How an actuary builds a statewide auto rate: a worked indication

The percentage in an "overall rate change" is a ratio. On one side sits the premium the insurer expects to need, built from old claim costs that have been completed, brought forward in time and then grossed up for expenses and profit. On the other sits the average premium at today's rates. If the first is 9.9 percent bigger than the second, the "indicated" change is +9.9 percent, and the insurer then decides how much of that to actually request.

The general rate-calculation guide shows which factors insurers use to price one driver. This article does the other job: it takes one invented insurer through the statewide arithmetic with round numbers, using the formulas in the Casualty Actuarial Society's ratemaking text, so you can see where a headline number comes from and which assumptions move it. Every figure below is made up for illustration. None of it describes a real company, state or filing.

The one equation behind every indication

Actuaries start from what the Casualty Actuarial Society's Basic Ratemaking text calls the fundamental insurance equation: premium equals losses plus loss adjustment expenses plus underwriting expenses plus underwriting profit (Werner and Modlin, 5th edition, 2016). Rate-making is the exercise of estimating each right-hand term for the future period the new rates will be in force and solving for the premium.

A few terms, defined as the text uses them:

• Pure premium. Expected losses plus loss adjustment expense (LAE) per exposure, which in auto is a car-year of coverage. It leaves out other expenses and profit.
• Loss adjustment expense. The cost of investigating and settling claims. Some is tied to a specific claim (lawyers, experts) and some is not (the claims department's general overhead).
• Variable expenses. Costs that scale with premium: agent commissions, state premium taxes and fees, and part of general overhead.
• Fixed expenses. Costs that are about the same for every car regardless of price, modeled per exposure.
• Target profit. The margin the insurer plans to earn on each premium dollar. The CAS text describes choosing an underwriting profit provision so that, together with investment income, it gives the insurer an appropriate total return for the risk.

The text gives two equivalent ways to turn this into an overall rate indication. The pure premium method produces an indicated average rate directly. The loss ratio method compares the expected loss ratio with the loss ratio the rates are designed for and produces an indicated change. The text notes that the pure premium method is attractive for personal auto, because auto rating plans have many variables and rewriting history at today's rates ("premium at current rate level") is hard. We will run the pure premium method and then check it with the loss ratio method.

The invented insurer and its data

Call it Example Mutual. It writes private passenger auto in one state, all coverages combined, on annual policies. It is preparing a filing in mid-2026 for rates effective July 1, 2026. Its experience comes from three accident years, with loss and LAE figures valued at December 31, 2025.

A regulator would see these as exhibits attached to the filing. As an example of a real requirement, California's insurance department told insurers in 2017 that the data period for a prior-approval auto filing must end no more than eight months before the filing date (California Department of Insurance FAQ). Other states set their own rules.

Step 1: complete the old claims (development)

The numbers in the table are not final. Claims from the most recent year are still open, and reserves are estimates. The CAS text describes the issue plainly: "the cost for the insurance product, unlike other industries, is not fully known when the contract is provided or even when a claim is first reported," and the process of adjusting immature losses to an estimated ultimate value "is known as loss development." The common tool is the chain ladder method, which assumes losses move from unpaid to paid in a pattern that is stable over time, so past patterns predict future ones.

Example Mutual's actuary applies factors read from its own history of how losses at each age grew to their final value. The factors are invented:

The newest year gets the biggest factor because it is the least mature. Liability coverages take longer to settle than collision, so the mix of coverages in the book decides how big the 2025 factor looks. A regulator can see the whole triangle behind each factor: California's filing instructions ask for loss development exhibits, and New Jersey's older filing checklist for limited rate filings, marked 9-07, specified that development factors come from the average of the middle three of the last five years' factors, with BI and PIP developed to 87 months and a tail factor of 1.05 (New Jersey Department of Banking and Insurance checklist). That checklist is an older document, so read it as an example of the level of detail, not as current New Jersey policy.

Step 2: move the losses forward in time (trend)

Claims from 2023 were paid at 2023 prices. The new rates will cover accidents from July 2026 through June 2028, with the average accident date, for annual policies written evenly across the year, around July 1, 2027. The CAS text defines loss trend as the change in frequency (claims per car) and severity (cost per claim) between the historical period and the period the rates will be in effect, and says actuaries measure it by fitting linear or exponential curves to historical data, usually looking at frequency and severity separately. Drivers include inflation, medical costs and safety technology as well as legal and social changes.

Example Mutual's actuary selects a net loss trend of 4.0 percent per year: frequency falling about 1 percent a year, severity rising about 5 percent, multiplying to roughly 4. The trend period for each accident year runs from the middle of that year (July 1) to July 1, 2027: four years for 2023, three for 2024, two for 2025.

The trended ultimate cost, divided by the 312,000 car-years across the three years, is a pure premium of about $803 per car-year.

Step 3: what each premium dollar must carry (permissible loss ratio)

Now the expense side. Suppose the actuary projects:

• Fixed underwriting expense of $40 per car-year.
• Variable expenses of 24 percent of premium: commissions, premium taxes, licenses and fees, other acquisition costs and general overhead that scales with premium.
• A target underwriting profit of 5 percent of premium.

The CAS text calls the share left over for losses and fixed expenses the variable permissible loss ratio, defined as one minus the variable expense percentage minus the target profit percentage. Here that is 1.00 − 0.24 − 0.05 = 0.71. Of every premium dollar, 71 cents is available for claims, claim handling and fixed costs; 24 cents goes to variable expenses; 5 cents is profit. New Jersey's older checklist uses a simpler version in which the permissible loss ratio is one minus capped expenses.

Step 4: solve for the indicated rate

The pure premium method in the CAS text is: indicated average rate equals pure premium plus fixed underwriting expense per exposure, all divided by one minus variable expense percentage minus target profit percentage. The text's own example uses a $300 pure premium, $25 of fixed expense, 25 percent variable expense and 10 percent profit to arrive at a $500 rate. Using Example Mutual's numbers:

Indicated average rate = ($803 + $40) ÷ 0.71 = $1,187 per car-year.

Step 5: compare with today's rates

Suppose Example Mutual's average premium, restated to today's rate level (what its in-force policies would pay at current rates, which actuaries call premium at current rate level), is $1,080 per car-year. The indicated change is $1,187 ÷ $1,080 − 1 = +9.9 percent.

The loss ratio method reaches the same place from the other side. At current rates, the projected loss ratio is $803 ÷ $1,080 = 74.4 percent, and the fixed expense ratio is $40 ÷ $1,080 = 3.7 percent. Their sum, 78.1 percent, divided by the 71 percent permissible ratio, gives 1.099, or +9.9 percent. The CAS text shows that the two methods are mathematically equivalent when the data and assumptions are consistent, and gives the reading: a result above 1.0 means current rates are inadequate, and the result minus 1.0 is the percentage change.

Notice what the calculation does not say. It does not say the insurer will charge each driver 9.9 percent more. It is an average over the whole book. Class and territory factors, covered in the CAS text's chapters on classification, are layered on top, which is why your own renewal can differ from the headline number. See why your premium went up at renewal with no claims and the renewal rate increase checker.

Why the answer is sensitive to judgment

Because the indication is built from projected, not observed, numbers, small changes in assumptions move it a lot. Holding everything else at the values above:

The last row is the reason regulators insist on documentation. Reported losses alone would suggest the insurer could cut rates. Adjusting for immature claims and for rising costs reverses the sign. That is also why reviewers question trend selections so closely: California's FAQ notes that the end of the trend period depends on assumptions such as policy terms and the timing of claims, so the insurer must document the periods it used. The same issue underlies the public debate about rising auto costs; our article on social inflation and nuclear verdicts: how lawsuits raise premiums covers one driver of severity trend.

Credibility: how much to believe a small state

Example Mutual's three years of experience in this state include far more claims than it needs. Suppose frequency is about 6 claims per 100 car-years across all coverages. That is roughly 18,700 claims over 312,000 car-years, well above the full-credibility standard the CAS text uses in its example: 1,082 claims, which comes from asking for a 90 percent probability that the observed result is within 5 percent of its expected value. Credibility, written Z, equals 1.00 once claims reach that standard.

Now suppose the same insurer also writes a tiny second state with about 270 claims over three years. The text's square root rule says credibility equals the square root of observed claims divided by the standard: the square root of 270 ÷ 1,082 is about 0.50. The state's own result is only half believable, so the actuary blends it with a related estimate (the "complement"):

Credibility-weighted indication = Z × state indication + (1 − Z) × complement.

If the small state's own indication is +14.0 percent and the complement, such as the insurer's broader regional indication, is +6.0 percent, the answer is 0.50 × 14.0 + 0.50 × 6.0 = +10.0 percent. The CAS text points out that the formula is widely used because it is simple, and also that it rests on simplifying assumptions, such as no variation in claim size, that may not hold.

Regulators set their own standards. California's 2017 FAQ gave 6,000 total claims as the standard for full credibility for private passenger auto loss trend. New Jersey's older checklist set claim-count standards of 3,000 to 4,000 for different coverages, applied the square root rule with a minimum credibility of 50 percent, and said how the complement of credibility is assigned. These are different standards for different purposes, which is a reminder that "credible" is a defined, jurisdiction-specific term and not a vague word.

Indicated is not selected

The last step is the one customers rarely see. The indication is a calculation. The selected change is what the insurer decides to file. Companies select below an indication for many reasons: competitors, expected loss of customers, regulatory limits or the judgment that some assumptions are too pessimistic. New Jersey's older checklist, for instance, limited a "limited rate filing" to the smaller of 7 percent or the indicated change overall, and limited any one policy's impact to 15 percent. California's Proposition 103 process allows a public hearing on request for a personal lines change above 7 percent, a threshold we cover in how car insurance rate approval works.

Say Example Mutual files +7.5 percent instead of +9.9. Its average premium rises to $1,161, and with the same cost and expense assumptions its expected profit margin is 1 − 0.24 − ($843 ÷ $1,161) = 3.4 percent rather than the 5 percent target. The shortfall is the cost of the discount to the indication. If the 4 percent trend turns out right, the insurer may be back next year asking for the difference. If claim costs come in lower, it will have been conservative in the customer's favor. Either way, the gap is where the word "selected" does its work.

How to read this in a real filing

1. Find the indication and the selected change. They are different numbers. Our guide to How to read a car insurance rate filing on SERFF shows where each sits.
2. Check the trend and development exhibits. These are the two assumptions in the table above that move the answer most.
3. Look at the permissible loss ratio. A larger expense or profit provision raises the indication even if claims do not change. See loss ratios and rate filings: how insurers justify an increase.
4. Ask how many claims sit behind the number. A small book relies on its complement of credibility.
5. Compare indicated and selected. A selected change far below the indication signals either a competitive market or a regulator-imposed cap.

Common questions

Where does the 4% trend come from?

In this example it is invented. In real filings it is selected from curves fitted to the insurer's own frequency and severity data or from an industry source, then justified in the actuarial memorandum. The CAS text recommends analyzing frequency and severity separately and warns that mix changes, such as a shift to higher deductibles, can hide behind a pure premium trend.

Can an indication be negative?

Yes. If projected pure premium is low relative to the premium being collected, the formula returns a number below zero, meaning current rates are more than adequate. Florida's Office of Insurance Regulation has reported that the top five groups' average rate change was +31.7 percent in 2023 and that the indicated change for 2026 was −8.0 percent, one example of indications turning down.

Does the actuary set the price?

The actuary estimates what rates are needed and certifies the analysis. Management decides what to file, and a regulator reviews or approves it according to state law. Rate-approval systems range from prior approval to file-and-use. See prior approval and file-and-use.

Does an indication show up in my bill?

Only indirectly. The overall change is spread across classes, territories and coverages by other analyses, and your own factors (driving record, vehicle, territory and so on) determine your share. The statewide percentage is a starting point for the conversation, not your renewal quote.

Key takeaways

• An overall rate indication equals the future premium needed to cover projected losses, claim-handling costs, fixed expenses and target profit, divided by the premium at today's rates, minus one.
• The two big judgment inputs are development, which completes immature claims, and trend, which brings old costs to the future period. In the example, dropping both flips +9.9 percent to −7.2 percent.
• The permissible loss ratio (here 71 percent) is what is left of each premium dollar after variable expenses and profit; a higher expense or profit load raises the indicated rate.
• Credibility, using the square root rule against a claim-count standard, decides how much a small state's own experience counts.
• Indicated and selected changes differ, and the selected change is the one filed with the regulator.