Breaking Down Liquidity

APRIL 25, 2019

The ability to easily buy or sell financial instruments can flow smoothly one moment and evaporate the next. Making sense of this often-mysterious characteristic requires an understanding of liquidity’s complex dynamics.

By Konstantin Gaber, Michael Kozlov and Radoslav Valkov

WorldQuant, LLC 1700 East Putnam Ave. Third Floor Old Greenwich, CT 06870 www.weareworldquant.com 04.25.19 BREAKING DOWN LIQUIDITY PERSPECTIVES

“The word liquidity has so many facets that it is the amount of that exposure, the liquidity of structured assets dried often counterproductive to use it without further up, making it difficult to value them. Central banks were forced to and closer definition.” inject liquidity into the markets. — British economist Charles Goodhart VARIETY OF FUNCTIONS A LIQUID IS A UNIQUE AND MULTIFACETED NATURAL SUB- In practice, financial market liquidity is nuanced and can fulfill a stance. It cannot be compressed, and it conforms to the variety of functions: central bank liquidity, funding liquidity, market shape of its container while retaining a nearly constant liquidity, interbank liquidity and asset-market liquidity. Central volume independent of pressure. A liquid is one of four fun- bank liquidity refers to the ability of a lender of last resort to supply damental states of matter, but it is the only state that has liquidity needed by the financial system — a flow of the monetary a definite volume and no fixed shape. Unlike a gas, a liquid base from a central bank to the financial system. This operations does not disperse to fill the available space and maintains a liquidity — the amount of liquidity provided through central bank nearly constant density. Liquids flow, and that flow can be auctions to money markets — depends on the bank’s monetary either smooth and easily calculated or turbulent, complex policy stance. For instance, the recent central bank policy known and chaotic — a continuing challenge to hydrodynamics, the as quantitative easing is a powerful mechanism to inject liquidity study of liquids in motion. into the financial system. Under QE, the central bank commits to buying a large number of targeted securities and thus reduces The financial concept of liquidity employs some of the physical char- liquidity premiums (the additional yield on an investment that acteristics of liquids, at least metaphorically. At its best, market or cannot be readily sold at its fair market value) and trading fric- financial liquidity is a state in which funds freely flow and securities tions. Quantitative tightening is the reverse of QE and involves are easily bought and sold. That’s the simplest definition of liquid- selling securities with the aim of normalizing interest rates, which ity. But, like liquids, market liquidity is complex, multifaceted and usually means raising them. nuanced. If we are to understand and quantify its many aspects, we must examine its components and tendencies more closely. The Basel Committee on Banking Supervision defines funding liquidity as “an entity’s capacity to finance increases in its volume Financial liquidity is believed to be extremely important to the of assets and to comply with its payment obligations on maturity, health of a financial entity.1 In the economic literature, liquidity without incurring unacceptable losses.” In this regard, liquidity risk refers to the ability of economic agents to exchange their existing is the probability of incurring losses because there are insufficient wealth for goods and services or other assets. Liquidity is con- liquid resources to meet payment obligations within a set period of sidered in terms of flows and refers to the ability to realize these time, taking into account the ability to sell assets in a reasonable flows. Failure to do so renders the financial asset illiquid — that is, time and at certain prices. From the point of view of traders or unsellable; an asset that cannot be sold cannot be valued. Liquidity investors, funding liquidity means their ability to raise capital or is often limited, creating various degrees of illiquidity, because of cash on short notice. Because funding liquidity is a flow concept, information asymmetries and incomplete markets. it can be interpreted as if it were a budget constraint: An entity is liquid as long as inflows are larger or at least equal to outflows. A sudden liquidity shock in even a single market segment or indi- This holds true for firms, banks, investors and traders. vidual instrument can cause damaging disruptions throughout interconnected global financial markets. In August 2007, for exam- Beginning with John Maynard Keynes’s A Treatise on Money3 in ple, markets began to reflect tensions as money market liquidity 1930, a number of studies have defined market liquidity as the plunged after credit rationing hit interbank lending markets.2 ability to trade an asset on short notice, at low cost and with little Banks refused to lend to one another because of uncertainties impact on price. As a result, market liquidity depends on several over their exposures to structured products; because no one knew variables, the most fundamental of which is the ability to trade. Market liquidity incorporates key elements of volume, time and transaction costs. A sudden liquidity shock in even a Liquid markets offer many benefits, including improved allocation single market segment or individual and information efficiency. Liquidity fosters a stable monetary instrument can cause damaging transmission mechanism and more efficient crisis management. And liquidity makes financial assets more attractive for risk-averse disruptions throughout interconnected investors, who can buy and sell them more easily. global financial markets.

THE FIVE DIMENSIONS Transaction cost measures Liquid assets tend to be characterized by low transaction costs, Transaction costs capture the explicit and implicit costs of trading easy trading, timely settlement and the capability of making large financial assets and frictions in secondary markets. Transaction trades that have only a limited impact on the market price. The costs are explicit when they refer to costs such as order processing importance of some of these characteristics changes over time. In a and taxes associated with trades, and implicit in terms of execu- period of stability, liquidity may primarily be reflected in transaction tion costs. High transaction costs reduce the demand for trades costs. In a period of stress and significantly changing fundamen- and therefore the number of potentially active participants in the tals, prompt price discovery and adjustment to a new equilibrium market. This in turn results in a more fragmented, shallow and become much more important. thin market, where transactions are less likely to occur around the equilibrium price of the asset, in contrast to what happens We can describe the liquidity of an asset through five different in a deep market. Not only are the depth and the breadth of the market dimensions. market dependent on transaction costs, so is the resiliency. The elasticity of order flows is much lower when transaction costs are • Tightness refers to low transaction costs, such as the difference high and the infrequency of trades results in price discontinuities. between buy and sell prices (bid-ask spreads in quote-driven markets), as well as implicit costs. The bid-ask spread is the basic transaction cost of trading and the • Immediacy describes the speed of execution and order set- most commonly referred-to measure when taking into account tlement. This reflects the efficiency of trading, clearing and explicit costs such as order processing, asymmetric information settlement systems. (commissions) and market structure. In a very simplistic case, • Depth refers to the existence of abundant orders, either actual the relative quoted spread is given by the normalized difference or easily uncovered by potential buyers and sellers. between the quoted bid and ask prices, PB and PA: • Breadth means that orders are both numerous and large in volume and can be traded with minimal impact on prices. • Resiliency describes how quickly new orders flow to correct imbalances, which tend to move prices away from the levels suggested by fundamentals.4 While the bid-ask spread is a measure of explicit transaction costs, When referring to an asset’s liquidity, we often initially focus on slippage is an estimate of implicit transaction costs. Slippage is tightness and immediacy, but depth, breadth and resiliency are defined as the difference between the asset’s average execution important characteristics of an asset’s market liquidity that must price and the initial midpoint of the bid and offer for a given quan- be considered. tity of that asset. Interestingly, there has been growing confusion over how these implicit transaction costs are reported since the FOUR MEASURES OF LIQUIDITY introduction of a new European Union market framework. The Liquidity is an abstraction that can be measured only indirectly. We Markets in Financial Instruments Directive II (MiFID II) comprises cannot capture it, weigh it or slap a tape measure on it. We can get EU regulations that mostly became effective last year and are a sense of it through four measures that reflect its ebb and flow. aimed at providing greater efficiency, resiliency and transparency These measures are different from the five market dimensions for market participants. MiFID II’s reporting requirements and tests we describe above, which attempt to capture narrower aspects of attempt to increase the amount of information available in market liquidity. The four measures laid out in this section affect specific operations and reduce the use of opaque dark pools and over-the- dimensions of the market — high transaction costs, for example, counter trading. 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 Volume-based measures phenomenon of market liquidity. Liquid markets can also be characterized by the volume of transactions compared with the price variability. Volume-based measures Liquid assets tend to be characterized mostly quantify breadth and to some extent depth. The latter fosters the former when large orders are divided into small orders by low transaction costs, easy trading, to minimize the impact on transaction prices. Recall that breadth timely settlement and the capability of is defined as numerous large orders that have a minimal effect on price. By measuring the traded dollar volume, dealers have a con- making large trades that have only a tinuous information source that reveals whether price changes are limited impact on the market price. permanent or ephemeral. In markets without breadth and depth,

the absence of the continuous information provided by frequent Note that both the permanent and the temporary impacts are sub- trades may result in price discontinuities and uncertainties about linear in the market participation rate — that is, ρ,φ є (0,1) which equilibrium prices. is consistent with the classical square-root model. This model has been widely adopted by the industry serving as a benchmark Trading volume measures the number of market participants and and employed in the Barra’s Market Impact Model (1998) and transactions. When we combine this with the outstanding volume Bloomberg’s Transaction Cost Analysis function (2005). of an instrument, we get the turnover rate, which measures the number of times the asset’s outstanding volume changes hands. A rough yet practical price impact measure considers the daily

This is the baseline volume-based measure. Given Pi and Qi, which ratio of the absolute stocks returns to its dollar volume, averaged are, respectively, the price and the quantity of the trade during a over some period. Following Kyle’s concept of liquidity, Amihud period i, the dollar volume V can be calculated by the equation: defines the ILLIQ measure8:

The turnover rate T is computed by dividing the dollar volume by the number of outstanding shares S times the average price P The ILLIQ measure facilitates the construction of a long time series over the period: 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. Price impact is a hybrid volume-based measure of liquidity that These measures specifically consider the resiliency of an asset’s emphasizes information transmission.5 It refers to the correlation market, suggesting that there is an underlying structural model to between an incoming order and the subsequent price change. identify the equilibrium price. For many assets, there are problems Informed traders may slowly execute trades to conceal information in postulating such a general model and determining whether new and minimize the price impact. That a buy would raise the price information affects them. Given these modeling issues, the mar- seems obvious and is easily demonstrated empirically. But for ket-efficiency coefficient (MEC) is used to measure the continuity traders, price impact is tantamount to a cost: Their second buy is, of the price movements: on average, more expensive than their first because of their own impact; this works in reverse for sells.

The most important questions about price impact6,7 are related to volume dependence (do larger trades affect prices more?) and Here, Var(Rt) is the variance of the logarithmic long-period returns, its temporal behavior (is the effect of a trade immediate, perma- Var(rt) is the variance of the logarithmic short-period returns, and nent or temporary, or is there some lag dependence?). Below is N is the number of short periods within each long period. The ratio a widely adopted model for realized price impact that combines would tend to be closer to but slightly below 1 in markets that are both permanent (time-independent) and temporary effects. Both more resilient. Low market resiliency translates to excessive short- are volume-dependent. 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 deter- mination following a partial adjustment to new information would dampen short-term volatility, causing the MEC to rise above 1.

θi = intraday bid-ask spread as a fraction

σd = daily stock volatility σi = intraday stock volatility Liquidity is an abstraction that can be α = spread coefficient 1 measured only indirectly. We cannot α2 = coefficient for permanent impact α3 = temporary impact coefficient capture it, weigh it or slap a tape P = market volume during execution Q = shares executed measure on it.

Low price volatility after a new equilibrium has been established During periods of stress the positive is related to the concept of orderly markets, where prices change smoothly rather than discontinuously. Orderly and resilient mar- correlation between volume and kets provide for greater price continuity, a desirable feature of liquid volatility found in many empirical markets. A feature of information-efficient markets is discontinuity in prices in order to reach a new equilibrium warranted by new studies may cease to exist. information. The MEC should not render an unfavorable verdict on liquidity and resiliency if it is calculated over a period of time in MARKET DATA which the equilibrium price changes in response to new information Now that we know what liquidity is and how it is measured, let’s and stabilizes quickly. consider information. The flow of information is closely related to liquidity, which is formalized in Kyle’s model and ongoing research. Market-adjusted measures Asymmetries in the inflow of information disrupt market efficiency Market-adjusted measures attempt to differentiate between price and dry up liquidity. Information is valuable, and demand for it is movements due to liquidity and those resulting from factors such high. The rise of algorithmic trading has fueled the competition as general market conditions or the arrival of new information. for information. Simply put, lunch is eaten by whoever sits first When new information becomes available, even small transac- at the table. tion volumes can be associated with large price movements. For instance, new information triggering a financial crisis may not Market data, the live streaming of trade-related data, is valuable result in large turnovers because market participants (as long as information, encompassing, among other things, prices, bid-ask they are not cash constrained) may prefer to wait and see what quotes and market volume.9 Market data is typically presented as happens. To capture price movements mainly caused by large a time-stamped collection of trades and quotes, showing sizes volumes (breadth), you need to extract price movements caused and prices. Investors most often consult real-time market data to by significant new information. make timely trading decisions and use historical data for various types of technical analysis. Market-data-related services account A distinction is often made in equity markets between systematic for a significant portion of exchanges’ revenues — for example, and unsystematic risk, based on the capital asset pricing model 44 percent for the Intercontinental Exchange and 26 percent for (CAPM), which also provides a way to extract market movements. the Nasdaq.10 Every few days, markets generate data equivalent Systematic risk cannot be diversified away because it affects all in volume to the Library of Congress print collection. 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 Fair access to market data allows all market participants to trade return Ri on that of the market Rm: based on the same information. Some exchanges, however, sell premium data services that allow customers to receive data feeds slightly faster than others in the market. One of these is the Nasdaq TotalView-ITCH FPGA, which costs a multiple of regular market

The regression residual ui is then used to relate its variance to the data-distribution fees. daily percentage change in the dollar volume traded ΔVi: Other participants attempt to reduce transmission time by finding the shortest geodesic line of communication and employing micro- wave products and lasers; they believe more timely information Market-adjusted liquidity uses the residual of a regression of the gives them a competitive edge. This is not a new phenomenon. asset’s return on the return of the market (thus purging it from Since markets have existed, success has demanded acting rela- systematic risk) to determine the intrinsic liquidity of the asset. tively quickly based on the most up-to-date information. During

The smaller γ2 is, the lower the impact of trading volume is on the the 1850s, Paul Reuter used pigeons to relay stock prices between variability of the asset’s price — meaning the asset is liquid. The Aachen and Brussels, shaving off hours of news propagation time. lower the coefficient, the more breadth the market has. (The telegraph eventually replaced the pigeon).

No single measure unequivocally measures tightness, immediacy, Since financial markets began to go electronic in the 1970s, com- depth, breadth and resiliency. However, from the perspective of petition has driven down both bid-ask spreads and commissions practitioners, it is possible to cluster securities based on tradability by more than 90 percent, significantly reducing costs for investors. difficulty, which depends on many factors but mostly on volatility, Though this is clearly beneficial to investors, the complexity of spread, price, queue size, volumes and so forth. navigating the environment has also greatly increased.

Consider, for example, these names: Ambush, Blaster, Cobra, In short, illiquidity is a symptom rather than a cause. Liquidity has Guerrilla, Komodo, NightHawk, Ninja, Sniper, Stealth. No, we’re an exact definition, but it can suddenly and unexpectedly appear not flipping TV channels. These are broker-built trading algorithms or disappear based on shifting market conditions, and it is mainly designed to efficiently navigate the complexity of electronic markets. governed by flows of supply and demand. The following joke illustrates this point well, because it is representative of typical Although financial markets are highly regulated, there remains an trading mechanics:12 element of the survival of the fittest as multiple parties compete for scarce resources — liquidity at favorable prices or queue pri- Customer: How much are these? ority. Recent advances in technology make such competition even Merchant: A buck fifty. fiercer. Broker creativity appears infinite, given the algo names, but Customer: I’ll take some. they are all trying to sell pretty much the same idea, which can be Merchant: They’re a buck fifty-one. roughly summed up as “eat or be eaten.” Customer: Um, you said a buck fifty. Merchant: That was before I knew you wanted some. FINAL THOUGHTS Customer: You can’t do that. Why do we need so many liquidity measures and dimensions? Merchant: It’s my shop. Mostly because they reveal often-conflicting information in periods Customer: But I need to buy a hundred! of stress, and that can be difficult to interpret. These underlying Merchant: A hundred? Then it’s a buck fifty-two. dimensions and measures allow us to glimpse the complex dynam- Customer: You’re ripping me off. ics of liquidity and illiquidity. Merchant: Supply and demand, pal. You want ’em or not?

Financial markets behave quite differently under stress than they do Is liquidity really about liquids? Well, liquidity is the lifeblood of the in more stable periods. With a continuous flow of new information, financial markets. When it disappears, markets no longer operate the spread and the turnover of an instrument are nearly constant efficiently. Given our era of Big Data, the competition for this life- and the price adjusts smoothly. During periods of stress, however, blood has grown fiercer. Liquidity, supply, demand and information the positive correlation between volume and volatility found in leakage need to be managed carefully. ■ many empirical studies may cease to exist. We can differentiate between two types of stress events:11 first, high volatility combined Konstantin Gaber is a Director of Quantitative Execution Services at with high turnover, which generally is good for market makers WorldQuant, LLC, and has a MS in operations research from Columbia because they can widen the spread but easily unload their positions; University. second, high volatility combined with low turnover, which is bad for Michael Kozlov is a Senior Executive Research Director at WorldQuant, market makers. Moreover, transaction costs that are important in LLC, and has a Ph.D. in theoretical physics from Tel Aviv University. normal circumstances may become insignificant compared with Radislav Valkov is a Senior Quantitative Researcher and has a Ph.D. in expected losses or gains in periods of stress. mathematics from the University of Antwerp.

ENDNOTES

1. Frank A. Fernandez. “Liquidity Risk: New Approaches to Measurement and 7. Robert Almgren, Chee Thum, Emmanuel Hauptmann and Hong Li. “Direct Monitoring.” Working paper, Security Industry Association (1999). Estimation of Equity Market Impact.” Risk 18, no. 7 (2005): 58-62. 2. Kleopatra Nikolaou. “Liquidity (Risk) Concepts, Definitions and Interactions.” 8. Yakov Amihud. “Illiquidity and Stock Returns: Cross-Section and Time-Series Working paper, European Central Bank (2009). Effects.” Journal of Financial Markets 5, no. 1 (2002): 31-56. 3. John Maynard Keynes. A Treatise on Money. London: Macmillan, 1930. 9. IG Group. https://www.ig.com/en/glossary-trading-terms/market-data-definition 4. Tonny Lybeck and Abdourahmane Sarr. “Measuring Liquidity in Financial 10. Bob Pisani. “NYSE’s New President Takes on Challenges as Exchanges Compete Markets.” Working paper, International Monetary Fund (2002). for IPOs, Fees.” CNBC, May 22, 2018. 5. Albert S. Kyle. “Continuous Auctions and Insider Trading.” Econometrica 53, 11. Francis Breedon. “Market Liquidity Under Stress: Observations from the FX no. 6 (1985): 1315-1335. Market.” Market Liquidity: Proceedings of a Workshop Held at the Bank for International Settlements 2 (2001): 149-151. 6. Jean-Philippe Bouchaud, Yuval Gefen, Marc Potters and Matthieu Wyart. “Fluctuations and Response in Financial Markets: The Subtle Nature of ‘Random’ 12. Michael Durbin. All About High-Frequency Trading. New York: McGraw-Hill Price Changes.” Quantitative Finance 4, no. 2 (2004): 176-190. Education, 2010.

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