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COMMONALITY IN
LIQUIDITY
Wouter van Weering
S3005909
Faculty of economics & business
University of Groningen
Master thesis MSc. Finance
Supervisor: dr. Gijsbert T.J. Zwart
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COMMONALITY IN LIQUIDITY
Wouter van Weering1 University of Groningen
ABSTRACT
This paper examines the dynamics of commonality in liquidity in a European-wide sample of stock markets, showing that commonality in liquidity is not constant but varies over time. I relate commonality in liquidity to supply explanations (volatility) and demand explanations (correlated trading). Furthermore, I show that commonality in liquidity in a country sample is related to volatility, but not to implied volatility, and that commonality in liquidity in the European sample shows less co-movement than in a country sample. Moreover, country pairs that invest more in each other, also have a higher commonality in liquidity. The findings imply that investors, who want to diversify their portfolios, should take into account that the liquidity of individual stocks co-move with the aggregated market-wide liquidity. These new empirical findings help to understand time-series variation in commonality in liquidity of individual stocks.
Keywords: Liquidity, International markets, Commonality in liquidity, Co-movement, Equity JEL Classification: G12, G14, G15
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TABLE OF CONTENTS
ABSTRACT ... 2 1. INTRODUCTION ... 4 2. LITERATURE ... 7 2.1 LIQUIDITY ... 7 2.2 COMMONALITY IN LIQUIDITY ... 8 2.3 LIQUIDITY SHOCKS ... 92.4 COMMONALITY IN LIQUIDITY AND ASSET RETURN CORRELATIONS ... 10
2.5 HYPOTHESES ... 10
3. DATA AND METHODOLOGY ... 11
3.1 DATA ... 11
3.2 DESCRIPTIVE STATISTICS... 13
3.3 METHODOLOGY ... 14
4. RESULTS ... 20
4.1 COMMONALITY IN LIQUIDITY ... 20
4.2 LIQUIDITY SHOCKS BETWEEN COUNTRIES ... 23
4.3 COMMONALITY IN LIQUIDITY AND ASSET RETURN CORRELATIONS ... 23
4.4 COMMONALITY IN LIQUIDITY AND VOLATILITY ... 25
4.5 COMMONALITY IN LIQUIDITY AND INVESTMENTS ... 28
5. DISCUSSION AND CONCLUSION ... 28
5.1 CONCLUSION ... 28
5.2 DISCUSSION ... 29
REFERENCES ... 30
APPENDICES ... 32
I. LITERATURE OVERVIEW ... 32
II. LIQUIDITY SHOCKS BETWEEN COUNTRIES ... 33
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1.
INTRODUCTION
Liquidity plays a central role in the functioning of financial markets. Liquidity is the ability to trade financial assets easily (the allowance of immediate trading of large volumes) and cheaply. It is not a constant variable but a variable that changes continuously over time. It depends entirely on the market participants‘ behaviour and their willingness to buy or sell financial assets. Without it, financial markets are unable to function, and no resource shifting can take place. This research looks at the positive linkage between individual stock liquidity co-moving with the market liquidity. This phenomenon is called liquidity commonality. To be perfectly clear, commonality in liquidity refers to the proposition that the liquidity of individual stocks responds to market-wide changes in liquidity (Fabre and Frino, 2004, p. 357).
Since the 2008 crisis, the importance of liquidity has become a much discussed topic. When the market liquidity dried up in 2008, many market participants were unable to sell their assets at reasonable costs. This had a huge impact on their portfolio returns, and sometimes, they were less diversified than they were aiming to be. Investors should recognise that portfolio returns are not the only correlation factor to consider; the co-movements in the liquidity of individual assets with the market liquidity should also be noticed. Research has shown that investors deal with these asset pricing implications by paying more for stocks that allow them to close their position during liquidity dry ups (Pástor and Stambaugh, 2003; Brunnermeier and Pedersen, 2005; Lee, 2011). The price premium that they pay serves to lower their systematic liquidity risk. This liquidity premium (the premium that investors receive for holding illiquid stocks) leads to higher expected stock returns. Amihud and Mendelson (1986) showed a positive return relationship with illiquidity in stocks.
The aim of this research is to extend the knowledge about the commonality in liquidity of individual stocks with the market liquidity. Past research has mainly focused on the U.S. stock markets, and little is known about stock markets in other countries. According to Karolyi et al. (2012, p. 83), only four other studies of commonality in liquidity other than in the U.S. stock market have been done (excluding their own studies). However, since the publication of that paper, I found another seven papers on liquidity commonality that included samples from European countries. Therefore, the focus on the U.S. stock market for research on commonality in liquidity is shifting to other markets as well.
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commonality in liquidity of individual stocks within a country. The interesting question is whether or not there is still liquidity commonality to be found when looking at individual firm liquidity compared to an aggregated liquidity of the market that consists of multiple countries. In this research, 14 different countries are used for the market liquidity. Based on the discussion above, the following research question was formulated:
Is there commonality in liquidity of individual stocks with the aggregated European-wide market liquidity?
This paper aims to get a better understanding of the sources that drive commonality in liquidity, one of those sources are funding constraints. Market participants face funding constraints during high volatility of asset prices. When markets become more volatile, their margins and/or the value of the collateral in pledged securities become less certain. In order to secure the financial position of the market participants, these positions need to be strengthened. An implication is that the presence of capital constraints might lead to co-movement in liquidity. This is due to market participants selling the same risky assets and shifting them to the same riskless assets because during volatile times, all investors who face these funding constraints are looking for liquidity. A second research question was formulated to investigate the link between volatility and commonality in liquidity further:
Is commonality in liquidity positively linked to volatility?
This paper also aims to provide a better understanding of how liquidity shocks move between countries. Due to financial integration, financial markets are increasingly linked to each other. A shock in financial markets distributes as a shockwave over the rest of the world, and a large group of instituions can be affected. To investigate how liquidity shocks move between countries, a third research question was developed:
How are liquidity shocks of different countries related to each other?
Commonality in liquidity has important asset pricing implications for portfolio diversification. Besides looking at asset returns and liquidity, it would be interesting to see how the commonality in liquidity between two countries is related to the asset return correlation between the same two countries. To investigate this, a fourth research question was developed:
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One of the drivers of commonality in liquidity is correlated trading activity. Correlated trading activity consists of the common buying or selling pressures that reinforce the degree of co-movement between securities prices and liquidity. If multiple investors from one country trade more in another country, it is more likely that the commonality in liquidity between those two countries is higher. To investigate this further, a fifth and final research question was developed:
How are the investments of one country in another country related to commonality in liquidity?
This study adds to the literature by using several different measurements of volatility. The results from the literature about commonality in liquidity and volatility are conflicting. This study provides information that implied volatility and volatility measured by the time series standard deviation provide different results, which explains the conflicting findings between commonality in liquidity and volatility. Furthermore, the study shows that commonality in liquidity is not only related within the country in question but can be explained in a European-wide context.
The results of the study are relevant for investors who want to diversify their portfolios. They should take into account that the liquidity of individual stocks co-move with the aggregated market-wide liquidity. An illiquidity premium might not be sufficient to compensate for the risk that investors have when they want to sell off their assets.
Using data from Thomas Reuters Datastream, investing.com, The Bank of International Settlements, and the World Bank, the results show that commonality in liquidity is found in a European-wide sample. I show that one of the supply-side drivers (volatility) is linked to commonality in liquidity in a country sample but not in a European sample. Furthermore, country pairs that invest more in each other also have a higher commonality in liquidity (demand-side drivers). Furthermore, I provide evidence that those countries that show a strong degree of association in liquidity shocks with another country are also more affected in terms of the relation between commonality in liquidity and asset return correlations.
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2.
LITERATURE
This chapter contains the literature review that focuses on liquidity, commonality in liquidity, commonality in liquidity related to liquidity shocks, asset return correlations, volatility, and investments. The hypotheses derived in this chapter are tested in Chapter four ‗results‘. For a quick overview of the most relevant literature on commonality in liquidity, please see Appendix I.
2.1 LIQUIDITY
Understanding the definition of liquidity is not a difficult idea to grasp. Being able to quickly trade larger sizes of financial assets at a reasonable cost is a clear definition. Yet, the major problem lies in the inability to directly observe liquidity in the financial market. Therefore, market participants need to find a way to measure market liquidity. However, measuring an unobservable variable might be a difficult task. The simplest liquidity measurements are unable to capture the three dimensions of liquidity. These dimensions were stated by Kyle (1985, p. 1316) as follows: ‗"tightness" (the cost of turning around a position over a short period of time), "depth" (the size of an order flow innovation required to change prices a given amount), and "resiliency" (the speed with which prices recover from a random, uninformative shock)‘. Simple liquidity proxies, capture most of the time, only one of the three dimensions, and therefore leaving market participants ill-informed about possible liquidity (risk) changes. The ‗tightness‘ factor can be captured by using, for example, the bid-ask spreads of the security in the market (Hasbrouck and Seppi, 2001). ‗Depth‘ is a factor that can be measured by using the trading volume and the turnover of the security in the market. Finally, ‗resiliency‘ can be captured by measuring the market impact.
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A large disadvantage of the Amihud liquidity measurement is the inability to capture volatile stock prices during the day. If the stock price at opening and closing is the same, no contribution to the calculation of liquidity is made. Second, it provides a non-definition for zero volume days. Other widely used liquidity measurements on commonality in liquidity include bid-ask spreads. Fong et al. (2017) showed that the Amihud liquidity proxy is among the best cost-per-volume proxy, therefore making the different spread measurements a less optimal liquidity measurement to use.
2.2 COMMONALITY IN LIQUIDITY
Prior to 2000, empirical research was only focused on individual stock liquidity. In their pioneering work, Chordia et al. (2000) provided evidence that firm-level liquidity co-moves with aggregated market-wide liquidity. This phenomenon is referred to as commonality in liquidity. They showed that there is a substantial variability over time in all the liquidity measures they used (see Appendix I for details). Their research triggered a significant amount of subsequent empirical research to confirm commonality in liquidity on the NYSE (Hasbrouck and Seppi, 2001; Huberman and Halka, 2001). These three studies used different research methodologies to arrive at the same conclusion: the existence of liquidity commonality. All three of these studies used U.S. data of single-exchange datasets spanning only one year. This raised the question whether liquidity commonality is unique to the U.S. market, resulting in subsequent studies that examined commonality in liquidity in different markets using different timeframes.
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Many common components in variations can be explained as potential drivers for commonality in liquidity. These can be classified as either supply-side or as demand-side driven sources.
Supply-side explanations of commonality in liquidity can be found in the funding constraints
that market participants‘ face. Brunnermeier and Pedersen (2008) showed that commonality in liquidity arises from funding constraints that market participants (financial intermediaries) face during high volatility or large market declines. Market participants can obtain financing by pledging securities as collateral or stay above a minimum margin requirement. When markets become more volatile, these margins and/or the value of the collateral in pledged securities become less certain. In order to secure the financial position of the market participants, these positions need to be strengthened. This forces them to liquidate security positions and triggers a negative market spiral in which securities prices keep dropping and the liquidity in the market dries up due to only having a sellers‘ market2
. This shows how the fragility in liquidity due to destabilizing margins and collaterals can trigger large market liquidity dry ups. Due to these funding constraints, market participants shift their investments from high-risk to low-risk securities. Investors who face these capital constraints look for liquidity during volatile times. An implication of this is that the presence of capital constraints leads to commonality in liquidity.
Demand-side explanations of commonality in liquidity can be explained by correlated trading
activity. Correlated trading activity consists of the common buying or selling pressures that reinforce the degree of co-movement between securities prices and liquidity. The idea is that investors with similar trading patterns also face similar shocks in prices and liquidity. When markets receive new available information, their trading behaviours are similar, resulting in correlated trading activities. Furthermore, basket trading by institutional investors is a potential driver for liquidity commonality. These institutional investors put common selling and buying pressure across individual stocks, which leads to common liquidity variations (Karolyi et al., 2012; Koch et al., 2016).
2.3 LIQUIDITY SHOCKS
How are liquidity shocks of different countries related to each other? Due to increasing financial integration, financial markets are increasingly linked to each other. A shock in financial markets distributes as a shockwave over the rest of the world, and a large group of
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institutions can be affected. The result of this risk-sharing is that the burden of a shock is distributed, and the financial system becomes overall more resilient. However, if this shock is sufficiently large, it can lead to a financial contagion. Kyle and Xiong (2001, p. 1402) defined contagion as ‗the rapid spread from one market to another of declining prices, declining liquidity, increasing volatility, and increased correlation associated with the financial intermediaries‘ own effect on the market in which they trade‘. When investors liquidate their position in case of extreme return shocks and start trading in the same direction as noise traders, this could result in prices of fundamental unrelated assets co-moving which each other. This can result in a financial contagion (Kyle and Xiong, 2001; Xiong, 2001).
2.4 COMMONALITY IN LIQUIDITY AND ASSET RETURN CORRELATIONS
The link between liquidity commonality and return co-movements has important asset pricing implications for portfolio diversification. Policymakers would want to understand how liquidity commonality and asset return co-movements are linked with each other in order to react to financial shocks and to mitigate financial contagion. Domowitz et al. (2005) showed that it is possible for assets to have little return correlations but high liquidity commonality. However, they used demand and supply schedules to determine liquidity (commonality). These measurements are not in line with other research on liquidity commonality.
2.5 HYPOTHESES
Based on the supply-side explanations of commonality in liquidity, how is commonality in
liquidity linked to volatility? Hoesli et al. (2017), using a dataset of real estate securities, did not find commonality in liquidity driven by market volatility measured by the VIX3 in real estate securities. Karolyi et al. (2002) showed a significant positive effect between market volatility and the average level of liquidity commonality. They measured volatility by the standard deviation of the market returns within a country. A similar result as Karolyi et al. (2002) was documented by Hameed et al. (2010).
These findings are conflicting in their conclusion. This might be due to the fact that they used a different sample, a different time horizon, and different measurements of market volatility. Whether or not the effects are also present when the average level of liquidity commonality is measured in the aggregated European-wide market liquidity sample is also unknown. Based on these facts, the following two hypotheses were derived:
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H1: Commonality in liquidity is positively linked to volatility measured by the historical
volatility.
H2: Commonality in liquidity is positively linked to volatility measured by the implied
volatility.
Hypotheses two and three were both tested on the commonality in liquidity measured by a country sample and measured by the aggregated European-wide sample.
Based on the demand-side explanations of commonality in liquidity, how is commonality in
liquidity linked to investments? Investors with similar trading patterns also face similar shocks in prices and liquidity, and their common trading activities reinforce the degree of co-movement between securities prices and liquidity. To analyze this further, the following hypothesis was developed:
H3: Countries that have higher investments from another country have a higher
commonality in liquidity
3.
DATA AND METHODOLOGY
This chapter discusses the data sources used and the definitions of the variables. After that, the used methodology is discussed.
3.1 DATA
The data required for analyzing the commonality in liquidity and analyzing how liquidity shocks between two countries are related to each other were extracted from Thomson Reuters Datastream (TR). The data collected consists of the daily trading volume of each individual stock expressed in thousands of shares, the market capitalization in millions of U.S. dollars for each individual stock, and the daily adjusted price in the local currency. I selected stocks from the major indices of the 14 countries used. An overview of the selected countries and their indices can be found in Table 1 in the chapter entitled ‗DESCRIPTIVE STATISTICS‘ (Chapter 3.2). The sample used dates from the beginning of 2015 until the end of 2016, which results in a total collection of two years of data.
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than two months of return observations in a year were removed from the sample for that specific year. This resulted in removing six stocks from the sample. If more than 90% of all the stocks within a certain country did not have any return observations in a certain month, then that month is considered to be non-trading for all stocks in that country.
This sample has the disadvantage that there might be a selection bias in the stock exchange selection. The sample is therefore also less comprehensive, which makes managing it more pleasant, but at the cost of accuracy. However, because these stocks are more liquid, the problems of infrequently traded firms are avoided. Because this could lead to spurious results due to unreliable liquidity estimates (Peranginangin et al., 2016.). Several other studies also include just the major indices and not all stocks in a country, with no reasons stated for including all stocks in their analysis, and it appears only to increase the accuracy of their findings and to avoid biased stock picking. In order to limit survivorship bias, dead or suspended stocks were included in the sample (for more information about this, see Sullivan et al., 1999). The implication of this is that several stocks do not have observations for some month(s), and therefore those stocks were excluded during those months.
In line with Karolyi et al. (2012), the daily return observations in the top or bottom 0.1% within a country are discarded. Ince and Porter (2006) set any return above 300% as missing, in this dataset, this problem came forward only once. However, due to having less than 15 trading days during that month, the concerned stock was excluded for that month, so no correction was necessary.
The additional data required for analyzing whether or not the commonality in liquidity is related to volatility and asset return correlations were extracted from multiple sources. In addition to the data described above, the total return index was extracted from Thomson Reuters Datastream for all 14 indices used. The total return index measures the performance of a stock index assuming that all cash distributions are reinvested, including dividends.
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of volatility. All three implied volatility indices were extracted on a monthly time frame from investing.com4.
The data used to analyze how commonality in liquidity is linked to investments were extracted from the Bank of International Settlements (BIS). The data provide a detailed view of the consolidated credit positions of counterparties residing in a certain country. These are claims on an immediate counterparty basis, in which the data provide the positions of the countries in credit to counterparties in the country in question. This means bank loans to other banks/companies/governments. Through the data, we can see the amount of investments of one country in another country. The data were extracted on a quarterly interval over the years 2015 and 2016 in millions of U.S. dollars from the 14 countries in question. The data are reasonably consistent, which is important to consider in order to filter for missing data. This means that the outstanding credit does not fluctuate heavily every quarter. The four quarters were averaged, so a yearly outstanding credit amount is provided. If one of the four quarters were missing, the average was taken over the three remaining quarters; this was done two times. If only one quarter was provided, we categorized the data as missing for that particular year, which also happened two times. Credit claims of country i to Denmark, Norway, and Portugal are always missing5.
Finally, the Gross Domestic Product (GDP) in millions of U.S. dollars for every country over the year 2015 and 2016 was extracted from the database of the World Bank.
3.2 DESCRIPTIVE STATISTICS
In Table 1, an overview of descriptive statistics is provided. This table provides an overview of the selected countries, stock markets, number of unique stocks, return observations, market returns, market volatility, and the market liquidity. Market returns and volatility are expressed as percentages per day. The Amihud liquidity measurement was measured in absolute returns, and by multiplying the results with the negative natural logarithm, we achieved a measurement that is negative by construction. Negative values closer to zero indicate greater liquidity. When comparing the descriptive statistics with Karolyi et al. (2012), the average market return mean and market volatility mean are lower. An explanation for this can be found in the sample period, in which more effects from stock market crashes were captured in the dataset of Karolyi et al. (2012).
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Multiple other sources confirm that the data is accurate.
14 TABLE 1:
DESCRIPTIVE STATISTICS
This table provides the descriptive statistics for the average market return, market volatility, and the market-level Amihud liquidity measure for 14 countries over the period 2015–2016. Countries are listed in alphabetical order, and the screening procedures applied in the selection of the sample are described in the chapter entitled: ‗DATA AND METHODOLOGY‘. The number of return observations is the count sum of all unique stock returns across the individual stocks in each country. The market return mean is the average of all daily absolute stock returns in the country reported in percentages. Market volatility mean is the average standard deviation of the absolute stock returns of all unique stocks in percentages within the country. For the return observation, market return mean, and market volatility mean, the reported results are after the adjustment of the discarded stock-day observations with a daily return in the top or the bottom 0.1%. The market liquidity mean for the individual stocks is the average of the daily Amihud measurement multiplied by 10,000, as computed in formula (1) in Chapter 3.3, ‗METHODOLOGY‘ within the country.
Country Stock market Unique stocks Return observations Market return mean (in %) Market volatility mean (in %) Market liquidity mean Austria ATX 20 9,629 0.0512 2.0059 -0.0644 Denmark OMXC 20 20 9,510 0.0677 1.9135 -0.0011 Finland HEX 25 25 11,935 0.0759 2.1220 -0.0213 France CAC 40 39 19,699 0.0452 1.8811 -0.0966 Germany DAX 30 15,217 0.0341 1.8498 -0.7651 Greece Athex 20 25 10,762 -0.0431 4.9901 -4.8774 Ireland ISEQ 38 13,514 0.0839 5.3592 -18.2314 Netherlands AEX 25 12,516 0.0552 2.0413 -0.0051 Norway OBX 25 12,192 0.0746 2.8899 -0.0702 Portugal PSI 20 19 9,037 0.0335 2.3804 -1.5300 Spain IBEX 35 35 17,634 0.0308 1.9716 -0.0077 Sweden OMXS 30 30 14,869 0.0570 2.1476 -0.0006 Switzerland SMI 20 9,951 0.0087 1.6597 -0.0018 United Kingdom FTSE 100 100 49,720 0.0394 1.9072 -0.0001
Total 451 216,185
3.3 METHODOLOGY
To measure liquidity, the widely used proxy of Amihud (2002) was used. The price impact proxy measures the daily absolute stock return divided by the dollar volume. Following the approach of Karolyi et al. (2012), a constant was added to the measurement, and natural logarithms were used to reduce the impact of outliers. Also, the results were multiplied by -1 because the Amihud measurement is a measurement for illiquidity, and the inverse was needed to get a liquidity measurement, meaning that the liquidity proxy was computed as follows:
( | |
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in which is the absolute stock return on day t in local currencies, is the price in local currency, and is the trading volume on day t. With the liquidity formula presented in equation 1, the construction of daily time series of liquidity for every stock within each country was completed. Syamala et al. (2014) showed that this liquidity measurement has a high correlation with other liquidity measurements, such as bid-ask spreads, quoted depth, Roll spreads and high-low spread estimators.
Following Karolyi et al. (2012), first, the day-of-the-week effects in liquidity had to be filtered, as documented by Chordia et al. (2005). Day-of-the-week effects are the anomaly that stocks move more on Fridays than on Mondays, and there is a bias towards positive market movements on Fridays. This naturally influences the liquidity in the market. Many other studies also have followed this approach (see for example Boudakri et al., 2017; Syamala et al., 2017). In order to filter these day-of-the-week effects, we started with the following basic auto-regression model:
in which the regression states that the liquidity of stock i at day t is the liquidity of yesterday, a constant term , and some noise (the error term on the right side). The focus is on the noise of the regression, which reflects unexpected innovations in liquidity. So far, we assumed that the regression coefficients are constant over time, which does not have to be the case. Therefore, by loosening this assumption a bit, we allowed the regression coefficients to be different every month, and the time factor t would result in a combination of day d and month
m.
By expanding this basic auto-regression model by using the following filtering regression for each stock i based on observations for each day d within each month m, the day-of-the week effects were filtered:
∑
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With regression (3), the day-of-the-week effects were filtered, then a measurement to find the commonality in liquidity had to be found. Morck et al. (2000) used the of a regression to measure how the individual stock returns and the market returns co-move between each other within a country (as inspired by Roll, 1988). Karolyi et al. (2012) employed a similar approach and use the of the regressions of the liquidity of individual stocks on market liquidity to obtain a measure of commonality in liquidity. I followed the same approach as Karolyi et al. (2012) and also used the as a measure of commonality in liquidity.
Regressions (4) and (5) provide answers to the following research question: ‗Is there commonality in liquidity of individual stocks with the aggregated European wide market liquidity?‘. To obtain the monthly measures of commonality in liquidity denoted by the for each stock i, the following OLS regression was used, based on daily observations d within a month m:
∑ ̂
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a certain country take a very large/small portion of the total weights. The country factor has a significant influence on the liquidity commonality in that country if the weight is significantly higher/lower in a certain country. In order to see how much this influences the results, the following monthly regression comparison was computed to obtain the monthly measures of commonality in liquidity:
∑ ̂
where denotes the sum total of aggregate market residuals from (3) in the complete European sample, which was computed as the equal-value-weighted mean average of the residuals for all stocks in the sample.
In order to compare the commonality in liquidity in the European sample with the commonality in liquidity in a country sample, an additional regression had to be done. This also provided information to compare the results with the commonality in liquidity computed by Karolyi et al. (2012). In order to see how the results are different, the monthly measures of commonality in liquidity were obtained and denoted by the for each stock i by using the following regression, based on daily observations within a month:
∑ ̂
where denotes the sum total of aggregate market residuals from (3) in the complete country sample, which is the equal-value-weighted mean average of the residuals for all stocks within the country. The equal-weighted mean of the residuals were used to avoid the possible (previously discussed) bias with the market-weighted residuals.
To get more insight in how the liquidity shocks between two countries co-move, an OLS regression was used. The regression measures the degrees of association (measured by commonality) in liquidity shocks between two countries. The market residuals ( ) from regression (6) were applied to compute the monthly measures of for each country i as follows:
̂
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measured by the was obtained. However, this raw measure of commonality in liquidity was not appropriate to use as a dependent in the regressions hereafter because their values always fall between 0 and 1. Therefore, the following logistic transformation by Morck et al. (2000) and Karolyi et al. (2012) of the was used:
*
+
in which is the monthly logistic transformation of the aggregated average commonality in liquidity for each country of regressions (5) and (6). The dependent variable in regressions (9) and (10) is the logistic transformation of the average commonality in liquidity ( ) of individual stocks within a country. The dependent variables were used from the European-wide sample (regression 5) and the country sample (regression 6). Therefore, we can compare the results of the different samples used. To see if commonality in liquidity is linked to volatility, the following time-series regression was used:
where is the logistic transformation of commonality in liquidity measured by regressions (5) and (6) for each country j, and denotes the time-series market volatility measured by the standard deviation of (absolute) market returns of a country index j in a certain month extracted from the total return index. The absolute market returns to measure volatility was used because, in construction of the Amihud liquidity measurement, the absolute returns were also used. However, for completeness, the non-absolute market returns were also employed for robustness.
To see if commonality in liquidity is linked to the implied volatility, the following regression was created:
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To investigate the link between commonality in liquidity of two countries and asset return correlations between the same countries, the following regression was used:
where is the commonality in the liquidity logistic transformation of commonality in liquidity measured by regression (7) between country i and country j. The is the monthly correlation between the absolute returns of the total return indices of country i and country j6. Whether or not the connection between commonality in liquidity and correlations in absolute asset returns is closely linked was measured by the beta.
In order to test how commonality in liquidity is linked to investments, the data from the Bank of International Settlements was used. The yearly outstanding credit of the country i in question to the 13 other countries j was be used. This yearly outstanding credit was divided by the GDP of the country that receives the investment (credit)7. This ratio was averaged for the country pairs, meaning that, for example, the investment ratios Spain–France and France– Spain were being averaged for the years 2015 and 2016. This resulted in a maximum of 91 country-pair observations for each year. The countries lacking observations in investments (as stated in the data section) were not averaged. Then, the link between investments and commonality in liquidity could be tested with the following cross-sectional regression:
where the dependent variable is the commonality in the liquidity logistic transformation of commonality in liquidity measured by regression (7) between country i and country j. The country pairs were averaged over the years 2015 and 2016. Therefore,
we obtained 91 observations over the full sample. The independent variable is the investment ratio averaged over the years 2015 and 2016 of all pairs. With this regression, we could investigate whether or not some pairs that have a higher commonality in liquidity also have a higher cross-investment holding. The single obtained beta is the result of interest.
6 For example, Netherlands and Germany:
| | | | .
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4.
RESULTS
This chapter provides the results of the analyses. It starts by presenting the results of the commonality in liquidity in the European sample and the country sample, followed by the liquidity shock relation between countries. After that, the relation between the commonality in liquidity and asset return correlations is discussed. Next the results of the supply-side explanation of commonality in liquidity are explained (in relation to volatility). Finally, the demand-side explanation of commonality in liquidity is discussed in relation to investments.
4.1 COMMONALITY IN LIQUIDITY
The results of the monthly measures of commonality in liquidity denoted by the for each country of regression (4) can be found in Table 2. When looking at the second column of the table, the market mean commonality in liquidity ( ) over the years 2015 and 2016, is on average, around 7.7 percent. This was calculated over the full sample. Although the countries‘ average commonalities in liquidity are very similar to each other, we can see that the variation in monthly commonality is large.
TABLE 2:
COMMONALITY IN LIQUIDITY – TOTAL SAMPLE
This table provides the results of the mean, standard deviation, maximum and minimum commonality in liquidity ( for 14 countries over the period 2015–2016 computed, as in regression (4). The market mean
is the commonality in liquidity of individual stocks measured by monthly regressions of the daily innovations in liquidity of individual stocks at the country level. The standard deviations, maximum, and minimum represent the monthly average of across the individual stocks in each country over the 24 months. The means are the time-series average computed as the monthly equal-weighted average across the individual stocks in each country displayed in percentages.
Total sample
Country market mean (in %)
market standard dev.
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By looking at the fourth and fifth column of Table 2, the maximum monthly liquidity commonality of 29.1 percent is in Germany in May, and the minimum of 2.1 percent is in Portugal in November. In this sample, the saying ‗sell in May and go away, but remember to come back in September‘ might be of particular interest since May exhibits, overall, the highest unreported commonality in a liquidity month (10.9 percent), followed by September (9.1 percent). Future research might focus on calendar effects in liquidity commonality.
22 TABLE 3:
COMMONALITY IN LIQUIDITY – PER YEAR
This table reports the market weight for each country, the commonality in liquidity, and, respectively their standard deviations spread over the period 2015 and 2016 for 14 countries. The second column represents the sum of market value weight for each stock within a country displayed in percentages, computed as the market value at the end of the previous year-weighted mean. This market value only influences the data in the third and fourth column in this table. The third column displays the commonality in liquidity of individual stocks measured by the of monthly regressions on the market-weighted European sample, which is the result of regression (4). The fifth column represents commonality in liquidity on the equal-weighted European sample, which is the result of regression (5). The seventh column is the liquidity commonality in the equal-weighted country sample, as computed in regression (6). The standard deviations represent the equally weighted monthly average of across the individual stocks in each country over 12 months. The means are the time-series average computed as the monthly equal-weighted average across the individual stocks in each country.
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4.2 LIQUIDITY SHOCKS BETWEEN COUNTRIES
The results of how liquidity shocks of different countries are related to each other can be found in Appendix II, which is the result of OLS regression (7). The degrees of association in liquidity shocks between two countries were measured by the . When we have a high , the liquidity shocks in one country show a strong degree of association with the liquidity shocks in another country. The results serve two functions in this paper: First the results were used as inputs (dependent variable) to investigate the link between commonality in liquidity of two countries and asset return correlations between the same countries (Chapter 4.3). The results were also used to test how commonality in liquidity is linked to investments (Chapter 4.5). Second, the numerical results from the table in Appendix II were used to see which country pairs have a higher degree of association in liquidity shocks between each other. These can be related to the results from Chapter 4.3. The table shows that the average degree of association in liquidity shocks between all countries is around 15% in the complete sample. The top five countries that show the strongest overall relation in liquidity shocks with other countries are Switzerland, the Netherlands, Sweden, Spain, and Finland.
4.3 COMMONALITY IN LIQUIDITY AND ASSET RETURN CORRELATIONS
24 TABLE 4:
COMMONALITY IN LIQUIDITY AND ASSET RETURN CORRELATIONS
This table reports the link between commonality and the asset return correlations. It is the result of regression (11) over the time period 2015–2016. The dependent variable is the logistic transformation of the commonality in liquidity of regression (7) between country i and country j, and the independent variable is the asset return correlation between the same countries of the absolute return indices. The coefficients are reported along with the corresponding robust standard errors in parentheses. Significances are reported as *p<0.10, **p<0.05, and *** p<0.01.
Year 2015 and 2016
Austria Denmark Finland France Germany Greece Ireland Netherlands Norway Portugal Spain Sweden Switzerland United
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4.4 COMMONALITY IN LIQUIDITY AND VOLATILITY
The results of regressions (9) and (10) – if commonality in liquidity is related to volatility – can be found in Table 5 and 6. The dependent variables are the logistic transformation of each country‘s commonality in liquidity, as stated in regression (8), and the independent variables are the used (implied) volatilities. The model relates to supply-side explanations of commonality in liquidity. The robust standard errors used are the White-Hinkley heteroskedasticity consistent standard errors and covariance. The number of observations of the logistic transformation on commonality in liquidity is 24 (one for each month in the two- year sample).
Table 5 contains information about the European sample, which shows almost no significant relation to volatility. Except for Portugal, no historical volatility measurement is related to commonality in liquidity. This makes sense because the commonality in liquidity is related to the European-wide sample. In other words, the liquidity of individual assets in a certain country co-moves with the changes in the market liquidity in 14 other countries. If we relate this to the volatility in the specific country only, we do not fully capture the volatility to which it should relate. Therefore, the implied volatility measurement, the VSTOXX, would be a better variable to use as a volatility measurement. However, this model also does not show that volatility is related to commonality in liquidity because only two out of the 14 countries show a significant effect. In conclusion, we can reject the hypothesis that commonality in liquidity in the European sample is related to the historical volatility over a two-year sample. Whether the implied volatility is related to commonality in liquidity in the European sample is still ambiguous. The VSTOXX is not a perfect proxy for implied volatility in this sample because it includes the volatility of stocks that are not included in the commonality in liquidity. Furthermore, the VCAC shows a significant effect.
26 TABLE 5:
COMMONALITY IN LIQUIDITY AND VOLATILITY EUROPEAN SAMPLE
27 TABLE 6:
COMMONALITY IN LIQUIDITY AND VOLATILITY COUNTRY SAMPLE
This table highlights the link between commonality in liquidity and (implied) volatility. It is the result of regressions (9) and (10) in 14 countries over the time period 2015–2016. The commonality in liquidity is the logistic transformation of the time series in country (j=14) over every month (m=24) in the total time period, which is the dependent variable. The table uses the commonality in liquidity in the country sample. The independent variables are measurements of the volatility. Column two shows the standard deviation of the absolute returns on the total return index. Column three contains data about the standard deviation of the non-absolute returns on the total return index. Column four reports the implied volatility of the VSTOXX 50. The fifth column reports the VCAC 40 implied volatility, and the final column is the VDAX-New implied volatility measurement. The coefficients are reported along with the corresponding robust standard errors in parentheses. Significances are reported as *p<0.10, **p<0.05, and ***p<0.01.
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4.5 COMMONALITY IN LIQUIDITY AND INVESTMENTS
The results of how commonality in liquidity is linked to investments, based on regression (12) are presented here. In total, 85 observations were used in the regression over the period 2015– 2016. The following country pairs were dropped from the regression due a lack of investment observations: Denmark–Norway, Denmark–Portugal, Denmark–Spain, Finland–Portugal, Norway–Portugal, and Norway–Spain. The robust standard errors used are the White-Hinkley heteroskedasticity consistent standard errors and covariance. The estimated beta from the regression with the corresponding standard error is 3.0859 and 1.2128. This means that the results are significant at the 5% level. The positive beta states that country pairs that have a higher investment intensity are also more related in terms of commonality in liquidity.
These results provide more evidence for the demand-side explanations of commonality in liquidity. Correlated trading reinforces the degree of co-movement between securities prices and liquidity. These results show that investors within the same country with similar investment patterns across borders also face similar shocks in liquidity, which should be considered for portfolio diversification.
5.
DISCUSSION AND CONCLUSION
This chapter begins with a presentation of the conclusions of this research, followed by a discussion in which the results are discussed and the limitations of the study are stated. Finally, some future research suggestions are stated.
5.1 CONCLUSION
This study uses data from Thomas Reuters Datastream to provide evidence that the firm-level liquidity of individual stocks co-moves with the aggregate wide liquidity. The market-wide liquidity contains the aggregated average liquidity of 450 stocks within 14 different countries in Europe. The results of this study provide evidence that those countries that show a strong degree of association in liquidity shocks with another country are also more affected in the relation between commonality in liquidity and asset return correlations. Furthermore, the results show that commonality in liquidity within the country sample is related to the volatility measured by time series standard deviation, but not to the implied volatility. The European-wide sample does not show any relation to volatility. Moreover, country pairs that have a higher investment intensity are also more related in terms of commonality in liquidity.
29
liquidity. An illiquidity premium might not be sufficient to compensate for the risk that investors become exposed to when they want to sell off their assets, because when the liquidity of their financial assets goes down, the liquidity of other financial assets also dries up. Therefore, they might not be able to shift their resources to less risky investments because there is no liquidity in the market. These new empirical findings help to understand time-series variation in commonality in liquidity of individual stocks.
5.2 DISCUSSION
The implied volatility measurement VSTOXX used for this study is not a perfect proxy for the implied volatility in this sample. The volatility measurement VSTOXX uses the volatility of stocks that are not used in the sample of commonality in liquidity. Therefore, we are comparing the volatility of different stocks.
The main limitation of this study is the sample size of 14 countries within Europe, which is relatively small, and the time horizon of two years is relative short. It would be worth researching whether the phenomenon of commonality in liquidity shows any dynamic patterns during recessions.
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APPENDICES
I. LITERATURE OVERVIEW
TABLE 7 LITERATURE OVERVIEW This table provides an overview on the most relevant literature on commonality in liquidity discussed in Chapter 2.
Authors (year) Measurement commonality Sample (years) Main findings—copied from the authors papers. Brunnermeier &
Pedersen (2008)
Model that links supply market liquidity to commonality, using funding constraints as a driver of market liquidity. Capital and margin requirements depend on market liquidity, using these requirements for testing commonality.
Theoretical model ‗Their model shows that market liquidity can suddenly dry up due destabilizing margins/pledged collateral These destabilizing margins can be the result of volatility in stock markets. This results in investors flying to liquid stocks, meaning that all investors are making a ―flight to quality‖. This flight to quality means that investors all actively go searching for stocks with high liquidity, which results in commonality in liquidity. Finally, they show that when funding becomes scares, speculators cut back on the market liquidity provision.‘
Chordia, Roll, & Subrahmanyam (2000)
Used market model regression: . Liquidity measures:
(1) Quoted spread (2) proportional quoted spread, (3) quoted depth, (4) effective spread, (5) proportional effective spread.
1169 NYSE stocks over the year 1992.
‗Recognizing the existence of commonality in liquidity using bid-spreads measurements in a regression analysis. They find are significant different from zero. This means there is a presence of common underlying determinants of liquidity. However, there regression obtains a very low coefficient of determination of around 4%.‘
Hasbrouck & Seppi (2001)
Used the following regression: . A principal component analysis on four interval order flow measures (signed trades, signed share volume, signed dollar volume, and signed square root of dollar volume) was used.
30 Dow Jones stocks over the year 1994
‗Using a principal component and canonical correlation analysis to find that common factors exist in both signed and absolute order flows. These explain partly of the common variation in signed and absolute returns. The findings are less supportive of economically significant common factors in liquidity. The strength of any common factors in spreads and related liquidity measures, as judged by the first principal components, is modest.‘
Huberman & Halka (2001)
A time-series model of the average liquidity proxy using an AR progress, and using proxies‘ depth and bid-ask spreads for liquidity.
240 NYSE stocks over the year 1996
‗Examine the common component in liquidity changes across stocks. They find a systematic time-varying component of liquidity. This initiated research on the effects of market-wide liquidity.‘
Karolyi et al. (2002) First, they filter out day-of-the-week effects in liquidity: ∑ .
From the residuals, they ran a regression to obtain the ̂ ∑ .
27,447 stocks from 40 countries over the years 1995– 2009
‗Finding potential drivers of commonality in liquidity that can be classified as either supply-side or as demand-side sources, furthermore examining how it varies across countries and over time. Commonality is linked to a number of market-wide characteristics (such as quality of legal protection for investors and transparency). Improving investors‘ property rights and enhancing transparency may lead to lower commonality in liquidity. Finally, they find that the most reliable explanation for commonality is correlated trading.‘
Coughenour & Saad, (2004)
Using the same market model method as Chordia er al. (2000), with adjustments to it for finding firm-specific commonalities.
259 stocks over the years June 1999 to 2001
‗Important supply-side sources of commonality in liquidity. Commonality across stocks is higher for stocks handled by NYSE specialist firms that face funding constraints. Since most market makers have net long positions, liquidity will tend to dry up most quickly when markets perform poorly, meaning that common market makers induce common liquidity movements.‘
Koch et al. (2016) .
Time-series regression of the firms daily change in illiquidity, , on changes in mutual fund ownership, , and changes in the market illiquidity,
, as well as control variables.
60,764 stocks over the years 1980– 2010
‗Important demand-side explanations of commonality in liquidity. Liquidity of stocks with high mutual fund ownership co-moves with that of other stocks that also have high mutual fund ownership. This is due to correlated liquidity demand of the stock‘s investors. This results in mutual funds having a high liquidity risk.‘
This study (2017) First day-of-the-week effects in liquidity were filtered: ∑
From the residuals a regression was done to obtain the
∑ ̂
451 stocks over the years 2015–2016
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II. LIQUIDITY SHOCKS BETWEEN COUNTRIES
TABLE 8:
LIQUIDITY SHOCKS BETWEEN COUNTRIES
This table reports the average liquidity shocks between countries for the year 2015 and 2016 over 14 countries computed as in regression (7). The numbers displayed below are the monthly average over the specific year.
34 TABLE 8:
LIQUIDITY SHOCKS BETWEEN COUNTRIES
(CONTINUED)
35 0% 5% 10% 15% Spain Finland Sweden Austria Norway Ireland Germany Portugal France Greece Denmark United Kingdom Switzerland Netherlands Liquidity Commonality
February 2015
0% 5% 10% 15% Switzerland Denmark Netherlands France Germany Sweden Portugal United Kingdom Finland Greece Norway Austria Spain Ireland Liquidity CommonalityDecember 2015
0% 5% 10% 15% Greece Denmark Ireland United Kingdom France Germany Norway Switzerland Sweden Portugal Netherlands Austria Spain Finland Liquidity CommonalityOctober 2016
III. COMMONALITY IN LIQUIDITY VISUALIZED
FIGURE 1
MONTHLY COMMONALITY IN LIQUIDITY
This figure presents the cross-country variation in commonality in liquidity ( ) in 14 countries in selected months over the period 2015-2016. The commonality in liquidity of individual stocks is measured by the at the country level. The mean (displayed in percentages) are used to capture the co-movement between changes in individual stocks‘ liquidity and the market liquidity.
36 0% 5% 10% 15% Finland Spain Sweden Austria Portugal Germany Norway Ireland Denmark Greece France Netherlands United Kingdom Switzerland Liquidity Commonality
February 2015
0% 5% 10% 15% Portugal Greece United Kingdom Netherlands France Austria Ireland Spain Switzerland Norway Denmark Finland Germany Sweden Liquidity CommonalityDecember 2015
0% 5% 10% 15% Greece Germany Denmark Ireland United Kingdom France Austria Sweden Norway Switzerland Finland Spain Netherlands Portugal Liquidity CommonalityOctober 2016
FIGURE 1MONTHLY COMMONALITY IN LIQUIDITY (CONTINOUD)
