Frequency, severity and the risk premium

Every premium a general insurer charges starts from an estimate of what the risk will cost in claims. That number is the risk premium. Expenses, commission and profit are loaded on top of it to reach the price the customer pays, and this lesson works through both steps on a single fleet of vehicles.

Exposure comes first

A claims count means nothing without a denominator. Forty claims from a corner shop's delivery vans is a catastrophe; forty from a national logistics fleet is a quiet Tuesday. The denominator is exposure: how much risk the insurer actually carried, and for how long.

For motor, the measure is vehicle-years, not vehicles. A van on cover for the full year contributes 1.0 vehicle-years; a van added in January and cancelled at the end of June contributes 0.5. The distinction matters because fleets churn constantly. Suppose 100 vehicles in your data were each insured for only six months. Count them as 100 full vehicles and your denominator is 50 vehicle-years too big, so the claim rate you measure is too low, so the premium you charge is too low. The underpricing is silent and only surfaces in next year's loss ratio. Other classes use other measures (sum insured for property, turnover or payroll for liability), but the job of exposure is the same everywhere: to measure how much risk was actually on cover.

Frequency × severity

The fleet book: 500 vehicle-years of exposure this year, 40 claims, average claim £3,750.

• Frequency, claims per unit of exposure: 40 ÷ 500 = 8%. Each vehicle-year is expected to produce 0.08 claims.
• Severity, average cost per claim: £3,750.
• Risk premium, frequency × severity: 0.08 × £3,750 = £300 per vehicle-year.

£300 is the expected claims cost of insuring one vehicle for one year, with no expenses, commission or profit in it. It is also called the expected loss cost, which says exactly what it is.

Pricing an account this way, one selected frequency and one selected severity for the whole risk, is how commercial lines pricing works. Personal lines prices each policyholder individually, with rating factors and GLMs, which is the next lesson.

Loading up to the office premium

The premium the customer actually pays, the office premium, has to fund the rest of the company. Say expenses and commission run at 25% of the office premium, and the target profit margin is 5%. Thirty pence of every premium pound is spoken for before a single claim is paid.

The instinctive calculation is £300 × 1.30 = £390, and it is wrong in a way that turns up in real spreadsheets. The loadings are percentages of the premium you charge, not of the risk premium. Charge £390 and 30% of it (£117) disappears into expenses, commission and profit, leaving £273 to pay £300 of expected claims. You have built a £27-per-vehicle loss into your own rate.

If loadings claim 30% of the office premium, the risk premium must be the surviving 70%:

office premium = risk premium ÷ (1 - total loading)

Divide by one minus the loading; never multiply by one plus it.

Frequency and severity move differently

Why estimate the two components separately rather than just tracking cost per vehicle-year? Because they move for different reasons, often in different directions. Suppose next year the fleet's frequency improves to 7% (safer vehicles, a telematics programme recording how each van is driven) while repair inflation pushes severity up 8%, to £3,750 × 1.08 = £4,050. The new risk premium is 0.07 × £4,050 = £283.50: a 12.5% frequency improvement more than absorbs the severity inflation, and the risk premium falls about 5.5%. One aggregate cost number would tell you that it fell; the split tells you why, and whether to believe it will continue.

UK motor has behaved exactly like this. Long-run claim frequency has improved (vehicle safety) while severity inflation stays stubborn: the ABI's Q1 2026 Motor Premium Tracker put the average accidental damage claim at £3,699 (up 8% in a single quarter, on repair complexity and parts costs) even as the average comprehensive premium actually paid drifted down to £560. Premiums fell while claim costs rose, and the frequency-severity split is what lets you explain both at once.

One year of data is the teaching version. In practice you would take several prior years of experience, trend each one to next year's cost level (claims inflation on severity, any drift in frequency), and then select the frequency and severity to price with. The selection is a judgement, not an average: the actuary decides which years to believe and how much weight the trend deserves.

Back to the fleet:

Build the rate

In practice the rate lives in a spreadsheet, with every assumption in its own cell, so that moving one assumption moves the whole answer and the loading stays visible rather than buried inside a formula. Build it with the fleet's own numbers, then price next year.