Reinsurance structure for a new term product
A life insurer is launching a 10-year level term product with a £300,000 sum assured and annual premium of £420. Expected mortality is 0.12% in year 1, rising 5% a year; lapses are 8% in year 1 and 6% thereafter. Initial commission is 120% of first premium, underwriting and admin costs are £250 per policy, and renewal expenses are £60 a year. The risk discount rate is 6%. The insurer has limited capital and wants to grow new business. It is considering 30% quota-share reinsurance with 18% ceding commission on gross premium, or a 50% quota share with 12% ceding commission on gross premium. The reinsurer will also offer a stop-loss cover above 130% of expected claims for a risk premium. The CFO wants to know which structure best balances new business strain, profit and risk.
1. Calculate the approximate first-year new business strain with and without the 30% quota share, and assess whether the reinsurance is value-accretive.
Read the worked answer
Without reinsurance: premium £420, expected claims 0.12% x £300,000 = £360, initial commission 120% x £420 = £504, admin £250. First-year net cash flow = 420 - 360 - 504 - 250 = -£694 per policy.
With 30% quota share: retained premium is 70% x £420 = £294; retained claims are 70% x £360 = £252; ceding commission is 18% x £420 = £75.6, so retained initial commission is £504 - £75.6 = £428.4; admin remains £250. Net cash flow = 294 - 252 - 428.4 - 250 = -£636.4. The improvement is only £57.6 per policy, about 8% of the strain.
The strain is dominated by initial commission and admin, not claims. Quota share helps only if the ceding commission is high enough. The 30% structure is mildly value-accretive on first-year cash flow, but the firm cedes 30% of future profits. Further analysis should compare the present value of retained profits, capital relief and return on capital, not just the first-year strain.
2. Recommend which reinsurance structure to choose, considering capital, profit sharing and risk, and explain what further analysis is needed.
Read the worked answer
The 50% quota share with 12% ceding commission gives: retained premium £210, retained claims £180, ceding commission 12% x £420 = £50.4, retained initial commission £453.6, admin £250. Net cash flow = 210 - 180 - 453.6 - 250 = -£673.6. It is worse than the 30% structure on first-year strain because the ceding commission is lower, even though it cedes more risk.
On these terms, the 30% quota share is the better balance: it reduces strain modestly and retains more profit. However, the firm should negotiate a higher ceding commission or use a stop-loss cover for catastrophic mortality. Stop-loss protects the tail but may not reduce new business strain and adds a risk premium.
Further analysis should include the present value of profits over 10 years, new business strain and capital consumption, internal rate of return, sensitivity to mortality, lapses and expenses, reinsurer credit risk, and the effect on the firm's risk appetite. A structure that looks best on first-year strain may not be best on value or risk.