When more is less: Using multiple constraints to reduce tail risk

Gordon J. Alexander, Alexandre M. Baptista, Shu Yan

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Financial institutions suffered large trading losses during the 2007-2009 global financial crisis. These losses cast doubt on the effectiveness of regulations and risk management systems based on a single Value-at-Risk (VaR) constraint. While some researchers have recommended using Conditional Value-at-Risk (CVaR) to control tail risk, VaR remains popular among practitioners and regulators. Accordingly, our paper examines the effectiveness of multiple VaR constraints in controlling CVaR. Under certain conditions, we theoretically show that they are more effective than a single VaR constraint. Furthermore, we numerically find that the maximum CVaR permitted by the constraints is notably smaller than with a single constraint. These results suggest that regulations and risk management systems based on multiple VaR constraints are more effective in reducing tail risk than those based on a single VaR constraint.

Original languageEnglish (US)
Pages (from-to)2693-2716
Number of pages24
JournalJournal of Banking and Finance
Issue number10
StatePublished - Oct 2012

Bibliographical note

Funding Information:
Our paper has benefited from the valuable comments and suggestions of Peter Christoffersen, Basile Maire, an anonymous referee, and session participants at the 2010 Australasian Finance and Banking Conference in Sydney, the 2011 Midwest Finance Association Meeting in Chicago, and the 2011 Financial Management Association Asian Conference in Queenstown. Baptista gratefully acknowledges research support from the School of Business at The George Washington University.

Copyright 2012 Elsevier B.V., All rights reserved.


  • Financial crisis
  • Financial institutions
  • Regulation
  • Risk management
  • Tail risk


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