Actuaries put a price on risk before it happens. The basic price, called the pure premium, is how often claims happen multiplied by how big they usually are. Then they add enough for expenses and profit by dividing by one minus those shares. The scorecard is the combined ratio: losses plus expenses divided by premium. Below 100% means the insurer made an underwriting profit.
Why it matters: The combined ratio tells you in one number whether insurance itself made money.
Summary: Actuaries price a policy as expected frequency × expected severity (the pure premium), then gross it up for expenses and profit by dividing by one minus those shares. The combined ratio, losses plus expenses over premium, is the scorecard: below 100% is an underwriting profit.
- A $300 pure premium with 20% expenses and a 5% profit target becomes $300 ÷ 0.75 = $400, not $375.
- Combined ratio = loss ratio (losses plus LAE over earned premium) + expense ratio.
- Investment income on float lets a line break even above 100%: 106.75% with float of 1.5× premium at a 4.5% yield.
- US P&C insurers ran 101.6% in 2023, 96.6% in 2024 and 92.9% in 2025, the last helped by light catastrophe losses.
- Relying on investment income to cover a 104% combined ratio turns a $27.5 million profit into a $17.5 million loss if yields fall 3 points.
An actuary uses statistics, probability theory, and financial mathematics to estimate the likelihood and financial magnitude of future uncertain events — principally, how much an insurer should charge in premium today to cover claims that will only be paid, and only fully known, at some point in the future. Actuarial pricing rests on three core estimated inputs: frequency (how often a claim event happens), severity (how large a typical claim is when it does happen), and an appropriate margin for the insurer’s own expenses, profit, and the genuine uncertainty in the frequency and severity estimates themselves.
An insurer estimates that, across a pool of 10,000 similar policyholders, 200 will file a claim in a given year (a 2% frequency), and the average claim will be $15,000 (the severity). Expected total claims = 10,000 × 2% × $15,000 = $3,000,000. Dividing by 10,000 policyholders gives a pure premium (expected claims per policy) of $3,000,000 ÷ 10,000 = $300.
The insurer wants expenses of 20% of premium and a profit of 5% of premium. Because both are shares of the final premium, the loading is applied by grossing up, not by marking up: premium = $300 ÷ (1 − 0.20 − 0.05) = $400. Check: $400 − $300 claims − $80 expenses = $20 profit, which is 5% of $400. The tempting shortcut, $300 × 1.25 = $375, leaves $375 − $300 − (20% × $375 = $75) = $0 profit; across 10,000 policies the intended $200,000 profit is gone and the book is $250,000 short of the $4,000,000 it needed. (The rupee version of this example is in the India Lens at the end of this Part.)
Pricing is a forecast; the combined ratio is the scorecard. It adds two parts. The loss ratio is incurred losses plus loss adjustment expenses (LAE, the cost of investigating and settling claims) divided by earned premium (the share of premium for coverage already provided). The expense ratio is the other underwriting expenses (commissions, staff, premium taxes) divided by premium; analysts divide by written premium on a “trade basis” and by earned premium on other bases, so check which one a report uses. Below 100% the insurer made an underwriting profit; above 100% it paid out more than it charged.
Worked numbers. Earned premium $100 million; incurred losses $62 million; LAE $8 million; underwriting expenses $28 million. Loss ratio = ($62m + $8m) ÷ $100m = 70%. Expense ratio = $28m ÷ $100m = 28%. Combined ratio = 70% + 28% = 98%, an underwriting profit of $100m − $62m − $8m − $28m = $2 million. Now add the float (Part 1.6: The Insurance Balance Sheet — Float and Investment Income): if $150 million of reserves and unearned premium is invested at 4.5%, investment income = $150m × 4.5% = $6.75 million, an investment income ratio of 6.75%. The operating ratio = 98% − 6.75% = 91.25%, so pretax operating income is $2m + $6.75m = $8.75 million.
That arithmetic shows why a combined ratio above 100% is not automatically a loss: the break-even combined ratio is 100% plus investment yield × (invested float ÷ premium) = 100% + 4.5% × 1.5 = 106.75% in this example. It also shows the danger, because that cushion shrinks the moment yields fall.
The industry scorecard. US property-casualty insurers ran a combined ratio of 101.6% in 2023, 96.6% in 2024 and 92.9% in 2025, according to Verisk and the American Property Casualty Insurance Association. Verisk attributed 2025’s near-record result more to unusually low catastrophe losses than to a structural change in risk, a reminder that one good year of a correlated line says little about its true expected loss (Part 1.1: Why Insurance Exists — Risk Pooling and the Law of Large Numbers).
Actuarial pricing is fundamentally a forward-looking statistical exercise, built on historical data that may not perfectly predict the future — climate change’s effect on catastrophe frequency and severity in P&C insurance is a live, actively debated example of exactly this challenge, where actuaries must decide how much weight to give to a changing underlying pattern versus decades of historical claims data.
Price by grossing up: premium = pure premium ÷ (1 − expense share − profit share), never pure premium × (1 + loading). Then test the target: a combined ratio above 100% is acceptable only if investment yield × (invested float ÷ premium) exceeds the excess over 100% and still does with yields 2 to 3 points lower. With float of 1.5 times premium, a 104% combined ratio needs a yield above (104% − 100%) ÷ 1.5 ≈ 2.7% just to break even. If the line is short-tailed and holds little float, then treat 100% as the ceiling.
“Cash-flow underwriting”: accepting a combined ratio above 100% because investment income will cover it. At 104% with float of 1.5 times premium, a 4.5% yield gives an operating ratio of 104% − 4.5% × 1.5 = 97.25%. If yields fall to 1.5%, it becomes 104% − 1.5% × 1.5 = 101.75%. On $1 billion of premium, a $27.5 million profit turns into a $17.5 million loss, a $45 million swing with identical claims. Price each line to stand on its underwriting result and treat investment income as a bonus.
What is a good combined ratio?
Anything below 100% is an underwriting profit, but the right target depends on the line. Short-tailed personal lines hold little float and need to stay under 100%; long-tailed liability lines can run slightly higher and still profit from investment income. The US property-casualty industry ran 101.6% in 2023, 96.6% in 2024 and 92.9% in 2025.
What is the difference between the loss ratio and the combined ratio?
The loss ratio counts claims and claim-handling costs against earned premium; the combined ratio adds the expense ratio for commissions, salaries and taxes. A 70% loss ratio plus a 28% expense ratio gives 98%. A low loss ratio can still hide an unprofitable business when acquisition costs are high.
How do actuaries calculate an insurance premium?
They multiply expected claim frequency by expected severity to get the pure premium, adjust for trends such as inflation and for each risk class, then gross up for expenses and profit by dividing by one minus those shares. A $300 pure premium with 20% expenses and a 5% profit target becomes $300 ÷ 0.75 = $400.
A premium starts from the pure premium, frequency × severity, and is grossed up for expenses and profit by dividing by one minus those shares, so $300 becomes $400 at 25% total loadings. The combined ratio, loss ratio plus expense ratio, shows whether pricing worked; investment income on float can carry a ratio slightly above 100%, but a business that depends on it loses money when yields fall.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. A policy has a 1% claim frequency and a $20,000 average claim. Expenses are 15% of premium and the profit target is 5% of premium. What premium meets the target?
- $200
- $240
- $250
- $220
Reveal Answer
Answer: C. Pure premium = 1% × $20,000 = $200; premium = $200 ÷ (1 − 0.15 − 0.05) = $250. Marking up by 20% would give only $240.
2. Earned premium is $100 million, incurred losses $55 million, loss adjustment expenses $10 million and other underwriting expenses $30 million. What is the combined ratio?
- 95%
- 65%
- 105%
- 85%
Reveal Answer
Answer: A. Loss ratio = (55 + 10) ÷ 100 = 65%; expense ratio = 30%; combined ratio = 95%.
3. An insurer holds invested float equal to 2 times premium and earns a 3% yield. Ignoring taxes, at what combined ratio does it break even overall?
- 100%
- 109%
- 103%
- 106%
Reveal Answer
Answer: D. Break-even combined ratio = 100% + yield × float ÷ premium = 100% + 3% × 2 = 106%.
4. A team marks up a pure premium by 25% to cover 20% expenses and a 5% profit, both stated as shares of premium. What happens?
- Expenses are only partly covered and claims go unpaid
- Expenses absorb the loading and no profit remains
- The policy earns more than the profit target
- The policy earns exactly the 5% profit target
Reveal Answer
Answer: B. On a $300 pure premium, $375 − $300 − 20% × $375 = $0; dividing by 0.75 to get $400 is required.