Capital allocation
Distribution of aggregate capital across lines, whose result governs each line's reported return, and where the method changes the conclusions more than the data does.
Michel Denault published Coherent Allocation of Risk Capital in 2001, in the Journal of Risk, carrying the 1953 Shapley value over to capital allocation. The starting problem: aggregation produces a total capital below the sum of standalone capitals. That diversification benefit has to be given back to the lines in order to measure their profitability. Three methods dominate. Pro rata on standalone capital is simple and wrong, because it treats a line that diversifies the portfolio the same way as a line that concentrates it. Euler allocation gives each line its marginal contribution to the aggregate risk measure; it is additive by construction and serves as the reference when the measure is TVaR. The Shapley value, borrowed from game theory, averages marginal contribution over every possible order of entry, which makes it fair but costly beyond a handful of lines. The choice is a matter of internal politics as much as of calculation. A line allocated under Euler on a 99% TVaR carries the capital of the scenarios where the whole group suffers. A catastrophe line is therefore charged far more than under pro rata, and its return on allocated capital collapses with underwriting unchanged.
Non-life group, 2026 profitability review, aggregate capital 712M EUR. Under pro rata, the natural catastrophe line receives 96M EUR and shows a 14% return on allocated capital. Under Euler allocation on a 99% TVaR it receives 171M EUR, because it appears in almost every group tail scenario, and its return falls to 7.9%, below the 9% internal cost of capital. No policy changed.
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