A Liquidation Risk Adjustment for Value at Risk and Expected Shortfall

17 Pages Posted: 3 Jan 2018

See all articles by Lakshithe Wagalath

Lakshithe Wagalath

IESEG School of Management

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA)

Date Written: December 29, 2017

Abstract

This paper proposes an intuitive and flexible framework to quantify liquidation risk for financial institutions. We develop a model where the "fundamental" dynamics of assets is modified by price impact from fund liquidations (if any). We characterize mathematically the liquidation schedule of financial institutions and study in detail the fire sales resulting endogenously from margin constraints when trading through an exchange. Our study enables to obtain tractable formulas for the value at risk and expected shortfall of a financial institution in the presence of fund liquidation. In particular, we find an additive decomposition for liquidation-adjusted risk measures which are equal to "fundamental" risk-measures plus a liquidation risk adjustment, which is proportional to the size of fund positions as a fraction of asset market depths. Our results may be used in practice by risk-management of financial institutions to better tackle liquidity events arising from fund liquidations and adjust their portfolio allocations to liquidation risk.

Keywords: liquidation risk, fire sales, value at risk, expected shortfall, risk management, price impact

JEL Classification: G11, G20, G32

Suggested Citation

Wagalath, Lakshithe and Zubelli, Jorge P., A Liquidation Risk Adjustment for Value at Risk and Expected Shortfall (December 29, 2017). Available at SSRN: https://ssrn.com/abstract=3095501 or http://dx.doi.org/10.2139/ssrn.3095501

Lakshithe Wagalath (Contact Author)

IESEG School of Management ( email )

1 Parvis de la Défense
Paris, 92044
France

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA) ( email )

Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro, 22460
Brazil

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