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Published in:
Returns and the Gaussian Hypothesis Read chapter Read first chapter

2020 | OriginalPaper | Chapter

7. Risk Measures and Capital Allocation

Author : Pierre Brugière

Published in: Quantitative Portfolio Management

Publisher: Springer International Publishing

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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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previous chapter Performance and Diversification Indicators
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Metadata
Title
Risk Measures and Capital Allocation
Author
Pierre Brugière
Copyright Year
2020
Book
Quantitative Portfolio Management

Print ISBN: 978-3-030-37739-7

Electronic ISBN: 978-3-030-37740-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-37740-3_7