Risk‐return optimization with different risk‐aggregation strategies

Stan Uryasev (University of Florida, Gainesville, Florida, USA)
Ursula A. Theiler (Risk Training, Kleinmachnow, Germany)
Gaia Serraino (American Optimal Decisions, Inc., Austin, Texas, USA)

Journal of Risk Finance

ISSN: 1526-5943

Publication date: 2 March 2010



New methods of integrated risk modeling play an important role in determining the efficiency of bank portfolio management. The purpose of this paper is to suggest a systematic approach for risk strategies formulation based on risk‐return optimized portfolios, which applies different methodologies of risk measurement in the context of actual regulatory requirements.


Optimization problems to illustrate different levels of integrated bank portfolio management has been set up. It constrains economic capital allocation using different risk aggregation methodologies. Novel methods of financial engineering to relate actual bank capital regulations to recently developed methods of risk measurement value‐at‐risk (VaR) and conditional value‐at‐risk (CVaR) deviation are applied. Optimization problems with the portfolio safeguard package by American Optimal Decision (web site: www.AOrDA.com) are run.


This paper finds evidence that risk aggregation in Internal Capital Adequacy Assessment Process (ICAAP) should be based on risk‐adjusted aggregation approaches, resulting in an efficient use of economic capital. By using different values of confidence level α in VaR and CVaR, deviation, it is possible to obtain optimal portfolios with similar properties. Before deciding to insert constraints on VaR or CVaR, one should analyze properties of the dataset on which computation are based, with particular focus on the model for the tails of the distribution, as none of them is “better” than the other.

Research limitations/implications

This study should further be extended by an inclusion of simulation‐based scenarios and copula approaches for integrated risk measurements.


The suggested optimization models support a systematic generation of risk‐return efficient target portfolios under the ICAAP. However, issues of practical implementation in risk aggregation and capital allocation still remain unsolved and require heuristic implementations.



Uryasev, S., Theiler, U. and Serraino, G. (2010), "Risk‐return optimization with different risk‐aggregation strategies", Journal of Risk Finance, Vol. 11 No. 2, pp. 129-146. https://doi.org/10.1108/15265941011025161

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