using the median market capitalisation each month. Each year in June the companies are ranked and the returns calculated from July t to June t+1. Also, the portfolio return for month t is calculated value-weighted and equal-weighted. The size factor available from the Kenneth French1 website is equal-weighted and build using top

(12)

12 and bottom 10 percent as the breakpoints while the Fama and French (1993) used value weighting. Since different weightings are plausible, I run the Equation 1 using both weightings.

The value factor is the difference of returns on high B/M portfolio and low B/M portfolio and is constructed following Fama and French (1993) paper with bottom and top 30 percent as the cut-off points. Each June companies in the bottom 30 percent form the low B/M portfolio and the top 30 percent the high B/M portfolio. December t-1 B/M values are used to rank companies each year but returns are calculated from July t to June t+1. Similar to Fama and French (1993), companies with negative B/M are excluded from the sample when constructing the HML factor. The returns of both high and low B/M portfolios are calculated using both value-weighted returns as in Fama and French (1993) and using equal-weighted returns. Equal-weighting is what Kenneth French nowadays uses to calculate the HML series on his website.

The momentum factor is constructed following the methodology of Carhart (1997). I calculate the cumulative returns of stocks over the period from t-12 to t-2. The winner and loser portfolios are formed at the end of month t-1 based on the lagged momentum returns over the previous 11 months such that the winner portfolio includes companies in the top 30th percentile with the highest cumulative returns. While the loser portfolio includes companies in the bottom 30th percentile with the lowest cumulative returns. The return is then calculated for both the winner and loser portfolios for month t+1 and then the portfolios are reformed on a monthly basis. As for the weighting scheme of the monthly portfolio returns of the winner and loser portfolios, I calculate both equal-weighted returns following Carhart (1997) and value-weighted returns. Lastly, the term

, is the residual in the Equation 1.

If more than one version of the IML factor has positive and statistically significant risk-adjusted excess returns, I will do a student’s t-test to check for the equality of these risk-adjusted excess returns. This means testing if the difference between the alphas from Equation 1 is statistically significant. One of the two alphas may be smaller than the other but this could be due to the larger standard error of that sample. Otherwise I would not be able to say just by looking at the size of the alphas if one of the two IML versions is better at capturing risk-adjusted excess return than the other.

This study follows Chen and Gel (2011) to perform this test if needed. Assuming, both variables are normally distributed, the t-test statistic is then

=

,

(2)

here sample means are = ∑ , / , the sample variances = ∑ ( , − )/( − 1). Under the

(13)

13

=

( )

.

(3)

4.3 The liquidity measures and their construction

As stated before, different measures of liquidity focus on different dimensions/aspects of liquidity. The Table 1 in the appendix shows the different liquidity measures that I test to build the liquidity risk factor of Amihud, Hameed, Kang, and Zhang (2015). The main two criteria for choosing the liquidity measures for testing are data availability for the measure and that a large spectrum of different dimensions is tested by the various measures chosen. Some measures like the market depth measure of Chordia (2001) were not chosen as they required specialist data on quoted depth by market makers. This measure could only be done for securities exchanges that use market makers and the Dutch market is an order driven market. The measure of Pastor and Stambaugh (2003) was not chosen as there were some data availability issues and it covered the same dimension as Amihud (2002) measure.

The relative bid-ask spread of Amihud and Mendelson (1986) is updated in this study to account for the improved quality of the daily frequency data that the original paper did not have available. Even Datar, Naik, and Radcliffe (1998) noted that data on a monthly frequency about bid-ask spread was not easily available for long periods of time in the late 90s. Since I could download daily bid-ask prices from Datastream, this measure is adjusted for higher frequency data available to improve the information content of this measure. Amihud and Mendelson (1986) define the relative spread as the currency (dollar) spread divided by the average of the bid and ask prices at the end of the year. Further, they state the actual spread used is the average of the beginning and end of the year relative spreads. The formula for relative spread is presented in Equation 4.

=

( )

(4)

In this study, daily bid-ask spreads are calculated for the sample companies when available. Then a rolling monthly average of this spread is calculated and pulled to monthly frequency to have the month end values of average bid-ask spreads. Regarding the average bid-ask price series, this measure is calculated using daily data after which I calculate a yearly average series of this data. Thus, I have as the year-end value the average of the bid and ask prices calculated using data over a given year. Lastly, the monthly bid-ask spread data is divided by the year-end average of the bid and ask prices to create relative spread series.

For the Amihud and Mendelson (1986) relative spread measure higher spread indicates greater illiquidity which is expected to yield higher return. Low relative spread indicates higher liquidity and lower expected return.

(14)

14 measure. Following the approach of Datar, Naik, and Radcliffe (1998), I have excluded the lowest and highest 1 percent of the turnover rates to prevent the results from being driven by extreme values.

=

. .

(5)

As daily data on turnover volumes is available, the monthly turnover volumes are calculated using daily data and aggregated to monthly frequency to improve the quality of the measure. Since daily data has some patchiness, I have aggregated daily data to three month sum and divided it by three to get average monthly turnover volumes. Monthly outstanding shares figures are used as it is improbable the denominator varies significantly on a daily frequency.

With Datar, Naik, and Radcliffe (1998) turnover rate, liquid securities are those with a high turnover rate while illiquid are those with a low turnover rate. The more illiquid securities are expected to earn higher returns and vice versa.

Amihud (2002) illiquidity measure is expressed in the Equation 6 and it is calculated for the sample companies over a period of three months. The version used in this study is the modified Amihud illiquidity measure used by Amihud, Hameed, Kang, and Zhang (2015). The illiquidity measure is the average of the ratio of absolute daily returns to daily euro denominated volume and it is denoted as , .

,

=

,

, ,, ,

(6)

In the Equation 6, , , represents the return on share on day over period . The denominator , ,

represents euro denominated trading volume for share on day over period . The euro volume is calculated by multiplying the daily trading volume with the closing price of the day as described by Amihud, Hameed, Kang, and Zhang (2015). Lastly, the , is the number of trading days that have non-zero volumes for share

in period .

Following Amihud (2014), I use a set of filters. A day is excluded when the trading volume is below 100 euro or the price of the share falls to zero. Similar to Amihud, Hameed, Kang, and Zhang (2015) companies included must have a minimum of ten daily observations regarding the price and volume during the three-month portfolio formation period. In-line with Brückner, Lehmann, Schmidt, and Stehle (2015) companies are included in the sample if their share price is above one euro over the sample period to avoid the results from being driven by high volatility, low priced penny stocks.

In the case of Amihud (2002) illiquidity measure, the higher value of it is associated with higher expected return while a lower value with lower expected return.

(15)

15 traded on a day t divided by the number of shares outstanding at the end of the same month. Instead of using daily figures for the number of shares outstanding to calculate the daily turnover, the monthly figure is in the denominator as this figure does not change daily. I use the same approximation of 252 trading days as Liu (2006) for the 12-month measure. The measure is constructed monthly for each company in the sample. Finally, the deflator is chosen such that 0 < /( )< 1. Here 2,700,000 is used to achieve this.

=

.

ℎ +

/( )

. (7)

Following Liu (2006), high LM12 value indicates higher illiquidity which means the security is expected to provide higher return and vice versa.

Figure 2 in the appendix shows the four liquidity measures both value- and equal-weighted for the sample. The purpose of these graphs is to demonstrate how the different liquidity measures respond to movements in the market excess return. I expect to see increases in the liquidity measures particularly in downturn markets and when the market excess return bottoms out. The graphs show that the value-weighted Amihud and Mendelson relative spread and Amihud illiquidity measure increases coincide with market downturns in-line with my expectations. While for both the equal-weighted measures show sharper spikes that do not exactly match with the lows of the market. I can say that smaller market capitalisation securities are the cause for the significantly higher spikes in the equal-weighted measures.

In the case of Datar, Naik, and Radcliffe (1998) liquidity measure, both equal- and value-weighted versions of this measure had a downward trend from the mid-1996 onwards. With this measure, the lower turnover rate is associated with greater illiquidity and despite the small drop in around mid-2001, the measure does not later increase even though the overall market conditions improve after bottoming out in mid-2003. During the 2008, the measure increases indicating an increase in liquidity, opposite to what I would expect. Lastly the flat shape of Datar, Naik, and Radcliffe measure post 2008 would indicate to me that the measure is no longer picking the impact of liquidity based on trading quantity.

(16)

16 Radcliffe and Liu are bad per se. Amihud and Mendelson (2015) have noted a trend that illiquidity has fallen over time, among their sample companies between 1950 and 2015. They do not offer any single explanation for this but state that the decline in illiquidity can partially have contributed to the increase in share prices via reduced risk premiums required by investors for illiquidity.

The Illiquid-minus-liquid factor is then constructed for these measures between July 1991 and December 2015 except for Amihud and Mendelson (1986) measure which due to data quality issues could only be calculated from July 1997 onwards.

5. Data and descriptive statistics

5.1 Sample construction

The sample used covers the Dutch stock market between July 1991 and December 2015. This study follows Griffin, Kelly, and Nardari (2010) and thus the sample consists only of common shares, excluding preferred stocks, exchange traded funds and REITs. Likewise the companies have to be listed in the Euronext Amsterdam stock exchange. The initial sample of companies downloaded from Datastream consisted of 606 dead and active companies. Following Christoffersen and Sarkissian (2009) this study uses 36 months or 3 years of observations as the minimum for companies to be included in the sample. This reduced the initial sample to 307 companies consisting of 215 dead and 92 active companies.

Dead companies were included in the sample to avoid survivorship bias in the results. Likewise the currency was limited to the euro and guilder. According to Datastream (2007) policy with historical data, they convert all data before the adoption of euro to euro using the last fixed six digit exchange rate. Thus Datastream provides the historical prices of old dead companies that used to have the guilder as their currency in euro. This study follows Brückner, Lehmann, Schmidt, and Stehle (2015) and considers companies that trade below 1 euro during the sample period as penny stocks. These companies are removed except for a few cases where a company is included in the sample when the share price fall below 1 euro is only temporary and the share price has subsequently recovered above this threshold. Penny stocks are removed to prevent the results from being influenced by highly volatile, low price shares.

To construct the high-minus-low factor of Fama and French (1993), book values are needed. Thus companies included in the sample have matching book values to form the M/P ratio for the same months as the share price. Some companies had to be removed as they did not have the M/P ratio available, thus the final sample used consisted of 237 companies of which 159 were dead and 78 alive. The companies need to pass a set of criteria to be included in the sample. As the filtering criteria reduce the sample size, the quality of the data improves and any subsequent conclusions drawn from the results should be of higher quality.

(17)

17 exchange according to Euronext (2016). As the alternative, AEX all-share price index is only available from late December 1994 onwards according to Datastream.

This study has three alternatives for the risk-free rate proxy. These were three-month interbank rate AIBOR, the Netherlands Government Datastream stored yield curve constant maturity one-year yield and JPM Netherlands one-month total return index. Once the series are converted from annualised yields to monthly frequency yields there are only minor differences between them as Figure 3 in the appendix demonstrates. Since this yield proxies for the risk-free rate, the government constant maturity yield is chosen after it is converted to a monthly rate.

Financial companies were included in this sample even though Fama and French excluded this segment in their 1992 paper. As Brückner, Lehmann, Schmidt, and Stehle (2015) point out, all the portfolios on the Kenneth French website include financials when building their factor series.

The following data series come from Datastream on a monthly frequency: turnover by volume, prices adjusted, bid-ask prices, market value for company, the price/book ratio, the number of shares outstanding and the risk-free rate. Furthermore, since the four liquidity measures require daily frequency data on their construction the daily prices adjusted series, turnover by volume and bid-ask prices are downloaded from Datastream. The Fama and French (1993) HML, SMB and WML as defined by Carhart (1997) are build using the monthly frequency data. Datar, Naik, and Radcliffe (1998), Amihud (2002) and Liu (2006) versions of the IML factors are constructed between July 1991 and December 2015. The Amihud and Mendelson (1986) IML factor is constructed between July 1997 and December 2015 because of the lack of data for the daily bid-ask prices and its poor quality before May 1997. Many sample companies have even negative spreads in the pre-May 1997 period.

5.2 Descriptive statistics

Table 2 in the appendix has the industry breakdown of the sample used in this study. The second column of the table states the total number of companies by industry while the columns to the right show the number of companies per industry by the year. Worldscope industry grouping is used to group the sample companies to major industry groups. Out of 26 major industry groups only tobacco and Reuters fundamentals sourced data groups are missing. Worldscope classification is chosen over the ICB industry classification provided by FTSE/Down Jones. For the Netherlands, Worldscope classification has better coverage of the sample companies. When a classification is missing, Orbis database is used to check for available industry classifications. Then, I checked the closest matching major industry group from Worldscope.

(18)

18 When constructing the SMB and HML factors, companies can fall from the portfolios due to de-listings and mergers during the year while new companies are only included in June next year. With the Carhart version of the WML, the portfolios get updated monthly and with the Amihud IML factor after three months.

The summary statistics for the liquidity measure used are presented in the appendix Table 3. The table presents the start year from which data is available for each measure, the number of months used to form the liquidity measure for each version of IML factor, the average number of companies per month in the sample period per liquidity measure and the total number of companies used to construct the different liquidity measures. Equal- and value-weighted mean values are presented for the different measures albeit the figures are not comparable per se. Lastly, Spearman rank correlations are presented for both equally- and value-weighted liquidity measures. One should note the smaller sample in terms of the shorter time period, the average number of companies and total number of companies used for the Amihud and Mendelson (1986) relative spread measure compared with the others. The smaller sample period for the relative spread is due to data quality issues with the measure in pre-1997 May period. Also, less companies in the sample had daily bid and ask prices available. In terms of correlations of Table 3, the value-weighted Spearman rank correlations show how Amihud (2002) and Amihud and Mendelson (1986) measures are quite strongly positively correlated (0.72) but have negative correlations with both Datar, Naik, and Radcliffe and Liu measures (0.49 and 0.21 for A&M and 0.18 and -0.17 for Amihud). In the equal-weighted case, the trend is similar but the values are smaller. The Amihud measure now has 0.01 or nearly no correlation with Liu measure, compared with the negative correlation in the value-weighted case. The Liu measure has a correlation of 0.57 with Datar, Naik, and Radcliffe (1998) measure. The main conclusion from this is that while different measures capture different dimensions of liquidity, some dimensions are correlated with others in the case of the Netherlands. The trading costs dimension of Amihud and Mendelson and the price impact dimension of Amihud move rather similarly albeit not one to one. The biggest surprise is that the Liu measure mainly correlates with the trading quantity dimension of Datar, Naik, and Radcliffe (1998) measure even though Liu stated that her measure could capture several dimensions of liquidity. Therefore, I expected the measure to have higher correlation with the Amihud and Mendelson measure as both measures capture trading costs dimension. I conclude that the Liu measure is less well-rounded to capture the multiple dimensions of liquidity because of the results than what the author claims. Since none of the measures is fully correlated with the others, I can conclude that the different measures detect different dimensions of liquidity and none is measuring the same thing. Thus there is a stronger basis for the argument that one of the measures is better than the others at capturing illiquidity in the Dutch stock market and that one of the IML factors would capture risk-adjusted excess return for liquidity risk after counting for the four factors.

(19)

19 in four groups with each of them using different weighting schemes. The same four factor groups are later tested in the results section. In the first group, all the factor portfolios are value-weighted. The second group has value-weighted IML and Rm-rf factor portfolios while size, value and momentum factor portfolios are equal-weighted. The third grouping has equal-weighted IML, size, value and momentum factors while the Rm-rf factor is value-weighted. In the fourth grouping, IML factors are volume-weighted, Rm-Rm-rf is value-weighted, size, value and momentum portfolios are equal-weighted. The Jarque-Bera test results indicate the non-normality of the return distribution for nearly all of the factors.

The different factor portfolios have rather large standard deviations. Following Carhart’s (1997) interpretation this indicates the factors can explain much of the time series variation. All of the mean and median returns of value-weighted IML factor portfolios have slightly negative values. None of the value-weighted IML factor portfolios performed well over the sample period as the figure 4 graphs in the appendix indicate. The second reason the mean and median returns are dampened both for the IML and other factors is that I use returns calculated from the price adjusted series of Datastream. These returns exclude dividend yields and the mean and median returns would have been higher if the dividend yield would have been included. For equal-weighted IML factors, only IML formed using Amihud measure has slightly positive mean and median values. For volume-weighted IML factors both Liu and Amihud versions have positive mean values and Amihud even a positive median value.

(20)

20 Comparing the correlations between the value-weighted IML factors, Datar, Naik, and Radcliffe (1998), Amihud (2002) and Liu (2006) variants have a moderate positive correlation with each other and only the Amihud and Mendelson version of IML factor has less than weak positive correlation with the other IML factors. With equally-weighted IML factors this pattern is even stronger as now the correlation between Datar, Naik, and Radcliffe (1998), Amihud (2002) and Liu (2006) based IML factors is strongly positive. Liu and Amihud based IML factors have a positive correlation of up to 0.84. Now Amihud and Mendelson IML has become weakly correlated with the other IML factors. Based on volume-weighted IML factor correlations, Datar, Naik, and Radcliffe (1998), Amihud (2002) and Liu (2006) based measures only have moderate positive correlation with each other while the Amihud and Mendelson IML has less than weak positive correlation with the other liquidity factors.

In contrast to the results regarding the correlation of the four liquidity measures, now Amihud (2002) and Amihud and Mendelson (1986) IML factors have no significant correlation with each other. The correlation found between Datar, Naik, and Radcliffe (1998) and Liu (2006) liquidity measures has remained with IML factors and here the Amihud based factor is rather correlated with them. Even though Liu states her measure also captures the trading cost dimension, the IML factor based on Liu measure is not correlated with the Amihud and Mendelson based IML factor even though both are supposed to cover the same dimension of liquidity. Despite the different liquidity measures picking different dimensions of liquidity, the IML factors build using them have mostly moderate to strong correlation between each other. However, I expect one of the IML factors is likely to perform better than the other three at capturing illiquidity related time series variation left unexplained by Fama and French and Momentum factors.

6. Results and robustness tests

(21)

21 The initial results indicate that stock illiquidity is priced in the Dutch market when the factor is constructed using Amihud (2002) illiquidity measure and portfolio returns are weighted equally. The results of the best performing equal-weighted factor constructed using Amihud (2002) liquidity measure show a positive and statistically significant monthly risk-adjusted excess return of 0.3033 percent per month at 5 percent significance level. This is on an annual basis 3.7 percent. The mean illiquidity premium of this measure is 0.96 percent annualised, bordering on being economically meaningful. These returns are calculated from the price adjusted series of Datastream that excludes dividend yields. Therefore, the annualised figures are biased downwards as they do not represent total returns.

The other notable result is that the equal-weighted built using Datar, Naik, and Radcliffe (1998) liquidity measure has a statistically significant and negative excess return of 0.5401% per month at 1% significance level. The mean illiquidity premium for this equal-weighted measure is -0.69% per month. The appendix graphs of Figure 4 show Datar, Naik, and Radcliffe based equal-weighted factor is among the worst performing ones and mostly its liquid portfolio has a higher return than the illiquid portfolio over three months holding period opposite to the expectations of the theory. As a contrast, the illiquid-minus-liquid portfolio constructed using Amihud liquidity measure is among the best performing ones as it increases over the sample period, performing particularly well during adverse market conditions such as late 2008 and 2009. Liu (2006) states that if the least liquid portfolio consistently outperforms the most liquid portfolio, the index created of the difference increases over time. The increasing index can be interpreted as the evidence of the presence of an illiquidity premium. In Figure 4, the best performing Amihud measure based stands out as having an index value that is mostly above the starting value 100 indicating the presence of an illiquidity premium. However, based on the results of Table 4, the mean illiquidity premium is negative for most variants with different weighting schemes. The risk-adjusted illiquidity premium is mostly insignificant in the regressions and weighting schemes of Table 5. I conclude that most liquidity measures and weighting schemes are unable to capture the illiquidity related premium left unexplained by the four factors in the Dutch market. Based on the results of Table 5, there is a liquidity measure and an illiquid-minus-liquid portfolio that can capture illiquidity premium. In this case it is Amihud liquidity measure based equal-weighted .

(22)

22 median values for correlation between IML (Datar, Naik, and Radcliffe) and Rm-rf are -0.6513 and -0.7186 while the mean and median correlation between IML (Amihud) and Rm-rf are -0.7471 and -0.7966. These results are in-line with Amihud, Hameed, Kang, and Zhang (2015) and show the strong negative relationship between the IML illiquidity premium and the Excess market return.

The SMB factor coefficients are positive in each reported regression and in most cases statistically significant. Following Amihud, Hameed, Kang, and Zhang (2015) this shows that the size premium is partly due to the illiquidity premium. I pointed out in the literature review that the size of a company is associated with liquidity with smaller listed firms being more illiquid.

With HML factor, the coefficient values vary from positive to negative with most values being statistically insignificant. There is no uniform and clear relation between illiquidity premium and value premium. For the best performing IML factor, the coefficient of HML is positive and statistically significant. In this result, there is evidence of illiquidity being associated with value companies that are smaller size. Following Amihud (2014) there is a connection between illiquidity premium and the premium on high B/M companies for the best performing IML factor. The premium on high B/M firms is according to Fama and French (1993) linked to these companies being in distress and it would make sense that these distressed companies suffer more from illiquidity.

(23)

23

Table 5 The risk-adjusted mean values of the illiquidity premium return and factor slope coefficients.

The table presents the risk-adjusted illiquidity premium for the Dutch stock market after accounting for the risk factors of Fama and French (1993) and momentum factor of Carhart (1997). The IML factor is constructed using four liquidity measures: the relative spread of Amihud and Mendelson (1986), turnover rate of Datar, Naik, and Radcliffe(1998), illiquidity measure of Amihud (2002) and the standardised turnover-adjusted number of zero daily trading volumes over the past 12 months of Liu (2006). The IML factor is constructed following Amihud, Hameed, Kang, and Zhang (2015). Each month sample companies are first sorted to terciles based on the standard deviation of their daily returns over the past three months t-3 to t-1. Then the companies in the three groups are ranked to quintiles based on one of the liquidity measures. The top quintile stocks in the three standard deviation buckets form the illiquid portfolio and the bottom quintile stocks form the liquid portfolio. Then returns are calculated for companies in these two groups for t+1, t+2 and t+3 months. Then I calculate returns for the illiquid and liquid portfolios using three weighting schemes: equal weighting (portfolio return is weighted by the sample companies used), value weighting (every month the market capitalisations of the sample companies in the previous month t are used for weighting) and volume weighting (portfolio return is weighted monthly by euro trading volumes of t-3 to t-1 months). The portfolio formation is repeated every three months. is the zero investment, illiquid-minus-liquid portfolio return on month t. IML is the

risk-adjusted excess return on the portfolio as defined by Amihud, Hameed, Kang, and Zhang (2015) and it is the intercept from the regression of on the Fama and French (1993) factors and momentum factor of Carhart (1997). The regression is:

= + ( , − ,) + + ℎ + + ,

The , − , represents the market excess return. The return on the market is calculated using the sample companies

and is value-weighted. The monthly risk-free rate is calculated from the Netherlands government constant maturity one-year yield. The is the small-minus-big factor return and is the high-minus-low book-to-market factor return, both are formed following Fama and French (1993). is the winner-minus-loser momentum factor return of Carhart (1997). The four columns below represent four weighting schemes used to run the regression. The first value-weighted column is calculated using only value-weighted factors. The second value-weighted column represents the results of regressions where all the factor returns and market excess returns are value-weighted, while the SMB, HML and WML factors are equal-weighted. The third column represents regressions using equal-weighted factors except for the market excess return factor which remains value-weighted. The last column contains the results of regressions with volume-weighted factor returns, value-weighted market excess return and equal-weighted SMB, HML and WML factor returns. T-statistics for each regression coefficients are in the parenthesis. ***, ** and * denote the statistical significance at 1 percent, 5 percent and 10 percent levels. All regressions using Amihud and Mendelson (1986) liquidity measure to construct the factor returns are calculated using a time period July 1997 to December 2015 due to data quality issues before this period. All the other regressions use a time period July 1991 to December 2015.

Value-weighted Value-weighted 2 Equal-weighted weighted Volume-Amihud & Mendelson -0,0045 -0,0039 -0,0002 -0,0052 (-1,39) (-1,14) (-0,05) (-1,26) , − , -0,1581 -0,1518 -0,1121 -0,2633 (-2,42)** (-2,03)** (-1,77)* (-2,92)*** 0,0524 0,0862 0,4121 0,0036 (0,56) (0,61) (3,44)*** (0,02) 0,0887 -0,0541 0,0147 0,0219 (1,52) (-0,54) (0,17) (0,18) 0,0675 0,0520 -0,0355 0,0599 (1,47) (0,76) (-0,61) (0,73) 0,0716 0,0510 0,1383 0,0799

(24)

24

Table 5 The risk-adjusted mean values of the illiquidity premium return and factor slope coefficients. (Continued)

Datar, Naik, and

Radcliffe Value-weighted Value-weighted 2 Equal-weighted weighted

Volume--0,0008 -0,0001 -0,0054 -0,0038 (-0,37) (-0,05) (-3,19)*** (-1,29) , − , -0,3442 -0,4045 -0,2987 -0,4405 (-7,72)*** (-7,75)*** (-7,61)*** (-6,37)*** 0,2955 0,1667 0,6124 0,2734 (4,61)*** (1,68)* (8,18)*** (2,07)** -0,0649 -0,0673 0,0440 -0,1354 (-1,62) (-0,95) (0,83) (-1,44) 0,0540 0,0212 0,0006 0,0124 (1,70)* (0,44) (0,02) (0,19) 0,3555 0,3118 0,5350 0,2496 Amihud -0,0024 -0,0007 0,0030 0,0018 (-1,59) (-0,41) (2,15)** (1,04) , − , -0,4431 -0,4097 -0,3604 -0,4995 (-13,36)*** (-10,38)*** (-11,01)*** (-12,77)*** 0,3898 0,4359 0,8517 0,4955 (8,18)*** (5,79)*** (13,65)*** (6,64)*** 0,0039 0,0214 0,0903 -0,0123 (0,13) (0,40) (2,03)** (-0,23) -0,0008 -0,0510 -0,0176 0,0315 (-0,03) (-1,40) (-0,59) (0,87) 0,5905 0,5472 0,7390 0,6436 Liu -0,0029 -0,0037 -0,0013 0,0010 (-0,85) (-1,04) (-0,76) (0,43) , − , -0,5036 -0,4498 -0,4507 -0,4731 (-6,93)*** (-5,47)*** (-11,28)*** (-8,67)*** 0,1692 0,2100 0,8118 0,2929 (1,62) (1,34) (10,65)*** (2,81)*** -0,0071 0,0774 -0,0224 -0,0304 (-0,11) (0,69) (-0,41) (-0,41) 0,0009 0,0693 0,0298 0,0649 (0,02) (0,92) (0,81) (1,29) 0,2145 0,2149 0,6847 0,4064

(25)

25 intercepts terms of Table 6 are smaller. Even the previously best performing Amihud (2002) measure based IML factor no longer has a statistically significant intercept term though the coefficient is still positive and this is because of the noise from the negative size premium. Following Amihud (2014) in the interpretation, the small differences in the size of the intercept terms when SMB is included or excluded indicates the IML premium is not related to the size effect.

As a further robustness test, I have tested if the IML illiquidity premium of the best performing measure is due to January effect. The papers by Datar, Naik, and Radcliffe (1998) Liu (2006), Amihud (2014) tested for the same effect and the overall conclusion in their papers is that either they found no January effect like Amihud (2014), and Datar, Naik and Radcliffe (1998) or like with Liu (2006) illiquidity premium was found not limited to January. The results for the best performing measure are reported at the end of Table 6 in the appendix. I follow Amihud (2014) by adding a January dummy variable to Equation 1. Here Jan=1 and otherwise 0. I find no evidence of January seasonality and the effect of January is statistically insignificant. The intercept remains positive and significant at 5 percent level for the Amihud (2002) based equal-weighted IML factor.

Next I conduct the principal components analysis to quantify the extent the different IML variants measure the same underlying common variation caused by the liquidity risk. The assumption here is that the first principal component represents how much the different IML variants measure common liquidity risk captured by the different liquidity measures. As Brooks (2008) states, the sum of the squares of the coefficients for each principal component is one as shown in Equation 9.

=

+

+ ⋯ +

(8)

+

+ ⋯ +

= 1

(9)

Here in Equation 8, represents principal component 1, represents the original explanatory variable k, and represents the coefficient on the explanatory variable in the principal component. Equation 9 provides me with the weights for each coefficient or IML factor to construct a weighted IML factor that comprises all the 12 IML variants. The main conclusion from the principal components analysis presented in Table 7 of the appendix is that there is relatively much common variation in the various IML factors since the first principal component counts for 54.25 percent of the total variance.

(26)

26 Given the number of hypothesis tests performed, it is possible that we find statistically significant results due to chance. Following Goldman (2008) the chance of finding one statistically significant result when testing 16 hypothesis as here with 5 percent significance level is:

(

1

) = 1 − (

)

(10)

= 1 − (1 − 0,05)

≈ 0,5599

Therefore the probability of having at least one significant results is about 56 percent, even though none of the results is really statistically significant. This is known as the type I error where one rejects the null hypothesis even though it is true and is referred to as the multiple comparisons problem. Here I adjust the p-values of the test statistics for the number of hypothesis tests performed by calculating the Bonferroni approximation that allows to control for the type I error. The equation of the Bonferroni approximation following Abdi (2007):

(11)

Here refers to the probability of making a type I error in case of a specific test. While denotes the probability of making at least one type I error in the whole set of tests. While refers to the number of hypothesis being tested. Here I assume = 0,05 or 5 percent and as there are 16 regressions or hypothesis being tested = 16. Thus the test result is significant following the approximation if the p-value is smaller than:

=

=

,

≈ 0.0031.

After controlling for type I error the p-value of the equally-weighted Amihud (2002) is larger than the approximation limit (0.0324) and is no longer statistically significant. Only the p-value of the Datar, Naik, and Radcliffe IML intercept that performed very poorly remains significant (0.0016). As a criticism for the Bonferroni approximation Goldman (2008) and Abdi (2007) point out that the method has a tendency to be too conservative that can cause a type II error of not rejecting the null even though it is false.

(27)

27 and negative and volume-weighted positive and insignificant for the best performing factor. While Amihud (2014) only tested the value-weighted variant of IML and found it to have statistically significant and positive risk-adjusted excess return for the US market.

It is possible the liquidity measures proxy for information asymmetry as well. According to Liu (2006) asymmetric information can cause illiquidity if uninformed investors become aware of informed investors and decline to trade in the market effectively reducing liquidity. Liu (2006) states that the private information premium of Easley, Hvidkjaer, and O’Hara (2010) could be captured by the illiquidity premium. Thus one would find stronger results for the IML factor among companies that are smaller, have greater relative spreads, lower turnover rates, less market depth and classified illiquid based on most liquidity measures. These are characteristics commonly associated with securities that have greater information asymmetry. This could potentially explain why the study of Amihud, Hameed, Kang, and Zhang (2015) found the IML premium to be larger in developing markets. If information asymmetry is captured by liquidity measures and by the IML factors, I would expect the effect of information asymmetry to be stronger in developing markets than in a developed market like the Netherlands.

Overall, according to the Bonferroni approximation the initial main finding would no longer be statistically significant, However, since the Bonferroni approximation risks being too conservative and the fact that Amihud, Hameed, Kang, and Zhang (2015) and Amihud (2014) found exactly the same Amihud (2002) liquidity measure based IML factor with many weighting schemes and in several markets to have positive and significant risk-adjusted excess returns, I would conclude that there is not a strong support for the inclusion of the IML factor into an existing four-factor model in the Dutch market even though one of the IML variants displays results that are in-line with my expectations given the research questions.

7. Conclusions

The purpose of this study has been to find out if systematic co-movements in liquidity risk are priced in the Dutch market after controlling for the four factors of Carhart (1997). Secondly, the paper compares different liquidity measures in a uniform framework of Amihud, Hameed, Kang, and Zhang (2015) to see which of them performs the best in the Dutch stock market. The results of this study also indicate whether an additional liquidity risk factor should be added to the well-known four-factor model.

(28)

28 the SMB factor. Based on the results I can conclude that most of the liquidity measures and IML factors built using them are unable to capture illiquidity related premium left unexplained by the four factors. As the main criticism of the initial finding, after doing the Bonferroni approximation it would no-longer be considered statistically significant.

The findings of this study provide additional insights into the existing literature regarding liquidity risk because of the limited evidence that liquidity risk is positively correlated with the expected returns of investors in the Dutch market. The results do not provide strong support for the inclusion of an additional IML factor to count for liquidity risk in the four-factor model. The results of this paper also contribute to the discussion regarding the performance of different liquidity measures as some of them performed better than others. Following Liu (2006) in the interpretation of the results, some liquidity measures are limited in their ability to capture liquidity risk such as the turnover rate of Datar, Naik, and Radcliffe (1998) while others like the Liu (2006) measure that claims to capture the multiple dimensions of liquidity fail to do so. Thirdly, this study produces the results on a less commonly used dataset and given the horse race testing of liquidity measures in this study, it is the first such for the Dutch stock market.

The initial findings of this paper are in-line with the main results of Amihud (2014) who finds a statistically significant and positive risk-adjusted excess return after controlling for Carhart four factors in the US market. Likewise the paper by Amihud, Hameed, Kang, and Zhang (2015) found a positive and significant average illiquidity premium across most of their 45 sample countries. They also found a risk-adjusted excess return similar to this study after controlling for three global and three regional Fama and French (1993) factors. Both of these studies used the same liquidity measure of Amihud (2002) to construct the IML factor. For the Netherlands Amihud, Hameed, Kang, and Zhang (2015) found a positive risk-adjusted excess return but it was statistically insignificant. Even though Amihud and Mendelson (1986), Datar, Naik, and Radcliffe (1998) and Liu (2006) found their liquidity measures significant, this study did not find any of the risk-adjusted excess return terms based on these other measures to be both positive and statistically significant. The volume-weighted IML factors built using Amihud (2002) and Liu (2006) liquidity measures have positive means according to Table 4 but neither have significant positive risk-adjusted excess returns in Table 5.

(29)

29 to calculate Datar, Naik, and Radcliffe (1998) liquidity measure. To overcome the issue, I aggregated the daily data to three month sum and divided the figure by three to get an average monthly turnover volumes. It is possible that the patchiness of the daily data might have impacted the quality of this liquidity measure and contributed to its rather poor performance. Regarding Liu’s (2006) measure, it would have been possible to form the measure using shorter holding periods such as 3 or 6 months instead of the 12 months used to robustness check the results. However, to keep the reporting of the results reasonable, analysis is done here using the 12-month period only. As a more significant limitation of the results is the fact that the study does not use total returns for calculating zero investment factor portfolio returns. This has the effect of biasing the returns downwards as dividend yields are ignored.

Referenties

GERELATEERDE DOCUMENTEN

Bijvoorbeeld man zit in het sub-menu INFORMATIE_EISENPAKliET en men .iet dat men de aanlooptijd (TYDA) niet ingegeven heeft terwijl men eist dat deze maximaal

replications of hybridization (F1) and nine generations of backcrossing (F2‐F10) using genetically vetted American black ducks (ABDU) and mallards (MALL) (Supporting Information

Singapore is able to do this because of its good reputation (people do not get cheated on by their agent or employer), which makes it an attractive destination. Yet,

Since the completion of the Human Genome Project, the hope that genetic markers would enable a predictive and preventive medicine, geared towards one’s genetic

The general mechanical design of the Twente humanoid head is presented in [5] and it had to be a trade-off between having few DOFs enabling fast motions and several DOFs

• congenitale naevi • café-au-lait-vlekken • hemangiomen • vaatmalformaties • midline laesies 6-8 weken Inspectie gehele huid:. • hemangiomen 5-6 maanden

Monetary policy arrangements and asset purchase programs Firstly, in this section is presented how monetary policy is arranged in the United States, the Euro Area, the United

The out of sample results for the PPP model, where the benchmark model in pa- rameterisation (2) is the value weighted portfolio, with different levels of relative risk aversion