Large-scale deleveraging of assets by distressed financial institutions have been recognized as an important channel for the contagion of losses during the recent financial crisis. We propose a mathematical model for analyzing the impact of fire sales on system-wide losses in a system with multiple financial institutions subject to a macroeconomic stress scenario. Our model emphasize the nonlinear threshold nature of deleveraging, as a result of which the volume of deleveraging is a convex function of initial asset losses. We show that the magnitude of spillover effects due to price-mediated contagion dependson "liquidity-weighted overlaps" of institutional asset holdings. A key concept which emerges from the model is the notion of indirect exposure of a financial institution to an asset class: we show that, when the impact of of fire sales is taken into account, the effective exposure of an institution to an asset class may be found to be much larger than the apparent exposure as revealed by the portfolio holdings alone. We illustrate these observations on a dataset of European banks.
Finally, we show that regulatory risk weights of asset classes may be used as a macroprudential tool for a a decentralized regulation of fire sales risk, by providing incentives to financial institutions to reduce their exposure to this contagion channel without revealing confidential information on institutional portfolio holdings.