Master Thesis

The Pricing of Liquidity Risk Around the World

Author: D.W.J. Röttger Studentnumber/ANR: u1255565/985824 Master Programme: Master in Finance, CFA track Faculty: Tilburg School of Economics and Management Submission Date: 29-09-2013 Date of Defense: 08-10-2013 Supervisor: dr. A. Manconi Second Reader: dr. B. Melenberg Abstract This thesis proposes that the illiquidity level of asset is of less importance for asset pricing than the international commonality in liquidity. Using a broad dataset of 23 developed countries, this thesis shows the persistence of liquidity on a global scale. I show that commonality in liquidity exists on an international level, and that the relationship is priced in an adjusted LCAPM framework. The outcomes suggest that the diversification of liquidity risk is possible by investing internationally. This thesis contradicts findings that the illiquidity level of securities is a priced risk character. I estimate a negative liquidity risk premium which suggest a flight to liquidity effect.

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“The journey of a thousand miles begins with a single step.” Lao Tzu

I thank my parents for giving me the opportunity to study and for supporting me all the way.

I would like to thank Cosmin, Erik, and Stergios who helped collecting the dataset, dr. Alberto Manconi for the helpful comments on my work, Maurits for thesis talks, and above all the support and encouragements of my girlfriend which helped me to reach the end of this journey.

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Table of Contents Abstract ...... 2

1. Introduction ...... 6

2. Theory Development ...... 8

2.1. What is liquidity and how to measure liquidity ...... 8

2.2. Liquidity characteristics ...... 8

2.3. Flight to liquidity ...... 11

3. Data and Methodology ...... 12

3.1. Data ...... 12

3.1.1. Data Sources ...... 12

3.1.2. Data Filtering: ...... 12

3.2. Methodology ...... 15

3.2.1. Illiquidity Measure ...... 15

3.2.2. Normalized Amihud Liquidity Measure ...... 16

3.2.3. Autocorrelation of the Liquidity Level ...... 16

3.2.4. Innovations calculation: ...... 17

3.2.5. Commonality in Liquidity Innovations: ...... 18

3.2.6. Distinction between non-local effects and local effects...... 19

3.2.7. Portfolio Construction ...... 19

3.2.8. Acharya and Pedersen (2005) LCAPM ...... 19

3.2.9. LCAPM with Non-Local Factors...... 22

3.2.10. Fama-MacBeth Cross-Sectional Regressions ...... 23

3.2.11. Testing Asset Pricing Models ...... 23

4. Empirical Results ...... 24

4.1. Liquidity persistence ...... 24

4.2. Liquidity risk is linear and positive priced ...... 25

4.3. Commonality in liquidity risk ...... 28

4.4. The flight to liquidity ...... 31

5. Conclusions ...... 32

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6. Bibliography ...... 33

7. Tabulations ...... 35

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1. Introduction

On 22 August 2013 NYSE Arca, an exchange operator, announced an issue processing trades. Later that in ceased for three hours and eleven minutes, traders were forced to search for direct trading partners, Bloomberg (Regan, Mamudi, and Kisling, 2013) and Reuters (Mikolajczak and Campos, 2013). Liquid can be defined as the tradability of an asset at the market price at the desired time (Cooper, Groth and Avera, 1985).The presence of stock liquidity is not always as visible as on August 22th. Trading trough the exchange ceased and limited the possibilities of stock trade to over-the-counter trades, leading to a drop in liquidity. Every has to deal with liquidity and therefore it is important to understand the level of liquidity for individual stocks, what the drivers of liquidity are, and how to diversify liquidity risk. Liquidity cost has four components: the bid-ask spread, a market-impact cost that occurs when large quantities are traded, delay and search costs, and direct transaction costs (Amihud and Mendelson, 1991). Amihud and Mendelson (1986) propose that stock return increases with the liquidity level of stock. In order to measure the liquidity level of assets a number of liquidity measures and proxies are usable (e.g. bid-ask spread and firm size), both for high and low frequency datasets. Goyenko, Holden and Trzcinka.,(2009) test these measures and find that the Amihud (2002) liquidity measure of price impact is the best for low frequency datasets. On the basis of the Amihud (2002) liquidty measure, a common systematic liquidity factor is found by Chordia, Roll and Subrahmanyam (2000) and Hasbrouck and Seppi (2001). Pástor and Stambaugh (2003) and Acharya and Pedersen (2005) find evidence of a premium for systematic liquidity risk. Sadka (2006) finds that the innovations in liquidity are priced. Furthermore Acharya and Pedersen (2005) develop a liquidity based capital asset price model (LCAPM) that includes empirical significant relations of liquidity with stock return. Korajczyk and Sadka (2008) find co-movement in liquidity measures implying a systematic liquidity factor. Pástor and Stambaugh (2003) describe the effects of a flight to liquidity in times of increased market . My thesis test the literature using an extensive dataset in order to determine the importance of liquidity risk in asset pricing and how the liquidity risk is driven by external (non-local) markets. The research question of this thesis is: Are non-local drivers of liquidity priced as a ? The dataset used in this thesis includes all the of 23 developed countries between 1995 to 2012. In order to answer the research question, the LCAPM of Acharya and Pedersen (2005) is used to measure if liquidity risk is priced. I test if the illiquidity level of stocks is a priced risk characteristic in asset pricing models and decompose global factors in order to determine the drivers in the co-movement of liquidity. I divide the overall dataset in four regions based on market integration (Fama and French, 2012). The regions are: Asia-Pacific (ex. Japan), Europe, Japan, and North America. The theory which leads to this research question is based on two characteristics of liquidity. First, the commonality (co-movement) in liquidity implies that the liquidity of individual stocks is driven by the local market (Karolyi, Lee and van Dijk, 2012). This thesis shows that not only the local market influences individual stocks and that the global market plays a key role in the liquidity innovations of individual stocks. Second the LCAPM of Acharya and Pedersen

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(2005) implies that commonality, amongst other characteristics, of liquidity with the market is priced. I propose that if commonality in liquidity exists between countries that external markets are influencing asset prices in the home market. I adjust the LCAPM of Acharya and Pedersen (2005) and use betas that capture the relation between portfolios sorted on liquidity in the local region and the non-local region. I decompose the non-local factors into regions and use it to determine the drivers of liquidity risk and compensation. The proposal is based on the trend of globalization, which implies that the local market is not independent from the global market and that domestic and foreign agents share risks (Henry, 2002). This thesis makes five contributions to the existing literature. First I estimate the persistence of stock liquidity and show that it is persistent around the world. This is important to understand the pricing of liquidity. Because the liquidity is persistent around the world the same pricing characteristics are possible. The finding is an addition to literature on the persistence of stock liquidity (see e.g. Amihud, 2002). Second, I find that the illiquidity level is not a priced risk factor in the LCAPM model of Acharya and Pedersen (2005) and that the illiquidity level is not a priced risk characteristic in the asset pricing theory. This is contrary to findings of Acharya and Pedersen (2005) and the proposition of Amihud and Mendelson (1986). The finding is in line with the proposition of Sadka (2006) who proposes that the variable part of the illiquidity level is priced. Third, I find commonality between the local market and foreign markets. This is in line with the commonality relationship as described in the literature e.g. Chordia, Sakar and Subrahmanyam (2000). The contribution is that the commonality is based on a international relationship and therefore it contributes to the literature on the diversification of liquidity risk. Current literature states that the ability to diversify systematic liquidity risk and aggregate liquidity shocks by holding large-cap stocks has declined (Kamara, Lou and Sadka, 2008). I contribute by showing how liquidity risk is driven internationally to the literature of on the cross-country drivers in liquidity (cf. e.g. Karolyi, Lee, van Dijk, 2012). Fourth, I find that the international commonality in liquidity is priced. The relationship of local liquidity risk with the international market rather than the home market is estimated to significant and positively price local asset portfolios sorted on liquidity. This is a contribution to the literature on liquidity risk and the pricing of liquidity risk. By extending the LCAPM, I make a contribution to the understanding of how liquidity risk is priced. Fifth, I estimate negative liquidity risk premiums what implies that are not rewarded for exposure to liquidity risk. This is in line with the literature on the flight to liquidity e.g. Vayanos (2004) and contributes by showing the term existence of the effect by estimating it in an unconditional asset pricing model. The remainder of the thesis is organized as follows. Chapter 2 discusses the theory development . Chapter 3 describes the dataset and methodology. Chapter 4 presents the empirical findings. A brief conclusion and discussion follows.

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2. Theory Development

2.1. What is liquidity and how to measure liquidity Assets are traded directly from trader to buyer or indirectly through an intermediary. The ease of the trade depends on the liquidity of the traded asset. The ease can be interpreted as the costs of trade, which are related to the liquidity of asset. A liquid asset is an asset that is tradable for buyers and sellers at the market price at the desired time (Cooper, Groth and Avera, 1985). Amihud (2002) describes liquidity as a reflection of the impact of order flow on the price of an asset. Illiquid stocks are characterized by the inability to trade, (have a low order flow) at the market price at the desired time which causes traders to make amendments, leading to an impact on the assets price. Liquidity can be divided into four components: the bid-ask spread, market-impact cost occurring when large quantities are traded, delay and search costs, and direct transaction costs (Amihud and Mendelson, 1991). The overall level of liquidity includes costs for which only limited information is available (Goyenko, Holden and Trzcinka, 2009). The liquidity literature include a number of liquidity proxies based on either spread or price impact. A spread measure uses the bid-ask spread to measure liquidity, a small spread is defined as liquid while an asset with a large spread is illiquid. Both type of measures are priced. Goyenko (2006) shows that the bid-ask spread is priced. Amihud (2002) and Pástor and Stambaugh (2003), using their own measures, show that illiquidity measures of price impact are priced. The overall performance of these measures, in other words do these measures really measure liquidity is tested by Goyenko, et al. (2009). Goyenko, et al. (2009) use liquidity benchmarks, e.g. effective spread and realized spread, conclude that the Amihud (2002) liquidity measure (ALM) is the best low frequency measure of liquidity. This thesis uses Amihud’s (2002) liquidity measure (hereafter ALM) for three main reasons: first, Goyenko, et al. (2009) compare several low frequency measures of liquidity with high frequency measures of liquidity and show that the ALM is the best low frequency liquidity measure. The difference between high and low frequency is defined by the frequency of data observations and is high when the measure depends on an intraday dataset or low when it depends on a daily dataset. This thesis uses daily data and is therefore limited to the low frequency liquidity measures. Second, the ALM measures price impact. This is important because this implies that the ALM can be used in asset pricing models in order to determine if liquidity risk is priced. Third, using the ALM makes this thesis representable in the literature.

2.2. Liquidity characteristics The literature defines several important characteristics of liquidity, namely: the persistence of the liquidity level, the pricing of liquidity risk, and the co-movement of liquidity (see e.g. Acharya and Pedersen, 2005; Amihud, 2002; Chordia, et al., 2005). All stocks have a liquidity level that expresses the relative liquidity of stocks. The liquidity level is related to return and excess return (asset return in excess of the risk-free rate) rises with illiquidity. The liquidity level is time-varying but persistent (e.g. Acharya and Pedersen, 2005; Amihud, 2002; Chorida et al.,

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2000; Pástor and Stambaugh, 2003). The persistence in liquidity is relevant for investors that want to limit or diversify their liquidity risk. If liquidity is persistent an investor can estimate the liquidity level of tomorrow with the data of today. Xin Liang and Wei (2012) find that the systematic level of liquidity differs between developed countries. The literature proposes that the liquidity is persistent. Still it is important to estimate the persistent of liquidity because this thesis uses a different dataset and observation period than existing literature. It is therefore important to estimate if the liquidity level is persistent around the world instead of assuming that the persistence exists. The first hypothesis is as follows:

H1: Liquidity is persistent and time-varying on a regional level.

By answering the hypothesis, H1, I estimate, using autocorrelation, that liquidity is persistent and time-varying around the world. The estimates show that liquidity is persistent implying that returns can be predicted on the basis of the illiquidity level. A low liquidity risk today is followed by a low liquidity risk tomorrow causing investors to require a low liquidity risk premium. The literature estimates that the liquidity level is priced (e.g. Pástor and Stambaugh, 2003). Acharya and Pedersen (2005), find that liquidity risk is positively priced using the ALM and a liquidity based asset pricing model (LCAPM). Acharya and Pedersen (2005) estimate a positive and significant relationship between illiquidity and required return. This implies that stocks with a higher liquidity risk (illiquid stocks), require a liquidity risk premium. Acharya and Pedersen (2005) and Sadka (2006) note that the variable part of the liquidity level is priced. Sadka (2006) notes that price and post-earnings-announcement drift are seemingly related with the variable part of liquidity. This implies that the pricing effect of liquidity is due to innovations in liquidity. The rationale given by Acharya and Pedersen (2005) is that investors want to be compensated for the liquidity risk to which they are exposed. A greater exposure, a higher illiquidity level, requires a higher excess return. The relation between liquidity risk and required return should therefore be positive. Pástor and Stambaugh (2003) suggest that investors accept a lower required return for liquid stocks in times of market illiquidity. Lynch and Tan (2011) propose that investors are willing to accept a lower required return for liquid stocks in a downward market. Acharya and Pedersen (2005) model these and the co–movement of stock liquidity with market liquidity in their liquidity adjusted asset pricing model, LCAPM. The literature has different suggestions on how liquidity affects return. This allows me to define hypothesis H2a in order to estimate if liquidity risk is positively priced around the world. Hypothesis H2b states that the illiquidity level of stocks is a positively priced risk factor.

H2a: The liquidity risk of stocks is positively and linear priced on a regional level. H2b: The illiquidity level of stocks is a positive and linear priced risk factor.

Hypotheses H2a and H2b will contribute to the literature in determining if the liquidity level or liquidity risk as a whole is priced. Testing H2a is intended to test the overall effect of liquidity on required

9 return. The LCAPM of Acharya and Pedersen (2005) is used to determine the overall effect and significance. By answering hypothesis H2b, the relative importance of liquidity risk, measured by the level of liquidity, is estimated. Hypothesis H2b will be answered using a similar approach as Sadka (2006), namely by testing if liquidity is a priced characteristic in the four factor model of Carhart (1997). The estimates show if the return of the liquidity portfolios are explained by the model. It is important to understand whether liquidity is equally priced or important around the world and to understand the rationale of investors. The third relation of liquidity noted in the literature is the co-movement between the liquidity level of assets and the illiquidity level of the market (see e.g. Korajczyk and Sadka, 2008; Karolyi, et al., 2012; Chordia, et al., 2000). When the liquidity risk of stock depends on the liquidity risk of the market, the required return of individual stocks is related to the illiquidity risk of the market. The important implication of this commonality between stocks and the market is that idiosyncratic liquidity risk cannot be fully diversified away using only marketable assets. The ability to diversify systematic liquidity risk and aggregate liquidity shocks by holding large-cap stocks has declined over time (Kamara, et al., 2008). The extensive dataset of this thesis makes it possible to understand the importance of commonality on a global level. For investors it is particular important to understand if it is possible to diversify its liquidity risk internationally. I propose two hypotheses that give more insight in the commonality of liquidity between regions. By testing commonality from a regional base it is possible to understand the international relations of the financial markets. Therefore I define foreign markets as the non-local global market and exclude the US from the global market. This results in a non-local-non-US market, e.g. in the case of Europe the non-local-non-US market consists of Asia-Pacific including Japan and Canada. The implied relationship is a positive relationship between liquidity risk and return.

H3a: Commonality in liquidity innovations exists on a global level between regional and non-local-non-US global innovations in liquidity. H3b: Commonality in liquidity innovations exists between regions and the US.

H3a and H3b are aimed at identifying a positive relationship between regional liquidity and global liquidity. This relationship is one of the keystones of this thesis and it is important to understand its drivers rather than only its existence. By decomposing the non-local factors into non-local-non-US and US factors, it is possible to determine the drivers of local liquidity. From the perspective of investors it is crucial to understand the risk they are exposed to and how to diversify the liquidity risk internationally. The literature on commonality implies that individual stocks co-move with the market in terms of liquidity. As explained in the methodology part of my thesis, the LCAPM is based on the relation of individual stocks with the market. In hypotheses H3a and H3b I propose that, part of, the illiquidity level of stocks is determined on an international level. If the illiquidity level of stocks is determined on a global level I propose that the required return of liquidity risk is determined on a global level. This allows me to define hypothesis H4a and H4b:

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H4a: Commonality in liquidity factors between regional and non-local-non-US global innovation is positive and linear priced. H4b: Commonality in liquidity factors between regional and US innovations is positive and linear priced.

H4a and H4b test whether the commonality in liquidity between regions has any economic importance. In other words, the hypotheses tests whether commonality in liquidity is priced. The hypotheses differentiate between the non-local-non-US global and US influences. It is important for market participants to understand what part of the commonality is priced and which is not priced in the model.

2.3. Flight to liquidity The characteristics of liquidity as described in the previous section are base case outcomes. In times of increased market uncertainty, such as economic crisis or international events that increase market volatility, investors prefer liquid assets. Vayanos (2004) theoretically shows that the liquidity premium increases in times of market volatility. This implies that investors require more return for liquid stocks in times high market volatility than in times of low market volatility. Vayanos (2004) suggests that investors become more risk averse in times of high market volatility. The flight to liquidity effect is shown empirically by Longstaff (2004) who shows that market participants prefer a more liquid bond when the uncertainty of the economic circumstances increases, measured by the consumer confidence index. Beber, et al. (2009) and Naes, et al. (2011) show that the liquidity of bonds is preferred over the in times of financial crisis. Rösch and Kaserer (2013) show that investment grade stocks have lower liquidity costs than speculative grade stocks. The effect is around five percent but intensifies in times of market volatility. Cooper, Groth and Avera (1985) use the CAPM of Sharpe (1964) and show that liquidity has a negative in down markets and a positive beta in upward markets. This suggests that liquidity risk is negatively priced in times of economic distress. Investors become more risk averse in times of market volatility causing the liquidity premiumto increase. I propose that the liquidity premium could overcome the illiquidity premium as investors are not willing to hold any speculative grade stocks. As mentioned before, Pástor and Stambaugh (2003) and Lynch and Tan (2011) propose that investors are willing to accept a lower required return for liquid stocks in a downward market. This implies that the required return of stock is negative, in a continuous down market, and linear priced with liquidity risk. My final hypothesis is that the flight to liquidity is visible and results in a negative relation between liquidity risk and required return.

H5: The liquidity risk of stocks negative and linear priced on a regional level.

Hypothesis H5 is the opposite from hypothesis H2a. This might look like the same proposal but in fact the hypotheses are based on different theories and the difference is not to be underestimated.

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3. Data and Methodology

3.1. Data

3.1.1. Data Sources The dataset used consists of daily data over the period 31 December 1994 to 31 December 2012 and includes 23 financial developed markets divided into four regions. The composition of the regions is equal to Fama and French (2012) who propose the composition because of the assumed market integration within the regions. Fama and French (2012) note that the market integration is questionable for the region Asia-Pacific (ex. Japan). Asia-Pacific (ex. Japan) consists of Australia, Hong Kong, New Zealand and Singapore. Europe consists of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom. The region Japan consists of Japan and North America is embodied by Canada and the United States of America (US). The regional factors are computed using only the developed markets within its territory, based on the FTSE (2012) and S&P (2012) index of developed markets. Both include the same 26 countries the dataset uses 23 developed markets in order to use the Fama-French factors obtainable from the website of K. French. The three excluded developed countries are Israel, Luxembourg and South-Korea. The data of K. French is used because producing the factors using data from Thomson Reuters Datastream and CRPS will result in misleading results as pointed out by Ince and Porter (2006). The data source is Thomson Reuters Datastream (TRDS) except for the US which data is obtained from the CRSP database. For each company, the dataset contains its daily price up to six decimals, market value, volume and the return index from 31 December 1994 to 31 December 2012. Additional data on the relative importance of the sample such as GDP, number of listed firms and are obtained from the DataBank of the World Bank Group. The Fama-French (1993), Carhart (1997) factors and the risk-free rate are downloaded from the website of K. French for each region and for a global developed market. The downloaded data includes the market premium, small minus big premium, high Book-to-Market ratio minus low Book-to-Market premium and the momentum premium. All variables are denominated in US dollars.

3.1.2. Data Filtering: The dataset is screened using static files on stock characteristics and filtered using daily data. The final dataset is a merge of the screened and filtered datasets and includes only stocks that are in both datasets. The dataset contains all available stock data within the 23 countries. This includes illiquid stocks and multiple cross- listings of stocks over the sample. Also the use of TRDS implies that a level of filtering is needed before the dataset is used in empirical tests. The goal of the filters is to obtain a dataset that is filtered of data errors and includes one stock per firm. Ince and Porter (2006) describe the flaws of TRDS and how to filter it properly of flaws and non-common equity.

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After a stock ceases trading TRDS continues to report the last valid observation over the observation period. These observations are filtered out by using backwards induction and Stata 12 which is used for all the tests and cleaning. Stocks with missing data on all four variables are filtered and no adjustments for rounding prices are made. Daily returns are calculated using the return index, monthly returns greater than absolute 300% and that are reversed within one month are set to missing (Ince and Porter, 2006). The reversal is expressed in equation (1), is the return of stock at month , is the return of stock at month . The result is that when an absolute return greater than 300% has occurred and it is corrected within the month this is assumed to be an error and it is filtered from the dataset.

( )( ) (1)

The stocks in the sample are screened to ensure that only common stocks are included in the sample. This is done by using only equity and primary listings on exchanges and per country. TRDS has several variables that indicate whether a stocks is equity or not. First the label of the stock is required to be equity, next the TRCS Description of the TRAD variable is used to filter out non-common equity, only the descriptions “Ordinary Shares”, “Fully Paid Ordinary Shares”, “UNKNOWN” and stocks with missing descriptions are not filtered. TRDS uses different type of coverage flags to indicate which data is available for a stock, stocks with coverage flag “C” are filtered because no market data is available, only Worldscope fundamentals data. Next to ensure that there are no obvious cases of non-common equity are included in the dataset Ince and Porter (2006) state a number of terms on which to filter stock descriptions on. Ince and Porter (2006) mention “REIT”, “PREF”, “PF” and “ADR” and state that they include more than 70 terms and abbreviations in the screening process. Next to the four mentioned abbreviations the additional terms “RESTRICTED”, “DEFERRED” and a list of country specific terms are filtered for. In order to cope with simultaneous trading the ADR parent code of TRDS is used to identify identical stocks. A stock is filtered by the ADR parent code if it trades simultaneously, has an more or less equal description and a shorter trading period than its duplicate. Stock with a different name or SICCODE, indicating it’s active in a different industry, are not filtered. In the case of type “A” and “B” class shares class “B” type shares are filtered out, based on the arguments discussed in Durnev, Morck and Yeung (2004). For the remaining duplicates the duplicated with the lowest average turnover (calculated as explained in equation (3)) is filtered from the dataset. During the cleaning procedure the support of the TRDS helpdesk resulted in the correction of certain data errors, for example a few Canadian stocks had price, volume and market value data but no return index because it had the “$$"ER", 2382, NO ” error. The error was a human error and the correct data was send in return. The US data are obtained from CRSP and require a different type of screening and filtering. The dataset includes all the stocks on all the US stock exchanges. This is not consistent with other liquidity research like Acharya and Pedersen (2005) who leave the NASDAQ out of their sample because of interdealer trades. The filters are set to only include common equity based on the share code of WRDS, all share codes of

13 which the first decile is one are ordinary common shares. Stocks with the share codes, 13, 14, 15 and 18 are filtered because they are Trusts, Closed-end Funds or Real Estate Investment Trusts (CRSP, 2013). Observations that include CRSP missing value codes are set to missing. Price, volume and are adjusted by their cumulative adjustment factors. When no trades are known CRSP quotes the closing ask price as a negative (CRSP, 2013). All prices are made absolute in the US dataset in order to calculate appropriate returns. Apart from the filtering required to work with CRSP and TRDS data, additional filtering and assumptions based on Amihud (2002) and Acharya and Pedersen (2005) are used. Stocks with begin of the month price greater than 1000 dollar or smaller than 5 dollar are dropped. The dataset includes only common stocks with at least 100 observations for return and volume within a year. Stocks with less than 15 observations within a month for volume and return are excluded for these particular months. Observations of daily volume greater than stocks outstanding are excluded from the dataset. Stocks with a monthly turnover greater than the 99th percentile, a daily return lower than the 0,1th percentile or greater than the 99,9th percentile or a monthly liquidity greater than the 99th percentile are dropped simultaneously (Karolyi, et al.,2012). An overview of countries and their characteristics are shown in Table 1. Table 1 is divided into panels on a regional basis and region characteristics are shown for every region in relation to the global sample. The country characteristics are obtained from the DataBank of the World Bank Group and are averages over the period 1995 to 2012. An important remark is the relative size of the regional stock markets in the dataset of the World Bank Group, column (3), and the relative size of the regional stock markets in the cleaned and filtered thesis dataset (9). Asia-Pacific (ex. Japan) is underweighted, from 5.69% to 2.49%. Europe is underweighted, from 30.99% to 26.63%. North America is overweighted from 51.93% to 54.50% of the world. Japan is overweighted from 11.39% of the global market to 16.37% within the global market of the screened and filtered dataset. For each stock as well as for each portfolio, daily and monthly computations of turnover and return are performed. The return of stocks and portfolios is calculated using the return index which includes dividends and is calculated as follows:

( ) (2)

is the total amount of dividends of stock in period t, is the price of stock at time and is the value of the return index at time for stock . Stock return is calculated as the percentage change of during the period. The turnover of a stock is a measure of the liquidity of a stock and is calculated as the ratio of monthly trading volume ( ∑ ) and stocks outstanding ( ).

∑ (3)

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Portfolio returns and other portfolio or market variables are calculated as the weighted average within the sample period. The weights used are equal and value weights based on the market capitalization in the observation period and are further specified when used in this thesis. The used method for weighted return averages is:

∑ ( ( )) (4)

is the return of portfolio at time , is the value or equal weight of stock in portfolio at time and is the return of stock in portfolio at time .

3.2. Methodology

3.2.1. Illiquidity Measure There are a number of liquidity measures and proxies, this paper uses the Amihud (2002) illiquidity factor. The ALM is a measure of price impact, it captures the absolute change of price in percentages per US dollar of aggregate trading volume per security (Amihud, 2002). The measure is not completely originated by Amihud (2002) (see e.g. Cooper, et al., 1985). The ALM is a measure of illiquidity because it measures the price impact of trading in percentages, a higher outcome hints a higher level of illiquidity. Because of two reasons. Firstly if the return of the market is similar for all stocks, paribus ceteris, the illiquid stocks are traded less and have a higher value of the ALM. Secondly if the trading volume is equal across the market, the absolute return of illiquid stocks will be greater, paribus ceteris. These phenomena are discussed by Acharya and Pedersen

(2005) in the description of their liquidity adjusted asset price model. The value of the ALM, , for security over the time period depends on the sum of the absolute return of securities, | | , calculated as the sum of daily, , returns, within time period, . The absolute return is divided by the sum of trading volume expressed in dollars, . The dollar price, closing price expressed in dollars, of a security at day in time period is expressed as , the total trading volume of security during day in time period is expressed as . The formula for the ALM is presented in equation (5).

| | ∑ (5) ( )

The sum of absolute return is calculated, in this thesis, using the return index of the securities over the complete period in order to protect against data errors in the daily return data. The sum of daily dollar volume of trades is calculated using daily price and volume data. The framework of equation (4) is used in order to calculate the ILLIQ on portfolio or market level. The ALM is used to determine the illiquidity of stocks and normalized in the tradition of Acharya and Pedersen (2005) in order to be used in the LCAPM. This is

15 described in section 3.2.2, section 3.2.3 describes how to adjust the ALM in order to calculated the commonality in liquidity innovations. In order to reduce the impact of outliers on the dataset, the ALM can be adjusted in several ways. It is important to adjust the outliers because in the case of an error in the dataset, the error is used in the calculation of liquidity innovation and in liquidity portfolios. This could lead to corrupt findings and therefore it is important to preclude that outliers corrupt the dataset. Acharya and Pedersen (2005) truncate the ALM to a level between 0.25 and 30 percent and normalize it before using it. Karolyi et al., (2012) use the natural logarithm to decrease the impact of outliers in the dataset. Both methods are separately used in this thesis.

3.2.2. Normalized Amihud Liquidity Measure Acharya and Pedersen (2005) normalize the ALM because of several reasons. Firstly the ALM is measured in percent per dollar, the LCAPM of Acharya and Pedersen (2005) implements dollar cost per dollar invested. This implies that is non-stationary and influenced by external parameters such as inflation which causes the price of stocks to rise over time. The normalization is needed in order to correct the non-stationary . Secondly the measures the cost of selling but not the actual illiquidity cost of a trade. Therefore the cost of trade is determined to be at least 0.25% and is allowed to be a value of 30.00% at maximum. Therefore the Amihud illiquidity measure is truncated at a maximum of 30.00% and a minimum of 0.25%. It is normalized by multiplying by the ratio of market capitalization. The market capitalization ratio ( of the market portfolio is calculated using the capitalization of the market portfolio at the end of month t-1 and the initial capitalization of the market portfolio at the end of December 1994. The normalized and truncated illiquidity for security at time , , is expressed as follows:

(6)

The normalized ALM is used as a measure of the liquidity cost in the LCAPM of Acharya and Pedersen (2005).

3.2.3. Autocorrelation of the Liquidity Level The liquidity level measured by the ALM is persistent. This means that future liquidity of stock can be predicted by the current level of liquidity. This makes the liquidity level an accurate tool to sort stocks on and see whether illiquid stocks require a return premium over liquid stocks. The persistence in liquidity is found by many of the empirical studies on liquidity (Acharya and Pedersen, 2005; Amihud, 2002; Chordia et al., 2000; Pástor and Stambaugh, 2003). A variable is persistent if the correlation between sequential time frames is greater than zero, . The autocorrelation of 25 equal weighted portfolios sorted on the truncated liquidity level of portfolios, , is 0.86 for Asia-Pacific (ex. Japan), 0.91 for Europe, 0.93 for Japan, 0.89 for

North America, and 0.92 for the global portfolios on a monthly basis. By proving that the liquidity level is

16 persistent, but time varying through innovations, the stocks in the dataset can be sorted in 25 portfolios on the basis of their liquidity level.

3.2.4. Innovations calculation: Innovations in liquidity are interpretable as liquidity shocks such as economic crises. Figure 1 shows the standardized normalized innovations in illiquidity, the innovations are standardized by their standard deviation. Therefore the four panels are comparable and intuitive. The historical liquidity shocks are clearly visible in the panels. The Asian Contagion is shown as the volatility spike in all the panels, starting in 1997 to 1999. And the Russian default, October 1998. The effect is at least one standard deviation from the mean in Panel B, C and D. The impact of the crisis is best seen in the region where the crisis originated, Panel A, Asia- Pacific (ex. Japan). The Dotcom crisis is visible as the increased volatility between 2000 to 2002 and caused a major negative innovation in liquidity for North America, Panel D. Acharya and Pedersen (2005) describe the existence of these increases in market volatility as well as the respectable period and names. The housing market bubble and the Credit Crisis lasted from 2007 to 2009 and are visible in all panels as an increase in volatility. Also the Euro crisis is visible in the European panel, B. The innovations in normalized illiquidity are calculated with an AR(2) type of regression. The innovations are the predicted residuals of the regression. The illiquidity level is computed using equal weights for all stocks in the market and represents the ALM of the market. In order to calculate the innovations in illiquidity on a portfolio level Acharya and Pedersen (2005) define an un-normalized illiquidity level per portfolio. The un-normalized illiquidity level is truncated for outliers using the same margins of minimal 0.25% and maximal 30.00% illiquidity cost per trade. The un-normalized illiquidity level is used in order to limit the influence of outliers in the dataset and is calculated as follows:

∑ ( ) (7)

The individual securities within the portfolio are truncated in the process of constructing the portfolio. This is done in the process of constructing the portfolio to ensure that the portfolios are cleaned of outliers before the innovations are calculated. The truncation is different from the normalization process described in equation (7). The portfolio level of un-normalized but truncated liquidity cost, , is the

sum of the equal weighted values, ∑ , with weight, , for stock, , in portfolio, . is a measure of cost of trade. In order to come to the defined range for cost of trade of 0.25% and 30.00% and normalize the

of a portfolio, in this case the market portfolio, Acharya and Pedersen (2005) use the same methodology as equation (6). The innovations in illiquidity are calculated using and no intermediate step for normalization is taken, the equation is as follows:

17

( ) ( ) ( ) (8)

All variables and parameters are discussed before, the above formula is combined with equation (7) is of an equal spirit with equation (6). The same methodology for truncation and normalization is used in the combination of (7) and (8) as in (6). The innovations in normalized illiquidity of the market portfolio are represented by the residuals, , of regression (8) , at time .

3.2.5. Commonality in Liquidity Innovations: In order to measure the commonality in liquidity innovations a similar procedure as Karolyi, et al., (2012) is used. Firstly a constant is added to the Amihud illiquidity measure, secondly the natural log is taken in order to reduce the impact of outliers and thirdly the measure is multiplied by -1 to transform it into a liquidity measure. The liquidity measure increases with the liquidity of individual stocks. This results in the following equation:

| | ( ) (9)

All the variables are known except for which is the value of the log-normal liquidity measure for stock on day . There is no major difference between the illiquidity and liquidity type of measures used in this paper. Both measures are based on the ALM but in order to obtain a liquidity measure from the ALM the ALM should be multiplied by -1, the measure will be increasing with liquidity. Chordia, et al.,(2000) find a statistical significant day of the week effects which is controlled for by adding a dummy variable for day of the week, (τ=1,…,5). The innovations in liquidity are calculated using an AR(1) framework. The innovations in liquidity are the residuals, , of the regression shown in equation (10). Equation (9) is constructed using the log-normal liquidity measure, , and the dummy variable, , that captures the day of the week effect and

is the innovation in liquidity, , for stock, , at day, of month, . (10)

The innovations are calculated for every stock in the sample using daily data. The monthly innovations in stock liquidity are calculated as the residuals of regression (10). The market liquidity innovation is calculated using the residuals from regression (10) and the methodology discussed in equation (4) for both region and world. Commonality between region and world is calculated by a linear regression of equation (11).

(11)

In order to calculate the non-local relationship the global innovations are decomposed as described in the next section.

18

3.2.6. Distinction between non-local effects and local effects. In order to find if liquidity is driven by non-local factors the innovations in liquidity are decomposed. The method used is the Jorion and Schwartz (1986) method of decomposition. The method is used to decompose the global illiquidity innovation factor in a US and a non-US part after excluding the domestic market. This is done using the following regression in which the non-local (W-D), , and non-local-non-US

((W-D)-US), , factors are residuals of the regressions.

(12)

(13)

The decomposition method is used for table three and five of the appendix which are discussed in chapter four.

3.2.7. Portfolio Construction A market portfolio is formed for each month using the method described in equation (4). For each year 25 illiquidity portfolios are formed on the basis of the average illiquidity over year of daily illiquidity calculated using equation (5). The stocks are sorted into 25 illiquidity portfolios based on the stock illiquidity of year . Portfolios are used in the asset pricing models that are tested in this thesis. The liquidity adjusted asset pricing model of Acharya and Pedersen (2005) is described in the next section.

3.2.8. Acharya and Pedersen (2005) LCAPM The LCAPM of Acharya and Pedersen (2005) is an unconditional equilibrium model with liquidity risk (Acharya and Pedersen, 2005). Because liquidity is persistence the assumption of constant conditional covariances of innovations in liquidity and returns has to be made in order for the unconditional model to hold (Acharya and Pedersen, 2005). From now on the abbreviation “LCAPM” refers to the LCAPM of Acharya and Pedersen (2005). The LCAPM is shown in equation (14). The model states that the required return of a security depends on the liquidity cost of the security, ( ), which depends on the holding period of the security. The used measure for the holding period is the turnover rate, . The used measure for the expected liquidity cost is ( ). Together these form a measure for the holding period cost of liquidity as described and empirically found by Amihud and Mendelson (1986). The liquidity level of the portfolios is based on a monthly value or equal weighted average of the portfolio. Next to the holding period cost of liquidity four betas and their risk premiums are used in the LCAPM.

( ( ) ( ) (14)

19

is the covariance between the return of a security and the market return. The market beta increases linear with the required return of securities. The numerator is the covariance between excess return

and the innovations in market return, . The excess return is calculated as the portfolio return minus the risk free rate. The denominator of each beta is the same and is calculated as the variance of market return innovations minus market illiquidity innovations [ ].

( ) (15)

[ ]

captures the increase in the expected return of a portfolio because of an the covariance between portfolio illiquidity and the illiquidity of the market. The covariance exists because investors holding securities, that become illiquid when the market itself becomes more illiquid, demand a higher return for the risk they are exposed to (Acharya and Pedersen, 2005). The empirical literature that describes this covariance is Chordia et al. (2000) which find stock illiquidity is positive related to market illiquidity. is calculated

using the same denominator as and the covariance of the portfolios innovation in liquidity, ( ), with the market innovations in liquidity, .

( ( ) ) (16)

[ ]

In times of market illiquidity investors are willing to accept a lower return for holding liquid securities. represent this phenomena and the rationale that investors value the possibility of liquid securities in times of market illiquidity. The acceptance of a lower required return is found empirically by

Pástor and Stambaugh (2003) and implemented as the covariance of the portfolios excess expected return and the illiquidity level of the market. It is calculated as the covariance of with the innovations in market liquidity divided by the denominator previously described.

( ) (17)

[ ]

captures the willingness of investors to accept a lower required return for liquid stock in a downward market. A downward market implies wealth losses for the investor, if the investor holds liquid stock the immediate sale of these securities does not harm the wealth of the investor as much as the immediate sale of illiquid securities. In the case the investor holds illiquid securities a buy-side investor has to be found whom, following the same rationale, prefers liquid asset more and therefore demand the securities at a discount. This effect is shown empirically by Lynch and Tan (2011) who show that the liquidity premium is greater when there is a negative covariance between transaction costs and wealth stocks. Acharya and

20

Pedersen (2005) calculate as the covariance between a securities liquidity level and the market return. The market return represents the wealth stocks of Lynch and Tan (2011) in the LCAPM.

( ( ) ) (18)

[ ]

The three liquidity betas capture the liquidity risk between security and the market in the LCAPM. Combined with the captured liquidity cost of holding a security the LCAPM can be used to distinguish between the importance of the different characteristics of liquidity. represents the commonality in liquidity innovations between security and market liquidity innovations. The commonality between portfolio and market, represented by , is tested empirically in this thesis. The commonality is decomposed using the methodology of Jorion and Schwartz (1986). The decomposition shows that both the US and non-local-non-US global factors influence local factors. This is in line with the theory discussed by Acharya and Pedersen (2005) if the market is defined as the global market. By assuming the theory on the liquidity characteristics is universal, which is partly confirmed by the empirical work in this thesis, the LCAPM can be constructed using a global market rather than only the US market. Another important side note is the fact that Acharya and Pedersen (2005) do not include the NASDAQ in their sample because of interdealer trades. This thesis includes the NASDAQ and all other stock exchanges across all countries in the dataset. Acharya and Pedersen (2005) show that the LCAPM holds for required returns net of liquidity costs. This implies that investors ideally have to understand the consequences of the liquidity of securities in all market circumstances. Firstly, the covariance of the liquidity of a security and the market, ( ), is positive related to required return. If the illiquidity of the market increases, the illiquidity of co moving investments will rises leading to higher required returns as investors want to be compensated for the increase in illiquidity. Secondly, the required return of a security is decreasing with covariance between the return of a

security and the illiquidity of the market, ( ). This means that investors accept a lower required return for liquid investments when the illiquidity of the market rises. Thirdly, the covariance between the

illiquidity of a security and the return of the market, ( ), shows that the liquidity level and thus the required return of investors decreases with the market (Acharya and Pedersen, 2005). Acharya and Pedersen (2005) are restricted by the multicollinearity within the LCAPM. Multicollinearity states that several variables are highly correlated resulting in statistical counterintuitive outcomes for the variables. This means that it is not possible to estimate the separate effects of the liquidity betas. In order to cope with the multicollinearity, Acharya and Pedersen (2005) construct the net beta, , as follows:

(19)

21

Another implementation problem is the negative value of the illiquidity cost, ( ), in the estimates of the LCAPM in this thesis. A negative value of the illiquidity cost implies that illiquidity lead to a lower required lower returns by investors. This is in conflict with the liquidity theory discussed in the theory development part of the thesis. In order to cope with both problems, the LCAPM will be adjusted with a net beta instead of four independent variables and the dependent variable, excess return, will be net liquidity cost. As a result the LCAPM becomes:

( ) ( ) (20)

In order to test if liquidity is priced, 25 portfolios are sorted on their yearly average liquidity level as calculated in equation (5). The stocks are assigned to the portfolios on the basis of their year value of the liquidity level. This results in the most liquid stocks being allocated to portfolio 1 and the most illiquid stocks to portfolio 25. The used liquidity level in the model is the normalized ALM as described in (normalized ALM) and calculated using (portfolio calculation). The calculations use an equal weighted market and value weighted portfolios. By using an equal weighted market in the calculation of market liquidity and return the sample is compensated for the over-representation of liquid stocks with a large market capitalization (Acharya and Pedersen, 2005). This is especially important because the dataset is filtered and includes only common equity which is a liquid asset type and excludes less liquid asset types such as investment funds and equity with voting rights. In other words the dataset is over-represented by liquid stocks, an equal weighted market portfolio is therefore a better presentation of the true market circumstances in the economy. This thesis test different combinations of equation (14) for both the local market and a global market. The global market is constructed using all the stocks in the dataset and the global market returns and liquidity are calculated as equal value averages using the methodology of equation (4).

3.2.9. LCAPM with Non-Local Factors. In order to test whether the non-local factors that influence illiquidity are priced in the LCAPM the original model is changed by adding the non-local factors calculated using the decomposition methodology of Jorion and Schwartz (1986). The net beta in the original LCAPM is exchanged for a non-local net beta. This non-local net beta is decomposed into an non-local-non-US net beta, , and a US net beta, . The required return is net of the risk free rate and liquidity costs. The net beta values are constructed following the methodology of Acharya and Pedersen (2005) but use instead the global factors as the interfering market, instead of the local factors. This leads to the following formula:

( ) ( ) (21)

22

3.2.10. Fama-MacBeth Cross-Sectional Regressions The LCAPM is tested using the Fama-MacBeth (1973) two pass approach for testing asset pricing models. For each factor in the LCAPM a beta is estimated. Because Acharya and Pedersen (2005) provide a direct way to obtain the beta values, no estimation is needed. For the adjusted CAPM, a time-series regression is used to estimate the beta values per portfolio. The next step is to calculate the common risk factor of the portfolios per beta by a cross-sectional regression for each time period. These two steps are the two pass approach of

Fama-MacBeth (1973). Equation (22) states the formula to estimate the beta, , of each risk factor per portfolio . The formula estimates the beta on basis of the excess return, , per portfolio, , at time, . The residual of the regression for portfolio, , at time, , is, , and is the constant for portfolio, . Equation (23) shows the formula which is used to estimate the risk premium of each risk factor. The excess return, , of portfolio, , at time, , is regressed on the estimated betas of the risk factors. The cross-sectional regression for each time period results in the risk premium, , for each risk factor used in the regression and in a constant, , per portfolio, . The regressions use standard deviations calculated using the Newey and West (1987) method with two lags.

t=1,2,...,T for each p. (22)

, P=1,2,…,N. (23)

3.2.11. Testing Asset Pricing Models The standard procedure for testing asset pricing models is followed, as decribed by Cochrane (2001, Chapter 20). The first step is to identify a characteristic that is associated with average returns. In this thesis the illiquidity level is used as the characteristic that is associated with average return. Table 2 shows the average return of the portfolios, . In order check whether there is a difference in the average pricing the average return of the five most liquid and most illiquid are compared. The five most liquid portfolios have an above average return in North America, 0.78 with a regional average of 0.26, and Asia-Pacific (ex. Japan), 0.98 with a regional average of 0.36. The most liquid portfolios have a return that is under average in Japan, -0.14 with a regional average of 0.04, and Europe, 0.55 with a regional average of 0.67. The most illiquid returns have an average return of -0.27 in Asia-Pacific (ex. Japan), -1.19 in North America, 0.81 in Europe and 0.37 in Japan. Therefore the most illiquid portfolios which supposed to be compensated for illiquidity risk have a risk premium in Europe and Japan. The most illiquid portfolios do not have a risk premium in North America and Asia-Pacific (ex. Japan). These portfolios have an, on average, negative return. Furthermore, the liquid portfolios perform better in these regions than the average portfolio. There is no unambiguous pattern in the average return of portfolios based on illiquidity, around the world. Therefore, the illiquidity level cannot be seen as a general anomaly of the CAPM. The CAPM of Sharpe (1964) and Lintner (1965) is the basis of the factor models of Fama and French (1997) and Carhart (1997). The original CAPM states that the required

23 return of stocks is explained by the beta it has with the market premium (Cochrane, 2001). The factors of Fama-French (1997) use the size and book-to-market anomaly of the CAPM and construct a factor based on the return of portfolios sorted on these stock characteristics (Fama and French, 1997). Carhart (1997) shows the existence of a momentum factor based on the momentum anomaly of the efficient market theory (Carhart, 1997). In order to test whether illiquidity is priced in the model cross-sectional regressions of regression (24) are used. The betas for each factor are estimated using time-series regressions and the factor premium is estimated using cross-sectional regressions for each time period. The variables used are the market premium,

, the size effect of Banz (1981), , the book-to-market effect, , the momentum factor, , and the liquidity factor, .

( ) (24)

In the next section the estimates for equation (20)-(21) and (24) are analyzed and discussed for empirical results.

4. Empirical Results

This section describes the results of the described tests in the previous chapter. It is organized following the structure provided by the hypotheses. First, I present the results of tests on the persistence of the illiquidity level. Second, I estimate if liquidity risk and the illiquidity level are positively and linear priced. Third, I estimate if commonality in the innovations of illiquidity exist. Fourth, I estimate if the commonality is priced. Fifth, I place the results in the context of the flight to liquidity.

4.1. Liquidity persistence The persistence of liquidity is described in the literature (see e.g. Acharya and Pedersen, 2005; Amihud, 2002; Chordia et al., 2000; Pástor and Stambaugh, 2003) and used as a key stone of research in market liquidity. If the liquidity level is persistent in my thesis, which it is, I can use the unconditional LCAPM which uses the persistence in liquidity level. Unconditional means that the used betas are static implying that conditional information does not influence the relationship between a risk factor and the required return. Acharya and Pedersen (2005) conclude that liquidity is persistent and assume that the innovations in liquidity and return have constant conditional covariances. This implies that they assume a constant risk premium in their unconditional model and this implies that they assume that the risk aversion level of investors does not change (Acharya and Pedersen, 2005). In order to estimate the persistence of the liquidity level, I use autoregressive models of different lags. A variable is persistent if the correlation between sequential time frames is greater than zero, . The autocorrelation of 25 equal weighted portfolios sorted on the truncated liquidity level of portfolios, , is

24

0.86 for Asia-Pacific (ex. Japan), 0.91 for Europe, 0.93 for Japan, 0.89 for North America, and 0.92 for the global portfolios on a monthly basis. The persistence of the liquidity level is visible using different numbers of lags, the persistence decreases with the number of lags. I accept hypothesis H1, liquidity is persistent but time-varying. This allows me to construct portfolios on the basis of the level of historical illiquidity and use these portfolios to test if liquidity risk is priced as a risk factor.

4.2. Liquidity risk is linear and positive priced The LCAPM is tested using the cross-sectional regression methodology as described in the methodology section of this thesis. The commonality in liquidity between stock and market as shown in table 3a and 3b is one of the three liquidity characteristics tested by Acharya and Pedersen (2005). The other two, sensitivity of the portfolio return to market illiquidity, , and the sensitivity of the portfolio illiquidity to the market return, , are tested on their empirical significance in the LCAPM of Acharya and Pedersen (2005). I assume that and are relevant liquidity characteristics in my dataset and use the approach of Acharya and Pedersen (2005) with regard to the pricing of liquidity risk. The characteristics will be tested in three steps. First, the local market is modeled in the LCAPM. Second, the local market returns are tested in a global market model. Third, the local market returns are modeled in an adjusted LCAPM that includes a decomposed non- local global factor. Based on this three step approach it is easy to understand whether the LCAPM, and therefore the liquidity relations, matter in a region, whether the required return in a region is driven by non- local factors and, if it is driven by non-local factors, which regions are the drivers of regional liquidity risk. Table 4 shows the results of combinations of the regression:

( ) ( ) (14)

The columns (1) to (8) are the output of regressions based on the interaction between local stocks and the local market. The columns (9)-(16) are the results of regressions based on the interaction between local stocks and the global market. The regression types are equal between panels based on the local market and panels based on the global market. In other words, regression (1) is the same combination of equation (14) as regression (9). The output of regression (1),(4) and (7) are based on a predetermined parameter, , for the expected liquidity level, ( ). The predetermined parameter is the average turnover in the sample period for the entire region per month. The estimated holding period of investors is , for example the

turnover rate in Europe is 0.04, implying a holding period of months. The model uses an estimation period of one month and the expected illiquidity level is an average of daily illiquidity in a month. Because the expected illiquidity is an average and not a cumulative of the daily illiquidity, the expected illiquidity is scaled by the turnover rate to obtain the effective illiquidity level per month. The scaling is done by multiplying the illiquidity level by the average turnover rate. The excess return and the estimated net beta are by definition scaled by time (Acharya and Pedersen, 2005) and are therefore not scaled by . Regression (6) does not

25 include the expected illiquidity level. Regressions (2),(3),(5)and (8) allow to be a free parameter in the regression. Regression (1) is the LCAPM of equation (20) and the only risk premium estimated, , is for the net beta, . The net beta is significant and negative for Asia-Pacific (ex. Japan), 5% level, and North America, 1% level. The negative risk premium is against the ideology of the model which states that required return increases with illiquidity. The constant is allowed to be non-zero in the model and it should be zero by approximation. As is shown in Panel A(1) and Panel G(1) the constant is significant different from zero for both Asia-Pacific (ex. Japan) and North America. Furthermore the model does not fit for Europe, Panel C (1), and Japan, Panel E (1). For both regressions the net beta and constant are not significant different from zero. This means that the net beta, net illiquidity effect, does not significantly influence the required return. The outcomes of regression (1) do not support the model and is an indication that illiquidity is not a linear and positive priced factor in this model. Regression (2) shows that when the parameter, , of the liquidity level is allowed to be a free parameter the illiquidity level will have a negative effect on expected return. The only exception is Japan but the illiquidity level is not significant different from zero for Japan, panel E (2). The negative effect is significant at the 10% level for Europe. This implies that investors require a higher return for liquid stocks. When testing the standard CAPM (3), in other words test the influence of , the market premium is negative and significant at the 1% level for North America. The market beta, , is negative and not significant for Asia-Pacific (ex. Japan) and Europe. Japan has a positive but insignificant effect of the market beta, furthermore the constant is always significantly different from zero, at least at the 5% level. Regressions of type (4) include both the market beta as the net beta. This is possible as the net effect of the regression would be that the market beta has its own premium and the net liquidity betas keep the net beta premium. In the case of Europe the type (4) regression is as follows:

( ) (25)

The estimates indicate a positive risk premium for the market beta and for the liquidity betas. Furthermore the net beta is significant at the 10% level for Europe and the constant is not significant different from zero. The output for Europe is one of the most supportive outcomes for the model in this thesis, although the market beta is not significant. Regression type (5) allows to be estimated. Regression type (6) excludes the liquidity level from the regression. Regression (7) and (8) include all the betas instead of the net beta. The multicolinearity problem is visible from the high coefficients, e.g. for Japan, Panel E, and the correlation matrix included with Table 2. The problem is described by Acharya and Pedersen (2005) and as a solution the net beta is used in their model. Regression type (7) used the predetermined level of , in type (8) regression is estimated. Acharya and Pedersen (2005) quote the goodness of fit for one moment cross-sectional regressions based on the excess return. When using a similar methodology the goodness of fit became negative mainly

26 caused by the liquidity level which only added variation in the regression instead of lowering the amount of variation. The hypothesis that illiquidity is positive and linear priced, H2a, can be partly rejected on the basis of the following arguments. Firstly the model predicts illiquidity to be priced positive and that the required return increases linear with the illiquidity level. In regression (1) the required return, if influenced significantly, decreases linear with the beta. For Europe the hypothesis is not rejected, because it shows that the illiquidity factors are positive and significantly priced at the 10% level, column (4) of Panel C. The illiquidity level increases the amount of variation in the model. Sorting stocks on the level of illiquidity does not indicate that the level of illiquidity is a character that determines the required return of stocks. Sadka (2006) finds that the variable part of the liquidity level is priced in the US as a risk factor in the CAPM of Fama-French-Carhart. A simple test to check whether the liquidity level can be used in asset pricing is by testing it in the CAPM model, both four (Carhart, 1997) and three factor (Fama and French, 1993) versions. The used methodology is described by Cochrane (2001) and discussed in the methodology chapter of this thesis. The used test is a cross-sectional regression of 25 equal and value weighted portfolios. The used CAPM factors are downloaded from the website of K. French, one of the originators of the Fama-French three factor model. The used country sample is identical to the countries which are used in the construction of the CAPM factors. For each portfolio the beta with a risk factor is estimated by a time-series regression between the return of the portfolio and the value of the risk factor. These betas are used as the risk beta and the cross- sectional regression is used to determine the risk premium. As a result the portfolios are tested on whether they are linear priced based on their factor beta and the risk premium of this beta. By doing this it is possible to find a stock characteristic that influences required return. In this case the characteristic is the illiquidity level, regressed using regression (24) with the Fama-MacBeth (1973) two-pass methodology. The output is shown in Table 6. The table can be used to conclude that the illiquidity level is not a priced risk factor in the CAPM. This can be concluded on the basis of the following arguments: firstly, the model states that the market premium, book to market premium, size premium and momentum premium are linear priced. From the different panels of Table 6 can be concluded that this is not the case for value weighted portfolios sorted on the illiquidity level. The panels show that the model has a better fit for equal weighted portfolios, especially for North America. The ILF beta is correlated with the SMB beta, size is a proxy for illiquidity. Small firms tend to be less liquid than big firms and require a size premium. The size premium could include a liquidity premium as size is a proxy for liquidity (Cooper, et al., 1985). The correlation matrix shows that the correlation becomes more positive or less negative if equal weighted portfolios are used instead of value weighted portfolios. The equal weighted portfolios are not driven by large liquid firms and therefore the fit of the model increases. The equal weighted portfolios show a better fit of the model, this is only true for Japan (panel C) and North America (panel D).

Not only the fit of the model is observable from Table 6, because the tested portfolios are sorted on the illiquidity level, the relation between the risk factors and the illiquidity level can be read. The ILF is not a

27 significantly priced risk factor when the extended CAPM is tested with value weighted portfolios. Column (2) shows the value weighted test results without the ILF. The observation can be made that SMB is significant for Asia-Pacific (ex. Japan), 5% level, and North America, 5% level. This indicates that the portfolios include a characteristic that includes a size premium. Column (4) shows the equal weighted results without the ILF and the SMB factor is significant and negative for Asia-Pacific (ex. Japan), 5% level, Europe, 1% level and Japan, 10% level. The negative premium implies that the smaller firms earned a lower return than the big firms during the observation period. This is in line with the findings of a possible flight to liquidity. I can reject hypothesis H2b on the basis of these outcomes. This is not a total rejection of the question if liquidity risk is priced but mere a rejection of the illiquidity level being a priced risk character. The finding is in line with the findings of Sadka (2006). The empirical findings for Asia-Pacific (ex. Japan) are to be weighted under the understanding that due to the low amount of stocks per year, average of 178 individual stocks per year, the 25 illiquidity portfolios include less than four stocks on average. As can be seen from the number of observations in Table 4, Panel A and Panel B, not every portfolio has data for each month in the estimation period. The portfolios are constructed based on the lagged value of the illiquidity level with certain requirements for number of trading days per stock. As a result of defaults or because of no trading data in a month the amount of observations is lower than for the other regions. A portfolio consisting of less than four stocks on average is also not comparable with the portfolios the other regions; Europe 99.48, japan 71.64 and North-America 196.08 individual stocks per portfolio, on average. These results of Asia-Pacific (ex. Japan) are driven by individual stocks rather than by a diversified portfolio of stocks with the same characteristics. Thus the results of Asia- Pacific (ex. Japan) are not merely the result of the illiquidity level but rather by the performance of individual stocks.

4.3. Commonality in liquidity risk The estimates of a time-series regression of equation (10) show the commonality in liquidity around the world. Table 3a shows the outcomes of the time-series regression for equation (10). Panel A shows the relationship between global innovations and local innovations. The global innovations include the local innovations and are significant and positive in all cases except for the equal weighted market portfolio of Asia- Pacific (ex. Japan). The fraction of variance explained by the model is low for the Asia-Pacific (ex. Japan) and Japan region. These regions have a minority stake in the composition of the world, 2.49% and 16.37%. Furthermore, the innovations in liquidity do not show identical patterns as can be seen in figure 1. Therefore, the equal weighted market portfolios of the Asia-Pacific (ex. Japan) and Japan have a low goodness of fit in the model. When using the US innovation in liquidity, Panel B, as the independent variable the outcomes show that the innovations in the US market influence the liquidity in the other regions. The relationship is significant in most but not all regressions. Europe is not significant related to the innovations in the US when using a value weighted market portfolio. Canada is not significant related to the innovations in the US when using an equal weighted market portfolio. These are both counter intuitive although the Euro crisis could be

28 part of an explanation for the outcome of the regressions of the Europe region, but this is only an assumption. Summarized table 3a shows that commonality in liquidity innovations exists although the drivers are not unambiguous across value and equal weighted market portfolios. Furthermore US and local factors are included in the global factors which increases the cautiousness needed for making a conclusion. Table 3b shows the results for equation (13) which makes a distinction between the local factor, the dependable variable, and non-local factors which are the regressions independent variables. From the table can be concluded that not all regions have the same driver of liquidity innovations. Canada represents the North-American (ex. US) region and is significantly influenced by the innovations in liquidity level of the US at the 1% level. Canada is not significantly influenced by the non-local-non-US innovations in liquidity both in an equal and value weighted market portfolio. The fraction of explained variance is 10% and 6% for value and equal based market portfolios. Asia-Pacific (ex. Japan) is significantly influenced by both the US and the non- local-non-US global factors at the 1% level for value weighted market portfolios. No significant relationship is determined under equal weighted market portfolios, the fraction of explained variance is 0% for the equal weighted regression and 12% for value weighted regressions. The region of Japan is significant related to the US at the 1% level in both value and equal weighted regressions. Japan is not influenced by the non-local-non- US global factors in the value weighted market. This signals that Europe and Asia-Pacific are significantly influenced by Japan, amongst other regions. The table can be used to understand the drivers in liquidity of a region and from the table it is evident that commonality in liquidity innovations exists on a global level between regional and non-local-non-US global and or US innovations in liquidity. This confirms H3a and H3b and furthermore implies that the local market is not an independent entity and it is important to understand that the local market is influenced by non-local factors. In other words from the table it is proven that Canada is influenced by the US, this is rational as the US is the only neighbor of Canada but rational does not mean the influence is statistically significant. In terms of economic importance, the goodness of fit gives a good indication of what part of local liquidity innovations is explained by non-local factors. This means that Europe is influenced the most, especially in the value weighted market where the constant of the regression is not statistically different from zero. This could mean that there are no significant internal drivers which are not related to non-local drivers. For the other regions, Asia-Pacific (ex. Japan), 12%, Japan, 11% and Canada, 10%, the goodness of fit lies between 10%-12% for the value weighted market portfolio. It can be concluded that regions are empirical significantly influenced by non-local factors and that the influence is of economic importance. From Table 3 can be concluded that commonality in liquidity exists and that it is driven by non-local factors. Table 4 shows the results of the tests whether commonality in liquidity is priced in the LCAPM. It is shown that the LCAPM based on global independent variables has approximately the same fit as the standard LCAPM. When regression (1)-(8) are done with global factors, regression (9)-(16), in panels B,D,F and H, the outcomes are similar and not supportive for the model. The overall goodness of fit is approximately the same, for the two groups of independent variables. The outcomes do not show why the outcomes are similar, for example, in Panel G and Panel H the outcomes for North America show the same empirical results. The next

29 section will decompose the global factors of the local factors and show whether the outcomes are similar because the global factors include the local factors, in this case North American factors. Furthermore, the non- local factors will be differentiated into non-local-non-US global factors and US global factors in order to understand the drivers of the empirical pattern. This section discusses the output of regression (21), shown in Table 5. The output is the result of cross-sectional regression based on equal and value weighted (market) portfolios. Table 5 shows that the required return of portfolios sorted on illiquidity is linear and significant priced by non-local factors. The pricing is positive and linear in general, the constant is significant only for Canada column (2). Regression (2) is influenced by multicolinearity between the non-local factors of non-local-non-US global and the US factor. The correlation between the factors is 0.78, consequently one of the two independent variables should be excluded from the regression. The net beta of the US has a significant and positive effect on the required return in Asia-Pacific (ex. Japan), 5% level and Europe, 10% level. The net beta of the non-local-non-US global factors has a significant and positive effect on Canada, 1% level and a significant and negative effect on Japan, 5% level. The significant and positive pricing implies that non-local factors result in an illiquidity premium that is linear priced for portfolios sorted on illiquidity level. This shows that illiquidity is priced on a global scale in which the innovations in illiquidity of other regions influence the required return in the local region. The relation is that the required return increases linear, in other words more illiquid stocks require a higher illiquidity premium. This is an empirical finding in line with the discussed theory on the illiquidity premium. Though there are some notes to be made before a conclusion can be made. Firstly, the net beta does not include only liquidity factors, as shown in equation (19) the net beta includes three liquidity betas and one market beta. Therefore, Table 5 shows that the model can be used with non-local factors and that these influence the required return. The conclusion cannot be that this is the sole result of liquidity characteristics. Secondly, the negative and significant coefficient of the non-local-non-US net beta is column (4) and (8) implies that the required return in Japan is negatively influenced by illiquidity and the non-local market premium. The role of the flight to liquidity as discussed by Beber et. Al. (2008) and Vayanos (2004) could be an explanation for this outcome. They find that in times of increase market volatility a liquidity premium exists. This can be used as an explanation for the negative illiquidity premium. The average illiquidity level between the regions can be an indication of the estimated outcomes. Japan has most liquid stocks with an averaged normalized illiquidity of 0.50%, Asia-Pacific (ex. Japan) has an average illiquidity level of 1.91, North America an average of 2.88 and Europe an average of 3.28. Because the illiquidity level spread in Japan is less than in the rest of the world, Japan is more liquid. This could imply that in case of an increased volatility in liquidity the Japanese stocks are used as a flight to liquidity. In sum, the non-local net beta factors can be used to understand the required return in a local region. Though the empirical relationships are not unambiguous, there is a difference in the pricing of the non-local factors. It can be concluded that the illiquidity factors of non-local regions influence the required return in the local region but in what extent is unclear. The extent is unclear because the net beta does not solely consists of liquidity factors. The LCAPM can be used as a global model if the right drivers of liquidity are used in the

30 model. But the assumptions of the model do not hold for all regions. H4a and H4b can be confirmed on the basis of table 5 which shows a positive and significant relation between the non-local factors and regional required return in the columns (1)-(3) and (5)-(6). H4a and H4b are rejected on the basis of column (4), (7)- (8) which show no and negative outcomes. The outcomes show a combination of liquidity risk pricing and the flight to the relative liquid Japan.

4.4. The flight to liquidity Hypothesis H2a is rejected based on the estimates of the LCAPM. The theory predicted the liquidity risk premium to be positive and rise with liquidity risk. The estimates are negative, indicating that a liquidity premium exists rather than an illiquidity premium. On the basis of the estimations the hypothesis is rejected. This does not reject the model as the negative estimates are possible, described by Acharya and Pedersen (2005), because of increased market volatility due to economic distress. Acharya and Pedersen (2005) assume unconditional risk premiums and risk aversion. This is against the suggestion of Vayanos (2004) who proposes that investors become more risk averse in times of market volatility. This causes the return of liquid stocks to rise because investors flee from illiquid stocks to liquid stocks, causing an above normal demand for liquidity which drives the price through the demand and supply mechanism of the market. This thought is emphasized by the work of e.g. Beber et al. (2009), Naes et al. (2011), and Rösch and Kaserer (2013). Hypothesis H5 states that liquidity risk is negative and linear priced. This is seen in the estimates in table 4 and table 5 for Japan. These negative estimates are explained by the flight to liquidity theory. Though it is important to understand that the model used is an unconditional model which assumes no change in the risk aversion of market participants. The observation period included some increases in market volatility and therefore hypothesis H5 is only accepted with great caution.

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5. Conclusions

Based on existing methodology and knowledge of liquidity characteristics this thesis has the following five conclusions. First, I show that the persistence of the level of liquidity exists around the world. This is important for market participants and researchers as it implies that the characteristics of liquidity are equal and the same base models and valuations methodology can be used in investments and empirical literature. Second, my estimations show that liquidity risk is not priced positively over the observation period. This finding is against the liquidity literature which states that required return increases with liquidity risk (e.g. Amihud and Mendelson, 1986). This finding is important for market participants, the relationship between return and liquidity risk should be well understood and implied in every investment strategy. The contradiction of the literature implies that investors need to reconsider their investment strategy with regards to liquidity risk. Third, I show that the liquidity level is not a priced characteristic in the LCAPM (Acharya and Pedersen, 2005) and the adjusted three (Fama and French, 1993) and four factor (Carhart, 1997) asset pricing model. This is also observable from the summary statistics where no obvious liquidity risk premium is observable. The finding that the liquidity level is not priced is in line with Sadka (2006). Fourth, I show that commonality in liquidity innovations exists internationally. The ability to diversify liquidity risk by investing in different regions, which do not significant co-move with each other, can be observed from the estimations. The commonality is economically important because it is priced in the LCAPM implying that part of the international relationship in liquidity risk is priced. Fifth, I show the possible existence of a flight to liquidity because of the negative risk premium for liquidity risk. The change in the behavior of market participants is at the base of the negative risk premium and contradict the assumptions of the LCAPM with regards to the risk and return properties of liquidity portfolios. The findings are important for all market participants and requires more research on how to diversify the liquidity risk internationally. Investors should also reconsider their liquidity investment strategy if they are focused on achieving an above normal excess returns by investing in assets with a high illiquidity level. Further research should determine whether the international version of the LCAPM yields a better result because of the international relationship in liquidity risk or because of the international commonality between stock return and market return. The use of Asia-Pacific (ex. Japan) as a region has to be reconsidered as the low amount of stocks in the region makes it impossible to use well diversified portfolios. The results of this thesis are based on an unconditional model which implies that the risk aversion and the liquidity risk of investors is constant. This implies that the risk premiums are constant. I propose that further research should use a conditional model to test the risk and return properties of the illiquidity level.

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6. Bibliography

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Henry, P. B. (2002). Stock market liberalization, economic reform, and emerging market equity prices. The Journal of Finance , 55, 529-564. Ince, O. S., & Porter, R. B. (2006). Individual Equity Return Data From Thomson Datastream: Handle With Care! The Journal of Financial Research , 29, 463-479. Jorion, P., & Schwartz, E. (1986). Integration vs. Segmentation in the Canadian Stock Market. Journal of Finance , 41, 603-614. Kamara, A., Lou, X., & Sadka, R. (2008). The divergence of liquidity commonality in the cross-section of stocks. Journal of Financial Economics , 89, 444-466. Karolyi, A., Lee, K., & van Dijk, M. A. (2012). Understanding commonality in liquidity around the world. Journal of Financial Economics , 105, 82-112. Korajczyk, R. A., & Sadka, R. (2008). Pricing the commonality across alternative measures of liquidty. Journal of Financial Economics , 87, 45-72. Lintner, J. (1965). The valueation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Revieq of Economics and Statistics , 47, 13-37. Longstaff, F. (2004). The flight-to-liquidity premium in US treasury bond prices. Journal of Business , 77, 511-526. Lynch, A. W., & Tan, S. (2011). Explaining the maginitude of liquidity premia: the role of return predictability, weath shocks and state-dependent transaction costs. The Journal of Finance , 66, 1329-1368. Mikolajczak, C., & Campos, R. (2013, 08 22). Nasdaq market paralyzed by three hour shutdown. Opgeroepen op 09 05, 2013, van Reuters.com: http://www.reuters.com/article/2013/08/22/us-nasdaq-halt- tapec-idUSBRE97L0V420130822 Naes, R., Skjeltorp, J. A., & Ödegaard, B. A. (2011). Stock market liquidity and the business cycle. The Journal of Finance , 66, 139-176. Pástor, L., & Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy , 111, 642-685. Regan, M. P., Mamudi, S., & Kisling, W. (2013, 08 26). Server Crash Spurs 3-Hour Nasdaq Halt as Data Link Lost. Opgeroepen op 09 05, 2013, van Bloomberg.com: http://www.bloomberg.com/news/2013-08- 26/nasdaq-three-hour-halt-highlights-vulnerability-in-market.html Rösch, C. G., & Kaserer, C. (2013). Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality. Journal of Banking & Finance , 37, 2284-2302. Sadka, R. (2006). Momentum and Post-Earnings Announcement Drift Anomalies: The Role of Liquidity Risk. Journal of Financial Economics , 80, 309-349. Sharpe, W. F. (1964). Capital asset prices -A theory of market equilibrium under conditions of risk. The Journal of Finance , 19, 425-442. Vayanos, D. (2004). Flight to quality, flight to liquidity and the pricing of risk. NBER working paper . Xin Liang, S., & Wei, J. K. (2012). Liquidity risk and stock returns around the world. Journal of Banking & Finance , 36, 3274-3288.

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7. Tabulations

Table 1: Overview of Regions and Countries within Dataset

The information in table 1 shows the coverage of the dataset. The variables in column (1)-(7) are obtained from the DataBank of the World Bank Group and are averages over the period 1995 to 2012. The columns (8) and (9) are constructed using the thesis dataset. The table is categorized by the following regions: Asia-Pacific (ex. Japan) consists of Australia, Hong Kong, New Zealand and Singapore. Europe consists of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland and the United Kingdom. The region Japan consists of Japan and North America is embodied by Canada and the United States of America (US). There are more details for the North American countries in order to give more information on the North America (ex. US) region. The global, world, region contains the 23 countries named above. The regions are computed using only the developed markets within its territory, based on the FTSE (2012) and S&P (2012) index of developed markets. Both include the same 26 countries, the dataset used in this thesis uses 23 developed markets in order to use the Fama-French factors obtainable from K. French website (French 2013). The three excluded developed countries are Israel, Luxembourg and South-Korea. Column (8) includes the number of stocks per country in the screened dataset which includes only common stock. Column (9) includes the number of stocks per region in the cleaned dataset which cleaning procedure is described in 3.1 Data. All currency variables are in US dollars. Column (1) shows the absolute market capitalization of listed companies where column (2) shows the relative market capitalization of listed companies in percentage of the country’s GDP. Column (3) shows the number of listed companies, column (4) represents the total value of stocks traded and column (5) shows the total value of stocks traded in percentage of the country’s GDP. Column (6) shows the turnover ratio of stocks traded and column (7) shows the GDP in constant 2005 billion US dollars. Information including total and average or relative to the world is printed beneath each region. The “Average” is calculated as the average of all country averages within the region. The “Total Sum” is the sum of all country averages within the region. The relative percentages between region and the world are based on the “Total Sum” row.

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Table 1: Overview of Regions and Countries within Dataset (1) (2) (3) (4) (5) (6) (7) (8) (9)

and and

Country/Region

over (%) ratio

dataset

Market Market capitalization listed of US$) (currentcompanies billion Market capitalization listed of GDP) of(%companies Listed total domestic companies, traded, (current Stocks valuetotal billion US$) traded,of (% Stocks value total GDP) traded, Stocks turn 2005US$) GDP(constant billion of Number in stocks screened dataset ofNumber infiltered stocks screened

Table 1: Overview of Regions and Countries within Dataset: Panel A: Asia-Pacific (ex. Japan) 731.66 103.13 1541.78 582.30 74.97 73.97 660.51 3526 Australia 722.29 369.38 983.67 646.41 307.57 79.03 174.17 1780 Hong Kong SAR, China 41.10 42.15 136.06 15.28 16.16 40.02 104.52 346 New Zealand 228.09 169.16 430.83 144.44 98.48 61.34 119.91 997 Singapore 430.78 170.96 773.08 347.11 124.30 63.59 264.78 178 Average 1723.14 3092.33 1388.43 1059.12 6649 658 Total Sum 2.49 % of world 5.69 13.29 3.34 3.38

76.81 44.13 -26.90 % difference from world

Table 1: Overview of Regions and Countries within Dataset: Panel B: Europe Austria 73.53 23.79 95.28 36.43 11.15 46.80 295.12 297 Belgium 223.02 63.75 170.33 90.56 23.33 37.17 363.83 549 Denmark 145.16 59.33 207.22 108.39 43.04 73.16 246.27 522 Finland 176.16 104.15 126.94 180.82 96.03 95.18 183.26 384 France 1472.17 73.84 809.61 1343.71 64.25 86.68 2045.81 2602 Germany 1187.61 44.84 703.89 1451.42 52.66 120.61 2761.17 2764 Greece 98.45 50.34 290.00 56.51 30.07 55.59 216.83 482 Ireland 81.76 54.06 63.33 37.46 24.14 44.75 198.26 143 Italy 569.83 36.83 275.67 713.76 42.72 119.46 1719.42 751 Netherlands 566.45 102.82 184.39 682.89 118.08 117.98 617.78 499 Norway 145.69 48.24 186.50 153.46 47.76 98.06 288.32 653 Portugal 64.99 37.56 82.72 42.26 23.86 60.67 183.90 310 Spain 788.52 75.40 2282.72 1195.67 115.48 154.85 1045.94 476 Sweden 369.29 104.91 284.83 383.22 105.33 102.10 350.24 1849 Switzerland 828.69 216.02 249.00 773.98 197.87 93.96 380.61 816 United Kingdom 2595.71 137.07 2262.56 2948.77 136.59 105.67 2133.70 7368 586.69 77.06 517.19 637.46 70.77 88.29 814.40 2487 Average 9387.02 8275.00 10199.33 13030.45 20465 7024 Total Sum 26.63 % of world 30.99 35.55 24.55 41.59

% difference from world -20.30 -17.94 1.50

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Table 1: Overview of Regions and Countries within Dataset - Continued (1) (2) (3) (4) (5) (6) (7) (8) (9)

Country/ Region

dataset

screened screened

Market Market capitalization of listed companies (current billion US$) Market capitalization of listed GDP) companies of (% Listed domestic companies, total traded, Stocks valuetotal (current billion US$) traded, (% Stocks value total of GDP) traded, Stocks turnover ratio (%) 2005GDP(constant billion US$) ofNumber in stocks screened dataset ofNumber infiltered stocks and

Table 1: Overview of Regions and Countries within Dataset: Panel C: North America Canada 1171.54 106.57 2828.61 829.70 71.92 69.54 1063.65 9112 1798 United States 14555.06 127.19 6064.11 25892.62 213.90 174.87 11728.51 14458 12577 437 Average per country 4465

7863.30 116.88 4446.36 13361.16 142.91 122.21 6396.08 4902 Average 15726.60 8892.72 26722.32 12792.16 23570 14375 Total Sum 54.50 % of world 51.93 38.21 64.32 40.83

% difference from world -12.22 2.62 8.92

Table 1: Overview of Regions and Countries within Dataset: Panel D: Japan Japan 3450.30 73.34 3015.11 3233.07 68.16 89.21 4450.11 5094

3450.30 73.34 3015.11 3233.07 68.16 89.21 4450.11 1791 Average 3450.30 3015.11 3233.07 4450.11 5094 4319 Total Sum 16.37 % of world 11.39 12.95 7.78 14.20

% difference from world -24.15 -20.97 2.56 Table 1: Overview of Regions and Countries within Dataset: Panel E: World World Total 30287.06 96.69 23275.17 41543.16 86.24 86.99 31331.85 55778 26376 World Average 9358

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Table 2: Summary Statistics

This table includes the summary statistics for the regions Asia-Pacific (ex. Japan), Europe, Japan, North America and Global (ex. US), sorted by 25 value weighted portfolios based on Amihud’s (2002) liquidity measure. The data source is Thomson Reuters Datastream except for the US which is obtained from the CRSP database. For each company the dataset contains its daily price, market value, volume and the return index from 31 December 1994 to 31 December 2012. The sample includes only common stocks with at least 100 observations for return and volume within a year. Stocks with less than 15 observations within a month for volume and return are excluded for these particular months. Observations of daily volume greater than stocks outstanding are dropped. Stocks with a monthly turnover greater than the 99th percentile, a daily return lower than the 0,1th percentile or greater than the 99,9th percentile or a monthly liquidity greater than the 99th percentile are dropped simultaneously. The LCAPM betas one to four represent the LCAPM regional betas of Acharya and Pedersen (2005). Beta one is the market beta as used in the original CAPM model, beta two to four are illiquidity betas respectively based on the covariance between normalized portfolio illiquidity and normalized market illiquidity, the covariance of portfolio return and normalized market illiquidity and the covariance of normalized portfolio illiquidity and market return. The LCAPM betas five to ten are based on the interaction of the portfolios with the global market. The global market consists of all the countries in the dataset. The regional market is an equal weighted average of all the stocks within the regional sample. The global market is constructed as a value weighted average of the stocks in the regional markets based on the market capitalization of the sample. E(cp) is the average value of the normalized Amihud’s illiquidity measure. The average standard deviation of this measures is denoted as σ(Δcp), the average portfolio excess return is denoted as E(re,p), its standard deviation as σ(rp). The average market value of the portfolio is denoted as Size and its turnover as trn. All data are expressed in US Dollars. The regions include all developed markets within its area as described in table 1, exceptions are mentioned in the table title. Absolute correlations greater than 0.50 are reported in parentheses.

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Table 2: Summary Statistics – Continued: Panel A: Asia-Pacific (ex. Japan) P β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) (%) (%) (%) (%) ($Bn) (%) 1 81.19 0.00 -4.29 0.00 65.13 0.00 -8.88 0.00 0.25 0.00 1.45 7.86 33915.00 6.67 2 75.00 0.01 -3.37 0.08 76.86 0.00 -5.31 -0.03 0.25 0.11 0.82 7.67 20237.00 6.29 3 59.64 0.00 -2.89 0.00 66.86 0.00 -3.80 0.00 0.25 0.00 0.54 6.53 16367.00 6.35 4 58.21 0.00 -1.67 0.00 61.00 0.00 -4.51 0.00 0.25 0.00 0.76 6.63 13342.00 7.58 5 58.00 0.00 -2.20 0.00 63.22 0.00 -4.05 0.00 0.25 0.00 1.34 5.97 11737.00 7.24 6 54.01 0.00 -2.36 0.00 50.45 0.00 -5.09 0.00 0.26 0.00 0.77 6.70 7524.00 7.48 7 47.93 0.00 -2.05 0.00 31.87 0.00 -5.43 -0.01 0.26 0.00 0.78 7.51 5128.00 7.36 8 65.26 0.03 -3.63 -0.17 55.15 0.02 -4.90 0.19 0.27 0.36 0.67 7.83 3930.00 7.10 9 60.98 0.00 -2.67 -0.01 58.08 0.00 -3.97 -0.02 0.28 0.00 0.62 7.34 3342.00 6.83 10 63.87 0.00 -2.92 -0.01 73.14 0.00 -5.84 0.00 0.29 0.01 0.93 8.02 2973.00 6.24 11 57.68 0.00 -4.26 0.01 55.52 0.00 -4.47 0.00 0.28 0.01 0.76 7.16 2601.00 5.39 12 49.77 0.03 -3.98 0.08 50.04 0.11 -5.34 -0.04 0.42 0.22 0.60 9.19 2311.00 5.80 13 66.13 0.06 -2.40 -0.21 58.20 0.07 -4.96 -0.29 0.59 0.27 -0.76 7.50 1634.00 5.99 14 60.33 0.02 -2.82 0.00 56.18 0.02 -3.36 0.13 0.49 0.08 0.40 7.92 1857.00 5.69 15 45.87 0.02 -3.06 -0.59 52.29 0.05 -3.47 -0.53 0.75 0.20 1.20 7.91 1343.00 6.40 16 71.72 0.05 -4.06 -0.68 101.10 0.11 -4.26 -0.27 1.12 0.45 -0.53 9.52 517.10 6.80 17 63.68 0.52 -3.01 3.65 56.80 -0.03 -4.80 2.14 2.26 2.36 -0.56 9.79 281.50 6.24 18 87.05 0.16 -7.02 -0.41 60.87 0.43 -8.03 -4.45 1.83 3.21 0.95 13.89 195.40 8.61 19 98.26 0.43 -5.68 10.68 89.19 1.16 -4.45 10.14 3.37 4.31 0.09 13.04 360.20 5.66 20 61.02 1.52 -3.89 0.26 51.79 0.52 -6.02 0.60 3.35 3.14 -0.45 12.58 100.70 7.43 21 55.23 2.52 -4.33 -11.55 21.20 0.96 -4.69 -5.78 3.85 3.83 -0.73 13.55 146.40 7.18 22 86.87 2.88 -6.28 -16.30 -13.98 1.09 -4.83 -13.08 5.07 4.65 -1.68 15.59 47.82 7.08 23 118.20 2.38 -4.17 -2.32 58.60 1.40 -4.16 28.12 6.49 6.32 -1.14 17.83 51.05 7.85 24 4.19 1.81 -4.92 -7.79 15.51 0.27 -1.29 -9.15 8.56 5.82 1.83 16.27 39.64 7.71 25 113.00 6.29 -13.31 7.42 7.41 0.92 -5.86 11.99 9.68 7.69 0.37 22.76 38.07 8.91 Total 65.72 0.68 -3.94 -0.68 53.59 0.27 -4.80 0.73 1.91 1.62 0.36 10.07 4842.00 6.84

Correlation Matrix of Table 2: Summary Statistics – Continued: Panel A: β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn β 1 1.00 β2 0.41 1.00 β3 (-0.52) (-0.80) 1.00 β4 0.29 -0.20 -0.10 1.00 β5 0.15 (-0.66) 0.39 (0.59) 1.00 β6 (0.61) (0.71) (-0.58) -0.19 -0.34 1.00 β7 -0.46 0.00 0.27 -0.19 -0.10 -0.04 1.00 β8 (0.64) 0.23 -0.17 (0.54) 0.31 0.41 -0.02 1.00 E(cp) 0.27 (0.89) (-0.72) -0.19 (-0.56) (0.74) 0.19 0.25 1.00 σ(Δcp) 0.42 (0.85) (-0.74) -0.14 -0.49 (0.85) 0.05 0.31 (0.96) 1.00 E(re,p) -0.04 -0.03 0.01 0.02 0.01 -0.04 0.00 -0.01 -0.02 -0.03 1.00 σ(rp) 0.46 (0.89) (-0.83) -0.15 (-0.50) (0.83) -0.04 0.30 (0.95) (0.97) -0.03 1.00 Size -0.02 -0.33 0.28 0.09 0.27 -0.40 -0.29 -0.07 -0.41 -0.45 0.03 -0.46 1.00 trn 0.21 (0.54) -0.45 -0.17 -0.40 0.34 -0.23 0.10 (0.53) (0.53) 0.00 (0.56) -0.08 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 2: Summary Statistics – Continued: Panel B: Europe P β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) (%) (%) (%) (%) ($Bn) (%)

1 61.35 0.00 -6.63 0.00 59.15 0.00 -4.11 0.00 0.26 0.00 0.53 5.13 23188.93 9.81 2 66.74 0.00 -7.35 0.00 55.72 0.00 -4.56 0.00 0.26 0.00 0.44 5.07 10067.39 9.73 3 64.09 0.00 -8.09 0.13 53.12 0.00 -4.99 0.04 0.28 0.06 0.52 5.46 7073.58 8.78 4 64.71 -0.01 -7.33 0.01 46.66 0.00 -4.19 0.00 0.28 0.05 0.67 5.12 5820.69 7.49 5 69.02 0.00 -7.72 -0.01 53.62 0.00 -4.67 0.01 0.30 0.02 0.57 5.51 4405.19 6.42 6 73.52 -0.01 -7.97 0.02 56.64 0.00 -5.05 0.00 0.33 0.06 0.40 5.89 3646.79 5.74 7 73.56 0.01 -7.69 -0.07 58.57 0.01 -5.06 -0.05 0.38 0.01 0.41 5.61 2473.82 5.02 8 60.83 0.00 -7.95 0.16 49.97 0.01 -4.55 0.12 0.49 0.08 0.62 5.49 1962.56 4.45 9 66.92 0.01 -7.13 0.13 56.18 0.01 -4.77 0.01 0.62 0.10 0.63 5.64 1363.14 4.25 10 51.56 0.04 -7.02 -0.11 41.64 0.04 -4.72 -0.16 0.75 0.09 0.62 5.48 1205.08 4.06 11 63.58 0.06 -6.75 -0.41 51.18 0.04 -4.33 -0.42 0.99 0.10 0.49 5.67 1258.00 3.51 12 50.22 0.13 -6.39 -0.24 32.51 0.10 -4.10 -0.26 1.13 0.21 0.54 5.38 855.32 3.24 13 56.51 0.13 -6.37 -1.07 41.35 0.08 -4.18 -1.04 1.45 0.19 0.80 5.26 870.01 3.15 14 49.32 0.27 -6.33 -0.13 44.36 0.21 -4.06 -0.29 1.63 0.36 0.75 5.24 768.66 2.91 15 43.41 0.24 -6.68 0.87 30.96 0.07 -4.32 1.43 1.91 0.50 0.58 4.95 613.11 2.69 16 45.16 0.51 -5.88 -1.34 39.75 0.35 -3.77 -0.49 2.27 0.56 1.09 5.43 510.68 2.54 17 51.26 0.52 -6.86 -1.21 33.22 0.31 -4.55 -0.48 2.53 0.45 0.85 5.49 520.84 2.35 18 52.37 0.62 -6.13 -1.07 38.70 0.47 -4.20 -0.73 3.12 0.77 0.76 5.46 398.95 2.25 19 47.35 1.14 -6.06 -0.16 37.67 0.44 -3.67 1.02 3.68 1.35 0.79 4.89 463.47 2.08 20 43.51 1.18 -6.26 -2.22 39.68 0.51 -4.24 -0.86 4.41 0.93 0.58 5.28 378.49 1.94 21 42.84 1.62 -6.58 0.01 26.80 0.83 -4.02 2.03 5.04 2.14 1.32 5.55 325.05 1.91 22 40.28 2.41 -5.35 -3.61 32.90 1.59 -3.56 -3.27 6.50 2.49 0.84 4.67 250.09 1.83 23 34.61 2.80 -5.75 -0.53 25.72 1.46 -4.03 1.65 8.62 2.41 0.23 6.44 189.60 1.77 24 32.20 4.10 -4.80 -0.68 27.20 1.74 -2.77 -2.32 13.26 3.73 0.95 4.75 116.62 1.60 25 27.42 3.91 -4.05 5.86 9.21 1.46 -2.45 8.08 21.45 3.88 0.69 4.85 73.48 1.17 Total 53.29 0.79 -6.61 -0.23 41.70 0.39 -4.20 0.16 3.28 0.82 0.67 5.35 2751.98 4.03

Correlation Matrix of Table 2: Summary Statistics – Continued: Panel B: β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn β 1 1.00 β2 (-0.82) 1.00 β3 (-0.88) (0.84) 1.00 β4 -0.11 0.21 0.16 1.00 β5 (0.93) (-0.79) (-0.81) -0.27 1.00 β6 (-0.82) (0.97) (0.82) 0.02 (-0.76) 1.00 β7 (-0.82) (0.84) (0.93) 0.28 (-0.77) (0.79) 1.00 β8 -0.30 0.31 0.28 (0.91) -0.45 0.16 0.33 1.00 E(cp) (-0.79) (0.94) (0.84) 0.47 (-0.81) (0.86) (0.85) (0.55) 1.00 σ(Δcp) (-0.84) (0.99) (0.84) 0.24 (-0.81) (0.96) (0.85) 0.35 (0.94) 1.00 E(re,p) -0.02 0.01 0.02 -0.01 -0.02 0.01 0.02 0.00 0.01 0.02 1.00 σ(rp) 0.32 -0.28 -0.43 -0.08 0.26 -0.24 (-0.57) 0.03 -0.31 -0.32 -0.02 1.00 Size 0.44 -0.34 -0.32 0.07 (0.55) -0.36 -0.21 -0.05 -0.32 -0.36 -0.01 -0.10 1.00 trn (0.74) (-0.58) (-0.67) 0.06 (0.76) (-0.61) (-0.53) -0.13 (-0.55) (-0.60) -0.02 0.05 (0.84) 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 2: Summary Statistics – Continued: Panel C: Japan P β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) (%) (%) (%) (%) ($Bn) (%)

1 83.35 0.00 -0.88 0.00 44.82 0.00 -2.95 0.00 0.25 0.00 -0.51 5.86 10472.00 8.76 2 73.43 0.00 -0.67 0.00 34.77 0.00 -2.22 0.00 0.25 0.00 -0.23 4.98 6001.00 8.08 3 74.31 0.00 -0.65 0.00 36.93 0.00 -2.09 0.00 0.25 0.00 -0.05 4.63 4289.00 7.72 4 79.05 0.00 -0.77 0.00 31.67 0.00 -1.86 -0.01 0.26 0.00 0.04 5.00 2767.00 7.21 5 81.13 0.00 -0.78 -0.01 34.96 0.00 -1.95 0.00 0.26 0.00 0.03 5.19 2024.00 6.77 6 76.99 0.00 -0.79 -0.01 38.02 0.00 -2.22 -0.01 0.26 0.00 -0.53 4.77 1584.00 5.95 7 75.50 0.00 -0.73 -0.02 35.35 0.00 -2.18 -0.01 0.27 0.00 -0.30 5.07 1233.00 5.80 8 82.76 0.00 -0.81 -0.03 40.16 0.00 -2.28 -0.02 0.27 0.00 -0.33 5.39 995.40 5.37 9 82.75 0.00 -0.73 -0.03 37.43 0.00 -1.91 -0.01 0.28 0.00 -0.04 5.31 857.70 5.55 10 85.77 0.00 -0.80 -0.06 37.93 0.00 -2.18 -0.04 0.29 0.01 0.06 5.41 740.50 4.58 11 75.78 0.00 -0.68 -0.09 28.36 0.00 -1.70 -0.05 0.31 0.01 -0.32 5.10 564.90 4.39 12 75.10 0.00 -0.69 -0.09 29.03 0.00 -1.88 -0.04 0.31 0.01 0.20 5.82 581.10 4.12 13 80.39 0.00 -0.69 -0.10 21.95 0.01 -1.98 -0.06 0.34 0.01 0.31 5.54 519.20 4.09 14 74.82 0.00 -0.75 -0.16 31.09 0.01 -2.20 -0.09 0.36 0.02 0.10 5.73 441.90 3.72 15 81.25 0.00 -0.66 -0.17 39.07 0.01 -1.46 -0.13 0.38 0.02 -0.04 5.30 379.80 3.53 16 82.89 0.00 -0.76 -0.24 34.13 0.01 -1.81 -0.22 0.40 0.04 0.22 5.31 310.90 3.45 17 79.97 0.00 -0.72 -0.28 29.22 0.02 -1.87 -0.20 0.43 0.04 0.39 5.68 322.50 3.09 18 84.44 0.01 -0.76 -0.49 38.53 0.03 -2.16 -0.22 0.45 0.06 -0.37 5.83 257.00 2.95 19 76.16 0.01 -0.64 -0.46 36.06 0.03 -1.19 -0.07 0.49 0.06 0.48 7.37 230.70 3.06 20 84.58 0.01 -0.63 -0.64 29.49 0.04 -1.82 -0.58 0.55 0.08 0.20 5.83 201.50 3.07 21 73.68 0.01 -0.71 -0.55 19.34 0.04 -1.92 -0.19 0.60 0.12 0.16 5.50 196.80 4.75 22 86.04 0.02 -0.67 -1.51 34.25 0.10 -2.19 -0.91 0.71 0.23 -0.05 6.44 150.20 2.86 23 63.36 0.04 -0.67 -1.45 16.04 0.09 -1.49 -0.71 0.83 0.22 -0.19 5.78 147.70 2.66 24 85.66 0.06 -0.71 -1.33 30.64 0.15 -1.83 -0.32 1.12 0.58 0.45 6.54 85.33 2.95 25 91.09 0.14 -0.81 -5.24 18.55 0.16 -1.64 1.59 2.98 1.08 1.50 11.46 40.54 3.47 Total 79.58 0.01 -0.73 -0.49 32.40 0.03 -1.96 -0.10 0.50 0.10 0.04 5.77 1415.00 4.73

Correlation Matrix of Table 2: Summary Statistics – Continued: Panel C: β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn β 1 1.00 β2 0.35 1.00 β3 -0.41 -0.11 1.00 β4 -0.35 (-0.98) 0.07 1.00 β5 0.30 (-0.51) -0.32 (0.52) 1.00 β6 0.30 (0.88) 0.09 (-0.87) (-0.50) 1.00 β7 -0.19 0.29 (0.61) -0.29 -0.48 0.30 1.00 β8 0.29 0.55 -0.43 (-0.51) -0.11 0.12 0.04 1.00 E(cp) 0.38 (0.99) -0.10 (-0.99) (-0.52) (0.85) 0.31 (0.58) 1.00 σ(Δcp) 0.40 (0.99) -0.10 (-0.96) -0.48 (0.91) 0.27 (0.51) (0.98) 1.00 E(re,p) 0.03 0.05 0.01 -0.05 -0.04 0.04 0.04 0.04 0.05 0.05 1.00 σ(rp) 0.44 (0.90) -0.12 (-0.92) -0.38 (0.74) 0.30 (0.60) (0.93) (0.88) 0.05 1.00 Size -0.07 -0.24 -0.37 0.27 0.46 -0.34 (-0.65) 0.11 -0.26 -0.25 -0.03 -0.22 1.00 trn -0.15 -0.35 -0.37 0.39 0.43 (-0.52) (-0.59) 0.24 -0.37 -0.36 -0.03 -0.39 (0.84) 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 2: Summary Statistics – Continued: Panel D North America P β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) (%) (%) (%) (%) ($Bn) (%)

1 47.55 0.00 -4.77 0.00 35.48 0.00 -4.79 0.00 0.30 0.00 1.29 5.73 20649.00 6.91 2 39.68 0.00 -4.25 0.00 42.84 0.00 -3.94 0.00 0.28 0.00 0.58 5.14 9696.00 7.23 3 55.05 0.00 -5.89 -0.01 49.48 0.00 -4.43 0.00 0.28 0.00 0.29 6.25 4919.00 7.58 4 50.65 0.00 -6.10 -0.01 42.85 0.00 -4.29 -0.01 0.30 0.00 1.02 5.85 3346.00 7.17 5 46.26 0.01 -6.07 -0.03 42.46 0.00 -4.51 0.00 0.28 0.01 0.71 6.20 2516.00 7.00 6 47.64 0.02 -5.74 -0.05 46.10 0.00 -4.84 0.01 0.34 0.01 0.50 6.17 2096.00 6.68 7 49.98 0.03 -6.12 -0.09 38.25 0.01 -4.70 0.00 0.35 0.02 0.83 6.23 1552.00 6.38 8 55.08 0.03 -6.60 -0.09 43.73 0.01 -4.50 0.04 0.41 0.03 0.54 5.97 1343.00 6.32 9 49.34 0.03 -4.98 -0.11 42.42 0.01 -4.75 0.01 0.41 0.03 0.70 6.19 1269.00 5.68 10 46.68 0.08 -6.04 -0.27 35.58 0.04 -6.09 0.08 0.59 0.12 0.35 6.99 991.70 5.48 11 53.50 0.11 -6.69 -0.32 28.05 0.06 -5.09 0.00 0.65 0.14 0.74 6.92 741.10 5.78 12 57.33 0.09 -5.90 -0.34 43.74 0.05 -5.03 -0.05 0.80 0.10 0.85 6.56 628.70 4.99 13 56.07 0.12 -7.81 -0.74 51.06 0.08 -5.06 -0.39 0.91 0.11 0.17 6.55 534.90 4.68 14 51.49 0.11 -5.84 -0.63 33.55 0.10 -4.41 -0.54 1.08 0.15 0.18 6.26 413.60 4.29 15 42.05 0.35 -5.98 -1.79 40.12 0.31 -5.09 -2.04 1.45 0.49 0.44 6.39 358.70 4.00 16 42.38 0.22 -5.35 -0.97 28.19 0.18 -3.56 0.76 1.67 0.35 0.41 6.12 416.20 4.02 17 41.10 0.29 -4.81 -1.75 24.00 0.19 -4.01 -0.68 2.17 0.39 0.85 6.57 347.60 4.05 18 44.79 0.37 -5.68 -2.38 39.08 0.41 -4.15 -2.04 2.60 0.75 0.26 6.35 310.00 3.97 19 44.56 0.32 -6.93 -0.66 27.27 0.36 -4.55 2.05 3.11 1.09 0.56 7.15 297.40 4.12 20 61.33 -0.10 -7.94 0.78 28.93 0.41 -5.71 2.08 4.24 1.57 1.15 9.55 200.90 4.38 21 54.01 0.54 -5.91 -1.48 44.31 0.60 -3.72 -3.76 5.23 2.24 0.29 8.24 180.30 4.90 22 73.78 3.73 -13.27 -14.75 20.48 1.99 -8.65 -8.18 7.78 3.65 -1.05 14.75 126.00 6.43 23 93.88 2.42 -17.53 -11.81 32.21 1.46 -6.16 -2.40 9.90 4.14 -1.28 13.11 35.72 8.72 24 75.31 5.13 -13.90 -17.62 33.97 3.55 -6.31 -3.95 12.34 6.74 -2.72 15.49 46.52 11.82 25 91.99 4.23 -14.19 -14.64 18.17 1.43 -6.74 -6.59 15.85 6.80 -1.21 22.90 17.06 12.46 Total 54.70 0.71 -7.35 -2.74 36.55 0.45 -5.00 -1.00 2.88 1.14 0.26 8.08 2081.00 6.17

Correlation Matrix of Table 2: Summary Statistics – Continued: Panel D: β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn β 1 1.00 β2 (0.79) 1.00 β3 (-0.94) (-0.86) 1.00 β4 (-0.82) (-0.99) (0.90) 1.00 β5 -0.37 (-0.50) 0.45 (0.51) 1.00 β6 (0.71) (0.95) (-0.82) (-0.94) -0.42 1.00 β7 (-0.71) (-0.73) (0.76) (0.74) 0.48 (-0.66) 1.00 β8 (-0.63) (-0.81) (0.65) (0.83) 0.36 (-0.71) (0.66) 1.00 E(cp) (0.85) (0.92) (-0.88) (-0.91) (-0.56) (0.86) (-0.62) (-0.73) 1.00 σ(Δcp) (0.84) (0.95) (-0.87) (-0.94) (-0.51) (0.92) (-0.64) (-0.74) (0.99) 1.00 E(re,p) -0.08 -0.09 0.09 0.09 0.03 -0.09 0.06 0.07 -0.09 -0.09 1.00 σ(rp) (0.87) (0.91) (-0.87) (-0.90) (-0.59) (0.80) (-0.74) (-0.76) (0.96) (0.95) -0.08 1.00 Size -0.25 -0.23 0.31 0.24 0.19 -0.25 0.19 0.20 -0.30 -0.27 0.03 -0.27 1.00 trn (0.69) (0.73) (-0.65) (-0.70) -0.13 (0.62) -0.45 -0.48 (0.67) (0.72) -0.07 (0.71) 0.14 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

42

Table 2: Summary Statistics – Continued: Panel E Global (ex. US) P β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) ( 100) (%) (%) (%) (%) ($Bn) (%)

1 55.00 0.02 -3.76 0.12 50.24 0.02 -4.23 0.13 2.16 0.12 0.22 7.75 957.70 4.11 2 58.09 -0.02 -3.63 1.01 42.43 -0.02 -4.15 1.24 2.12 0.31 0.49 6.38 1178.00 4.81 3 70.50 0.01 -4.94 -0.22 60.07 0.01 -5.32 -0.12 1.92 0.07 0.14 7.53 1208.00 10.05 4 52.79 0.05 -3.59 -0.54 38.57 0.06 -4.26 -0.63 2.41 0.84 0.38 6.62 981.00 4.40 5 57.10 0.03 -3.75 0.37 46.72 0.04 -4.23 0.42 2.10 0.25 0.02 7.69 1251.00 4.67 6 61.20 0.07 -4.17 -0.57 41.17 0.09 -4.39 -0.13 2.30 0.26 0.92 8.92 1103.00 4.42 7 44.47 0.06 -3.78 0.39 38.80 0.08 -4.69 0.04 2.06 0.44 1.43 7.02 1066.00 4.69 8 62.91 0.11 -4.32 0.16 48.30 0.14 -4.97 0.09 2.05 0.43 0.46 7.83 1108.00 4.54 9 64.13 0.04 -3.80 -0.13 63.35 0.06 -4.49 -0.19 2.19 0.20 0.12 7.51 1165.00 5.09 10 75.56 0.01 -3.45 -0.05 57.12 0.02 -3.99 -0.04 2.02 0.20 0.24 7.50 2020.00 5.31 11 61.10 0.03 -4.12 -0.15 53.96 0.03 -4.90 -0.04 2.12 0.15 0.30 7.21 1113.00 5.26 12 58.67 0.03 -3.45 -0.02 49.18 0.03 -4.20 0.08 2.06 0.13 1.02 7.31 1451.00 4.81 13 80.60 -0.04 -4.85 -0.13 60.77 -0.04 -5.37 -0.04 2.09 0.21 -0.10 9.13 1123.00 5.31 14 72.18 0.04 -4.40 -0.27 62.79 0.06 -4.91 -0.39 2.18 0.13 -0.07 8.30 1286.00 4.93 15 70.56 0.01 -4.43 -0.02 62.86 0.01 -4.90 0.01 2.06 0.08 0.34 8.51 1773.00 5.49 16 75.53 0.06 -4.35 0.72 62.53 0.08 -5.13 0.30 2.33 0.30 0.28 8.42 953.50 10.17 17 53.28 0.03 -3.39 -1.22 41.66 0.03 -4.06 -1.70 2.11 0.46 0.27 8.33 1390.00 15.08 18 62.02 0.17 -4.87 0.37 44.75 0.20 -5.65 4.98 1.97 1.62 0.59 8.10 953.50 8.01 19 52.18 0.05 -3.41 -0.18 45.94 0.08 -3.73 -0.06 2.35 0.53 0.45 7.52 991.70 5.00 20 62.32 0.03 -4.06 -0.20 40.29 0.04 -5.05 -0.23 2.18 0.08 0.28 8.12 1762.00 5.42 21 49.73 0.00 -3.27 0.25 36.54 0.01 -3.87 0.27 2.00 0.11 0.14 6.43 1080.00 5.78 22 65.79 0.03 -4.27 -0.07 56.95 0.03 -4.99 -0.16 2.09 0.10 0.60 7.37 1224.00 4.94 23 49.17 0.03 -2.73 -0.74 37.19 0.03 -3.00 -0.60 2.48 0.17 0.58 6.89 1219.00 5.61 24 59.25 0.03 -3.46 0.19 53.19 0.05 -3.95 0.48 2.46 0.19 -0.11 6.78 973.20 5.03 25 53.33 0.03 -4.06 -0.21 46.96 0.03 -5.06 -0.53 2.54 0.18 0.37 8.38 2317.00 5.15 Total 61.10 0.04 -3.93 -0.04 49.69 0.05 -4.54 0.13 2.17 0.30 0.37 7.66 1266.00 5.92

Correlation Matrix of Table 2: Summary Statistics – Continued: Panel E: β1 β2 β3 β4 β5 β6 β7 β8 E(cp) σ(Δcp) E(re,p) σ(rp) Size trn β 1 1.00 β2 -0.16 1.00 β3 (-0.65) -0.20 1.00 β4 0.13 0.05 -0.19 1.00 β5 (0.82) -0.20 (-0.54) 0.14 1.00 β6 -0.13 (0.99) -0.21 0.08 -0.16 1.00 β7 (-0.55) -0.24 (0.94) -0.24 -0.46 -0.24 1.00 β8 0.08 (0.54) -0.36 (0.57) -0.05 (0.54) -0.35 1.00 E(cp) -0.30 0.00 0.37 -0.24 -0.19 -0.02 0.34 -0.30 1.00 σ(Δcp) -0.17 (0.72) -0.17 0.08 -0.31 (0.72) -0.20 (0.69) -0.08 1.00 E(re,p) -0.02 0.02 0.01 0.00 -0.02 0.02 0.00 0.00 0.00 0.01 1.00 σ(rp) (0.54) 0.17 (-0.57) -0.25 0.38 0.17 (-0.51) -0.04 -0.08 0.02 0.00 1.00 Size 0.15 -0.26 0.03 -0.21 0.10 -0.30 -0.08 -0.28 0.07 -0.33 0.00 0.25 1.00 trn 0.12 0.06 -0.12 -0.29 0.06 0.06 -0.13 -0.07 -0.20 0.20 -0.01 0.27 -0.02 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

43

Table 3a: Commonality in Liquidity Innovations Around the World

Table 3 reports the estimates of the model:

The dependent variable is the innovation in illiquidity for region i in month t of year y. The independent innovations variable is the value of the global innovations in illiquidity in month t of year y .The innovations are predicted as the residuals of the following monthly regression using daily data within countries:

where represents the Amihud liquidity measure of stock i at day d in month m, D is a day of the week dummy. is the one-day-lagged value of ILLIQ. The regions and the world are constructed using monthly, value or equal weighted, data. The columns represent the four regions of the world. The sample consists of all common stock within financial developed countries in the regions of Asia-Pacific (ex. Japan), Europe, Japan and North America. In panel B, North America is reduced to Canada because the US is the used as an independent variable. Stock observations with daily volume greater than stocks outstanding are excluded from the sample. Daily returns in the bottom 0.1% or top 0.1% and stocks with monthly turnover or monthly Illiq in the top 1% where simultaneously dropped within each country. All used variables are measured in US dollars. T-statistics are reported between parentheses. Statistical significance coefficients are denoted with ***, ** or * for significance at the 1%, 5% or 10% level.

Table 3a: Commonality in Liquidity Innovation Value Weighted Equal Weighted

Panel A (1) (2) (3) (4) (5) (6) (7) (8) Asia-Pacific Europe Japan North America Asia-Pacific Europe Japan North America

World Innovation 0.01** 0.05*** 0.03* 0.11*** -0.03*** 0.06*** 0.02* 0.11*** (2.15) (8.96) (1.95) (6.60) (-3.34) (7.06) (1.65) (7.36)

Constant 0.03** 0.15*** 0.27*** 0.09** -0.13*** -0.19*** 0.13*** 0.01 (2.28) (9.86) (7.89) (2.12) (-5.81) (-9.25) (4.23) (0.29)

N. Obs. 214 214 214 214 214 214 214 214 Adj. R2 0.02 0.27 0.01 0.17 0.05 0.19 0.01 0.20 Panel B Asia-Pacific Europe Japan Canada Asia-Pacific Europe Japan Canada US Innovation 0.04* -0.01 -0.26*** 0.62** -0.16*** 0.11*** -0.23*** 0.19 (1.87) (-0.52) (-5.24) (1.99) (-4.46) (3.01) (-5.03) (0.61)

Constant 0.05*** 0.27*** 0.38*** 2.53*** -0.18*** -0.07*** 0.18*** 2.15*** (6.59) (27.34) (20.56) (21.91) (-16.78) (-6.27) (12.81) (22.77)

N. Obs. 214 214 214 214 214 214 214 214 Adj. R2 0.01 0.00 0.11 0.01 0.08 0.04 0.10 0.00

44

Table 3b: Commonality in Liquidity Innovations Around the World

Table 3b is an extension of Table 3a and it distinct between commonality between regional, non-local-non-US global and US factors. The factors are decomposed following the methodology of Jorion and Schwartz(1986).

and are calculated as the residuals of the regressions described above. T-statistics are reported between parentheses. Statistical significance coefficients are denoted with ***, ** or * for significance at the 1%, 5% or 10% level. Absolute correlation greater than 0.50 are reported within parenthesis of the correlation matrix. All used variables are measured in US dollars.

Table 3b: Commonality in Liquidity Innovation Value Weighted Equal Weighted

(1) (2) (3) (4) (5) (6) (7) (8)

Asia- Asia- Europe Japan Canada Europe Japan Canada Pacific Pacific non-local-non-US Global -0.07*** 0.11*** 0.00 0.02 -0.02 0.21*** 0.04** -0.02 (-4.43) (13.27) (-0.14) (0.33) (-0.75) (26.19) (2.30) (-0.27) US 0.26*** -0.10*** -0.26*** 0.81*** 0.06 -0.02 -0.25*** 0.60*** (4.21) (-3.38) (-4.90) (5.20) (0.92) (-1.19) (-5.40) (3.88)

Constant 0.18*** -0.02 0.38*** 1.26*** -0.03 -0.21*** 0.16*** 1.08*** (6.22) (-1.16) (16.32) (21.86) (-1.30) (-26.46) (9.99) (22.72) Adj. R2 0.12 0.45 0.11 0.10 0.00 0.76 0.12 0.06 N. Obs. 216 216 216 216 216 216 216 216 Correlation Matrix of Table 3b: Commonality in Liquidity Innovation (1) (5) Regional 1.00 Regional 1.00 World -0.24 1.00 World -0.04 1.00 US 0.22 0.18 1.00 US 0.06 0.11 1.00 (2) (6) Regional 1.00 Regional 1.00 World (0.65) 1.00 World (0.87) 1.00 US 0.02 0.28 1.00 US 0.07 0.12 1.00 (3) (7) Regional 1.00 Regional 1.00 World -0.12 1.00 World 0.09 1.00 US -0.33 0.33 1.00 US -0.33 0.17 1.00 (4) (8) Regional 1.00 Regional 1.00 World 0.02 1.00 World -0.02 1.00 US 0.34 0.00 1.00 US 0.26 0.00 1.00

45

Table 4:Regional LCAPM and Regional LCAPM with Global Factors

This table reports the estimated coefficients of different combinations of the LCAPM of Acharya and Pedersen (2005) in panel A,C,E and G. The world based LCAPM as developed in this paper is reported in panel B,D,F and H. The combinations of the LCAPM are derived from:

( ) ( )

The factor consists of and the factor is formed as . In column (1), (4) and (7), k is a constant and represents the monthly average turnover rate, in the other regressions k is estimated. All regressions are cross-sectional regressions based on 25 liquidity sorted portfolios based on Amihud’s (2002) liquidity measure of price impact. The sample consists of all common equity within the region and is cleaned following Ince and Porter (2006) and Karolyi, Lee and van Dijk as described in detail in the data handling section of this paper. Panel A is based on value weighted portfolios and an equal weighted market while panel B is based on value weighted portfolios and a value weighted world market, constructed from equal weighted regional markets. The t-statistics of the estimates are reported in parentheses. All used variables are measured in US dollars. The adjusted R2 is obtained from single moment cross-sectional regressions. Statistical significance coefficients are denoted with ***, ** or * for significance at the 1%, 5% or 10% level.

46

Table 4: Regional LCAPM and Regional LCAPM with Global Factors - Continued Panel A: Asia-Pacific (ex. Japan) LCAPM Estimates (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi)

β1 -1.69 5.21 2.63 3.85 -2.17* -2.47* (-1.60) (1.39) (0.67) (1.07) (-1.75) (-1.89) β2 -57.39** 9.26 (-2.05) (0.27) β3 -18.05 -26.94* (-1.21) (-1.82) β4 3.49 6.66 (0.72) (1.20) E(cp) 0.07 -0.10 0.07 -0.03 0.07 -0.48* - (-0.53) - (-0.16) - (-1.89) βnet -2.58** -1.10 -7.45* -3.90 -5.56 (-2.25) (-0.93) (-1.92) (-0.97) (-1.50) Constant 2.04*** 1.33 1.48** 2.06*** 1.50* 1.75** 1.27* 1.35* (2.77) (1.65) (2.05) (2.81) (1.84) (2.32) (1.82) (1.94)

Observations 4,534 4,534 4,629 4,534 4,534 4,579 4,534 4,534 R-squared 0.13 0.22 0.12 0.22 0.30 0.21 0.38 0.44 N. of groups 202 202 204 202 202 202 202 202 Table 4: Panel B: Asia-Pacific (ex. Japan) Global LCAPM Estimates (9) (10) (11) (12) (13) (14) (15) (16) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi)

β5 -0.96 4.79 2.59 4.94 -0.51 -0.26 (-1.09) (1.19) (0.65) (1.27) (-0.48) (-0.25) β 6 -76.50** 5.58 (-2.35) (0.12) β 7 -3.58 -0.54 (-0.28) (-0.04) β 8 5.90 4.86 (1.39) (0.92) E(cp) 0.07 -0.08 0.07 -0.03 0.07 -0.36 - (-0.46) - (-0.16) - (-1.09) βnet2 -1.45 -0.57 -5.83 -2.92 -5.72 (-1.58) (-0.57) (-1.44) (-0.73) (-1.47) Constant 1.37* 1.05 1.05 1.42* 1.01 1.32* 0.60 0.85 (1.81) (1.24) (1.39) (1.91) (1.21) (1.71) (0.73) (0.93)

Observations 4,534 4,534 4,629 4,534 4,534 4,579 4,534 4,534 R-squared 0.11 0.23 0.11 0.20 0.31 0.19 0.36 0.45 N. of groups 202 202 204 202 202 202 202 202 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

47

Table 4: Regional LCAPM and Regional LCAPM with Global Factors - Continued Table 4: Panel C: Europe LCAPM Estimates (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) Panel A: Acharya and Pedersen LCAPM β1 -0.75 -4.24 0.24 -2.55 -0.97 -0.98 (-1.40) (-1.51) (0.08) (-0.91) (-1.30) (-1.27) β2 -19.90*** 16.66 (-3.54) (0.68) β3 0.55 6.46 (0.06) (0.65) β4 -6.80** -0.27 (-2.41) (-0.04) E(cp) 0.04 -0.02* 0.04 -0.02* 0.04 -0.06 - (-1.68) - (-1.84) - (-1.02) βnet 0.73 -1.13** 4.90* -1.32 1.78 (1.40) (-2.09) (1.85) (-0.49) (0.68) Constant 0.07 1.36*** 1.07*** -0.21 1.35** 0.93** 1.20** 1.68*** (0.16) (2.71) (2.71) (-0.52) (2.57) (2.31) (2.19) (3.29)

Observations 5,050 5,050 5,100 5,050 5,050 5,050 5,050 5,050 R-squared 0.13 0.18 0.13 0.18 0.23 0.18 0.27 0.31 N. of groups 202 202 204 202 202 202 202 202 Table 4: Panel D: Europe Global LCAPM Estimates (9) (10) (11) (12) (13) (14) (15) (16) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) β5 -0.96 -1.56 -0.45 -1.44 0.28 -1.27 (-1.63) (-0.73) (-0.20) (-0.68) (0.35) (-1.61) β 6 -40.41** 80.17*** (-2.58) (2.85) β 7 12.26 6.06 (1.23) (0.62) β 8 -16.28*** 23.59*** (-3.32) (2.70) E(cp) 0.04 -0.03** 0.04 -0.03** 0.04 -0.07*** - (-2.09) - (-2.11) - (-3.04) βnet2 0.67 -1.75*** 2.16 -1.30 0.46 (1.24) (-2.83) (1.11) (-0.61) (0.24) Constant 0.12 1.73*** 1.16*** 0.06 1.69*** 1.13*** 1.07** 1.71*** (0.30) (3.61) (3.04) (0.16) (3.27) (2.99) (2.07) (3.03)

Observations 5,050 5,050 5,100 5,050 5,050 5,050 5,050 5,050 R-squared 0.12 0.17 0.12 0.18 0.23 0.18 0.28 0.34 N. groups 202 202 204 202 202 202 202 202 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

48

Table 4: Regional LCAPM and Regional LCAPM with Global Factors - Continued Table 4: Panel E: Japan LCAPM Estimates (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi)

β1 1.95 10.10 -14.32 6.33 2.78*** 2.74*** (1.55) (0.57) (-0.68) (0.36) (2.82) (3.01) β2 1,927.88 5,115.66** (0.94) (2.17) β3 250.69*** 290.71*** (2.65) (3.54) β4 42.45 57.77 (0.91) (1.19) E(cp) 0.10 0.36 0.10 -0.32 0.10 -1.70 - (0.72) - (-0.32) - (-1.13) βnet 1.89 2.30* -8.73 15.12 -5.02 (1.35) (1.90) (-0.50) (0.72) (-0.29) Constant -1.57 -1.91** -1.54* -1.09 -0.68 -1.04 -0.45 0.36 (-1.52) (-2.01) (-1.67) (-1.47) (-0.92) (-1.39) (-0.55) (0.41)

Observations 4,991 4,991 5,047 4,991 4,991 4,997 4,991 4,991 R-squared 0.08 0.20 0.06 0.22 0.29 0.22 0.33 0.38 N. of groups 202 202 204 202 202 202 202 202 Table 4: Panel F: Japan Global LCAPM Estimates (9) (10) (11) (12) (13) (14) (15) (16) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) β5 -1.83* 24.36** 16.51 23.29** -3.11* -1.87 (-1.89) (2.25) (1.35) (2.16) (-1.85) (-1.28) β 6 -844.66 -53.70 (-1.53) (-0.12) β 7 -4.55 7.86 (-0.29) (0.53) β 8 -59.98 5.38 (-0.88) (0.08) E(cp) 0.10 0.41 0.10 1.07* 0.10 2.41* - (0.85) - (1.82) - (1.81) βnet2 -1.75* -2.15** -25.40** -17.79 -24.61** (-1.88) (-2.48) (-2.45) (-1.54) (-2.38) Constant 0.65 0.78 0.67 1.14* 0.75 1.26** 1.08* 0.31 (1.05) (1.52) (1.11) (1.88) (1.52) (2.06) (1.84) (0.50)

Observations 4,991 4,991 5,047 4,991 4,991 4,997 4,991 4,991 R-squared 0.09 0.22 0.09 0.17 0.29 0.17 0.32 0.40 N. of groups 202 202 204 202 202 202 202 202 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

49

Table 4: Regional LCAPM and Regional LCAPM with Global Factors - Continued Table 4: Panel G: North America LCAPM Estimates (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) Panel A: Acharya and Pedersen LCAPM β1 -4.57** 15.48*** 3.77 13.10*** 1.41 1.68 (-2.57) (3.11) (0.68) (2.67) (0.51) (0.73) β2 -78.76 -10.64 (-1.08) (-0.14) β3 13.34 6.67 (0.92) (0.46) β4 -4.06 4.11 (-0.20) (0.20) E(cp) 0.06 -0.12 0.06 -0.13 0.06 -0.12 - (-1.58) - (-1.46) - (-1.28) βnet -4.51*** -0.68 -13.69*** -3.11 -11.03*** (-3.92) (-0.54) (-3.93) (-0.70) (-3.22) Constant 3.00*** 1.09 2.78*** 0.54 0.59 0.30 0.70 0.27 (4.69) (1.56) (3.37) (0.62) (0.77) (0.35) (0.79) (0.37)

Observations 5,001 5,001 5,051 5,001 5,001 5,001 5,001 5,001 R-squared 0.21 0.32 0.18 0.29 0.40 0.27 0.42 0.50 N. of groups 202 202 204 202 202 202 202 202 Table 4: Panel H: North America Global LCAPM Estimates (9) (10) (11) (12) (13) (14) (15) (6) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) E(rpi-rfi) E(rpi-rfi)-kE(cp) E(rpi-rfi) β5 -4.63*** 12.49*** 2.92 10.29*** -0.43 -0.13 (-2.62) (3.38) (0.66) (2.83) (-0.24) (-0.09) β 6 -44.78 5.89 (-0.85) (0.10) β 7 1.03 -1.72 (0.08) (-0.14) β 8 6.26 9.73 (0.52) (0.77) E(cp) 0.06 -0.12 0.06 -0.14 0.06 -0.08 - (-1.57) - (-1.45) - (-0.77) βnet2 -4.51*** -0.60 -11.56*** -2.41 -9.10*** (-3.97) (-0.49) (-4.17) (-0.63) (-3.33) Constant 3.71*** 1.15 3.48*** 0.84 0.58 0.54 0.97 0.67 (4.78) (1.36) (3.34) (0.95) (0.73) (0.61) (1.14) (0.90)

Observations 5,001 5,001 5,051 5,001 5,001 5,001 5,001 5,001 R-squared 0.21 0.32 0.17 0.27 0.39 0.26 0.40 0.51 N. of groups 202 202 204 202 202 202 202 202 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

50

Table 5: Regional LCAPM with Non-Local and US Factors

Table five shows the results of a cross-sectional test of the following equation:

( ) ( ) is the non-local-non-US unconditional LCAPM net beta for portofolio p calculated using the methodology of Jorion and Schwartz (1986). is the unconditional LCAPM net beta for portfolio p with the US as the regional market. Statistical significance coefficients are denoted with ***, ** or * for significance at the 1%, 5% or 10% level. Column (1)- (4) are based on equal weighted portfolios within the region and an equal weighted global market based on individual stocks, column (5)-(8) are based on value weighted portfolios and an value weighted global market based on individual stocks. Absolute correlation greater than 0.50 are reported within parenthesis of the correlation matrix. Table 5: Regional LCAPM with Non-Local and US Factors Equal Weighted Value Weighted (1) (2) (3) (4) (5) (6) (7) (8) Asia- Canada Europe Japan Asia- Canada Europe Japan Pacific Pacific VARIABLES E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- E(rpi-rfi)- kE(cp) kE(cp) kE(cp) kE(cp) kE(cp) kE(cp) kE(cp) kE(cp)

βnet,World ex. US 0.01 0.42*** -0.01 -0.18** -0.19 1.79*** -1.28 -1.47** (0.061) (4.744) (-0.048) (-1.979) (-0.382) (2.729) (-0.829) (-2.276) βnet,US 1.36** -1.57 0.76* -0.42 1.48** 0.87 0.67 -1.59* (1.988) (-1.438) (1.923) (-0.572) (2.274) (0.939) (1.565) (-1.695) Constant -0.25 1.41*** 0.31 -0.21 0.02 0.12 0.41 -0.73 (-0.387) (2.751) (0.817) (-0.512) (0.028) (0.253) (0.995) (-1.586)

Observations 4,534 4,952 5,050 4,991 4,534 4,952 5,050 4,991 Number of groups 202 202 202 202 202 202 202 202 R-squared 0.18 0.22 0.16 0.18 0.17 0.23 0.12 0.15 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

Correlation Matrix of Table 5: Regional LCAPM with Non-Local and US Factors net,World ex. US net,US p f p net,World ex. US net,US p f p β β E(r i-r i)-kE(c ) β β E(r i-r i)-kE(c ) (1) (2) βnet,World ex. US 1.00 1.00 βnet,US -0.20 1.00 (0.78) 1.00 E(rpi-rfi)-kE(cp) 0.00 0.04 1.00 0.11 0.07 1.00 (3) (4) βnet,World ex. US 1.00 1.00 βnet,US 0.25 1.00 0.48 1.00 E(rpi-rfi)-kE(cp) 0.00 0.02 1.00 -0.05 -0.03 1.00 (5) (6) βnet,World ex. US 1.00 1.00 βnet,US (0.52) 1.00 0.40 1.00 E(rpi-rfi)-kE(cp) 0.01 0.05 1.00 0.08 0.05 1.00 (7) (8) βnet,World ex. US 1.00 1.00 βnet,US 0.28 1.00 -0.25 1.00 E(rpi-rfi)-kE(cp) 0.00 0.01 1.00 -0.01 -0.03 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 6: Five Factor Model Europe

This table contains the estimates obtained from a five factor model based on the four factor model of Carhart (1997):

( ) The additional illiquidity factor is constructed using 25 equal or value weighted portfolios sorted on Amihud’s (2002) illiquidity factor. The factor is the difference in return between the most illiquid and liquid portfolios per month. Data are obtained from Kenneth French website. The estimates are based on cross-sectional regressions of the 25 portfolios. Column (1) and (3) include the liquidity factor (ILF) and column (2) and (4) represent the four factor model of Carhart (1997). Column (1)-(2) are based on value weighted portfolios and column (3)-(4) are based on equal weighted portfolios. Stock observations with daily volume greater than stocks outstanding are excluded from the sample. Daily returns in the bottom 0.1% or top 0.1% and stocks with monthly turnover or monthly Illiq in the top 1% where simultaneously censored within each country. T- statistics are reported between parentheses. The correlation matrix reports absolute correlations greater than 0.50 in parentheses.

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Table 6: Five Factor Model Europe - Continued: Panel A: Asia-Pacific (ex. Japan)

Value Weighted Equal Weighted (1) (2) (3) (4) p f p f p f p f Variables E(r i-r i) E(r i-r i) E(r i-r i) E(r i-r i)

Market-rf 0.48 2.14 0.80 -0.94 (0.739) (1.383) (1.043) (-0.430) SMB -0.48 -1.36** -0.64** -1.35** (-1.621) (-2.226) (-2.196) (-2.476) HML -0.39 0.84 -0.42 -0.20 (-0.919) (0.763) (-1.038) (-0.223) WML 0.67 0.65 -0.70 1.20 (1.546) (0.462) (-1.192) (1.113) ILF -1.21 0.21 (-0.662) (0.131) Constant 0.50 0.35 0.41 1.84 (0.886) (0.425) (0.571) (1.475)

Observations 4,629 4,629 4,629 4,629 R-squared 0.42 0.29 0.42 0.28 Number of groups 204 204 204 204 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

Correlation Matrix of Table 6: Five Factor Model Europe: Panel A: Asia-Pacific (ex. Japan) Value Weighted Equal Weighted (1) (3) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.02 1.00 0.05 1.00 SMB -0.06 -0.28 1.00 -0.06 (-0.57) 1.00 HML -0.03 0.07 0.39 1.00 -0.02 -0.08 0.03 1.00 WML 0.00 -0.18 0.18 0.10 1.00 -0.02 -0.08 0.10 0.11 1.00 ILF 0.00 0.06 -0.04 -0.12 0.10 1.00 -0.01 -0.13 0.20 -0.21 -0.04 1.00 (2) (4) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.01 1.00 0.02 1.00 SMB -0.05 -0.04 1.00 -0.06 (-0.52) 1.00 HML -0.01 -0.19 0.41 1.00 0.01 0.00 0.08 1.00 WML 0.00 -0.02 0.46 0.50 1.00 0.04 -0.15 -0.03 0.40 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 6: Five Factor Model Europe - Continued: Panel B: Europe

Value Weighted Equal Weighted (1) (2) (3) (4) p f p f p f p f Variables E(r i-r i) E(r i-r i) E(r i-r i) E(r i-r i)

Market-rf -1.06 -0.62 0.67 0.77 (-1.229) (-0.879) (0.651) (0.902) SMB 0.06 0.02 -0.89** -0.91*** (0.189) (0.051) (-2.542) (-2.988) HML 0.10 0.22 -0.55 -0.53 (0.231) (0.465) (-1.160) (-1.098) WML 1.14 0.65 1.71* 1.65* (1.561) (0.948) (1.919) (1.934) ILF 0.18 -0.21 (0.489) (-0.564) Constant 1.22*** 0.98** 1.07* 1.03** (2.725) (2.487) (1.954) (2.100)

Observations 5,100 5,100 5,100 5,100 R-squared 0.31 0.26 0.46 0.42 Number of groups 204 204 204 204 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

Correlation Matrix of Table 6: Five Factor Model Europe: Panel B: Europe Value Weighted Equal Weighted (1) (3) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf -0.01 1.00 -0.01 1.00 SMB 0.00 0.34 1.00 -0.02 (0.88) 1.00 HML 0.01 -0.46 0.04 1.00 0.01 -0.47 -0.47 1.00 WML 0.01 0.28 0.30 -0.10 1.00 0.01 0.03 0.01 0.18 1.00 ILF 0.01 -0.16 -0.26 -0.14 0.03 1.00 0.00 -0.24 -0.14 -0.32 0.08 1.00 (2) (4) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf -0.01 1.00 -0.01 1.00 SMB 0.00 0.15 1.00 -0.02 0.38 1.00 HML 0.01 -0.42 0.01 1.00 0.01 -0.24 (-0.57) 1.00 WML 0.01 -0.19 0.35 -0.05 1.00 0.00 (-0.63) 0.22 -0.05 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 6: Five Factor Model Europe - Continued: Panel C: Japan

Value Weighted Equal Weighted (1) (2) (3) (4) p f p f p f p f Variables E(r i-r i) E(r i-r i) E(r i-r i) E(r i-r i)

Market-rf 1.42 0.48 -2.74** -2.05 (0.967) (0.329) (-2.290) (-1.551) SMB 0.73 0.54 0.15 1.18* (1.538) (1.050) (0.298) (1.956) HML 0.79 0.60 -0.38 0.84 (0.933) (0.777) (-0.579) (1.297) WML 1.83** 1.84* -1.30* -2.64** (2.290) (1.941) (-1.711) (-2.118) ILF 1.34 2.14** (1.301) (2.550) Constant -1.07 -0.50 1.28* 0.47 (-1.386) (-0.589) (1.776) (0.557)

Observations 5,047 5,047 5,047 5,047 R-squared 0.39 0.34 0.47 0.41 Number of groups 204 204 204 204 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

Correlation Matrix of Table 6: Five Factor Model Europe: Panel C: Japan Value Weighted Equal Weighted (1) (3) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.00 1.00 0.00 1.00 SMB 0.00 (-0.69) 1.00 0.00 -0.43 1.00 HML 0.01 (-0.55) 0.19 1.00 -0.01 0.06 0.12 1.00 WML -0.01 0.11 0.27 -0.39 1.00 -0.02 -0.32 0.40 0.18 1.00 ILF 0.04 0.20 -0.24 0.12 -0.29 1.00 0.04 0.20 -0.03 0.03 -0.24 1.00 (2) (4) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.02 1.00 -0.01 1.00 SMB 0.05 -0.14 1.00 0.06 -0.13 1.00 HML 0.04 0.15 0.49 1.00 0.00 0.11 0.12 1.00 WML 0.02 -0.05 0.41 -0.16 1.00 -0.02 -0.31 0.29 0.40 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Table 6: Five Factor Model Europe - Continued: Panel D: North America

Value Weighted Equal Weighted (1) (2) (3) (4) p f p f p f p f Variables E(r i-r i) E(r i-r i) E(r i-r i) E(r i-r i)

Market-rf 1.24 -0.73 0.01** 2.15* (1.602) (-0.633) (2.473) (1.927) SMB -1.65* -2.46** -0.00 -0.87 (-1.733) (-2.122) (-1.614) (-1.018) HML 1.71** 2.96*** 0.02*** 0.27 (2.305) (2.910) (3.187) (0.373) WML 0.19 -0.27 -0.01 -1.10 (0.148) (-0.210) (-0.884) (-0.940) ILF -2.66 -0.02*** (-1.596) (-3.616) Constant 0.37 1.11* -0.24*** -0.55 (0.640) (1.657) (-10.655) (-0.718)

Observations 5,051 5,051 5,098 5,098 R-squared 0.45 0.40 0.69 0.39 Number of groups 204 204 204 204 t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1

Correlation Matrix of Table 6: Five Factor Model Europe: Panel D: North America Value Weighted Equal Weighted (1) (3) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.03 1.00 0.02 1.00 SMB -0.02 (-0.53) 1.00 -0.03 (-0.76) 1.00 HML 0.03 (0.74) -0.30 1.00 0.02 (0.71) -0.41 1.00 WML -0.01 -0.28 0.21 -0.45 1.00 -0.02 -0.18 0.44 -0.16 1.00 ILF -0.05 0.02 0.00 -0.03 0.04 1.00 -0.04 0.01 0.02 0.00 0.21 1.00 (2) (4) p f f p f f E(r i-r i) Market-r SMB HML WML ILF E(r i-r i) Market-r SMB HML WML ILF p f E(r i-r i) 1.00 1.00 Market-rf 0.01 1.00 0.04 1.00 SMB -0.07 -0.06 1.00 -0.05 -0.04 1.00 HML 0.06 0.43 -0.34 1.00 0.05 0.40 (-0.60) 1.00 WML -0.05 0.24 0.41 -0.47 1.00 -0.04 0.17 (0.82) -0.49 1.00 Absolute correlations greater than 0.50 are reported in parentheses.

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Figure 1: Standardized Innovations in Normalized Market Illiquidity from 1995-2012. Figure one shows the standardized innovations in normalized market illiquidity. The illiquidity measure used is the Amihud illiquidity measured which is normalized with the equation:

30.00)

where is the normalized illiquidity, Amihud’s illiquidity measure and is the capitalization ratio of the market portfolio, calculated with the market portfolios capitalization at the end of month t-1 and the initial capitalization of the market portfolio at the end of December 1994. The innovations are calculated as the residuals of the following regression:

in which is computed using equal weights for all stocks in the market. The normalized illiquidity innovations are standardized by dividing it by its standard deviation. Panel A: Asia-Pacific (ex. Japan) Panel B: Europe

Panel C: Japan Panel D: North America

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