Coherent Moment-Based Approximations of Risk Functionals

33 Pages Posted: 31 Oct 2013

Date Written: August 28, 2013


The paper introduces a new, moment-based representation of version independent, coherent risk functionals for distributions with a finite second moment. The representation is based on L-moments. We analyze the second- and the third-order approximations and provide a method for constructing coherent approximations with the first few moments of the distribution. The method can be applied to coherent and non-coherent risk functionals and is interpreted in terms of a weighted average of particular Bayesian versions of Conditional Value-at-Risk. We formulate a conservative risk functional and a minimax portfolio construction problem which is non-parametric, convex, and exhibits a relative statistical robustness of the optimal solution compared to the classical utility-based approach. The developed approach bridges the gap between the intuitive utility-based higher-order moment portfolio construction and the formal construct of coherent risk functionals.

Keywords: coherent risk functionals, conditional value-at-risk, value-at-risk, L-moments, portfolio construction, convexity.

JEL Classification: C46 , G11, G17

Suggested Citation

Stoyanov, Stoyan Veselinov, Coherent Moment-Based Approximations of Risk Functionals (August 28, 2013). Available at SSRN: or

Stoyan Veselinov Stoyanov (Contact Author)

Charles Schwab ( email )

101 Montgomery Street (120K-15)
San Francisco, CA 94104
United States

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