Five Lines of Business and a One-Off Marine Loss
A regional office reviews five lines of business for the year just ended. Premium collected (₹ crore), claims paid (₹ crore) and management expenses (₹ crore) are: Fire 480, 288, 144; Marine 320, 224, 96; Motor 900, 675, 162; Health 600, 480, 150; Miscellaneous 200, 110, 50. The board's instruction is that the regional combined ratio must come down, and the only measure cleared for next year is a 10 per cent cut in management expenses in every line, with premium rates and claims experience assumed unchanged. One marine claim of ₹64 crore, arising from a single port fire, is included in the marine claims figure, and the reinsurer treats it as a one-off event. The regional manager also has ₹50 crore of additional capital to deploy and must decide which line to grow, without breaching a 100 per cent combined-ratio ceiling in any line.
1. Compute the combined ratio for each line before and after the 10 per cent expense cut, and for the region as a whole. Which line is still above 100 per cent?
Read the worked answer
Combined ratio = (claims + expenses) ÷ premium.
| Line | Premium | Claims | Expenses | CR now | Expenses after 10% cut | CR after cut |
|---|---|---|---|---|---|---|
| Fire | 480 | 288 | 144 | 432/480 = 90.0% | 129.6 | 417.6/480 = 87.0% |
| Marine | 320 | 224 | 96 | 320/320 = 100.0% | 86.4 | 310.4/320 = 97.0% |
| Motor | 900 | 675 | 162 | 837/900 = 93.0% | 145.8 | 820.8/900 = 91.2% |
| Health | 600 | 480 | 150 | 630/600 = 105.0% | 135.0 | 615/600 = 102.5% |
| Misc | 200 | 110 | 50 | 160/200 = 80.0% | 45.0 | 155/200 = 77.5% |
| Region | 2500 | 1777 | 602 | 2379/2500 = 95.16% | 541.8 | 2318.8/2500 = 92.75% |
Health is the only line still above 100 per cent (102.5%) after the expense cut. The region moves from 95.16% to 92.75%, a gain of about 2.4 percentage points, with ₹60.2 crore of expense saved. Note the trap: the region already looks compliant at 95.16%, so a manager who only reads the regional number will miss that one line is loss-making and is being cross-subsidised.
2. Health must be brought to exactly 100 per cent. How much claims reduction is needed, and can premium growth alone achieve the target?
Read the worked answer
Claims route. After the cut, Health has expenses of ₹135 crore and premium of ₹600 crore. For CR = 100%: claims + 135 = 600, so claims must be ₹465 crore. Claims are ₹480 crore, so the required reduction is ₹15 crore, i.e. 15/480 = 3.125% of Health claims. Alternatively, the loss ratio must fall from 80% to 77.5%.
Premium route - it fails, and this is the point of the question. Let extra premium be X with claims and expenses scaling proportionally (loss ratio 80%, expense ratio 25%). New CR = (0.80(600+X) + 0.25(600+X)) / (600+X) = 1.05 - unchanged at 105% before the cut, or 102.5% after it. Growth in a proportionally loss-making line simply enlarges the loss in absolute rupees.
What would work. Either (a) a rate correction large enough to move the loss ratio itself - with every 1 percentage point of loss-ratio improvement worth about ₹6 crore of premium at this scale - or (b) claims control: provider tariffs, pre-authorisation discipline, claim-document audits. Only these change the ratio; expense cuts and volume growth do not.
Recommendation to the manager: set Health a hard 3.2% claims-reduction target before approving any premium growth, otherwise the ₹50 crore will deepen the deficit.
3. Marine shows a 100 per cent combined ratio, the worst after Health. Should marine be treated as a problem line, and how does the answer shape the ₹50 crore deployment?
Read the worked answer
Recompute marine excluding the one-off. Marine claims of ₹224 crore include ₹64 crore from a single port fire. Excluding it: claims = ₹160 crore, expenses = ₹96 crore, so CR = 256/320 = 80% now and (160 + 86.4)/320 = 77% after the expense cut - the second-best line in the book.
Judgement. Marine is not an underwriting problem; the reported 100 per cent is a catastrophe artefact. Treating it as a problem line would be a double error: it would trigger rate increases in a profitable portfolio (driving away good business) while the real issue - the size of the catastrophe exposure and whether the treaty reinstatement was correctly charged - goes unaddressed. The correct follow-ups are catastrophe loading in pricing, checking that the ₹64 crore loss was charged to the reinsurer rather than retained, and tracking the ex-cat ratio separately for at least three years.
Deployment of ₹50 crore. Rank by sustainable combined ratio and by capacity to absorb growth: Fire (87%) and Miscellaneous (77.5%) are the strongest, but Misc is small and may not absorb capital; Marine (77% ex-cat) can absorb premium but only with cat cover in place. Motor (91.2%) is acceptable but thin. Health should receive no growth capital until the 3.2% claims reduction is delivered, because growth at 102.5% converts every rupee of new premium into a known loss. The decision therefore depends on the ex-cat view of marine and on the loss ratio of each line, not on the headline combined ratio.