The Pricing of Liquidity Risk Around the World

Transcription

1 Master Thesis The Pricing of Liquidity Risk Around the World Author: D.W.J. Röttger Studentnumber/ANR: u / Master Programme: Master in Finance, CFA track Faculty: Tilburg School of Economics and Management Submission Date: Date of Defense: Supervisor: dr. A. Manconi Second Reader: dr. B. Melenberg

2 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 stock 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. 2

3 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. 3

4 Table of Contents Abstract Introduction Theory Development What is liquidity and how to measure liquidity Liquidity characteristics Flight to liquidity Data and Methodology Data Data Sources Data Filtering: Methodology Illiquidity Measure Normalized Amihud Liquidity Measure Autocorrelation of the Liquidity Level Innovations calculation: Commonality in Liquidity Innovations: Distinction between non-local effects and local effects Portfolio Construction Acharya and Pedersen (2005) LCAPM LCAPM with Non-Local Factors Fama-MacBeth Cross-Sectional Regressions Testing Asset Pricing Models Empirical Results Liquidity persistence Liquidity risk is linear and positive priced Commonality in liquidity risk The flight to liquidity Conclusions

5 6. Bibliography Tabulations

6 1. Introduction On 22 August 2013 NYSE Arca, an exchange operator, announced an issue processing trades. Later that day trading in NASDAQ stocks 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 investor 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 volatility. 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 risk factor? The dataset used in this thesis includes all the common stock of 23 developed countries between 1995 to 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 6

7 (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 investors 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 long 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. 7

8 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 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., 8

9 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 momentum 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

10 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: 10

11 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 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 stock market 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 beta 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. 11

12 3. Data and Methodology 3.1. Data 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 Additional data on the relative importance of the sample such as GDP, number of listed firms and market capitalization 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 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 crosslistings 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. 12

13 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 DIVIDENDS 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

14 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 shares outstanding 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 99 th percentile, a daily return lower than the 0,1 th percentile or greater than the 99,9 th percentile or a monthly liquidity greater than the 99 th 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 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) 14

15 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 Methodology 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

16 described in section 3.2.2, section 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 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 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) 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

17 persistent, but time varying through innovations, the stocks in the dataset can be sorted in 25 portfolios on the basis of their liquidity level 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 And the Russian default, October 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

18 ( ) ( ) ( ) (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 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

19 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 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 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

20 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

21 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 stock exchange 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