Risk Management for Whales: Adjusting Risk Measures to Liquidity Risk

Lakshithe Wagalath (IESEG School of Management, France):

Abstract: Quantitative models commonly used in financial risk management have mainly focused on the statistical modeling of variations in the (mark-to-) market value of financial portfolios, in order to estimate a risk measure – such as Value-at-Risk or Expected shortfall – related to market losses over a given time horizon. These risk measures are then used for determining for example capital requirements or margin requirements in order to provision for losses in extreme risk scenarios. Typically, when such losses materialize, the financial institution is led to liquidate a sizable portion of its portfolio and the realized liquidation value may be quite different from the (pre-liquidation) market value used in the model. The difference – which represents the liquidation cost – can be significant if the portfolio contains large, concentrated positions. Not accounting for this liquidation cost in risk calculations may result in a serious underestimation of portfolio losses in a stress scenario.

In this short course, we propose a portfolio risk model which integrates market risk with liquidation costs. The model provides a framework for computing liquidation-adjusted risk measures such as Liquidation-adjusted VaR (LVaR). Calculation of liquidation-adjusted Value-at-Risk (LVaR) for simulated and real-life examples reveals a substantial impact of liquidation costs on portfolio risk for portfolios with large concentrated positions.