Insurance unit economics: the combined ratio at work
Build an insurer's profit from premiums, claims, expenses, and investment income, and see what reinsurance keeps off the books.
Industry brief, with a one-minute summary: InsuranceKey takeaways
- An insurer's profit is premiums minus claims minus expenses, plus investment income.
- For term life, the basic price is the chance of death times the amount paid (the sum assured), plus a loading for expenses and profit.
- Reinsurance changes what the insurer keeps.
Key idea
An insurer's profit is premiums minus claims minus expenses, plus investment income. Small moves in the loss ratio change profit a lot, because claims are by far the biggest cost.
Worked case
Profit of a motor insurer in Saudi Arabia
The prompt
A motor insurer in Saudi Arabia earns premiums of SAR 1,000 million in a year. Claims are SAR 720 million, commissions SAR 100 million, and administration costs SAR 130 million. It holds on average SAR 1,500 million of investments for future claims and earns 4 percent on them. Calculate the loss, expense, and combined ratios and the profit before tax. Then say what happens if repair costs push claims up by 5 percentage points of premium.
The structure
- Insurer profit before tax
- Underwriting result = premiums minus claims minus expenses
- Investment income = invested assets x yield
- Ratios: loss, expense, combined
Working it through
1. Loss ratio
Claims divided by premiums.
Loss ratio (percent):720 ÷ 1,000 × 100 = 722. Expense ratio
Commissions plus administration, divided by premiums.
Expense ratio (percent):(100 + 130) ÷ 1,000 × 100 = 233. Combined ratio
Loss ratio plus expense ratio.
Combined ratio (percent):72 + 23 = 954. Underwriting result
Premiums minus claims minus all expenses.
Underwriting profit (SAR millions):1,000 - 720 - 100 - 130 = 505. Investment income
4 percent on SAR 1,500 million.
Investment income (SAR millions):1,500 × 0.04 = 606. Profit before tax
Underwriting profit plus investment income.
Profit before tax (SAR millions):50 + 60 = 1107. Claims shock
The loss ratio rises from 72 to 77 percent, so claims rise by SAR 50 million and the underwriting profit disappears.
Underwriting result after the shock (SAR millions):1,000 - 770 - 100 - 130 = 08. Profit after the shock
Only investment income is left, a fall of 50 out of 110.
Fall in profit (percent):(110 - 60) ÷ 110 × 100 = 45.45
The recommendation
The insurer should act now on claims costs, because a 5 point rise in the loss ratio would cut profit before tax from SAR 110 million to SAR 60 million, about 45 percent. First, its combined ratio is already 95 percent, so underwriting earns only SAR 50 million. Second, investment income of SAR 60 million is the larger part of profit. The priorities are repricing the riskiest customer groups, controlling repair costs through approved garages and fighting claims fraud. The risk is that higher prices push good drivers to competitors. As a next step, track claims cost per policy by customer group each month.
Risks: Raising prices can push good drivers to competitors; Investment income falls if interest rates fall; Reserves for this year's claims may still change.
A home insurer in the UK earns GBP 400 million of premiums. Claims are GBP 260 million and expenses are GBP 120 million. What is its combined ratio, in percent?
Reinsurance changes what the insurer keeps. With an excess of loss treaty, the insurer pays the first part of a big loss (the retention) and the reinsurer pays the part above it, up to a limit. Anything above the limit comes back to the insurer. Reinsurance costs money, so insurers balance protection against its price.
A cyclone causes INR 900 crore of claims for an insurer in India. Its reinsurance pays all losses above INR 200 crore, up to a limit of INR 500 crore of cover. How much of the loss does the insurer keep, in INR crore?
For term life, the basic price is the chance of death times the amount paid (the sum assured), plus a loading for expenses and profit. For savings products, the insurer earns a spread between what its investments earn and what it credits to customers, or a fee on assets. That is why life insurers care so much about interest rates and about customers who keep paying (persistency).
A health insurer's loss ratio rises from 80 to 86 percent while its expense ratio stays at 15 percent. What happened to its underwriting result?
Sources for this lesson (1)
- Recognized public explanations of case-interview concepts and frameworks
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