Price Impact Under Heterogeneous Beliefs and Restricted Participation

TL;DR

This paper models a thin financial market with heterogeneous beliefs and participation restrictions, proving equilibrium existence and showing restrictions can sometimes enhance market welfare depending on belief heterogeneity.

Contribution

It introduces a new equilibrium model accounting for trading restrictions and heterogeneity in beliefs and risk profiles, with an efficient algorithm for equilibrium computation.

Findings

Restrictions can increase market welfare with belief heterogeneity.

Equilibrium prices remain unchanged when traders agree on covariance matrix.

The model highlights the importance of belief heterogeneity in market dynamics.

Abstract

We consider a financial market in which traders potentially face restrictions in trading some of the available securities. Traders are heterogeneous with respect to their beliefs and risk profiles, and the market is assumed thin: traders strategically trade against their price impacts. We prove existence and uniqueness of a corresponding equilibrium, and provide an efficient algorithm to numerically obtain the equilibrium prices and allocations given market's inputs. We find that restrictions may increase the market's welfare if traders have different views regarding the covariance matrix of securities returns. The latter heterogeneity regarding covariance matrix disagreement is essential in modelling; for instance, when traders agree on the covariance matrix, restricting participation in some securities for some traders leaves equilibrium prices unaltered in the unrestricted securities, a certainly undesirable model effect.