The influence of financial asset liquidity on
financial asset returns
A study of Dutch listed companies during the past ten years
Name: Mark Stevens, Student number: 10003961
Faculty: Economics and Business, Major: Finance,
Supervisor: J.E. Ligterink, Date: July 8, 2013
Abstract
This paper investigates whether liquidity is an important variable for asset pricing. Data from Dutch listed companies in the time span 2002 till 2012 are used to build a model. In the model the relative bid-‐ask spread of stocks is the measure for illiquidity. The model predicts a higher expected return for stocks which have low liquidity. Other results show that the financial crisis has a significant effect on the influence of liquidity on stock returns. It can be concluded that liquidity is an important variable for asset pricing.
1. Introduction
During finance courses at the University of Amsterdam, the capital asset pricing model (CAPM) is the model which is widely used in applications, such as evaluating the expected performance of portfolios or to estimate the cost of capital for firms. Fama and French (2004) state that the CAPM is often the only asset pricing model which is used during investment courses. Financial asset pricing is important for many investment plans to determine the expected return of assets, but the often-‐used CAPM model faces problems. For example, the risk of a stock should be measured relative to a comprehensive market portfolio. However, this portfolio is difficult to estimate, because in principle this portfolio can include not just tradable financial assets but real estate, human capital and consumer variables as well (Fama and French, 2004). Although it is a simplified model and is easy to use, there could be other factors which influence the return on a financial asset. These factors have to be taken into
consideration when studying or determining financial asset prices.
Therefore, this thesis measures whether the liquidity of financial assets correlates with financial asset returns to determine whether this is a factor which has to be taken into consideration when an asset is priced. The main question in the thesis is: Does asset liquidity affect financial asset returns in the Netherlands? A test will be done for both a linear and a non-‐linear relationship between liquidity and excess returns. Another interesting question is whether an economic crisis changes the influence of liquidity on stock returns. This is relevant due to the recent financial crisis and the problems with difficulties in asset pricing which can be seen as a cause for this crisis. Therefore, to formulate an answer for the sub-‐question, the thesis also investigates liquidity of financial assets during the recent financial crisis and the period beforehand.
Most of the previous research on liquidity and financial asset returns has been done for American markets. The first study on this topic was executed by Amihud and Mendelson (1986). In their study, they use data from NYSE listed companies between 1961-‐1980. A more recent study by Acharya and Pedersen (2003) uses data from companies listed on the NYSE and AMEX in the period 1963 till 1999. Nowadays the trading environment is different if compared to the trading environment in the period used in these previous study’s. It has changed especially due to technological
innovations. High-‐frequency trading for example, is a new way of trading which is done with the help of computers. Computers react on information which becomes available in the market. If there is an arbitrage opportunity, computers act immediately. Zhang (2010) concludes that high-‐frequency increases liquidity in the market. The scope of this research is the Dutch stock market between 2002 and 2012. For this study, Dutch companies are used which are listed on the AEX or AMX stock index. By examining liquidity effects during this period and in the Dutch stock market, the thesis can respond to the changes in the investment environment and focuses on a different market than other study’s use for their data.
For the selected listed firms on the Dutch stock market, information is collected about the bid and ask prices to determine the relative bid-‐ask spread, which is the measure for liquidity in this
study. Other information required is information about company’s market capitalization as the measure for size. Returns on the market and on the individual stocks are determined with the return index. Besides knowing the returns in itself, the returns on the stocks and the market are important to determine the risk of the stock relative to the market. A model can be build with the variables
mentioned above and a dummy variable is added to correct for differences between years. To test a non-‐linear relationship between liquidity and returns, the stocks are grouped based on their liquidity. Group dummies are added to the model, to investigate whether this yields different slopes. When investigating the sub-‐question, another dummy variable for the crisis is added to the model. The ordinary least squares (OLS) method is used to determine a model.
In the next paragraph, a review of related literature is discussed. Then, the research methodology of this study is explained. After the research methodology, there is a paragraph with research results. In the last paragraph, the results are discussed and conclusions are drawn.
2. Literature review
Although liquidity and marketability are important parts of investment plans, the role of liquidity in capital markets was hardly reflected in academic literature until the 1980s. Amihud and Mendelson (1986) were the first researchers who wrote a paper on this topic by studying the effects of illiquidity on asset pricing by using data from American listed firms between 1961-‐1980. In their paper, they stated that an investor faces a trade-‐off when making a transaction. An investor who wants to buy an asset, has to pay a premium for direct buying. On the other hand, if an investor wants to sell an asset, he has to do a concession. This is due to the difference in bid and ask prices. The gap between both prices is called the bid-‐ask spread. If there are more players in the market who want to transact in a particular stock, the width of the spread becomes smaller. Amihud and Mendelson therefore measured the illiquidity as the width of this spread. Thus, in that context, a wider spread implies less liquidity than a comparable asset. The study concludes that returns are higher for assets which have less liquidity than comparable assets, due to the risk involved in holding these former assets. An important aspect of their conclusion is that the relationship between the relative spread and asset return is concave, which implies the decreasing sensitivity of a stock when the spread increases.
Other research on liquidity risk and stock returns by Pastor and Stambough (2003) found that stocks that are more sensitive to aggregate liquidity yield higher returns. This is also the conclusion of Jones (2002). He studied the effects of turnover and spreads and found that higher spreads predict high stock returns in the future. If a link is made to pricing models, liquidity plays also an important role in the pricing of assets. Acharya and Pedersen (2005) found that an adjustment for liquidity in the well-‐known capital asset pricing model (CAPM) explains returns better than the original model does. The study’s mentioned above all yield the same conclusions about the impact of liquidity on returns of financial assets. Also, they all mention the relative subordinate role liquidity plays in asset
pricing. Their study’s are therefore important to consider liquidity as an important predictor of asset prices.
Taking these study’s as a starting point for this thesis, it is expected that illiquidity is positively related to returns. Although the relation is often examined, this study is different from the others. In this paper, the influence of asset liquidity on financial asset returns in the Netherlands is studied. Data is used from the period 2002-‐2012, which is more recent than the data used in previous study’s on liquidity effects. It is expected that the overall conclusion will be the same as made by other
researchers, but there will be differences in the coefficients. This is due to technical innovations past decades which resulted in easier and faster trade possibilities. Although technical innovations and new possibilities, such as high-‐frequency trading, have increased the tradability of assets, there are still positive bid-‐ask spreads present in the market. Assets which are less easier tradable than comparable assets include liquidity risk. Therefore, it is necessary to compensate investors for this liquidity risk with a higher expected return.
As a first step to answer the main question in this thesis, does asset liquidity affect financial asset returns in the Netherlands, a hypothesis is needed. Taking into consideration the previous study’s on the same topic, the testable hypothesis for the main question in this study is that assets with a higher bid-‐ask spread than comparable assets which are traded in the Netherlands yield higher observed returns. This implies a negative relationship between liquidity and the return on financial assets. It is expected that investors see illiquidity as a negative implication of a stock and therefore want to be compensated with a higher expected return.
Formulating a hypothesis for the sub-‐question is more difficult, because the financial crisis has recently occurred. The sub-‐question investigates whether an economic crisis changes the influence of liquidity on stock returns. In order to formulate a hypothesis for the sub-‐question, study’s about liquidity during crisis periods are evaluated. One of these study’s is one of Bernanke (1983), who analyzed the great depression during 1930s. He stated that people prefer more liquidity during a crisis. This is a result of the increased risk-‐averseness during a downturn of the economy. As people become more risk-‐averse, the compensation for liquidity risk has to be higher. Therefore, it is expected that the influence of liquidity of assets has more impact on the return when the economy is in crisis. In the next paragraph the research methodology is explained, which is used to answer the stated hypotheses.
3. Research methodology
The central question in this thesis states: Does asset liquidity affect financial asset returns in the Netherlands? In order to answer this central question, a step-‐by-‐step research method is chosen, to separate different effects on the return of assets. In this paragraph, the research methodology is explained to test the hypotheses. First, information about the data is discussed. Thereafter, the steps
towards the determination of a model are explained for the main question. In the third section, a model is determined which is used to estimate a non-‐linear relationship between liquidity and return. In the remainder of the paragraph, a model is build to explain the influence of a crisis on the relation between liquidity and returns of financial assets.
3.1 Data
To analyze the Dutch stock market, data is used from AEX and AMX listed firms in the interval 2002-‐ 2012. Datastream, a financial database from Thomson Reuters, is used to obtain the required data. Currently, twenty-‐five companies are listed on the AEX and on the AMX, twenty-‐five companies are listed as well. However, only information from firms which were listed during the full period are used. Firms are omitted, because otherwise an equal comparison between the period during the crisis and the period beforehand cannot be made. Companies which are omitted from the dataset are Aperam, DE Master Blenders and TNT for the AEX, and AMG, Delta Lloyd, TomTom and Ziggo for the AMX. The total number of firms in the dataset becomes 43 after the correction. One point to mention is that the omitted stocks, which are new stocks on the AEX or AMX, possibly have a different liquidity than stocks which are listed on stock indices for a longer time. In line with the hypotheses, it is expected that these stocks yield different returns. Omitting these firms from the sample data does therefore not result in a large potential selection bias, because these firms are omitted based on the available data and not as a result of specific data implications such as outliers. The thesis investigates monthly data which are averaged to obtain the average yearly data for the time span between 2002 and 2012. This yields 473 different observations during this interval. Although the data is obtained from different years, the data are pooled together to run a regression.
3.2 The influence of liquidity on the return
In this thesis, the influence of liquidity on returns of financial assets is examined. Therefore, the excess return on a stock states on the left-‐hand side of the model. In the models, excess returns are used instead of normal returns, because differences in returns are easier to interpret if the return is corrected for the risk free rate. In determining the variables for the right-‐hand side of the model, the variables used in the study of Amihud and Mendelson (1986) are taken into consideration. The same variables are used, but in another way.
To study the effect of liquidity on asset returns, a measure needs to be defined for liquidity as this is not directly measurable. Amihud and Mendelson (1986) use the relative bid-‐ask spread as a measure for illiquidity, because the width of the spread is the cost of a direct transaction. In this study the same measure for liquidity is used, because it is a reasonable measure which can be determined from available data. Instead of the normal bid-‐ask spread, the relative bid-‐ask spread is used to correct for differences in stock prices. The relative bid-‐ask spread is measured as the average bid-‐ask spread of a stock during a year. Average bid-‐ask spreads during a year are obtained from weekly bid and ask
prices from stocks listed on the AEX and AMX indices. The subtraction of the bid price from the ask price yields the bid-‐ask spread. Averaging these weekly spreads per year result in an average bid-‐ask spread for a year. The average bid-‐ask spread is then divided by the average of the bid and ask prices of that particular year to determine the relative bid-‐ask spread. As a result, liquidity can be better interpreted, because the relative bid-‐ask spread is a percentage.
The next step is to add control variables. This generates a better model, because control variables decreases under or overestimation of variables. The first control variable is the relative risk to the market for a stock. This variable is chosen, because the riskiness of an asset influences the return of an asset. To determine the relative risk, the CAPM model is used, which measures the relative risk to the market as beta (β). For the risk-‐free rate, the average 3-‐month T-‐bill rate is used. To obtain the returns on the stocks and the market return, the return indexes are used with weekly intervals. Measuring the returns per week and averaging them thereafter yield the average return on a stock per year. Then, with the CAPM model, the average betas per year for the stocks are estimated.
Company sizes differ across different stocks. Therefore, a control variable is added for the company size. The company size is measured as the market capitalization of a company. As other study’s do, the market capitalization is replaced by its natural logarithm to allow for a possible non-‐ linear relationship.
Another variable is needed to eliminate differences between years. It is important that the model allows for differences between the years, because in this way the model corrects for specific events shocking the economy for a small period. For each particular stock, there are eleven yearly numbers of the variables. These observations are numbered for the years. In this way, a set of ten dummy variables for the years is created to correct for these differences.
When combining these variables, the following model can be estimated:
(1) Rexcess
=
a0
+
a
1*βi + b*Si + ∑c*DYn + d*SIZEi + e.In this model (1)
a0
,
a1, b, c and d are the coefficients and e is the error term.Here, beta (βi) is the relative risk of stock i. The second variable, Si, is the relative bid-‐ask spread for stock i, which is explained in the first section of this paragraph. DYn is the dummy variable where n implies the different years. DYn is one when de stock is in year n and zero otherwise. The variable SIZE is the variable which measures the size of the company. The size of a company is measured as the natural logarithm of the market capitalization for a listed company.
Estimation of the model is done with the Ordinary Least Squares (OLS). When estimating the model with OLS, a regression of the excess returns (Rexcess) on relative risk (βi), the relative spread (Si), the year-‐dummy variables (DYn) and the size of the company measured by it market
capitalization (SIZEi) is run.
3.3 Estimation of a non-‐linear relationship
Model one (1) is a linear regression, which implies a straight line. However, Amihud and Mendelson (1986) build a model which tests their hypothesis that the observed market return is not only increasing but also a concave function of the relative spread. This implies that the larger the relative bid-‐ask spread of an asset is, the smaller the increase in the realized return becomes on the asset compared to the return on an asset with a smaller relative spread. Testing for this concave relationship requires the model to allow for different slopes. In this way, the model will be more precise if the slope of the line is different for the different portfolios. To allow for these different slopes, the variable S is decomposed in different variables, where Si,g = S if the spread of stock i is in group g and zero otherwise. The groups are divided based on their spread, where group one has the lowest average spread and group 6 the largest. When testing for a concave regression, the following model is used:
(2) Rexcess
= a0
+
a1*βi + ∑b*Si,g + ∑c*DYn + e.
3.4 Influence of an economic crisis
The thesis also wants to estimate the effect of the coefficient of liquidity on the return of a financial asset, when the economy is in crisis. Therefore, it is important that the model allows for a change in the liquidity coefficient when the economy is in crisis. A dummy variable is added which yields one if the economy is in crisis and zero if not. Next to the dummy variable, an interaction variable is added to the model, to study whether a crisis strengthens or weakens the effect of liquidity on return. Because data is used between 2002 and 2012, the crisis period is defined from 2008-‐2012. Adding a dummy variable and an interaction variable related to a crisis, to the original model yields the following model:
(3) Rexcess
= a0
+ a1*βi + b*Si + ∑c*DYn + f*DC + g*Int + e.
After this model is estimated with OLS, the effect of a crisis on the coefficient of liquidity can
be interpreted.
The description of the execution of the research method is given in the next paragraph. Also
the different models are summarized together.
4. Research results
Stata was used to obtain the research results from the models explained in the previous paragraph. Before regressions of the models, it is important to evaluate the correlations between the main coefficients of the model. The correlation coefficients are shown in table 1.
Correlation coefficients
Rexcess and βi Rexcess and Si Si And βi
0.1585 0.0186 -‐0.1339
Table 1
None of the correlations are very high, which implies that the coefficients in the models are not highly interrelated. The thesis now turns to the part where the models are estimated. First of all, different regressions are discussed. Thereafter, all the regressions will be summarized and shown in a table. As a first step, an OLS regression is executed of the excess returns on the relative risk to the market (β), the relative spread, and the year dummy variables (t-‐statistics are in parentheses):
(A) Rexcess
= 0.00248 + 0.000187 *βi + ∑c*DYn + e (1.44)
and
(B) Rexcess
= 0.00215 + 0.000213 *βi + 0.151*Si + ∑c*DYn + e. (1.66) (3.67)
The results show that excess returns are increasing in both β and the relative spread. The coefficient of Si implies that an increase of the relative bid-‐ask spread with 1% is associated with an increase of 0.151% in the excess return. Furthermore, the coefficient of β does not significantly change when the relative spread variable is added to the model.
Next, the variable for the size of company is added to the model which yields
(C) Rexcess
= 0.00373 + 0.000213 *βi + 0.127*Si + ∑c*DYn -‐ 0.000195*SIZEi + e. (1.66) (2.73) (-‐1.13)
The results indicate that adding a variable for the size of a company does not contribute to the validity of the model, because the variable for size is not significant if an alpha of five percent is used. However, this is possibly due to the relative small number of companies used in this study. In other study’s,
researchers found a very small relation between the company size and the returns of stocks (Amihud and Mendelson, 1986).
Now a simple linear model has been determined, a test for a non-‐linear relationship is executed by grouping the companies in six different spread groups. Therefore, five different spread dummies were created. In this way, the thesis tests whether different spread groups yield different slopes. Replacing the original bid-‐ask spread variable for the six dummy variables yields the following model.
(D) Rexcess
= 0.00635 + 0.00024 *βi + ∑b*Si,g + ∑c*DYn + e. (1.90)
From table 2 it can be stated that the dummy variables are all significantly different from zero if an alpha of five percent is used. However, the hypothesis that the influence of liquidity on excess return decreases when the relative bid-‐ask spread increases cannot be stated as true, based on this data. This is because the coefficients of group two and four are not in line with the hypothesis. It was expected that the coefficients tend to go to zero if the stock moved up to a higher group, but the coefficients of group two and four are tending to go more away from zero than their previous group did. Thus, the concave relationship between the bid-‐ask spread and returns on financial assets, as suggested by Amihud and Mendelson (1986), cannot be found using this dataset.
Estimated regression coefficients Variable OLS coefficients T-‐statistic
Si,1 -‐.0040599*** -‐3.60
Si,2 -‐.0047992*** -‐4.42
Si,3 -‐.0034803** -‐2.95
Si,4 -‐.0041107*** -‐3.70
Si,5 -‐.0025343** -‐2.24
(*,**,*** imply significance levels of 0.10, 0.05 and 0.01) Table 2
The sub-‐question in this paper questions whether a crisis has impact on the influence of liquidity. Therefore, a crisis dummy and an interaction variable of crisis and liquidity are added to the model. When a regression is run of excess return on relative risk to the market, the relative bid-‐ask spread, year-‐dummy variables, the crisis dummy and the interaction variable of crisis and liquidity, the following model is estimated:
(E) Rexcess
= -‐0.0451+ 0.000217*βi + 0.224*Si + ∑c*DYn + 0.0476*DC – 0.282*Int + e.
(1.71) (4.72) (39.89) (-‐3.02)
From the model, it can be derived that the crisis dummy and the interaction variable are both significant for an alpha of five percent. The hypothesis states that an economic crisis increases the influence of liquidity, because people prefer safer assets during a period of economic downturn. For the crisis to have a positive effect on the liquidity effect, the coefficient of the relative bid-‐ask spread in this model has to be significantly different from the model without the crisis dummy and the
interaction variable. Using a T-‐test between the coefficients of the liquidity coefficient in regression B and E yields a value of 25.07 which implies a highly significant positive change of liquidity coefficient when the crisis variables are included in the model. Thus, from this data, it can be derived that the liquidity of financial assets becomes more important if the economy is in crisis. This conclusion supports the statement of Bernanke (1983) that investors have other liquidity preferences during an economic downturn.
In table 3, all the regressions are summarized. The coefficients of the spread groups are not shown in this table, because these are already shown in table 2. Also, the coefficients of the dummy year variables are excluded in this table, because these are not the most relevant variables. These coefficients are showed in table 4 in Appendix 1.
Summary statistics with excess return as dependent variable
Regression
Variable A B C D E
βi 0.000187 (1.44) 0.000213* (1.66) 0.000213* (1.66) 0.000244* (1.90) 0.000217* (1.71) Si -‐ 0.152*** (3.67) 0.127* (2.73) -‐ 0.224*** (4.72) logSize -‐ -‐ -‐0.00195 (-‐1.13) -‐ -‐ DC -‐ -‐ -‐ -‐ 0.0476*** (39.89) DInt -‐ -‐ -‐ -‐ -‐0.282** (-‐3.02) Intercept 0.0025** 0.0023** 0.0037** 0.0064*** -‐0.0451*** Observations 473 473 473 473 473 F-‐statistic 396.37 374.30 345.81 283.94 352.30 R-‐squared 0.9044 0.9071 0.9074 0.9088 0.9088 Adj. R-‐squared 0.9021 0.9047 0.9047 0.9055 0.9063
(*,**,*** imply significance levels of 0.10, 0.05 and 0.01) Table 3
5. Conclusion and discussion
This thesis studies the effect of the liquidity of financial assets on their returns. To measure illiquidity, the relative bid-‐ask spread is used. The bid-‐ask spread represents the costs for an investor willing to transact directly on a market. Data from companies which are listed at the two biggest stock exchanges in the Netherlands during the period between 2002-‐2012 are investigated to estimate a model with OLS. The variables which are used in the model are obtained from a previous study’s on the effects of liquidity.
The main hypothesis stated that stocks with a higher relative bid-‐ask spread yield higher returns. From the models which were determined in the previous paragraph, it can be concluded that liquidity actually influences the returns of financial assets. When the bid-‐ask spread increases, a larger excess return is expected. An increase in the spread implies less liquidity for an asset, because the gap between askers and bidders increases. As stated before, the predicted higher return can be seen as the direct result of the extra risk involved in holding these assets. Investors facing more risk, have to be compensated for a larger return. The return in the model is already risk-‐adjusted, because the stocks’ relative risk to the market is included in the model. However, the beta variable in the model isn’t significant for an alpha of five percent. But, following the CAPM model, stocks which involve more risk relative to the market yield higher expected returns.
Another interesting fact from this data is a negative correlation between risk and the relative spread. Normally, a positive correlation is expected, because assets with a higher spread include more risk, due to the liquidity risk. A negative correlation can be explained, because there is a crisis period involved. During a crisis, betas become less positive due to bad performance of stocks. At the same time, there will be less investors trading in the stock market, because investors prefer saver assets. This results in a larger bid-‐ask spread. Decreasing and negative betas while the bid-‐ask spread
increases result in the negative correlation between the relative bid-‐ask spread and the beta of stocks. Because the time interval includes a period of the recent financial crisis, it was interesting to compare the effect of liquidity in a period of economic downturn with a normal economic period. Therefore, a dummy variable for crisis and an interaction variable between the relative bid-‐ask spread and the crisis were added to the model. The coefficient of the liquidity variable positively changed significantly when the model was adjusted for these crisis-‐related variables. It can be concluded that during an economic downturn the direct effect of liquidity becomes more important for investors. Investors expect a higher return on their assets, because the liquidity-‐risk is higher valued during times of economic downturn.
In the introduction of this thesis, asset pricing with only the CAPM model was questioned. With the outcome of this study, it can be stated that it is also important to take other factors into
consideration when studying or determining asset returns. Liquidity measured as the bid-‐ask spread is easily interpretable and is therefore a good topic to discuss in finance courses. Previous study’s on
liquidity made this relationship already clear, but this thesis which is focused on more recent data confirms that this conclusion still holds and is also applicable to the Dutch market.
The research methodology in this thesis is more simplified compared to the research method in other papers where liquidity effects on asset pricing are studied. Nevertheless, with this research method, the research questions can be answered and the subject of liquidity can be studied. Amihud and Mendelson (1986) grouped stocks in portfolios based on their bid-‐ask spread and relative risk to the market. Unfortunately, this was not possible when analyzing Dutch stocks. There are far less companies listed on the Dutch stock market than there are on American markets. Research is therefore more limited. To obtain more data, a larger time span can be used in a next study. In this way, a better prediction can be made. This time period was especially chosen to use the same amount of data for the crisis period as in the period beforehand. Another important thing to mention is that the current time span which is used in this study is maybe not representative to normal economic
circumstances. At the start of the interval in 2002, the market was still rehabilitating from the internet bubble which had occurred at the start of the century. With the upcoming high-‐frequency trading and the start of the financial crisis, the data were difficult to interpret because all the events were present at the same time. When the economic downturn is over, this period can be analyzed again and with a broader overview, more precise conclusions can be drawn.
6. Literature References
Acharya, V.V. and L.H. Pedersen (2005). Asset Pricing with Liquidity Risk. Journal of Financial Economics. Number 77, pages 375-‐410.
Amihud, Y. and H. Mendelson (1986). Asset Pricing and the Bid-‐Ask Spread. Journal of Financial Economics. Number 17, pages 223-‐249.
Bernanke, B.S. (1983). Non-‐Monetary Effects of the Financial Crisis in the Propagation of the Great Depression. The American Economic Review. Volume 73, number 3, pages 257-‐276.
Fama, E.F. and J.D. MacBeth (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81, 607-‐636.
Fama, E.F. and K.R. French (2004). The Capital Asset Pricing Model: Theory and Evidence. The Journal of Economic Perspectives. Volume 18, number 3, pages 25-‐46.
Jones, C.M. (2001). A Century of Stock Market Liquidity and Trading Costs. Graduate School of Business, Columbia University working paper.
Pastor, L. and R.F. Stambough (2003). Liquidity Risk and Expected Stock Returns. Journal of Political Economy. 111, 3, pages 642-‐685.
Zhang, X.F. (2010). High-‐Frequency Trading, Stock Volatility, and Price Discovery. Yale University School of Management working paper.
Appendix 1
In addition to the paragraph with research results, table 4 shows the coefficients of the dummy year variables.
Summary statistics with excess return as dependent variable
Regression
Variable A B C D E
DY, 2002 -‐0.0253*** (-‐20.95) -‐0.0265*** (-‐21.45) -‐0.0264*** (-‐21.39) -‐0.0267*** (-‐21.33) 0.0200*** (16.24) DY, 2003 -‐0.0067*** (-‐5.51) -‐0.0074*** (-‐6.13) -‐0.0074*** (-‐6.14) -‐0.0077*** (-‐6.26) 0.0393*** (32.63) DY, 2004 -‐0.0107*** (-‐8.82) -‐0.0112*** (-‐9.33) -‐0.0112*** (-‐9.32) -‐0.0116*** (-‐9.34) 0.0356*** (29.87) DY, 2005 -‐0.0268*** (-‐22.26) -‐0.0270*** (-‐22.69) -‐0.0270*** (-‐22.68) -‐0.0270*** (-‐22.43) 0.0200*** (16.94) DY, 2006 -‐0.0435*** (-‐36.10) -‐0.0436*** (-‐36.64) -‐0.0435*** (-‐36.53) -‐0.0435*** (-‐36.50) 0.0034** (2.91) DY, 2007 -‐0.0470*** (-‐39.02) -‐0.0471*** (-‐39.56) -‐0.0470*** (-‐39.41) -‐0.0468*** (-‐39.38) Omitted because of collinearity DY, 2008 -‐0.0247*** (-‐20.48) -‐0.0248*** (-‐20.85) -‐0.0248*** (-‐20.81) -‐0.0247*** (-‐20.75) -‐0.0246*** (-‐20.85) DY, 2009 0.0058*** (4.81) 0.0057*** (4.76) 0.0057*** (4.75) 0.0057*** (4.81) 0.0058*** (4.94) DY, 2010 -‐0.0007* (-‐0.59) -‐0.0005 (-‐0.44) -‐0.0005 (-‐0.45) -‐0.0009 (-‐0.73) -‐0.0009 (-‐0.72) DY, 2011 -‐0.0074*** (-‐6.12) -‐0.0074*** (-‐6.20) -‐0.0074*** (-‐6.18) -‐0.0073*** (-‐6.08) -‐0.0075*** (-‐6.29) (*,**,*** imply significance levels of 0.10, 0.05 and 0.01)
Table 4
