The Marginal Cost of Risk, Risk Measures, and Capital Allocation

41 Pages Posted: 15 Mar 2011 Last revised: 28 May 2013

See all articles by Daniel Bauer

Daniel Bauer

University of Alabama

George H. Zanjani

Georgia State University - Risk Management & Insurance Department

Date Written: May 2013

Abstract

The Euler (or gradient) allocation technique defines a financial institution’s marginal cost of a risk exposure via calculation of the gradient of a risk measure evaluated at the institution’s current portfolio position. The technique, however, relies on an arbitrary selection of a risk measure. We reverse the sequence of this approach by calculating the marginal costs of risk exposures for a profit maximizing financial institution with risk averse counterparties, and then identifying a closed-form solution for the risk measure whose gradient delivers the correct marginal costs. We compare the properties of allocations derived in this manner to those obtained through application of the Euler technique to Expected Shortfall (ES), showing that ES generally yields economically inefficient allocations.

Keywords: Capital Allocation, Risk Measure, Profit Maximization, Counterparty Risk Aversion

JEL Classification: G20, G22

Suggested Citation

Bauer, Daniel and Zanjani, George H., The Marginal Cost of Risk, Risk Measures, and Capital Allocation (May 2013). Available at SSRN: https://ssrn.com/abstract=1787145 or http://dx.doi.org/10.2139/ssrn.1787145

Daniel Bauer

University of Alabama ( email )

361 Stadium Drive
Tuscaloosa, AL 35487
United States

George H. Zanjani (Contact Author)

Georgia State University - Risk Management & Insurance Department ( email )

P.O. Box 4036
Atlanta, GA 30302-4036
United States
404-413-7464 (Phone)
404-413-7499 (Fax)

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