A Liquidation Risk Adjustment for Value at Risk and Expected Shortfall

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