Insurance fundamentals
Insurance lets many people share the cost of a loss that would ruin one of them. A household pays a premium, and the insurer pays the claim if the loss happens. This lesson shows what a premium, a deductible and a limit are, why insurance costs more on average than going without it, and why that can still be worth paying. It reads the 2025 results of two large insurers, Progressive and Allstate, to see what the business keeps, and a calculator tests the chance of a loss, the deductible and the insurer's payout.
- Level
- Beginner
- Reading time
- About 24 minutes
- Know this first
- Paying down debt
By the end you will be able to:
- explain how insurance transfers a risk and why many policyholders share it
- define a premium, a deductible and a coverage limit
- work out the expected cost of a risk with and without insurance
- read a combined ratio and an underwriting margin
- say why a higher deductible lowers the premium and raises the worst-case cost
Sharing a loss that would ruin one person
Most households face a small chance of a very large cost: a house fire, a serious accident, a lawsuit, a major medical bill. An emergency fund can cover a surprise of a few thousand dollars, as the last lessons showed, but not one of tens of thousands. Insurance is the other tool. The household pays a small, certain amount each year, called the premium, and the insurer agrees to pay for a defined loss if it happens. The risk moves from the household to the insurer, which is why finance calls it risk transfer.
This lesson works out what that costs, using an invented loss of $20,000 that the household faces with a small yearly chance. It then reads the 2025 results of two large US insurers, Progressive and Allstate, to see how much of every premium dollar an insurer keeps. The lesson explains how insurance works. It does not say what any person should buy.
How a policy works
Four terms describe nearly every policy. The premium is the price, usually paid each year or month. The deductible is the part of a loss the policyholder pays first. The coverage limit is the most the insurer will pay. A claim is the request for payment after a loss. If a $20,000 loss happens and the deductible is $1,000, the insurer pays $19,000 and the household pays $1,000, as long as the limit is at least $19,000.
An insurer can offer this because it sells to a very large number of people. Any one household’s loss is unpredictable, but across a large pool the share of households that have a loss is much more stable, and the insurer can set premiums to cover the claims it expects plus its own costs. This is the same idea as the spreading of risk in diversification. It also uses the measure of expected loss: the chance of a loss multiplied by its size.
Why insurance costs more than the average loss
Take a loss of $20,000 with a 4% chance each year. The expected loss is 4% of $20,000, which is $800 a year. That is an average over many years, not what any one year costs: most years cost nothing and a rare year costs $20,000. Now suppose the insurer pays, on average, 65 cents in claims for every dollar of premium, and keeps the rest to pay its costs and profit. With a $1,000 deductible, its expected claim payment is 4% of $19,000, which is $760, so the premium that makes claims 65% of premiums is $760 ÷ 0.65, about $1,169.
The household pays that premium and, in a bad year, also the deductible. Its average yearly cost is the premium plus 4% of the $1,000 deductible: $1,209.0. Without insurance the average is $800.0. So insurance costs $409.0 more a year on average. That is not a flaw. It is the price of what insurance does: it turns an unpredictable cost into a predictable one, and caps the worst year at $2,169 instead of $20,000. Whether that is worth paying depends on whether the household could absorb the loss, which is a question about its own resources.
What two insurers keep
Insurers report a combined ratio: the cost of claims and of running the business as a share of the premiums earned. Below 100 means the insurer made an underwriting profit, before any income from investing premiums. Allstate states that its underwriting margin is 100 less the combined ratio. Progressive and Allstate are both large US auto insurers, which makes them a fair pair. Allstate’s figures below are for its Property-Liability business, and Progressive’s are for the whole company.
| 2025, millions of dollars unless stated | Progressive | Allstate, Property-Liability |
|---|---|---|
| Premiums earned | 81,661 | 57,682 |
| Premiums earned in 2024 | 70,799 | 53,866 |
| Growth in premiums earned | 15.3% | 7.1% |
| Combined ratio, 2025 | 87.4 | 85.2 |
| Underwriting margin (100 less the combined ratio) | 12.6% | 14.8% |
| Net income, whole company | 11,308 | 10,266 |
Progressive earned $81,661 million in premiums in 2025, 15.3% more than in 2024, and reported a companywide combined ratio of 87.4, an underwriting margin of 12.6%. Its Personal Lines business, the one that sells to households, ran at 87.5. Its income statement shows losses and loss adjustment expenses of $53,959 million, which is 66.1% of premiums earned. That ratio is calculated here from the two lines. It is not a figure Progressive states. Allstate’s Property-Liability premiums were $57,682 million, up 7.1%, and its recorded combined ratio was 85.2, a margin of 14.8%.
Two things stand out. The year before, Allstate’s combined ratio was 94.3, so in one year it improved by 9.1 points. Allstate also reports an underlying combined ratio that leaves out catastrophes and other items. It was 79.4 in 2025 against 84.6 in 2024, an improvement of 5.2 points. Catastrophe losses of $4,959 million added 8.6 points to the 2025 ratio and 9.2 points in 2024. A catastrophe year, such as one with severe storms, can move an insurer’s result a great deal, which is why the two measures are shown. The sources do not give a comparable catastrophe figure for Progressive, and net income in the table covers each company as a whole, so it should not be set against the underwriting margin.
The lesson’s calculator assumes the insurer pays out 65% of premiums in claims. That is chosen to be close to the 66.1% calculated for Progressive and is not a rule. Each insurer, product and year is different.
Test a policy
The household faces one loss of $20,000. Set the yearly chance of the loss, the deductible, and the share of premiums the insurer pays out in claims. The calculator finds the premium, the household’s average yearly cost with and without insurance, and the worst year in each case. It also shows how many years of premiums add up to one loss.
With a 4% yearly chance of a $20,000 loss, a $1,000 deductible and an insurer that pays out 65% of premiums in claims, the premium is $1,169 a year. On average the household pays $1,209 a year with the policy against $800 without it, which is $409 more. The worst year costs $2,169 instead of $20,000.
Four experiments. First, leave the starting settings alone. The premium is $1,169, the average yearly cost is $1,209.0 with the policy against $800.0 without it, and the worst year is $2,169 instead of $20,000. It takes 17.1 years of premiums to add up to one loss. Second, raise the deductible to $5,000. The premium falls to $923 and the extra cost falls to $323.0, but the worst year rises to $5,923. A higher deductible makes the policy cheaper and the protection thinner. Third, double the chance of the loss to 8%. The premium rises to $2,338 and the average cost without insurance to $1,600.0, but the extra cost of the policy rises too, to $818.0. The more likely the loss, the more the insurer has to charge. Fourth, return to 4% and a $1,000 deductible and raise the payout to 90%. The premium falls to $844 and the extra cost to $84.0. The more of each premium dollar the insurer returns as claims, the less the household pays for the protection.
What this lesson leaves out
- One invented risk. The $20,000 loss, its chance and the household are made up. Real losses vary in size, and real chances are not known to the policyholder.
- A simple premium rule. The calculator sets the premium as expected claims divided by the share paid out. Real premiums reflect many things, including the insurer’s competition and rules.
- No limit, exclusions or taxes. Real policies list what they do not cover, cap what they pay, and may have fees or taxes added.
- Averages are not experience. Over a lifetime, a household may pay many premiums and never claim, or claim early. The average cost does not predict either case.
- Two companies, one year. Progressive and Allstate describe two insurers in 2025. They do not describe every insurer, and the combined ratio ignores any income from investing premiums.
- No advice. The lesson does not say which insurance to buy, how much, or from whom.
Common mistakes
Expecting to come out ahead
On average the household pays more than the expected loss, as the calculator shows. The value is the protection against the bad year, not the average.
Choosing a deductible only for the lower premium
A higher deductible lowers the premium but raises what the household must pay when a loss happens. Check that the deductible is an amount that could be paid.
Assuming the limit covers everything
The insurer pays up to the limit. A loss above it falls on the policyholder.
Mixing up a premium with a loss ratio
A premium is a price. The share of premiums paid out in claims is something about the insurer. They are different things.
Comparing combined ratios without checking what they cover
Allstate’s figure here is for its Property-Liability business and Progressive’s is for the whole company. Check what each includes before comparing.
Try it yourself
1. A loss of $20,000 has a 4% yearly chance. What is the expected loss?
Show the working
0.04 × 20,000 = $800.0 a year.
2. The deductible is $1,000. How much does the insurer pay on a $20,000 loss, and what does the household pay?
Show the working
The insurer pays 20,000 − 1,000 = $19,000. The household pays the $1,000 deductible.
3. The insurer pays out 65% of premiums in claims, and its expected claim is 4% of $19,000. What premium covers that?
Show the working
0.04 × 19,000 = 760. Then 760 ÷ 0.65 = about $1,169.
4. With that premium and the $1,000 deductible, what is the worst year with the policy, and what is the average yearly cost?
Show the working
The worst year is the premium plus the deductible: $2,169. The average is the premium plus 4% of the deductible: 1,169 + 40 = $1,209.0.
5. Allstate’s recorded combined ratio for Property-Liability in 2025 was 85.2. What was its underwriting margin?
Show the working
100 − 85.2 = 14.8%, which is about 14.8 cents of underwriting profit on each premium dollar earned.
Where this is used
- A household compares the premium and deductible of policies to see what it would pay in a bad year.
- A lender may require insurance on a property before it lends against it.
- An insurer sets premiums so that expected claims and costs are covered across its pool.
- An analyst reads an insurer’s combined ratio, and its underlying version, to judge underwriting results.
- A business insures against losses it could not absorb, such as a large liability claim.
Key terms
- Insurance
- A contract in which an insurer pays for a defined loss in return for a premium.
- Premium
- The price paid for the policy.
- Deductible
- The part of a loss the policyholder pays first.
- Coverage limit
- The most the insurer will pay for a loss.
- Claim
- A request to the insurer for payment after a loss.
- Risk transfer
- Moving the financial effect of a possible loss to another party.
- Expected loss
- The chance of a loss multiplied by its size.
- Combined ratio
- An insurer’s claims and operating costs as a share of premiums earned.
- Underwriting margin
- 100% less the combined ratio.
- Catastrophe loss
- A large loss from an event, such as a severe storm, that affects many policyholders at once.
Questions people ask
Why does insurance cost more than the average loss?
Because the insurer has to cover its costs as well as the claims. In the calculator, a payout of 65% means 35 cents of each premium dollar goes to other costs and profit.
Why does a higher deductible lower the premium?
Because the insurer pays less on each claim, so it expects to pay out less.
What does a combined ratio under 100 mean?
The insurer’s claims and costs were less than the premiums earned, so it made an underwriting profit. Both companies here were below 100 in 2025.
Why show the underlying combined ratio as well?
Because catastrophes and other items can move the recorded ratio sharply from year to year. Allstate reports both so the underlying trend can be seen.
Sources and review
- The Progressive Corporation, 2025 Annual Report, for the companywide combined ratio of 87.4, the Personal Lines combined ratio of 87.5, net premiums earned of $81,661 million for 2025 and $70,799 million for 2024, and net income of $11,308 million.
- The Progressive Corporation, Form 10-K for the year ended 31 December 2025, for the consolidated statement of comprehensive income, including losses and loss adjustment expenses of $53,959 million.
- The Allstate Corporation, Fourth quarter and full year 2025 results (Form 8-K earnings release), for Property-Liability premiums earned, the recorded and underlying combined ratios, catastrophe losses and net income.
How the numbers were checked: the premium, the average and worst-year costs and the four experiments were recomputed in plain code, and the growth rates, margins and the loss ratio shown for Progressive were recalculated from the figures in the sources. Progressive’s loss ratio is calculated from two income statement lines and is not a figure it reports. The calculator, which runs separately, was compared with that code for every combination of settings it allows. The household and its loss are invented.