Liquidity and the Stock Market

Transcription

1 UNIVERSITEIT VAN TILBURG Liquidity and the Stock Market BACHELOR THESIS FINANCE S.A.M. Nieuwenburg S Bedrijfseconomie Supervisor Sohail Ahmed Finance Department 13 th August 2010 (Resit) -Abstract- The goal of this paper is to understand if liquidity has changed after the 2007 financial crisis. Therefore, a relation between liquidity (spread) and return is made. I used amongst others the Three Factor Model and the ILLIQ model of Amihud. First there will be a theoretical base about liquidity. In the second part, the results of the research are given.

2 Index 1. Introduction Literature Review The Factors of Liquidity and how it can be measured Liquidity and Expected Stock Returns Liquidity and the CAPM Liquidity and the crisis of Research Methodology Data Variables Three Factor Model ILLIQUID-Model Working Method Empirical Results Conclusion References Appendix Appendix Appendix Appendix Appendix

3 1. Introduction As an investor, you want to trade without affecting the price of the security. But there are several frictions in the market, for example trading costs and short sale restrictions. The definition of liquidity will be the ability to buy or sell large quantities of an asset quickly at low cost, without affecting the price. In this definition there are three causes, namely execution cost, quantity and time (Gomber, P., 2007). Moreover, it is well known that liquidity is one of the most important factors of the market quality (Chordia, T., et al, 2003). This is the reason why liquidity has attracted the attention of investors. Therefore, it is interesting to study the relationship between liquidity and the expected return of a stock. If the liquidity is low (or in other words high illiquidity), than these costs should be compensated with a higher expected return on the stock. This loss means for example high transactions cost. In other words, there should be a risk premium (Amihud 2002). Besides that, Pastor and Stambaugh R.F. (2003) found that stocks liquidity beta s play a significant role in asset pricing. As mentioned before, stocks with low liquidity should have a higher expected return, to compensate the cost due holding the stock. In other words, stocks with a higher liquidity beta, should have a higher return. Therefore, Amihud makes the assumption that stock excess return, traditionally interpreted as risk premium, includes a premium for illiquidity. Also, liquidity is an important factor that determines the cost of capital of a stock. If liquidity is high, then the cost of capital will be low. With, for example, more active investor relation activities, the cost of information to the market will be reduced, which leads to a higher liquidity. A consequence of a lower cost of capital is a high market capitalization (Brennan, 2000). The last subject that is discussed in this paper, and is the main subject and the goal of this paper, is the influence of the financial crisis of Diamond and Dybvig (1983) suggest that in times of crisis, there will be an increased demand in liquid assets. So the question is of liquidity of stocks has changed over time, in the period , because of the current financial crisis. So, according to Diamond and Dybvig, the liquidity in 2009 should be higher than in the beginning of the first decade of the twenty-first century. A more recent study is the one of Brunnermeier (2008). In his paper Deciphering the Liquidity and Credit Crunch, he explains that many people had invested, in the period of 2006, in many 3

4 illiquid, long-maturity assets. So investors were exposed to liquidity risk. The sponsoring bank granted a credit line to guarantee funding liquidity, which has as a consequence that the bank system, still bears the liquidity risk. Another factor was the illiquidity of junior CDO s. It was possible to smooth the returns over time and therefore it seems to be less risky. Two other components that could have been contributed to the crisis are the so called loss spiral and the margin spiral. An explanation is given in the next section. In the past decades, there have been many researches that have studied the relationship between liquidity and expected stock returns. Most of them studied stock markets in the years before the year This paper works with data from the 2000 till To measure the liquidity, the model of Amihud (2002) and Acharya and Pedersen (2003) are used. This model measures the illiquidity of a stock with the specific return of a stock and the traded volume of that stock in that period. This model is also be used to see if there is a relation between liquidity and the (beta of the) CAPM and if liquidity has changed after the finacial crisis of There is a comparison given between the illiquidity of the period , and The next section, chapter 2, contains the literature review. It is a summary of other papers, which has studied the relation between liquidity, expected stock returns and the CAPM before. Also a definition of liquidity is given, with the factors that influence liquidity. At last, the relationship between liquidity and the financial crisis is explained. The model used for the empirical research is described in section 3. The fourth section contains the results of the research that has been done. In the last section, chapter 5, the results are summarized and concluded. 4

5 2. Literature Review 2.1 The Factors of Liquidity and how it can be measured It is a commonplace that liquidity is one of the most important parameters of the market quality (Chordia, T., et al, 2003). It is risky and varies over time for both the total market and individual stocks (Hasbrouck and Seppi, 2001). Liquidity determines, amongst other things, transaction costs for investors, short sale restrictions, voting rights and circuit breakers (Gomber et al, 2004). Gomber gives a definition: An asset is liquid if it can be bought or sold immediately and without adversely affecting the price. In this definition there are three liquidity factors, namely execution cost, quantity and time. Brunnermeier (2009) called this the bid-ask spread (how much you lose if you sell the stock and buy it immediately back), market depth (how many stocks you are able to buy without affecting the price) and market resiliency (if the price drops, how long it takes to get back to the normal stock price).this is important for the market as a whole and for investors who trade large orders. Gomber et al (2004) proved that investors with large trades wait until the liquidity in the market is low enough. As described above, liquidity has a certain risk. Chordia et al (2003) distinguish three different risks: commonality in liquidity with the market liquidity, return sensitivity to market liquidity and liquidity sensitivity to market returns. They found that these liquidity risks contribute 1.1% annually to the difference in risk premium between stocks with high liquidity and stocks with low liquidity. A factor that could influence liquidity is the publication of the corporate financial statements. A reason for this could be that investors react and anticipate on announcements made in the news. Gomber (2004) came to the conclusion that liquidity decreases if a financial announcement will be made at a pre-specified time. Another relation that could be made is the relation between volatility in the market and market liquidity. It turned out that when market volatility is high, liquidity tends to be low (Pastor& Stambaugh, 2003); they found a correlation of This seems logical, because the compensation that an investors demands due to illiquidity, could be greater when volatility is higher. Third, they found a relation between liquidity and the size of a stock. They found that smaller stocks are less liquid and more sensitive to liquidity. 5

6 Behavior is a last factor that could influence liquidity. Often, investors are sensitive to very high optimism or pessimism. When they are (over-) optimistic, investors are most likely more active on the stock market which leads to higher stock market liquidity and a lower bid-ask spread. In the contrary, if they are pessimistic, they will hold the stock and avoid trading, which makes the market illiquid and the spreads will increase (Chordia, 2003). Measurements of Liquidity There are many ways how liquidity could be measured. In this paper, I use the ILLIQUID-model of Amihud (2002), in combination with the model used in the paper of Acharya and Pedersen (2003). This model of Amihud is explained in the next section (3.3). One of the simplest measurements is the bid-ask spread. Figure 2.1 Bid-ask spread. Source: Stulz, R. Risk Management and Derivatives The bid-ask spread, as shown in figure 2.1, is the difference between price of selling stock and price of buying it back. In the figure, Deceuninck Plastics is more illiquid then Philips, because of the higher spread. The reason for this difference lies in the transaction costs, such as commissions and brokerage fees. Besides that, adverse selection could influence the bid-ask spread. If the adverse selection varies over time, it should be positively related with equity returns (Jones, 2000). Professional market-makers could also be the main source of bid-ask spreads. The spread reflects than only the financial condition of brokerage houses and financial institutions. Another reason is inventory costs, which can cause the bidask spreads to be wider. 6

7 Pastor & Stambaugh (2003) use, like Amihud (2002) and Acharya & Pedersen (2003), returns and volumes of a stock. If stock prices move a lot due to a relative small transaction of the stock, it is illiquid. But there are differences in the approach of Amihud and Acharya & Pedersen (2003). Where Amihud (2002) discusses illiquidity, Acharya and Pedersen talk about liquidity risk. The first one calculates the ILLIQ, which is the ratio of absolute stock return to its trading volume. This is explained in more detail in section 3. The other two researchers use a different model. They use also the ILLIQ, but use four betas that represent liquidity risk. In this way, they show how liquidity risk affects returns and propose an extension of CAPM. A complete different method is the one of Gomber et al (2004). They use the Exchange Liquidity Measure (XLM). It measures the cost of a roundtrip trade of size V. They measured how long it takes for the XLM to return to a normal value after a (endogenous and exogenous to the market) liquidity shock. 2.2 Liquidity and Expected Stock Returns It seems to be clear that there must be a relation between liquidity and the expected return of a stock. Pastor and Stambaugh (2003) give an example of this phenomenon. Suppose an investor faces a situation of finacial distress and have to sell a part of his assets. The chance that he could sell a liquid asset is much greater then selling an illiquid asset, because it is costlier when liquidity is low. This would not be preferable for an investor who has already lost a part of his portfolio value. So, if the return of a liquid and an illiquid stock are the same, an investor would always prefer the liquid asset. For this reason, holding an illiquid stock should give a higher return to compensate the illiquidity. And indeed, Pastor and Stambaugh (2003) confirmed this relation for the period Stocks with a higher liquidity beta, the sensitivity to liquidity, exhibit higher expected returns. Also Amihud (2002) has studied this relation, except he compared stocks with the total market liquidity. But Chordia et al (2001) concluded in their paper that there is a negative relation between the volatility of the stocks liquidity and the expected return of the stock. They give two possible reasons for this. If the variability of trading activity proxies for heterogeneity in the set of investors holding the stock then an increase in such heterogeneity would lower the required rate of return on the stock. Another possible reason is that increased volatility will lead to the entry of institutions that enhance liquidity in a fashion which cannot be measured with the bid-ask spread. 7

8 Jones (2000) suggests that there is another factor that plays a role in the relation between liquidity and expected returns. If the covariance is zero between those two elements, then there is only a mechanical link between stock returns and liquidity (transaction costs). This is called the pure transaction cost hypothesis. In this case there should be a positive relation between the expected stock return with spreads, commissions and turnover, because each of these components increases the transaction costs. In the second case, the covariance is not zero; the priced liquidity hypothesis. This means that the earlier mentioned components could be correlated with the expected stock return. Decreasing expected returns in liquidity, means more liquidity should predict a lower expected return. In this case, according to Jones (2000), spreads should have a positive relation with expected returns and the turnover should have a negative slope. Commission levels are not correlated with liquidity and therefore commissions could not predict the future returns. These two hypotheses make the same relation between spreads and expected returns, which is also confirmed by Chordia (2003). If there is absolutely no relationship between liquidity and expected return, it is called the random walk null. Acharya and Pedersen (2003) suggest that there is not only a relation between the expected return and the liquidity of that stock, but also with the liquidity of the market as a whole. So, the return increases with the covariance between the asset s illiquidity and the market illiquidity, again for compensating holding a stock that becomes illiquid if the market becomes illiquid. Investors require a risk premium for holding these assets. A second effect that they mention is the fact that investors are willing to accept a lower return on an asset with a high return if the market is illiquid. The third aspect that they discuss is about the covariance between the liquidity of the stock and the market return. Investors are willing to accept a lower return for a liquid stock if the market becomes more illiquid. It is valuable for investors to sell their stocks relative cheaper if the market is falling. 2.3 Liquidity and the CAPM The Capital Asset Pricing Model, also known as CAPM, is a widely accepted asset pricing model to determine the required (expected) rate of return of an asset. The variables needed to calculate this are the expected return of the market, the expected return of the risk-free rate and the beta (ß), which is 8

9 the systematic risk. This model could be used for individual assets, but also for portfolios. In the last decade, the model has been criticized due to its shortcomings such as the assumption that asset returns are normally distributed and all investors have access to all and the same information. In this paper I want to explore the relationship between liquidity and the CAPM and investigate how much liquidity captures the unexplained variation of returns from the CAPM. Like mentioned before, illiquidity is a risk for the investor and therefore his required rate of return should be higher. One of the researchers that investigated the relation between liquidity and the CAPM are Martínez et al (2003). They adjust the model by adding a liquidity risk factor: ILLQ alpha. This ILLQ is Amihud s Illiq measure (ratio of the returns and volumes). They find that the ILLQ could be used as a measurement for this risk. In this way, you would get a required rate of return adjusted. But this adjusted model does not change the relation between the CAPM and liquidity. In both the version, with and without liquidity risk, they found a significant relation, the beta should be higher if liquidity is low, because a higher return is demand if there is a sudden liquidity shock and there is illiquidity. Acharya and Pedersen (2003) also studied the relation of liquidity and returns and proposed an adjusted CAPM model considering the effect of liquidity risk on expected returns. They surprisingly find that the expected return increases if liquidity goes down and therefore the beta of the CAPM is influenced by the liquidity of its asset. This adjusted model is better, according to them, because of a higher R 2 (from 0.22 to 0.73).They includes different betas which stand for the different liquidity risks. 2.4 Liquidity and the crisis of 2007 The recent finacial crisis has consequences for almost everyone; it is one of the greatest crises in the history of modern economy. There have been many studies about this crisis and these researchers suggest its many causes. It started to escalate in the summer of 2007 when house prices were stagnating and sometimes even depreciating and banks started to default. (Gorton, 2008). One of the main factors was the subprime mortgage market because of the difficulties that arose in the financial 9

10 market (Demyanyk & Van Hemert, 2008). Other, possible, causes were the influence of rating agencies (Calomiris, 2008) and the agency problem (Schwartz, 2009 & Calomiris, 2008). But there could be another factor that influenced the 2007 crisis. In several crises before, liquidity had a great share of causing a crisis or at least accelerating it. A good example is the stock market crash in Exactly on the day of the crash, October 19, both spot and futures stock market was highly illiquid (Grossman and Miller, 1988). Amihud, Mendelson, and Wood (1990) proved that this low liquidity was definitely part of the cause of the stock crash in 87. The second largest illiquid period was in November 1973, when the Mid-East oil embargo began (Pastor& Stambaugh, 2003). A third drop in liquidity was in 1997, a period that faced the top of the Asian crisis. Chordia (2003) has also studied the relation between crises and liquidity. In the more recent financials crises in the last two decades, Chordia (2003) found also that liquidity often declined and sometimes even disappeared. This has a major influence on the price of a stock. So in the last stock market crashes, liquidity has often been one of the factors causing the crisis. In the next section I am going to study if liquidity has remained the same or changed before, during and after the crisis of 2007 in the stock market. But not all the stock market crashes are caused by illiquidity in the market. Sometimes it doesn t even have an influence on the crises. As explained before, the bid-ask spread is one of the ways how liquidity could be measured. One of the moments that this spread was extremely high was in the great depression after Black Thursday in A consequence of lower market liquidity is a decline in the initial price. With illiquidity, the requirements of funding for finacial institutions increase. One cause of this not preferred consequence of illiquidity is that investors are unable to pay back their short term loans, because of the decrease on their portfolio value. It becomes a vicious circle. But there is not always a relation between a stock market crash and the illiquidity of that market. That was the case in for example 1920, 1937 and 1962 (Jones, 2000). Jones proved this with a simple correlation. In his study, the correlation between stock market crashes and the appearance of illiquidity was only This means that liquidity is most of all not a factor of stock market crashes, but it could be the cause. 10

11 But Brunnermeier (2009) suggests in his paper about the current financial crisis that there are three possible mechanisms that could explain why liquidity suddenly collapses. One of them is loss spiral. It is a commonplace that to avoid moral hazard and/ or adverse selection, investors have to put in their own capital. When the value of invested assets falls, the amount an investor can borrow falls. Suppose an investor buys 50 billion worth of assets and he has to finance it with 45 billion of debt. Then he has a leverage ratio of 10:9. If the value then drops to 47.5 billion, his own capital halves to 2.5 billion. With the same leverage ratio, he must decrease his position. This sale has a consequence that the price drops further. And the first assets you want to sell as an investor are your liquid assets to minimize the cost. Investors hold their illiquid assets which decreases the market liquidity. Diamond and Dybvig (1983) suggest that in times of crisis, there will be an increased demand in liquid assets. The cause of this would be that liquidation is costlier when liquidity is low. These costs are not preferred by an investor and especially not when he is in finacial distress. In crises, most investors lose much value on their portfolio and especially then they want cost as low as possible. So, according to Diamond and Dybvig, the liquidity in 2009 should be higher than in the beginning of the first decade of the twenty-first century. To achieve higher liquidity in the market, the government or the central banks should take an active position. With a different monetary policy, the Fed could improve market liquidity by loosening up their policy. A lower illiquidity could encourage more trading by making it less costly and by improving the ability of traders to finance their positions (Chordia, T., Sarkar, A. & Subrahmanyam A., 2003). In 2007, the Fed injected several times billions of dollars in the US economy and several times the Federal Reserve lowered the interest rate. In 2008, the Fed continued their policy and interest rate dropped even to 0.0% 0.25%. Like mentioned before, in section four I tried to find if there is a significant change in liquidity due to the crisis and the policy of the Federal Reserve. But monetary policy by the Fed and other central banks at crises is often predictable. Therefore Chordia et al (2003) suggest that investors only react on surprising elements in the policies of central banks. An unexpected loosening of the financial policy (a decrease in net borrowed reserves) has as result an increase in stock liquidity. 11

12 3. Research Methodology 3.1 Data For the collection of the data I used Fama/French data, available on their website, and Compustat/ WRDS. I used the S&P 500 as main stock exchange, but also other companies are used. They are all listed on US stock markets. I used 242 companies to complete the data. The date of the annual data contains the last trading day of the previous year. So, for example, the market value of a company in 2000, is downloaded as 28 th December The criteria whether to use a company was the availability of information. If most of the information was complete and they were available for every year, than I used that specific company, otherwise I excluded the company. I used a time frame of 10 years ( ) with a frequency of one month. Monthly data is more reliable than annual data and with the years , I will compare liquidity before, during and after the crisis. For the processing of the data, SPSS is mostly be used, but also Microsoft Excel. 3.2 Variables The variables requested at Compustat/ WRDS are: - Price (closing price) o This is the price of each specific stock at the end of each month between If the price was not available, WRDS used the average of the closing bid price and the closing ask price of the stock in that specific month. - Absolute return on stock o This is the return of a specific stock in a month in dollars ($) - Percentage return on stock o This is the return of a specific stock in a month in percentage (%). This number was not directly available, so I have to compute this number myself. The formula in Microsoft Excel I used was ln - Market Capitalization o The closing share price times shares outstanding of a company in a specific month - Book Value o Book value of a company in a specific month. Calculated: Book value per share times shares outstanding 12

13 - Risk free rate o Downloaded fro the Fama/French website. Given in percentage (for example 4.5) - Excess Return o This is the return on the stock (multiplied by 100, to have equal numbers in my case) minus the risk free rate. - ILLIQ o This is a measure of liquidity by Amihud. This variable is explained in 3.4 (return/traded volume) - MKT-Rf o This is the return of the market minus the risk free rate in that month in percentage (%). This variable is downloaded from the Fama/French website. It is the first factor of the Three Factor Model - SMB o Downloaded from the Fama/French website. It is the second factor of the Three Factor Model; monthly data - HML o Downloaded from the Fama/French website. It is the third factor of the Three Factor Model; monthly data - Bid Price o This is the bid price of each specific stock at the end of each month between It is the closing bid price of that month - Ask Price o This is the ask price of each specific stock at the end of each month between It is the closing ask price of that month - Bid-Ask Spread o This is the difference between the earlier mentioned ask price and bid price - Traded Volume o Number of traded stocks in that month of that specific stock 13

14 3.3 Three Factor Model In section 2 I discussed the relation between the CAPM and liquidity. But where CAPM uses only one factor, the beta, there is a model that uses three factors: The Three Factor Model. This should give a higher R². r R = α + β ( R R + β SMB + β HML f 1 m F ) 2 3 The SMB stand for small minus big (market capitalization) and HML stand for high minus low (book-toprice-ratio) 3.4 ILLIQUID-Model To measure liquidity, actually it measures the illiquidity, I use the model of Amihud (2002); the ILLIQmeasure. It is a cross-sectional model and. The problem with liquidity is that it cannot be directly measured, but rather has a number of aspects that cannot be captured in a single measure (Amihud, 2002). Illiquidity reflects the impact of order flow on price, which results from adverse selection costs and inventory costs. There must be said that there are better ways to measure the liquidity of a stock, but these methods are complicated and time consuming. Liquidity could be measured for example with bid-ask spread, but it does not necessarily measure well the cost of selling many shares (Acharya & Pedersen, 2004). The formula that Amihud used in his study and is also be used in this paper is: ILLIQ iy = 1/ D D iy iy t 1 R iyd / VOLD ivyd The illiquidity of the stock is here defined as the average ratio of the daily absolute return to the trading volume of that day ( R iyd /VOLD iyd ). R iyd is the return of a specific stock i on day d of year y. VOLD iyd is the volume traded of that specific stock (i) on that day (d) in that year (y). But in stead of the daily return, I use monthly returns and volumes, so the d should be replaced with an m. This ratio gives the absolute/ percentage price change per dollar of weekly trading volume, or the weekly price impact of the order flow (Amihud, 2002). D iy was originally the number of days for which the data was available for the stock (i) in that year (y). Also this D is replaced by an M, because of the use of monthly data. Size does matter in this case, because a larger stock issue has smaller price impact for a given order-flow and a smaller bid-ask spread. So, the higher the ILLIQ, how more illiquid the stock is (Amihud, 2002). In other words, if the stock s price moves a lot in response to little volume, the stock is illiquid. 14

15 3.5 Working Method The first thing I had to do was to complete the data. Because not all the variables are downloadable, I have to compute these variables myself, for example the return and book value, as explained in section 3.2. After the data was completed I made portfolios. The portfolios are based on annual data. The first portfolio was based on market capitalization. Of every year, I made twenty portfolios. The number of companies in a portfolio is the number of companies in a year divided by twenty. The first portfolio is based on market capitalization. The companies are sorted from small to big. So the companies with the lowest market capitalization are in MC1 (the first portfolio based on market cap) and the companies with the highest market cap are numbered with 20. The second portfolio is based on the ILLIQ measure of Amihud (section 3.4). Again, the companies with the lowest ILLIQ are listed in the first portfolio based on ILLIQ, the companies with the highest ILLIQ are listed in portfolio 20. The third portfolio is based on the book value-market capitalization ratio. Like the other portfolios, the companies are sorted from companies with the lowest ratio to companies with the highest ratio. The last portfolio is based on spread, like the ILLIQ a liquidity measure. Like the three other portfolios, these companies are also sorted from ones with small spread to businesses with the highest spread. After I assigned portfolios to companies with annual data, I had to transform the annual portfolios in monthly portfolios. For example, if a company AA is listed in the first portfolio of market cap in the year 2000, than every month, January till December, are listed in the portfolio 1 based on market cap. After I had done this I made tables of average excess return and spread. This means, I calculated the average excess return of every portfolio in every year. The same I did for spread. In this case I got four tables for excess return (one for every portfolio; market cap, ILLIQ, book value/market cap and spread) and four tables for the average spread. The next step was to make betas. The regression I used: Excess _ portfolio _ returni = α + β1 ( MKT Rf ) i + β 2SMBi + β 3HMLi + ε This is a time-series regression. For every portfolio I made this regression, where MKT-Rf is the excess market return. For this reason, I got 80 regressions, which means 240 betas (80x3 betas). I notated for every beta if it was significant or not and the R² of the regression. After this, I know how much betas are significant and positive and what the average R² is. This table is notated the Appendix. 15

16 The last step is to regress the average excess portfolio return (from the eight tables I made earlier) with the betas calculated in the previous step and with the spread, also calculated before. These regressions are cross-sectional. I did this for each four portfolio and for every year. Therefore, I have 4 tables based on every portfolio with each 10 regressions; for each year one. These tables are also notated in the Appendix and explained in the next section. When the numbers are significant, these tables/ regressions show what happen with liquidity premium over the years. Hypothesis: Liquidity has increased after the financial crisis of 2007 In the next section I will discuss the results. 16

17 4. Empirical Results In this section I will show the results of the research. In the previous section I explained what I have done with the time-series regressions. In appendix 1, the 80 regressions are given. For these betas I used: Excess _ portfolio _ returni = α + β1 ( MKT Rf ) i + β 2SMBi + β 3HMLi + ε In table 4.1 is shown that not every beta is significant. The first beta (Excess Market return) was significant; all 80 betas were significant and positive. It is a different story for the other two betas, the beta of the SMB and the HML. About only fifty per cent of the betas were significant and there were even negative significant betas. As shown in the table below, seven of the 43 significant betas were negative. The average R², which is a measure of how good a model could predict future outcomes, is around 16%, which is not very high. It means that the model explains only 16% of the dependent variable, which is in this case the excess portfolio return. The whole list of betas is given in Appendix 1. Beta1 Beta2 Beta3 Aantal sign Aantal pos + sig Aantal neg + sig Aant pos + nsig Aant neg + nsig Average R² Max R² Min R² Table 4.2, R² Table 4.1, Significance of the betas of the time-series regression The next step is to regress the average excess portfolio return (from the eight tables I made earlier) with the betas calculated (table 4.1) and with the spread. The spread and the excess return are given in Appendix 2 and 3. The problem with the tables in Appendix 2 (excess return), is that there is not a clear relation between the portfolio numbers and the excess return. You should expect that there is be a difference between portfolio number 1 and portfolio number 20 and that there is a clear relation between all these 20 portfolios. But this is not the case. This is one of the reasons, which I will also show in this section, that the research is not significant. This is the same for the spread, or liquidity measure. I expected that, for example, the smaller firms (table 1, Appendix 3) are more illiquid than bigger companies. Also you would expect that the liquid firms (low spread, table 4 Appendix 3), have the lowest spread, explained in section 2. Both are not the case. This is the second problem why the last regressions are not significant. This holds not only for the three tables I explained above, also the other five tables have not a clear relation between the portfolios and the excess return or spread. 17

18 The results of the cross-sectional regressions are showed in Appendix 4. Like I mentioned before, I made 40 cross-sectional regressions. With dependent variable average excess portfolio return, and independent variables the betas of the Excess Market return, SMB, HML and the average portfolio spreads. The excess return and spread are shown in Appendix 2 and 3, the betas of the three factor model in Appendix 1. The first thing to notice is the very low adjusted R². The closer this number to zero, the more useless the regression is. The following remarkable number, are the negative betas, for example the negative (and sometimes even significant) betas of the market premium. The reason for this, like I mentioned before, is due to the average portfolio returns and the average spread, because these two variables do not have a clear relation with the portfolio number. The portfolios are made on an annual base, and not a monthly base. So when these two variables are not linked with the portfolios, the cross-sectional regressions would be insignificant, as in this case. Though, I will shortly explain all four tables separately. The first table of Appendix 4 is based on the market capitalization portfolios. The table shows that only a few betas are significant. Only three of the 40 betas are very significant. The hypothesis was to look if liquidity (premium) has changed during the crisis. But also showed in table 1, only two betas of the liquidity premium are significant. The only thing you may conclude is that liquidity in the recovery of the economy (2009) is a little higher than in the beginning of the crisis. But you can not really conclude anything from these tables, because a lot of numbers are insignificant. This is the same for table 2 (IILIQ portfolios) in Appendix 4. Although more betas are significant (ten significant betas), it is hard to conclude anything from this. Also in this table, much of the betas are negative, which is odd, because you will expect positive betas. For example, some of the liquidity risk betas are positive and significant, others are negative and significant. Unfortunately, I have no explanation for this, except the one I already gave. So, also for this table, it is hard, if not impossible, to draw conclusions. This is the same for table 3, which is based on the book value-market capitalization ratio. Only three betas of the liquidity premium are significant (2001, 2004 and 2007). Also for this, it is impossible to say what happened with liquidity, due to the crisis. The last table of Appendix 4, table 4, shows the results based on the spread portfolios. This is the table with the most significant betas, with 12 significant and six of them very significant. But this is still very low and there is not a clear relation between those betas. Some of them are positive, some of them negative. The market risk premium has even 7 negative betas, two of them (very) significant. 18

19 5. Conclusion The aim of this paper was if liquidity has changed due to the crisis. In times of crisis, the demand for high liquid stocks is high, because it is expensive to have illiquid assets in an investor s portfolio. To measure the liquidity of a stock I used the ILLIQ model of Amihud (2002) and the spread of the stock. When Illiq and the spread are high, liquidity will be low. In section 4, where I showed my results, you could see that most of the betas and results are insignificant. Therefore, I can not say if liquidity has changed due to the crisis. Also, I could say nothing about liquidity before the crisis, because these results were insignificant as well. The reasons I gave for this, was due to the fact that there was not any clear relation between the average portfolio excess return. Because of this, the cross-sectional regressions were insignificant, since the excess return was my dependent variable. Therefore, all of the regressions were not useful. Only 41 betas are at least significant at a level of 0.15 (15%) from a total of 160 betas. The restrictions of this paper were, amongst other things, the timeframe. I used only monthly database covering 10 years. Besides that, were still in the after shocks of the crisis and therefore I couldn t study exactly if liquidity will drop at the end of the crisis when the world economy will grow again. Plus I only used companies traded on US stock markets. It is possible that liquidity reacts differently on a crisis in Europe or Asia. 19

20 References 1. Acharya, V.V., Pedersen, L.H. (2003) Asset Pricing with Liquidity Risk, Journal of Financial Economics 2. Amihud, Y., Mendelson, H., Wood R.A., (1990) Liquidity and the 1987 stock market crash, The Journal of Portfolio Management. 3. Amihud Y. (2002) Illiquidity and stock returns: cross-section and time-series effects, Stern School of Business, New York University. 4. Anshuman V.R., Chordia T., Subrahmanyam A. (2001) Trading activity and expected stock returns, Journal of Financial Economics. 5. Avramov, D., Chordia, T., Goyal, A. (2005) Liquidity and Autocorrelations in Individual Stock Returns, SSRN. 6. Bhide, A. (1991) The hidden costs of stock market liquidity, Harvard University. 7. Brennan, Michael J. (2000) Investor Relations, Liquidity, and Stock Prices, Journal of Applied Corporate Finance. 8. Brunnermeier, M.K. (2009) Deciphering the Liquidity and Credit Crunch , Journal of Economic Perspectives - Volume 23, Number 1 - Winter Pages Calomiris, Charles, W., 2008, The Subprime Turmoil: What s Old, What s New, and What s Next, working paper, Columbia University. 10. Chordia, T., Sarkar, A. & Subrahmanyam A. (2003) An Empirical Analysis of Stock and Bond Market Liquidity, Oxford Journal. 11. Datar, V.T., Naik N.Y. & Radcliff, R. (1998) Liquidity and stock returns: An alternative test, Journal of Financial Markets. 12. Demyanyk, Yuliya and Van Hemert, Otto, 2008, Understanding the Subprime Mortgage Crisis, working paper, NYU. 13. Diamond D.W. & Dybvig P.H. (1983) Bank Runs, Deposit Insurance, and Liquidity, Federal Reserve Bank of Minneapolis Quarterly Review. 14. Gomber, P., Schweickert, U. & Theissen, E. (2004) Zooming in on Liquidity, University of Tuebingen. 15. Gorton, Gary, 2008, The Panic of 2007, working paper, Yale University. 16. Grossman S.J. & Miller M.H. (1988) Liquidity and Market Structure, The Journal of Finance. 20

21 17. Hasbrouck J. & and Seppi D.J. (2001) Common Factors in Prices, Order Flows and Liquidity, Journal of financial Economics. 18. Jones, C.M. (2000) A Century Of Stock Market Liquidity and Trading Costs, Columbia University. 19. Martínez, M.A., Nieto, B., Rubioa, G., Tapiac, M. (2003) Asset pricing and systematic liquidity risk: An empirical investigation of the Spanish stock market, International Review of Economics & Finance, 2005, vol. 14, nº 1, p Pastor, L.; Stambaugh R.F. (2003) Liquidity risk and expected stock returns, The Journal of Political Economy. 21. Yakov Amihud (2002) Illiquidity and stock returns: cross-section and time-series effects, Stern School of Business, New York University. 22. Uddin, H. (2009) Reexamination of stock liquidity risk with a relative measure, Studies in Economics and Finance. 21

22 Appendix 1 Portfolio # Constant Beta 1 Sig Beta 2 Sig Beta 3 Sig R² Market Cap Illiq BV/MC Spread =yes 0=no Beta1 Beta2 Beta3 Excess Market return SMB HML 22

23 Appendix 2 Excess return (MC) Excess return (ILLIQ)

24 Excess return (BV/MC) Excess return (Spread)