Amsterdam Business School
MSc Finance – Asset Management Track
Master Thesis
Student: Dong Hyun Kang (11377224) Supervisor: Liang Zou
Submitted on July 1, 2017
Stock Market Reaction to Liquidity Shocks: Evidence
from the Netherlands
i Statement of Originality
This document is written by Student Donghyun Kang who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
1 Abstract
This research empirically tests the stock market reaction to liquidity shocks in the Netherlands. Main liquidity measures are the illiquidity measure by Amihud (2002) and Closing Percent Quoted Spread by Chung and Zhang (2014). I find that the Dutch stock market incorporates the effect of liquidity shocks immediately. There is a positive relation between liquidity shocks and contemporaneous returns which is consistent with the model by Acharya and Pedersen (2005). Contrary to what Bali et al. (2014) find in the U.S. stock market, shocks to liquidity do not predict future returns in the Dutch stock market. Return continuation of stocks in the following month can be explained by the Fama-French (1993) three-factor model. The result holds robust after controlling for various asset characteristics and risk factors.
2 Table of Contents Abstract ... 1 Table of Contents ... 2 1. Introduction ... 3 2. Literature Review ... 5
2.1. Liquidity and asset pricing ... 5
2.2. Measuring liquidity... 8
3. Methodology ... 11
3.1. Hypothesis ... 12
3.2. Measures of liquidity and liquidity shocks ... 12
3.3. Univariate portfolio-level analysis ... 13
3.4. Stock-level cross-sectional regressions ... 15
3.5. Control variables for stock-level regressions ... 16
4. Data and Descriptive Statistics ... 17
4.1. Sample construction and data treatment ... 17
4.2. Descriptive statistics ... 19
5. Results ... 22
5.1. Univariate portfolio-level analysis ... 22
5.2. Stock-level cross-sectional analysis ... 28
6. Robustness Checks... 31
7. Summary and Conclusion ... 38
Appendix ... 40
3 1. Introduction
Liquidity of an asset refers to the ease of trading without involving significant price impact or transaction costs. Liquidity of an asset can affect its returns. As transaction costs incur when a trade is executed, investors in turn require a premium for holding an illiquid asset. Amihud and Mendelson (1986) point out that the level of liquidity of a stock is negatively related to returns. Moreover, if liquidity is time-varying and a change in liquidity is systematic, liquidity risk should also affect asset prices.
Previous studies such as Amihud (2002) suggest that liquidity is persistent: illiquidity of today is positively associated with expected future illiquidity. When a negative shock occurs, it implies higher expected illiquidity, which leads to a higher required return. Therefore, the stock price adjusts to this by lowering its current price. From this, Acharya and Pedersen (2005) formulate a model that a negative shock in liquidity leads to low contemporaneous returns and high future returns.
Accordingly, shocks to liquidity should lead to a change in prices. Bali et al. (2014) are the first to note that price adjustment to stock-level liquidity shocks does not finish within a month. Particularly, stocks with positive liquidity shocks continue to show positive returns in the following months even after controlling for various known risk factors. The authors argue that the stock market underreacts to liquidity shocks. They attribute this to investor
inattention and market illiquidity. However, this result is contrary to what would happen in an efficient market, such as in Malkiel and Fama (1970), where every new information is
incorporated into price immediately. Moreover, Korajczyk and Sadka (2008) point out that liquidity shocks do not appear to affect future returns.
This research fills this gap in the literature on the stock market reaction to liquidity shocks in international markets. If the liquidity premium exists outside the U.S. (Amihud et al. (2015)), it is also possible that the reported underreaction to liquidity shocks can occur there. Therefore, the main research question is: how does the Dutch stock market react to liquidity shocks?
I use a dataset consists of a total of 287 stocks in the Amsterdam Stock Exchange
(Euronext Amsterdam) from January 1990 to December 2010. The total number of stocks is 287 across the sample period and I include both listed and delisted securities. One of the
4 challenges for international studies is to find a suitable proxy for liquidity. For instance, intraday data such as the one from Trade and Quote in the New York Stock Exchange are not available in the Netherlands. Therefore, based on a recent survey by Fong, Holden, and Trzcinka (2017), I adopt two proxies that they recommend to be applicable and the most effective for international research. They are the Amihud (2002) illiquidity measure and Closing Percent Quoted Spread (denoted by CPQ Spread) by Chung and Zhang (2014). Particularly, the advantage of using CPQ Spread is that it relies on readily available information and that it is a good proxy for liquidity.
The stock market reaction to liquidity shocks is examined in two ways. I first examine it by sorting stocks into decile portfolios according to liquidity shocks and compare the average returns and risk-adjusted returns of each portfolio in month t. After this, one-month-ahead returns after liquidity shocks are reviewed. Along with the portfolio-level analysis, I further conduct stock-level cross-sectional regressions of one-month-ahead returns on lagged liquidity shock variables. In this way, I can jointly control for various factors and stock characteristics which could affect stock returns. Furthermore, in Robustness section, I explore the possibility of different market reactions to the direction of a liquidity shock. One would suspect whether the market either underreacts to negative liquidity shocks or overreacts to positive liquidity shocks.
This research contributes to the literature by shedding light on the short-term relationship between stock-level liquidity shocks and future returns in the Dutch market. In addition to this, it adds to the studies on how stock markets react to an idiosyncratic shock. According to the standard asset pricing theory (or the efficient market hypothesis), every new public information is immediately reflected into price regardless of the information it contains. Thus, examining market reactions to a particular type of information, such as liquidity shocks, can help us to better understand the assumptions of the efficient market hypothesis, i.e., fully rational investors etc. Moreover, if the underreaction hypothesis holds true, investors can exploit this by forming a long-short strategy on stocks with positive and negative liquidity shocks.
The rest of the thesis is outlined as follows. In Section 2, I review the literature on liquidity and asset pricing. Section 3 starts with the hypothesis and explains the methodology used. Section 4 describes the data. Empirical results showing that the market does not underreact to
5 liquidity shocks are presented in Section 5. Section 6 provides a set of robustness tests. Lastly, Section 7 provides the summary and concludes the thesis.
2. Literature Review
In this section, I outline the existing literature on liquidity and stock returns in two parts. First in Section 2.1, I review the literature on liquidity and asset pricing. Both theoretical models and empirical evidence for the return-liquidity relationship are examined. Later in Section 2.2, I study the literature on liquidity proxies. Main issues concern the effectiveness of low-frequency proxies for a global research.
2.1. Liquidity and asset pricing
The liquidity of a stock is aptly defined by Black (1971) as follows: (1) whether a small amount of trade can be executed immediately; (2) whether the bid-ask spread is small; (3) whether large amounts can be traded without much impact on the current price.
There is now a fairly substantial amount of the literature linking liquidity to asset pricing. This is in contrast to the standard asset pricing theory. It assumes a perfectly liquid market, where a trade can be executed without incurring any cost. However, previous studies have shown the level of liquidity commands the premium. In their celebrated paper, Amihud and Mendelson (1986) advance a simple model that accounts for the cross-sectional return-liquidity relationship. They assume that an investor reflects the costs of trading in their valuation of an asset. She may choose to trade instantaneously at the expense of higher transaction costs. As a result, the ask price includes a premium for the immediate purchase and the bid price incorporates a discount for the immediate sale. This premium or discount is consequently reflected in the valuation of the security. For instance, the discount coming from an expected increase in illiquidity suppresses the current price. This means that illiquid stocks require a higher rate of return relative to their perfectly liquid counterparts. Using bid-ask spreads as a liquidity proxy, they posit that expected asset returns are an increasing function of the spread at the cross-section. Their empirical result with NYSE stocks supports this model. This study shows that the level of liquidity (or liquidity as a characteristic) affects the asset price.
6 In a subsequent study concerning the effect of liquidity as a characteristic, Amihud et al. (2015) find support for the international liquidity premium. They test for the stock-level liquidity premium in 45 countries by comparing monthly return series of illiquid-minus- liquid (IML) portfolios after controlling for various asset characteristics and risks. They report that the average IML return ranges from 0.45% to 0.82% depending on countries and portfolio weights. Another methodology they use is the Fama-MacBeth (1973)
cross-sectional regression which produces a similar result. Overall, their results are consistent with previous studies in the U.S. that stock illiquidity and price exhibit a positive relationship.
There is another strand in the liquidity literature linking the liquidity risk to asset returns. It is motivated by commonality in liquidity from empirical studies. It attests to the systematic liquidity, which cannot be diversified away. If so, investors require compensation for carrying such risk and the exposure (liquidity risk or liquidity beta) to it should be priced. One of the first article to document this is Pástor and Stambaugh (2003). They consider liquidity as risk rather than as a characteristic. They argue that asset prices should reflect a premium for stocks that are more sensitive to market-wide liquidity. It is comparable to the capital asset pricing model, which states that stocks with a higher exposure to the systematic risk (or market risk premium) command a higher expected return. Their results show that stocks with higher liquidity betas earn a higher return than the ones with lower liquidity betas. They also develop a stock-level illiquidity measure (Pástor and Stambaugh (PS) measure). It involves a complex regression. However, they note that this measure is too noisy to be applied at the individual stock level (Pástor and Stambaugh (2003, p.679)).
Furthermore, Acharya and Pedersen (2005) theorize a comprehensive framework that incorporates both the level of liquidity and liquidity risk. They derive a simple model of liquidity called liquidity-adjusted capital asset pricing model (LCAPM). In their model, expected returns are not only driven by the expected illiquidity level, but also by the exposure to market-wide liquidity. The model also suggests that persistent negative shocks to liquidity can lead to low contemporaneous returns and can predict high future returns. Their empirical analysis with LCAPM shows that the liquidity level and liquidity risk are positively related to returns.
The ongoing debate over the difference between the level of liquidity and liquidity risk has been reviewed in several studies. Acharya and Pedersen (2005) acknowledge that, in U.S.
7 data they tested, they find only weak evidence that liquidity risk earns significantly more premium than the level of liquidity. They report that the total annual liquidity risk premium is estimated to 1.1%, while the liquidity level premium amounts to 3.5%. This is consistent with Korajczyk and Sadka (2008) in that the level of liquidity is also priced when they control for liquidity risk. Therefore, as Holden, Jacobsen, and Subrahmanyam (2014) state in their exhaustive survey of liquidity premium, “the literature on liquidity and asset pricing demonstrates that both average liquidity cost and liquidity risk are priced” and so that they are inseparable.
Given that liquidity is priced, whether as a characteristic or risk, if liquidity of an asset is time-varying, its expected return could change over time accordingly. Amihud (2002)
examines the time-series relationship between liquidity and stock returns. He finds that future returns are positively correlated to unexpected negative market-wide liquidity shocks. It is because liquidity is persistent; that is, current illiquidity predicts a high expected illiquidity in the future. As a result, as Amihud and Mendelson (2015) explain, “higher expected illiquidity implies a higher required return, which is achieved by lowering the current price.” In
addition, he proposes a widely-used liquidity measure called the Amihud illiquidity measure. The relevance of this measure is covered more thoroughly in following Section 2.2.
Along the lines of Amihud (2002), Bekaert, Harvey, and Lundblad (2007) show that unexpected shocks to market-wide liquidity are positively correlated with contemporaneous returns in emerging markets as well. Their sample consists of 19 emerging markets and the U.S. and they adopt a liquidity proxy called Zeros by Lesmond, Ogden, and Trzcinka (1999). More detailed description of this simple measure is given in the subsequent Section 2.2.
Furthermore, Bali et al. (2014) find that stock-level liquidity shocks are not promptly incorporated into stock prices. Liquidity shocks are defined here as a change in the level of liquidity compared to the past 12-month average level of liquidity. As Acharya and Pedersen (2005) propose, persistent positive shocks should be positively associated with
contemporaneous returns and negatively with future returns. However, what Bali et al. (2014) document is that liquidity shocks are also positively correlated to future returns. In other words, what they find is that the stock market underreacts to initial liquidity shocks.
Therefore, contrary to what would happen in an efficient market, the stock return continues to drift in subsequent periods. Using the Amihud (2002) illiquidity measure and
volume-8 weighted effective spread as liquidity proxies, they employ two methodologies to test this. In their portfolio analysis, ten portfolios are formed at each month according to innovations in liquidity. Cross-sectional regressions on portfolios’ returns reveal that the return difference between high and low liquidity shock portfolios are positive and statistically significant both in the same month and the following months. Another test involves the Fama-MacBeth (1973) cross-sectional regressions. They regress each stock’s returns against lagged liquidity shock variables along with control variables. Results confirm that liquidity shocks can predict future stock returns. Their results hold robust with an alternative liquidity proxy. They report this return predictability can last up to six months. This is called the stock market
underreaction hypothesis. They associate their findings with limited investor attention theory and the market-wide illiquidity. Their analysis is based on the U.S. data from 1963 to 2010.
In contrast to Bali et al. (2014), Korajczyk and Sadka (2008) suggest that lagged liquidity shocks are not correlated with future returns. They report that it is return shocks that predict liquidity shocks, not vice versa. They employ a different methodology from Bali et al. (2014) to test the return predictability of liquidity shocks. It is based on a canonical correlation between liquidity shocks and lagged returns rather than a portfolio analysis. Moreover, they adopt a different liquidity proxy, which is based on high-frequency data. Their use of intraday data over 18 years in the U.S. means their liquidity measure is much finer. Accordingly, liquidity shock is defined differently: it is computed as the residuals from a second order autocorrelation model (AR(2)).
2.2. Measuring liquidity
One of the main issues in the liquidity literature concerns how to measure liquidity. As pointed out by Bekaert, Harvey, and Lundblad (2007), “liquidity and transactions costs are notoriously difficult to measure.” Moreover, there are challenges for international research on liquidity. For instance, some data like intraday bid-ask spreads are available only in the U.S. This subsection addresses this issue by providing a brief survey of liquidity measures. Subsequently, it aims to find the liquidity measure(s) which is both appropriate and applicable to this research.
In their comprehensive survey of liquidity measures, Goyenko, Holden, and Trzcinka (2009) categorize them into two groups depending on the aspect of liquidity they capture:
9 spread and price impact. The spread denotes transaction costs between traders. The larger the spread, the more trading costs incur to the demand side of liquidity. On the other hand, the price impact represents the change in stock prices caused by trading. If the stock is more liquid, large trading volumes can be executed without a greater impact on prices.
A prevailing topic in liquidity studies is whether to construct a liquidity proxy based on high-frequency or low-frequency data. High-frequency proxies, such as effective bid-ask spreads, which are available on intraday basis, have been regarded ideal at capturing actual transaction costs than low-frequency counterparts, which are available on daily or monthly basis. Past studies in the U.S. have used the Trade and Quote (TAQ) data, which provides intraday quotes. However, intraday data, such as from the TAQ database, are not easily attainable outside the U.S. and can only be available for a relatively short amount of time. Moreover, building a daily liquidity measure based on intraday data requires considerable physical computing power and time. Holden, Jacobsen, and Subrahmanyam (2014) mention that trade and quote data have increased exponentially over time. It is even more relevant considering the increase in the high-frequency trading (HFT) run by algorithms. Therefore, prior literature has attempted to develop reliable low-frequency estimates of high-frequency liquidity measures.
The issue between choosing high- or low-frequency proxies is thoroughly reviewed in Goyenko, Holden, and Trzcinka (2009). In their study, they test several low-frequency measures’ performance against that of high-frequency measures. Setting the TAQ- and Rule 605-based spreads as benchmarks, they state that a few low-frequency measures give reliable estimates of actual transaction costs. Their results show that, along with their new proposed proxies for spread, the Amihud illiquidity measure does the best in approximating both the spread and price impact dimensions of liquidity. The strong performance of the Amihud measure is consistent with Hasbrouck (2009) too.
Amihud (2002) proposes a liquidity proxy called the Amihud illiquidity measure. The measure captures the price impact of one currency unit of trade by quantifying the absolute daily changes in stock return scaled by the currency trading volume. If it is high, it means that a trade would induce a larger price change. It can be averaged over a certain period (e.g., monthly) to represent the price impact across the period. The logic behind the measure is the model by Kyle (1985). He posits that as market makers cannot distinguish whether the order
10 flow is coming from informed trader or not, they set prices as an increasing function of the order flow. From here comes a positive relationship between the order flow and price change on which this measure is based. The main advantage of this measure is that it is obtainable in most stock markets since it only requires daily stock data.
Lesmond, Ogden, and Trzcinka (1999) propose an intuitive and simple liquidity measure called Zeros. It is calculated as the ratio of the number of zero return days to the number of days within a month. A more frequently traded stock is likely to have fewer days with zero returns and a higher Zeros implies higher liquidity. Its apparent appeal has received a lot of attention in international studies and has been used extensively according to Lee (2011). In his study of international liquidity risk, Lee (2011) reports that the strength of this measure has been tested both in the U.S. and world markets. However, Bekaert, Harvey, and Lundblad (2007) point that Zeros should be treated carefully because a zero return day would simply occur due to a lack of news.
Chung and Zhang (2014) develop an alternative liquidity measure based on closing ask and bid quotes available in CRSP. It is called Closing Percent Quoted Spread (denoted by CPQ Spread). This measure relates to the spread dimension of transaction costs. It is computed as the ratio of the closing bid-ask spread to the closing mid-price. One can obtain the monthly spread by averaging daily CPQ Spreads in a month. They test this new spread measure in capturing the TAQ spread and report that it offers a good approximation of the intraday bid-ask spread. It is published after Goyenko, Holden, and Trzcinka (2009), therefore it is not reviewed there. However, they argue that it outperforms any other low-frequency measures they tested, including Zeros, the Amihud illiquidity measure, and Pastor and Stambaugh (PS) measure etc. The strength of this measure is that it requires only closing ask and bid quotes. Thomson Datastream provides such data for Dutch stocks starting 1996.
As seen, studies have proposed a wide range of liquidity measures to test liquidity premium. However, it is possible that such measures account for multiple liquidity premia rather than a single liquidity premium. Addressing this issue, Korajczyk and Sadka (2008) report that widely-used measures (e.g., the Amihud illiquidity and turnover ratio) show the commonality which attests to a common liquidity factor.
11 However, the last remaining question for this research is that what constitutes the relevant and effective liquidity proxy for global research. The aforementioned measures and their reviews by Goyenko, Holden, and Trzcinka (2009) and Hasbrouck (2009) is limited to the U.S. data. Moreover, outside the U.S. market, a few liquidity proxies are not available because the underlying quote data are not always easily accessible. Concerning this, Fong, Holden, and Trzcinka (2017) examine a number of liquidity measures in the global setting. They define liquidity measures into two categories, “percent-cost” and “cost-per-volume” proxies. The first proxy is defined as the transaction cost of executing a small trade. The second proxy represents marginal transaction cost per monetary unit volume. They compare the accuracy of liquidity proxies using global intraday dataset. Based on their result, for measuring monthly percent-cost, they recommend the aforementioned CPQ Spread by Chung and Zhang (2014) as the best. As with cost-per-volume measures, they argue the five proxies (Closing Percent Quoted Spread Impact, LOT Mixed Impact, High-Low impact, FHT Impact, and Amihud) that they tested perform equally well on the monthly level.
Based on this review, I use the Amihud (2002) illiquidity measure and CPQ Spread by Chung and Zhang (2014) for liquidity proxies in this research. They complement the lack of high-frequency data in the Dutch stock market. In addition, the robustness of low-frequency measures allow me to use these two measures. Furthermore, they are relatively free from intensive computation required for a few measures like LOT by Lesmond, Ogden, and Trzcinka (1999). Lastly, they have been recommended for use in international environments.
3. Methodology
First, I formulate hypotheses for this research. Then, in Section 3.2, I first describe several liquidity proxies reviewed in Section 2. In Section 3.3, I explain the univariate portfolio-level analysis. In short, I form ten portfolios each month according to the liquidity shock measure and derive the long-short portfolio returns. Additionally, the description of the Fama-MacBeth (1973) cross-sectional regression model is provided in Section 3.4. This helps studying the relationship between liquidity shocks and future returns on the stock level. In Section 3.5, I describe major control variables for the study.
12 3.1. Hypothesis
My research relates to the gap in the existing literature. In preceding sections, I have reviewed theoretical frameworks about return-liquidity relationship such as the ones by Amihud and Mendelson (1986) and Acharya and Pedersen (2005). Empirical evidence (Amihud (2002) and Acharya and Pedersen (2005) etc.) supports the theory that liquidity is priced and shows that illiquid stocks are positively correlated with higher stock returns. The relationship is also witnessed in international markets (Amihud et al. (2015)). Furthermore, Bali et al. (2014) report an interesting phenomenon that unexpected shocks in liquidity are positively correlated with both contemporaneous returns and future returns. Yet, Korajczyk and Sadka (2008) offer contrasting evidence that liquidity shocks cannot predict future returns.
Thus, it is natural to ask that how non-U.S. markets react to liquidity shocks, which is defined here as a change in the level of liquidity. As seen, if the liquidity is time-varying and also known to be priced at the international level, liquidity shocks should be priced. The remaining question is whether we can predict future returns using liquidity shocks.
Considering that the main research question is to examine the Dutch stock market’s reaction to liquidity shocks, I formulate following hypotheses of this research.
𝐻 : The return predictability of liquidity shocks should be observed in the Dutch stock market.
𝐻 : The return predictability of liquidity shocks should not be observed in the Dutch stock market
3.2. Measures of liquidity and liquidity shocks
For this study, I employ two measures for liquidity proxy. The first measure is the Amihud (2002) illiquidity measure, denoted by ILLIQ. It measures the price impact. The monthly Amihud illiquidity measure is constructed as follows:
𝐼𝐿𝐿𝐼𝑄, = 1 𝑁⁄ ,
𝑟, ,
𝑣𝑜𝑙, ,
13 where 𝑟, , is the absolute value of return on stock i on day d in month t, 𝑣𝑜𝑙, , is the
euro trading volume of stock i on day d in month t, and 𝑁, is the number of trading days for stock i in month t. In essence, it is the average ratio of absolute daily stock return to the daily trading volume within a month.
Another measure is Closing Percent Quoted Spread (denoted by CPQ Spread) proposed by Chung and Zhang (2014). It is a monthly percent-cost proxy. Daily CPQ Spread is calculated as follows:
𝐶𝑙𝑜𝑠𝑖𝑛𝑔 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑄𝑢𝑜𝑡𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑, = (𝐴𝑠𝑘, − 𝐵𝑖𝑑, ) 𝑀⁄ , ,
where 𝐴𝑠𝑘, is the closing ask price of stock i on day d; 𝐵𝑖𝑑, is the closing bid price;
and 𝑀, is the mid-price, which is the mean of 𝐴𝑠𝑘, and 𝐵𝑖𝑑, . Then it is scaled by 100.
CPQ Spread for month t is computed by averaging the daily CPQ Spreads within month t. To measure stock-specific liquidity shocks, following Bali et al. (2014), I define liquidity shock (denoted by Δ𝐿𝐼𝑄) as the negative difference between the monthly Amihud illiquidity measure and its past 12-month average:
Δ𝐿𝐼𝑄, = − 𝐼𝐿𝐿𝐼𝑄, − 𝐴𝑉𝐺𝐼𝐿𝐿𝐼𝑄,| , | ,
where 𝐴𝑉𝐺𝐼𝐿𝐿𝐼𝑄,| , | is the mean of the Amihud Illiquidity measure over the last 12
months. According to the formula, positive liquidity shock is related to an increase in the stock liquidity, and vice versa (ceteris paribus). Shocks to Closing Percent Quoted Spread (denoted by Δ𝑆𝑝𝑟𝑒𝑎𝑑, ) is defined in the same method.
3.3. Univariate portfolio-level analysis
To test the underreaction hypothesis, at each month, I sort every stock into decile portfolios according to one of the liquidity shock proxies, Δ𝐿𝐼𝑄 and Δ𝑆𝑝𝑟𝑒𝑎𝑑. Two types of portfolio returns, which are equal-weighted and value-weighted, are constructed for comparison.
Based on these portfolios, I study the relation between liquidity shocks and returns. If returns increase as liquidity shock increases, we can assume a positive relation between them. In addition, I assume a high-minus-low portfolio with a long position on the top decile portfolio and a short position on the bottom decile portfolio. This is equivalent of a return
14 differential between the most positive and the most negative liquidity shock portfolio. I examine the same-month and one-month-ahead average returns of this long-short portfolio. Previous studies on the liquidity premium suggest that the long-short portfolio would generate a positive contemporaneous return. Furthermore, if the high-minus-low portfolio’s future returns are positive and statistically significant even after adjusting for risks, this supports the underreaction hypothesis. It indicates that the stock market reacts slowly to the initial liquidity shock, leading to a further price adjustment in the following months.
In addition, I calculate three-factor alphas obtained from time-series regressions using the Fama-French (1993) model. I run regressions for each of the ten portfolios. The alphas represent returns that are not explained by the given factors. The three-factor alphas are computed from regressing portfolios’ returns against the Fama-French three factors as follows:
𝑟, − 𝑟, = 𝛼 + 𝑏 𝑀𝐾𝑇 + 𝑠 ∗ 𝑆𝑀𝐵 + ℎ ∗ 𝐻𝑀𝐿 + 𝜀, ,
where 𝑟, is the raw return of an equal-weighted or value-weighted portfolio i in month t, and
𝑟, is the risk-free rate. On the right side of the formula, 𝛼 is the three-factor alpha of
portfolio i; 𝑀𝐾𝑇 is the market risk premium in month t; 𝑆𝑀𝐵 denotes the size factor (Small – Big market capitalization); and 𝐻𝑀𝐿 stands for the value factor (High B/M – Low B/M). If the null hypothesis holds true, the three-factor alpha of the long-short portfolio’s future returns should be positive and statistically significant. I obtain the three factors in the Dutch market from the publicly available CCRS-DBF Risk Factor Database.1
Last but not least, there can be an issue to apply the Fama-French model in non-U.S. markets since it was originally developed and tested in the U.S. market. However, in the empirical research, it has been gained international evidence, including the Netherlands (Moerman (2005), Fama and French (2012), Schmidt et al. (2017)) and has been used extensively in the literature. Nevertheless, I employ the capital asset pricing model (CAPM) to obtain alphas for robustness in Section 6.
1 Available at the website www.bf.uzh.ch/go/riskfactors. Brief explanation on how this database constructs the factors is provided in Appendix A.
15 3.4. Stock-level cross-sectional regressions
I conduct stock-level cross-sectional regressions in addition to the univariate portfolio analysis. It can complement the portfolio analysis described in the preceding section. One advantage is that it allows for the joint test of various control variables at the same time. Another is that it uses a larger number of individual stock return data, so the testing power can increase.
I run Fama-MacBeth (1973) cross-sectional regressions on the one-month-ahead return. This methodology is conducted in two steps. In the first stage, I run time-series regressions using stocks’ monthly excess returns. Here we obtain the coefficient estimates (𝛽) using the following model:
𝑟, − 𝑟 , = 𝛼 + 𝛽 𝑓 + 𝜀 ,
where the left side of the equation represents the excess return of a stock in month t+1. On the right side, 𝑓 are a set of independent variables of stock i. It consists of a liquidity shock variable (Δ𝐿𝐼𝑄, or Δ𝑆𝑝𝑟𝑒𝑎𝑑) and a number of control variables in month t. The list of
control variables are given in Section 3.5.
As a second step, for each specific date in time, I run cross-sectional regressions. The estimates of beta coefficients (𝛽) from the first step are used as the independent variable in the following equation:
𝑟, − 𝑟 , = 𝛽 𝜆 + 𝛼, ,
where estimated coefficients here are lambdas (𝜆 ), one of which includes our main explanatory variable, the liquidity shock variable. If the time-series average slope of the liquidity shock is positive and statistically significant, it is consistent with the null hypothesis. It indicates that liquidity shocks are positively related to one-month-ahead stock returns.
I examine two sets of specifications for stock-level cross-sectional regressions. In the basic specification, one-month-ahead returns are regressed on liquidity shock variables, market beta, natural logarithm of market value, natural logarithm of book-to-market equity ratio, and price momentum. In the expanded specification, in addition to the previously mentioned variables, following control variables are included: short-term reversal, extreme positive daily
16 return, analyst dispersion, level of illiquidity, coefficient of variance in the Amihud
illiquidity, standard deviation of turnover, unexpected earnings, and abnormal euro trading volume. By employing the basic and expanded specifications, I can examine the effect of liquidity shocks on future returns more thoroughly.
3.5. Control variables for stock-level regressions
This section details on control variables in stock-level cross-sectional regressions described in the preceding section. In a similar fashion to Bali et al. (2014), the control variables encompass a large set of factors which are known to affect cross-sectional expected returns.
The control variables in the first specification are the historical market beta, natural logarithm of the market capitalization, natural logarithm of the book-to-market equity ratio, and price momentum. The first three variables are based on Fama and French (1992). They report that size and book-to-market ratio captures the cross-sectional variations in returns. Based on their result, I expect a negative relation between size and stock returns and a positive relation between book-to-market ratio and stock returns. Price momentum by Jegadeesh and Titman (1993) implies that well-performing stocks in the past continue to perform better in following months than poor-performing stocks in the past. These four control variables are widely used in the international asset pricing context (Fama and French (2012), and Schmidt et al. (2017)). Especially, Fama and French (1998) show that the value premium exists in international settings.
Moreover, in their international survey of momentum strategies, short-term reversal, and post-earnings drift, Griffin, Kelly, and Nardari (2010) report that price momentum can affect cross-sectional returns in the Netherlands. They find that short-term reversal, post-earnings drift factors (i.e., earnings shock) do not significantly affect the returns in the Dutch market. Therefore, I include momentum in the first specification. Moreover, in the expanded
specification, I add the remaining variables (short-term reversal and earnings shock) in the analysis.
In the second specification with expanded control variables, short-term reversal is included following Jegadeesh (1990). The author shows that there is a negative first-order serial correlation in monthly stock returns up to a month. Bali, Cakici, and Whitelaw (2011) suggest that extreme positive daily return has a negative relation with expected returns.
17 Analyst dispersion by Diether, Malloy, and Scherbina (2002) implies that stocks with higher dispersion have lower future returns. Petkova, Akbas, and Armstrong (2011) argue that the coefficient of variance in the Amihud illiquidity represents the idiosyncratic liquidity risk. They show that it is positively priced in the cross-section of stock returns. Following Chordia, Subrahmanyam, and Anshuman (2001), the standard deviation of turnover denotes the
volatility of trading activity. They report a negative relation between stock returns and variations in trading activity. One major factor that can lead to stock underreaction is the well-known post-earnings-announcement drift (PEAD) anomaly, which was first noted by Ball and Brown (1968). When liquidity shocks coincide with earnings shocks, it is difficult to tell which one causes the underreaction. The unexpected earnings (or earnings shock)
variable is introduced to control for this effect. Lastly, abnormal euro trading volume controls for a possible volume premium reported by Gervais, Kaniel, and Mingelgrin (2001). They report that unexpected volume change is positively related to stock returns in the following month.2
4. Data and Descriptive Statistics
My sample consists of 287 securities listed in the Dutch stock market from January 1990 to December 2010. I use Thomson Datastream for obtaining stock data from Euronext
Amsterdam. A descriptive table on the sample stocks in each year is provided in Appendix D. 4.1. Sample construction and data treatment
Daily variables include the price (closing, closing bid, and closing ask), trading volume by shares (whose unit is in thousands), the return index, and the market capitalization of each stock. The number of shares outstanding is computed from the daily market value divided by the stock price. I then obtain monthly variables including the monthly return, firm size, the historical market beta, book value per share, and book value of the equity. Lastly, I download quarterly variables such as earnings per share (EPS) and analysts’ EPS forecasts, the last of
18 which are available via I/B/E/S. When I merge the quarterly dataset into the monthly one, I assume quarterly values remain the same within the quarter.
Several filters are applied for the sample construction. From Datastream, I download only securities that are identified as equity and whose issuers are located in the Netherlands. In addition, I only include securities that are listed as primary quote in Euronext Amsterdam, and that are in the local currency, which are the euro and the Dutch guilder.3 I exclude
securities with secondary listings (e.g., preferred shares). Lastly, two filters are applied manually. First, using filters suggested by Griffin, Kelly, and Nardari (2010),4 I search for
and remove non-common equity stocks such as investment trusts, ETF funds, or REITs. Secondly, I remove securities which became inactive before the starting of the sample period or have no data during the period. To avoid survivorship bias, I include inactive (i.e., dead or delisted) stocks. Since Datastream does not provide delisting returns or reasons for such stocks, they are treated in the delisting month as -100%.
In Euronext Amsterdam, although Datastream provides data from 1973, the data
availability of CPQ Spread before 1990 is lower. Daily bid and ask prices are only available for a limited number of stocks since 1996.5
There are noteworthy caveats (Ince and Porter (2006), Lee (2011), and Amihud et al. (2015)) on treating data from Datastream. In a similar fashion to Amihud et al. (2015)’s treatise on international liquidity premium, I apply several filters to replace noisy quotes and to ensure data consistency. First, daily returns from Datastream are set as missing if they are greater than 200% or if (1 + 𝑟, ) ∗ (1 + 𝑟, ) − 1 ≤ 50%, where 𝑟, is the return of stock
i on trading day d and at least either 𝑟, or 𝑟, being greater than 100%. Similarly, monthly
returns are set as missing if they are above 500% or they are above 300% and are reversed within the following month. Data of penny stocks with price less than 0.1 euros are replaced with missing values. Daily volume is set to be missing if it is lower than 100 Euros. I drop a
3 Stocks became inactive (e.g., dead or delisted) before the adoption of the euro are denominated in the Dutch guilder. To ensure comparability across the sample, all the values in the guilder are converted into euros using a Datastream function.
4 Detailed description of the filters is in Appendix C.
19 stock-month observation from the sample if the total number of non-missing return days in month t-1 is less than 3. Lastly, since bid-ask spreads cannot be negative, I discard such cases and treat them as missing values.
4.2. Descriptive statistics
Throughout this section, in order to obtain descriptive statistics, I first calculate cross-sectional averages of descriptive statistics at each month and average them again over the sample period. It is because the data availability of variables is uneven across the sample period. This double-averaging rather than a simple average would ensure that each month’s data is represented equally in the summary statistics.
Table 1 shows the series averages of descriptive statistics of the variables. The time-series median of the stock return is negative at -0.03% and the standard deviation is large at 13.46, which suggests a large variation in stock returns. The means of liquidity shock variables, which are Δ𝐿𝐼𝑄 and Δ𝑆𝑝𝑟𝑒𝑎𝑑, are negative at -0.08 and -0.18 and the medians (0.00 and 0.01) are close to zero. Together with this, the negative skewness (not reported here) of liquidity shock variables implies that there are more months where stocks experience positive liquidity shocks.
Before presenting the correlation table between variables, I inspect the time-series
characteristics of the stock-specific illiquidity measures. I derive the cross-sectional averages of first-order autocorrelation coefficients of the Amihud illiquidity measure and CPQ Spread. The result shows that they are moderately autocorrelated with an average coefficient of 0.44 and 0.65 for the Amihud illiquidity measure and CPQ Spread, respectively. This is consistent with empirical studies on liquidity which document that the level of liquidity is persistent over time (Amihud and Mendelson (2015, p.157)).
Table 2 reports the time-series averages of the cross-sectional Pearson correlation coefficients for the major variables. It shows that liquidity proxies, the Amihud illiquidity measure and CPQ Spread, are moderately correlated with the coefficient of 52.49% and the coefficient is significant at the 90% significance level. This indicates that our liquidity proxies capture the similar aspect of liquidity. This connection between two liquidity measures can also be seen in the market-wide liquidity over time in Appendix - Figure 1.
20 Table 1 - Time-series averages of descriptive statistics of the variables
This table shows time-series averages of the mean, median, and standard deviations of the monthly variables. Monthly return is in percentages. 𝐼𝐿𝐿𝐼𝑄 is the monthly average of the daily Amihud (2002) illiquidity measure, which is computed as the average ratio of absolute daily stock return to the daily trading volume within a month. Closing Percent Quoted Spread is the average of daily Closing Percent Quoted Spreads within a month, which are computed as the bid-ask spread over the mid-price. Δ𝐿𝐼𝑄 denotes the negative Amihud (2002) illiquidity measure demeaned by its past 12-month average. Δ𝑆𝑝𝑟𝑒𝑎𝑑 denotes CPQ Spread demeaned by its past 12-month average. Beta is the historical market beta obtained from past 60-months stock price. Ln(Market value) is the natural logarithm of the market capitalization of the stock. Ln(Book-to-market equity ratio) is the natural logarithm of the book-to-market equity ratio. Momentum is the momentum return. Short-term reversal by Jegadeesh (1990) is defined as the stock return over the prior month. Extreme positive daily return (Bali, Cakici, and Whitelaw (2011)) is the maximum daily return in a month. Analyst dispersion is the analyst earnings per share (EPS) forecast dispersion. Earnings shock is the standardized unexpected earnings. Abnormal euro volume is the euro trading volume shock, computed in the same method as liquidity shock. CV of Amihud illiquidity is the coefficient of variation in the Amihud illiquidity, computed as standard deviation of the Amihud illiquidity within a month scaled by the monthly Amihud illiquidity. Trading activity calculated as the standard deviation of the monthly turnover over the past 12 months. The sample consists of 287 Dutch stocks from January 1990 to December 2010.
Mean Median Std. dev.
Monthly return 0.02 -0.03 13.46
𝐼𝐿𝐿𝐼𝑄 0.61 0.02 3.68
Closing Percent Quoted Spread 3.09 1.16 7.74
Δ𝐿𝐼𝑄 -0.08 0.00 2.44
Δ𝑆𝑝𝑟𝑒𝑎𝑑 -0.18 0.01 4.17
Beta 0.70 0.65 0.71
Ln(Market value) 5.13 5.03 2.31
Ln(Book-to-market equity ratio) -0.60 -0.55 0.85
Momentum 8.48 4.74 41.28
Short-term reversal -0.09 0.06 27.79
Extreme positive daily return 5.56 3.89 7.15
Analyst dispersion 0.34 0.09 1.16
Earnings shock 0.36 0.09 2.96
Abnormal euro volume 0.21 -0.02 15.60
CV of Amihud illiquidity 1.34 1.20 0.60
21 T ab le 2 – C or re la ti on b et w ee n m aj or v ar ia bl es T he ta bl e re po rt s th e ti m e-se ri es a ve ra ge s of th e Pe ar so n cr os s-se ct io na l c or re la tio n co ef fi ci en t o f m aj or v ar ia bl es . 𝑟 is th e co nt em po ra ne ou s re tu rn a nd 𝑟 is th e on e-m on th -a he ad r et ur n. 𝐼 𝐿 𝐿 𝐼𝑄 is th e m on th ly a ve ra ge o f th e da ily A m ih ud ( 20 02 ) ill iq ui di ty m ea su re , w hi ch is c om pu te d as th e av er ag e ra tio o f ab so lu te d ai ly s to ck r et ur n to th e da ily tr ad in g vo lu m e w ith in a m on th . C lo si ng P er ce nt Q uo te d Sp re ad is th e m on th ly a ve ra ge o f da ily C P Q S pr ea ds , w hi ch is c om pu te d as th e bi d-as k sp re ad o ve r th e m id -p ri ce . Δ 𝐿 𝐼𝑄 d en ot es th e ne ga tiv e A m ih ud ( 20 02 ) ill iq ui di ty m ea su re d em ea ne d by it s pa st 1 2-m on th a ve ra ge . Δ 𝑆 𝑝 𝑟𝑒 𝑎 𝑑 d en ot es C lo si ng P er ce nt Q uo te d Sp re ad d em ea ne d by it s pa st 1 2-m on th a ve ra ge . B et a is th e hi st or ic al m ar ke t b et a ob ta in ed f ro m p as t 6 0-m on th s st oc k pr ic e. L n( M ar ke t v al ue ) is th e na tu ra l l og ar it hm o f th e m ar ke t c ap ita liz at io n of th e st oc k. L n( B oo k-to -m ar ke t e qu ity r at io ) is th e na tu ra l l og ar ith m o f th e bo ok -t o-m ar ke t e qu ity r at io . M om en tu m is th e m om en tu m r et ur n. A ll co rr el at io n co ef fi ci en ts a re in pe rc en ta ge s. T he s am pl e co ns is ts o f 28 7 D ut ch s to ck s fr om J an ua ry 1 99 0 to D ec em be r 20 10 . (1 ) (2 ) (3 ) (4 ) (5 ) (6 ) (7 ) (8 ) (9 ) (1 0) 𝑟 (1 ) 10 0. 00 𝑟 (2 ) 1. 29 10 0. 00 𝐼𝐿 𝐿 𝐼𝑄 (3 ) -3 .8 0 -1 .9 4 10 0. 00 C lo si ng P er ce nt Q uo te d Sp re ad (4 ) -2 .2 7 -1 .1 4 52 .4 9 10 0. 00 Δ 𝐿 𝐼𝑄 (5 ) 3. 98 0. 77 -3 9. 90 -5 .0 2 10 0. 00 Δ 𝑆 𝑝 𝑟𝑒 𝑎 𝑑 (6 ) 7. 40 1. 79 -1 6. 10 -5 0. 31 20 .0 2 10 0. 00 B et a (7 ) -0 .2 0 -0 .2 9 -1 2. 55 -1 4. 06 -2 .5 3 -1 .2 9 10 0. 00 L n( M ar ke t v al ue ) (8 ) 2. 86 2. 64 -3 4. 66 -5 2. 22 -2 .4 5 8. 41 19 .0 5 10 0. 00 L n( B oo k-to -m ar ke t e qu ity r at io ) (9 ) -5 .2 4 4. 78 7. 75 1. 09 -1 .6 3 2. 54 -2 .6 7 -1 7. 83 10 0. 00 M om en tu m (1 0) 4. 68 5. 36 -8 .4 2 -4 .9 3 10 .0 9 9. 34 -6 .4 1 15 .2 4 -1 6. 89 10 0. 00
22 The average correlation coefficients of the contemporaneous stock return and the liquidity shock variables are positive at 3.98% and 7.40% for Δ𝐿𝐼𝑄 and Δ𝑆𝑝𝑟𝑒𝑎𝑑, respectively, but not statistically significant. It casts doubt on the theory that liquidity is priced. According to the liquidity premium theory, a positive liquidity shock induces a decrease in the future stock return and an increase in the current price. Considering that it reports only the time-series averages of correlation coefficients, I investigate this issue further in a formal portfolio analysis in Section 5. Furthermore, contrary to the underreaction hypothesis, the average correlation coefficients of the liquidity shock measures and one-month-ahead returns are even smaller (0.77% and 1.79% for Δ𝐿𝐼𝑄 and Δ𝑆𝑝𝑟𝑒𝑎𝑑, respectively) and also not significant.
In addition, the coefficients between Ln(Market value) and the illiquidity measures are negative -34.66% and -52.22% for the Amihud illiquidity measure and CPQ Spread at 99% and 90% significance level, respectively. This is also related to the literature that bigger stocks are more liquid (Holden, Jacobsen, and Subrahmanyam (2014, p. 293)) and that the size and illiquidity are negatively correlated (Amihud and Mendelson (1986, p.243) and Amihud (2002, p.37)).
5. Results
The positive but not statistically significant correlation between liquidity shocks and one-month-ahead stock returns indicate that the stock market may not underreact to liquidity shocks. In this section, I formally test the hypothesis whether the return predictability of liquidity shocks are observed in the Dutch stock market. I first employ the portfolio-level analysis, followed by the stock-level cross-sectional regression analysis. The results show that although positive liquidity shocks are correlated with positive contemporaneous returns, the relationship disappears in the one-month-ahead returns.
5.1. Univariate portfolio-level analysis
In this section, I apply the methodology described in Section 3.3. At each month, I sort stocks into decile portfolios according to liquidity shocks. I then compare the returns of
high-liquidity shock portfolios with those of low-high-liquidity shock portfolios in the same month and in the following month. If return differences in the following month are observed, it suggests
23 that the market underreacts to initial liquidity shocks. I first start the analysis by examining contemporaneous average returns and risk-adjusted returns of the ten portfolios.
Table 3 shows time-series averages of contemporaneous excess returns and the Fama-French (1993) three-factor alphas of each Δ𝐿𝐼𝑄-sorted portfolios. The portfolios are composed of a total of 287 Dutch stocks over the sample period. The risk-free rate is the minimum of either the Netherland Interbank 3-month rate (IBR) or the Euro 3-month OIS rate. In addition, average portfolio characteristics are presented as separate columns. They are an average of liquidity shocks (Avg. 𝛥𝐿𝐼𝑄), an average of mean illiquidity level(Avg.
𝐼𝐿𝐿𝐼𝑄), and corresponding market share (Mkt. shr.) of each decile portfolio. In the last row of Table 3, it reports a hypothetical portfolio consists of a long position in Decile 10 portfolio (one with the most positive liquidity shock) and a short position in Decile 1 portfolio (one with the most negative liquidity shock). Naturally, the average value of liquidity shock (Avg. 𝛥𝐿𝐼𝑄) increases monotonically as the order of decile increases. For instance, the average liquidity shock of Decile 1 portfolio is negative at -2.4307, which implies an overall decrease in the level of liquidity of stocks. To account for potential autocorrelation, the coefficients and their statistical significance are calculated using Newey-West standard errors.
Table 3 – Contemporaneous excess returns and risk-adjusted returns and characteristics for portfolios formed on 𝜟𝑳𝑰𝑸
This table reports contemporaneous excess returns (denoted by Avg. ret.), risk-adjusted returns (denoted by Alpha), and characteristics of ten portfolios consist of 287 Dutch stocks formed at each month t. The raw returns are subtracted by the risk-free rate using either the minimum of either the Netherland Interbank 3-month rate (IBR) or the Euro 3-month OIS rate. Portfolios are sorted according to the liquidity shock (Δ𝐿𝐼𝑄) in the month t. Δ𝐿𝐼𝑄 is defined as the negative Amihud (2002) illiquidity measure demeaned by its past 12-month average. The table contains both equal-weighted and value-equal-weighted portfolio returns and alphas corresponding to the Fama-French (1993) three-factors. The returns are time-series averages of monthly excess returns over January 1990 to December 2010. The three-factors in the Netherlands are provided by Schmidt et al. (2017). Columns Avg. 𝛥𝐿𝐼𝑄 and Avg. 𝐼𝐿𝐿𝐼𝑄 denote the average of 𝛥𝐿𝐼𝑄 and 𝐼𝐿𝐿𝐼𝑄 in each portfolio decile. 𝐼𝐿𝐿𝐼𝑄 is the monthly average of the daily Amihud (2002) illiquidity measure, which is computed as the average ratio of absolute daily stock return to the daily trading volume within a month. Column Mkt. shr. represents the market share of each portfolio decile. Each row represents a decile portfolio ordered by the magnitude of liquidity shocks from the lowest to the highest. The last row (High-Low) denotes the differences in monthly returns between high- and low-𝛥𝐿𝐼𝑄 decile portfolios. Newey-West t-statistics that account for autocorrelation are given in parentheses. Monthly returns and alphas are in percentages. The sample covers the period from January 1990 to December 2010.
24 Table 3 – Continued
Equal-weighted Value-weighted
Decile Avg. ret. Alpha Avg. ret. Alpha Avg. 𝛥𝐿𝐼𝑄 Avg. 𝐼𝐿𝐿𝐼𝑄 Mkt. shr.
1 (Low) -2.77 -3.28 -2.42 -3.09 -2.4307 3.4992 2.50% (-5.02) (-6.48) (-4.71) (-7.13) 2 -1.45 -2.24 -1.35 -2.15 -0.0890 0.2120 14.16% (-2.71) (-6.70) (-1.59) (-3.26) 3 -1.11 -1.88 -0.61 -1.55 -0.0176 0.0544 14.65% (-1.73) (-5.10) (-0.76) (-3.16) 4 -0.23 -1.14 0.25 -0.72 -0.0036 0.0151 16.25% (-0.41) (-3.96) (0.36) (-2.31) 5 0.27 -0.60 0.50 -0.42 0.0005 0.0083 15.00% (0.43) (-1.80) (0.68) (-0.94) 6 0.72 -0.11 1.47 0.47 0.0045 0.0122 16.07% (1.46) (-0.41) (2.68) (1.46) 7 1.24 0.44 2.10 1.20 0.0127 0.0223 11.82% (2.77) (1.99) (4.33) (5.70) 8 1.40 0.67 1.24 0.46 0.0374 0.0518 6.75% (3.01) (1.95) (1.75) (0.92) 9 0.71 0.16 1.36 0.67 0.1332 0.1271 2.76% (1.80) (0.65) (2.83) (2.04) 10 (High) 1.45 1.04 2.15 1.80 1.6461 0.6551 0.04% (2.94) (2.52) (3.72) (4.09) High-Low 3.90 4.01 4.25 4.57 (7.08) (7.86) (6.21) (7.35)
Table 3 reveals that liquidity shocks are positively related to stock returns in the same month. The portfolio with the most positive liquidity shocks (Decile 10) exhibits the highest average return of 1.45% for equal-weighted returns and 2.15% for value-weighted returns. On the other hand, the portfolio with the most negative liquidity shocks (Decile 1) earns the lowest average return at -2.77% for equal-weighted returns and -2.42% for value-weighted returns. Portfolio returns do not increase monotonically as liquidity shock increases. For instance, the return of Decile 9 portfolio is 0.71% for the equal-weighted return, which is lower than the preceding Decile 8 portfolio’s return of 1.40%. A similar pattern is observed in value-weighted returns: Decile 8 and Decile 9 portfolio returns of 1.24% and 1.36% are smaller than Decile 7 portfolio return of 2.10%. This indicates that portfolios with more positive liquidity shocks do not always experience higher contemporaneous returns on average. This mild violation of a monotonic increase is in contrast to the literature.
25 The high-minus-low liquidity shock portfolio earns 3.90% and 4.25% of equal- and value-weighted returns, respectively. Corresponding risk-adjusted returns with respect to the Fama-French three-factors are also significant at the 99% level: the amount of return that cannot be explained by the three-factors are 4.01% and 4.57% for equal-weighted and value-weighted returns, respectively.
Looking at portfolio characteristics, stocks at each extreme of liquidity shocks scale take only a small amount of market share: stocks with the most negative liquidity change (Decile 1) account for 2.50% of the total market share; at the other end, stocks in Decile 10 only comprises 0.04% of the total market capitalization. Besides, I find that liquidity shocks do not show a monotonic relation with the average level of liquidity (Avg. ILLIQ) or market share. Lastly, value-weighted returns of portfolios are always higher than equal-weighted returns of portfolios except for Decile 8 portfolio, whose the equal-weighted return of 1.40% is higher than the value-weighted return of 1.24%.
Overall, Table 3 presents evidence consistent with the positive relationship between liquidity shocks and contemporaneous returns: a negative and persistent (the last of which are discussed in Section 4.2) liquidity shock is associated with a low contemporaneous return. I find a similar result using portfolios formed on 𝛥𝑆𝑝𝑟𝑒𝑎𝑑 which is presented in Appendix E, Table 10.
Next, we investigate the relation between liquidity shocks and one-month-ahead returns. Table 4 reports average excess returns in month t+1 of portfolios sorted by 𝛥𝐿𝐼𝑄 and
𝛥𝑆𝑝𝑟𝑒𝑎𝑑. The raw returns are subtracted by the risk-free rate in the same method from Table 3. The first four columns on the left represent returns of portfolios sorted by shocks to the Amihud illiquidity measure (Δ𝐿𝐼𝑄). The last four columns on the right report returns of portfolios sorted by shocks to Closing Percent Quoted Spread (𝛥𝑆𝑝𝑟𝑒𝑎𝑑). Each portfolio is formed in month t according to the magnitude of liquidity shock.
26 Table 4 – One-month-ahead excess returns and risk-adjusted returns for portfolios
formed on liquidity shocks
This table reports one-month-ahead excess returns (denoted by Avg. ret.) and risk-adjusted returns (denoted by Alpha) of ten portfolios consist of 287 Dutch stocks formed at each month t. The returns are subtracted by the risk-free rate using either the minimum of either the Netherland Interbank 3-month rate (IBR) or the Euro 3-3-month OIS rate. Portfolios are sorted according to shocks to the Amihud illiquidity measure (Δ𝐿𝐼𝑄) or shock to Closing Percent Quoted Spread (𝛥𝑆𝑝𝑟𝑒𝑎𝑑) in the month t. Δ𝐿𝐼𝑄 is defined as the negative Amihud (2002) illiquidity measure demeaned by its past 12-month average. 𝛥𝑆𝑝𝑟𝑒𝑎𝑑 is defined as a shock to the 12-monthly average Closing Percent Quoted Spread and is computed in a similar way to Δ𝐿𝐼𝑄. The table contains both equal-weighted and value-weighted portfolio returns and alphas corresponding to the Fama-French (1993) three-factors. The returns are time-series averages of monthly excess returns over January 1990 to December 2010. The three-factors in the Netherlands are provided by Schmidt et al. (2017). Each row represents a decile portfolio ordered by the magnitude of liquidity shocks from the lowest to the highest. The last row (High-Low) denotes the differences in monthly returns between high- and low-𝛥𝐿𝐼𝑄 decile portfolios. Newey-West t-statistics that account for autocorrelation are given in parentheses. Monthly returns and alphas are in percentages. The sample covers the period from January 1990 to December 2010.
𝛥𝐿𝐼𝑄 𝛥𝑆𝑝𝑟𝑒𝑎𝑑
Equal-weighted Value-weighted Equal-weighted Value-weighted
Decile Avg. ret. Alpha Avg. ret. Alpha Avg. ret. Alpha Avg. ret. Alpha
1 (Low) -0.59 -0.96 -0.92 -1.25 -0.97 -1.06 -1.45 -1.64 (-0.84) (-1.34) (-1.55) (-2.07) (-0.91) (-1.04) (-1.32) (-1.60) 2 -0.22 -0.43 -0.65 -0.81 -0.26 -0.40 -0.81 -0.77 (-0.43) (-0.87) (-0.92) (-1.23) (-0.39) (-0.60) (-0.82) (-0.81) 3 -0.33 -0.64 -0.57 -0.85 -0.30 -0.42 -0.86 -0.94 (-0.57) (-1.21) (-0.82) (-1.27) (-0.42) (-0.62) (-0.79) (-0.88) 4 -0.19 -0.41 0.18 -0.01 -0.01 -0.18 -0.12 -0.24 (-0.33) (-0.79) (0.30) (-0.01) (-0.02) (-0.27) (-0.13) (-0.24) 5 0.15 -0.09 0.51 0.17 0.62 0.49 0.38 0.24 (0.29) (-0.16) (0.83) (0.26) (0.80) (0.57) (0.54) (0.30) 6 0.52 0.19 0.44 0.13 0.38 0.11 0.40 0.31 (0.98) (0.39) (0.66) (0.20) (0.55) (0.15) (0.75) (0.49) 7 0.69 0.51 1.02 0.70 0.37 0.22 0.90 0.81 (1.39) (1.17) (1.99) (1.54) (0.63) (0.39) (1.60) (1.48) 8 0.54 0.32 0.50 0.32 0.92 0.80 0.83 0.78 (1.17) (0.77) (1.12) (0.78) (1.16) (1.05) (0.91) (0.82) 9 -0.12 -0.23 -0.28 -0.41 -0.06 -0.33 -0.16 -0.33 (-0.25) (-0.54) (-0.40) (-0.65) (-0.12) (-0.77) (-0.26) (-0.66) 10 (High) -0.18 -0.29 -0.28 -0.43 -0.42 -0.64 -1.12 -1.34 (-0.44) (-0.78) (-0.45) (-0.87) (-0.53) (-0.86) (-1.12) (-1.33) High-Low 0.09 0.35 0.33 0.50 0.83 0.65 -1.09 -1.00 (0.14) (0.52) (0.59) (0.80) (0.91) (0.65) (-1.16) (-0.99)
27 In Columns 1 and 3, average portfolio returns in month t+1 do not increase monotonically as liquidity shock in month t increases. It is the stocks in Decile 7 that have the highest equal- and value-weighted returns of 0.69% and 1.02% in month t+1. Accordingly, stocks with the most positive liquidity shock (Decile 10) do not always perform the best in month t+1: both the equal-and value-weighted average returns are actually negative at -0.18% and -0.28%. The high-minus-low portfolio still earns positive average returns in month t+1. However, their corresponding three-factor alphas are not statistically significant: the equal- and value-weighted alphas are positive at 0.35% and 0.50%, but the t-statistics are 0.52 and 0.80, respectively.
In Columns 1-4, although lower decile portfolios (Deciles 1-4) generally continue to show negative average returns in month t+1, their corresponding alphas are not significantly different from zero. The only exception is the valueweighted alpha in Decile 1, which is -1.25% with a t-statistic of -2.07. At the other end, stocks with extremely positive liquidity shocks (Decile 10) actually exhibit return reversals in month t+1: the average returns in equal- and value-weighted portfolios are -0.18% and -0.28%. If we recall, in month t, both are positive. In addition, the corresponding risk-adjusted returns (i.e., alphas) of Decile 10 portfolio are not significantly different from zero. In the last row, the high-minus-low portfolios still earn positive returns of 0.09% and 0.33% in the equal- and value-weighted terms, respectively. However, their corresponding alphas are not statistically significant. It means that after adjusting for the three-factors, the return differences between Decile 10 and Decile 1 are not significantly different from zero.
In Columns 5-8, portfolios sorted by Δ𝑆𝑝𝑟𝑒𝑎𝑑 exhibit a similar pattern. The average returns do not increase monotonically as liquidity shocks increase. Also, we observe the negative average returns on the top two decile portfolios: the equal-weighted (the value-weighted) returns of Decile 9 and Decile 10 are -0.06% and -0.42% (-0.16% and -1.12%), respectively. The high-minus-low portfolios earn a positive equal-weighted return of 0.83%, but its value-weighted return is negative at -1.09%. Moreover, the corresponding alphas of
28 the high-minus-low portfolio are not significant: the equal- and value-weighted alphas are 0.65% and -1.00%, but they are not statistically significant.6
In Columns 5-8, a similar pattern is observed for lower decile portfolios (Decile 1-4) as in Columns 1-4: stocks in Deciles 1-4 continue to show negative average returns in month t+1, but their corresponding alphas are not significant at the 95% level. For instance, in Decile 1, the risk-adjusted return for equal-weighted (value-weighted) portfolio is -1.06% (-1.64%), but not statistically significant. At the other end, Decile 10 portfolio shows negative returns of -0.42 and -1.12% for equal- and value-weighted returns, respectively. Nevertheless, after adjusting for the Fama-French three-factors, the returns are not significant: the average equal-and value-weighted alphas are -0.64% equal-and -1.34%, but their t-statistics are very low at -0.86 and -1.33, respectively. Accordingly, the performance of the high-minus-low portfolio is weak and its alphas are not significant: its average value-weighted return is actually negative at -1.09%, even though the alpha is not significant.
In general, the result in Table 4 suggests that there is no strong evidence that changes in stock-level liquidity can predict one-month-ahead returns: the relation between liquidity shocks and one-month-ahead returns is not monotonic and the high-minus-low portfolio does not report positive risk-adjusted returns that are significantly different from zero. In other words, it indicates that the stock market does not underreact to liquidity shocks. One interesting result is that, although the risk-adjusted returns of Decile 9 and Decile 10 are not significantly different from zero, the average returns turn to negative in month t+1 from positive in month t. This is contradictory to our initial hypothesis. From this, we can suspect whether the market overreacts to extremely positive liquidity shocks. This possibility is investigated in Section 6, Robustness Checks.
5.2. Stock-level cross-sectional analysis
We have seen in the previous section that positive liquidity shocks are not related to positive returns in month t+1. Furthermore, the relationship between liquidity shocks and
6 Note that for portfolios sorted by 𝛥𝑆𝑝𝑟𝑒𝑎𝑑, even after subtracting the risk-free rate, the average returns and
alphas of the high-minus-low portfolio are not exactly equal to the difference between those of Decile 1 and Decile 10 portfolios. It is because a small amount of monthly return data are missing for Decile 10 portfolios sorted by 𝛥𝑆𝑝𝑟𝑒𝑎𝑑. The impact does not significantly affect the result.
29 ahead returns is not monotonic. Note that this previous analysis is based on the portfolio-level. In this section, we further study the effect of liquidity shocks on future returns by conducting cross-sectional stock-level analyses. As described in Section 3.4, we run a predictive form of the Fama-Macbeth cross-sectional regression on future returns using lagged explanatory variables. In short, we run the following formula:
𝑟, − 𝑟, = 𝛼 + 𝛽 𝐿𝐼𝑄, + 𝛾 𝑋, + ϵ, ,
where the left side of the equation refers to the excess return of a stock in month t+1, and 𝐿𝐼𝑄, denotes either Δ𝐿𝐼𝑄, or Δ𝑆𝑝𝑟𝑒𝑎𝑑, in month t. 𝑋, is a set of control variables in month t.
Table 5 reports the result of time-series averages of slope coefficients from monthly cross-sectional regressions at the stock level. Monthly excess returns in month t+1 are regressed on a set of control variables in month t using the Fama-MacBeth (1973) methodology.
Coefficients of each variable with their t-statistics in parentheses are given.
Table 5 – Average slopes from monthly cross-sectional regressions of one-month-ahead returns
This table reports time-series averages of slopes of each variable with their t-statistics in parentheses. Monthly excess returns in month t+1 are regressed on a set of control variables in month t using the Fama-MacBeth (1973) methodology. The first row reports coefficients of either Δ𝐿𝐼𝑄 or Δ𝑆𝑝𝑟𝑒𝑎𝑑. Δ𝐿𝐼𝑄 denotes the negative Amihud (2002) illiquidity measure demeaned by its past 12-month
average. 𝛥𝑆𝑝𝑟𝑒𝑎𝑑 is defined as a shock to the monthly average Closing Percent Quoted Spread and is computed in a similar way to Δ𝐿𝐼𝑄. Beta is the historical market beta obtained from past 60-months stock price. Ln(Market value) is the natural logarithm of the market capitalization of the stock. Ln(Book-to-market equity ratio) is the natural logarithm of the book-to-market equity ratio.
Momentum is the momentum return. Short-term reversal is defined as the stock return over the prior month. Extreme positive daily return is the maximum daily return in a month. Analyst dispersion is the analyst earnings per share (EPS) forecast dispersion. 𝐼𝐿𝐿𝐼𝑄 is the monthly average of the daily Amihud (2002) illiquidity measure of each stock, which is computed as the average ratio of absolute daily stock return to the daily trading volume within a month. CV of Amihud illiquidity is the coefficient of variation in the Amihud illiquidity, computed as standard deviation of the Amihud illiquidity within a month scaled by the monthly Amihud illiquidity. Trading activity is calculated as the standard deviation of the monthly turnover over the past 12 months. Earnings shock is the standardized unexpected earnings. Abnormal euro volume is the euro trading volume shock, computed in the same method as liquidity shock. The last row reports average 𝑅 from the Fama-MacBeth (1973) first-stage regression. The sample consists of 287 Dutch stocks from January 1990 to December 2010.
30 Table 5 – Continued Δ𝐿𝐼𝑄 Δ𝑆𝑝𝑟𝑒𝑎𝑑 (1) (2) (3) (4) Liquidity shock (Δ𝐿𝐼𝑄 or Δ𝑆𝑝𝑟𝑒𝑎𝑑) 0.180 11.289 -0.773 1.445 (0.38) (1.68) (-1.01) (1.15) Beta 0.098 0.450 0.686 5.208 (0.28) (1.11) (1.14) (1.65) Ln(Market value) 0.026 0.025 0.153 -0.345 (0.46) (0.26) (1.09) (-0.58)
Ln(Book-to-market equity ratio) 0.635 0.406 0.573 -0.280
(5.68) (2.82) (3.36) (-0.24)
Momentum 0.839 0.009 -0.949 0.024
(2.22) (1.64) (-0.74) (1.01)
Short-term reversal -0.009 0.168
(-0.56) (0.74)
Extreme positive daily return -0.057 -0.193
(-1.19) (-0.45) Analyst dispersion 0.053 -6.483 (0.12) (-1.05) 𝐼𝐿𝐿𝐼𝑄 5.511 -578.05 (1.38) (-0.16) CV of Amihud illiquidity 0.323 3.467 (1.19) (0.66) Trading activity -0.073 0.645 (-0.51) (1.16) Earnings shock -0.001 -0.091 (-0.02) (-0.17)
Abnormal euro volume -0.006 0.141
(-0.38) (1.36)
𝑅 0.11 0.34 0.18 0.49
It shows regression results using two proxies for liquidity shocks, which are Δ𝐿𝐼𝑄 and Δ𝑆𝑝𝑟𝑒𝑎𝑑. I also try two different specifications to test the predictive power of liquidity shocks. Columns (1) and (3) report the basic specification, where control variables are the beta, natural logarithm of market capitalization (Ln(Market value)), natural logarithm of book-to-market equity ratio (Ln(Book-to-market equity ratio)), and price momentum. Columns (2) and (4) contain the expanded specification, where additional control variables are the short-term reversal, extreme positive daily return, the degree of analyst dispersion, individual stock’s level of illiquidity (ILLIQ), the coefficient of variance in the Amihud
