New on FinoLib · Volume III: Finance Encyclopedia
My latest article is now live on FinoLib, the free finance library I write: What Does an Actuary Do? How Insurers Price Risk, from Volume III: Finance Encyclopedia. Read the summary below for the substance of the topic, then continue to FinoLib for the complete treatment.
The idea in plain words
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.
Key points
■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.
A closer look
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.
A worked example
Worked Example — Basic Premium Pricing
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.
Under the hood
Under the Hood: The Combined Ratio — Did the Pricing Work?
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.
Decision rule
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.
The costliest mistake
“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.
Recap
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.
What the full article covers
The full article includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume III: Finance Encyclopedia
Read the full article on FinoLib
The complete article, What Does an Actuary Do? How Insurers Price Risk, with every worked example, diagram, quiz and source, is free to read in Volume III, Finance Encyclopedia on finolib.com.
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