WP 2013-04 The Marginal Cost of Risk, Risk Measures, and Capital Allocation

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Published in 2016 in Management Science, Volume 62, Issue 5.

ABSTRACT. Financial institutions define their marginal cost of risk on the basis of the gradients of arbitrarily chosen risk measures. We reverse this approach by calculating the marginal cost for a profit-maximizing firm with risk-averse counterparties, and then identifying the risk measure delivering the correct marginal cost. The resulting measure is a weighted average of three parts, each corresponding to one of three drivers of firm capitalization: (1) An external risk measure reflecting regulatory concerns; (2) Value-at-Risk emerging from shareholder concerns; and (3) a novel risk measure that encapsulates counterparty preferences in default states. Our results demonstrate that risk measures used for pricing and performance measurement should be chosen based on economic fundamentals rather than mathematical properties.