The Branch Combined Ratio Squeeze
A UIIC branch writes general insurance business in two lines. Last year it had 2,400 policies, an average premium of ₹9,500 per policy, 180 claims and an average claim of ₹85,000. Commission was 10% of premium and branch expenses were 22% of premium. For the coming year the branch projects that the number of policies will fall by 5% and the average premium per policy will rise by 8%, while the number of claims will fall in line with the policy count and average claim severity will rise by 12%. The regional office wants a combined ratio (loss ratio plus expense ratio plus commission ratio) of 99% or better, and will not allow the expense or commission rates to change. The branch manager must decide whether the projected average premium increase is sufficient, and if not, what further increase in average premium is needed, assuming the policy count and claim assumptions stay unchanged.
1. Compute the current loss ratio and combined ratio.
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Current premium = 2,400 × ₹9,500 = ₹2,28,00,000. Current claims = 180 × ₹85,000 = ₹1,53,00,000. Loss ratio = 1,53,00,000 ÷ 2,28,00,000 = 0.67105, i.e. 67.11%. Expense ratio = 22% and commission ratio = 10%, so combined ratio = 67.11 + 22 + 10 = 99.11%.
The branch is already marginally above the 99% target, with an underwriting loss of about 0.11% of premium.
2. Compute the projected loss ratio and combined ratio for the coming year.
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Policies fall by 5%: 2,400 × 0.95 = 2,280. Average premium rises by 8%: ₹9,500 × 1.08 = ₹10,260. Projected premium = 2,280 × ₹10,260 = ₹2,33,92,800.
Claims count falls with policies: 180 × 0.95 = 171. Average claim rises by 12%: ₹85,000 × 1.12 = ₹95,200. Projected claims = 171 × ₹95,200 = ₹1,62,79,200.
Projected loss ratio = 1,62,79,200 ÷ 2,33,92,800 = 0.69594, i.e. 69.59%. Combined ratio = 69.59 + 22 + 10 = 101.59%. The projected premium increase is therefore not sufficient; the branch would miss the target by about 2.59 percentage points.
3. What further increase in average premium is needed to reach the 99% combined ratio?
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With expenses and commission fixed at 32% combined, the loss ratio must be 99% − 32% = 67%. Required premium = projected claims ÷ 0.67 = ₹1,62,79,200 ÷ 0.67 = ₹2,42,97,313 (approximately).
Projected premium is ₹2,33,92,800. Additional premium needed = ₹2,42,97,313 − ₹2,33,92,800 = ₹9,04,513.
Additional increase over the projected premium = 9,04,513 ÷ 2,33,92,800 = 0.03867, i.e. about 3.87%. The average premium would need to be about ₹10,657 per policy (₹2,42,97,313 ÷ 2,280), which is roughly 3.87% above the already increased projection of ₹10,260. A useful check: at that premium the loss ratio is 67%, and 67 + 22 + 10 = 99%.