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#### AN INVESTIGATION OF EQUITY MARKET LIQUIDITY MEASURES AND THEIR RESPONSE TO VOLATILITY: THE CASE OF THE UK MARKET

Abstract

This paper discusses methods that can be used to estimate market liquidity and then uses daily data to evaluate the UK market. It is demonstrated that there is a significant positive correlation between the liquidity measures and the levels of liquidity have increased significantly since the financial crisis. Regression analysis used to investigate the relationship between liquidity and volatility showed a significant correlation between the variables, with approximately half of the changes in liquidity that can be explained by changes in volatility. The meaning of the findings is that a volatile market is also likely illiquid, which implies that during a market downturn, illiquidity can increase the magnitude of the market decline.

Table of Contents

**Chapter 1. Introduction** **3**

**Chapter 2. Literature Review** **4**

**Chapter 3. Overview of the Liquidity Measures** **4**

Chapter 3.1. Trading Volume and Price Impact Measures 5

Chapter 3.1.1 Amihud Illiquidity Ratio 6

Chapter 3.1.2 Turnover 6

Chapter 3.2. Transaction Cost Measures 5

Chapter 3.2.2 Quoted Spread 6

**Chapter 4. Data Analysis and Results** **4**

Chapter 4.1. Data Overview 5

Chapter 4.2. Descriptive Statistics and Results 6

**Chapter 5. Liquidity Measures and Volatility** **4**

**Chapter 6. Limitations and Further Work** **4**

**Chapter 7. Conclusion** **4**

**Chapter 8. Bibliography** **4**

**Chapter 1. Introduction**

Recent financial crises have shown that conditions in the market can be severe and levels of liquidity can drastically decline or even disappear (Chordia et al., 2005). Sudden declines in liquidity during market downturns can have a major impact on the magnitude of price decrease across the market. Implications of liquidity decline on the market make it an important area of research. This dissertation will provide a critical overview of the classical measures used to estimate market liquidity and make a contribution to the area of research by analysing the UK market using the time-series approach. It also makes a key original input by testing the relationship between liquidity and volatility.

There is no widely accepted definition of liquidity and a liquid market has been described as one in which assets can be transacted quickly and easily, without experiencing high transaction costs or making a big impact on the price of an asset. Some studies choose to say that a market is liquid if it has these characteristics: tightness (low transaction costs), immediacy (speed at which orders can be executed), depth (existence of abundant orders), breadth (orders can be large in volume with minimal impact on prices), resiliency (orders move quickly to correct order imbalances) (Sarr, Lybek, 2002). To grasp most of the liquid market characteristics with the data that is available, this study will focus transaction costs, volume and price impact aspects of liquidity.

Since liquidity is not directly observable, methods were created to estimate its levels in the market. Classical measures of liquidity can be divided into volume-based and transaction-based categories. Volume consists of the amount exchanged between market actors and can be seen as an indication of demand and supply in the market. Volume-based measures adopted in this dissertation are Amihud illiquidity ratio, ILLIQ, and Turnover ratio. ILLIQ can be regarded as a measure of price impact and is a daily price response to a one-point change in volume (Amihud, 2002). Turnover shows what proportion of company’s shares available for trading have been traded in a defined time period. Many papers, including Brennan et al. (1998) have found it as a useful proxy for liquidity. Therefore, it has been adopted as one of the measures in this study. However, there has been some disagreement between scholars about the role of Turnover as liquidity estimator. Research done by Subrahmanyam (2005) finds that Turnover is not a good proxy for liquidity across the US stocks, supported by empirical findings by Lesmond (2005) in emerging markets.

Transaction cost measures is a more commonly used method that has been the centre of liquidity discussion since the start of research in the area. In a modern market, an asset is liquid if it can be sold at a minimal cost or, in other words, at a minimal bid-ask spread. It can be defined as a difference between the highest amount a buyer is willing to pay for an asset and the lowest price at which the seller would agree to sell it. Research shows that bid-ask spreads can be influenced by number of factors, such as financial news, herding behaviour and uncertainty surrounding equilibrium price (Maltz, 2007). Since bid-ask spreads capture all of these factors that affect the market, it can be used as a good indicator of liquidity and market sentiment. The method used to estimate transaction costs in this study will be Quoted Spread – the difference between end-of-day bid and ask prices, divided by the midpoint price, as used by Korajczyk and Sadka (2008).

This dissertation uses daily data obtained from DataStream to compute daily values of ILLIQ, lnILLIQ and Quoted Spread measures for each stock for the sample period of fifteen years. Then the monthly average is taken across stocks to analyse descriptive statistics and correlation. There was only yearly data was available for the Turnover variable, allowing for only 15 samples, therefore, a separate correlation matrix table is provided to show the relationship between Turnover and other liquidity measures.

Analysis shows significant positive correlation between the liquidity measures, in line with the expectation since they are trying to capture the same aspect of the market. Plotted on a time-series graph (Graph 1), the ratios demonstrate strong comovement and a significant peak around the 2007/8 financial crisis, showing decreased levels of liquidity around the period. Another thing to notice that levels of liquidity have increased significantly since the crisis, with almost 45% decrease in transaction costs between 2014-2018. However, Turnover does not exhibit the same pattern and is not correlated with any of liquidity measures, adding more evidence to the critique of Turnover as an effective measure of liquidity. However, due to only 15 observations for the Turnover ratio, results should not be taken with complete confidence.

To investigate liquidity further, this paper analyses the relationship between liquidity and volatility in order to see whether they move together and rapid change in prices are also accompanied by low levels of volatility. Correlation analysis shows that liquidity is indeed positively correlated with volatility, with average positive correlation of over 0.7 across measures. Regression analysis used to estimate the relationship between each of liquidity measures and volatility shows that around 50% of changes in the liquidity level can be accounted for by changes in volatility. Regression analysis shows that Turnover and volatility have no strong relationship but the results are not statistically significant, likely due to a small sample.

Results show that there is an obvious comovement between liquidity measures and volatility, meaning that a volatile stock market is also likely illiquid. This can be seen from the time series graph (Graph 3) and the results of correlation and regression analysis. A possible implication of this relationship is that during market stress, a person who is trying to sell and asset, in addition to experiencing lack of demand, also experiences high transaction costs, receiving an even lower return on the asset. Also, the sale makes an even bigger impact on market price through the Amihud ratio. This meaning that at a market downturn illiquidity can increase the magnitude of the market decline.

**Chapter 2. Literature Review**

One of the ways market liquidity can be described is by how quickly and cheaply one can sell or buy an asset in the market without making a big change to the asset price. Liquidity is an essential feature of a financial market and it is used as an indicator for smooth operation of an economy (Salighehdar et al., 2017) and can be seen as a characteristic of an efficient market. However, it is not directly observable in the financial markets and attempts to measure liquidity started a few decades ago, with papers including Black’s (1971) analysis of what constitutes an efficient market and Amihud and Mendelson’s (1986) study on transaction costs’ effect on asset pricing. However, a majority of research papers on the subject state that financial market liquidity and its measures are a relatively new area that has only lately seen an increase in interest and research and problems in quantifying liquidity still exist. Therefore, defining a globally accepted proxy for liquidity is still an active area of research (Salighehdar et al., 2017).

Many advocate that it is important to study the concept in detail due to many advantages it can provide. Firstly, Amihud (2002) claims that the movement in liquidity can forecast the aggregate returns; in other words, liquidity can be a market sentiment indicator (Baker & Stein, 2004). An abnormal, illiquid market implies that the asset’s price is dominated by irrational investors (Vinh Vo, 2017). Secondly, they allow financial institutions to accept larger asset-liability mismatches, making assets easily obtainable and thus reducing the risk of the central bank having to act as a lender of the last resort (Saarr, Lybek, 2002). Furthermore, it makes financial assets more attractive to investors, who can transact in them more easily (Saarr, Lybek, 2002). The liquidity crisis during the 2007-2008 market crash has drawn even more attention to the importance of the subject and also triggered studies on how to better judge the state of market liquidity in order to prevent any further systematic liquidity crises.

Whilst liquid markets can be described in a number of ways and there is no widely accepted definition of market liquidity, we generally perceive liquid investment instruments as desirable due to several benefits that they offer to investors and investment managers. Generally, liquid assets have lower transaction costs, are easier to transact in from both a trading and settlement perspective, have an increased level of information efficiency and trading large volumes in these markets is likely to have a lower level of market impact. They also allow investors to transact money more easily and permit financial institutions to accept more asset‐liability. Sarr and Lybek (2002) adopt a multi-dimensional definition of a liquid market and describe five key characteristics of liquidity while discussing several commonly used measures that can be used to gauge these characteristics across global equity markets. Three of the major characteristics that make up the definition of a liquid market were taken as proposed by Kyle (1985) – tightness, depth, resiliency – while in addition immediacy and breadth were added by Sarr and Lybek (2002). Following the liquidity definition, the authors classify the liquidity measures into four categories: transaction cost measures, volume-based measures, equilibrium price-based measures and market-impact measures. Every measure captures one or a couple of the mentioned liquidity characteristics. This dissertation will focus on volume, transaction cost and price impact measures.

Sarr and Lybek (2002) propose using transaction cost measures to calculate the price of trading the assets, therefore integrating analysis of market depth and tightness. They point out that high transaction costs reduce the demand for trades, therefore reducing the number of active participants in the market and available liquidity. They advocate using a bid-ask spread as a transaction cost measure. A later study, done by Korajczyka and Sadka (2008), looks across various liquidity measures to analyse latent factor models of liquidity. Their set of liquidity measures included quoted and effective spreads, share turnover, components of price impact (fixed versus variable and temporary versus permanent), and the absolute returns to volume ratio. They find that common liquidity factors are especially exhibited in spreads (both quoted and effective) and the fixed components of price impact.

One of the criticisms expressed by some authors is that the data on the bid-ask spreads and trading costs is tough to obtain and even unreliable in the context of international markets, even though looking at bid-ask spreads makes different stocks easily comparable to each over. While this study focuses on single UK market, due to the criticism of spread limitations, in this research project additional measures will be adopted to test liquidity. As proposed by Sarr and Lybek (2002), volume-based measures distinguish liquid markets when analysing trade sizes and corresponding price movements, primarily to measure breadth and depth (Sarr, Lybek, 2002). Volume is considered to provide markets liquidity because a large number of trades is a valuable source of information to market participants, especially dealers, as data gained from order flows and imbalances can inform them about the inaccuracy of their quoted prices. Changes from these quoted prices towards equilibrium ones lead to balancing of order flows and balances the price movements that are not caused by stock fundamentals, creating market resiliency (Sarr, Lybek, 2002). One of the measures that includes volume and corresponding price movements is Amihud illiquidity ratio, adopted in this study and discussed in detail in Chapter 3.

However, some researchers believe that volume is not an appropriate way to measure liquidity. Gabrielsen et al. (2001) state that the reason behind this is the issue if double counting, as a transaction on the buy side can also be recorded as a transaction on the seller side. This issue is even more apparent when testing the effects of high-frequency trading. Van Kervel (2015), when analyzing the link between order duplication and market fragmentation, finds that high-frequency traders, who have access to two or more venues, have an incentive to duplicate limit orders across venues (ESMA, 2016, citing Van Kervel, 2015). By using order book data for 10 FTSE 100 stocks that are cross-listed listed on five venues, Van Kervel (2015) finds that fulfilled buy trade leads to immediate order cancellations on other exchange venues and more than half of the Chi-X trade size is cancelled on LSE. The European Markets and Securities Authority found that 20% of the orders in the tested sample were duplicated orders and in 24% of trades the trader cancels immediately. (ESMA, 2016). They believe that duplication of orders and immediate cancellation of duplicates after a trade has become part of the strategy to ensure execution in fragmented markets, e.g. for market makers or where institutional investors are searching for liquidity. This shows that taking duplicated orders into account when measuring liquidity leads to overestimation of available liquidity in fragmented markets (Rosov, 2015) and measuring liquidity cannot be solely based on trading volume. Using multiple measuring methods in this study provides a fuller view of the market and allows for more credible results.

The relationship between the different measures of liquidity has not yet been thoroughly investigated. Research done by Arbuzov and Frovola (2012) constructs own Relative Transaction Cost Index (RTCI) and then estimates the relationship between RTCI and common measures of liquidity. They found that volume has the biggest impact on RTCI, meaning that increase in volume also significantly decreases transaction costs, showing that these measures of liquidity are connected. I am planning to further examine the correlation between common equity market liquidity measures in the UK market and then look at their relationship with volatility.

More recent studies have been focused on commonality and liquidity risk pricing. One of the studies conducted to test whether liquidity is a systematic characteristic of a market was done by Pukthuanthong-Le and Visaltanachoti (2009). They studied commonality of stocks listed on Stock Exchange of Thailand (SET) using eight years tick data. The study reported empirical evidence in favour of market-wide commonality across various liquidity proxies. Also, it is found that industry-wide commonality is stronger than market-wide commonality. They state that implications of commonality in liquidity on investors are not fully understood. However, intuitively, commonality means that shocks to liquidity are not usually contained within a single stock. It implies that a risk to investors of a significant decline in market liquidity which may not be fully diversifiable and could constitute a priced risk factor (Foran et al., 2014). Therefore, studies in commonality have also induced research on pricing of liquidity and how it relates to stock returns. Anderson et al. (2013) investigate whether investors are compensated for taking on commonality risk in equity portfolios. This study reports economical and statistical significance of return premium for commonality risk in NYSE stocks. The commonality risk premium is robust to various measures of liquidity and estimating its systematic component. While this dissertation does not aim to examine the commonality and pricing effects, the existence of commonality across stocks means that a sample of stocks can be used to estimate market-wide liquidity, and pricing of liquidity risk makes the ability to measure market liquidity even more meaningful.

**Chapter 3. Overview of Liquidity Measures**

**Chapter 3.1. Trading Volume and Price Impact Measures**

Volume-based measures are commonly used in examining market breadth. Volume consists of the amount exchanged between market actors in buying and selling activities for a single asset or for the market as a whole. Transactors and dealers obtain information from order flows: a high flow of orders makes it easier for prices to adjust with regard to demand and available supply, therefore helping to evaluate the equilibrium price in the market and to maintain market resiliency. However, as mentioned earlier, if a substantial proportion of orders are affected by duplicated orders, volume based market‐wide measures of liquidity may overstate the actual liquidity available to investors. In addition, some criticisms of these volume-based liquidity ratios mention the inability to distinguish between asset illiquidity and sudden price and volume movements due to new information that arrived to the market. Therefore, these calculations should be used only as a reference and combined together with broader research into the market.

**3.1.1 Amihud Illiquidity Ratio**

Amihud (2002) proposes a measure of illiquidity, called ILLIQ, which is the ratio of daily stock return divided by the daily volume, averaged over some time (monthly in this study). The Amihud ratio can interpreted as a measure of price impact, or market breadth, as it is a daily price response associated with a one-point change in volume (Amihud, 2002).

ILLQ=1ns,m* ∑t=1ns,mrs,tdvols,t

Where

dvols,tis the dollar volume of stock *s* on day *t*,

rs,tis the return on of the stock *s* on day *t* and

ns,mis the number of daily observations in the month *m*. In this paper

dvols,tis replaced by daily volume to negate the market capitalization and price inflation effects.

This is based on the earlier study done my Amihud and Mendelson (1986) which finds that stock return increases when there is an increase in illiquidity. This can be explained by understanding that generally, one unit of excess return of the stock is a form of compensation for taking on a unit of risk. Therefore, expected stock excess return reflects the compensation for expected market illiquidity, which has been mostly confirmed by the recent studies in liquidity pricing (as in Korajczyk, Sadka, 2008). This effect of expectations is due to the fact that higher current illiquidity raises the expected illiquidity levels which in turn raise the expected returns of the stocks and lower the stocks prices (Amihud, 2002).

Due to the issue of severe outliers in this ratio that can be caused when trading activity is very low and volume is close to zero, following Lu and Hwang (2007) and Foran et al. (2014), Atilgan (2016), this paper considers the logarithmic value of the ratio to minimize the effects of these outliers. The adjusted form of Amihud ratio is given by:

lnILLQ=1ns,m* ∑t=1ns,mlnrs,tvols,t

**3.1.2 Turnover**

Another popular measure associated with volume is Turnover. Defined as a ratio of trading volume to shares outstanding, researchers have considered it as a proxy for liquidity and liquidity risk for decades (see Datar et al., 1998). In the 1998 paper, Brennan et al. found that turnover is useful in predicting stock returns and is an appropriate proxy to estimate the liquidity of a stock. They also add to Amihud and Mendelson’s (1986) liquidity pricing theory by postulating that turnover might represent liquidity premium (Subrahmanyam, 2005). Others also argue that turnover is a good indicator of market sentiment (Bake, Stein 2004) or liquidity (Datar et al. 1998), Sarr and Lybek (2002). The paper by Subrahmanyam (2005) states that due to many roles assigned to liquidity, it seems as the real function of turnover remains an unresolved issue. Therefore, he attempts to investigate the role of the ratio in the cross-section of expected stock returns of US stocks. Subrahmanyam finds that turnover is negatively related to stocks with abnormally low performance and positively related to well-performing stocks, therefore, casting doubt on Turnover as a liquidity proxy (Subrahmanyam, 2005). A study by Lesmond (2005) examined the correlation between Bid-Ask Spreads and Turnover across 23 emerging countries and found that Turnover and the Bid-Ask Spread are negatively and significantly correlated in only 40% percent of the markets tested, adding support Subrahmanyam’s claim. This dissertation will look at the correlation between Turnover, ILLIQ and Quoted Spread in the UK market to add a perspective to the ongoing discussion.

Turnover, the ratio of monthly volume and shares outstanding, is given by:

Turnoveri,t= ∑j=1dmvols,jSOs,m

Where

voli,mis the volume of stock *s* on day *j* of month *m*,

SOs,mare the number of shares outstanding for stock *s* at the end of the month *m*. Due to unavailability of data for monthly number of shares outstanding, this project adapts the equation to measure yearly, not monthly, turnover.

**3.2. Transaction Costs Measures**

Transaction costs are the other commonly used liquidity measure. They have been in the centre of market liquidity discussion since the start, including analysis in papers by Black (1971), Cohen et al. (1981), Amihud and Mendelson (1986). Bid‐ask spreads are the most commonly used measure of transaction costs as it captures both expenses such as order processing and taxes related to trades. A rather trivial fact about bid‐ask spreads is that infrequently traded stocks are characterized by large bid‐ask spreads (Muranaga, Oshawa, 1999) ‐ an asset is liquid if it can be quickly exchanged at a minimal cost. A similar definition can be applied also to an asset market as a whole. In a modern market, high transaction costs represent a source of a low liquidity. In this sense, a market is liquid if it is possible to buy and sell assets at a minimal cost, therefore, also at a minimal bid‐ask spread. While talking about liquid market characteristics, immediacy, for instance, is dependent on the existence of dealers willing to buy and sell at the quoted bid‐ask spreads. If the transaction costs are high, they can reduce the demand for trades and therefore the number of potential participants in the market. This reduces breadth and resiliency. The infrequency of trades is also likely to induce price discontinuity. The liquidity risk arising from the bid‐ask spread is often called “exogenous” because the trader cannot influence the spread by trading more or less, but can only decide whether and how much to trade at a given spread. However, this is true only to a certain extent; sometimes spreads can be affected by financial news and herding behaviour. It often occurs that bid‐ask spreads widen because of greater uncertainty about the equilibrium price in the overall market, because short‐term volatility has risen, or because dealers have less confidence that a lumpy order can be redistributed to other market participants without loss (Maltz, 2007).

Empirical evidence shows that bid-ask spreads also depend on trading behaviour throughout the day. In their paper, Muranaga and Oshawa (1999) mention that in Japanese equity market, which has two sessions per day, bid‐ask spreads tend to behave in a ‘W’ shaped pattern: they peak at open, close and just before lunch time. Volume and volatility seem to exhibit the same shape; in contrast, US equity markets behave in a ‘U’ shape as the equity market only has one session per day. This clearly shows that trading is more expensive in transaction cost sense when the market is opening and closing, and that there is a high correlation between bid‐ask spreads and volatility. While the intraday bid-ask spread analysis is not available to due lack of available data, the relationship between volatility and quoted spread derived from daily data will be examined in Chapter 5 of the dissertation.

Return volatility is also dependent on bid‐ask spreads, which is a further reason to look at this measure. A first well‐known fact documented by Amihud and Mendelson (1987) with regard to NYSE stocks’ intraday price movement is that open‐to‐open return volatility is higher than close‐to‐close return volatility in the markets applying the call‐clearing procedure at the opening session. Stoll and Whaley (1990) argue that the wider bid‐ask spreads are caused by specialists using their monopoly position at the opening call. It makes prices more volatile since transaction prices tend to bounce between bid and ask prices (Muranaga, Oshawa ).

**3.2.1 Quoted Spread**

While the difference between bid and ask prices is designed to measure trading costs, due to the definition of a liquid market it can be used as a proxy for liquidity. Quoted spread is the difference between the end-of-day bid and ask prices, indicated as a relation to midpoint price.

Qs,m=1ns,m*∑t=1ns,mPs,tA- Ps,tBms,t

Where

Ps,tAis the ask priceof stock *s* on day *t*,

Ps,tBis the bid price of stock *s* on day *t*,

ns,mis the number of daily observations for stock* s* in month *m* and

ms,t=(Ps,tA+ Ps,tB)/2is described as the midpoint of bid-ask price (Korajczyk, Sadka, 2008).

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**Chapter 4. Data Analysis and Results**

**Chapter 4.1. Data Overview**

One of the basic assumptions of this dissertation is that useful proxies for liquidity can be constructed from daily data on UK equity market across all industries. The sample period covers the last 15 years, from the start of 2003 to 2018. The daily values of bid and ask prices, volume, price are have been obtained from DataStream. Daily or month-end values for shares outstanding were unavailable, therefore, year-end values were used. Following Foran et al. (2015), both surviving and non-surviving stocks are included to control for survivorship bias. The Amihud and Quoted Spread ratios are constructed and calculated daily for each stock and divided by the number of observations in a month to obtain a monthly value. Turnover ratio was calculated yearly with the year-end value of shares outstanding. Even though the original data set is comprised of more than 3000 stocks, stocks with less than 300 daily price observations were eliminated. The necessity of daily, not monthly prices and volume to be available when calculating Amihud illiquidity, restricted the final sample to include 648 stocks.

Data for measuring market volatility has also been obtained from Datastream. This paper uses FTSE 100 Volatility Price Index (VFTSE) by NYSE Euronext and FTSE Group, which captures implied volatility embedded in the prices of FTSE 100 constituents’ put and call options (**Hedgeweek.com, 2008**). Other studies examining the impact of volatility on financial markets often use the VIX volatility index (such as Xi et al., 2016), which is made up from S&P 500 index mid-quote prices and call and put options (Cboe.com, 2018). While VIX is a more recognised measure of volatility across financial markets, it is derived from USA stocks. Since this research is exploring the UK stock market, VFTSE is a more appropriate measure of volatility relating to the analysis of this paper.

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**Chapter 4.2. Descriptive Statistics and Results**

Descriptive Statistics

This table represents the summary statistics and correlation for ratios used in the research project.

__Panel A__shows the descriptive statistics for the liquidity measures. ILLIQ is the Amihud ratio, the monthly ratio of the absolute return to the trading volume. lnILLIQ is the natural logarithmic form of the Amihud ratio. Quoted Spread is the monthly ratio of the difference between the bid and ask price to the midpoint price.

__Panel B__shows the correlations between monthly averages of liquidity measures.

__Panel C__shows the correlations between the yearly averages yearly of the liquidity measures, including Turnover.

__Panel A__

__Panel B__

__Panel C__

__Graph 1__

The table displays the descriptive statistics of calculated liquidity measures, with ILLIQ mean of 0.002459, lnILLIQ mean of -9.53883 and Quoted Spread mean of 0.036471. The only other relevant research paper examining similar aspects of the UK market liquidity was written by Foran et al. (2015). Results they achieved are similar, with a little higher value across ratios. Mean of lnILLIQ is -8.32 with the standard deviation of 1.87 compared to -9.54 and standard deviation of 0.42 in this study, suggesting that this study thinds the UK market more liquid with less values far away from the mean than in one done by Foran et al. (2015). Turnover mean is 0.29 with the standard deviation of 0.30 compared to 0.0034 and 0.0011 in this paper (however, low value of only 15 observations in this project must be kept in mid). Quoted spread average is 0.0785 with 0.0675 standard deviation in relation to 0.036 and 0.01. The higher values of ratios and standard deviations in the study by Foran et al. (2015) due to two reasons. First, the methodology for counting the ratios is different: they use cross-sectional approach by estimating the average of the sample period for each individual stock, rather than calculating the monthly average across all stocks. Second, the sample size used in the Foran et al. (2015) study is substantially higher, ranging from 1274 to 2240 stocks in different years in contrast to 646 used in this study. This is an issue not only because estimation is more accurate when using a bigger sample, but also because the use of 646 stocks in this study was mostly due to unavailability of daily data for one or more of the measures for the rest of the original 2000 stocks. The stocks that are more likely to have daily data are those that are more frequently traded and more liquid. Therefore, the smaller sample size in this dissertation likely overestimated the available liquidity in the UK market, leading to different values of liquidity ratios between the two studies.

As seen in Panel B, the monthly correlation between Amihud ratios and quoted spread is strong, with 0.785 correlation between Amihud and Quoted Spread. In addition, as can be observed from Graph 1, Quoted Spread can react quite significantly during a change in market conditions which may mean that transaction costs see an even more significant increase during the times of liquidity stress. During the financial crisis, between September 2007 and December 2008, the quoted spread grew by 121.5%. Bigger fluctuations in the quoted spread mean that investors experience significant costs in trading during times of illiquidity. Generally, UK equity market could be perceived as less volatile and more liquid in the recent years – average value of the Amihud measure in the years 2014-2018 has been 3 times lower than the financial crisis average. The quoted spread has also seen an average of 44.55% decrease since the financial crisis. Panel C shows a separate table of correlation between the measures on a yearly basis. Correlation is even stronger when looking at the Quoted Spread and Amihud illiquidity. However, Turnover seems to be not strongly connected with the other ratios. This is also illustrated in the graphs, where it is shown that the Turnover ratio tends to not move in the same direction as illiquidity and spread ratios. This is in line with a test conducted by Lesmond in 2005, the examining correlation between Bid-Ask Spreads and Turnover across 23 emerging countries. The research finds that Turnover and the Bid-Ask Spread are negatively and significantly correlated in only 40% percent of the markets tested, which casts doubt on the validity of Turnover as a liquidity measure. However, no strong conclusions can be drawn from this in this paper due to a small sample size of only 15 observations for the comparison in Panel C.

Not a lot of previous research can be found on this subject, therefore making it difficult to conduct a comparison of results between the UK at other countries. The value of the ratios appears to be sufficiently low to state that the UK market is liquid. The research done on the Istanbul equity market (Atilgan et al., 2015) looks at various forms of Amihud ILLIQ ratio. They do not use Quoted Spread or Turnover. They computed the value of the ILLIQ ratio of 0.0225, with the standard deviation of 0.4054. This is higher than the results computed for the UK market, with ILLIQ value of 0.002459 and the standard deviation of 0.00207. The conclusion drawn from this could be that the illiquidity in the UK is a lot smaller than in Istanbul, therefore, according to Amihud ratio, UK stock market is more efficient from liquidity point of view.

The original paper by Amihud (2002) on his ILLIQ ratio looks at NYSE stock during years 1963-1996. He finds that mean of annual means of ILLIQ during the sample period is 0.337 with the standard deviation of 0.512, in contrast of finding of this study with 0.00238 (mean of annual means) and standard deviation of 0.0159. The ratio for NSYE stocks is significantly higher, which would imply that the New York stock market is less liquid than one in UK. However, things to keep in mind are that, firstly, the stock sample size in Amihud study is higher than in this paper (from 1061 to 2291, depending on the year). The sample size of this paper is 646, largely due to the fact that daily data is unavailable for less frequently traded stocks. Broader range of stocks in Amihud (2002) study means that even the less frequently traded stocks are included, making the ratios higher. This is supported by the bigger positive skew of 3.095 in the Amihud study, compared to 2.016 observed in this paper. Secondly, data is a few decades old, dating back from 1963. This could significantly impact the ratios. In the 15 years data for this study starting at 2003, Amihud ratio went from 0.003299 yearly average of 2003 to 0.00082 average in 2017. That is an over 75% decrease, which adds to the explanation of the difference in the results. This, however, makes the values in the studies hard to compare.

_{FOOOTER EXPALING THE NYSE STOCKS}

**Chapter 5. Liquidity Measures under Volatility**

Volatility is generally perceived as a magnitude and frequency of movements in the price of a financial asset or, in words used by VIX volatility index website, “Volatility measures the frequency and magnitude of price movements, both up and down, that a financial instrument experiences over a certain period of time. The more dramatic the price swings in that instrument, the higher the level of volatility” (Cboe, 2018). Intuitively, the expectation is that changes in market volatility should be accompanied by changes in available liquidity. The analysis in this chapter will discuss the relationship between volatility and liquidity measures defined in the previous chapters.

**CHARTS TABLE**

The table above shows the results for linear regression and correlation of the relationship between volatility and the liquidity measures. In table X, all the relationships of the liquidity variables are positive and significant at the 5% significance level. Volatility and ILLIQ ratio are defined by an R of 0.685 and R^{2} of 0.469. This means they are positively connected and almost 47% of movement in ILLIQ ratio can be accounted for by level of volatility. These statistics are even higher for the logarithmic form of the Amihud measure (lnILLIQ) with R of 0.783 and R^{2} of 0.613. Quoted Spread is even more correlated with volatility with R value equal to 0.728 and R^{2} of 0.529. The standard error and p value for all three regressions are close to zero, meaning the results are accurate and statistically significant.

On the other hand, analysis on Turnover and Volatility yielded R and R square that are close to zero. This would mean there is very little relationship between the Turnover ratio and volatility index. However, the p value is very high, likely due to a very small sample size, and the results of this analysis are statistically insignificant. Therefore, turnover and volatility regression results are omitted from this analysis.

Graph X

The results of this analysis are in line with expectations. ILLIQ, lnILLIQ and Quoted Spread ratios exhibit high correlation with volatility and the regression results show a significant relationship between the liquidity measures and volatility. The co-movement between the liquidity measures and volatility can be observed in Graph X. The obvious trend of increase in Amihud illiquidity measure (ILLIQ) and Quoted Spread during the times of increased volatility is evident. This means that volatile stock market is also likely illiquid, with high transaction costs and high volume impact on prices. A possible implication of this relationship is that, during market downturn and stress, a person wanting to sell a security not only experiences lack of demand, but also incurs high selling (transaction) costs and the exchange of the asset makes a bigger impact on price than during normal market conditions. This would mean that illiquidity significantly influences the magnitude of market downturns.

While there is no relevant research that examines the relationship between liquidity measures and volatility to conduct comparison of the results, some past papers do examine impact of volatility on various aspects of the market. Chordia et al. (2002) examine daily changes in liquidity variables, spreads and market depth (defined as the average of quoted bid and ask depths), and trading activity. They found that decrease in trading activity around weekend and holidays causes a decrease in market depth and an increase in quoted spread. An intriguing result of the research was that quoted and effective spreads increase dramatically in down markets and only marginally in up markets (Chordia et al., 2002). This could be seen as a supporting argument towards the idea proposed in previous paragraph: decrease in liquidity and an increase in transaction costs can cause a more significant market decline than one markets would experience if liquidity levels were held constant. However, the paper also finds conflicting evidence relating to the impact of volatility on levels of liquidity. They state that, contrary to intuition, recent market volatility tends to reduce spreads, however, leaving the other chosen liquidity measure, market depth, unaffected. This difference in finding could be explained by the choice of volatility measure. Chordia et al. (2002) use the returns of CRSP daily index return as a measure of volatility as opposed to VFTSE volatility index, constructed by averaging option prices. Another explanation is that the period examined in the study, 1988 to 1998, “is a relentless bull market” (Chordia et al., 2002), which can cause the observed differences in a liquidity and volatility relationship.

The relationship between volatility and liquidity is evident, however, no conclusions from this analysis can be drawn about the possible causality. There is no previous research that has examined whether sudden decreases in liquidity have been caused by spikes in market volatility. However, one could speculate that an increase in trading activity and change in demand for assets in the stock market are caused by changes macroeconomic changes and news cycles. A paper by Hamilton and Lin (1996) finds that economic recessions are the largest factor determining the stock price volatility. Another point of view might argue that decrease in volume and increase in transaction costs can lead to decrease in returns from trading and make a significant impact on stock prices, leading to an increase in volatility. While there is no proof of either of these theories being true, this paper demonstrates that both volatility and liquidity have a big role during market upturns and downturns.

**Chapter 6. Limitations and Further Work**

One of the limitations of this analysis is that some results might be insignificant due to a small number of observations. This is especially evident in the case of Turnover, as due to unavailability of daily or monthly Shares Outstanding data allowed for only 15 values of the measure to be calculated during the sample period. This makes the analysis done on Turnover not reliable and makes the task of comparison of the liquidity measures difficult. Although the correlation results between the Turnover ratio and other measures show that critiques of Turnover as a liquidity measure probably have merit, the results cannot demonstrate significant evidence to support such claim. In addition, the stock sample size in this dissertation is smaller than in the other studies on the subject. This is largely due to unavailability of daily data for the less frequently traded stocks. This is a significant issue which may lead to selection bias towards more liquid stocks and over-estimation of how liquid the UK market is, as well as differences in statistics in regards to other studies.

Availability of high-frequency data would also allow for a more sophisticated analysis and allow to test intra-day liquidity levels. However, the analysis performed in the paper by Goyenko et al. (2009) shows that daily observations can be an acceptable proxy for high-frequency data.

Possible issues with double counting could mean negative implications for the reliability of measures which involve volume. The evidence of volume over-estimation and duplicated orders in ESMA research (2016) suggests that liquidity information provided by turnover and ILLIQ measures may be over-estimated. This could mean that

Further work on the subject could include looking at the statistics from cross-section analysis point of view instead of a time-series point approach. This would have allowed to sort stocks into groups, such as quintiles, according to their varying levels of liquidity, and looking at the interaction of measures and effects of volatility at the varying liquidity levels. Further research should also be done to investigate the implications of duplicated orders on measuring market liquidity.

**Chapter 7. Conclusion**

This paper discusses different methods that can be used to measure liquidity and adopts select few to analyse the UK market. There are no specific values that the measures have to obtain to make a market liquid, therefore, the analysis needs to be put in the context of time period and other studies. Results show that the UK stock market is liquid when compared to Istanbul, and the levels of liquidity have over the years. Analysis of the relationship between liquidity and volatility concludes that around half of changes in levels of liquidity can be explained by changes in market volatility.

Previous research suggests that Amihud ratio is one of the most effective and widely adopted measures of price impact, making it one of the key ratios in this study. Turnover is another popular measure associated with trading volume which is adopted in this research, however, broad analysis could not be done on this due to lack of data. Quoted Spread is a measure which has been in the centre of liquidity discussion since the start of research into the subject and is adopted in this paper to estimate the level of transaction costs as a proxy to liquidity. Calculated values of the liquidity ratios suggest that the UK equity market is liquid, with only 0.002459 mean in ILLIQ ratio, compared to 0.0225 mean in Istanbul study, suggesting lower levels of illiquidity and confirming the statement in the first paragraph. The levels of liquidity have grown over the years, especially since the financial crisis and correlation results show that there is a strong positive relationship between the ratios, which adds confidence to the effectiveness of the measures.

The effectiveness of turnover as a measure of liquidity has been criticised in a number of papers, including ones by Lesmond (2005) and (Subrahmanyam, 2005). The findings in this paper would support the critique but they are not statistically significant due to the low number of observations. Since Turnover has been used as a proxy for liquidity for years, it important that further research with more data is done on this measure to prevent mistakes by investors in estimating liquidity that is available in the market.

Analysis of the relationship between volatility and liquidity suggests strong positive correlation between volatility and the measures with R^{2} between volatility and ILLIQ is 0.469, 0.613 between volatility and lnILLIQ and 0.529 with Quoted spread. This shows that around 50% of changes in levels of liquidity can be accounted for by changes in volatility and both volatility and liquidity are likely to have a big role during market upturns and downturns.

The main finding of this paper is the significant relationship between volatility and liquidity, which can have many implications to the financial markets. This raises questions for future research about the causality of this relationship and calls for further analysis whether a decline in liquidity can significantly increase the degree of a market crash.

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