The marginal cost of risk, risk measures, and capital allocation

Financial institutions use risk measures to calculate the marginal capital cost when expanding the exposure to a certain risk within their portfolio. We reverse this approach by calculating the marginal cost based on economic fundamentals for a profit-maximizing firm and then by identifying the risk measure delivering the correct marginal cost. The resulting measure depends on context. Whereas familiar measures can be recovered in some circumstances, other circumstances yield unfamiliar forms. In all cases, the risk preferences of the institution's claimants determine how the correct risk measure must weight various default states. Our results demonstrate that risk measures used for pricing and performance measurement should be chosen based on economic fundamentals and may not necessarily adhere to the mathematical properties typically imposed in the literature. Keywords: capital allocation; risk measure; profit maximization; counterparty risk History: Received May 15, 2013; accepted January 16, 2015, by Jerome B. Detemple, finance. Published online in Articles in Advance October 15, 2015.
1. Introduction Risk measures are widely used by financial institutions for pricing and performance measurement. (1) The question of which measure to use is thus of great practical importance and [...]