Volume, liquidity, and liquidity risk

Abstract

Many classes of microstructure models, as well as intuition, suggest that it should be easier to trade when markets are more active. In the data, however, volume and liquidity seem unrelated over time. This paper offers an explanation for this fact based on a simple frictionless model in which liquidity reflects the average risk-bearing capacity of the economy and volume reflects the changing contribution of individuals to that average. Volume and liquidity are unrelated in the model, but volume is positively related to the variance of liquidity, or liquidity risk. Empirical evidence from the U.S. government bond and stock markets supports this new prediction.

Introduction

Recent empirical studies of liquidity dynamics have turned up a surprising negative result: higher volume does not necessarily lead to more liquid markets. In annual vector autoregressions using the Dow Jones 30 industrial stocks, Jones (2002) finds no significant effect of changes in turnover on changes in bid-ask spreads. Using monthly aggregate stock market data, Fujimoto (2004) finds mostly insignificant impulse responses to turnover shocks for several liquidity measures. Evans and Lyons (2002) and Galati (2000) find no association between liquidity and level of activity on the foreign exchange market, while Danielsson and Payne (2002) find a negative relationship. Similar negative findings are reported in Foster and Viswanathan (1993) and Lee, Mucklow, and Ready (1993) for individual stocks.¹ In the U.S. Treasury market, Fleming (2003) finds that neither trading volume nor trading frequency are consistently correlated with price impact or bid-ask spreads.

These results seem to challenge the basic intuition that it ought to be easier to trade in more active markets. This intuition certainly seems to find support cross-sectionally. Larger, more active markets are usually more liquid. Indeed, this was the original finding of Demsetz (1968), which is sometimes viewed as the starting point of the field of market microstructure. More frequently traded stocks have lower bid-ask spreads.

To Demsetz, the result was an unsurprising consequence of competitive intermediation: higher transaction demand leads to more profit for dealers and hence cheaper provision of liquidity services. Further, lower costs should naturally elicit more trade, as in any other product market. Underlying this view, of course, is the conception of liquidity as the output of a sector with access to a particular intermediation technology.

However, the same conclusion applies for different reasons in some classical models of asymmetric information. In Kyle (1985), equilibrium in the game between informed traders and liquidity suppliers requires that informed demand (and hence volume) scales with uninformed demand, while illiquidity (Kyle's lambda) is inversely proportional to the scale of uninformed demand because more noise makes total order flow less informative. Hence more volume means higher liquidity. This is a comparative static result. However, the logic is borne out in dynamic extensions such as Admati and Pfleiderer (1988) and Foster and Viswanathan (1990). Again, when uninformed traders are allowed to respond to variations in liquidity, the relationship is strengthened.²

Finally, a third trading paradigm, search models, also implies that more active markets are more liquid. When there is more search activity for whatever reason, then liquidity—measured by the opportunity cost of the searching time—will be shorter, almost by definition (see Lippman and McCall, 1986).

The lack of a dynamic relationship between liquidity and volume thus seems to pose something of a challenge, both to intuition and to several classes of model. The consistency of the non-finding across several types of asset, market structure, and frequency suggests that there is indeed something to explain here. Moreover, all the empirical studies cited above control for things such as returns and volatility. So it is not the case, for example, that liquidity fails to rise with volume because volume rises with uncertainty.

Understanding liquidity dynamics is important for a number of reasons. Since liquidity directly determines the feasibility and costs of dynamic trading strategies, any investor or institution that needs to implement such a strategy must quantify the liquidity risk involved. Because investors care about it, studying the consequences of liquidity risk has become a central topic in asset pricing (see Pástor and Stambaugh, 2003, Acharya and Pedersen, 2004). Finally, liquidity risk is important from a policy perspective because of the danger posed by large drops in liquidity, which may lead to price distortions, disruptions in risk transfer, and possibly inefficient liquidation of real investments.

Perhaps especially for this latter reason, a crucial aspect of our understanding of liquidity dynamics is pinning down the role played by intermediaries or “liquidity providers.” It is here that the empirical volume–liquidity results are directly relevant. By falsifying a basic intuition, they seem to call into question the view of liquidity as a service output provided by a segmented sector. This view underlies much policy analysis of market fragility, which regards the capital constraints of intermediaries as the key determinant of liquidity risk.

An alternative view, in which intermediaries play no role, models liquidity as the average willingness of the market as a whole (or a representative agent) to accommodate trade at prevailing prices (Pagano, 1989). This willingness may fluctuate as the underlying state of the economy changes. In general, agents are more flexible and asset prices respond less to trade demand when a marginal perturbation to their portfolios has a low impact on their intertemporal marginal rate of substitution (discount rates). Johnson (2006) develops the calculation of this liquidity in representative agent economies and illustrates its endogenous dynamics in several examples. By definition, however, there is no trade in representative agent economies, meaning that the examples in that paper can shed no light on the connection between volume and liquidity.

This paper extends Johnson (2006) by computing the equilibrium price-response measure of liquidity in a simple multi-agent economy with trade. The derivation explicitly connects the (shadow) illiquidity characterizing a representative agent's demand curve for shares with the actual trade impact costs that affect the portfolio decisions of disaggregated agents. Hence, the paper presents further evidence on the usefulness of the underlying concept of price elasticity by using it to show exactly how liquidity and volume are jointly determined.

The setting is a frictionless model of stochastically participating agents whose arrivals and departures generate (exogenous) trade demand. Liquidity fluctuates as the aggregate risk-bearing capacity of the economy changes due to changes in total participation. Despite its simplicity, the model delivers an aggregate liquidity process that behaves realistically, covarying positively with asset prices and negatively with volatility, for example. Other aggregate relationships are also sensible: volume covaries positively with volatility, and volatility covaries negatively with returns (see Appendix B).

The model implies, however, that there should be no relationship between the levels of liquidity and volume. Volume is simply driven by the degree of flux of the population, which is independent of the level of participation. The usual intuition that it is easier to transact in a busy market fails because high turnover does not make providing liquidity any less costly to the remaining agents. Trade per se has no real effects.

While accounting for the non-relationship between volume and liquidity resolves a conceptual puzzle, the model goes further and delivers a novel positive implication. If volume reflects compositional rearrangement, then large increases or decreases in willingness to bear risk should both necessitate high volume. Conversely, higher trading intensity makes higher population flux more likely—in either direction. Hence volume should be associated with the second moment of liquidity changes, that is, with liquidity risk. Moreover, this relationship should hold independent of any changes in volatility.

While alternative explanations for the lack of a (first-moment) relationship between liquidity and volume can be found, it is not at all clear that any such alternative would also make the second-moment prediction I suggest here. If liquidity provision were non-competitive, for example, higher volume might just lead to higher intermediary profits without any reduction in trading costs. In that case, however, there would also be no connection between volume and liquidity risk. If asymmetric information risk rises with volume but the signal-to-noise ratio in order flow is constant (as happens in Bernhardt and Hughson, 2002, for example), then liquidity is unaltered in either direction when volume increases. In short, the volume-liquidity risk hypothesis is not necessarily unique to this paper, but it does not seem to have been previously articulated.

I examine this hypothesis in the context of the U.S. government bond and stock markets, and the evidence is supportive. The effect appears to be both significant and robust. An additional contribution of the work, then, is to sharpen our understanding of the drivers of liquidity fluctuation.

The model ignores information asymmetries and many other important factors that affect trading in real markets. Moreover, the focus is exclusively on dynamic patterns, leaving many interesting cross-sectional questions unaddressed. Nevertheless, the findings may have important implications. They suggest that one widely accepted determinant of liquidity risk—the organization and financial position of intermediaries—may not matter as much as one might think. At the same time, the argument suggests that another factor usually thought to indicate market health—higher turnover—may actually be associated with increased liquidity risk.

The rest of the paper is organized as follows. Section 2 introduces the model and establishes its predictions. Section 3 presents numerical evidence on the model's main properties. Section 4 presents the empirical evidence. A final section summarizes the paper's contribution and implications.