Quota Share or Excess of Loss: Reading a Reinsurance Proposal for the Board
A general insurer writes commercial lines with gross written premium of Rs 800 crore, all earned in the year. The loss ratio is 72% and the expense ratio is 27%, of which 11 points is commission paid to agents and 16 points is other underwriting costs. Free reserves are Rs 600 crore and the solvency ratio is 1.65 against a regulatory minimum of 1.50. For next year the board is considering one of two reinsurance options: (a) a 40% quota share with a 32% ceding commission on ceded premium; or (b) a per-risk excess of loss cover of Rs 200 lakh in excess of Rs 100 lakh, rated at 4.5% of gross written premium with one free reinstatement. The broker estimates recoveries under option (b) at Rs 23 crore in an average year. The largest single risk on the books is a Rs 900 lakh petrochemical plant. Management has said it wants the combined ratio below 95%.
1. Compute the net combined ratio under the quota share and explain precisely where the improvement comes from and what it costs.
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Quota share mechanics (Rs crore): ceded premium = 40% x 800 = 320; ceding commission = 32% x 320 = 102.4; net retained premium = 480.
Gross losses = 72% x 800 = 576; ceded losses = 40% x 576 = 230.4; net losses = 345.6, so the net loss ratio is 345.6/480 = 72.0% - unchanged.
Gross expenses = 27% x 800 = 216; less ceding commission received 102.4 = net expenses 113.6; net expense ratio = 113.6/480 = 23.7%.
Net combined ratio = 72.0 + 23.7 = 95.7%, an improvement of 3.3 points on the gross 99%.
Where it comes from. The whole improvement is the gap between the ceding commission (32%) and the expense ratio (27%), 5 points, grossed up over the retained 60%: (32 - 27) x 0.4/0.6 = 3.3. Nothing has been done about the underlying loss ratio - the same 72% is still being written. If the ceding commission were 27%, the net combined ratio would be unchanged at 99%; if it were 24%, the net combined ratio would be 101%.
What it costs. The insurer gives away 40% of premium and 40% of the profit in good years, and its absolute underwriting result falls: gross underwriting loss is Rs 8 crore (99% on 800), net underwriting loss is Rs 20.6 crore (95.7% on 480). The ratio improved while the rupee result got worse - a point that must be stated plainly to the board rather than buried under a better-looking percentage.
2. Evaluate the excess of loss option on the same premium base, using the expected recovery, the rate on line and the loss ratio on the cover. Would it meet the board's 95% target?
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Cost and benefit (Rs crore): reinsurance premium = 4.5% x 800 = 36; expected recovery in an average year = 23; expected net cost = 13, or 1.63 points of the combined ratio. Expected net combined ratio = 72 + 27 + 1.63 = 100.6%. It does not meet the 95% target, and no non-proportional structure on these terms could - the cover cannot fix a 99% gross combined ratio that is driven by the loss ratio and the expense ratio.
Is the price reasonable? Rate on line = 36/200 = 18%. Expected recovery as a percentage of limit = 23/200 = 11.5%. Loss ratio on the cover = 23/36 = 64%. That is not an obviously expensive cover; a reinsurer needs a margin over expected loss plus its own expenses and capital cost, and 64% is within the normal range for a working layer. The rate is not the problem; the gross result is.
What the cover actually buys. Protection against severity, not an improvement in the average result. On the Rs 900 lakh petrochemical risk, the insurer retains Rs 100 lakh plus premium instead of the full Rs 900 lakh - a reduction of Rs 800 lakh in single-risk volatility. Whether that is worth 1.63 points depends on capital: the solvency margin is charged on net retained exposure, so the cover earns capital relief even when its expected cost exceeds its expected recovery.
Do not overlook: the reinstatement is free, which is generous on a working layer and should be tested against a second event; the cover is per risk, so it does nothing for an accumulation of many Rs 150 lakh losses from one event, which is a catastrophe question, not a per-risk question.
3. Recommend a structure to the board and set out the criteria you would use, including the risk-transfer test and the effect on solvency.
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Recommendation: a hybrid, not either/or. Something like 20% quota share plus the per-risk excess of loss. Reasons:
- Neither option meets the 95% target on its own, and the board should be told that no reinsurance purchase can, because the gross loss ratio is 72%. Rate adequacy in commercial lines is the real lever.
- A 40% quota share is too much to give away for a company with free reserves of Rs 600 crore. It halves the retained book, hands 40% of future profits to the reinsurer, and converts the underwriting ratio from 99% to 95.7% only because the ceding commission exceeds the expense ratio.
- The per-risk cover is needed regardless because of the Rs 900 lakh petrochemical exposure. A single total loss without the cover would consume 1.5 times free reserves.
Criteria to apply: risk-transfer adequacy (a quota share with a 32% ceding commission must genuinely transfer significant insurance risk, or it is financing and must be accounted for as such); the effect on the solvency ratio - both structures reduce net premium and net claims, so the required solvency margin falls and the ratio improves, but only the excess of loss reduces the variance of the result; counterparty credit quality and collateral of the reinsurer; reinstatement cost and the price of the second layer; whether the structure supports growth the company actually wants; and the interaction with any catastrophe cover already purchased, to avoid paying twice for the same severity.
Finally, present the board with a rupee result and a ratio for each option, not a ratio alone.