Optimization of Conditional Value-at-Risk
R. Tyrrell Ro ckafellar
1
and Stanislav Uryasev
2
A new approach to optimizing or hedging a p ortfolio of nancial instruments to reduce risk is
presented and tested on applications. It fo cuses on minimizing Conditional Value-at-Risk (CVaR)
rather than minimizing Value-at-Risk (VaR), but portfolios with lowCVaR necessarily havelow
VaR as well. CVaR, also called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway
considered to b e a more consistent measure of risk than VaR.
Central to the new approach is a technique for p ortfolio optimization which calculates VaR
and optimizes CVaR simultaneously. This technique is suitable for use byinvestment companies,
brokerage rms, mutual funds, and any business that evaluates risks. It can be combined with
analytical or scenario-based metho ds to optimize p ortfolios with large numb ers of instruments, in
which case the calculations often come down to linear programming or nonsmo oth programming.
The metho dology can be applied also to the optimization of p ercentiles in contexts outside of
nance.
Septemb er 5, 1999
Correspondence should b e addressed to: Stanislav Uryasev
1
UniversityofWashington, Dept. of Applied Mathematics, 408 L Guggenheim Hall, Box 352420, Seattle, WA
98195-2420, E-mail: rtr@math.washington.edu
2
University of Florida, Dept. of Industrial and Systems Engineering, PO Box 116595, 303 Weil Hall, Gainesville,
FL 32611-6595, E-mail: uryasev@ise.u.edu
, URL: http://www.ise.u.edu/uryasev
1
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