Insurance & Risk Management Insurance & Actuarial Math NAIC Annual Statement definitions

Insurance Loss Ratio Calculator

The loss ratio is incurred losses divided by earned premium, and it is the single number that says whether an insurance rate is working. This calculator builds it correctly — incurred losses are what you paid plus the change in the reserve for claims you have not paid yet, not simply the cheques written — adds the loss adjustment expense that turns it into the ratio underwriters actually manage against, and converts the result into the rate change your experience indicates relative to a target.

Calculator

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Inputs this calculator takes, with typical values
InputWhat to enterExample
Paid lossesClaim payments made during the period, before any recoveries you have not already netted off.6200000 $
Change in loss reservesClosing reserve minus opening reserve; enter a negative number when reserves were released.450000 $
Loss adjustment expenseAllocated and unallocated cost of investigating, defending and settling claims; enter 0 for a pure loss ratio.780000 $
Earned premiumPremium earned over the period, not premium written — the two differ whenever the book is growing or shrinking.9500000 $
Target loss & LAE ratioThe permissible loss and LAE ratio your pricing assumes, which is 1 minus the expense ratio and profit provision.70 %

It returns

  • Loss ratio — Incurred losses divided by earned premium.
  • Loss & LAE ratio
  • Incurred losses
  • Indicated rate change — Before any adjustment for loss development, trend or credibility.
  • Premium needed to hit the target

The formula

Loss ratio=P+ΔRE
Δrate=actualtarget1

In plain text: Loss ratio = (paid losses + change in reserves) ÷ earned premium; Loss & LAE ratio = (incurred losses + LAE) ÷ earned premium

  • PLosses paid during the period ($)
  • ΔRClosing loss reserve minus opening loss reserve ($)
  • EPremium earned during the period ($)
  • LAEAllocated and unallocated loss adjustment expense ($)

Incurred losses are payments plus the movement in the reserve, so a period in which reserves are released can show incurred losses below paid losses. The ratio is a statement about the period's accounting, not only about the claims that occurred in it.

Updated Category Insurance & Actuarial Math Verified against published test cases Reading time 11 min

What the loss ratio measures and what it does not

The loss ratio is the share of each premium dollar consumed by claims. At 70% an insurer keeps 30 cents to pay commission, taxes, salaries, reinsurance and shareholders, so whether 70% is good depends entirely on what those 30 cents have to cover. That is why the loss ratio is never read alone: it is read against a target, and the target is 1 minus the expense ratio and profit provision. A carrier with a 25% expense ratio and a 5% profit provision is aiming at 70%, and a direct writer with a 20% expense ratio can live with 75%.

The subtlety is entirely in the numerator. Incurred losses are what you paid during the period plus the change in the reserve for claims not yet paid. A period in which reserves were strengthened shows incurred losses above payments; a period in which earlier reserves were released shows them below. Because reserves are estimates, the loss ratio is partly a measurement and partly an opinion, and the opinion can be revised.

The denominator has its own trap. Use earned premium, not written premium. Written premium is what you sold; earned premium is what has been exposed to loss so far. A book growing quickly writes far more than it earns, so a loss ratio computed on written premium looks artificially good, and one computed on written premium in a shrinking book looks artificially bad. Growth alone can move that ratio by ten points without anything changing in the underwriting.

The target ratio in this calculator is the permissible loss ratio built in the pure premium calculator, and adding the underwriting expense ratio to the result gives the combined ratio computed by the insurance combined ratio calculator.

Which loss ratio, on which basis

Three definitional choices change the answer materially, and any figure quoted without stating them is unusable.

Loss, or loss and LAE. Loss adjustment expense is the cost of investigating, defending and settling claims. Allocated LAE attaches to a specific claim — defence counsel, experts, independent adjusters. Unallocated LAE is the claims department. On lines dominated by defence cost, LAE can exceed half of losses, so the pure loss ratio understates the cost of claims badly. Underwriters manage against the loss and LAE ratio for that reason, and this calculator reports both.

Gross or net of reinsurance. A gross ratio describes the business you wrote; a net ratio describes what you kept. They diverge sharply on a book with a large excess-of-loss programme in a year with a big claim. Compare like with like: a gross loss ratio against a gross expense ratio, never one of each.

Accident year, policy year, or calendar year. Calendar year is what the income statement shows: everything that moved in the twelve months, including development on claims from a decade ago. Accident year groups losses by when the accident happened, which is what pricing needs. Policy year groups them by which policy covered them, which is what an experience-rated account needs. A calendar-year ratio can look excellent purely because reserves from earlier years were released, and this calculator's favourable-development warning fires on exactly that case.

The indicated rate change follows in one line: if the ratio you achieved is a and the ratio you can afford is t, then rates need to move by a/t − 1. Note the division rather than the subtraction: a 78% ratio against a 70% target is not an 8% rate increase, it is 78/70 − 1 = 11.4%, because the increase applies to the premium in the denominator as well.

Worked example: a $9.5m book at a 70% target

A book earned $9,500,000 in premium. During the period it paid $6,200,000 of claims and increased its loss reserves by $450,000. Loss adjustment expense was $780,000. Pricing assumed a 70% loss and LAE target.

  1. Incurred losses. $6,200,000 + $450,000 = $6,650,000.
  2. Loss ratio. $6,650,000 ÷ $9,500,000 = 70.00%.
  3. Loss and LAE ratio. ($6,650,000 + $780,000) ÷ $9,500,000 = $7,430,000 ÷ $9,500,000 = 78.21%.
  4. Indicated rate change. 78.21 ÷ 70 − 1 = +11.73%.
  5. Premium needed. $7,430,000 ÷ 0.70 = $10,614,286, which is $1,114,286 more than was earned.

The example is chosen to make one point sharply. The pure loss ratio is exactly on target at 70.00%, and an underwriter reading only that number would conclude the book is priced correctly. Add LAE and it is 8.21 points over, indicating an 11.73% rate increase. The $780,000 of LAE is 8.2% of earned premium and it does not appear in the loss ratio at all.

Notice also that the rate indication is not 8.21%. Raising rates 8.21% would lift earned premium to $10,279,950 and the loss and LAE ratio to 72.28%, still short of target, because the extra premium sits in the denominator. Dividing rather than subtracting is what gets you to a ratio of exactly 70%.

How to read the ratio

Compare against your own target first, not against an industry figure. Published industry loss ratios blend lines with completely different expense structures, and a 60% ratio on a heavily brokered specialty line can be worse than a 78% ratio on a direct personal line. The target is the benchmark; everything else is context.

Next, check the maturity of the accident years in the numerator. A recent accident year's incurred losses are incomplete because claims have not all been reported, so a calendar-year ratio dominated by recent business is understated until it develops. Develop the losses to ultimate with the IBNR reserve calculator before treating the ratio as a pricing signal — this is the most common way a growing book convinces itself it is profitable.

Then ask how credible the experience is. One year of a small book is noise. The credibility weighting calculator quantifies exactly how much of an indication like this one to act on, and for a small account the honest answer is often very little.

Finally, treat the indicated rate change as the beginning of a rate calculation, not the end. A filed indication also adjusts historical premium to current rate level, trends both losses and premium forward to the period the new rate will cover, and blends the result against a broader complement. The figure here is the raw signal from one period's experience, which is a useful diagnostic and an insufficient basis for a rate filing.

What each loss and LAE ratio indicates against a 70% target

Indicated rate change is the achieved ratio divided by the 70% target, minus one. The last column shows the earned premium that would produce each ratio on $7,430,000 of losses and LAE.
Loss & LAE ratioIndicated rate changePremium that produces it
50%−28.57%$14,860,000
60%−14.29%$12,383,333
65%−7.14%$11,430,769
70%0.00%$10,614,286
75%+7.14%$9,906,667
80%+14.29%$9,287,500
90%+28.57%$8,255,556
100%+42.86%$7,430,000

Both columns are generated by the calculator's own expressions. Note that the indication is symmetric in the ratio but not in premium: ten points of ratio is worth 14.29% of rate either side of the target, because the target is the denominator in both directions.

Medical loss ratio is a different calculation with the same name

In US health insurance the medical loss ratio is defined by statute rather than by convention. Under the Affordable Care Act and its implementing regulation at 45 CFR Part 158, insurers must spend at least 80% of premium in the individual and small group markets, or 85% in the large group market, on claims and on activities that improve health care quality, and must rebate the shortfall to policyholders. The numerator includes quality improvement expenses that a property-casualty loss ratio would classify as underwriting expense, and the denominator is premium net of taxes and regulatory fees. If you are computing an MLR for compliance, use the regulatory definition, not the one on this page.

Where a loss ratio misleads

  • Written premium in the denominator. A fast-growing book writes far more than it earns, so a written-premium ratio flatters it. Always use earned premium.
  • Undeveloped recent years. Claims from the most recent accident year are incomplete, so the ratio rises as they develop. A book that keeps growing keeps hiding that development behind newer, greener business.
  • Calendar-year reserve movements. A calendar-year ratio includes development on all prior years. Releasing redundant reserves improves the current year's ratio without improving the current year's underwriting.
  • Ignoring LAE. On defence-heavy lines, LAE can exceed half of losses. A loss ratio on target with LAE excluded can be well over target once it is included, as the worked example shows.
  • Mixing gross and net. A net loss ratio against a gross expense ratio produces a combined ratio that means nothing. Ceded premium and ceded losses must move together.
  • Catastrophe years. A single event can move a ratio thirty points. Pricing indications should normally exclude catastrophe losses from the experience and carry a separate modelled catastrophe load.

From loss ratio to combined ratio, and what actually decides profit

The loss ratio measures claims; the expense ratio measures the cost of acquiring and servicing the business; and their sum is the combined ratio, the headline measure of underwriting profitability. Below 100% the underwriting made money; above 100% it did not, and the insurer relies on investment income to make up the difference. On long-tailed lines that reliance is entirely rational, because premium is held and invested for years before claims settle, and a combined ratio slightly above 100% can still be an acceptable return.

Two conventions differ in how the expense ratio is calculated and it is worth knowing which you are looking at. Statutory accounting divides underwriting expenses by written premium, while GAAP divides them by earned premium. On a growing book the statutory expense ratio is lower, so the statutory combined ratio looks better. The NAIC Annual Statement is where the statutory figures live, and Schedule P is where the loss development behind them is disclosed.

For an individual account rather than a book, the same ratio drives experience rating. The loss ratio a specific insured produces, weighted for credibility against the class expectation, is precisely what the workers comp experience modifier formalises, and what a broker means when they say an account is running at 45%. And for a business deciding how much risk to keep, a persistently low loss ratio is the clearest signal that a higher retention is worth pricing — run it through the self-insured retention break-even calculator before the next renewal.

Frequently asked questions

What is a good loss ratio?

Whatever your target is, and the target is 1 minus your expense ratio and profit provision. A carrier with 25% expenses and a 5% profit provision needs 70%; a low-cost direct writer with 20% expenses can run at 75% and earn the same margin. Comparing a loss ratio against an industry average without matching the expense structures is meaningless, which is why this calculator asks for your own target rather than assuming one.

What is the difference between paid and incurred losses?

Paid losses are cheques written during the period. Incurred losses are paid losses plus the change in the reserve for claims not yet paid, so they include the insurer's estimate of what it still owes. Incurred is the right numerator for a loss ratio because it matches claim cost to the period the premium was earned in. It is also partly an estimate, which is why loss ratios get restated as reserves develop.

Why use earned premium instead of written premium?

Because earned premium is the portion that has actually been exposed to loss. A policy written on 1 December earns only one twelfth of its premium by year end, but any claim under it is fully in the numerator. A growing book writes far more than it earns, so a written-premium loss ratio understates the true figure, and the distortion is largest exactly when growth is fastest and scrutiny is lowest.

Should LAE be in the loss ratio?

It depends what you are measuring, so report both. The pure loss ratio isolates claim cost; the loss and LAE ratio measures what claims actually cost the business including the expense of handling them. For pricing and for reserve adequacy, loss and LAE is the meaningful figure, because the permissible loss ratio in a rate calculation is set against loss and LAE. On liability lines where defence cost is large, the two ratios can differ by ten points or more.

Why is the indicated rate change bigger than the gap in the ratio?

Because rate increases raise the denominator as well. A 78.21% ratio against a 70% target is 8.21 points over, but the indication is 78.21 ÷ 70 − 1 = 11.73%, since the additional premium also lands in earned premium. Subtracting the ratios instead of dividing them consistently understates the increase required, and the error grows as the gap widens.

Can a loss ratio be negative?

Yes, when reserve releases in the period exceed claim payments, which makes incurred losses negative. It happens on runoff books and on lines where earlier years were reserved very conservatively. The number is arithmetically correct but says nothing about the business written in the period — it is a statement about how conservative earlier reserving was, and it should never be used as a pricing signal.

What is the difference between accident year and calendar year loss ratios?

Accident year groups losses by when the accident occurred and is the right basis for pricing, because it matches losses to the exposure that produced them. Calendar year includes everything that moved in the twelve months, including development on claims from earlier years, and is what the income statement reports. A calendar-year ratio can look excellent purely because prior-year reserves were released, which is why analysts separate current-year and prior-year development when reading results.

How does the loss ratio relate to the combined ratio?

The combined ratio is the loss and LAE ratio plus the underwriting expense ratio. Below 100% the underwriting was profitable in its own right; above 100% the insurer depends on investment income. Be careful with the convention: statutory accounting divides underwriting expenses by written premium and GAAP divides them by earned premium, so the same book can report two different combined ratios without any disagreement about the underlying numbers.

References

  • Annual Statement Instructions, Property and Casualty (Schedule P) — National Association of Insurance Commissioners (NAIC)
  • Medical Loss Ratio requirements, 45 CFR Part 158U.S. Department of Health & Human Services
  • Basic Ratemaking, 5th ed. — Casualty Actuarial Society