The Dynamics of Financially Constrained Arbitrage

Abstract

We develop a model of financially constrained arbitrage, and use it to study the dynamics of arbitrage capital, liquidity, and asset prices. Arbitrageurs exploit price discrepancies between assets traded in segmented markets, and in doing so provide liquidity to investors. A collateral constraint limits their positions as a function of capital. We show that the dynamics of arbitrage activity are self-correcting: following a shock that depletes arbitrage capital, profitability increases, and this allows capital to be gradually replenished. Spreads increase more and recover faster for more volatile trades, although arbitrageurs cut their positions in these trades the least. When arbitrage capital is more mobile across markets, liquidity in each market generally becomes less volatile, but the reverse may hold for aggregate liquidity because of mobility-induced contagion.Keywords: Arbitrage, liquidity, financial constraints, financial crises. This paper is published as part of the Systemic Risk Centre's Discussion Paper Series. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without the prior permission in writing of the publisher nor be issued to the public or circulated in any form other than that in which it is published.Requests for permission to reproduce any article or part of the Working Paper should be sent to the editor at the above address. AbstractWe develop a model of financially constrained arbitrage, and use it to study the dynamics of arbitrage capital, liquidity, and asset prices. Arbitrageurs exploit price discrepancies between assets traded in segmented markets, and in doing so provide liquidity to investors. A collateral constraint limits their positions as a function of capital. We show that the dynamics of arbitrage activity are self-correcting: following a shock that depletes arbitrage capital, profitability increases, and this allows capital to be gradually replenished. Spreads increase more and recover faster for more volatile trades, although arbitrageurs cut their positions in these trades the least.When arbitrage capital is more mobile across markets, liquidity in each market generally becomes less volatile, but the reverse may hold for aggregate liquidity because of mobility-induced contagion.

Arbitrage with Production, Collateral Constraint and Heterogeneous Belief

“…Second it captures the phenomenon of assets or portfolios that have highly correlated payoffs but are traded at significantly diverging prices in different markets. As illustrated in Gromb and Vayanos (2015), examples of such assets include the Siamese-Twin stocks, traded in different markets but with identical dividend payoffs and identical stocks issued from the same company traded both in Shanghai exchange and Hong Kong exchange. Also bonds with identical coupon rates and time to maturity, like on-and off-the run bonds, can also be generally abstracted and modelled with this feature.…”

“…For instance, as illustrated in Gromb and Vayanos (2015), the demand of the domestic-equity mutual funds, which can only invest in their own domestic markets, are influenced by inflows and outflows of the investing capital. Also the bonds demand from different pension funds could be driven by their diverse needs for asset-liability management.…”

“…Similar to the settings of Gromb and Vayanos (2015), we model the collateral constraint such that not only the intermediaries must fully collateralize their asset positions, but also they are obliged to put collateral separately in each market. Due to the market segmentation, the position they take in one market is not recognized by the custodians in the other country and hence cannot serve as collateral to back up the opposite positions taken in other market.…”

“…Different from Gromb and Vayanos (2015), in this model we do not model a riskless asset with exogenous return as collateral. Instead, we generalize the riskless asset to the capital investment of some technology without uncertainty.…”