Choosing between an aggregate stop-loss and a larger quota share on group IP
You are the capital actuary of a UK health insurer. The group income protection account has best-estimate reserves of £310m and a Solvency UK SCR of £140m, of which £70m is premium and claims risk. The account has 11 large schemes; the largest, a 14,000-member scheme concentrated in one occupational sector, is 31% of premium. Management is choosing between three options: (a) an aggregate stop-loss over group IP claims in excess of £26m up to £60m, quoted at £9.4m a year with one reinstatement and a 36-month minimum term; (b) increasing the existing quota share from 25% to 40%, which carries a 26% ceding commission and 20% profit commission above a 92% loss ratio; (c) retaining the risk. The capital model estimates the stop-loss would cut premium and claims risk by 35% and lapse risk by 5%, but the model has not been calibrated to the treaty. The reinsurer is rated A-, and the board targets a 12% return on equity.
1. Compare the three options on a risk-adjusted basis. Set out the calculation framework, the key assumptions and the limitations of the 35% figure.
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Framework. For each option, compute expected cost, capital released, and return on the capital that remains.
- Stop-loss. Premium £9.4m plus the time value of the 36-month lock-in. Expected recoveries must be estimated from the claims distribution, not the mean: if the attachment is around the 75th percentile, expected recoveries may be £4-6m, so the expected net cost is £3-5m a year. Capital released ≈ 0.35 × £70m = £24.5m, plus a diversification effect from the lapse-risk reduction. Cost per unit of capital released = net cost/£24.5m. That is the number to compare with the 12% ROE hurdle and the group's cost of capital.
- Quota share 25% → 40%. Cedes a further 15% of premium, claims and reserves. Cost is the margin given away, net of the 26% ceding commission and the profit commission, which returns value in good years and is worth nothing in bad ones. It reduces capital proportionally and more predictably than the stop-loss, but it also reduces diversification benefit if the account is being used to diversify other group risks.
- Retain. Zero premium cost, full £140m SCR, and full exposure to the single-scheme concentration.
Limitations of the 35%. The model was not calibrated to the treaty: it will not know the attachment point, the reinstatement structure, the claims definition or the timing of recoveries. It probably applies the reduction as if the treaty paid an instantaneous shock, when the SCR is a one-year shock and the treaty pays on incurred claims over that year. Treat 35% as an upper bound and stress it at 20-25%. Also, the A- rating means recoverables attract a counterparty charge in the SCR; a default scenario should be modelled explicitly given the size of the cession relative to the reinsurer's capital.
2. What basis risk does the aggregate stop-loss carry, and how would you tighten the treaty terms?
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Sources of basis risk.
- Definition risk. The treaty triggers on its own definition of a claim - usually paid claims, or incurred with a reporting lag - while the insurer's SCR and reserving use incurred. A large late-reported claim can fall in the wrong period.
- Aggregation risk. The attachment of £26m is fixed in nominal terms for three years. With IP claims inflation and a growing scheme, the probability of recovery rises while the limit does not.
- Event definition. If the treaty aggregates claims by event, a pandemic, a sector-wide redundancy wave or a single employer's closure may be treated as one event and either swept into, or excluded from, the cover in an unexpected way.
- Scope mismatch. The largest scheme is 31% of premium and sector-concentrated; if the treaty excludes or sub-limits that scheme, the cover does not address the risk the board is actually worried about.
- Recovery timing and credit. The insurer recognises the capital benefit immediately; the cash arrives months later from an A- counterparty with no collateral.
Tightening. Align the claims definition with the internal basis; index the attachment and limit annually; write an explicit aggregation clause covering multiple schemes affected by one cause; secure collateral or a trust fund, or cap the cession to any single reinsurer; require a commutation option at each anniversary; reduce the minimum term to 24 months or negotiate a break clause with a pre-agreed exit cost; and confirm the reinstatement premium is pre-agreed rather than at the reinsurer's option. Model a default scenario as part of the recommendation, not as an afterthought.
3. Make a recommendation to the board and explain how you would present the trade-off, including the treatment of the model limitations.
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Recommendation. A blended solution, not a binary choice. Increase the quota share modestly - to around 32-35% - which reduces the concentration and the premium and claims risk proportionally and cheaply, given the ceding and profit commission. Then place a smaller aggregate stop-loss, attached higher and with a lower limit, to protect against the tail from the concentrated scheme. Retain the rest.
Why not (a) alone. It buys tail protection but leaves the single-scheme concentration intact, locks pricing for 36 months when IP claims inflation is uncertain, and relies on an uncalibrated 35% capital benefit that I would stress down to 20-25% before presenting it.
Why not (b) alone. It is predictable and cheap in capital terms, but it gives away 15% of the upside permanently, including the profit commission that the current treaty generates.
Why not (c). The concentration is 31% of premium in one sector. Retaining it is a board-level risk appetite decision, not a capital-efficiency one.
Presenting it. Lead with the concentration, not the treaty. Show a one-page table: expected net cost, capital released, cost per unit of capital released, ROE impact against the 12% target, and the downside scenario in each case. State explicitly that the 35% is an estimate pending calibration, show the result at 20% and 35%, and show the counterparty-default scenario. Give the board a clear recommendation with the conditions attached, and record the decision and the assumptions in the ORSA and the capital plan.