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Risk Measures and Capital Allocation

In: Quantitative Portfolio Management

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  • Pierre Brugière

    (University Paris Dauphine-PSL)

Abstract

Risk measures are widely used in risk management, and to calculate capital requirements Capital requirement when investing or conducting banking or insurance activities. In this chapter, we study risk measures Risk measure in the context of asset allocation, and explain the notions of Value at Risk Value at risk , Expected Shortfall Expected Shortfall and Return on Risk-Adjusted Capital (RORAC Return on Risk-Adjusted Capital (RORAC) ). We provide some explicit formulas in the Gaussian framework and an example of calculation based on historical data, without any model assumptions. Euler’s formula Euler’s formula is presented, for standard homogeneous risk measures, as well as its applications for capital allocation between risky positions. We also prove that, when the capital is allocated according to Euler’s formula, each position produces the same RORAC.

Suggested Citation

  • Pierre Brugière, 2020. "Risk Measures and Capital Allocation," Springer Texts in Business and Economics, in: Quantitative Portfolio Management, chapter 0, pages 103-123, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-37740-3_7
    DOI: 10.1007/978-3-030-37740-3_7
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