Journal of Risk

This issue of The Journal of Risk touches on several facets of an integrated financial risk management system within a firm. They include regulatory capital requirements, risk metric estimation and optimization, internal incentives, and data sufficiency and integrity. In the first paper in this issue, "A Fourier approach to the computation of conditional value-at-risk and optimized certainty equivalents", Samuel Drapeau, Michael Kupper and Antonis Papapantoleon make use of the Fourier transform technique to estimate conditional value-at-risk (CVaR) through specific law-invariant risk measures: namely, optimized certainty equivalents. Through this approach, the computational burden of CVaR estimation is significantly reduced, making this coherent risk measure very competitive compared with the popular, but not coherent, value-at-risk measure. Regulatory capital is set at an aggregate level for a given financial institution and is explicitly affected by the risk measure in use. In turn, this capital can be split across various subportfolios for performance evaluation. This disaggregation is intimately linked with required mathematical characteristics - such as continuity, positive homogeneity or Gâteaux differentiability - of the related risk measure.

In the second paper in this issue, "Suitability of capital allocations for performance measurement", Eduard Kromer and Ludger Overbeck relax some of these requirements to analyze the appropriateness of certain practical performance metrics. They further generalize their approach to cooperative game-theoretic settings and show how these results apply with minimal assumptions on risk measures. The value of the risk measure for a portfolio depends critically on the estimate of the covariance between its different components.

In our third paper, "General covariance, the spectrum of Riemannium and a stress test calculation formula", Piotr Chmielowski proposes a first-order perturbation approach based on random matrix theory to test the robustness of the covariance matrix, which is then illustrated on a relative-value portfolio of crude oil futures. The use of derivatives, such as options, can alter the risk-return trade-off of an equity portfolio in very significant ways.

In the fourth and final paper in the issue, "Modeling a risk-based criterion for a portfolio with options", Geng Deng, Tim Dulaney and Craig McCann propose using a quadratic criterion to optimize optioned portfolios. Their approach is shown to be computationally efficient and to be particularly well-suited to the scenario-based margins required by the Chicago Mercantile Exchange.

Farid AitSahlia
Warrington College of Business Administration,
University of Florida

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