Bank Risk Management with Value-at-Risk and Stress Testing: An Alternative to Conditional Value-at-Risk?

Recognizing the drawbacks of Value-at-Risk (VaR), researchers have advocated the use of Conditional Value-at-Risk (CVaR). However, the current popularity of VaR and Stress Testing (ST) among bank regulators raises the question of whether a risk management system based on both VaR and ST constraints is an effective alternative to a system based on CVaR. We show that when the VaR and ST bounds are appropriately chosen and short selling is disallowed, the constraints lead to the selection of portfolios with relatively small CVaRs. However, when short selling is allowed, the constraints may not lead to the selection of such portfolios. Since large banks often have short positions in their trading books, regulators should be aware that the joint use of VaR and ST is unreliable in controlling CVaR for such