Economic Modelling · Run-off triangles

Loss Ratio Method and Comparing Reserving Methods

Updated 11 October 2026 · Fact-checked

The loss ratio method sets ultimate claims equal to earned premium times an expected loss ratio, then subtracts claims paid to date to get the reserve. It ignores the triangle's own experience. You choose between it, chain ladder and Bornhuetter-Ferguson by judging how stable the data is and how long the tail is.

Understand Loss Ratio and Other Reserving Methods

A reserve is the amount you set aside for claims that have happened but are not yet fully paid. Run-off triangle methods estimate it from past claims data. The loss ratio method is the simplest. It does not use the triangle's development pattern at all.

The idea: if you know the premium earned for an accident year and you have a good view of how much of that premium goes on claims, you can predict ultimate claims directly. Ultimate claims = earned premium × expected loss ratio. The reserve is ultimate claims minus what you have already paid (or minus incurred, if you are reserving IBNR only). The expected loss ratio comes from pricing, past years, or market data. It is an a priori estimate.

This makes the method very stable. A single odd claim in the triangle does not move it. But it also does not react to the data. If a year is running worse than expected, the loss ratio method will not notice. It is only as good as the expected loss ratio and the premium figure.

Chain ladder is the opposite. It projects ultimate claims from the latest cumulative claims using development factors. It responds fully to the data. That is good when the data is large and stable. It is poor for recent accident years, where the latest figure is small and a small random swing is multiplied by a large factor. It is also poor for long-tail business, where early development is thin and volatile.

Bornhuetter-Ferguson (BF) sits between the two. It takes claims paid to date as fact. It then adds the expected unpaid part, using the a priori ultimate times the proportion still to emerge, which is 1 − 1/CDF. It is a weighted average of chain ladder and the loss ratio method, with weight 1/CDF on chain ladder. As the year matures, BF moves towards chain ladder.

Suitability: for long-tail classes and the latest accident years, where little has emerged, the loss ratio or BF method is usually more reliable than pure chain ladder. For short-tail classes with mature, stable data, chain ladder works well. Average cost per claim methods suit classes where claim numbers and severity can be modelled separately.

Key rules to remember

Loss ratio ultimate: Ultimate = Earned premium × Expected loss ratio; The expected loss ratio is an a priori assumption. It does not come from the triangle.
Loss ratio reserve: Reserve = Ultimate − Claims paid to date; Use incurred instead of paid if you want the IBNR only. State which basis you use.
Chain ladder ultimate: Ultimate = Latest cumulative claims × CDF; CDF is the product of the remaining development factors, from the current development year to ultimate.
Proportion developed: p = 1 ÷ CDF; The share of ultimate claims expected to have emerged so far.
Bornhuetter-Ferguson ultimate: Ultimate = Claims to date + A priori ultimate × (1 − 1/CDF); The a priori ultimate is usually premium × expected loss ratio.
BF as a weighted average: BF ultimate = p × Chain ladder ultimate + (1 − p) × Loss ratio ultimate; Here p = 1/CDF. Valid when the same a priori ultimate and CDF are used in all three methods.

How to solve Loss Ratio and Other Reserving Methods questions

Use this approach for any question that asks you to calculate reserves or compare methods.

1Read which basis is used (paid or incurred) and whether the answer wants ultimate claims or the reserve.
2Write down the data for each accident year: earned premium, claims to date, and development factors or CDFs.
3Compute the a priori ultimate as premium × expected loss ratio. Do this first, since it is needed for both the loss ratio method and BF.
4Compute the chain ladder ultimate as latest claims × CDF, if asked.
5Compute the BF ultimate as claims to date + a priori ultimate × (1 − 1/CDF).
6Subtract claims to date from each ultimate to get the reserves. Add up across years only if asked.
7Check that the BF figure lies between the other two. If it does not, you have made an error.
8For discussion parts, state the assumption of each method, then say which suits the class of business and why.

Quickest way: Three ultimates in one pass

When to use it: When a question gives premium, expected loss ratio, claims to date and a CDF for one accident year and asks you to compare methods.

Find 1/CDF first. This is the proportion developed.
Loss ratio ultimate = premium × loss ratio.
Chain ladder ultimate = claims to date × CDF.
BF ultimate = claims to date + loss ratio ultimate × (1 − 1/CDF).
Cross-check: BF = p × chain ladder + (1 − p) × loss ratio.
Reserve = ultimate − claims to date for each method.

Common mistakes in Loss Ratio and Other Reserving Methods

Using 1/CDF instead of 1 − 1/CDF as the BF unpaid proportion
Students mix up the proportion developed with the proportion still to emerge.
Fix: Remember that BF adds the expected unpaid part. That is 1 − 1/CDF. Check that a CDF of 2.5 gives 60% unpaid, not 40%.
Forgetting to subtract claims to date to get the reserve
The method produces an ultimate, and students stop there.
Fix: Read the question for the word reserve. Always write Reserve = Ultimate − Claims to date as your last line.
Using premium written instead of earned premium
Both figures appear in data tables.
Fix: The loss ratio is applied to the premium earned for the accident year, because only that premium covers exposure that has occurred. Use the earned figure unless told otherwise.
Saying the loss ratio method uses the triangle's development pattern
It is taught in the same chapter as the triangle methods.
Fix: State clearly that it uses no development factors. Its only inputs are premium and an assumed loss ratio.
Recommending chain ladder for the latest accident year of long-tail business without comment
Chain ladder is the default method students practise.
Fix: Say that a large CDF multiplies a small and volatile figure. Recommend BF or the loss ratio method for immature years and give that reason.
Mixing paid and incurred figures with factors from the other basis
Both triangles may be shown in one question.
Fix: Match the factors to the data. Paid claims need paid CDFs. Incurred claims need incurred CDFs.

Worked examples

Example 1

For an accident year, earned premium is ₹50,00,000. The expected loss ratio is 70%. Claims paid to date are ₹22,00,000. Using the loss ratio method, find the ultimate claims and the reserve.

Show the solution

Ultimate = earned premium × expected loss ratio = 50,00,000 × 0.70 = ₹35,00,000.
Reserve = ultimate − paid to date = 35,00,000 − 22,00,000 = ₹13,00,000.

Answer: Ultimate claims ₹35,00,000. Reserve ₹13,00,000, on a paid basis.

Example 2

For an accident year, earned premium is ₹80,00,000 and the expected loss ratio is 75%. Claims paid to date are ₹27,00,000. The cumulative development factor to ultimate is 2.5. Find the reserve under the loss ratio, chain ladder and Bornhuetter-Ferguson methods, and comment.

Show the solution

Loss ratio: ultimate = 80,00,000 × 0.75 = ₹60,00,000. Reserve = 60,00,000 − 27,00,000 = ₹33,00,000.
Chain ladder: ultimate = 27,00,000 × 2.5 = ₹67,50,000. Reserve = 67,50,000 − 27,00,000 = ₹40,50,000.
Proportion developed = 1 ÷ 2.5 = 0.4. Proportion unpaid = 0.6.
BF: ultimate = 27,00,000 + 60,00,000 × 0.6 = 27,00,000 + 36,00,000 = ₹63,00,000. Reserve = 63,00,000 − 27,00,000 = ₹36,00,000.
Check: 0.4 × 67,50,000 + 0.6 × 60,00,000 = 27,00,000 + 36,00,000 = ₹63,00,000. This agrees.
Comment: only 40% is expected to have emerged, so chain ladder scales up a small figure by 2.5 and is volatile. BF uses the experience to date but relies on the a priori for the rest, so it lies between the other two. For an immature year in a long-tail class, BF is the more balanced choice.

Answer: Reserves: loss ratio ₹33,00,000; chain ladder ₹40,50,000; BF ₹36,00,000. BF lies between the other two and is usually preferred for this immature year.

Exam tips

Show the a priori ultimate line first. Marks are usually awarded for each method's formula and each correct intermediate figure.
State your assumptions explicitly: basis (paid or incurred), no inflation or inflation allowed for, and where the expected loss ratio comes from.
In discussion questions, give an assumption, a strength and a weakness for each method, then link to the class of business. Short bullet points score well.
Use the weighted average check to catch arithmetic slips in the BF figure.
For the computer-based paper, keep the premium, loss ratio and CDF as separate input cells so you can change one and see the effect on each method.

Practice questions from Run-off triangles

Loss Ratio and Other Reserving Methods: frequently asked questions

What is the loss ratio method in reserving?

It sets ultimate claims for an accident year equal to earned premium times an expected loss ratio. The reserve is that ultimate minus claims already paid. It uses no development factors.

When is the loss ratio method most useful?

It is most useful when data is thin or volatile, such as the latest accident years or a new class of business. It also helps for long-tail business where little has emerged. It needs a reliable expected loss ratio.

Which reserving method should I use for long-tail business?

For the older, more developed years, chain ladder can work if the pattern is stable. For recent years, BF or the loss ratio method is usually better, because early claims figures are a poor guide to ultimate claims.

What are the main limitations of run-off triangle methods?

They assume the past development pattern continues. They can be distorted by changes in claims handling, mix of business, inflation, reinsurance or case reserving. They also give a single estimate and no measure of uncertainty unless extended.