Title: Risk budgeting and Value-at-Risk

Authors: Keith Pilbeam, Rehan Noronha

Addresses: City University, Northampton Square, London EC1V 0HB, UK. ' Barclays Commercial Bank, 1 Churchill Place E14 5HP, UK

Abstract: Value-at-Risk (VaR) is a popular risk-metric for reporting financial exposure, for evaluating fund/manager performance and for regulatory disclosures. Yet, VaR is not a coherent risk measure because it is not sub-additive. This paper applies the methodology of risk budgeting to determine if VaR qualifies as a coherent risk measure. We show that the tools of risk budgeting allow VaR to be treated as a coherent risk measure, even though it does not restore sub-additivity. The main finding is that the additional analysis provided by risk budgeting means that VaR is a useful tool even if it is not sub-additive.

Keywords: value-at-risk; VaR; risk budgeting; risk management; risk attribution; risk decomposition; risk measures.

DOI: 10.1504/IJMEF.2008.019219

International Journal of Monetary Economics and Finance, 2008 Vol.1 No.2, pp.149 - 161

Published online: 02 Jul 2008 *

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