Asset Pricing with Liquidity Risk, Evidence from the Dutch Stock Market

Asset pricing with liquidity risk, evidence from the Dutch stock market

Bo Spiljard

Master thesis for the study: Finance, Tilburg University

Abstract

In the recent financial crisis the liquidity of the stock market has changed intensively and the CAPM seems not to work at all in periods of low liquidity. In this paper a relative new theory is tested on the Dutch market in a period that includes the recent financial crisis, the liquidity- adjusted CAPM. This new model is evolved from the CAPM by combining three theories of liquidity into the CAPM. As expected applying this model to the Dutch stock market, there is a premium for holding illiquid securities above liquid securities. However the betas are not statistical significant, the premium is 0.69% a year.

Content

1. Introduction ...... 3 2. The CAPM ...... 4 2.1 The evolution of the CAPM ...... 4 2.2 Adding liquidity ...... 8 3. The liquidity-adjusted CAPM ...... 10 3.1 The channels of the Liquidity-Adjusted CAPM...... 11 3.2 Related theory to the Liquidity-Adjusted CAPM ...... 13 4. The Dutch stock market ...... 16 4.1 Data and Methodology ...... 17 4.2 Why the CAPM does not work ...... 20 4.2.1 Fama-Macbeth ...... 22 5. Empirical research ...... 24 6. Results from the cross-sectional regressions ...... 34 7. Additional results ...... 37 7.1 Testing the model with the Fama-Macbeth 2-step regression...... 37 7.2 Removing crisis data ...... 40 7.3 Portfolios created based on the MCAP ...... 42 7.4 Portfolios created on basis of last year return ...... 44 7.5 Alternative measure of illiquidity ...... 46 8. Summary and Conclusions ...... 50 Appendix ...... 52 References ...... 53

1. Introduction

The recent financial crisis that started in 2008 caused a shortage of liquidity, this crisis is therefor also known as the liquidity crisis. The first downward shock on the stock market caused flight-to-quality, which was caused by investors that wanted to invest in relative safer investments (like T-bills and commodities) and selloff their risky investment. Together with the flight-to-quality also flight-to-liquidity occurs, since most of the risky investments contain more illiquid securities (and less risky investment contain more liquid securities).

The market is constantly changing, sometimes even with rigorous developments like in the recent financial crisis. The CAPM-theory states that more risk has to be compensated for a higher return or vice versa. However in periods with low liquidity on the market this is not always the case, which is also shown in figure 1 by testing the CAPM on the period of the recent financial crisis. Acharya and Pedersen developed a model in 2005 that takes care of periods of low liquidity with the “Liquidity-adjusted CAPM”. The theory combines three existing liquidity theories with the standard CAPM-model. They developed this model to indicate that asset prices are affected by liquidity risk and commonality in liquidity.

In this paper both the standard CAPM and the liquidity-adjusted CAPM are tested on the Dutch market between 1993 and 2013. This period is chosen so both the models could be tested on a period including and excluding the recent financial crisis. There is just one stock market in the Netherlands, and all registered stocks on the NYSE Euronext Amsterdam are included to test the models on the complete Dutch stock market. First the standard CAPM- model is tested for the complete market and this model is also tested with the Fama- Macbeth test. Further the liquidity-adjusted CAPM model is tested for the complete market, and also this model is tested with the Fama-Macbeth test. As additional test the portfolios are sorted on some alternative methods, and another additional test is done for adding an extra variable.

Before actually discussing the main model, first an overview is given of the origin of the CAPM. In the third part the liquidity is added to the CAPM-model, which converts the model to the liquidity-adjusted CAPM. In the fourth part the Dutch market is described and the data that is used to test the model is explained. As additional test it is described why the

CAPM does not hold by testing the general CAPM-model on the Dutch market. In the fifth part the liquidity-adjusted CAPM model is executed on the Dutch market and in part six these results are described. In the seventh part some additional tests are performed on the liquidity-adjusted CAPM-model and in the final part the summary and conclusions are given.

2. The CAPM

In the academic world of Finance every time if a new theory is found, other academics try to proof the theory is either wrong or right (and try to improve the model). But in this same world something strange is going on, a theory found in 1965 called the “Capital Asset Pricing”-Model (CAPM-model), which is already proven many times it does not work, is still the most used theory in academic papers, being lectured at school, and even the most used tool in corporations (Graham and Harvey, 2001). The main reason for this is because of its simplicity and because it is the broadest adopted theory in real life applications (Fama and French, 2004). Researchers in Finance continuous try to find the missing link for predicting the expected returns, and the CAPM is one of these attempts. The attempt to predict the expected returns with the CAPM is based on the theory that increasing risk has to be compensated by increasing the expected returns. There are some more accurate alternatives that try to predict the expected returns, like the 3-factor model (Fama & French, 1993), but most use the CAPM-model as its base to build the model. The model discussed in this paper, the “Liquidity-adjusted CAPM”, is as it is clear in its name also using the CAPM as a base. The model is found by Acharya and Pedersen in 2005 and they added some channels of liquidity to predict the expected returns.

2.1 The evolution of the CAPM

One of the basic theories in Finance is the Modern Portfolio Theory (MPT). This theory is found by Harry Markowitz in 1952 (Markowitz, 1952), and believes there is a relation between expected return and the risk (volatility). The aim of this theory is either to maximize return for a given level of risk, or to minimize risk for a given level of return. The theory is very basic and could only be executed on very small or moderate portfolios (how bigger the

4 portfolio, how harder it is to implement). The goal of this theory is to calculate the optimal weights of each of the assets in the portfolio.

This is done by first creating all possible combinations of weights for all combination of securities that are used within the portfolio. Then calculate the risk and return of each combination and remove all inefficient combinations. What is left is called the efficient frontier. Now by using the indifference curves (the personal utility curve of the investor) the optimal portfolio for each individual investor could be obtained. Following the efficient frontier to the left gives efficient portfolios for more risk-averse investors, and following the efficient frontier to the right gives efficient portfolios for investors that want to take more risk for a higher return.

In order to apply diversification in the MPT-theory, the Capital Asset Pricing Model was found by two researchers separately: Sharpe in 1964 (“Capital Asset Prices: A theory of market equilibrium under conditions of risk”) and Lintner in 1965 (“The valuation of risk assets and selection of risky investments in stock portfolios and capital budgets”). Together they created the Capital Asset Pricing Model (CAPM) by extending the MPT-model. The CAPM implicates that an investor demands an expected return equal to the risk-free rate plus a risk premium for the amount of risk taken. The model assumes an individual investment has both systematic risk (market risk) and non-systematic risk (firm specific risk). The non-systematic risk could be decreased by diversifying the portfolio. The systematic risk could not be decreased by diversifying the portfolio, this is the overall risk retrieved by the market and is called the beta (β) component. The beta-component introduced in this model is the start as using the beta as a risk-factor. The con of the CAPM-model is that it needs some exceptional assumptions (i.e. for the whole holding period the number of securities keeps stable, the market is perfectly competitive, the markets work frictionless and information is costless and simultaneously available to all investors, and there are no taxes). The beta coefficient describes how the returns of a security (or portfolio) react on changes in the market as a whole. This gives the next regression model:

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Various researchers proof the CAPM-model is not a very strong model. One prominent model to test the CAPM-model is the “Fama-Macbeth”-model developed by Fama &

Macbeth (1973). Their finding is that the relationship between stock returns and beta is not as strong as Sharpe (1964) and Lintner (1965) stated. With their model they find that the alpha and the beta are not significant and that the slope is less steep than the market risk premium, and also not significant.

By combining the efficient frontier with the risk-free rate, the Capital Market Line (CML) is constructed. The CML is a straight line, starting at the risk-free rate and through the point where it is tangent with the efficient frontier. If each investor is rational, they all would invest in a portfolio on the CML. For a risk averse investors in a portfolio on the CML close to the risk-free rate and for a risk loving investor in a portfolio on the CML right from the tangent portfolio (going short). Each point on the CML equals the maximum sharp ratio. Sharpe found its measure initial in 1975 as a measure for the performance of mutual funds, which was called the reward-to-variability ratio. 15 years later researchers still used this measure to a wider variation of applications, and not exclusively for mutual funds. There was no official name for this measure, until Sharpe (1994) decided to make its measure official by naming it the “Sharpe-ratio” and publish the theory. The target of the Sharpe-ratio is that the investor could find how well he is compensated in returns for the amount of risk taken. The measure is in general used by comparing two (or more) securities; the security with the highest Sharp ratio gives a better proportion of return for the amount of risk taken.

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After retrieving the market risk premia, the security market line (SML) could be drawn. The SML puts the beta against the expected return in a graph and has the same shape as the CML, it states that the return of each security has the same beta. In a perfect world all securities should align on the SML. But in reality most of the securities do not align the SML, in theory securities below the SML are overvalued (negative alpha) and securities above the SML are undervalued (positive alpha).

Since the CAPM is found, various researchers try to proof the model does not hold. One piece of prominent evidence is the test of Black, Jensen and Scholes (1972). They tested that by creating portfolios based on the beta, and after that re-estimating the betas for these portfolios these are not (close to) one anymore. This theory shows that there is a less strong

6 relation between the systematic risk and the returns of the portfolios (and in some cases the systematic risk is even lower for portfolios with higher returns and higher for portfolios with lower return). To perform this test, first the betas of each of the securities are retrieved, than portfolios are formed based on these betas. If the CAPM holds, the alpha for each of these portfolios should be close to zero and the beta should be close to one. In their results they found negative alphas for large beta portfolios and positive alphas for small beta portfolios. Another prominent piece of evidence is found by Black (1993). He mimicked the CAPM by executing the initial CAPM theory of Sharpe and Lintner, but using a longer time window. His finding is that the CAPM does not work well over the last couple decades. He tested the theory with data between 1966 and 1991, and this gives a downward relation between the average risk premium and the betas of the portfolios.

However there is an extended body of proof that the CAPM-model is not perfect, the model is still widely used in business- and research applications as a base model. Like said before this is because the model is relative easy to implement and to understand (“everyone knows how to use it”). This is pointed out by Graham and Harvey (2001), who performed a survey on CFOs of the US market. They found that the CAPM (or equal models) are the most used method to calculate the cost of equity.

The CAPM-model is called a single-factor model, because it only has one specific risk value (the beta). The beta measures the non-systematic risk and could not be diversified away. It measures how the security responds to changes in the market. A beta close to one means the return of a security moves the same as the market. A beta close to zero means the return of a security moves uncorrelated as the market and a beta bigger than one means is more volatile than the market. In a perfect world, securities with a high beta have bigger returns than the market, but also incur more risk (Black, 1993).

A successful attempt to improve the CAPM-model is the 3-factor model developed by Fama and French (1993), which adds two risk factors to the beta of the CAPM-model. So in this model there are three variables that together try to explain the return of a security (or portfolio) with the returns of the market as a whole. The added variables are the SMB (small minus big) and HML (high minus low) factors (Fama & French, 1993) which both separate tend to outperform the market. The SMB-ratio states that small firms tend to outperform

7 large firms, this is also called the “small firm effect”. The HML-ratio states that companies with a high book-to-market ratio (value stocks) outperform companies with a low book-to- market ratio (growth stocks). By combining these two factors with the CAPM-model, the Fama-French model is created.

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Carhart added a fourth factor to the model, the momentum factor (Carhart, 1997). Carhart found that assets with high returns in the past three to twelve months will continue to perform well in the short run. On the other side, assets that perform poorly in the past three to twelve months will continue to perform poorly in the short run. By combining this momentum factor with the Fama-French three factor model, the Carhart four-factor model is created.

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2.2 Adding liquidity

Liquidity on the security market is a measure of the ability to convert the security into cash, without affecting the price of the security. A security that is relative more liquid could be easier converted into cash while less value is lost on the trade. The more liquid the traded security is, the less this trade affects the price of this security. Illiquidity is the opposite of liquidity, and the more illiquid the security is, the harder it is to sell the security without losing value. In case the security is illiquid a single trade could affect the price of the security, and how more illiquid the security is, the more this trade affects the price. There is no observation or measure for (il)liquidity, but it could be approached by using proxies. In this paper the proxy for illiquidity is created by taking the average values per month for the absolute returns divided by the volume traded each day.

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Holding illiquid securities over liquid securities gives a liquidity premium. This liquidity premium could be explained by multiple reasons (De Jong & Driessen, 2013). The premium could be a compensation for the cost of trading the security, or a compensation for the correlation between the security and the whole market. An alternative explanation could be that there is a difference between the trading horizons among investors, which is caused because securities that are more illiquid are in general traded by investors with increasing investment horizons. This means that securities that are relative more illiquid are being traded less, which causes less sharing of the risk and the expected returns are higher.

A distinction could be made between the liquidity of a single security and the liquidity of the total market (of a product). The market and a single security on this market do not have to be in the same state of liquidity, it could be that the market is very liquid while a particular security on this market is very illiquid (for example a stock that is hardly traded in an liquid market). The most liquid security is cash itself, since this value is used to measure the liquidity. Illiquidity is the opposite of liquidity and also in this case a security does not have to be in the same state of illiquidity as its total market, it could be that the market is very illiquid while a particular security in this market is very liquid (for example a stock that is traded constantly in times of a liquidity crisis). An example of a market that is illiquid from itself is the non-listed real-estate, this market is not transparent since there is no trading activity on the open market (there is no open and complete supply and demand market) (Hoesli & Lekander, 2008).

Liquidity is not something new, and researchers already try to exploit theories based on liquidity to predict the expected returns. For example Amihud and Medelson (1986) found a link between liquidity and the stock returns, where investors require a higher expected return for an asset if this asset has a higher bid-ask spread. Another example is from Ibbotson, Chen, Kim and Hu (2008) who tested the liquidity by using glamour stocks. Glamour stocks are popular stocks that have a high growth rate and are relative more expensive than non-glamour stocks because the demand is higher (so glamour stocks could be seen as a liquid security).

3. The liquidity-adjusted CAPM

Like stated in the introduction, Acharya and Pedersen developed a model based on liquidity to predict returns for securities. The model is only recently developed in 2005, which makes it a relative new theory. In this Liquidity-Adjusted CAPM model the beta is decomposed into the standard market beta and three different channels of liquidity. Two of the channels were already developed theories by other researchers, and Acharya and Pedersen combined these channels together with a third channel into the CAPM to create a complete new model.

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The base model of the liquidity-adjusted CAPM model exists out of four separate betas. Each of the betas exists out of a regression between the market and the portfolios, and different combinations between returns and illiquidities. To prevent for autocorrelation first the returns and illiquidities are transformed into innovations, which is performed by retrieving the residual terms from an AR(2)-regressions for each of the portfolios (including the market portfolio). The innovations are the differences between the actual values in the time series, and the predicted values retrieved from the AR(2)-regressions.

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3.1 The channels of the Liquidity-Adjusted CAPM

The first channel is found by Chordia, Roll, and Subrahmanyam (2000) and has the least impact of the three channels. They state that there is a covariation between the individual asset liquidity and the overall liquidity of the whole market, also called commonality in liquidity. The expectation is that there is a positive relationship between this channel and the expected excess returns, because investors would like to be compensated for holding stocks with decreasing liquidity when the liquidity on the market decreases. Acharya and Pedersen found a return premium of 0.08% for the first channel by testing their model on the U.S. market.

When a new theory is found other researchers try to reject or accept it. If they think the theory does not hold they try to improve or invalidate it, and if they think the theory does hold they give additional proof the theory is working, by for example testing it on another market or on another period. This also happened for the theory of each of the channels. For the first channel Hasbrouck and Seppi (2001) found small proof that by using several proxies for the liquidity (i.e. bid-ask spread) this will explain the trade impact. Coughenour and Saad (2004) test the effect of liquidity with the specialist1 firms on the NYSE. They found that the individual stock liquidity co-varies with the specialist portfolio liquidity, unique from information, causing co-variation with market liquidity. Brockman, Chung, and Perignon (2009) tested a wide number of stock exchanges on commonality in liquidity using the intraday spreads and show that changes in the global spreads have significant effect on changes in liquidity at the exchange level. Kamara, Lou, and Sadka (2008) tested how the commonality moves over time in the U.S. market, and find that this commonality increases significantly for large firms but decreases significantly for small firms. Karolyi, Lee, and van Dijk (2011) also test the commonality in liquidity over time, but also how it varies across countries. They found that commonality is greater in countries that suffer from high market volatility, and if the trading activity is more correlated.

The second channel is original founded by Pastor and Stambaugh (2003); they state that a return premium is paid if a security has high returns if the total market is illiquid. In

1 Specialists are member of the exchange company who act as the market maker, also called the traders on the floor, these specialists primarily price the stocks.

11 this case investors are willing to accept lower returns if a particular stock has higher returns when the market is illiquid. The expectations is that there is a negative relationship between this channel and the expected excess returns, since investors would like to be compensated for holding high return stocks when the overall market is illiquid. Acharya and Pedersen found a return premium of 0.16% for the second channel by testing their model on the U.S. market. In a perfect world each investor holds the market portfolio, and if the total market is illiquid it is relative hard to sell securities, which could affect the price of the security. In this case investors are more likely to pay higher prices for securities that give higher returns. In the higher price a compensation for this illiquidity is incorporated, which is also called the illiquidity premium. This theory is already tested positive in many studies, but also rejected by some studies.

Vayanos (1998) found that the transaction costs of frequently traded stocks decreases, while the transaction costs of infrequently traded stocks increases. But they also found that the price of a stock decreases when the transaction cost of a relative more liquid stock decreases. Liu (2009) tested the theory of the liquidity risk premium for a longer period, namely from 1926 to 2005, and also tested two subsamples within this period (data split on 1963). The results in this paper show that the liquidity risk premium is strong for both periods, and that this premium is even stronger than the most used premia like the size, value, and momentum factors from the Carhart four-factor model. Korajczyk and Sadka (2008) tested different proxies for the liquidity measures that try to explain the liquidity premium. They found that there is commonality across assets and also that the different liquidity measures are correlated with each other. Additional they found that liquidity shocks are neutralized over time. Watanabe and Watanabe (2008) tested that stock returns are sensitive to fluctuations in liquidity over time. They found different responses on the returns across two different states of liquidity beta (high liquidity beta that gives lower returns versus low liquidity beta that gives higher returns). Asparouhova, Bessembinder, and Kalcheva (2010) use microstructure noise as a proxy for illiquidity, and test if this noise is already priced in the cross-section of stock returns. They found that the upward bias is larger when illiquid securities are used in the sample. Lou and Sadka (2010) test how illiquidity is priced in different periods of crisis. They found that in these periods the liquid stocks under-

12 perform on illiquid stocks. In their research they try to highlight that not only the level of liquidity is important, but also the liquidity risk is important (the liquidity beta).

The third channel is added by Acharya and Pedersen themselves and states that investors are willing to pay a premium for a security that is liquid when the market return is low. In a perfect world each investor is holding the market portfolio. Investors are willing to pay a premium for securities that are liquid if the market returns are low. Expected is that there is a negative relationship between this channel and the expected excess returns. This reaction is caused by investors that are willing to pay a premium for stocks that become more liquid in a down-market. Acharya and Pedersen found a return premium of 0.82% for the third channel by testing their model on the U.S. market.

Compared to the other channels this last channel is only limited tested by other researchers, because the theory on this channel is relative new. Brunnermeier and Pedersen (2009) find flight to quality when funding becomes difficult. Investors decrease the will to buy securities with a liquidity provision, especially for capital intensive assets (i.e. high margin assets). Wagner (2011) shows an implementation for this channel: if many investors need to sell their securities at the same time (i.e. like fire-sales in the recent financial crisis), prices of the securities are under pressure. In this case investors are willing to sell their stocks at a lower price and they are willing to pay a premium to sell their securities. This is also called liquidation risk and is an important element for this channel.

3.2 Related theory to the Liquidity-Adjusted CAPM

As mentioned before the Liquidity-adjusted CAPM theory was originally found by Acharya and Pedersen in 2005. They tested the model on the US stock market from July 1st 1962 until December 31st 1999, specifically on the stocks listed on the NYSE and the AMEX. The US stock market is the best choice to test a model, since it is a big and extremely diversified stock market, however there was only weak evidence the model gave the results they expected. The first channel gives a premium of 0.08%, the second channel gives a premium of 0.16%, and the third channel gives a premium of 0.82%. So in total the liquidity risk explains about 1.1% of the cross-sectional returns. After the model of Acharya and Pedersen was published, many researchers tested this theory on alternative markets and for

13 alternative securities. Some researchers like Chai, Faff, and Gharghori (2010) use alternative methods to approach the (il)liquidity, but most of the theories were based on the liquidity measure that Acharya and Pedersen also used. But as Chai, Faff, and Gharghori (2010) concluded, most of the (il)liquidity proxies are correlated to each other. However they found some exceptions because some proxies have different reactions to the trading characteristics, this is because these proxies only capture a particular element of the (il)liquidity. Many researchers have faith in this Liquidity-adjusted CAPM approach and believe the theoretical model could have a relative good approach to predict the expected returns. What followed is that this model is extensively tested and that researchers try to find further evidence that this model could be used to approach the expected returns. For example Hagströmer, Hansson and Nilsson (2011) reproduced the data (stocks listed on the NYSE and AMEX) of the original test but increased the time window to 1926 - 2010 (36 year before and 11 year after the original data). They used the efficient spread developed by Holden (2009) as a proxy for the measure of liquidity and sorted the portfolios on illiquidity. He found an average annual illiquidity premium of 1.55%, which is split to 1.15% caused by the illiquidity level and 0.40% caused by the three different channels of illiquidity.

However many papers give a more in depth analysis by testing the liquidity-adjusted CAPM on just the stock market for one country. Also some papers tested the theory on other financial products than stocks or over multiple countries. Lee (2011) tested the theory on a big sample of developed and emerging markets, and he proved the model reacts differently in each market. For the European market Bank, Larch, and Peter (2010) tested the theory on the German stock market. They find that expected illiquidity has a positive impact on the returns while unexpected illiquidity has a negative impact on returns. Hwang and Lu (2007) used the model on the stock market of the United Kingdom, and they find robust results if there are distress factors. In the Asian markets Li, Sun and Wang (2011) tested the theory on the Japanese stock market. The results on the Japanese market are not as consistent as in the test of Acharya and Pedersen. And Chen, Li, and Wang (2011) tested the theory on the Chinese stock market and find that the expected returns of a security is dependent on the cost of expected liquidity. They also find that the liquidity-adjusted CAPM fits the realized returns better than in the various traditional CAPM models. In Oceanië Chai, Do, and Vu (2012) tested the theory on the Australian stock market and find evidence that liquidity risk

14 is related to the cross-section of the Australian equity returns. For their calculations they used several proxies as measures of illiquidity. Minovic and Zivkovic (2010) tested the stock market for the frontier markets, they used Serbia as testing ground and conclude it is a good tool for approaching the expected return.

The Liquidity-adjusted CAPM theory is not only tested on the stock market, but also on markets for several other financial products. Jacoby, Theocharides, and Zeheng (2008) tested the theory on the corporate bond market in the US and find evidence that liquidity risk is already priced in the corporate bond market. Panyanukul (2010) tested the theory on sovereign US dollar bonds in emerging markets and found that both the liquidity level and the channels of liquidity risk affect the factors of the expected excess returns. The theory is also tested for the CDS market in Europe by Lesplingart, Majois, and Petitjean (2012). They find that the level, risk, and spillover of liquidity are already priced in the CDS market. However they also found that the liquidity risk is not priced in the premia of the CDS. They state that the impact of liquidity would improve in the future since the market for CDS is becoming much more transparent (because of the standardization of CDS laws in the European markets). Banti, Phylaktis, and Sarno (2011) tested the theory on the currency market. They find proof that there is a strong common component in liquidity across currencies after applying the theory on 20 US dollar exchange rates. They conclude that the liquidity risk is already priced in the currency market and that the liquidity risk premium on this market is around 5% per annum.

As an addition, in this research the liquidity-adjusted CAPM is tested on the Dutch stock market (the NYSE Euronext Amsterdam). Expected is that the test of the liquidity-adjusted CAPM on the Dutch stock market gives positive results, since equal stock markets with same characteristics also give positive results.

As an addition on the theory the model is tested on how well the theory works in illiquid periods, like in the recent financial crisis that started in 2008. To perform this test the recent financial crisis is isolated from the data and it is tested how well the liquidity is an indicator to predict the returns in the period of the recent financial crisis. Expected is that by performing the regular CAPM-model by including the recent financial crisis, the results are worse than when this period is excluded. And expected is that by performing the Liquidity-

15 adjusted CAPM including the recent financial crisis the results actually increase compared to when the recent financial crisis is excluded, since the model automatically corrects for the illiquidity of the market.

The Liquidity-adjusted CAPM is a model, and is a simplification of the real world, and because of this some assumptions have to be made. The most important assumption for this model is that the investor liquidates its portfolio every period (Novy-Marx, 2003), which is unrealistic in real life applications for the average investor.

4. The Dutch stock market

Acharya and Pedersen used data of the New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX) from the United States stock market to test their model. By using the companies registered on these two stock exchanges, a diversified chunk of companies is used. Now the AMEX is acquired by the NYSE, so both the stock exchange fall now under the NYSE. The NYSE has a total of about 28002 listed companies with a market capitalization of about $18 trillion, which are enough companies to have a diversified number of companies to test a model on. In the Netherlands there is just one stock market and before 2000 all the listed companies in the Netherlands were listed on the Amsterdam Stock Exchange. In 2000 the stock exchange of Amsterdam merged with the stock exchange of Brussels and Paris into the NYSE Euronext. The Amsterdam Stock Exchange after this merger is called the NYSE Euronext Amsterdam and on January 2013 there were only 145 companies listed. There are some differences between the companies and investors between the European stock market and the US stock market. First of all there are many companies listed on the NYSE that are the result of a cross-listing between the listing of another country’s market and the NYSE, which results that the companies that are listed on the NYSE are from all over the world. Also the ownership of public companies in European market is relative more concentrated than for public companies on the US market (Pagano and Roell (1998)). Besides this there is a size inequality between the NYSE and the European markets. In each of the European markets there are only limited firms listed, and also the average market capitalization for

2 http://www.nyse.com/content/faqs/1050241764950.html

16 each firm is smaller compared to the firms listed on the NYSE (most of the European markets only contain a couple very large public firms and a lot of relative smaller firms).

By testing the Liquidity-adjusted CAPM a small adjustment have to be made. In the original research by Acharya and Pedersen they created 25 portfolios, which is possible because of the large amount of firms listed on the NYSE. However since the number of firms listed on the NYSE Euronext Amsterdam, creating 25 portfolios would result in only a couple firms per portfolio. So instead of 25 portfolio there are 10 portfolios created to increase the number of firms per portfolio, just like Chai, Do, and Vu (2012) did for the Liquidity-adjusted CAPM test on the Australian market (the Australian market has even a smaller amount of public firms listed on their local market).

4.1 Data and Methodology

The Netherlands has a well-developed stock market and the period between January 1st 1993 and December 31th 2012 is used to test the model. Data is retrieved from the “NYSE Amsterdam Euronext”, which contains all listed companies in the Netherlands. Daily data is retrieved from Datastream for the price of the stocks, market value of the firms, turnover by volume of shares sold, the bid price of the stock, the ask price of the stock, and the amount of shares outstanding for the firms. Only common stocks of the NYSE Euronext Amsterdam are included in the sample. To calculate the illiquidity measure, stocks are excluded if there was no trading activity at t or t-1. To keep data manageable for the liquidity measure only the months are included that have at least 15 trading days in that month, because if there is too little trading data the liquidity measure of the stock is not accurate enough (Pastor and Stambaugh, 2003).

The daily returns are retrieved from the return index in Datastream. The advantage by using this return index is that the dividend payouts are incorporated into the price, since the returns are based on the daily prices adjusted for the dividend of the stocks. In this method the dividends are reinvested to create the return index.

The market capitalization is retrieved by multiplying the number of shares outstanding at time t by the price of the stock at time t. The market capitalization is used as a proxy for the

17 size of the company. Higher (lower) market capitalization means the company is larger (smaller).

In Datastream the bid- and ask prices are only reported since March 29th 1996. These bid- and ask prices are used to calculate the bid-ask spread of the stocks at time t. The bid-ask spread is needed to normalize the illiquidity, and because of the limitation of having only spread data from March 29th 1996 till December 31th 2012, the normalization is based on data within this period.

The turnover by volume is the amount of shares traded at time t. This value states how many units of the stocks are sold (and thus also automatically bought) at time t and is used to define the illiquidity of the stocks for each month.

The turnover measures the percentage of the total amount of shares traded in each month. It is a measure to calculate how long it takes till all shares of a company are traded (so when the turnover is 100%). This measure transforms the volume data into a relative measure, which makes the value comparable with other firms. Firms that are bigger and mostly are also more known have a higher turnover, since the frequency of trading in these firms is higher.

After retrieving daily data for all companies listed on the Amsterdam stock exchange for 20 years, the summary statistics are collected. In table 1 both the firm average and firm-year averages are given for the most important used variables in this paper. Between 1993 and 2013 there are 276 firms listed with a total of 3443 of firm-year data. The average monthly illiquidity level over all firms is 0.91%, the average market capitalization is €8.20 million and the average excess daily return is 0.51%. By testing the CAPM and liquidity-adjusted CAPM before and after the recent financial crisis, the data is split in 2008. The first sub-period is the period before the recent financial crisis, and the second sub-period is the period of the recent financial crisis. In the first sub-period the illiquidity is 0.89% and average daily returns

18 are 0.48%. The average market capitalization is €8.31 million and the average number of shares outstanding is 38.58 thousand. For the second sub-period, the period of the recent financial crisis, the average daily excess returns are -1.44% and average illiquidity is 1.47%. The average market capitalization is €3.51 million and on average 184.88 thousand of outstanding shares.

Table 1 Summary statistics. This table presents the summary statistics of all the base data used. The return are based on the daily returns in percentages, the excess return are the daily return minus the daily risk-free rate in percentages, the MV is the market value of the capital, the VO is the turnover by volume, NOSH is the number of shares outstanding in thousands, the MCAP is the market capitalization in millions of dollars, and the illiq is the average illiquidity of the stock in percentages. For each of the items the number of observations, the average (mean), minimum (min), maximum (max), standard deviation (SD), the 25th percentile value (25%), the 50th percentile value (median), and the 75th percentile value (75%).

Based on firm average 1993 – 2013 # obs mean min Max SD 0.25 Median 0.75 Return 276 0.53% -60.07% 160.00% 12.06% -0.54% 0.00% 0.70% excess return 276 0.51% -60.08% 159.98% 12.06% -0.56% -0.02% 0.68% MV 276 1390.90 0 105647.50 7152.27 31.31 122.73 446.08 VO 276 1.23 0 53893.60 4716.43 4.30 52.45 549.90 NOSH (*1.000) 276 44.77 0 2081.72 0.16 1.79 6.16 22.30 MCAP(*1.000.000) 276 8.20 0 1370.00 90.50 0.02 0.07 0.32 Illiq 276 0.91% 0.00% 33.37% 3.05% 0.01% 0.04% 0.26%

Based on firm average 1993 – 2008 # obs mean min Max SD 0.25 median 0.75 Return 269 0.49% -60.07% 160.00% 12.20% -0.53% 0.00% 0.65% excess return 269 0.48% -60.08% 159.98% 12.20% -0.55% -0.02% 0.64% MV 269 1330.66 0 105647.50 7220.44 31.28 121.99 411.04 VO 269 1119.54 0 53893.60 4684.61 3.00 46.20 453.80 NOSH (*1.000) 269 38.58 0 2081.72 147.13 1.77 5.94 21.10 MCAP(*1.000.000) 269 8.31 0 1370.00 91.60 0.01 0.07 0.29 Illiq 269 0.89% 0.00% 33.37% 30.51% 0.01% 0.04% 0.26%

Based on firm average 2008-2012 # obs mean min Max SD 0.25 median 0.75 Return 138 -1.43% -14.29% 50.00% 5.28% -3.23% -1.82% 0.00% excess return 138 -1.44% -14.30% 49.99% 5.28% -3.24% -1.83% -0.01% MV 138 3650.29 0.03 90413.81 11804.94 64.42 394.52 1536.33 VO 138 1494.44 0.00 30979.40 4187.03 3.70 74.90 497.95 NOSH (*1.000) 138 184.88 0.04 3547.03 470.27 10.00 33.98 85.80 MCAP(*1.000.000) 138 3.51 0 90.40 11.40 0.07 0.43 1.54 Illiq 127 1.47% 0.00% 41.09% 4.68% 0.00% 0.05% 0.77%

The minimum and maximum values are mainly driven by outliers, this could be observed by the extreme positive and negative return and illiquidity values. As expected the average excess return in times of crisis are negative and much lower than when there was no crisis. Also the illiquidity is much higher in times of crisis, which could be explained by the lower trading on the stock market.

4.2 Why the CAPM does not work

Before starting the empirical research, the standard CAPM is tested to see if this theory holds on the 20 year data of the Netherlands. If the theory works well, all securities must be aligned on the Security Market Line (SML). The SML is a solid line from the risk-free rate through the excess market return, which has respectively a beta of 0 and a beta of 1. The CAPM is tested by sorting the stocks into portfolios based on the market capitalization, and theoretical the CAPM should still hold for these portfolios. The risk-free rate is retrieved from Datastream and is used to convert the daily returns into daily excess returns. The daily risk-free rates are retrieved by dividing the annual risk-free rate each day by the amount of trading days in that year. The excess market returns is the weighted sum of all active companies on the Dutch stock market for daily data. The portfolios are created based on the initial market capitalization for each month. Portfolio 1 includes firms with the smallest 10% market capitalizations and portfolio 10 includes firms with the biggest 10% market capitalizations. The returns for each of the portfolios are based on the equally weighted cross-sectional average returns of the daily data for the accompanying portfolio. The betas of the portfolios are retrieved by regressing the excess returns of the portfolio by the excess market returns, where the portfolio returns are the average weighted daily returns for each of the portfolios and the market returns are the average daily returns for all firms. If the theory holds, the betas retrieved from each portfolio must be aligned on the SML. The results are described in figure 1, with the beta on the x-axis and the average excess daily returns on the y-axis. The CAPM is tested for the full period (graph 1), but also tested for the sub-period before the financial crisis (first sub-period, graph 2), and for the sub-period after the recent financial crisis (second sub-period, graph 3). The financial crisis roughly started in the second quarter of 2008 in the Netherlands, and expected is that returns after the financial crisis decreased.

Figure 1 Original CAPM test. This graph represents the original CAPM results for the full period (1993-2013), the second graph for the first sub-period (1993-2008) and the third graph for the second sub-period (2008-2013). In the graph the ten portfolios, its trend line (blue line) and the security market line (SML, red line) are included. The portfolios are created based on the market capitalization, portfolio 1 contains firms with the smallest MCAP and portfolio 10 contains firms with the biggest MCAP. The beta is on the horizontal axis and the average excess daily returns in percentage on the vertical axis. The beta is based on the beta retrieved by regressing the excess return by the market returns for each of the portfolios. The average excess returns are the averages monthly returns for each of the portfolios over the whole period.

0.09%

0.07%

0.05%

0.03%

0.01%

-0.01% 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Average Excess Daily Returns Daily Excess Average -0.03%

-0.05% Beta

0.09%

0.07% 0.05%

0.03%

0.01%

-0.01% 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.03% Average Excess Daily Returns Daily Excess Average -0.05% Beta

0.09%

0.07%

0.05%

0.03%

0.01%

-0.01% 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.03% Average Excess Daily Returns Daily Excess Average -0.05% Beta

That the original CAPM-theory does not hold could be concluded since none of the portfolios lays exactly on the SML. If the CAPM would hold, the trend line of the portfolios should be close to the SML. The portfolios in graph 1 have relative steady results; all betas are between 0.75 and 1.2, and the average daily excess returns are all around 0.03%. By adding a trend- line through the portfolios, the trend is almost horizontal (and even a bit decreasing). For a second test data is removed that includes the recent financial crisis, the results are somewhat improving compared to the test that includes the full data. The trend-line in this second graph is sloping up and is matching the SML relative more than in the test with the full data. Combining the results of these two graphs means that by conducting the CAPM on the crisis period, the results should be even worse than the test with the full data, which could also be observed in graph 3. The average excess returns in the financial crisis are close to zero and even negative for many stocks. This could also be observed in graph 3, where some of the portfolios are below the zero percent line, even while some of these betas are close to one. The SML in graph 3 is much flatter than in the other 2 graphs, which concludes that the overall market also performs worse. Also the distance between the portfolios and the SML (the alpha measure) is bigger than in the other graphs, which is caused by the negative excess returns for some of the portfolios. This concludes that the CAPM is not as strong as the theory predicts by testing it on the Dutch market between 1993 and 2013, and also that the result in the period of the recent financial crisis in the Netherlands is even worse.

4.2.1 Fama-Macbeth

To test how well the beta explains the excess returns, the Fama-Macbeth 2-step regression is performed on the standard CAPM-model. In the first step the pre-ranking betas are retrieved by regressing the excess returns per firm on the excess returns of the market for each period. Then for each year the stocks are ranked based on the pre-ranked betas to create 10 portfolios. For the second step the post-ranking betas are retrieved by regressing the weighted excess returns for each portfolio on the excess market return. For the last step each year the excess returns are regressed with the post-ranking betas to retrieve a time- series of the slopes. If the CAPM-theory does not hold, the average slope over the years is

22 close to zero. The more the average slope deflects from zero, the more the beta explains the stock returns.

Table 2

Fama-Macbeth time-series results in a table. The results in this table are data points of the time-series regressions retrieved from the Fama-Macbeth 2-step regression based on the standard CAPM on the Dutch market between 1992 and 2012. The left column represents the years and the right column represents the slopes for each of the years between 2002 and 2012. Regressions performed for a certain year are based on data of the last 10 year of data. In the last two rows the average slope over all years and the standard error is given).

Year Slope 2002 -0.15092 2003 0.646089 2004 0.079016 2005 0.176703 2006 -0.00323 2007 -0.02727 2008 -0.30243 2009 0.253116 2010 0.100863 2011 -0.25691 2012 -0.06493 Average 0.040919 Standard Error 0.058359

Figure 2

Fama-Macbeth time-series results in a graph. This graph represents the time-series of the slopes over time from table 2 but sketched in a graph. The years are on the horizontal axis and the value of the slope is on the vertical axis.

0.8

0.6

0.4

0.2

0 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 -0.2

-0.4

Each year between 2002 and 2012 a slope is retrieved based on this Fama-Macbeth test, which represents the time-series of the slopes. The average over these years gives a slope which is closely to zero, this means that the CAPM-theory does not hold (based on the specifications used in this model). In table 2 and figure 2 detailed information is represented of the time-series of the Fama-Macbeth slopes over the years. In some of the years the slopes are seem to be relatively high, like in 2003. However for the scale that is used these values are still relatively close to zero. In the graph could be observed that the overall values are between 0.2 and -0.2, and together with an average value of 0.041 it could be observed that the slopes are close to zero, which concludes that the theory does not work and that the beta does not explain the stock returns as was predicted in the CAPM-theory. From the Fama-Macbeth regression also the standard error is retrieved. This standard error is corrected for autocorrelation and measures how well the sample (the created portfolios) explains the real life data. How smaller the standard error is, how better the slopes are a representation of the truth. In this case the standard error is 0.058, which is a relative big value compared to the individual slopes.

5. Empirical research

In order to test the Liquidity-adjusted CAPM, first the illiquidity and the various betas have to be estimated. To retrieve these values for each security the monthly excess returns and normalized illiquidities are calculated. Based on the illiquidity of last year the 10 testing portfolios are created. The market portfolio is created based on equal weights of the active stocks each year. By using these values the innovations in illiquidity and in excess returns could be retrieved by retrieving the residuals for the AR(2)-regressions for all time-series per portfolio (including the market portfolio). After the betas are retrieved the Liquidity-adjusted CAPM model could be tested, together with various other regressions. The empirical research will extensively follow the five steps of the theory on the liquidity-adjusted CAPM that Acharya and Pedersen created, with some additions of theories of other researchers.

First step is to calculate the illiquidity, for which the daily absolute returns and trading volume (in millions) are needed for each firm. Then divide the absolute returns with the trading volume for each day, and sum this value for each firm each month to create

24 weighted monthly data. Now divide this monthly data by the amount of trading days in that month to retrieve the adjusted average value of returns divided by the trading volume, which is the illiquidity. However this illiquidity measure is hard to work with because it is measured in a percentage for each dollar, and to make it more usable it has to be normalized into costs per dollar. Normalization is accomplished by transforming the illiquidity into a value that contains stationary values, and this is implemented in two methods. In the first method the theory of Chalmers and Kadlec (1998) is followed to convert each of the portfolios in such a way that the normalized illiquidity for size-decile portfolios has about the same level and variance as the half-spread. To implement this theory first the data is dropped that does not contain bid or ask prices. As mentioned before Datastream only reports the Bid and Ask price after March 29th 1996, so all data before this date is dropped. Now the percentage value of the bid-ask spread is retrieved by subtracting the bid-ask spread by the price of the stock. Expected is that there are only positive values, however also some negative values are created. These negative values are dropped, together with an upper bound of 1 (which is still relative high) to discard the outliers. The next step is to regress the bid-ask spread on the adjusted illiquidity (the illiquidity adjusted for the inflation, which is also explained in the second method). The values retrieved in this regression to normalize the illiquidity are an alpha of 0.17 and a beta of 0.21. In the second method the illiquidity is smoothen over time by adjusting the illiquidity for inflation. The illiquidity-measure is adjusted by dividing the ratio of market capitalization of last month by the market capitalization at the end of the first month available in the data (in this case January 1ste 1993). To take care of the outliers in this process the maximum value is capped by a value of 30%.

( )

Both the illiquidity and normalized illiquidity are based on monthly data and are retrieved for each firm separate. By multiplying the illiquidity with the weights of the portfolios, and take the sum of all firms for each portfolio in each month (including for the market portfolio), the weighted illiquidities for each op the portfolio are retrieved. For graphical clarification of the illiquidity and normalized illiquidity, the evolvement over time of the illiquidities and normalized illiquidities are represented in figure 3. In these graphs it could be observed that the normalized illiquidity is a transformation from the illiquidity.

Figure 3 Illiquidity and normalized illiquidity over time. The upper 2 graphs give the evolvement of illiquidity over time for all data between 1993 and 2013. The years are on the horizontal axis and the illiquidity in percentage is on the vertical axis. The first graph gives the evolvement of illiquidity over time for one of the portfolios (in this case portfolio 5). The second graph gives the evolvement of illiquidity over time for the market portfolio. The lower 2 graphs give the evolvement of normalized illiquidity over time for all data between 1993 and 2013. The years are on the horizontal axis and the normalized illiquidity in cost per dollar is on the vertical axis. The third graph gives the evolvement of the normalized illiquidity over time for one of the portfolios (in this case portfolio 5). The fourth graph gives the evolvement of the normalized illiquidity over time for the market portfolio.

0.6

0.4

0.2

0 94 94 95 95 96 96 97 98 98 99 99 00 01 01 02 02 03 03 04 05 05 06 06 07 08 08 09 09 10 10 11 12 12

2.5 2 1.5 1 0.5 0 94 94 95 95 96 96 97 98 98 99 99 00 01 01 02 02 03 03 04 05 05 06 06 07 08 08 09 09 10 10 11 12 12

3.17

2.17

1.17

0.17 94 94 95 95 96 96 97 98 98 99 99 00 01 01 02 02 03 03 04 05 05 06 06 07 08 08 09 09 10 10 11 12 12

5.17 4.17 3.17 2.17 1.17 0.17 94 94 95 95 96 96 97 98 98 99 99 00 01 01 02 02 03 03 04 05 05 06 06 07 08 08 09 09 10 10 11 12 12

It is not a complete shift over the axis, but the spikes could be noticed in both graphs (this could be observed in the conversion between the illiquidity and the normalized illiquidity for the graphs of portfolio 5). By comparing the normalized illiquidity of portfolio 5 with the market portfolio it is shown that there is a (slightly) positive correlation. For portfolio 10 (not reported) the positive correlation is much bigger, which means both graphs move in the same direction.

Second step is to create the market portfolio and ten testing portfolios. The market portfolio is based on equally weights, and is based on all firms active in each period. To create a fair market portfolio, shares with a value below €5 and above €1000 at the start of the month are dropped, and only periods of firms that have at least 15 days return in that month are applied.

Acharya and Pedersen (2005) used in their study 25 portfolios based on all firms active on the NYSE and AMEX, which represents a large part of the U.S. stock market. The Dutch stock market is substantial smaller than the U.S. stock market, and if 25 portfolios are created each portfolio only consist out of a couple stocks. In an equal study of Chai, Do and Vu (2012), they tested the liquidity-adjusted CAPM on the Australian stock market (an even smaller stock market than the Dutch stock market), and they performed the model with only 10 portfolios. Their results were consistent with the results of Acharya and Pedersen. Consistent with the paper of Chai, Do and Vu (2012), each year 10 portfolios are created within the Dutch stock market. Portfolios are created based on the last year illiquidity, and stocks with a price at the beginning of the year below €1 and above €1000 are dropped from the sample. Also to make sure there is enough data, years are dropped that have less than 100 days of trading in the last year. After creating the portfolios, each stocks characteristic is multiplied by the weights to get the weighted portfolio values of these characteristics (i.e. illiquidity, excess returns). The weights are based on equally weighted portfolios, and not on value weighted portfolios since some stocks are heavily over weighted which affect the results negatively. The portfolio characteristics are described in table 2 as the summary statistics of the portfolios.

Third step is computing the innovations for the returns and for the normalized illiquidities. Innovations are used because autocorrelations of the returns and normalized

27 illiquidities is relative strong. The use of innovations over the normal time-series data because of the autocorrelation gives more liable results in the regressions. The innovations are the predicted values retrieved from an AR(2)-regression for both the returns and the illiquidities, and are used as input for retrieving the betas.

The innovation for the excess returns are retrieved for each of the portfolios, including the market portfolio and is described as: ( ) . This residual term is retrieved by using an AR(2)-regression on the returns of last 2 months.

( ) ( )

For the normalized illiquidity innovations, the same expressions are used, but changing the returns into the normalized illiquidities. For each of the portfolios (including the market portfolio) this term is described as: ( ) . This residual term is retrieved by an adjusted AR(2)-regression on the normalized illiquidities of last 2 months. This is to prevent

to predict changes in the -term, so the term is used for the non-lagged and both lagged expressions.

̅̅̅̅̅̅̅̅ ( ) ̅̅̅̅̅̅̅̅ ̅̅̅̅̅̅̅̅ ( ) ( )

Figure 4

Innovation over time of the market illiquidity. The innovations of the normalized illiquidities are retrieved by calculating the residuals over a daily AR(2)-regression. The daily innovations are retrieved and sketched in a graph to get the evolvement of the innovations over time. The years are on the horizontal axis and the innovations are on the vertical axis. The innovations are the differences between the realized illiquidities on the market and the predicted illiquidities by the AR(2)-regression.

2.5 2 1.5 1 0.5 0 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 -0.5 -1 -1.5 -2

To get a graphical understanding of the innovations, the time-series of daily residuals of the normalized illiquidities for the market is sketched in Figure 4. There are two periods of relative extremely volatility, which means there was a “liquidity crisis”. A liquidity crisis happens if the market has lack of liquidity, which is caused by the lack of trading of shares in the market (in this case in the Netherlands). The first period of extreme volatility is around 2000, which also familiar as the “dot-com crisis”. The second period of extreme volatility is around 2008, when the consequences of the recent financial crisis in America arrived in the Netherlands.

Fourth step is to calculate the four betas ( ) for each portfolio by using the innovations retrieved in step 3. The beta is retrieved by regressing the time-series of innovations for the portfolio on the time-series of innovations for the market. For each beta a different combination is used of either the innovations of excess returns or the innovations of normalized illiquidity, in this way there are 4 combinations possible, each for one of the betas.

The first beta looks like the original CAPM beta that regresses the portfolio returns by the market returns. The difference with the original beta is that in this case the innovations instead of the normal returns are used. For the Liquidity-adjusted CAPM the first beta

( ) is , and is retrieved by regressing the excess return innovations in a portfolio ( ) by the excess return innovations for the whole market. Expected is that these betas are positive and are statistical significant.

( ) The second beta is , and is retrieved by regressing the normalized illiquidity ( ) innovation in a portfolio by the normalized illiquidity innovation for the whole market. Expected is that this value is positive and increasing over the portfolios, since the amount of illiquid stocks in the portfolio is increasing with the portfolios. Also is expected that the values are relative small and that the riskiness of the portfolio increases with the rise in illiquidity, which means a higher risk premium is required for portfolios with higher illiquidity.

( ) The third beta is , and is retrieved by regressing the excess return innovation ( ) in a portfolio by the normalized illiquidity innovation for the whole market. Expected is that the values are negative and decreasing deeper negative over the portfolios, and that the values are relative small.

( ) The fourth beta is , and is retrieved by regressing the normalized illiquidity ( ) innovation in a portfolio by the excess return innovation for the whole market. Expected is that the values are negative and decreasing deeper negative over the portfolios, and that the values are relative small.

The net beta is a total beta created by using the four betas together. Beta 1 and beta 2 both have a positive influence on the model and beta 3 and beta 4 have a negative influence on the model. So to create the net beta, beta 1 and beta 2 are summed and beta 3 and beta 4 are subtracted. The total of these betas represents the risk premia of the whole model.

Table 2 described the characteristics of the betas, return, normalized illiquidity, turnover and market capitalization of each of the portfolios. Portfolios are created based on the illiquidity of last year and are based on equal weighted portfolios, as described above. The portfolios are created based on illiquidity, which explains the positive relation between the portfolios and the raising normalized illiquidity. Portfolio 1 contains the firms with the lowest average normalized illiquidity, with a level of 0.17%. Portfolio 10 contains firms with the highest average normalized illiquidity, with a level of 8.72%. The portfolios in between contains of firms which the illiquidity is increasing with the value of the portfolio. By sorting stocks with illiquidity this also causes relations between the portfolios and other characteristics. On average firms in portfolio 1 have lower excess returns, are bigger (higher market capitalization, which is a proxy for size of the company) and have a higher turnover, while on average firms in portfolio 10 have higher excess returns, are smaller and have lower turnover.

The results from table 2 could be explained from a theoretical point of view. Expected is that bigger firms are more well-known with relative more public information, which most

30 investors favor instead of companies with less public information. And how relative more the shares of a company are traded how higher the turnover becomes. Also bigger firms have relative less volatile share prices than smaller firms, which causes lower excess returns, while the more volatile smaller firms have higher excess returns. The results from table 2 are in line with the theoretical expectations. Portfolio 1 has an average excess return of 0.59% per month, an average market capitalization of €17.9 million, and an average turnover of 26.13% per month (which means once every 3.83 months all shares are turned over). Portfolio 10 has an average excess return of 1.65% per month, an average market capitalization of €0.364 million and an average turnover of 2.91% per month (which means once every 34.36 months all shares are turned over). The average excess return has a positive relation with the portfolios, and both the market capitalization and turnover has a negative relation with the portfolios. It also attracts attention that portfolio 10 has relative extreme values in each of the characteristics, the difference between portfolio 9 and 10 is relatively large compared with the other differences between two portfolios. This tenth portfolio contains mainly stocks that are very illiquid and thus are relatively limited traded, also the stocks within this portfolio are relatively small and the returns seems to be relatively high compared with the other portfolios (even doubled from portfolio 9). The t-statistics of the betas are almost all very high and are almost all statistical significant to the 5% or even 1%. For the first beta even all values are statistical significant, and for the other 3 betas more than three-quarters of the values are statistical significant.

For the four betas (all multiplied with 100 in table 2) the relations with the portfolios are somewhat mixed. Beta 2 and beta 4 both have pretty strong relations with the portfolios like expected. Beta 2 starts with a value close to zero in portfolio 1 and increases consistently over the portfolios to a value of 4.59 in portfolio 10. Beta 4 starts also with a value close to zero in portfolio 1 and increases negatively to -8.86 in portfolio 10. For the betas 1 and 3 the relations with the portfolios are not that strong, beta 1 gives a somewhat solid value of approximately 0.55. Beta 3 gives a relation that starts decreasing from portfolio 1 and starts increasing from portfolio 5. The net beta however gives a slightly positive relation with the portfolios. Keep in mind that all values are multiplied by 100 for graphical clarifications, which makes the values for beta 2, beta 3, and beta 4 relative small.

Table 3 Characteristics of the illiquidity portfolios. For each of the ten portfolios the four betas, net beta, and the most important characteristics are retrieved that are used for the cross- sectional regressions. Portfolios are revised each year for 20 years (1993-2012). First the values of market beta and the three liquidity betas are given for each portfolio. In brackets the t-statistics are described, which are almost in all cases statistical significant to the 1%- level. Also for each of the portfolios the monthly excess returns ( ( )) in percentages, the normalized illiquidity ( ( )) in percentages, market capitalization (used as a proxy for size) in millions of Euros, and turnover in percentages are given.

( ) ( ) Size (MCAP) Turnover Portfolio (*100) (*100) (*100) (*100) (*100) (%) (%) In Mln € (%) 1 50.03 0.00 -4.86 -0.00 54.89 0.59 0.17 17.900 26.13 (12.96) (-2.46) (5.16) (2.35) 2 57.37 0.00 -5.63 -0.00 63.00 0.05 0.18 4.806 25.07 (12.64) (-0.13) (5.13) (-0.07) 3 61.92 0.03 -4.46 -0.02 66.43 0.69 0.21 1.588 24.36 (13.58) (2.93) (3.83) (-0.44) 4 54.25 0.08 -4.34 -0.11 58.78 0.82 0.24 1.594 21.77 (13.69) (5.10) (4.31) (-1.3) 5 51.82 0.16 -4.05 -0.27 56.30 0.65 0.37 0.634 17.68 (11.95) (3.70) (3.87) (-1.23) 6 53.35 0.36 -4.67 -0.36 58.73 0.64 0.56 0.922 11.11 (12.03) (5.67) (4.38) (-1.03) 7 54.39 0.65 -4.83 -1.12 60.99 0.61 0.95 1.140 8.72 (11.67) (9.17) (4.36) (2.70) 8 55.35 1.20 -4.83 -1.94 63.31 0.84 1.91 1.242 9.41 (12.16) (10.58) (4.40) (2.76) 9 49.67 2.42 -5.80 -5.40 63.30 0.43 3.85 0.244 3.71 (10.13) (13.10) (5.33) (4.47) 10 58.59 4.59 -5.75 -8.86 77.80 1.65 8.72 0.364 2.91 (8.09) (10.66) (3.69) (3.35)

Fifth step is to perform cross-sectional regressions on the betas and firm characteristics using the ten portfolios, to test the empirical fit of the liquidity-adjusted CAPM. The portfolios are created based on the firm illiquidity of last year, so each portfolio has the characteristics of a certain level of illiquidity. In this part different cross-sectional regressions are tested, each with a different set of input. In each regression the average normalized illiquidity is applied as the -variable, apart for some of the control regressions. The -variable is in this case the average holding period, which is a measure for when all shares are turned over once. Monthly turnover with a value greater than 1 is dropped, since these might not be representative turnover values (i.e. takeover). The average turnover in the sample is 0.0983, which means in each month 9.83% of all the shares are turned over.

This corresponds to a standard holding period of months. However in real life applications each investor has an alternative holding period. To take care of these alternate holding periods, the characteristics could be multiplied by the amount of standard holding periods that fits in the holding period of the investor. To retrieve the holding characteristics of this investor, the values (i.e. return) have to multiplied by this multiplier. For example if the standard holding period is one month and the holding period of an investor is three months, the multiplier is 3.

For the first couple cross-sectional regressions just the single betas are used to observe the effect of the beta. For example the cross-sectional regressions by just applying the first beta

looks like: ( ) ( ) (for the other betas just the beta-coefficient changes in the regression). Also a regression is performed with only using the net beta,

which is the base regression in the paper: ( ) ( ) . To check the results also cross-sectional tests are performed by regressing the net beta with beta 1:

( ) ( ) and also by replacing the net beta by the four separate betas: ( ) ( ) . As addition some other combinations of betas are added to the graph to check the results. The results of these cross-sectional regressions are described in the next part.

Table 4

Correlations for illiquidity portfolios This correlation-table gives the correlations between each of the four betas. Portfolios are created based on the illiquidity of last year and are reassigned each year between 1993 and 2013.

beta1 beta2 beta3 beta4 beta1 1.000 0.112 -0.034 -0.073 beta2 1.000 -0.671 -0.996 beta3 1.000 0.697 beta4 1.000

6. Results from the cross-sectional regressions

The results of the cross-sectional regressions are described in table 5. For the results of the cross-sectional regressions all possible combinations with the betas are regressed, but only 12 regressions are reported in the table. Each line represents one regression, and for each regression the upper value is the coefficient and the value between brackets is the t- statistics. The R-squares are also reported, in this case the upper value is the regular R- square and the value between brackets is the adjusted R-square. The results are reported in a way that it is easy to understand, however because of this the main result of the theory is in the middle. This regression is reported in line 8 and regresses the excess return on the normalized illiquidity together with the net beta. However this result is not statistical significant, all the coefficients are positive which is in line with the expectations. The R- square for this regression is relative low compared to the other reported regressions, which means the model is only limited explained by the variables compared with the other regressions. Next to this main regression some other control regressions are reported. One of these regressions is a mimic of the original CAPM-model and is reported in line 2. These regressions give a very low R-square and the adjusted R-square is even negative. Comparing the CAPM with the Liquidity-adjusted CAPM, the new model improves the predictability of the expected returns. By isolating the effect of the liquidity risk over the liquidity level

together with the market risk (beta 1), the regression becomes: ( ) ( )

. In this regression all the elements are significant and the R-square is relative high with a value of 0.9. However the net-beta coefficient in this regression gives a negative value, which means there is a negative premium for holding illiquid securities over liquid securities. Another control regression is to transform the net betas with the four betas

separate. This regression becomes: ( ) ( )

. In this regression only the third beta gives a statistical significant value to the 1%-level. The other betas have relative high statistical values, however not to the statistical significant level of 5%. The R-square in this regression increases significantly to a value of 0.95 (the adjusted R-square is 0.88), which is exceptional high. By combining these results in this regression it is possible that one of the risk variables is not empirically relevant. However most of the coefficients in this last regression are not statistical significant, these

34 still could be used to approach the premia for each of the channels. The illiquidity premium is a measure of holding illiquid securities over liquid securities, and is in this case approached by holding portfolio 10 over portfolio 1. Now subtract for each of the betas the value of portfolio 10 from the value of portfolio 1, and multiply these values with the common risk premium (retrieved from in table 3, line 8). The value retrieved is a monthly premium and to convert this to an annual premium this value has to be multiplied by 12. For the first channel of the liquidity-adjusted CAPM (beta 2) the premium is: ( ) . For the second channel (beta 3) the premium is: ( ) . And for the third channel (beta 4) the premium is: ( ) . To retrieve the annual illiquidity premium for the returns the three separate premia has to be added up to each other. This is the premium to hold illiquid securities rather than liquid securities, and has a value of 0.69% a year. However keep in mind the betas and the common risk premia did not have statistical significant values, which makes this result not very reliable.

The cross-sectional regressions could be performed with portfolios based on equally weights or value weights. The base results in this study are based on portfolios that are equally weighted, and also the market is based on equally weighted values. By using value weights instead of equally weights for the portfolios, the results become worse (these results are added in appendix A). None of the coefficients are statistical significant, and all the adjusted R-squares become much worse compared to the R-squares retrieved in the regressions based on equally weighted portfolios. The liquidity premium has a high coefficient, but because this value is not statistical significant and the R-square is relative low, this does not explain anything.

Table 5

Cross-sectional regressions This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on equal weighted portfolios. The data is based on monthly data between 1993 and 2013 with equal-weighted market portfolio. Portfolios are based on last year illiquidity. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R-squares are reported in the brackets.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β β β R 1 0.511 0.11 0.55

(4.72)** (3.15)* (0.5)

2 -0.963 3.04 0.08

(0.50) -0.86 (-0.03)

3 -0.447 0.106 1.82 0.58 (0.34) (2.90)* (0.70) (0.46) 4 0.52 0.537 -78.262 0.64 (5.01)** (1.63) (1.30) (0.54) 5 2.892 0.185 51.015 0.9 (5.88)** (7.86)** (4.87)** (0.86) 6 0.492 0.506 36.571 0.75 (5.62)** (2.90)* (2.30) (0.67) 7 2.545 0.326 -0.037 24.204 41.55 26.478 0.95 (2.72) (1.63) (0.02) (0.42) (3.62)* (1.30) (0.88) 8 0.275 0.102 0.4 0.56 (0.16) (1.48) (0.14) (0.43) 9 2.344 0.607 26.859 -27.861 0.9 (2.42) (5.32)** (4.64)** (4.45)** (0.85) 10 1.032 0.592 -18.138 -0.866 0.65 (0.59) (1.48) (1.24) (0.29) (0.47) 11 2.309 0.165 51.77 1.05 0.91 (2.44) (4.51)** (4.75)** (0.73) (0.86) 12 1.455 0.586 40.881 -1.638 0.76 (1.01) (2.70)* (2.30) (0.67) (0.65) 13 -1.798 4.005 0.42 (1.71) (2.39)* (0.35) * p<0.05; ** p<0.01

7. Additional results

In this part four alternative procedures are tested within the liquidity-adjusted CAPM theory. Each of the alternative procedures takes place on another moment in the model. In the first part the beta results are tested with the Fama-Macbeth 2-step regression. In the second part all data within the period of the recent financial crisis is dropped. In the third part the portfolios are not based on the average illiquidity of last year but are based on the market capitalization. And in the fourth part the portfolios are based on the average return of last year. In the last part a new proxy for illiquidity is implemented into the model and is tested if the model could be expanded by a new channel of liquidity.

7.1 Testing the model with the Fama-Macbeth 2-step regression

Earlier the Fama-Macbeth 2-step regression was performed on the CAPM to test how well the standard CAPM-beta explains the returns. In this part this methodology is repeated for the liquidity-adjusted CAPM model to test how well the illiquidity betas explain the returns. To implement the Fama-Macbeth model on the Liquidity-adjusted CAPM, the betas retrieved in table 3 are combined with the weighted excess annual returns for each year for each portfolio. Then each year a regression is performed on the annual excess returns and the (net) betas, to retrieve a time-series of the slopes over the years on the betas.

Table 6 Fama-Macbeth on Liquidity-adjusted CAPM In this table the results are reported of the Fama-Macbeth 2-step regression based on the liquidity-adjusted CAPM on the Dutch market between 1992 and 2012. The reported coefficients are retrieved from annual cross-sectional regressions based on the ten equally- weighted illiquidity portfolios and are performed to retrieve the standard errors and t-statistics, based on the Fama-Macbeth method. The upper values are the coefficients of the regression, the middle value are the standard errors, and the lower value is the t-statistic. There are several regressions performed, first for each beta separate, than for all betas combined, and as last for the net beta. These regressions are also performed including the illiquidity. In the last row the R-squares and the adjusted R-squares (in parentheses) reported.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β β β R 1 0.033 -0.496 0.92

(0.014) (0.036) (0.91)

(2.37)* (13.82)**

2 0.039 -0.010 0.09

(0.016) (0.008) (0.03)

(2.43)* (1.28)

3 0.039 0.051 0.77

(0.015) (0.007) (0.76)

(2.70)* (7.59)**

4 0.040 0.190 0.09 (0.162) (0.015) (0.03) (2.46)* (1.27) 5 0.048 -0.380 -0.016 0.060 0.031 0.94 (0.015) (0.056) (0.007) (0.009) (0.015) (0.92) (3.18)** (6.79)** (2.24)* (6.33)** (2.00)** 6 0.036 -0.612 0.95 (0.016) (0.036) (0.94) (2.31)* (17.23)** 7 0.038 -0.005 -0.437 0.9 (0.014) (0.003) (0.040) (0.89) (2.76)* (1.35) (11.09)** 8 0.027 -0.001 0.000 0.07 (0.015) (0.003) (0.007) (-0.05) (1.86) (0.6) (0.02) 9 0.033 -0.001 0.047 0.54 (0.017) (0.004) (0.011) (0.48) (1.88) (0.19) (4.08)** 10 0.042 -0.003 0.018 0.25 (0.014) (0.002) (0.008) (0.16) (3.09)** (1.80) (2.32)* 11 0.033 -0.001 -0.418 -0.004 0.056 0.010 0.94 (0.014) (0.001) (0.049) (0.004) (0.007) (0.007) (0.92) (2.34)* (0.99) (8.60)** (1.11) (7.58)** (1.44) 12 0.030 -0.001 -0.507 0.93 (0.014) (0.004) (0.039) (0.92) (2.16)* (0.29) (13.14)**

To perform the Fama-Macbeth procedure on the Liquidity-adjusted CAPM the theory is followed that is described in Acharya and Pedersen (2003). This paper of Acharya and Pedersen is an early version of the Liquidity-adjusted CAPM which uses the Fama-Macbeth theory as a base for the regressions. The final results of the 2-step Fama-Macbeth regressions are reported in table 6 and are performed on the same regressions as the cross- sectional regressions performed in table 5. Each row in table 6 supports one regression, and is performed over the average annual coefficients for the illiquidity and the returns. In each of the regressions the expected return is the dependent variable, and in the lower half of the regressions the expected illiquidity is added to the regressions. For each of the coefficients the standard errors and test statistics are reported below each of the coefficients within parentheses. The test statistics and standard errors reported in table 6 are used to correct the test statistics in the cross-sectional regressions in table 5. This is because in table 5 the test statistics do not give the proper measure since these values are affected by the cross- sectional correlation.

In the results of table 6 that present the Fama-Macbeth-like regressions performed on the Liquidity-adjusted CAPM, the coefficient with a value close to zero assumes this model does not work. The standard errors that are also reported in table 6 measure how liable these coefficients are, the closer these standard errors are towards the zero level how more reliable the coefficient is. The last reported value between parentheses is the test statistics, which measures whether the coefficient is statistical significant or not.

The first thing that attracts attention is that most of the coefficients in the Fama-Macbeth regressions are more statistical significant than the results retrieved in the cross-sectional regressions in table 5. Most of the coefficients, other than the illiquidity coefficient, are statistical significant to the 5% level or even to the 1% level. The illiquidity coefficients however has values close to zero and none are statistical significant. Different regressions that have beta 2 included show that this beta only limited adds value to the model. The coefficients for the beta 2 are relative close to zero, have low statistical values, and have very low for R-square values. The main regressions in this table are described in line 11 and line 12 and show for most coefficients a statistical significance to the 1% level (except for the beta 2 and beta 4 coefficients), which means the model is not statistical rejected. Overall in

39 this table it is not clear if these Fama-Macbeth regressions test whether the illiquidity coefficients add value, but overall the results are generally consistent with the model.

7.2 Removing crisis data

Earlier in the test of the standard CAPM on the Dutch stock market, a distinction was made between the period before and after the recent financial crisis. Testing the model on the period that only includes the period of the financial crisis (second quarter of 2008 and later), the results of the CAPM become worse. In this part this test is repeated on the theory of the Liquidity-adjusted CAPM, by excluding the period of the recent financial crisis. So the Liquidity-Adjusted CAPM is tested with data between January 1993 and July 2008.

After running the cross-sectional regressions, most of the statistical significant values disappeared, however a lot of the t-statistics that were before not statistical significant increases (not enough to get a statistical significant level of 5%).

Also all of the R-squares and adjusted R-squares decreased in all the regressions, which concludes that the data on the recent financial crisis is needed to strengthen the results of the Liquidity-adjusted CAPM. That the results deteriorate could have multiple causes, it could be that the model only works if there is a period of higher illiquidity included (in this case the recent financial crisis). Another explanation could be that there is an important chunk of data removed that is needed for the model to work, which could be an acceptable explanation since in the new period only data of 15.5 years is included instead of the 20 years. As concluding remark, contrary to the regular CAPM-model the Liquidity-adjusted CAPM model could handle periods of illiquidity, however by testing the model on a smaller period (that excludes the recent financial crisis) the model does not hold anymore.

Table 7

Cross-sectional regressions This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on equal weighted portfolios. The data is based on monthly data between 1993 and 2008 with equal-weighted market portfolio. Portfolios are based on last year illiquidity. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R-squares are reported in the brackets.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β Β β R 1 0.725 0.137 0.52

(6.27)** (2.93) (0.46)

2 0.856 0.16 0

(0.51) (0.04) (-0.12)

3 1.124 0.139 -0.89 0.52 (0.90) (2.78)* (0.32) (0.39) 4 0.726 1.72 -5.817 0.52 (5.84)** (0.45) (0.09) (0.38) 5 2.086 0.193 30.226 0.68 (2.87)* (3.84) (1.89) (0.59) 6 0.706 0.369 22.259 0.54 (5.66)** (0.94) (0.60) (0.41) 7 2.696 0.549 -1.653 30.713 28.483 51.94 0.74 (1.72) (1.10) (0.49) (0.35) (1.44) (0.87 (0.41) 8 1.546 0.172 -1.668 0.54 (1.14) (2.29) (0.61) (0.41) 9 2.646 0.633 25.206 -26.835 0.71 (2.01) (2.43) (1.83) (1.93) (0.56) 11 1.677 0.292 -18.905 -1.924 0.55 (1.09) (0.65) (0.27) (0.62) (0.32) 12 2.148 0.195 29.828 -0.162 0.68 (1.68) (2.82)* (1.62) (0.06) (0.52) 13 2.255 0.65 42.822 -3.182 0.61 (1.48) (1.36) (1.02) (1.02) (0.41) 14 -0.702 3.114 0.2 (0.61) (1.42) (0.10) * p<0.05; ** p<0.01

7.3 Portfolios created based on the MCAP

In table 2 a clear relation is described between the market capitalization and the level of illiquidity. The market capitalization is a proxy for the size of a company, and how bigger the company, how smaller the average normalized illiquidity is in terms of the portfolios. This relation could be explained since stocks of bigger companies have a higher turnover since bigger firms are more known by investors than smaller firms (Ibbotson, Chen, Kim and Hu, 2008). Smaller firms, or firms that are less known by investors have lower turnover and thus are being traded less. This could conclude that smaller firms are from nature more illiquid than bigger firms. By combining these findings it could be concluded that there is a negative relation between market capitalization and illiquidity. By sorting on market capitalization the biggest firms are included in portfolio 1 and the smallest firms are included in portfolio 10. If the illiquidity has a positive relation with the market capitalization there is a chance the results are equal or even will improve.

After running the cross-sectional regressions with the portfolios based on the market capitalization, this has a positive influence on the coefficients and the t-statistics compared with the regressions in table 5. In all the reported regressions the normalized illiquidity are positive and statistical significant to the 5% or 1% level. Also the R-square increases relative well in all regressions, which means the variables explain the models more than when the portfolios were created based on last year illiquidity. However the big con in these regressions, is that the net beta coefficient in all reported regressions is negative. This means that the risk premium λ is negative, which is not in line with the expected results since this implies a negative premium for investing in illiquid securities.

Table 8

Cross-sectional regressions, portfolios based on market capitalization This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on equal weighted portfolios. The data is based on monthly data between 1993 and 2013 with equal-weighted market portfolio. Portfolios are based on market capitalization. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R-squares are reported in the brackets.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β β β R 1 0.294 0.391 0.83

(1.78) (6.36)** (0.81)

2 -0.309 2.511 0.1

(0.10) (0.47) (-0.1)

3 1.49 0.41 -2.215 0.85 (1.16) (6.28)** (0.94) (0.81) 4 0.256 1.032 -113.381 0.91 (2.01) (4.04)** (2.55)* (0.89) 5 0.854 0.436 13.559 0.84 (0.59) (3.28)* (0.39) (0.79) 6 0.294 0.764 36.745 0.96 (3.59)** (9.52)** (5.03)** (0.95) 7 -1.349 0.953 4.224 -2.317 15.476 52.638 0.99 (2.09) (5.12)** (3.06)* (0.06) (1.11) (5.25)** (0.98) 8 1.702 0.459 -2.424 0.87 (1.52) (5.76)** (1.27) (0.83) 9 -0.810 1.148 47.209 -41.980 0.98 (1.25) (9.20)** (5.74)** (6.05)** (0.97) 10 -0.488 1.156 -141.507 1.264 0.92 (0.33) (3.18)* (1.95) (0.51) (0.88) 11 1.402 0.426 -13.877 -2.894 0.87 (0.94) (3.28)* (0.34) (1.17) (0.80) 12 -1.53 0.856 54.434 3.139 0.99 (2.60)* (13.98)** (7.27)** (3.11)* (0.98) 13 -2.038 4.904 0.23 (1.00) (1.55) (0.13) * p<0.05; ** p<0.01

7.4 Portfolios created on basis of last year return

In table 2 also a relation between the average excess returns and the illiquidity is described. However this relation is not as strong as with the market capitalization, so expected is that the results from the cross-sectional regressions are not as strong as in table 8. The results from the cross-sectional regressions are even a little disappointed. Only a couple variables are statistical significant and the R-squares and adjusted R-squares decreases compared with the R-squares in table 5. Surprisingly the net beta coefficient in the main regression for illiquidity (line 8) is statistically significant, but not useable since the value is negative. In theory a positive premium is expected for holding illiquid securities over liquid securities.

Table 9

Cross-sectional regressions, portfolios based on last year return This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on equal weighted portfolios. The data is based on monthly data between 1993 and 2013 with equal-weighted market portfolio. Portfolios are based on last year’s return. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R- squares are reported in the brackets.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β β β R 1 0.172 0.311 0.1

(0.28) (0.92)

2 1.130 -0.753 0.05

(1.71) (0.64)

3 0.735 1.064 -3.44 0.55 (1.45) (2.79)* (2.65)* 4 0.249 0.701 -86.964 0.15 (0.34) (1.00) (0.64) 5 -0.208 -0.073 -22.572 0.34 (0.34) (0.19) (1.61) 6 -0.096 0.83 40.409 0.5 (0.19) (2.41)* (2.40)* 7 -0.781 -0.107 0.357 93.023 -30.159 45.962 0.78 (0.88) (0.12) (0.16) (0.79) (1.72) (1.92) 8 0.76 1.163 -3.364 0.54 (1.47) (2.78)* (2.59)* 9 0.730 1.047 -3.943 0.501 0.55 (1.31) (1.93) (0.37) (0.05) 10 0.785 1.354 -47.923 -3.268 0.55 (1.42) (2.20) (0.45) (2.34) 11 0.445 0.805 -13.124 -2.83 0.61 (0.75) (1.49) (1.05) (2.04) 12 0.411 1.124 20.784 -2.155 0.59 (0.62) (2.63)* (0.86) (1.12) 13 1.042 -0.525 0.03 (1.52) (0.48) * p<0.05; ** p<0.01

7.5 Alternative measure of illiquidity

As mentioned before the liquidity measure is not a readily observable measure and could only be approached by using a proxy. In theory there are different proxies used for (il)liquidity, and most of the proxies measure different elements of the liquidity. Some proxies are quiet correlated to each other (Korajczyk & Sadka, 2008), but there are also proxies that are not correlated at all. In this part the low level of correlation is exploited to combine two proxies of illiquidity to test if they could replenish each other by combining these proxies. Acharya and Pedersen (2005) base their proxy for (il)liquidity on the averages per month over the absolute returns divided by the turnover volume. This measure only focuses on the trading part, and misses input of the non-trading part. As an addition an alternative proxy is added to the model that focuses its measure for illiquidity with another method, which also includes the non-trading characteristic of liquidity. The theory used is found in 1999 by Lesmond, Ogden, and Trzcinka and uses the percentage of zero-returns for each security in a year as a proxy. A zero return is caused by non-trading of a security and they state that a higher percentage of zero returns, causes the security to be more illiquid.

Lesmond (2002) used the theory of percentage zero-returns on a practical perspective by using the measure on multiple emerging markets. He finds that there is a statistical significant relation between the zero returns and the transaction costs. This means if in general the transaction costs become too high, the volume trading decreases, or even become zero. To check if the theory also works on the Dutch market, the relation is tested on the Dutch stock market. In this test the percentage of zero returns is regressed on the average percentage spread for each year. The regression is performed on 1438 firm years and the results are statistical significant to the 1% level which means there is a strong relation. The results are also in line with the results of the regressions with the emerging countries in Lesmond (2002).

Table 10 Regression between percentage zero-returns and the bid-ask spread Percentage zero-returns are calculated by the amount of zero returns for each security in each year. The average spread is calculated by the percentage bid minus the percentage ask price. The regression performed is stated as: . Both elements are statistical significant to the 1%.

Dutch Stock Market Percentage zero-returns 0.025 (7.52)** Average spread 6.960 (44.89)** R2 0.58 N 1,438 * p<0.05; ** p<0.01

In the theory of Lesmond, Ogden, and Trzcinka (1999) they explain that a zero return is caused if the value of an information signal is not big enough to exceed the costs of trading, so marginal investor will reduce the amount of trading or not trade at all. The costs of trading in this case are the complete transaction costs. Securities with high transaction costs have a higher chance of retrieving a zero return, compared to securities with lower transaction costs. This would mean the zero returns could be explained by the transaction costs. This theory exploits the zero-returns to approach the liquidity of the security. In table 11 the correlations between the relevant proxies in the discussed papers are retrieved. The Illiquidity is the proxy used in the paper of Acharya and Pedersen (2005). The other proxies are all applied in the papers of Lesmond, Ogden, and Trzcinka (1999). The Spread is the difference between the bid- and ask price (also known as the bid-ask spread). The % 0 returns is the proxy measured by the amount of zero return for each security in each year. The % spread is an adjusted calculation of the spread, by using the percentage value of the bid- and ask price. As expected the spread and adjusted spread are highly correlated to each other (which is logical since they measure almost the same value). As Lesmond, Ogden, and Trzcinka (1999) stated the zero returns show high correlation between the zero returns and the spread, which is also the case in table 11, which show a relative high correlation. What attracts attention is that the proxies used in both papers have relative low correlation between the two papers. The correlations are relative close to zero, which means they are uncorrelated. This could verify that both the proxies measure different characteristic of the (il)liquidity and that it is possible they could replenish each other.

Table 11 Correlations between different proxies of (il)liquidity This table represents four different proxies for liquidity that are relevant in both the theory for Acharya and Pedersen (illiquidity) and the theory in Lesmond, Ogden, and Trzcinka (Spread, % 0 returns, and % spread). The illiquidity is the average value per month over the absolute returns divided by the volume by turnover. The spread is the difference between the bid- and ask price (the bid-ask spread). The %spread is the difference between the percentage price of the bid- and ask price. The % 0 returns are the percentages of zero returns for each security in each year.

Correlation between different proxies Illiquidity Spread % 0 returns % Spread Illiquidity 1.000 0.112 -0.034 -0.073 Spread 1.000 -0.671 -0.996 % 0 returns 1.000 0.697 % Spread 1.000

To add the theory of Lesmond, Ogden, and Trzcinka (1999) into the Liquidity-adjusted CAPM the zero-returns proxy is used. However to get the theory in line with the theory of Acharya and Pedersen (2005), monthly percentages of zero returns are used instead of the annual percentages. This variable is transformed into a beta variable the same way as the return- variable is transformed into the beta 2 variable, but based on the new proxy for illiquidity. So for each security each month the percentage zero-returns are calculated, and are adjusted to the portfolio variables. Then the residuals of the autocorrelation regression (one and two times lagged) are performed to retrieve the innovation. Finally for each portfolio the variable is regressed against the market innovation to retrieve the fifth beta, which is based on the new proxy of illiquidity. So this fifth beta is the covariation between the innovation of percentage of zero returns (the proxy for illiquidity) and the innovation for market returns.

( ) The function used is: , and is retrieved by regressing the normalized ( ) illiquidity innovation in a portfolio by the excess return innovation in the whole market. This beta is the fifth beta that is added as a fourth channel of illiquidity to the model.

The new model becomes:

( ) ( )

The results of the cross-sectional regressions are added into table 12 and are not as strong as expected. By adding this variable all statistical significance is gone and the R-square and

48 adjusted R-square decreased. So this new beta does not add any value and does even decrease the already obtained results.

Table 12

Cross-sectional regressions This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on equal weighted portfolios. As addition a fifth beta is added that is based on the zero-returns. The data is based on monthly data between 1993 and 2013 with equal-weighted market portfolio. Portfolios are based on last year illiquidity. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R-squares are reported in the brackets.

p 1p 2p 3p 4p 5p net,p 2 Constant E(c ) β β β β β β R 1 -0.347 0.138 1.51 0.58

(0.17) (3.08)* (0.4) (0.45)

2 0.475 0.659 -93.23 0.67

(3.95)** (1.85) (1.48) (0.58)

3 1.866 0.147 28.655 0.74 (2.85)* (4.18)** (2.17) (0.67) 4 0.464 0.459 31.211 0.78 (4.73)** (3.59)** (2.60)* (0.72) 5 0.263 0.185 547.26 0.59 + (0.72) (2.00) (0.60) (0.47) 6 3.147 0.427 -3.222 -4.959 19.408 25.066 0.84 (1.29) (1.02) (0.85) (0.05) (1.09) (1.15) (0.64) 7 3.379 0.459 -3.770 -8.688 21.494 22.377 445.709 0.85 (1.23) (0.98) (0.86) (0.09) (1.06) (0.90) (0.50) (0.56) 8 1.950 0.174 -2.527 0.59 (0.75) (2.19) (0.57) (0.47) 9 3.332 0.473 17.544 -20.952 0.84 (1.84) (4.24)** (3.06)* (3.11)* (0.76) 10 2.925 0.812 -109.243 -4.168 0.72 (1.23) (2.12) (1.69) (1.03) (0.58) 11 3.827 0.197 29.776 -3.245 0.77 (1.71) (3.04)* (2.22) (0.91) (0.66) 12 2.176 0.508 31.706 -2.914 0.81 (1.13) (3.60)* (2.60)* (0.89) (0.71) 13 2.165 0.25 713.888 -3.344 0.62 (0.80) (1.89) (0.73) (0.731) (0.43) * p<0.05; ** p<0.01

8. Summary and Conclusions

In this paper both the CAPM and liquidity-adjusted CAPM are tested. By performing the standard CAPM-model on the Dutch market excluding the period of the financial crisis the model reasonable explains the expected returns. However by adding the period of the recent financial crisis the results of the model get worse. As addition the standard CAPM is also tested on the period only including the recent financial crisis, and the model seems not to hold at all. That the standard CAPM is not a perfect model is also proved with the Fama- Macbeth test, performed on the Dutch market between 1993 and 2013. The average slope over the whole period is close to zero, which means the standard market beta does not seems to predict the returns.

By performing the liquidity-adjusted CAPM model on the full period of the Dutch market, the results improves a lot compared to the regular CAPM-model. The theory is performed using equally weighted portfolios, because by using value weighted portfolios the results are not as expected. The relation between the characteristics of the portfolios and the portfolios self are not as strong as in the original paper of Acharya and Pedersen, however they could be used to perform the cross-sectional regressions. The relations of beta 2 and beta 4 with the portfolios are exactly the same as in Acharya and Pedersen, the other betas and the different characteristics have slightly worse relations with the portfolios. The premium retrieved in the Liquidity-adjusted CAPM for holding illiquid portfolios over liquid portfolios is 0.69%, which is a relative small premium (and which is not based on statistical significant values). By removing the period of the recent financial crisis the results get worse. This could be caused that some period of illiquidity is needed before the theory to work, or that this period is too short for the model.

Also some additional theories are implemented and combined onto the theory. By performing the Fama-Macbeth model on the Liquidity-adjusted CAPM model, it could be concluded that beta 1 explains the expected returns the worst (this beta is equal to the regular CAPM-model beta). The second beta explains the expected returns the best (which is the covariation between the individual asset liquidity and the overall liquidity of the market).

In earlier tests was already found that there was a relatively strong relation between illiquidity and the market capitalization and a slightly worse relation between the illiquidity and the excess returns. In the original model the portfolios are based on the last year illiquidity, so expected is that portfolios based on these characteristics still would hold. By base the portfolios on market capitalization the results improve, but there is a negative premium for holding illiquid securities, which is not in line with the theory. By base the portfolios on the excess returns of last year all the results get worse, since both the R- squares and statistical significance decreases in all regressions.

Appendix Appendix A

Table A

Cross-sectional regressions, based on value-weighted portfolios This table represents the results of the cross-sectional regression of the liquidity-adjusted CAPM and some additional cross-sectional regressions. The normalized illiquidity, betas, and net beta are based on value weighted portfolios and the market is based on equally weights. The data is based on monthly data between 1993 and 2013 with equal-weighted market portfolio. Portfolios are based on last year illiquidity. The t-statistics are in brackets and significant values are marked with stars. For each of the cross-sectional regressions the R-squares are retrieved, and the adjusted R-squares are reported in the brackets.

p 1p 2p 3p 4p net,p 2 Constant E(c ) β β β β β R 1 0.038 0.146 0.32

(0.19) -1.95 (0.24)

2 -0.6 1.929 0.1

(0.66) -0.96 (-0.01)

3 -0.678 0.14 1.63 0.4 (0.84) (1.84) (0.92) (0.22) 4 0.222 -0.347 58.113 0.74 (1.54) (2.23) (3.34)* (0.66) 5 0.091 0.195 210.695 0.34 (0.38) (1.46) (0.45) (0.15) 6 0.037 0.163 0.174 0.32 (0.17) (0.91) (0.11) (0.13) 7 -0.114 0.01 1.305 57.638 979.68 1.335 0.89 (0.19) (0.03) (0.94) (3.33)* (2.16) (0.91) (0.76) 8 -0.568 -0.009 1.408 0.39 (0.77) (0.04) (0.86) (0.21) 9 -0.886 0.039 1.191 0.934 0.42 (0.93) (0.17) (0.57) (0.49) (0.13) 10 -0.07 -0.4 55.780 0.662 0.75 (0.13) (2.12) (2.98)* (0.57) (0.63) 11 -0.49 0.032 121.399 1.296 0.39 (0.57) (0.12) (0.24) (0.71) (0.09) 12 -0.924 0.036 1.372 2.216 0.43 (1.00) (0.17) (0.69) (1.07) (0.15) 13 -0.541 1.341 0.39 (1.39) (2.25) (0.31) * p<0.05; ** p<0.01

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