Measuring Liquidity in Financial instruments

Part two of the series titled, “Understanding Liquidity”

Liquid assets tend to be characterized by low transaction costs, easy trading, timely settlement and the capability of making large trades that have only a limited impact on the market price. The importance of some of these characteristics changes over time. In a period of stability, liquidity may primarily be reflected in transaction costs. In a period of stress and significantly changing fundamentals, prompt price discovery and adjustment to a new equilibrium become much more important. Liquidity of a financial asset can be described in five dimensions;

1. Resiliency describes how quickly new orders flow to correct imbalances, which tend to move prices away from the levels suggested by fundamentals.

2. Tightness refers to low transaction costs, such as the difference between buy and sell prices (bid-ask spreads in quote-driven markets), as well as implicit costs.

3. Immediacy describes the speed of execution and order settlement. This reflects the efficiency of trading, clearing and settlement systems.

4. Depth refers to the existence of abundant orders, either actual or easily uncovered by potential buyers and sellers.

5. Breadth means that orders are both numerous and large in volume and can be traded with minimal impact on prices.

When referring to an asset’s liquidity, we often initially focus on tightness and immediacy, but depth, breadth and resiliency are important characteristics of an asset’s market liquidity that must be considered.

Liquidity is an abstraction that can be measured only indirectly. We cannot capture it, weigh it or slap a tape measure on it. We can get a sense of it through four measures that reflect its ebb and flow. These measures are different from the five market dimensions we describe above, which attempt to capture narrower aspects of liquidity. The four measures laid out in this section affect specific dimensions of the market — high transaction costs, for example, help determine breadth, depth and resiliency — but they really are the means we use to get a sense of what is happening to the larger phenomenon of market liquidity. 

  1. Transaction cost measures

Transaction cost measurement captures the explicit and implicit costs of trading financial assets and frictions in secondary markets. Transaction costs are explicit when they refer to costs such as order processing and taxes associated with trades, and implicit in terms of execution costs. High transaction costs reduce the demand for trades and therefore the number of potentially active participants in the market. This in turn results in a more fragmented, shallow and thin market, where transactions are less likely to occur around the equilibrium price of the asset, in contrast to what happens in a deep market.  Not only are the depth and the breadth of the market dependent on transaction costs, so is the resiliency. The elasticity of order flows is much lower when transaction costs are high and the infrequency of trades results in price discontinuities.

The bid-ask spread is the basic transaction cost of trading and the most commonly referred-to measure when taking into account explicit costs such as order processing, asymmetric information (commissions) and market structure. In a very simplistic case, the relative quoted spread is given by the normalized difference between the quoted bid and ask prices, PB and PA.

Formula 1.jpg

While the bid-ask spread is a measure of explicit transaction costs, slippage is an estimate of implicit transaction costs. Slippage is defined as the difference between the asset’s average execution price and the initial midpoint of the bid and offer for a given quantity of that asset. Interestingly, there has been growing confusion over how these implicit transaction costs are reported since the introduction of a new European Union market framework. The Markets in Financial Instruments Directive II (MiFID II) comprises EU regulations that mostly became effective last year and are aimed at providing greater efficiency, resiliency and transparency for market participants. MiFID II’s reporting requirements and tests attempt to increase the amount of information available in market operations and reduce the use of opaque dark pools and over-the-counter trading.

  • Volume-based measures

Liquid markets can also be characterized by the volume of transactions compared with the price variability. Volume-based measures mostly quantify breadth and to some extent depth. The latter fosters the former when large orders are divided into small orders to minimize the impact on transaction prices. Recall that breadth is defined as numerous large orders that have a minimal effect on price. By measuring the traded dollar volume, dealers have a continuous information source that reveals whether price changes are permanent or ephemeral. In markets without breadth and depth, the absence of the continuous information provided by frequent trades may result in price discontinuities and uncertainties about equilibrium prices.

Trading volume measures the number of market participants and transactions. When we combine this with the outstanding volume of an instrument, we get the turnover rate, which measures the number of times the asset’s outstanding volume changes hands. This is the baseline volume-based measure. Given Pi and Qi, which are, respectively, the price and the quantity of the trade during a period i, the dollar volume V can be calculated by the equation:

Formula 2.jpg

The turnover rate T is computed by dividing the dollar volume by the number of outstanding shares S times the average price P over the period:

Formula 3.jpg

Price impact is a hybrid volume-based measure of liquidity that emphasizes information transmission. It refers to the correlation between an incoming order and the subsequent price change. Informed traders may slowly execute trades to conceal information and minimize the price impact. That a buy would raise the price seems obvious and is easily demonstrated empirically. But for traders, price impact is tantamount to a cost: Their second buy is, on average, more expensive than their first because of their own impact; this works in reverse for sells.

The most important questions about price impact are related to volume dependence (do larger trades affect prices more?) and its temporal behavior (is the effect of a trade immediate, permanent or temporary, or is there some lag dependence?). Below is a widely adopted model for realized price impact that combines both permanent (time-independent) and temporary effects. Both are volume-dependent.

Formula 4.jpg

Note that both the permanent and the temporary impacts are sublinear in the market participation rate — that is,  ρ, φ ∈ (0,1), which is consistent with the classical square-root model. This model has been widely adopted by the industry serving as a benchmark and employed in the Barra’s Market Impact Model (1998) and Bloomberg’s Transaction Cost Analysis function (2005).

A rough yet practical price impact measure considers the daily ratio of the absolute stocks returns to its dollar volume, averaged over some period. Following Kyle’s concept of liquidity, Amihud Yaskov defines the ILLIQ measure:

Formula 5.jpg

The ILLIQ measure facilitates the construction of a long time series to test the effects of illiquidity over time.

  • Equilibrium measures

Equilibrium price-based measures try to capture orderly movements toward equilibrium prices, mainly to measure resiliency. These measures specifically consider the resiliency of an asset’s market, suggesting that there is an underlying structural model to identify the equilibrium price. For many assets, there are problems in postulating such a general model and determining whether new information affects them. Given these modeling issues, the market-efficiency coefficient (MEC) is used to measure the continuity of the price movements:

Formula 6.jpg

Here, Var(Rt) is the variance of the logarithmic long-period returns, Var(rt) is the variance of the logarithmic short-period returns, and N is the number of short periods within each long period. The ratio would tend to be closer to but slightly below 1 in markets that are more resilient. Low market resiliency translates to excessive short-term volatility, and factors such as price rounding, spreads and inaccurate price discovery would drive the MEC well below 1. Factors such as a market-maker intervention and inaccurate price determination following a partial adjustment to new information would dampen short-term volatility, causing the MEC to rise above 1.

Low price volatility after a new equilibrium has been established is related to the concept of orderly markets, where prices change smoothly rather than discontinuously. Orderly and resilient markets provide for greater price continuity, a desirable feature of liquid markets. A feature of information-efficient markets is discontinuity in prices in order to reach a new equilibrium warranted by new information. The MEC should not render an unfavorable verdict on liquidity and resiliency if it is calculated over a period of time in which the equilibrium price changes in response to new information and stabilizes quickly.

  • Market-adjusted measures

Market-adjusted measures attempt to differentiate between price movements due to liquidity and those resulting from factors such as general market conditions or the arrival of new information. When new information becomes available, even small transaction volumes can be associated with large price movements. For instance, new information triggering a financial crisis may not result in large turnovers because market participants (as long as they are not cash constrained) may prefer to wait and see what happens. To capture price movements mainly caused by large volumes (breadth), you need to extract price movements caused by significant new information.

A distinction is often made in equity markets between systematic and unsystematic risk, based on the capital asset pricing model (CAPM), which also provides a way to extract market movements. Systematic risk cannot be diversified away because it affects all securities. The degree of systematic risk is called the beta β of the stock, which refers to the regression coefficient of a stock’s daily return Ri on that of the market Rm:

Formula 7.jpg

The regression residual ui is then used to relate its variance to the daily percentage change in the dollar volume traded ΔVi:

Formula 8.jpg

Market-adjusted liquidity uses the residual of a regression of the asset’s return on the return of the market (thus purging it from systematic risk) to determine the intrinsic liquidity of the asset. The smaller γ2 is, the lower the impact of trading volume is on the variability of the asset’s price — meaning the asset is liquid. The lower the coefficient, the more breadth the market has.

No single measure unequivocally measures tightness, immediacy, depth, breadth and resiliency. However, from the perspective of practitioners, it is possible to cluster securities based on tradability difficulty, which depends on many factors but mostly on volatility, spread, price, queue size, volumes and so forth.