In Search Of Liquidity
Zeki Kurt
*1545752
Master Thesis Finance
Faculty of Economics and Business, University of Groningen, Groningen, NL
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Supervisor:
B.A. Boonstra
Abstract:
This paper analyzes the relation between market wide variables and the liquidity proxies of the AEX and AMX during the period 2007-2011. This paper finds evidence that liquidity is determined by the market wide variables during the financial crisis in the AEX as well as the AMX. The market wide variables (stock return co-movement, beta and systematic volatility) and company specific variables (company size, turnover and price inverse) are used to measure the relation with the liquidity proxies (bid-ask spread, price impact and Amihud (2002) measure) by using time-series cross-sectional estimation method.
Keywords:
Volatility, liquidity, stock returns, Dutch stock market, market microstructure.
JEL Classification:
G12, G14
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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. By using the theory of market microstructure the process by which traders’ demands are turned into transactions on the stock market can be studied. The way a stock market is organized affects the price setting mechanism and, implicitly, the liquidity of assets. Liquidity suggests the ability to trade large quantities of assets rapidly, with minimum trading costs and slight price impact. Stoll (1978), Ho and Stoll (1981), and Stoll (2000) have conducted research in understanding the cross-sectional and time-series variation of liquidity in the equity markets. A key determinant of liquidity is the volatility of underling stocks. The increase in stock return volatility indicates that the liquidity suppliers will face higher adverse selection risk due to increased likelihood of transacting with informed investors and also higher inventory risk arising from order imbalances. Consequently, higher stock volatility leads to lower liquidity. There were also developments that would cause liquidity to increase. One of these important developments is the single order book. The NYSE Euronext initiated the single order book for Amsterdam, Brussels and Paris Euronext markets that connects trading, clearing and settlement through the stock exchanges. This would mean that orders are focused in one order book, bid-ask spreads will improve, and investors will have access to other large markets. Hence, liquidity increases as a result of an enlargement in the market size. However, such stock markets no longer serve the purpose they were made to serve; aiding small and midsize companies grow by obtaining capital cheaply from the public. In its place, the large stock exchanges gradually compete with each other to serve the largest companies and to create low margin trading volume that comes from computers seeking out opportunities like trading rebates.
Instead of focusing on all the countries within the NYSE Euronext group, the Dutch stock exchange is chosen as the main focus. Since the Netherlands endures macro-economic difficulties that can tarnish its financial market, the Dutch case shows a more troublesome scenario. According to the CPB1, a Dutch think tank, a serious threat to the Dutch economy is the drop of 10% in house prices since the peak in 2008. Rendering a possible repetition of the American mortgage crises in the Netherlands by negatively affecting financial institutions and hence the financial markets.
Aside from the macro-economic situation, the financial markets suffered heavy drawbacks during the financial crisis. Due to the rising uncertainty on the American stock market, the AEX index plummeted to 400 index points. When these uncertainties remained, Dutch financial institutions reported less profit. This in turn caused the AEX's index points to drop even further. In the beginning of the year 2008, the AEX recovered only gradually. This recovery went as far as reaching almost 500 index points, yet it plunged again. On 29 September 2008 the AEX index decreased by 8,8 percent and a week later it dropped another 9 percent. 8 October 2008 marked the day that the AEX's index points got below 300. Because of the continuing poor economic developments in the U.S., the AEX dropped another 10 percent, to reach 254 index points. Meaning that in less than a year the AEX dropped from almost 500 points, to just 254 point. The AEX closed 2008 at 245 points, which means that the AEX index approximately 52 percent in nearly a year. The problem that is presented revolves around all these points:
Despite the efforts of increasing liquidity, the Dutch stock market index levels have shown to decrease during 2007-2009 and even showed a 52 percent decrease 2008 in one-year time due to on holding uncertainty and volatility in the Netherlands.
This paper tries to analyze is the Dutch stock exchanges, that have allegedly increased liquidity through the merger of the NYSE and Euronext. The research question focuses around whether stock volatility in the Dutch stock markets has affected liquidity during the financial crisis, or:
Did the stock volatility in the Dutch stock market of AEX and AMX considerably affect the liquidity during the financial crisis?
This research question is relevant for two cases. The first reason is that it analyzes the Dutch stock 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 meant 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 financial crisis.
volatility fills this academic gap. The uniqueness of this research is that it focuses on a very topical case of the Dutch stock market, which has not yet been researched in empirical work. Furthermore, this thesis expands the economic theory and models to a rare market microstructure change: The separate analysis of the AEX and AMX stock exchanges by estimating stock volatility with respect to liquidity is not a frequently researched area. Moreover, the stock price synchronicity hypothesis is used as a guideline for the hypothesis testing. This hypothesis states that stock volatility and liquidity are positively related.
This research is relevant in the sense that stocks usually show minor movements in the usual daily market circumstances. This is mainly due to the availability of new information; stock prices move up (down) and recover to their initial position afterwards. 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 volatility and liquidity more thorough. The literature regarding the topic of liquidity is vast, yet there is room to extrapolate this phenomenon when circumstances are reversed.
2
Literature review
Market microstructure is an important field in finance that can explain the workings of the financial market in great detail. There have been various scholars that have analyzed the relation between stock volatility and liquidity.
2.1 Market microstructure
Regarding the role of financial intermediaries, Stoll (1978) provides supplementary concepts of how liquidity-supplying 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 a market maker pays to cover 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. This implies that intermediaries act as an investor with a preferred investment portfolio based on the investment opportunities. 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.
is difficult to continuously gain by speculating in the market, except if the market maker is a true monopolist.
2.2 Liquidity proxies
Liquidity is tenuous and can be modeled in various ways. Therefore capturing liquidity is a difficult endeavor that requires certain approximations reflecting the state of liquescency in the market. Out of the various proxies that are commonly accepted, this analysis focuses on three liquidity measures. The first measure is the bid-ask spread, which is according to Stoll (1978, 2000), Ho and Stoll (1981) and Harris (1994), a measure that is lower for larger companies that have many shares, since these assets have a higher likelihood of finding a party to trade. Therefore, the market maker has lower inventory and order processing costs. They also show that spreads are higher for stocks with high return variance due to compensation for inventory risks as well as the risk of trading with an informed 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 company 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.
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. This method does not depend on intraday transaction data. It rather focuses on relative stock price changes. 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 with one dollar of trading volume, thus aiding as a rough portion of price impact. The liquidity measure allows building data samples of liquidity that are essential to check the effects of liquidity on simultaneous stock return. This would be hard to accomplish with the other microstructure measures of liquidity.
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.
is commonality in the returns of individual stocks in the U.S. (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. Certain financial intermediaries act as market makers by attracting temporary liquidity shocks. According to Kyle and Xiong (2001), Gromb and Vayanos (2002), Morris and Shin (2004), and Brunnermeier and Pedersen (2009), these market makers experience capital constraints and receive their funding by having margins or having asset collaterals. When the market uncertainty increases, these market makers observe a value decrease in the collateral or impose larger margins. This forces the market makers to liquidate their positions. The shared attribute of these models is that there is an expectation that when the conditions in the market deteriorate, the demand for liquidity increases. This happens because market participants liquidate their holdings and therefore reduce the liquidity since the liquidity suppliers approach their funding constraints. Consequently, commonality in stock returns, liquidity, and trading turnover all ascend instinctively and, most essentially, the degree of commonality is strengthened throughout phases of high market volatility. However, up until now there is insufficient empirical proof to support this theory. Yet, Ang and Chen (2002) demonstrate that the stock returns in US markets become more correlated during market declines. However, they do not contemplate co-movement in liquidity or even trading turnover. Hameed, et al. (2010) shows that co-movement in liquidity among stocks increases and liquidity of stocks decreases during large market regressions and when capital accumulation constraints of market makers are straining.
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 a rise in informed traders to 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 centers around the relation between stock return co-movement and the respective liquidity drivers. The three important liquidity determinants that define the magnitude in the Dutch stock market are:
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 relation with price impact.
Hypothesis 1c
H0: Stock return co-movement has no relation with the daily return of one-euro trading
volume.2
2.3.2 Beta
Ball, et al. (1976) find proof regarding the Australian market of a positive relation between beta and average returns. Nonetheless, Wood (1991) discovers weak evidence in the Australian markets and Faff (1991) shows moderate evidence, though Faff (2001) indicates that there is no relation 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 relation 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 relation 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.
discovers that a cross-sectional regression coefficient on total variance for size sensitive portfolios causes an insignificant and negative relation.
The second set of hypotheses focuses on the relation between the beta and 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 beta is unrelated to the liquidity proxies. The hypotheses concerning the beta are:
Hypothesis 2a
H0: Beta does not affect bid-ask spread.
Hypothesis 2b
H0: Beta has no relation with price impact.
Hypothesis 2c
H0: Beta has no relation with the daily return of one-euro 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) demonstrates that market-wide variables positively and significantly determines the liquidity for approximately 55% of NYSE stocks. Huberman and Halka (2001) discover similar results, exposing that liquidity across stocks has certain systematic factor in the sample of daily NYSE data. Concerning the reasons, Coughenour and Saad (2004) claim from liquidity supply point of view that market makers are one cause of liquidity commonality.
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 symbolizes worsening in investment prospects. Risk-averse investors demand stocks to 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 as a result and return decreases as well. 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.
The magnitude of liquidity trading is not always exogenous. According to Subrahmanyam (1991), the endogenous liquidity traders occur because it exhibits the least amount of adverse selection risk. Assets that possess a large systematic component usually have low level of adverse selection. These liquidity traders adapt their portfolio by minimizing liquidity cost by focusing on their trading strategy to include assets that posses a large systematic component to enhance 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 it 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. share of international trading volume. This model expects that delivery of trading volume across exchanges competing for orders have a relation with the cross-listed asset returns and the returns of other assets traded in their subsequent markets.
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 a risk-return trade-off. However, Bali, et al. (2005) prove that the idiosyncratic volatility could act as an exemplification of 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 relation with price impact.
Hypothesis 3c
H0: Systematic volatility has no relation with the daily return for one-euro trading volume.
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 proxies 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. 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 impact companies in various ways. Some companies that have abundant physical assets and large debts may witness increasing interest costs that might reduce expected profits. Others might have abundant human capital and less debt and can invest retained earnings in other profitable investment opportunities to increase their expected profits. Meaning, to determine liquidity, market wide and company specific variations are both crucial and are not mutually exclusive.
3.2 Liquidity
The liquidity, the degree of tradability, is stimulated by a couple of characteristics of order driven trade. One of these characteristics is that the order book is anonymous. Investors can see the orders but not its source. Meaning that traders cannot trace back the order to its owner. Also, the presences of the liquidity providers, especially for funds that have low orders, play an important role. Liquidity providers stimulate the trade by continuously placing buy and sell orders. The liquidity providers are bound to the maximum disparity between the bid-ask spread. Stock price movement and liquidity is important for short-term investors. They require to trade at a high velocity. Since short term investors profit from small gains and are therefore very dependent on liquid markets and well-organized stock market. For the day-trader it would be cumbersome if he bought shares and cannot sell them on the same day because there are no counter orders. For the long-term investors the velocity is less important. If a long term investors plans to hold an asset for a long time, he prefers to have transparency and good financial prospects of the company.
Market with high liquidity allows investors to trade assets relatively simply into cash equivalents and diminishes risk while for low liquidity assets trade may be more difficult and therefore even more expensive. An essential paper in empirical research on the relation between liquidity and return is Amihud and Mendelson (1986). They use the bid-ask spread as a proxy of liquidity to test the relation between stock returns, relative risk and spread. Their conclusion was that a large bid-ask spread suggests an illiquid stock. Moreover, beta and excess return are also positively correlated with the bid-ask spread. They witnessed that risk-adjusted returns increased with the bid-ask spread and that the liquidity effect was correlated with company size (Banz, 1981). Abundant journals published their groundbreaking work and reached a comparable conclusion: Stocks with lower liquidity require a higher risk-adjusted expected return.
3.2.1 Definition of liquidity
trade immediately at either the bid or ask price or place a limit order at a more profitable price and wait for trade to commence with a counterparty. Liquid assets have largely scattered ownership, and large volumes of supply and demand interrelate to limit price movements comparative to trading volume. Companies with a small market capitalization are more simply manipulated by supply and demand, and stock prices can show comparatively large variations for small trading volumes. Cooper et al. (1985) note that illiquidity is an unfavourable trait of a stock as “…liquidity risk should lower the price of a security and increase the required rate of return”. These definitions of liquidity can easily be translated into the findings of the equilibrium asset pricing models such as the CAPM. This would mean that low liquidity stocks have a higher beta and necessitate, ceteris paribus, a liquidity premium on expected return in comparison to higher liquidity stocks. Hence, theoretical models predict an increasing effect of the liquidity premium on asset prices.
3.2.2 Drawback of liquidity
The inconvenience in defining liquidity is the entanglement with correlated traits such as market capitalization and company size. Liquidity can be seen as an outcome of market responses to more essential aspects of a security. For example, low P/E ratio entices profit-maximizing investors and therefore increases the demand of a stock. Order imbalance causes a rise in the price of the stock and liquidity increases. This logic is reversed in the case of the causal relation between liquidity and expected returns defined above (Cooper et al., 1985).
3.2.3 Bid-ask spread
BAS = !∗|!!! !!"|
!!" (3.2)
where pt equals the trade price and pmq equals the midquote of the stock. The bid-ask spread is negatively related to liquidity. Meaning, that when the spread increases, assets become more expensive to trade causing lower liquidity.
Grossman and Miller (1988) examine various inadequacies of using the bid-ask spread as a measure of liquidity. Most noteworthy in their examination is that the bid-ask premium is influenced by institutional aspects and is consequently not only a measure of liquidity. The market quote is the result of a premium required by the market maker and therefore measures exactly the return for providing liquidity. Though the price which traders are willing to pay, compared to the market maker’s bid price, may be considerably lower which leads the authors to think that the real bid-ask spread might be larger than assessed by the market maker. Furthermore, the bid-ask spread may be an applicable proxy of liquidity for small investors since they can finish their order at the best bid or ask price. Larger investors might be incapable to trade at the optimum bid or ask price. Hence, the large investor’s cost of liquidity is larger than presumed by the bid-ask spread (Marshall, 2006).
3.2.4 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. Where 𝜎!! is the variance of stock return and 𝜎 !! is
the variance of the market return on a weekly basis. 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 relation between the price impact and liquidity.
According to Kyle (1985), the price impact solution implies that an increase in R2 decreases
and price impact are inversely related. This would suggest the following. If the stock co-movement increases, market makers could learn more from the information of the index market. This way the adverse selection risk which they are exposed to will reduce when they trade with the informed traders. Subsequently, market makers will correct the stock prices less compared to the order flows, which causes the market makers to increase liquidity. According to this derivation, liquidity is based on the market depth. This deduction is derived from the Kyle (1985) model.
Concurring with Kyle (1985), the price impact determines the price increase of an extra buy order. The reciprocal of price impact can be regarded as the market depth. If 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 this happens due to the following reason. The market maker loses to the insider that makes a profit, yet the market makers 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.
3.2.5 The Amihud (2002) measure
returns, coherent with illiquidity premium in asset returns. Hence, this illiquidity measure is the daily ratio of absolute stock return to its volume, or:
AIL = |!!|
!"#! (3.4)
where r is the daily stock return and VOL is the daily volume of the respective company i. 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) measure are negatively related.
3.3 Market wide variables
Modeling stock market volatility has been the subject of vast empirical and theoretical investigation over the past decade or so by academics and practitioners alike. There are a number of motivations for this line of inquiry. Arguably, volatility is one of the most important concepts in finance. Volatility, as measured by the standard deviation or variance of returns, is often used as a crude measure of the total risk of financial assets. Many value-at-risk models for measuring market value-at-risk require the estimation or forecast of a volatility parameter.
of volatility cannot be undermined. Therefore, three market wide variables are discussed and explained to what extent they may influence liquidity. These market wide variables are all different forms of volatility measures and therefore the nature of the market wide component is the same as stock volatility.
The gross of the research has focused on the relation of stock volatility on liquidity proxies and rarely of liquidity on stock volatility. Since, liquidity is a broad and general concept that envelops the entire market, liquidity is affected by the stock volatility. Therefore, the causal relation is not investigated in this analysis. The focus is on the effect of market wide variables on liquidity proxies. One reason why this is the case is that the bid-ask spread is determined by the stock volatility.
3.3.1 Beta
Seminal work by Banz (1981) and Fama & French (1992, 1993) explain the need to expand the CAPM with extra risk factors for book-to-market value, size, term structure, leverage and default risk. They recognized that the dependability of beta is reliant on the sample period. Also the limitation of the Fama and MacBeth (1973) conclusions is the likely violation of independence between the stock assets and the factors as beta is estimated from the dataset. They conclude that, in the cross section of stock returns, their factors for size and book-to-market equity do a good job explaining average returns on NYSE, AMEX and NASDAQ stocks for the 1963 – 1990 period. In the following decades researchers and quantitative analysts alike using macro-economic variables have expanded these multi-factor models. Evidently beta shows important traits in explaining the relation with returns. Beta, as correlated volatility, measures the sensitivity of an assets return with respect to the market return. By measuring beta it can give insight about the relation between volatility and liquidity in the market. For each security i the weekly beta was calculated:
βi,t = !"#(!!"#(!!,!!)
!) (3.5)
where ri and rm is respectively, the returns for security i and the market m. Here, beta
While prevailing studies demonstrate that an increase in volatility lowers liquidity, there is little research on the separate effects of systematic volatility and idiosyncratic volatility on liquidity. Rendering to the adverse selection models or inventory risk models, the effect of systematic volatility on liquidity would be diverse from that of idiosyncratic volatility, given that systematic risk can be hedged to a certain degree. Additionally, Baruch, et al. (2007) and Baruch and Saar (2009) claim that stock return co-movement touches the trade of a stock and so its liquidity. This is due to the correlation of stock returns with the market measures the extent of market wide information comparative to company specific information. While market makers can perceive the market wide information easily, it is harder for them to observe company specific information. When an individual stock has a high correlation with the market, market makers can trust more on the information he perceives from the market movement so that the stock price changes are less sensitive to its own order flow. Thus, liquidity and informed traders prefer to trade a larger amount of the cross-listed stock in the exchange with the higher return correlation with the domestic assets. Meaning that proportionally more volume migrates to the market in which the cross-listed asset has greater correlation with the other assets traded on the market. Thus higher systematic volatility, the lower the liquidity of stocks will be and therefore illiquid markets. Hence, systematic volatility has a theoretical importance in explaining the development in liquidity. In this case the systematic volatility is the square root of the systematic variance of the stock:
S-vol = 𝛽!𝑉𝑎𝑟(𝑅
!) (3.6)
where Rm is the market return.
3.3.3 Idiosyncratic volatility
In unraveling the impacts of market capitalization, liquidity and idiosyncratic volatility in US markets, Spiegel and Wang (2005) find that companies with high idiosyncratic volatility tend to have small capitalization and low liquidity, and that stock returns are increasing with idiosyncratic volatility and decreasing with capitalization and liquidity. They state that though all their explanatory variables seem to have a systematic relation with the stock returns, the relation of idiosyncratic volatility with the stock returns comprises the relation of both capitalization and liquidity with returns. The idiosyncratic volatility 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:
where Ri is the return on stock i and Rm is the market return.
3.4 Company specific variables
Company specific factors can have an impact on liquidity as well. There have been various studies that tried to reveal the relation between liquidity and company specific determinants by researching the cross-security variation in liquidity. Breen, et al. (2002) shows that the price impact is connected to certain company specific variables. They show that the company’s market capitalization, absolute return, institutional ownership and volume all have an explanatory effect on the relation between price impact and liquidity. These variables are independent of the market-wide information and have a strong link with the company-specific information.
3.4.1 Company size
Company size is a determinant of liquidity that has been frequently used in papers. Since company size is a simple way of measuring the impact on liquidity. With validation of the Fama and French three-factor model, a consideration of a company’s market capitalization has become almost standard practice. In the Australia market, Beedles, et al. (1988) find that the company size is predominant and is robust to some methodological modifications. They find evidence that transaction costs can enlighten a part of the size irregularity but that they do not develop to be the leading factor. Coherent with the findings of Banz in the US, they find that the relation between firm size and returns is located in the smallest stocks. 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. 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:
where MCi is the market capitalization of company i.
3.4.2 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 relation 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. As mentioned, turnover is ratio measurement of the daily trading volume with respect to the number of shares outstanding:
Turnover = Log(Trading Volume) (3.9)
3.4.3 Price inverse
The price inverse is included in the empirical analysis since it is possible that the cross-sectional variation in liquidity is moved by disparities in the price levels (Chan and Faff, 2003). Therefore, including the price inverse as a determinant might reveal important insight for the spread and price impact. The price inverse is 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 Stock price synchronicity hypothesis
(beta) and systematic volatility (S-vol). In the regression, idiosyncratic volatility (I-vol) is incorporated and controlled for as an explanatory variable. Furthermore, the control variables that other studies have shown to affect company level liquidity are included as well as being independent of the amount of market wide information. The first control variable is company size, which is equal to the log of market capitalization at the beginning of the year. Company size is also a proxy for adverse selection risk, which might affect the liquidity of the stock. The second control variable is turnover, which is the log of trading volume. The third control variable is the inverse of price where price is the beginning of year price for the firm. When the liquidity proxies are measured it is likely that the cross-sectional variation in liquidity is affected by changes in the price levels.
3.5.2 Time-series cross-sectional analysis
The estimation method is a pooled analysis that is a combination of time series and cross-sections (TSCS) estimation. Pooled data of AEX and AMX have a characteristic of repetitive observations (days) on fixed factors (companies). This allows pooled data clusters to combine cross-sectional data on N spatial units and T time periods to create a considerably larger data set of N×T observations. Though, if the cross-section units are more abundant than time-based units (N>T), the pool is 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 (3.10)
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.
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 relation 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 (3.11)
here, liquidity acts as the dependent variable of stock return co-movement, company size, turnover and price inverse. Equation (3.1) and (3.11) 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:
Liqit = α0 + β1Betait + β2 I-volit + β3Sizeit + β4TOit + β5PIit + εit (3.12)
Equation (3.12) shows an important difference that it has two market determinants instead of one as in equation (3.11). Here, it can be seen that the market determinant is measured by beta and idiosyncratic volatility while equation (3.11) 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:
Equations (3.12) and (3.13) are almost similar, expect for the market determinant. In equation (3.13) beta is replaced with systematic volatility. In the event of large discrepancies in the results of equations (3.12) and (3.13), the substituted market determinants are the main cause. The meanings of the variables in equations (3.11)-(3.13) are as follows; Liqit is one of the
three liquidity measures for company i in time t, R2
itis the 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 (3.11), 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 (3.12), the null hypotheses 2a-c are tested to see whether beta affects liquidity. The null hypotheses 3a-c are tested using equation (3.13).
3.5.3 Estimation limitations
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.
3.5.4 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.
3.5.5 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 zero. 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.
3.5.6 Testing for validity of over-identifying restrictions
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. The method of testing for validity is rather straightforward. The incremental regression equations are estimated according to the TSLS procedure with the proper instruments. From the results, the residuals are saved to act as a dependent variable 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 not to reject the null hypothesis. In order to do that, either the R-square or the N observations should be small.
3.5.7 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 structured 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.
3.5.8 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. First of all, the Dutch stock market is separated into three exchanges; large cap (AEX), mid cap (AMX) and small cap (ASCX). Data is collected for AEX and AMX, but not for ASCX. Even though it would be interesting to know how liquidity was affected in the ASCX, the ASCX simply has insufficient data variables available to produce regression according to the regression models in section 5. Therefore, there exists a trade-off: either incorporate 3 stock exchanges to get a more complete picture, or use the AEX and AMX that has more data available to produce better regression and therefore conduct research. In light of conducting better research due to the availability of more data I have chosen to use only the AEX and AMX.
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 dataset ranges from 01-07-2007 to 31-12-2011 and envelopes the financial crisis. The idea behind this choice stems from the case prior to the financial crisis (2007), during the crisis (2008-2009) and period when the stock markets where trying to recover from the financial crisis (2010-2011). So along with the tools and dataset, the aim is to see whether the variables and relations that are claimed to hold in the literature section will be regressed. In addition, a yearly analysis is also performed in section 5 that will reflect the disparities between the years and the effect on liquidity.
According to Estrada (2000), weekly data is trust worthier than daily data and contains less idiosyncratic volatility while keeping the size of the dataset the same. More observations are favored to less and would improve the significance levels of the research.The sample consists of daily data regarding the respective variables and is transformed into weekly observations. The choice for week observations is to ensure that there is sufficient number of market wide variable observations. For example, beta cannot be captured daily since it would lack an accurate benchmark to be able to compare the stock return development. Therefore to ensure that market wide variables can capture the variance over several observations, weekly data is used that are derived, i.e. calculated, from daily observations. This causes the sample size to decrease by a factor of five. 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 the determinants and proxies to measure the liquidity. This is achieved by calculating; the beta, R2, the three liquidity
measures and the two volatility measures.
4.2 Descriptive statistics
return is used in order to confer with Kyle (1985). Beta is the covariance of a stock return with the market return divided by the variance of market return. The sum of idiosyncratic and systematic volatility is the total volatility. Total volatility is calculated as the variance of the market return, from total volatility systematic and idiosyncratic volatility is derived. In order to solve the scale problem, the control variables company size and turnover are logarithms of market capitalization and trading turnover respectively and price inverse is the inverse of the stock price.
Table 3 presents that summary of descriptive statistics of the AEX. The liquidity proxies show differing sizes, yet in all the cases the mean is close to the median, which means that the data is evenly divided around the mean. Even though price impact shows a considerable large maximum and minimum, it also shows that the standard deviation is substantially larger than the bid-ask spread. Signifying that price impact shows a more volatile nature than bid-ask spread. The stock volatility measures –stock return co-movement, beta and systematic volatility- show varying results. The stock return co-movement, or R2, has a negative mean while the median is just positive. The maximum and minimum values also appear to show large difference. The maximum is 0.999769 while the minimum is -413.9856. This could be an indication that the values for R2 are more skewed towards negative numbers.This negative
skewness differs from the findings of Hoque et al. (2007) and Kim and Shamsuddin (2008). Though, given the negative return –the significant drop in returns during the financial crisis- over the selected time period this should not surprise the reader. The high standard deviation is also a signal that R2 is volatile. The other stock volatilities –beta, idiosyncratic and systematic volatility- show more similar signs. For all these variables the mean is close to the median. This is also reflected by the maximum and minimum values that do not deviate too much from the mean and median. Therefore, the standard deviation is small.
Table 3: Descriptive statistics AEX
Mean Median Maximum Minimum Std. Dev.
B-A spread 0.000939 0.000701 0.027622 0.000042 0.001180 P-impact 0.980856 1.064250 229.9489 -105.0854 8.650416 Amihud 0.000000 0.000000 0.000001 0.000000 0.000000 R2 -2.033967 0.588104 0.999769 -413.9856 11.62971 Beta 0.557203 0.535168 4.860746 0.065845 0.553581 I-vol 0.245759 0.186421 1.378915 -0.001755 0.184790 S-vol 0.266807 0.201049 1.414464 0.026641 0.195365 Size 16.41394 16.11900 19.56635 13.89750 1.235427 Turnover 7.803600 7.931966 11.42615 1.701105 1.441405 P-Inverse 0.066846 0.045777 0.482602 0.014183 0.055075
Table 4 presents the summary of the descriptive statistics of AMX. For the AMX, the liquidity proxies vary more in size than it does for the AEX. The mean of the bid-ask spread is considerably large while the median is relatively small. This is also reflected by the maximum and minimum values that show a large difference. For the price impact the mean and median show similar signs and sizes, yet the maximum and minimum show an entirely different picture. Meaning that on average the maximum and minimum values equate around the mean and median. For beta, the mean and median show similar signs, while maximum and minimum show a somewhat extreme numbers for beta. Beta with a value of one means that the stock moves generally in the same direction as its benchmark, which in this case is the AMX market, yet here there are cases where the stock moves in the same direction but more than the market (5.113479). There were also moments the reverse was true, where the stock would move in the opposite direction as the AMX market (-2.619178). Nevertheless, the low standard deviation is a sign that beta did not differentiate too much from the mean and median values. The idiosyncratic and systematic volatility and the control variables show similar signs and sizes and indicate that the data points are fairly close to each other and therefore evenly divided around the mean. Note, that there are big outliers for the bid-ask spread; price impact and stock return co-movement. This is observed due to the large differences between the maximum and minimum values with the mean and median.
4.3 Correlation
Tables 5 and 6 show the correlation matrix. The liquidity measures are mainly positively correlated in the AEX. Another observation is that the bid-ask spread and Amihud (2002) measure shows similarity in signs with respect to the other variables. This could indicate that these two liquidity proxies move more alike compared to the price impact. The price impact may show different results compared to the other liquidity proxies.
Table 4: Descriptive statistics AMX
Mean Median Maximum Minimum Std. Dev.
B-A spread 6.797145 0.002175 184.8411 0.000192 32.57973 P-impact 1.428478 1.014453 6411.570 -1688.108 93.92363 Amihud 0.000000 0.000000 0.000003 0.000000 0.000000 R2 -8.767230 0.212767 0.999864 -20287.38 281.2170 Beta 0.463061 0.422528 5.113479 -2.619178 0.478285 I-vol 0.285503 0.248781 1.512368 0.008703 0.189768 S-vol 0.307258 0.267030 1.542070 0.039801 0.198870 Size 14.23809 14.14525 17.97391 11.95293 1.042427 Turnover 5.522846 5.53256 10.65323 1.560248 1.277427 P-Inverse 0.081866 0.062234 0.696449 0.005374 0.076518
