In Search For Liquidity
Zeki Kurt
*1545752
Master Thesis Economics
Faculty of Economics and Business, University of Groningen, Groningen, NL
____________________________________________________________________ Supervisors:
G. Kuper Abstract:
This paper analyzes the relation between market wide variables and liquidity of the AEX and AMX during the period 2007-2011. To measure this relationship, market wide variables are determined from stock movements. Together with company specific determinants, that are unrelated to the market performance, using time series and cross-sectional estimation the effect on liquidity is determined. The results show that stock return co-movement does not affect liquidity while beta and systematic volatility do have an effect on liquidity.
Keywords:
Volatility, liquidity, stock returns, Dutch stock market, market microstructure. JEL Classification:
G12, G14
_________________________
1
Introduction
Liquidity is `...a slippery and elusive concept, in part because it encompasses a number of transactional properties of markets' (Kyle, 1985). Unsurprisingly, liquidity is a complex concept that is determined by important properties of the stock markets.
During the financial crisis of 2007-2008, the importance of liquidity became very apparent. Since financial institutions were faced with market tightness for credit. Financial institutions were reluctant to lend to each other fearing that it would end up in more credit drought. This fear clearly affected the liquidity of the market. The spillover effect caused banks to vastly reduce their lending towards the companies and households.
The effect of the financial crisis also reached the Netherlands. Not only did the financial institutions suffer, the equity markets in general were hit severely. Although the source of the crisis was the subprime mortgages, the effects to the economy were amplified through the financial institutions, since they were the parties that suffered the most. Due to the financial crisis, the Dutch stock markets tumbled as well.
Previous research has mainly focused on time-series data alone to question the effect of stock price movement on liquidity (Campbell and Hentschel, 1992 and Glosten, et al., 1993). However, the question of how stock return and volatility affects the cross-section of liquidity measurements has received considerable less attention. In addition, most research regarding stock markets is predominantly done for the US market.
Even though it is fully understandable why the general focus is on the large US equity markets. It is, however, important to shift attention to other stock markets that endured the financial crisis as well. The relevance of the Dutch stock markets comes from the idea that equity markets from Anglo-Saxon regions differ from pan-European regions (Allen and Gale, 2004). Therefore, there is a ground to investigate the Dutch stock market to analyze the relation between the stock movement and liquidity.
By studying the important determinants of liquidity, financial institutions and market participants can find out what drives the speed of buying and selling of stocks. There is, however, ample research regarding the liquidity of the Dutch stock markets after the period of the financial turmoil. Investigating the relation between liquidity and stock movements fills this academic gap.
What makes this investigation so special? Even though the focus is on the thoroughly analyzed financial crisis, the combination of the empirical tools and market focus has not been done before. Firstly, this paper analyzes the stock market in an unusual way by not focusing only on time-series but also on cross-section, thus a combination of both. Secondly, the research centers itself on the Dutch market.
The red thread of this study is the effect of market wide variables on liquidity. The focus, however, is on the Dutch stock markets during the period of 2007-2011. Therefore, the research question is; did market wide determinants affect the liquidity in the Dutch stock markets during 2007-2011.
is that there exists no relation between liquidity and the liquidity proxies during the financial crisis. Consequently, by testing the relation between market wide variables and liquidity proxies, it can be shown whether liquidity in the Dutch equity markets was affected during the 2007-2011 period.
This research question is relevant for two cases. The first reason is that it analyzes the Dutch equity markets and the relation with liquidity during the financial crisis. Not only is the relevant liquidity determinant exposed, this paper also provide criticism and potential areas where research can continue. The second reason is for the stock trader. Traders that formulate a trading strategy for the Dutch market can observe whether market wide determinants interact with liquidity during a crisis.
Stock on the equity markets in daily market circumstances show minor movements. This is mainly due to the availability of new information; stock prices move up (down) and recover to their initial position afterwards, at least this is the most frequent occurring trend. The genuine stock value increase occurs over time when companies perform better. So, it can be argued that stock markets, at least in the short run, rarely show real movement.
Therefore, the financial crisis created an opening to look into the mechanism of stock movement and liquidity. The financial crisis on the equity markets granted a great opportunity to investigate the relation between stock movement and liquidity more thorough. The literature regarding the topic of liquidity is vast, yet there is some room to extrapolate this phenomenon when circumstances are reversed. Implying strong negative market growth with bad economic outlook.
2
Literature review
2.1 Market microstructure
Regarding the role of financial intermediaries, Stoll (1978) provides supplementary concepts of how liquidity-providing intermediaries clear markets. Stoll (1978) states that the market maker is a market participant that is willing to change its own portfolio to accommodate the trading behavior of the market traders. Since the market maker is a market participant, the market maker is assumed to be risk averse and must be compensated for bearing the risk. This compensation comes from the bid-ask spread that also reflects the cost the market makers makes to endure the risk. Implying that when the bid-ask spread is low, the cost of risk exposure is low as well.
Furthermore, Stoll (1978) suggests that the cost of providing and enhancing liquidity is determined through three factors. Firstly, the cost of holding the asset imposed by the suboptimal portfolio position that causes a risk exposure. Secondly, there is order-processing cost. Thirdly, the asymmetric information cost that arises when informed traders are present in the market. The implications to intermediaries are that they act as an investor with a preferred investment portfolio based on the investment opportunities and preferences.
In this context, providing liquidity means that the intermediary deviates from its optimal portfolio in order to supply and demand the stocks the intermediary is specialized in handling them. This causes the intermediary to be exposed to unnecessary risk and moves to a risk return trade-off level that does not match its preferences. Therefore, the intermediary compensates for bearing excess risk by creating a margin, or a bid-ask spread, between the buying and selling of an asset.
According to Amihud and Mendelson (1980), the market maker’s actions can be described as a stochastic flow of buy and sell orders whose mean rate per unit of time is price dependent. The market maker should follow a strategy of linking prices to inventories to evade major losses. Stock price becomes a monotonically decreasing function of inventory, resulting with a positive spread. Additionally, the explicit behavior of the bid-ask spread with volume can be interpreted as a function of the inventory position, proving that the optimal pricing policy is consistent with the efficient market hypothesis. Amihud and Mendelson (1980) suggest that it is difficult to continuously gain by speculating in the market, except if the market maker is a true monopolist.
2.2 Liquidity proxies
trader.
The three propositions of Ho and Stoll (1981) are important clarifications why bid-ask spread movement is used. Firstly, the bid-ask spread is subject to the time horizon of the market maker. Meaning that when the period closes to its end, the risk that arises through intermediation decreases for the market maker since the time period of which the market maker must hold inventory decreases. Secondly, the bid-ask spread depends on the market maker’s risk aversion, the size of the transaction and stock volatility risk. Thirdly, the bid-ask spread is independent of the inventory level.
Also, Hasbrouck (1991) report that the price impact along with the adverse selection risk is higher for smaller firms. Breen, et al. (2002) shows that the price impact of a certain trade is related to a number of firm specific variables. Just like the price impact that is proposed by Kyle (1985), it is an apt method of measuring the relation to liquidity of financial assets in the stock markets.
Corresponding with Kyle (1985), the price impact determines the price increase of an extra buy order. The reciprocal of the price impact can be regarded as the market depth. If the price impact is low, a supplementary order will not cause a large price change, meaning that the market is considerably liquid. When there is a small price impact of an additional order, characterized by a low price impact, this would cause the insider to trade more frequently and aggressively. This expected profit is increasing in σG processes the informational advantage of the insider. A higher
variance of u, the noise traders, advocates more liquidity trading this specifies more prospects for the insider to hide his trading pattern based on the information asymmetry. The market maker breaks even on average due to the losses to the insider that makes a profit of the same size as the loss of the market maker. Yet, the market maker gains the same amount from trading with the noise traders. Accordingly, the insiders’ expected profit is the noise traders’ expected trading costs. Half of the information that the insider possesses is exposed after one trading round, this means, the latest variance of the true value of the stock conditional on the net order flow is just half of the original unconditional variance.
Another measure that is used for liquidity is based on the absolute daily return of a stock divided by the firm’s daily dollar volume. Amihud (2002) derived this method of price impact on trade are considered liquid if a large volume of shares is being able to trade without distorting the price considerably.
2.3 Market wide variables 2.3.1 Stock return co-movement
The relation between liquidity and stock returns shows a pattern. Meaning that liquidity properties of stocks indicate that illiquid assets do have a higher expected return (Amihud and Mendelson, 1986; Amihud and Mendelson, 1989; Brennan and Subrahmanyam 1996; Brennan, et al., 1998; Amihud 2002; Chordia, et al., 2009).
According to Persaud (2003), liquidity of individual stocks shows a dynamic pattern. Indicating that high volatility of stock returns increases the uncertainty of the stock position and the investor finds it more difficult to trade that specific stock. These stocks become illiquid. For example, an investor that needs to reduce the risk in his portfolio may choose to sell his stock at fire-sale prices or by selling his most liquid assets. In some cases, a market may become illiquid and thus eradicating the chance for the investor to enter or exit the position.
Several other studies record that stock return co-movement among individual stocks is noticeably higher in certain countries than others and that it is of a relatively low level in the U.S. (Morck, et al., 2000; Campbell, Lettau, et al., 2001; Jin and Myers, 2006). Whereas there is commonality in the returns of individual stocks in the U.S. (among others, Chordia, et al., 2000; Hasbrouck and Seppi, 2001; Huberman and Halka, 2001; Coughenour and Saad, 2004). This is an indication that research of the U.S. market has not reached a clear consensus.
The theory of market microstructure creates a function for liquidity in the price-setting process and trading process of assets. Some studies demonstrate that liquidity is valued as a determinant or as a systematic cause of risk (Amihud and Mendelson, 1986; Pastor and Stambaugh, 2003; Acharya and Pedersen, 2005; Lee 2006; Sadka 2006; Korajczyk and Sadka, 2008). Stock returns that are strongly related to liquidity show signs of high co-variation.
Correspondingly, it is empirically proven that stock return co-movement to have an effect on liquidity. (Hasbrouck and Seppi, 2001; Chordia, et al., 2000; and Huberman and Halka, 2001). Co-movement in liquidity implies that liquidity is formed through common factors. If traders would put orders to market makers to either buy or sell an asset simultaneously, the inventories of market makers would be significantly affected and this would have implications with respect to liquidity.
According to Baruch, et al. (2007), asset returns on the exchanges are correlated, meaning that a competitive market maker obtains information from all order flows. Furthermore, Baruch, et al. (2007) propose that when the model is in equilibrium the stock returns that are highly correlated are more important in pricing the other stock to which it is correlated with. This means that liquidity traders choose where the investment of the cross-listed assets should occur. Since, higher correlation of the cross-listed stock returns with the native stock implies more informative native order flow. Resulting into increasing liquidity and informed traders form a larger share of their order of the cross-listed stock. Meaning, more volume trade occurs on the exchange where the cross-listed stocks have higher correlation on the other exchange.
Additionally, Baruch, et al. (2007) also show that high correlation between two stocks eases trade since the adverse selection risk decreases and increases the incentives to trade the stock and decreases the sensitivity of the stock price to its own order flow. Therefore, stock return co-movement is positively related to liquidity.
Stock return co-movement also can have a positive relation with liquidity. According to Baruch and Saar (2009), liquidity increases when stocks are listed on an exchange along with other comparable stocks. Baruch and Saar (2009) show that when stocks move from one exchange market to another, the stocks show a return movement that is comparable to the stock that in the new exchange. Furthermore, they indicate that liquidity improvements for the companies that switch exchanges have similar stock return movements.
The first set of hypotheses focuses on the relation between stock return co-movement and the respective liquidity drivers. Here, there are three important liquidity determinants that define the magnitude in the Dutch market:
Hypothesis 1a
H0: Stock return co-movement does not have an effect on bid-ask
spread. Hypothesis 1b
H0: Stock return co-movement has no relationship with price impact.
Hypothesis 1c
H0: Stock return co-movement has no relation with the daily return
of one-dollar trading volume.1
2.3.2 Beta
relationship between beta and average returns. Nonetheless, Wood (1991) discovered just weak evidence in the Australian markets and Faff (1991) shows moderate evidence, though Faff (2001) indicates that there is no relationship between returns for the standard CAPM and beta. Halliwell, et al. (1999) reproduces the Fama and French (1993) analysis and discover the extent and significance of the parameters to be in line with the results obtained by Fama and French (1993).
Amihud and Mendelson (1986) focused on the relationship between liquidity and stock returns. Overall, they find a negative (positive) relation between stock returns and a variety of liquidity (illiquidity) measures. Nevertheless, there is no clear consensus among scholars. For example, recently, Acharya and Pedersen (2005) document that there are premiums for liquidity risks. However, Chordia, et al. (2001) find a negative and strong relation between liquidity volatility and expected stock returns, even after controlling for the size, book-to-market ratio, momentum, price level and dividend yield effects, which is inconsistent with the notion that investors are risk averse to fluctuations in liquidity.
The generally accepted and complementary component to the beta is idiosyncratic share. Economic theory proposes that idiosyncratic volatility has to have a positive relationship with stock returns. According to Malkiel and Xu (2006) and Jones and Rhodes-Kropf (2003), when investors cannot diversify their risk, the demand a premium that covers that risk. Merton (1987) advocates that in information segmented market companies with superior company-specific variances necessitate greater average stock returns to recompense investors for holding imperfectly diversified investment portfolios. So, in the case of high exposure to aggregate volatility risk, expected stock returns tends to be low.
The literature regarding idiosyncratic volatility shows two important results. The first being is that there is a significant and positive relation between idiosyncratic volatility and stock returns. The second is the failure to find any significant relation between idiosyncratic volatility and stock returns. Lintner (1965) illustrates that idiosyncratic volatility conveys a positive coefficient in cross-sectional regressions. Lehmann (1990) demonstrates a significant and positive coefficient on idiosyncratic volatility during its sample period. Correspondingly, Tinic and West (1986) and Malkiel and Xu (2006) explicitly show that portfolios with considerably higher idiosyncratic volatility have higher stock returns, yet they do not present significance levels for their idiosyncratic volatility premiums. Instead, Longstaff (1989) discovers that a cross-sectional regression coefficient on total variance for size sensitive portfolios brings an insignificant negative relationship.
The second set of hypotheses focuses on the relation between the beta and the liquidity. Since beta is considered as the correlated volatility of a stock with respect to the volatility to the market. Here it is considered that the beta is negatively related with the liquidity proxies. The hypotheses concerning the beta are:
Hypothesis 2a
H0: Beta does not affect bid-ask spread.
Hypothesis 2b
Hypothesis 2c
H0: Beta has no relation with the daily return of one-dollar trading
volume. 2.3.3 Systematic volatility
Investors with comparable trading strategies could show correlated transaction patterns. According to Chordia, et al. (2000), this implication could prompt changes in market makers’ inventory. Market makers that deal with portfolios have to be prepared when orders of buying or selling comes in high quantities. Therefore, systematic risk would have a negative effect on the liquidity provisions of market makers. This negative effect, however, could be smaller than the negative effect of idiosyncratic risk on the liquidity provisions of market makers.
In addition, Chordia, et al. (2000) sdemonstrates that market-wide variables positively and significantly determine liquidity for approximately 55% of NYSE stocks. Huberman and Halka (2001) discover similar results, exposing that liquidity across stocks has certain systematic factor in a sample of daily NYSE data. Concerning the reasons, Coughenour and Saad (2004) claim from a liquidity supply viewpoint that market makers are one cause of liquidity commonality.
For markets without liquidity providers, Brockman and Chung (2002) and Bauer (2004) record the presence of liquidity commonality in the virtuously order-driven venues of the Hong Kong Stock Exchange and the Swiss Stock Exchange. Brockman and Chung (2006) express that equity index merging is a noteworthy foundation of commonality in liquidity for stocks transacted on the Hong Kong stock exchange, whereas Chordia, et al. (2000), Hasbrouck and Seppi (2001) do not allocate an explanatory role to the market. Instead, they perform a principal factor and correlation analysis to examine whether there are common factors in the order flow, stock return and liquidity. Though the liquidity of the Dow stocks in 1994 presents a single common factor, the commonality in liquidity is not strong and is even weaker than the commonality in stock return and order flow.
Investors want to diversify the risk when market volatility changes. According to Campbell (1993, 1996) and Chen (2002), increasing volatility characterizes worsening in investment prospects. Risk-averse investors demand stocks that hedge against this possibility. According to French, et al. (1987) and Campbell and Hentschel (1992), episodes of high volatility also tend to correspond with descending market movements.
Assets with high sensitivities to market volatility risk offer hedging possibilities against market downside movement. According to Bakshi and Kapadia (2003), when the demand for assets with high systematic volatility increases, the asset price increases and returns decreases. Additionally, poor performing stocks have in the case of increasing volatility a negatively skewed stock returns over transitional horizons, whereas stocks that perform well when volatility increases tend to have positively skewed stock returns.
on their trading strategy to include assets that posses a larger systematic component can result into enhancing liquidity.
Baruch, et al. (2007) study the market-wide volatility with respect to company-specific volatility to obtain the stock return co-movement to show that stock return co-movement has an effect on trading volume and therefore on the liquidity. Baruch, et al. (2007) develop a model of multi-market trading to clarify movements in the U.S. part of international trading volume. This model expects that the delivery of trading volume across exchange markets competing for orders have a relation with the cross-listed asset returns and the returns of other assets traded in their subsequent markets.
In addition, the relation of idiosyncratic and systematic volatility with respect to liquidity is insufficiently researched for the Dutch market to make a clear statement about the interaction. Since, these volatilities differ significantly in their nature they should have a considerable impact on the liquidity as well. Goyal and Santa-Clara (2003) show empirically that there is a positive relation between the idiosyncratic volatility and average stock returns. Here, increasing idiosyncratic volatility would suggest increasing returns. Yet, one would simply argue that this is risk-return trade-off. However, Bali, et al. (2005) prove that the idiosyncratic volatility could act as a representation for liquidity, meaning that the evidence shown by Goyal and Santa-Clara (2003) is only a reproduction of a premium on liquidity.
The third set of hypotheses focus around the systematic volatility and the liquidity proxies. This volatility is always present yet can change during periods of high and low uncertainty. When there is high uncertainty in the market, as it was the case after the financial crisis of 2007-2008, market are subject to high systematic volatility. The hypotheses are:
Hypothesis 3a
H0: Systematic volatility does not affect bid-ask spread.
Hypothesis 3b
H0: Systematic volatility has no relationship with price impact.
Hypothesis 3c
H0: Systematic volatility has no relation with the daily return for
one-dollar trading volume. 2.4 Company specific determinants
2.4.1 Company size
According to Amihud (2002), company size, or the market capitalization, is usually positively correlated with a stock’s liquidity. Consequently, liquidity offers a possible clarification for the size effect. Consistently, in Australian markets, Beedles, et al. (1988) have found that large companies have stocks with better liquidity and suggest that liquidity partly explains the size effect. Amihud and Mendelson (1986) propose that liquidity is an imperative characteristic of a financial investment and should control a premium in asset pricing. The company size is a proxy for the adverse selection risk.
2.4.2 Turnover
Turnover is ratio measurement of the daily trading volume with respect to the number of shares outstanding. Chan and Faff (2003) use turnover as a determinant for liquidity and discover that turnover is negatively related to stock returns and that this continues even after controlling for company size, beta and momentum. In addition, Marshall and Young (2003) study the liquidity in the Australian market, and similar to the results of Chan and Faff (2003) they conclude that there exists a negative relationship between turnover and stock returns.
Looking at the trading volume, which is determined as the aggregate of order flows, it can have a relation with liquidity as well. Hasbrouck and Seppi (2001) show that common features in stock returns have a microstructure foundation in order flows. While, Cremers and Mei (2007) find that trading volume is crucial since systematic stock returns can be the reason for a big fraction of co-variation in stock turnover.
2.4.3 Price inverse
3
Methodology
3.1 Relations
Variation in liquidity is explained by two important determinants. Namely market wide and company specific components. Through empirical analysis, the extent of these determinants on liquidity is measured.
Liquidity proxies = Market wide + Company specific (3.1)
The market wide component is basically the correlation a single company has with all the listed companies. This component reveals the movement of a single firm compared with the rest of the companies. Therefore it is a fairly imperative part since it shows how a company responds to economic events. If exogenous forces influence all companies some might move different compared to others. The company specific determinants have an influence in the matter as well.
In this part, market movements do not determine the characteristics of the company. Which is why this is vital in partially explaining the role of the market wide component. For example, an increase in the interest rate can affect companies in different ways. Some companies that have abundant physical assets and large debts may witness increasing interest costs that might reduce expected profits. Others might have large human capital and less debt and can invest retained earnings in other profitable investment opportunities to increase their expected profits. Meaning that in determining liquidity, market wide and company specific variations are both crucial and not mutually exclusive.
The relation between market wide components and liquidity proxies is considered to be negative. If market wide variables increase, it is expected that the liquidity proxies decrease. Since the relation between the liquidity proxies and liquidity is negative as well. Increasing market wide variables is expected to increase liquidity. Through, empirical analysis the validity of this claim is tested
3.2 Liquidity proxies 3.2.1 Effective bid-ask spread
The most frequently used liquidity proxy is a measure of the bid-ask spread. In the literature review, the role of the bid-ask spread has been thoroughly discussed. Here, it could be seen that the movement of the bid-ask spread can reveal valuable insight that might be important in determining and explaining liquidity. Glosten and Harris (1988) and Stoll (1978) show that the market maker includes in the bid-ask spread an adverse selection cost when trading with informed traders. In accordance, the proportional effective spread between the bid and ask prices is calculated based on the two times absolute difference trade price and the midquote which the total is divided by the midquote or,
BAS = !∗|!!! !!"|
!!" (3.2)
spread is negatively related to liquidity. Meaning, that when the spread increases, assets become more expensive to trade. This could cause illiquidity.
3.2.2 Stock return co-movement and Price impact
The second liquidity measure focuses on the relation between the variances of the company specific factor and the stock. By doing so, the role of the firm on its own stock is measured. To obtain the relation between the market and the stock movements the relation between the variations of market and stock has to be measured. The alternative method is to obtain the rest value between the company factor and stock value. This is done as:
R2 = 1- !!!
!!! (3.3)
which is a measure of stock co-movement. The new price impact solution implies that an increase in R2 decreases the price impact; in turn this would lead to an increase in the marked depth. Since market depth and Kyle’s lambda are inversely related. Evidently, there is a negative relationship between the price impact and liquidity.
3.2.3 The Amihud (2002) illiquidity measure
The third proxy is based on the absolute daily return of a stock divided by the firm’s daily dollar volume. Amihud (2002) derived this method of price impact on trade are considered liquid if a large volume of shares is being able to trade without distorting the price considerably. This method of estimating the liquidity is different than the two proxies described above. Namely, this method does not depend on intraday transaction data. Rather, this method focuses on relative price changes related. Prior research on this matter shows that firms with higher expected illiquidity are positively related to higher expected returns, coherent with illiquidity premium in asset returns.
The illiquidity measure is the daily ratio of absolute stock return to its dollar volume. It can be translated as the daily price reaction related to one dollar of trading volume, thus aiding as a rough portion of price impact. In other words, liquidity and the Amihud (2002) illiquidity measure are negatively related.
3.3 Market wide variables 3.3.1 Beta
For each security i the weekly beta was calculated. This was done according to:
βi,t =
!"#(!!,!!!)
!"#(!!) (3.4)
where ri,m and rm is respectively, the returns for security i and the market m. Here,
3.3.2 Systematic volatility
The systematic volatility is the volatility that is subject to market conditions. In this case the systematic volatility is the square root of the systematic variance of the stock. This means that the calculations are formed according to:
S-vol = 𝛽!𝑉𝑎𝑟(𝑅
!) (3.5)
3.3.3 Idiosyncratic volatility
The idiosyncratic volatility is the volatility that focuses on the volatility caused by a specific company. In this case, the idiosyncratic volatility is the square root of the difference between the total variance of the stock i and systematic variance or:
I-vol = 𝑉𝑎𝑟 𝑅! − 𝛽!𝑉𝑎𝑟(𝑅
!) (3.6)
3.4 Company specific variables 3.4.1 Company size
The company size is the logarithm of the market capitalization of each listed firm is expressed in thousands. The purpose of including the company size is to capture to what extent growth in market capitalization has an effect on liquidity variations:
Size = log(1000𝑀𝐶𝑖) (3.7)
where MCi is the market capitalization of company i.
3.4.2 Turnover
This shows the aggregation of the number of shares for each stock in the index traded on a particular day. The figure is always expressed in thousands.
3.4.3 Price inverse
The third variable is the inverse of price, measured as the beginning of year price for the company. It is likely that the cross-sectional variation in liquidity is affected by disparities in the price levels.
3.5 Empirical framework
3.5.1 Time-series cross-sectional analysis
regularly theorized as cross-sectional dominant. Contrariwise, when the time-based units are more abundant than spatial units (T>N), the pool is termed temporal dominant (Stimson 1985).
According to this explanation, the pooled linear regression model can be written by using the Ordinary Least Squares (OLS)
yit = αit + !!!!𝛽kxkit + eit (3.8)
Where i = 1,2, … N signifies to cross-sectional component, t = 1,2, … T signifies to the time period and k = 1,2, … K signifies to the explanatory variable. This means that yit and xkit are respectively dependent and independent variables for unit i and
time t, whilst eit is the error term, αit is the constant and βk is the parameter.
The first cause why TSCS analysis should be implemented is due to the known small N problem experienced by time series and cross-sectional analysis. In this analysis the stock market has 25 companies, which is on the low side. The inadequate number of spatial units and available data over time caused data sets of time series and cross-sectional to violate fundamental assumption of statistical analysis. More precisely, the small sample (25 companies) of the usual comparisons shows a discrepancy between abundant explanatory variables and limited observations. Subsequently, the small sample size causes the total number of the impending explanatory variables surpasses the degree of freedom necessitated to estimate the relationship between the dependent and independent variables. However, due to pooled TSCS estimations, this constraint can be relaxed. Since, within the pooled TSCS analysis, the observations are company-year (or NT observations) starting from the company i in year t, then company i in year t + 1 up to company
i+n in year t+n. This creates the opportunity to examine the influence of a large
number of estimators on the level and change in the dependent variable within the framework of this analysis (Schmidt, 1997).
Additionally, pooled TSCS analysis also regards the probability to capture variation through time and space, meaning that the variations in these dimensions are not mutually exclusive. Instead of estimating a time series for one company using time series data or a cross-sectional for all companies at one point in time, a TSCS tests for all companies through time (Pennings et al., 1999).
The TSCS estimations are all similar to each other since they are based on the format of equation (3.1). Indicating that liquidity is the sum of market wide and company specific variables. The stock return co-movement estimation is:
Liqit = α0 + β1R2it + β2Sizeit + β3TOit + β4PIit + εit (3.9)
here, liquidity acts as dependent variables of stock return co-movement, company size, turnover and price inverse. Equation (3.1) and (3.9) share the same attributes, namely the division of liquidity into market and company components. In this equation, the market wide determinant is R2, while the other variables are the
company specific determinants. The beta estimation is:
Equation (3.10) shows an important difference that it has two market determinants instead of one as in equation (3.9). Here, it can be seen that the market determinant is measured by beta and idiosyncratic volatility while equation (3.9) has stock return co-movement as R2 to be the sole determinant. Implying that R2 should have the
same impact on liquidity as beta and idiosyncratic volatility together. The systematic volatility equation is:
Liqit = α0 + β1I-volit + β2S-volit + β3Sizeit + β4TOit + β5PIit + εit (3.11)
Equations (3.10) and (3.11) are almost similar, expect for the market determinant. In equation (3.11) beta is replaced with systematic volatility. In the event of large discrepancies in the results of equations (3.10) and (3.11), the substituted market determinants are the main cause.
The meanings of the variables in equations (3.9)-(3.11) are as follows; Liqit is one
of the three liquidity measures for company i in time t, R2itis the log R2 for company
i in time t, Betait is the beta of the stock for company i in time t and its relation with
respect to the market, I-volit is idiosyncratic volatility for company i in time t, S-volit
is systematic volatility for company i in time t, Sizeit is the company size for
company i in time t, TOit is turnover for company i in time t, PIit is price inverse for
company i in time t and εit is the error term with the normal distribution or εit ~ N(0,σ2).
In equation (3.9), null hypotheses 1a-c are tested. Here, the relation between the stock return co-movement with control variables is estimated with the liquidity proxies. In equation (3.10), the null hypotheses 2a-c are tested to see whether beta affects liquidity. The null hypotheses 3a-c are tested using equation (3.11).
3.5.2 Estimation limitations
The pooled TSCS analysis is an unassailable instrument for the improvement of comparative research. Yet, the recognition of this statistical technique does not depend only on its application in practical research, but also recent research discussing operational issues (Stimson 1985; Beck and Katz 1995; 1996). Especially, the last study is more abundant now since pooled TSCS designs frequently violate the OLS assumptions about the error process. Actually, the OLS regression estimates are likely to be inconsistent, inefficient and biased when they are used with pooled datasets. Because the errors for regression equations estimated from pooled data using OLS method incline to cause five impediments.
First, errors incline to be dependent from one period to the next. Implying, there might be serial correlation, so that errors in company i at time t are correlated with errors in company i at time t+1. Because, the observations and attributes that exemplify them tend to be interdependent across time.
Second, the errors can be correlated across companies. These errors could be synchronously correlated, so that errors in company i at time t are correlated with errors in company j at time t.
Fourth, errors might encompass both longitudinal and cross-sectional factors reflecting cross-sectional and longitudinal effects. The errors incline to obscure unit and period effects. Meaning, even if the data is homoscedastic and not auto-correlated, chances exist, that the regression being generated with observed heteroskedastic and auto-correlated errors, are present. This is due to heteroskedasticity and auto-correlation being a function of also model misspecification.
This misspecification, that is eccentric of pooled data, is the assumption of homogeneity of level of dependent variable across longitudinal and cross-sectional data. Especially, if the assumption that longitudinal and cross-sectional period is homogeneous in the level (as standard OLS estimation would require) and they are proven not to be. Then, least squares predictors are conciliation, and questionable to be a good predictor of the time periods and the cross-sectional units. This causes the seemingly level of heteroskedasticity and auto-correlation to be considerably overestimated (Stimson 1985).
Fifth, errors may not be random across unit and time periods since the parameters could be heterogeneous across the subsets of units. Implying, that the developments linking dependent and independent variables tend to fluctuate across the subsets of companies and time periods. While errors show certain causal heterogeneity across spatial or temporal units (Stimson 1985). Consequently, this impediment can be translated as a misspecification function. The estimated constant-coefficients models cannot show the causal heterogeneity through temporal and spatial units.
3.5.3 Endogeneity
The most common concern in OLS estimation is that variables are correlated with the error term, this causes inconsistent OLS estimates for β. The instrumental variables should have no correlation with the error term when the estimation is done according to the two-stage least squares (TSLS) as an alternative to the OLS. In this format the estimation assumes a linear relation between the explanatory variable and the instrumental variables.
There are several instrumental variables z1,i, z2,I, z3,i.. zn,i for the independent
market and company variables x2,I, x3,i.. xn,i. where the x1,I is the exogenous variable
that is uncorrelated with the error term. Estimating the expected endogenous variable as a dependent variable where the instrumental variables are added to replace the expected endogenous variable. When estimated the residuals are saved. In the new estimation, the dependent and independent variables in their initial form is estimated including the saved residuals.
3.5.4 Testing for instrument relevance
Instruments, however, cannot be chosen arbitrarily. In the appendix, box 1 presents the instruments used in this endogeneity test are shown. There are two important rules that instruments must hold for it to be a “right” instrument. The first rule is relevance. The instruments must be relevant, as it has to be correlated with the explanatory variable. There must be some sort of relation between the explanatory variable and instrumental variables. Since, the instrumental variables act as replacement for the explanatory variable. The stock return co-movement and systematic variables are substituted for instrumental variables based on accounting determinants. Return on equity, return on assets, dividend yield, earnings per share are all examples of variables that are related to a certain extent with the explanatory variables. This test is crucial since uncorrelated variables are “weak” instruments that yield biased and possibly inconsistent results.
The relevance is observed by the covariance between the IV and the dependent variables. In this case, the covariance between the instrumental variables and the market wide component must be larger or smaller than 0. This relevance analysis is important since weak, or irrelevant, instruments the IV analysis can yield biased results and may even prove to be inconsistent. Setting the independent market wide variable as the dependent variable tests the relevance. Also, the instrumental variables act as the independent variable along side the control variables. Setting the coefficients of the instruments equal to zero tests the null hypothesis. The alternative is that at least one of the coefficients of the instruments is not equal to zero.
3.5.5 Testing for validity of over-identifying restrictions
The instrumental variables and the error term must be uncorrelated otherwise the instrumental variables are endogenous. This test requires at least N + 1 instruments for N endogenous variables. Since, in a precisely identified model the validity hypothesis cannot be tested, due to the exclusion restriction being valid. In this scenario, the assumption of valid instrument is taken on faith, meaning that the theoretical arguments underlying the exclusion restriction have to be taken for granted. However, when the model is over-identified it can be tested for validity of the over-identifying restrictions. This test does not exam instrument validity. The statement, “these instruments are unconditionally valid” cannot be the results of this test. The null hypothesis would be that the over-identifying instruments are orthogonal to the residual. The reason why this test is conducted is that it is the first obstacle that needs to be overcome when using the IV analysis.
Basically put, validity is the guarantee that the instrumental variables itself are not endogenous. By testing for validity the correlation between the instruments and error term is revealed. This relation between the instruments and the error term should be zero, or uncorrelated. Moreover, for this test to work the requirement is that there are more instruments than potential endogenous variables. The test is conducted by regression the incremental regression equation as TSLS using the instrumental variables as instruments.
in the next estimation. In the next estimation, the residuals act as independent variable with the control, or certain exogenous, variables and instrument variables. The most important part of these results is the R-square and the total number of observations; the product of these two values is used to determine the p-value of the chi-square. The null hypothesis states that exogenous and instrumental variables are uncorrelated with the error term. So, it is in the best interest of this research to not to reject the null hypothesis. In order to do that, either the R-square or the N observations should be small.
3.5.6 Two-stage least squares estimation
This technique is applicable for the estimation of over identified systems. In fact, it can also be employed for estimating the coefficients of just identified systems. TSLS is done in two stages; 1) Find and estimate the reduced form equations using OLS estimation. Save the fitted values for the dependent variables; 2) Estimate the structural equations using OLS estimation. Substitute any endogenous variables with their fitted values.
In this framework, it is worrying whether the typical assumptions of the classical linear regression model are binding or not, still some of the test statistics necessitate alterations to be pertinent in the systems context. To exemplify one possible consequence of the violation of the classical linear regression model assumptions, if the disruptions in the structural equations are auto-correlated, the TSLS estimator is inconsistent.
3.5.7 Robustness check
4
Data and Sample
4.1 Dataset characteristics
The data used for the empirical analysis centers around two Dutch stock exchanges. The AEX and AMX both comprise of companies with the highest market capitalization. Where the companies in the AEX have a larger market capitalization than in the AMX. The market capitalization is the value of the tradable share and is sometimes considered as the firm net worth. Therefore, it can be regarded that in the AEX the companies are viewed as larger, in terms of capitalization, compared to the AMX.
4.1.1 Data source
Thomson DataStream is the most respected historical financial numerical database, covering an unmatched amount of financial instruments, equity securities, fixed-income securities and economic and financial indicators for over 175 countries and 60 markets worldwide. The data, collected from Reuters’ DataStream, provides nearly all the data required for the companies listed in the AEX and AMX.
4.1.2 Filter rules
The sample consists of all AEX and AMX stocks over the period of January 2007 to December 2011. Table 1 and 2 present the companies of the AEX and AMX respectively. Only common stocks are taken for the empirical analysis. The reason for the exclusion of other types of funds is the difference from common stock when it comes to liquidity measurements. In the model of Kyle (1985), only the stocks of companies determine the market depth and price impact. Since including other funds will only make liquidity explanations more complex, only stocks are used to measure these determinants of market liquidity.
The sample consists of daily data regarding the respective variables and is transformed into weekly observations in the case of stock return co-movement, beta, and systematic and idiosyncratic volatilities. This causes the sample size to decrease by a factor of 5. Even so, the total dataset consists of approximately 50 companies each having a 5-year time span of daily data.
In addition, several control variables are introduced that serves as determinants of liquidity. The types of raw data used are daily stock price, daily volume trades, market-capitalization, bid prices and ask prices. However, this raw data is not used for estimation. This data is used to calculate important determinants and proxies to measure the liquidity. This is achieved by calculating; the beta, (log) R2, the three liquidity measures and the two volatility measures.
4.2 Descriptive statistics
Table 3a: Descriptive statistics of AEX companies
Here BAS is the bid-ask spread. PRI is the price impact. AIL is the Amihud (2002) illiquidity measure. R2 is the
stock return co-movement. I-vol is idiosyncratic volatility. S-vol is systematic volatility. Size is company size through market capitalization, Turnover is shares bought and sold, P.Inverse is price inverse.
* For AIL the values are exceedingly small yet are rounded to 0 in the table.
exchanges. It is important to note that after the financial crisis, the stock returns have been decreasing along with the stock market index.
There are, however, noteworthy observations when looking at the mean of the liquidity measures. The result is that in the AEX the means for the bid-ask spread (0.0036) and price impact (0.0008) are closer to the minimum of zero, whereas the mean of Amihud (2002) liquidity measure is closer to the maximum. This might mean that the Amihud (2002) liquidity measure captures relatively more higher liquidity observations compared to the bid-ask spread and price impact. For the AMX, the Amihud (2002) liquidity measure and the bid-ask spread are similar to the AEX case; however, the price impact (1.613) is closer to the maximum (1.848). There seems to be a disparity between he AEX and AMX, where the AMX has relatively higher liquidity values for the price impact and Amihud (2002) compared to the AEX with only the Amihud (2002). This observation is in no way detrimental in the final conclusion. However, this might be the first sign of the difference in liquidity in the AEX and AMX.
This difference is also observable for the systematic and idiosyncratic volatility. Here, the systematic and idiosyncratic volatilities are closer to their minimum value than they are for their maximum value. This observation might imply that the volatility is low and relatively ‘stable’. Indicating that the fluctuations in the stock and market returns are smaller than first anticipated. Either way the empirical analysis should shed more light on this matter.
Table 3b: Continued
I-volt S-volt Sizet Turnovert P Inverset
Mean 0.1997 0.2193 1.6354 4.0493 0.0442 Median 0.1618 0.1776 1.6004 1.5134 0.0357 Maximum 1.3568 1.4144 1.9504 62.304 0.4606 Minimum -0.0017 0.0266 1.3897 1.1920 0.0141 St.dev 0.1449 0.1543 0.1237 0.5463 0.0311 Observation 2584 2584 2584 2584 2584
BASt PRIt AILt* R2t Betat
Table 4a: Descriptive statistics of AMX companies
Here BAS is the bid-ask spread. PRI is the price impact. AIL is the Amihud (2002) illiquidity measure. R2 is the
stock return co-movement. I-vol is idiosyncratic volatility. S-vol is systematic volatility. Size is company size through market capitalization, Turnover is shares bought and sold, P.Inverse is price inverse.
* For AIL the values are exceedingly small yet are rounded to 0 in the table.
4.3 Correlation
Tables 5 and 6 show the correlation between the variables. The liquidity measures are positive correlated in the AEX, whereas the same liquidity measures are negatively correlated in the AMX. This is an unexpected correlation, but may reveal the nature of the AMX in terms of liquidity. One can expect that this reflect into the results, namely for the AEX all three of the liquidity perform as a proxy and therefore show a positive relationship among them. In other words, the liquidity measures in the AEX move all in the same direction.
For the AMX this is clearly not the case. Another interesting observation is the movement of the idiosyncratic and systematic volatility. Both of these volatilities have to a certain extent the same signs and correlations with all the other variables. This is not surprising since the correlation between the two variables is considerably high. In other words, there should not be large differences in the results of the estimation. Hence, both of the variables move in the same fashion.
Table 4b: Continued
I-volt S-volt Sizet Turnovert Price inverset
Mean 0.2251 0.2459 1.4296 1.3169 0.0487 Median 0.1867 0.2034 1.4290 2.6110 0.0446 Maximum 1.4857 1.5420 1.7973 42.3291 0.3576 Minimum 0.0087 0.0398 1.1952 4.7600 0.0053 St.dev 0.1466 0.1539 0.8614 3.6002 0.0334 Observation 2212 2212 2212 2212 2212
BASt PRIt AILt* R2t Betat
Table 5: Correlation table of (in)dependent variables regarding AEX companies
BASt PRIt AILt R2t Betat I-volt S-volt Sizet TOt PIt
BASt 1 PRIt 0.412 1 AILt 0.379 0.570 1 R2t 0.051 0.029 0.0412 1 Betat 0.036 0.028 0.044 0.066 1 I-volt 0.061 0.088 0.047 -0.198 0.000 1 S-volt 0.034 0.096 0.054 -0.186 0.023 0.997 1 Sizet -0.051 -0.154 -0.075 -0.107 -0.001 -0.067 -0.071 1 TOt -0.014 -0.162 -0.060 -0.192 0.126 -0.023 -0.013 0.701 1 PIt -0.051 0.032 -0.129 -0.363 0.154 -0.069 -0.054 0.123 0.504 1
Here BAS is the bid-ask spread. PRI is the price impact. AIL is the Amihud (2002) illiquidity measure. R2 is the
stock return co-movement. I-vol is idiosyncratic volatility. S-vol is systematic volatility, Size is company size through market capitalization, TO is shares bought and sold, PI is price inverse.
Another observation of the correlation matrix is that, the relation of the liquidity variables with market-wide variables are all positively related, whereas the relation with the control variables are all negatively related. From this observation it could be said that an increase in the R2, beta, systematic volatility and idiosyncratic volatility increases the bid-ask spread, the price impact and the Amihud (2002) illiquidity measure. This would imply that the market wide variables are showing the decrease in liquidity and that stock movements are the driving force behind illiquidity. However, the control variables that are of company specific nature show a negative relation with the liquidity measures. Meaning that company specific determinants are liquidity improving.
Table 6: Correlation table of (in)dependent variables regarding AMX companies
BASt PRIt AILt R2t Betat I-volt S-volt Sizet TOt PIt
BASt 1 PRIt -0.152 1 AILt -0.152 -0.156 1 R2t -0.194 -0.013 0.075 1 Betat 0.415 0.216 -0.067 -0.190 1 I-volt 0.294 0.144 0.104 -0.178 -0.036 1 S-volt 0.217 0.140 0.120 0.027 -0.002 0.997 1 Sizet 0.141 0.120 -0.398 0.033 -0.002 -0.016 -0.023 1 TOt 0.481 0.797 -0.152 0.182 0.026 0.159 0.161 0.157 1 PIt 0.184 -0.390 0.201 -0.306 0.195 -0.077 -0.054 -0.041 -0.288 1
Here BAS is the bid-ask spread. PRI is the price impact. AIL is the Amihud (2002) illiquidity measure. R2 is the stock return co-movement. I-vol is idiosyncratic volatility. S-vol is systematic volatility, Size is company size through market capitalization, TO is shares bought and sold, PI is price inverse.
5
Empirical results
5.1 TSCS estimation results
In this section the empirical results are explained in each subdivision of market wide variables. Table 9 corresponds for the AEX and table 11 for AMX. In addition, there are supplementary tables showing the effect on the null hypotheses.
5.1.1 Stock return co-movement
Table 7: Test results of null hypotheses 1a-c
Table 7 shows whether the hypotheses 1a-c are rejected or not. It can be seen that for the AEX and AMX the null hypotheses are –mainly- not be rejected. The main source of this failure to reject comes from the fact that the stock return co-movement is chiefly insignificant. However, H2b for the AMX is significant and has a positive relationship with the price impact. Meaning that the null hypothesis of H2b is rejected. The stock return co-movement in the AEX is statistically significant at the 1% level. Indicating that this market wide variable has a positive effect (1.495) on the price impact.
Apparently, the stock return co-movement does not have a significant relation with liquidity during the period 2007-2011. So, the null hypothesis is mainly failed to reject. According to the literature, stock return co-movement has a relation with liquidity. Yet, the empirical results show no relation between stock return co-movement and liquidity proxies. Meaning that for the Dutch case during the financial crisis, the theoretical and empirical evidence of a relation between stock return co-movement and liquidity is not present.
Only null hypothesis 1b for the AMX is rejected. Comparing the results of this estimation with all the other stock return co-movement cases has certain implications. It reveals that only the company size is insignificant only for the null hypothesis 1b in the AMX case and that the prince inverse is negative. Shedding a different light to the other cases.
5.1.2 Beta
According to table 8, the null hypotheses are rejected because beta has significant p-values. The control variables have significant effect as well. Except for the size of AEX companies with respect to the price impact.
What does this mean? It could be pointed out that the beta, which takes the market as a whole as a benchmark of how the stock is performing, explains the, mostly positive, relation with the liquidity proxies. Therefore, the null hypotheses do no hold. Increasing market wide variables means that the liquidity proxies increase as well. In most cases is the beta statistically significant at the 1% level, except for the price impact of AMX companies.
Hypothesis AEX AMX
1a Failed to reject Failed to reject
1b Failed to reject Reject
Table 8: Test results of null hypotheses 2a-c
The idiosyncratic volatility shows similarity with respect the sign and significance. Namely, there is a considerable explanatory power of idiosyncratic volatility on the liquidity proxies. This relation is also predominantly positive. Apparently, an increase in the company specific volatility does have a positive effect on the liquidity proxies.
It is noteworthy that the effect of beta on the dependent variables is rather small; except for H2b of AMX. Beta that has a positive relation with the liquidity proxies has only a small impact. Whereas beta that has a negative relation has a relative large effect. So the effect of beta on the liquidity proxies is either positively small or negatively large.
The company specific variables that are estimated alongside the beta show significance and indicate explanatory power. This result however bears no unique importance since most company specific variables are shown to be significant.
In a nutshell, beta shows positive relation with the liquidity proxies. Taken into account of the negative relationship between the liquidity proxies and liquidity, it would appear that during 2007-2011 beta has decreased liquidity. Therefore, the null hypotheses are rejected and there is a significant –mainly positive- relation between beta and the liquidity proxies.
Table 9: TSCS analysis of AEX companies (t-values in brackets)
Constant LR2 Beta I-vol S-vol Size TO PI R2
Bid-ask 0.0031* 0.000 -0.022* 0.000* 0.0012* 0.067 Spread (2.513) (-0.93) (-1.862) (-6.224) (2.466) 0.0052 0.0001* 0.0011* -0.008* 0.000* 0.0011* 0.033 (0.853) (2.872) (5.679) (-2.462) (-8.890) (3.214) 0.0009* 0.000* 0.001* -0.002* 0.000* 0.0001* 0.045 (3.533) (-5.098) (5.689) (-2.824) (-8.826) (2.890) Price 0.0014* 0.000 0.000*** 0.000* 0.0040* 0.039 Impact (4.366) (1.272) (-1.835) (-5.999) (6.286) 0.0008* 0.0009* 0.0011* -0.000 0.000* 0.0032* 0.065 (2.737) (3.084) (11.599) (-0.827) (-8.505) (8.640) 0.0001 -0.014* 0.015* 0.000 0.000* 0.003* 0.089 (0.542) (-10.57) (11.345) (1.354) (-11.414) (8.723) Amihud 0.000* 0.000 0.000* 0.000* 0.000* 0.022 (2002) (-2.186) (0.396) (2.422) (-6.974) (6.343) Illiquidity 0.000 0.000* 0.000* 0.000*** 0.000* 0.000* 0.009 (-1.562) (1.958) (3.529) (1.620) (-4.986) (3.088) 0.000* 0.000* 0.000* 0.000* 0.000* 0.0005* 0.011 (-2.433) (-4.258) (4.477) (2.497) (-5.859) (3.021)
*= Significant at the 1% level; **= Significant at the 5% level; ***= Significant at the 10% level
Table 9 presents results of cross-sectional analysis of the AEX where liquidity is the dependent variable and consists of the three proxies of liquidity. The first liquidity measure is the bid-ask spread, the second liquidity measure is the price impact and the third liquidity measure is the daily return per daily dollar volume. The explanatory variables are the stock return co-movement proxies of the logit R2, beta and volatility measures dissected into idiosyncratic volatility, I-vol, and systematic volatility, s-vol.
in addition there are three control variables that are known to have a relation with liquidity that is not determined by price setting process using market-wide information. The first is the Size of the company, which is measured as the company capitalization. The second is the turnover, which is a determinant of trading volume that may have an influence in the liquidity measures and finally, the stock price inverse.
Hypothesis AEX AMX
2a Reject Reject
2b Reject Reject
5.1.3 Systematic volatility
Table 10: Test results of null hypotheses 3a-c
Does systematic volatility affect Dutch liquidity during the financial crisis? After the investor hedges all the risk of its portfolio, he is only exposed to systematic risk. This risk, however, cannot be diversified and the portfolio should be as liquid as possible. The portfolio consisting of only systematic risk indicates that the portfolio is subject to market wide information. This means lower adverse selection risk. Implying that lower systematic volatility would cause lower adverse selection risk and the securities on the market are traded more easily. Hence, market becomes liquid. However, table 10 shows otherwise.
According to tables 9 and 11, the results are similar to the beta case. Meaning that there is a –mainly positive and significant- relationship with the liquidity proxies. The null hypotheses that state no relation between the systematic volatility are rejected.
The predominantly positive effect of systematic volatility on the liquidity proxies shows that liquidity deteriorated during the 2007-2011 period. Just like with beta, the coefficients are either positive and small or negative and large. These positive results are in line with what the literature had shown. Market makers that operate with portfolios have to be prepared when orders come in high quantities. Therefore, systematic risk would have a negative effect on the liquidity provisions of market makers.
Table 11: TSCS analysis of AMX companies (t-values in brackets)
Constant LR2 Beta I-vol S-vol Size TO PI R2
Bid-ask 6.382* 0.026 -1.871* 0.0002* 7.230* 0.12 Spread (3.670) (1.023) (-3.485) (4.892) (4.627) 7.920* 0.034* 0.842* -0.068* 0.0012* 7.892* 0.14 (6.428) (5.344) (4.824) (-3.121) (4.602) (6.822) 4.226* 0.000* 0.0001* -0.045* 0.0007* 6.632* 0.21 (6.892) (-2.792) (2.948) (-4.014) (2.786) (6.365) Price 24.740* 1.495* -0.962 0.010* -176.84* 0.65 Impact (2.790) (2.219) (-1.570) (67.844) (-11.975) 20.457* -9.418*** -1.785 -1.130* 0.010* -58.461* 0.65 (5.338) (-1.634) (-1.227) (-4.235) (95.337) (-16.065) 21.052* 61.620* -60.681* -1.173* 0.0106* -57.084* 0.65 (5.486) (2.913) (-3.001) (-4.398) (95.358) (-15.522) Amihud 0.000* 0.000 0.000* 0.000* 0.000* 0.21 (2002) (23.022) (1.018) (-22.40) (-2.626) (10.79) Illiquidity 0.000* 0.000* 0.000* 0.000* 0.000** 0.000* 0.03 (9.966) (3.094) (5.821) (-10.149) (-1.919) (3.599) 0.000* 0.000* 0.000* 0.000* 0.000* 0.000* 0.04 (9.502) (-8.177) (8.594) (-9.777) (-2.478) (2.359)
*= Significant at the 1% level; **= Significant at the 5% level; ***= Significant at the 10% level
Table 11 presents results of cross-sectional analysis of the AMX where liquidity is the dependent variable and consists of the three proxies of liquidity. The first liquidity measure is the bid-ask spread, the second liquidity measure is the price impact and the third liquidity measure is the daily return per daily dollar volume. The explanatory variables are the stock return co-movement proxies of the logit R2, beta and volatility measures dissected into idiosyncratic volatility, I-vol, and systematic
volatility, s-vol. in addition there are three control variables that are known to have a relation with liquidity that is not determined by price setting process using market-wide information. The first is the Size of the company, which is measured as the company capitalization. The second is the turnover, which is a determinant of trading volume that may have an influence in the liquidity measures and finally, the stock price inverse.
Hypothesis AEX AMX
3a Reject Reject
3b Reject Reject
5.2 Endogeneity
Endogenous relations between the variables can cause biased results and could portray an inaccurate estimation. To prevent this endogeneity the Hausman test is performed. Variables in the estimation can be endogenous for various reasons including measurement error, reverse causation and omitted variable bias. If there is an unobserved part in the dependent variable this part is then omitted and the market and company specific determinants can be overestimated. The Hausman test for endogeneity can determine the presence of omitted variable bias in the regression.
Table 12: Endogeneity test of AEX companies during 2007-2011 (t-values in brackets)
Constant LR2 Beta I-vol S-vol Size TO PI Resid R2
Bid -0.723* 0.0001* 0.0822* 0.0000* 0.0083* -0.0031* 0.09 Ask (-6.774) (5.457) (7.163) (-6.568) (4.734) (-3.121) Spread -0.971* 0.0015* 0.0062* 0.0426* 0.0000* 0.0075* -0.0107* 0.12 (-7.897) (8.256) (5.643) (6.247) (-6.423) (5.246) (-3.916) -0.365* -0.0071* 0.0541* 0.0093* 0.0000* 0.0004* -0.0893* 0.16 (-5.845) (-4.238) (5.492) (6.357) (-7.356) (3.856) (-3.522) Price -0.0002 0.0025* 0.0000* 0.0000* 0.0238* -0.0025* 0.06 Impact (-0.7356) (7.674) (3.284) (-7.002) (9.471) (-7.614) -0.0033* 0.0241* 0.0014* 0.0001* 0.0000* 0.0046* -0.024* 0.09 (-6.8027) (12.628) (13.779) (6.405) (-14.02) (11.140) (-12.387) -0.0028* -0.0651* 0.0630* 0.0001* 0.000* 0.0041* -0.0536* 0.11 (-6.389) (-12.78) (12.987) (7.365) (-14.68) (9.982) (-10.515) Amihud 0.000* 0.0000* 0.000* 0.0000* 0.0000* 0.0000* 0.01 (2002) (-3.092) (3.178) (3.295) (-5.226) (4.008) (-3.077) Illiquidity 0.000* 0.000* 0.000* 0.000* 0.0000* 0.0000* 0.0000* 0.01 (-4.689) (4.974) (2.982) (4.579) (-7.176) (3.859) (-4.719) 0.000* 0.000* 0.000* 0.000* 0.0000* 0.0000** 0.0000* 0.01 (4.662) (-3.671) (4.940) (4.539) (-7.309) (2.353) (-3.589)
Table 13: Endogeneity test of AMX companies during 2007-2011 (t-values in brackets)
Constant LR2 Beta I-vol S-vol Size TO PI Resid R2
Bid 4.325* 0.020* -0.512* -0.006* 0.033* 0.953* 0.4 Ask (5.633) (4.633) (-3.481) (-4.262) (5.268) (5.363) Spread 7.321 0.323* 0.3066* -0.241* -0.0032 -0.0633* -0.683* 0.4 (6.272) (6.748) (5.235) (-2.569) (-0.268) (-3.557) (-3.936) 3.836 -0.602* 0.703* -0.616* -0.001 0.084* 0.976* 0.5 (5.778) (-3.842) (3.939) (-3.237) (-1.255) (3.638) (4.275) Price -102.5* -5.224* 9.554* 0.009* -700.54* 5.195* 0.7 Impact (-13.20) (-19.50) (15.288) (71.134) (-21.99) (19.348) -0.5164 439.38* 2.670* -0.768* 0.0099* -124.69* -444.57* 0.7 (-0.073) (2.866) (1.254) (-1.974) (46.202) (-8.902) (-2.895) -7.720 -1256.0* 1203.3** 0.4975 0.0098* -137.97* -1251.0* 0.6 (-0.947) (-3.338) (3.337) (1.055) (47.186) (-8.609) (-3.460) Amihud 0.000* 0.000* 0.000* 0.000 0.000* 0.000* 0.1 (2002) (10.893) (5.355) (-10.11) (1.271) (6.008) (-5.218) Illiquidity 0.000* 0.000 0.000* 0.000* 0.000** 0.000 0.000 0.1 (6.171) (1.567) (4.546) (-9.663) (-1.946) (-0.020) (-1.436) 0.000* 0.000* 0.000* 0.000* 0.000* 0.000* 0.000* 0.1 (9.570) (4.308) (-4.287) (-10.28) (2.644) (5.249) (4.828)
*= Significant at the 1% level; **= Significant at the 5% level; ***= Significant at the 10% level
Table 12 and 13 presents results of TSCS analysis of the AMX where liquidity is the dependent variable and consists of the three proxies of liquidity. The first liquidity measure is the bid-ask spread, the second liquidity measure is the price impact and the third liquidity measure is the daily return per daily dollar volume. The explanatory variables are the stock return co-movement proxies of the logit R2, beta and volatility measures dissected into idiosyncratic volatility, I-vol, and systematic volatility, s-vol.
