capital allocation and diversification benefit
Three friends share a flat. Together their total rent, food and bills are far less than what each would pay living alone — sharing creates a saving. But then comes the awkward dinner-table question: how do we split the shared saving fairly, given that one cooks every night and another travels half the month? Capital allocation and the diversification benefit are exactly this pair of ideas for an insurer: combining many lines of business needs less capital than the lines would alone (the saving), and then that combined capital must be split back across the lines (the allocation).
The diversification benefit is the gap between the sum of standalone capital and the capital needed for the whole. If three business lines would individually need 60, 50 and 20 — total 130 — but together, because their bad years rarely coincide, the combined requirement is only 100, then 30 is the diversification benefit. It exists because risks that are not perfectly correlated partly cancel. Capital allocation is then the reverse exercise: taking that combined 100 and assigning a share to each line, so that each product can be measured for return on the capital it truly consumes. Common methods include the marginal (Euler) approach — charge each line for how much it adds to the total — and proportional or covariance-based splits; the choice matters because it decides which products look profitable.
This matters because allocation is the link between the capital number and real management decisions: pricing must recover the cost of capital each product uses, and performance is judged on return relative to allocated capital. The deep caveat is that the diversification benefit is real but fragile — it depends entirely on the assumed correlations, and in a genuine crisis correlations tend to jump toward one (everything falls together), so the saving you counted on can evaporate exactly when you need it. Allocating it back is also not unique: different reasonable methods give different answers, so capital allocation is partly an art with consequences, not a single correct number.
A multiline insurer needs 130 if its motor, property and life lines stood alone, but only 100 combined — a 30 diversification benefit. It then allocates the 100 back: motor gets charged less because it diversifies well against life, life slightly more, sharpening which products must raise prices to earn their capital.
Combining cuts total capital; allocating the saving back guides pricing.
Diversification benefit depends entirely on assumed correlations, which often spike toward one in a real crisis — so the saving can vanish exactly when needed.