An Information‐Based Theory of Time‐Varying Liquidity

• Author: BRETT GREEN,BRENDAN DALEY
• Date: 01 April 2016
• Published date: 01 April 2016
• DOI: http://doi.org/10.1111/jofi.12272

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 2 •APRIL 2016

An Information-Based Theory of Time-Varying

Liquidity

BRENDAN DALEY and BRETT GREEN∗

ABSTRACT

Wepropose an information-based theory to explain time variation in liquidity and link

it to a variety of patterns in asset markets. In “normal times,” the market is fully liquid

and gains from trade are realized immediately.However, the equilibrium also involves

periods during which liquidity “dries up,” which leads to endogenous liquidation costs.

Traders correctly anticipate such costs, which reduces their willingness to pay. This

foresight leads to a novel feedback effect between prices and market liquidity, which

are jointly determined in equilibrium. The model also predicts that contagious sell-offs

can occur after sufficiently bad news.

ASSET MARKETS ARE SUSCEPTIBLE to periods of illiquidity. Recent examples of

this phenomenon include real estate (Clayton, MacKinnon, and Peng (2008)),

mortgage-backed securities (Gorton (2009), Acharya and Schnabl (2010),

Dwyer and Tkac (2009)), the repo market (Gorton and Metrick (2012)), struc-

tured credit (Brunnermeier (2009)), commercial paper (Anderson and Gascon

(2009)), and money market funds (Krishnamurthy, Nagel, and Orlov (2012)).

In conjunction with this evidence, a literature has developed that exoge-

nously specifies time variation and risk in the ability to trade securities and

then explores the implications for asset prices. Examples include Longstaff

(2001,2009), Acharya and Pedersen (2005), Watanabe and Watanabe (2008),

Gˆ

arleanu (2009), and Ang, Papanikolaou, and Westerfield (2014). Yet the un-

derlying mechanism driving this phenomenon is not well understood. What

can explain dramatic changes in the amount of liquidity in markets? What are

the implications for asset prices? What is the nature of the interaction between

prices and liquidity? For instance, do asset prices affect liquidity in ways that

∗Brendan Daley is at the Fuqua School of Business at Duke University. Brett Green is at

the Haas School of Business at University of California–Berkeley. The authors are grateful to

Bruno Biais, an anonymous Associate Editor, and two anonymous referees for their valuable

feedback and suggestions. We are also are grateful to Jim Anton, Snehal Banerjee, Peter DeMarzo,

Mike Fishman, Nicolae Gˆ

arleanu, Ravi Jagannathan, Arvind Krishnamurthy,Tyler Muir, Dimitris

Papanikolaou, Yuliy Sannikov, Andy Skrzypacz, Chester Spatt, Dimitri Vayanos,and Bob Wilson.

In addition, we thank seminar participants at Princeton, Harvard/MIT, Berkeley, UCLA, Caltech,

Chicago Booth, Penn State, and the University of Illinois as well as conference participants at FRA,

WFA, FIRS, FTG, Csef-Igier,and the Multinational Finance Conference for useful comments. The

authors declare that they have no relevent or material financial inerests related to the research in

this paper.

DOI: 10.1111/jofi.12272

809

810 The Journal of Finance R

models with exogenously specified illiquidity risk cannot capture? In this pa-

per, we propose answers to these questions by developing a theory in which

time variation in market liquidity arises endogenously.

Our theory is developed within a dynamic economy with rational, risk-

neutral agents. The model features three key elements. First, traders have

private information about the future cash flows generated by their assets. Sec-

ond, the market receives information about these cash flows, which we refer to

as news stochastically over time. And third, all agents are subject to idiosyn-

cratic preference shocks (e.g., financial/liquidity constraints); a trader who is

hit by a shock has a reason to sell, though she is not forced to do so. This last

ingredient implies that a trader who purchases an asset today cares about the

expected liquidity of that asset in the future, which we refer to as an (exoge-

nous) demand for future liquidity.

We indeed find that the risk of future illiquidity has important implications

for asset prices. Consider two traders: Ais the current owner of an asset and

Bis a potential buyer. Trader B, when considering the purchase of the asset,

realizes that his ability to sell it in the future may be limited by endogenous

frictions stemming from asymmetric information. This foresight reduces his

willingness to pay for the asset today. As a result, prices are driven below

fundamentals, leading to an illiquidity discount, which varies over time with

the degree of the information asymmetry.However, because prices and liquidity

are jointly determined in our theory, the story does not end here. The reduction

in asset prices feeds back into determining liquidity in the market. Trader

A, when considering the sale of the asset, is now less inclined to sell at the

depressed prices if she has positive (private) information about the asset. This

in turn makes Trader Beven more hesitant to offer a pooling price, which

exacerbates the adverse selection problem and leads to further deterioration in

market liquidity.In short, the information friction generates illiquidity, and the

demand for future liquidity amplifies the consequences. These forces negatively

feed back on one another until the price function and degree of liquidity reach

a fixed point.

Our formal analysis begins in a single-asset, two-period environment in

which we highlight the intuition underlying the mechanism. Then, building

on the framework developed in Daley and Green (2012) (hereafter DG12), we

extend our analysis to a continuous-time, infinite-horizon model in which news

is revealed via a diffusion process, and observable shocks arrive according to

a Poisson process. We construct an equilibrium in which the amount of liq-

uidity in the market crucially depends on the market belief about the asset

value, which evolves over time. As in DG12, the equilibrium partitions the be-

lief space into three distinct regions: (1) when the belief about the asset’s type

is favorable, efficient trade occurs immediately at a “fair” price; (2) when the

market is pessimistic about the asset, the owner is forced to either sell at a

low price or wait (a trader with a low-value asset mixes over these two alter-

natives, whereas one with a high-value asset waits); and (3) when the market

completely breaks down, both sides of the market wait until either sufficient

good news restores confidence to (1) or enough bad news forces (2).

An Information-Based Theory of Time-Varying Liquidity 811

Figure 1. Sample path of market liquidity dynamics.

Figure 1illustrates a sample path of the equilibrium dynamics. To elaborate,

suppose Trader Aowns a share of the asset, and she experiences a shock while

the market belief happens to be favorable. In this case, which we interpret as

“normal times,” the market is fully liquid; Trader Asells immediately to, say,

Trader B, without affecting the market belief. While Trader Bis in possession,

bad news arrives such that the belief drifts down into the middle region, at

which point Trader Bexperiences a shock. In this case, the market is fully

illiquid; Trader Bwill be unwilling to sell at the highest price buyers are

willing to offer, and inefficient delay will ensue. These equilibrium dynamics

can explain what is often referred to as “liquidity drying up.” If the asset is of

low quality and sufficient bad news arrives, Trader Bmay capitulate and sell

at a low price. Or she may hold out, waiting for sufficient good news to arrive

and market liquidity to be restored. If the asset is of high quality, Trader B

will wait until enough good news restores market liquidity, meaning that not

selling at a low price is a positive signal to the market.

After demonstrating the existence of an equilibrium that features these dra-

matic changes in market liquidity, we study the implications. First, what are

the implications for asset prices? One immediate implication is that, during

normal times (i.e., when the belief is above βin Figure 1), the asset trades

at a discount relative to its fundamental value because potential buyers cor-

rectly anticipate the future risk of illiquidity. As the market belief increases

further above β, the risk of future illiquidity decreases, and so too does the dis-

count. Another implication is that the price process exhibits excess volatility

in response to news, because news provides information not only about funda-

mentals, but also about future illiquidity risk. That is, bad news decreases the

belief about fundamentals as well as the expected future liquidity of the asset.