Abstract
This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents’ demands.
Summary
This paper introduces portfolio choice into the Duffie-Garleanu-Pedersen (DGP) search-based equilibrium framework, where agents can only trade at Poisson arrival times with intensity lambda. A continuum of agents with CARA utility have types rho_i (correlation between their endowment and the asset dividend) that switch according to an irreducible Markov chain. In the near-risk-neutral limit (gamma → 0 with gamma*sigma^2 fixed), the model is solved in closed form.
The central result (Theorem 1, equation 25) is striking: the equilibrium price P = P^W is exactly equal to the Walrasian (frictionless) price, independent of the liquidity level lambda. This occurs because illiquidity has offsetting effects on buyers’ and sellers’ demands — buyers hold less and sellers hold more, and these effects cancel in aggregate. However, portfolio choice (equation 29) and welfare (equation 33) are highly sensitive to liquidity.
The paper connects search frictions to the transaction cost literature (Section 4.2), showing that with proportional costs q, the price becomes P = P^W - q(mu^b - mu^s), where the price impact is proportional to the cost times the imbalance between buyers and sellers. Short-sale constraints (Proposition 3) also restore price sensitivity to illiquidity, consistent with empirical evidence.
Key Contributions
- First equilibrium model with unrestricted portfolio choice under search frictions
- Price independence of liquidity (Theorem 1) — overturns the conventional wisdom from the DGP literature
- Welfare is sensitive to liquidity even when price is not (Section 3.3)
- Extension to proportional transaction costs (Section 4.2, Proposition 4)
- Short-sale constraints restore price sensitivity (Proposition 3)
- Explains why the DGP search literature finds large price impacts: they restrict agents to binary positions
Methodology
The model uses CARA utility with Markov-switching types in continuous time. Agents solve a Bellman equation (11) for value-function coefficients a_j(theta) that satisfy a system of nonlinear ODEs (15). The near-risk-neutral approximation linearises the system, yielding closed-form solutions. Market clearing determines the equilibrium price.
Key Findings
- With unrestricted portfolio choice, illiquidity has a negligible price impact — the (partial) cancellation of opposing demand effects is nearly complete
- Portfolio positions are less extreme in illiquid markets: agents tilt toward positions desired in likely future states
- Higher liquidity increases welfare through better hedging, even without changing the price
- Transaction costs create a price wedge P = P^W - q(mu^b - mu^s), proportional to the buyer-seller mass imbalance
- The key condition for significant price impact: binding portfolio constraints (e.g., short-sale restrictions) or slopes of marginal utilities that vary significantly with holdings
Important References
- Dynamic Trading with Predictable Returns and Transaction Costs — Garleanu and Pedersen (2013), the single-agent quadratic cost extension
- Over-the-Counter Markets — Duffie, Garleanu, Pedersen (2005), the foundational search model with binary positions
- Equilibrium Returns with Transaction Costs — Herdegen, Muhle-Karbe (2018), multi-agent equilibrium extending this framework