Abstract
Risk measures are widely used in risk management, and to calculate capital requirements when investing or conducting banking or insurance activities. In this chapter, we study risk measures in the context of asset allocation, and explain the notions of Value at Risk , Expected Shortfall and 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 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.
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References
Abada, P., Benitob, S., & Lopez, C. (2014). A comprehensive review of value at risk methodologies. The Spanish Review of Financial Economics, 12(1), 15–32.
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.
Bank for International Settlement. (2016, January). Standards: Minimum capital requirements for market risk. ISBN 978-92-9197-416-0 (online).
Bank for International Settlement. (2019, Jan). Minimum capital requirements for market risk (136 pp.). Revised Feb 2019. https://www.bis.org/bcbs/publ/d457.pdf.
Bank for International Settlement. (2019). Instructions for Basel III monitoring. July 2019. https://www.bis.org/bcbs/qis/biiiimplmoninstr_jul19.pdf.
Barone-Adesi, G., & Giannopoulos, K. (2000). Non-parametric VaR techniques. Myths and realities. Economic Notes, 30, 167–181.
Boonen, T. J. (2017). Solvency II solvency capital requirement for life insurance companies based on expected shortfall. European Actuarial Journal, 7(2), 405–434.
Cai, Z., Fang, Y., & Tian, D. (2018). Econometric modeling of risk measures: A selective review of the recent literature. Working Paper, October 10, 2018.
Davidson, A. C., & Hinkley, B. V. (1997). Bootstrap methods and their application. Cambridge Series in Statistical and Probabilistic Mathematics (592 pp.). Cambridge: Cambridge University Press.
Dowd, K. (2005). Measuring market risk (2nd ed., 410 pp.). New York: Wiley.
Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap (430 pp.). London: Chapman and Hall. New edition, due date December 18, 2019.
Engle, R. F., & Manganelli, S. (2001). Value at risk models in finance. ECB Working Paper, No. 75, August 2001.
Lie, H., Li, Y., Fan, X., Zhou, Y., Jin, Z., & Liu, Z. (2012). Approaches to VaR, Document Standford University.
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Brugière, P. (2020). Risk Measures and Capital Allocation. In: Quantitative Portfolio Management . Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-37740-3_7
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DOI: https://doi.org/10.1007/978-3-030-37740-3_7
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