Market Liquidity Definitions And Measures

Published Date: 02 Nov 2017

In order to point out the relevance of market liquidity in the investment management field and develop the analysis, this section lays out the basic theoretical dimensions by reporting the distinction between the two forms of liquidity, funding liquidity and market liquidity and their related risks depending on the context in which they have been used in past researches. The literature overview focuses mainly on two aspects: 1) market liquidity sources and dimensions, 2) market liquidity measures for individual securities as mostly used in different fields, such as asset pricing, market microstructure and market efficiency.

2.1 Basic concepts and definitions

"The word liquidity has so many facets that is often counter-productive to use it without further and closer definition". [1] Charles Goodhart (2008)

The term liquidity in empirical finance represents a shorthand for two distinct forms of liquidity: market (or trading) liquidity and funding liquidity. In general, the first term indicates the ease with which an asset can be traded, while the second one refers to the ease with which either a market agent or a company can have access to funding (Brunnermeier and Pedersen, 2008). Liquidity risk, on the opposite, can be associated to all the frictions and impediments hampering the assets’ trading or the access to funding. Although simple definitions may be provided, the meaning of both market liquidity and funding liquidity varies depending on whether the term is referred to a single tradable security, to an entire market (secondary market) or to financial institutions.

2.1.1 Funding Liquidity

Funding liquidity and its related risk have been central concepts since the beginning of the financial crisis in 2007. Recalling emblematic episodes, such as Lehman Brothers filing for bankruptcy in 2008 or Northern Rock asking for bailouts from the UK government, makes clear how critical the role of liquidity can be not only for financial institutions, but also for the financial system as a whole. In September 2008 TED spreads [2] , one of the most commonly used measures to gauge the funding liquidity, dramatically reached their maximum levels since the Black Monday in 1987. In such a context, several financial institutions had to ask for bailouts or experienced a bankruptcy due to funding liquidity deterioration which resulted in the increase of the cost of funding and the tightening of credit to firms and households.

In literature, funding liquidity has been mainly attributed to financial institutions: the Basel Committee of Banking Supervision (2008), providing with a definition which is similar to the one given by IMF (2009), defines funding liquidity as the ability of a financial institution to meet its liabilities, settle or unwind its positions as they come due.

On the other hand, the concept for which an entity can be considered liquid "as long as inflows are bigger or at least equal to outflows" can hold for both financial institutions as well as for market agents. As a result, funding liquidity assumes several facets depending on the context in which it has been adopted. It has been referred to firms, by indicating their short-term solvency, but also to market makers and traders, meaning the ability to raise cash with very little lead time (Strahan, Brunnemeier and Pedersen, 2009).

2.1.2 Market Liquidity

Many authors and researchers defined market liquidity in different ways and contexts. Keynes (1930) and Hicks (1962) defined market liquidity in the context of economics, whereas Bagehot (1971) defined the market liquidity with reference to the adverse selection and information asymmetry problems. Over the past thirty years, market or trading liquidity concept has been mainly attributed to a single tradable security and it has been accordingly defined as the quality which enables agents to buy or sell a security quickly, anonymously, at a market price which is equal to its fair value and with a small price impact (Liu, 2006). Outlining the concept in a proper way entangles the reference to the concepts of transaction and time costs, as the main sources of uncertainty in an order request.

The order execution of a liquid asset must take place with not too much delay from the order placement and at a price which is as close as possible to the one prevailing in the market at the time of the order placement. Accordingly, the definition is similar when referred to a secondary market, market liquidity is associated with the possibility of immediate execution of large volumes of trades with minimum effect or little uncertainties on the execution price.

In this context, the starting point to be considered is that markets are far from perfection and that factors affecting this type of liquidity are linked to the specific market microstructure and to the demand and supply pressure effects. By taking into account these aspects, it becomes clear that market liquidity is a multi-dimensional concept which makes elusive any precise definition and difficult its measurement.

For the purposes of this work, we will focus on market liquidity, but it is worth to point out that funding and trading liquidity are strictly linked. In particular during financial downturns, the two forms of liquidity tends to dry up and to be mutually reinforcing, leading to liquidity spirals. An interesting research by Brunneimer and Pedersen (2008), studying the interaction between the two forms of liquidity, found out that capital and collateral requirements permit a strong linkage between funding and trading liquidity of financial intermediaries: a funding liquidity shock forces asset sales, generating a potential sharp fall in price and lowering market liquidity, at the same time, market liquidity shocks lead to higher margin calls, fuelling funding liquidity risk as out-flows rise. Especially during financial downturns, as funding liquidity deteriorates, liquidity providers may be unable to fund their positions from collateralized loans due to the higher margin requirements.

As a result, they are forced to shift their provisions towards lower-margins stocks (flight to quality), which in turn lower the market liquidity and activate liquidity spirals. The financial crisis has shown this mechanism, as liquidity spirals may affect multiple market agents and financial institutions, ultimately contributing to systemic risk (Brunnermeier, Krishnamurthy and Gorton, 2012) [3] .

Source of illiquidity and dimensions of market liquidity

Market liquidity sources can be analyzed by taking into account the market microstructure theoretical findings, which deal with issues of markets’ structure and trading mechanisms and concerns with how those can affect price formation and price discovery, market information, transaction and timing costs (O’ Hara, 1995). A vast literature has identified the factors which have the greater impact both on the market microstructure and the market liquidity with reference to information asymmetry and markets’ frictions. In dealer markets, market makers are the main liquidity providers and in order to make profits they enters into positions that are opposite to those of institutional investors by buying at a bid price (Pb) from investors that are willing to sell and by selling at a higher ask price (Pa) to investors that are willing to buy.

Less liquid or illiquid assets are then associated with high transaction costs in terms of commissions, fees and bid/ask spreads faced by market participants and, as a result, low levels of market liquidity make difficult for investors to execute big volumes of trades without facing high trading costs. Amihud, Mendelson and Pedersen (2005) identified the main sources of illiquidity in the exogenous transaction costs (for instance, brokerage fees paid by investors for transactions and services both on the sell and buy side), the inventory costs (related to the difficulties with which agents match buy and sell positions), the time needed to execute the trades (timing costs), the participation costs and counterparties search frictions (arising with particular evidence in OTC markets), but also the spectre of asymmetric information (Copeland, Galai, 1983; Glosten and Milgrom, 1985).

Within the context of market microstructure theory, the possibility to define the main liquidity dimensions, incorporating elements of transaction costs, timeliness and volume (Fernandez, 1999), also allows us to distinguish between the diverse liquidity measures. There are five dimensions of market liquidity which reflect the microstructure of a market:

Depth:

is generally associated to the number of orders for sale/purchases or trading volume that can be attainable, within a little time span, without having impact on the current prices of the security. Abundance of volumes and high power of trades absorption can be easily referred to highly liquid markets.

Tightness:

has been usually defined as the quality which makes possible in a market to buy or sell a security at about the same price. It shows the execution costs or implicit costs in the market microstructure, being commonly measured by the level or percentage bid-ask spreads.

Resiliency:

concerns the trades’ price impact and refers to the speed at which the of a security prices correct their divergences from their fundamental value after large trades have been executed, by taking into account both the market demand and market supply elasticity.

Breadth:

I is related to the size of orders, both numerous and large in volume orders would qualify a market as liquid.

Immediacy:

is the time required for effective trades’ execution, commonly measured by the time elapsed between trade placement and trade execution.

Where there is no market impact and the market resiliency is high the uncertainty of trade execution price will be minimal and the market participants need not worry about price uncertainties at the time of trade execution. This kind of market is regarded as a market which has also depth and high liquidity. The figure reported below explain the relationship between volumes, prices and the liquidity dimensions as a supply-demand function for a given asset.

Figure 2.2: Liquidity Dimensions and their relationship to volumes and prices [4] (Kerry, 2009).

Market liquidity measures in literature

An appropriate measure of market liquidity is any factor which represents the magnitude of the uncertainty related to the execution price in a trade. The multi-dimensional nature itself of market liquidity and the tendency of liquidity dimensions to overlap in their definitions makes difficult to identify a single comprehensive measure. The literature about is abundant and this part provides with an overview of the most common proxies that have been used in the past for individual securities, also considering that when they are aggregated in a proper way these proxies can provide good measures of the liquidity in a market as whole.

From a practical perspective, a market is identified as liquid when it shows low execution and timing costs, in turn these costs depend on market participants, trading venues, trade sizes and other micro-structural factors. Moreover, the key point of market liquidity concept is that it would allow to exchange a given security without having a significant impact on the price. As a result, empirical evaluations of this main point are difficult to implement since the degree of liquidity is by itself an unobservable variable.

Firstly, a natural way, even though, to summarize the measures is to distinguish between proxies which attempt to capture a single dimension and those which, by construction, provide with a proxy for several dimensions (Aitken and Comerton-Forde [5] , 2003). Moreover, it is possible to distinguish between measures constructed from high-frequency (intra-day) data and measures constructed from low-frequency data (typically daily, as registered at the end of the trading day, weekly or monthly). The main advantage of using low-frequency measures relies on the ease to collect data and quotes, making it possible to lower the computational burden and easier further development in all the research fields in which liquidity plays a critical role.

Given the abundance of the literature about, we limit the measures’ review to the proxies which have been proven to perform well in recent studies (Goyenko, Holden, Trzcina,2009;Fong, Holden, Trzcinka, 2011), providing with formulas in Appendix A for those measures on which we will not focus our attention in the research.

Depending on the data used to gauge liquidity and the liquidity dimensions captured, it is possible to divide the low-frequency proxies for individual securities in three categories:

Measures related to trade execution costs

Measures related to trading quantities

Price-impact measures

Measures related to trade execution costs

They capture the tightness dimension of liquidity by gauging the prevailing trading implicit and explicit costs in a market. This category includes mainly bid/ask spread proxies and are used by practitioners to approximate the prevailing transaction costs associated to a single tradable security and are measured, in their simplest forms, by the difference (in absolute or relative terms) between the ask price and the bid price prevailing in the market in a given period:

The main idea is that trading costs existence generate distortions in securities’ prices and returns. As a result, low-frequency proxies are based on time series of stock prices and returns. Roll (1984) defined a proxy for the effective spread [6] based on the serial covariance between price changes, Hasbrouk (2004) followed up with a bayesian estimation method for the Roll’s model, Holden in 2009 proposed an extension of the same measure by considering the prices changes expressed as a function of regression residuals obtained from a market model of stock returns. Lesmod, Odgen and Trzcina (1999), following the intuition that very illiquid stocks often exhibit zero-volume trading day, often equivalent to zero-return days, developed a simple liquidity proxy (i.e. Zeros) measured by the proportion of zero-returns day in a given period.

Goyenko, Holden and Trzcina (2009) implemented a similar proxy, called Zeros2, by considering the proportion of days with zero-return but positive volumes, in this case stock’s liquidity is associated to the capability to incorporate information relevant to generate potential positive returns. These two proxies attempt to capture also the trading speed related to the time dimension of liquidity. Other proxies able to capture the trading speed along with the tightness dimension are the LOT Mixed (Lesmod, Odgen and Trzcina, 1999) and LOT Y-split (Goyenko, Holden and Trzcina, 2009) that are based on more complex market model specifications.

For the sake of simplicity, we report the descriptions and formulas for the all the above-mentioned proxies in Appendix A. In the empirical analysis whose methodology will be described in Section 4, we are going to use percentage spreads from daily data in order to take into account transaction costs in the portfolio approach.

Measures related to trading quantities

These measures are used to gauge the market depth dimension, but can be referred also to the market breadth dimension of liquidity. They have been largely used as liquidity proxies both in asset pricing and market efficiency research, generally confirming a negative relation between these measures and risk-adjusted stock market returns.

Trading Volume is the most simple one and it is computed by considering the quantities of a single tradable security (or their equivalent value expressed in the currency of denomination) per time unit. Other measures, such as the Market Depth account for the quantities associated to both bid and offer quotes in the security’s currency denomination (not always available) or consider the frequency of trading a particular security [7] .

Share Turnover Ratio is expressed by the ratio between the volumes traded in a given period and the total number of share outstanding (often on average):

It indicates, on average, the speed with which market agents change their trading position in relation to the total number of share outstanding. On average, securities registering low turnover in the past have been able to generate significant higher returns than heavily traded securities (Datar, Naik and Radcliffe, 1998).

In choosing a proxy for market liquidity researchers look for a measure which can substitute the high-frequency benchmarks and can be easily computed from market data. Literature relevant for this analysis has extensively adopted volume-related liquidity proxies for simplicity purposes. Relevant literature for this work have extensively used volume-related liquidity proxies. In their studies to assess whether liquidity can be considered an investment style other than the traditional ones, Chen, Ibbotson & Hu (2011) considered liquidity as measured by trading volumes and turnover ratios. However the authors acknowledged that these proxies are not the most precise nor the most effective measures to capture liquidity.

For instance, Lee and Swaminiathan (2000) in their study on momentum and value investment strategies showed how the premium arising from a long winners/short losers strategy is relevantly higher for stocks showing past high trading volumes, even if either losers’ or winners’ low-volumes stocks should have been able to generate higher returns than highly traded securities, given the negative relation commonly found between this measure and stock returns.

Price-impact measures

These proxies estimate the quality which enables to execute trades on a security with a minimal effect on price, by taking into account the price or orders changes due to the general market conditions and the effects of new information absorption in the market. To capture these effects very commonly used measures employ both returns and volumes data: the idea is that liquid high-volume stock should have a little price impact.

The Amivest liquidity ratio (Cooper, Groth & Avera, 1985) directly compare the average daily share volume () to the average absolute stock return ():

with t=1,…,n indicating the time interval and excluding zero return days.

Amihud (2002) proposed, conversely, a measure for the lack of liquidity (Illiquidity Ratio) computed by the ratio between the average absolute daily return and average daily trading dollar volume over a given period t which includes also zero return days:

Big stock’s price movements subsequent to a little volume traded would result in an high value for the Amihud measure, suggesting that the security is illiquid. Amihud (2002) found a positive cross-sectional relation between expected stock returns and illiquidity, confirming it is a priced factor [8] .

Other popular measures to estimate the market impact cost incorporate price and order flow changes by using regression approaches. For instance, some asset pricing studies have extensively adopted the Lambda’s measure proposed by Kyle (1985) as a price impact liquidity benchmark computed by regressing stocks returns over trade size changes, while more recent studies used the Pastor-Stambaugh’s Gamma (2004), which is the coefficient which captures the stock returns exposure to illiquidity and is obtained via a Fama-Mac-Beth approach explaining returns as a function of stock return reversal and trading volumes [9] . While they still rely on market data and may be computed on low-frequency data, often a proper estimation involves the use of high-frequency data so that they are mostly treated in literature as liquidity benchmarks.

In their research, Fong, Holden and Trzcina (2011) extended the validation of the Amihud measure (2002) beyond the US stock markets (as per Goyenko, Holden and Trzcina, 2009), by showing that the proxy has performed relatively well in gauging global liquidity in comparison with other price impact proxies, they found it highly correlated cross-sectionally with its price impact high-frequency benchmark.

In this work, we will use a modified version of the Amihud Illiquidity ratio (2002), as it will be explained subsequently in this work, chosen as the liquidity proxy in our analysis.