298 Optimizing Optimization
away from solving the original problem by solving related but yet different
problems. Each of their solutions showed economic and sometimes statistical
shortcomings that could not be reconciled with basic economic axioms. While
Acerbi (2004) tried to fix many of theses issues, he really (willingly or unwill-
ingly) reinstated expected utility maximization. Science works, but sometimes it
works very slowly. Given these implications, it is of little surprise that spectral
risk measures had yet little impact on both the theoretical as well as the applied
literature. After all, investors are well advised to read the original literature of
the 1950s, or its more recent reincarnations like Kritzman and Adler (2007).
There is no need for a new framework. Expected utility maximization is the
route to follow. The implementation problem will be identical, but the concep-
tional flaw of CVaR can be avoided. Computationally, we can always piece-
wise linearize a given utility function and use linear programming technology.
12.7 Conclusion
We split our critique on CVaR into implementation and concept issues. While
implementation issues can be overcome at the cost of sophisticated statisti-
cal procedures that are not yet widely available, they pose a strong objection
against current na ï ve use of CVaR. Estimation error sensitivity amplified by
approximation error and difficulties in modeling fast updating scenario matri-
ces for nonnormal multivariate return distributions will stop many practition-
ers from applying CVaR. More limiting in our view, however, is the inability
of CVaR to integrate well into the way investors think about risk. Averaging
across small and extremely large losses, i.e., giving them the same weight, does
not reflect rising risk aversion against extreme losses, which is probably the
most agreeable part of expected utility theory.
Acknowledgment
I thank K. Scherer for many valuable suggestions. All errors remain mine.
References
Acerbi , C. ( 2002 ). Spectral measures of risk: A coherent representation of subjective
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Artzner , Ph. , Delbaen , F. , Eber , J.-M. , & Heath , D. ( 1997 ). Thinking coherently. RISK ,
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Kahnemann , D. , & Tversky , A. ( 1979 ). Prospect theory: An analysis of decision under
risk. Econometrica , 47 ( 2 ) , 263 – 291.
Kritzman , M. , & Adler , T. ( 2007 ). Mean variance versus full scale optimisation: In and
out of sample. Journal of Asset Management.