Equilibrium Liquidity Research Articles

Should Basel-style liquidity requirements be set countercyclically? Evidence from a numerical analysis

We develop a model to compare the changes in banks' equilibrium capital and liquidity holdings under various versions of Basel-style requirements across economic cycles. We find that banks' liquidity is countercyclical while capital buffer is procyclical. Countercyclical liquidity-holding behaviour causes a larger liquidation of loans in economic expansions. We also find that Basel-style liquidity requirements help to lower banks' loan liquidations in economic upturns, although it is of limited effectiveness in economic downturns. We thus suggest that similar to capital requirements, liquidity requirements should also be set in a countercyclical manner. Our results show that capital requirements and liquidity requirements are complements in economic upturns in terms of enhancing banking stability and obtaining social welfare. Furthermore, Basel III outperforms previous regulatory versions in enhancing bank stability and social welfare in extreme situations.

Structural Change in Post Keynesian Monetary Theory: A Non-Compensatory Disequilibrium Framework

Post Keynesian Economics has shifted away and even renegade from Keynes' original research program, i.e., the Unemployment Equilibrium thesis, endogenous money and liquidity preference determination of interest rate in which money and uncertainty play a fundamental part. This paper attempts to bring back the Keynesian counter-revolution spirit into Post Keynesian Monetary Theory by introducing a Non-Compensatory Disequilibrium Framework (NCDF) that allows structural breaks in budget constraints that lead to a model where Walras’ Law does not hold.

Lazy Liquidity in Automated Market Making

A growing number of blockchain-based decentralized exchanges have adopted automated market makers to attract liquidity, and they replace the traditional order book system for trade execution. This paper studies the equilibrium liquidity provision via constant product market makers, one of the simplest and widely adopted algorithms of automated market making. The model derives the optimal behavior of liquidity providers and the aggregate size of the liquidity pool on a constant product market. As suggested by the traditional market microstructure literature, I demonstrate that information asymmetry between traders leads to an adverse selection problem and plays a key role in determining equilibrium liquidity on an automated market. Moreover, when liquidity providers are strategic, I find that competition between them exhibits both strategic substitution and complementarity, making the best response function of each liquidity provider non-monotonic in her rivals' liquidity supply. The model also shows that the equilibrium market liquidity tends to be stable and does not diverge or evaporate even if a (small) temporary shock hits the market.

Liquidity Fluctuations in Over-the-Counter Markets

This paper presents a model of opaque secondary markets. Investors meet over-the-counter to trade heterogeneous assets under asymmetric information. An endogenous composition effect emerges whereby high liquidity alters the quality of the pool of sellers and decreases future liquidity. With impatient investors, cyclical equilibria arise: Price and volume oscillate without any fundamental shock. With patient investors, the equilibrium is driven instead by a resale effect: Liquidity depends primarily on investors' expectations about future liquidity, and multiple steady states coexist. In each case, equilibrium liquidity is driven by the opaqueness about asset quality and trade history typical of over-the-counter markets.

Breaking the Curse of Kareken and Wallace with Private Information

We study the endogenous choice to accept at objects as media of exchange and their implications for nominal exchange rate determination. We consider a two-country environment with two currencies which can be used to settle any transactions. However, currencies can be counterfeited at a xed cost and the decision to counterfeit is private information. This induces equilibrium liquidity constraints on the currencies in circulation. We show that the threat of counterfeiting can pin down the nominal exchange rate even when the currencies are perfect substitutes, thus breaking the Kareken-Wallace indeterminacy result. When the two currencies are not perfect substitutes, an international currency can exist whereby one country has two currencies circulating while the other country uses only one. We also nd that with appropriate scal policies we can enlarge the set of monetary equilibria with determinate nominal exchange rates. Finally, we show that the threat of counterfeiting can also help determine nominal exchange rates in a variety of dierent trading environments.

Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.

Asset Pricing with Large Investors

We derive closed form expressions for equilibrium asset prices and liquidity in an economy populated by a finite number of large, strategic, risk averse investors. The model allows for arbitrary risk preferences, any number of assets, and an arbitrary distribution of asset payoffs. In equilibrium, assets are priced according to the standard consumption Euler equation plus a correction term accounting for market illiquidity (price impact), linked to an endogenous measure of systemic risk that puts a large weight on low consumption states. Wealth effects imply that price impact is generally asymmetric, which leads to the emergence of endogenous systemic assets: That is, assets whose sell-off triggers large moves in all security prices. Market liquidity is non-monotonic in funding liquidity and may decrease in the number of investors. In the presence of liquidity shortage, price impact becomes negative and gives rise to an illiquidity premium in asset prices.

Private Money Creation and Equilibrium Liquidity

Can creation of private money fulfill the liquidity needs of the economy? The answer is no if the market of private money is run only by forces of perfect competition. Multiple equilibria are possible: there exist good equilibria with complete satiation of liquidity and absence of default on private money, and bad equilibria characterized by shortage of liquidity and partial default. In this framework, capital requirements, distortions to the demand or supply of private money, and the role of public liquidity in substituting private liquidity or in offsetting liquidity crises are investigated.

Equilibrium liquidity premia of private equity funds

Purpose – The purpose of this paper is to propose a novel theory of the equilibrium liquidity premia of private equity funds and explore its asset-pricing implications. Design/methodology/approach – The theory assumes that investors are exposed to the risk of facing surprise liquidity shocks, which upon arrival force them to liquidate their positions on the secondary private equity markets at some stochastic discount to the fund’s current net asset value. Assuming a competitive market where fund managers capture all rents from managing the funds and investors just break even on their positions, liquidity premia are defined as the risk-adjusted excess returns that fund managers must generate to compensate investors for the costs of illiquidity. The model is calibrated to data of buyout funds and is illustrated by using numerical simulations. Findings – The model analysis generates a rich set of novel implications. These concern how fund characteristics affect liquidity premia, the role of the investors’ propensities of liquidity shocks in determining liquidity premia and the impact of market conditions and cycles on liquidity premia. Originality/value – This is the first paper that derives liquidity premia of private equity funds in an equilibrium setting in which investors are exposed to the risk of facing surprise liquidity shocks.

Nominal Exchange Rate Determinacy Under the Threat of Currency Counterfeiting

We study the endogenous choice to accept fiat objects as media of exchange and their implications for nominal exchange rate determination. We consider a two-country environment with two currencies which can be used to settle any transactions. However, currencies can be counterfeited at a fixed cost and the decision to counterfeit is private information. This induces equilibrium liquidity constraints on the currencies in circulation. We show that the threat of counterfeiting can pin down the nominal exchange rate even when the currencies are perfect substitutes, thus breaking the Kareken-Wallace indeterminacy result. When the two currencies are not perfect substitutes, an international currency can exist whereby one country has two currencies circulating while the other country uses only one. We also find that with appropriate fiscal policies we can enlarge the set of monetary equilibria with determinate nominal exchange rates. Finally, we show that the threat of counterfeiting can also help determine nominal exchange rates in a variety of different trading environments.

Nominal Exchange Rate Determinacy under the Threat of Currency Counterfeiting

We study the endogenous choice to accept fiat objects as media of exchange and their implications for nominal exchange rate determination. We consider a two-country environment with two currencies that can be used to settle any transactions. However, currencies can be counterfeited at a fixed cost and the decision to counterfeit is private information. This induces equilibrium liquidity constraints on the currencies in circulation. We show that the threat of counterfeiting can pin down the nominal exchange rate even when the currencies are perfect substitutes, thus breaking the famous Kareken-Wallace indeterminacy result. (JEL D82, E42, F31)

Competition for Order Flow with Fast and Slow Traders

The rise of computerized trading strategies in equity markets has spurred competition between trading venues. This paper shows that cross-venue strategies create highly interlinked markets: trades on one venue are followed by sizeable cancellations of limit orders on competing venues. These cancellations are explained in a simple model of competition between two limit order markets with fast and slow traders. Only the fast traders can access the liquidity of both venues simultaneously. Empirically, we confirm the predictions that the fraction of fast traders (1) reduces the equilibrium liquidity supply and (2) reduces the magnitude of the cancellations following a trade.

Equilibrium Liquidity Premia of Private Equity Funds

This paper proposes a theory of the equilibrium liquidity premia of private equity funds and explores its asset-pricing implications. The theory is based on the notion that investors are exposed to the risk of facing surprise liquidity shocks, which upon arrival force them to liquidate their positions on the secondary private equity markets at some stochastic discount to the fund’s current net asset value. Assuming a competitive market where fund managers capture all rents from managing the funds and investors just break even, equilibrium liquidity premia are defined as the risk-adjusted excess returns that fund managers must generate in order to compensate investors for the costs of illiquidity. The model is calibrated such that parameters closely match data of buyout funds and is illustrated by using numerical simulations. The theory generates a rich set of novel implications. These concern (i) how fund characteristics (i.e., systematic risk, and the drawdown and distribution dynamics of a fund) affect liquidity premia, (ii) the role of the investors’ propensities of liquidity shocks and secondary market discount dynamics in determining liquidity premia, and (iii) the impact of market conditions and cycles on liquidity premia.

Equilibrium Discovery and Preopening Mechanisms in an Experimental Market

We experimentally analyze how to design preopening mechanisms facilitating coordination on high equilibrium liquidity and gains from trade. We allow a call auction to be preceded by a preopening or...

Equilibrium Discovery and Preopening Mechanisms in an Experimental Market

We experimentally analyze how to design preopening mechanisms facilitating coordination on high equilibrium liquidity and gains from trade. We allow a call auction to be preceded by a preopening or not, preopening orders to be binding or not, and the opening time to be deterministic or random. When the preopening is nonbinding, traders place manipulative orders, reducing the credibility of preplay communication. Random market opening deters manipulation, but also hinders communication by making it costly. Gains from trade are maximized when preopening orders are binding. This enables some traders to place early limit orders, attracting further liquidity.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1787 .This paper was accepted by Wei Xiong, finance.

Equilibrium Price of Immediacy and Infrequent Trade

The paper studies the equilibrium value of bid-ask spreads and time- to-trade in a continuous-time, intermediated financial market. The endogenous spreads are the price at which brokers are willing to offer immediacy. In case intermediaries pay trading costs, it includes them too. We determine equilibrium trading policies, prices, returns and liquidity premium, as well as value functions of all the agents and intervention barriers of the investors, who trade only infrequently. Intervention times are endogenous too. We show that competition among brokers does not drive the spread to zero - and does not make trade continuous - unless investors are risk-neutral. The paper predicts spreads and times between successive trades increasing with the difference in agents' risk attitudes. Bid-ask prices and trading barriers react asymetrically to an increase in the difference of risk aversions. They are symmetric in trading costs.

Liquidity: What You See is What You Get?

The rise of computerized trading strategies in equity markets has spurred competition between trading venues. This paper shows that cross-venue strategies create highly interlinked markets: trades on one venue are followed by sizeable cancellations of limit orders on competing venues. These cancellations are explained in a simple model of competition between two limit order markets with fast and slow traders. Only the fast traders can access the liquidity of both venues simultaneously. Empirically, we confirm the predictions that the fraction of fast traders (i) reduces the equilibrium liquidity supply and (ii) reduces the magnitude of the cancellations following a trade.

Equilibrium Security Design and Liquidity Creation by Privately Informed Issuers

We examine optimal provision of riskless government bonds under asymmetric information and safe asset scarcity. Paradoxically, corporations have incentives to issue junk debt precisely when intrinsic demand for safe debt is high since uninformed investors then migrate to risky overheated debt markets. Uninformed demand stimulates informed speculation which drives junk debt prices closer to fundamentals, encouraging pooling at high leverage. Acting as borrower of first resort, the government can issue safe bonds which siphon off uninformed demand for risky corporate debt and reduce socially wasteful informed speculation. Thus, government bonds either eliminate pooling at high leverage or improve risk sharing in such equilibria. The optimal quantity of government bonds is increasing in intrinsic demand for safe assets and non-monotonic in marginal Q.

Information and Liquidity Trading at Optimal Frequencies

This paper studies an asset market where, as in major world exchanges, informed and liquidity investors continuously control the timing of orders and whether to take or provide liquidity. In equilibrium, investors demand and supply liquidity simultaneously, following distinctive time-varying patterns previously found in experiments. The resulting linkages between prices, order frequency and depths shed light on empirical regularities. By nesting limit-order and dealer markets, I find that the speed of information transmission is higher in the former and increases with investor sophistication. Evidence from proprietary NYSE data provides support for the implied liquidity provision behavior of investors.

Large Investors: Implications for Equilibrium Asset, Returns, Shock Absorption, and Liquidity

The growing share of financial assets that are held and managed by large institutional investors whose desired trades move asset prices is at odds with the traditional competitive assumption that investors are small and take prices as given. This paper relaxes the traditional price-taking assumption and instead presents a dynamic multiple asset model of imperfect competition in asset markets among large investors who differ in their risk aversion. The model is used to study asset price dynamics during an LTCM-like scenario in which market rumors of distressed asset sales are followed at a later date by the sales themselves. Using the model, it is shown that large investors front-run distressed sales; asset prices overshoot their long-run fundamentals; and asset pricing models experience temporary breakdown. During the period of model breakdown assets equilibrium returns are explained by the market portfolio and by transient liquidity factors.