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.
Aggregation produces a total capital below the sum of standalone capitals, and 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 exactly like a line that concentrates it. Euler allocation gives each line its marginal contribution to the aggregate risk measure, it is additive by construction, and it is 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 not technical, it is political: a line allocated under Euler on a 99% TVaR carries the capital of the scenarios where the whole group suffers, so a catastrophe line is 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.
allocation d'Euler, Euler allocation, répartition du capital par branche, contribution marginale au capital