Encyclopedia of Financial Models, 3 Volume Set

Average Value-at-Risk

STOYAN V. STOYANOV, PhD

Professor of Finance at EDHEC Business School and Head of Research for EDHEC Risk Institute-Asia

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair-Professor, Department of Applied Mathematics & Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Despite the fact that the value-at-risk (VaR) measure has been adopted as a standard risk measure in the financial industry, it has a number of deficiencies recognized by financial professionals. It is not a coherent risk measure. This is because it does not satisfy the subadditivity property requirement of a coherent risk measure. That is, there are cases in which the portfolio VaR is larger than the sum of the VaRs of the portfolio constituents, supporting the view that VaR cannot be used as a true risk measure. Unlike VaR, the average value-at-risk measure (AVaR)—also referred to as conditional value-at-risk and expected shortfall—is a coherent risk measure and has other advantages that result in its greater acceptance in risk modeling.

The average value-at-risk (AVaR) is a risk measure that is a superior alternative to VaR. Not only does it lack the deficiencies of VaR, but it also has an intuitive interpretation. There are convenient ways for computing and estimating AVaR, which allows its application in optimal portfolio problems. Moreover, it satisfies all axioms of ...