Friedland08.ExpectedClms
Reading: Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.
Chapter 8: Expected Claims Method
Contents
Pop Quiz
- If your selected LDF for 48-60 months was 1.5, would you need a tail factor?
- Is a selected LDF for 48-60 months of 1.001 more likely to be for an auto liability or auto physical damage line?
Study Tips
VIDEO: F-08 (001) Expected Claims Ratio Method → 5:00 Forum
The previous chapter, chapter 7, on the development method was a very long slog. That's because the development method is the foundational method in both pricing and reserving. Most of the remaining chapters on reserving follow a much simpler pattern. We'll look at 2 or 3 archetypal examples of each method to learn the mechanics. Then we'll look at where each method works well and where it doesn't, and any other concepts necessary to use the method effectively. There's a little bit of memorization but it's mostly just working problems. Some of the methods are quite complicated so it will take perseverance to master them but they are all within reach of anyone who has made it this far in the exam process.
For Chapter 8 on the Expected Claims Method, you'll learn the method by studying 4 examples and then master it by practicing on old exam problems. Chapter 8, along with Chapter 9 on the Bornhuetter-Ferguson Method and Chapter 10 on the Cape Cod method are closely related. Chapter 8 is listed in the Ranking Table as being in the bottom 20% but because of its relationship to other chapters, you still have to learn it quite well.
Estimated study time: 3 days (not including subsequent review time)
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- calculating ultimate / unpaid / IBNR incorporating loss trends and tort reform
- situations where the ECR method works well
reference part (a) part (b) part (c) part (d) E (2017.Spring #18) unpaid & IBNR:
- ECR methodFriedland09.BornFerg E (2016.Spring #16) unpaid claims:
- ECR methodFriedland07.Development Friedland09.BornFerg E (2015.Fall #17) Friedland07.Development ultimate claims:
- ECR method + trendE (2015.Spring #18) ultimate claims:
- ECR method + trendE (2014.Fall #15) IBNR:
- ECR method + trend/tortE (2014.Spring #19) ultimate claims:
- ECR method + trend
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In Plain English!
Example A: Intro to ECR Method
Recall that LR normally stands for Loss Ratio, and that this is the same thing as CR or Claims Ratio. Let ECR stand for Expected Claims Ratio. ECR is a projection, or an expectation of what the loss ratio or claims ratio is going to be in a future period. Let's start with a very simple example. Suppose you're given:
- ECR2025 = 75% (AY value based on historical CRs from AY 2020 to 2024 which were all 75%)
- EP2025 = 1,000 (CY value)
Then by the ECR method:
- ultimate claims for AY 2025 = ECR2025 x EP2025 = 75% x 1,000 = 750
To say this in words, if you think the ultimate claims ratio for a particular year is going to be 75%, and you also know the EP is 1,000, then the ultimate claims (in dollars) is obviously just the product of ECR and EP. This is also sometimes called an a-priori (initial) estimate. Let's extend this example a little bit by supposing you also know:
- paid loss = 475
- reported loss = 600
Then using Alice's Pro Tip & Mega-Useful Formulas we can calculate the following:
- IBNR = (ultimate loss) – (reported loss) = 750 – 600 = 150
- case O/S = (reported loss) – (paid loss) = 600 – 475 = 125
Then it's an easy matter to get:
- total unpaid = (case O/S) + (IBNR) = 150 + 125 = 275
This is all you need to know to do part (a) of these 2 exam problems. Give them a try now. They should only take a few minutes each.
The above 2 exam problems are also included in the quiz so you can keep track of how you did on them and also when you last did them.
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Example B: Estimating ECR using Loss Trends
In the previous example the actuary came up with an estimate of 75% for the ECR (for estimating the ultimate for AY 2025) just by looking at past years and assumed nothing would change going forward. The data may have looked something like this:
AY OLEP 1 ultimate
claimsultimate
claims
ratio2020 1,000 750 75% 2021 1,000 750 75% 2022 1,000 750 75% 2023 1,000 750 75% 2024 1,000 750 75% 2025 1,000 750 75% x selection -- -- ECR = 75%
- 1 OLEP = On-Level Earned Premium. This is a pricing concept where the EPs used in calculating a rate change are brought to current level by adjusting prior years' premiums using rate change information over the intervening period.
- x Exclude AY 2025 when coming up with the ECR. This is because AY 2025 is the year whose ultimate we're trying to estimate.
Based on the above table, projecting an ECR of 75% for AY 2025 looks reasonable, but estimating the ECR is the key to this method so let's see if we can be a little more sophisticated. Suppose you're also told:
- annual frequency trend = 20%
- annual severity trend = -15%
so that,
- annual loss trend = (1 + 20%) x (1 - 15%) - 1 = 2%
Then we can insert 2 columns into the table for the trend factor and trended ultimate claims.
AY OLEP ultimate
claimstrend
factor 2trended
ultimate
claims 3trended
ultimate
claims
ratio2020 1,000 750 1.025 828 82.8% 2021 1,000 750 1.024 812 81.2% 2022 1,000 750 1.023 796 79.6% 2023 1,000 750 1.022 783 78.0% 2024 1,000 750 1.021 765 76.5% 2025 1,000 750 1.020 750 75% x selection -- -- -- -- ECR = 79.6%
- 2 Assume claims (losses) are trended from mid-year to mid-year so trend exponents are integers.
- 3 trended ultimate claims = (ultimate claims) x (trend factor).
- x Exclude AY 2025 when coming up with the ECR. This is because AY 2025 is the year whose ultimate we're trying to estimate.
I selected the ECR to be the average of prior years. Actually this probably isn't the greatest example because it looks like there's a downward trend in ultimate loss ratios. That means it would also be reasonable to select 75% for the ECR, which is what we had in the first place without the trending! But you get the point: In general, losses should be trended to their current level to get a more accurate ECR estimate. Then the final ECR selection is a matter of judgment.
Further down is a link to a pretty straightforward exam problem using the ECR method with a claim trend. But there is a small catch: You are not given any ultimate claim amounts. You have to calculate them yourself in part (a) of the problem using the reported development method. Alice has some advice you'll need...
Alice's ECR Tip #1: To get the ECR method "started", you need ultimate claim estimates from some other method, often the paid or reported development method.
- Comment: If the paid and reported development methods are stable and give you good answers then you really don't need the ECR method. But if you're unsure about the accuracy of the development methods (maybe the paid and reported methods produce widely varying estimates for no discernible reason) you can instead use them as a starting point to come up with a judgmentally selected ECR.
Alice's ECR Tip #2: If you want to appy the ECR method to a particular AY, make sure to exclude that year when coming up with your ECR.
- Comment: If you are asked to estimate the ultimate for AY 2025 and you have initial claims estimates for AY 2020 to AY 2025 from the development method, do not include the initial estimate for AY 2025 when coming up with your ECR. Make sure to read the examiner's comments for the problem below as points were deducted for not following Alice's ECR Tip #2.
Once you have the ECR, the rest of the ECR method is easy and follows the pattern from Example A. Ok, here's the exam problem that uses trends. See if you can do it.
- E (2015.Fall #17)
This next exam problem is very similar except instead of Expected Claims Ratio, you use Pure Premium. Pure premium is covered in the pricing material.
Pure Premium = claims / EE
- Comment: EE = Earned Exposures is an exposure base roughly similar to Earned Premiums. It's a measure of the level of risk. For example in auto insurance, we can use Earned Car-Years as an exposure base. If 1 person has a policy valid for 1 year, then over the course a year EE = 1. In the problem below, the exposure base is occupied hospital beds so the formula for pure premium (or ECR) in this case is (claims)/(occupied hospital beds).
So, give it a try. There are no other tricks.
- E (2015.Spring #18)
A few other examples of alternate exposure bases for different lines of business include payroll for Worker's Comp, miles driven for auto liability, and sales or square footage for corporate GL (General Liability). The above exam problems are also included in the quiz.
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Example C: Estimating ECR under Tort Reform
We're going to look at a simplified version of the exam problem below. You can glance at it but you don't have to try to solve it right away. We need to first go over how to handle tort reform in the context of the ECR method.
- E (2014.Fall #15)
Suppose you're told:
- there was tort reform effective April 1, 2022 that caused an estimated reduction of 15% in all claims occurring after that date
How are we going to incorporate that when coming up with the ECR for estimating the ultimate claims amount for AY 2025?
Tort Reform concept: We need to adjust claims reported before April 1, 2022 downward by 15% so they are on the same basis as claims reported after that date.
The final results are in this table with the explanation below it. The adjustment for AY 2022 is tricky. See explanation below table.
AY OLEP reported
claimsCDF
to
ultimatetort reform
adjustmentadjusted
ultimate
claims 4adjusted
ultimate
claims
ratio2020 1,000 743 1.01 0.85 638 63.8% 2021 1,000 728 1.03 0.85 637 63.7% 2022 1,000 682 1.10 0.9577 718 71.8% 2023 1,000 600 1.25 1.00 750 75.0% 2024 1,000 500 1.50 1.00 750 75.0% 2025 1,000 375 2.00 1.00 750 75.0% x selection -- -- -- -- -- ECR = 73.9%
- 4 (adjusted ultimate claims) = (reported claims) x CDF x (tort reform adjustment)
- x Exclude AY 2025 when coming up with the ECR. This is because AY 2025 is the year whose ultimate we're trying to estimate.
I selected an average of the last 3 years' for my ECR. There seems to be an upward trend so I decided to exclude the 2 oldest AYs. Remember that you must not include AY 2025 when coming up with the ECR to be applied to AY 2025.
Explanation: (for tort reform adjustments given in the above table)
- AY 2020:
- all reported claims from AY 2020 are at the prior level, which we can arbitrarily say is 1.0
- so the average level of these claims is 1.0 (obvious)
- we want to restate these claims as if the 15% reduction had always been in effect (in other words to a level of 0.85)
- the adjustment required to get from the prior average level of 1.0 to the new level of 0.85 is 0.85
- AY 2021: same as AY 2020 because all claims reported for AY 2021 are still at the prior level of 1.0
- AY 2022: If the tort reform was effective April 1, 2022 then
- 1/4 of reported claims from AY 2022 are at the prior level of 1.0
- 3/4 of reported claims from AY 2022 are at the new level of 0.85
- the average level of reported claims from AY 2022 is (1/4 x 1.0) + (3/4 x 0.85) = 0.8875
- we want to restate these claims to the new level of 0.85
- by simple algebra, to get from the prior average level of 0.8875 to the new level of 0.85 you have to multiply the value of 0.8875 by 0.85 / 0.8875 or 0.9577
- AY 2023, 2024: no adjustment necessary because these reported claims are all already at the new level of 0.85
| Pop Quiz A! :-o |
- Suppose you want an ECR for calculating the ultimate loss for AY 2025. If there was tort reform requiring a 10% reduction in claims reported after May 1, 2022, what would the ECR adjustment factor be for (a) AY 2020 & 2021 (b) AY 2022 (c) AY 2023 & 2024 Click for Answer
| Pop Quiz B! :-o |
- Suppose for the example in this section you instead want an ECR to calculate the ultimate loss for AY 2024. Using an average of the 3 most recent available years of data, what would the ECR be? Click for Answer
Now, you should be able to solve the exam problem referenced at the beginning of this section. Give it a try!
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Example D: Adjusting EP to OLEP
Recall that OLEP is On-Level Earned Premium and that concept is discussed in detail in the pricing material. For the exam problems on reserving however, you likely won't have to worry about it. Sometimes you're given OLEP, sometimes you're given EP, but you normally would just use whatever they give you. They aren't testing your ability to do the on-level calculation here – they want to see if you know the reserving method.
If they do happen to give you EP, and also rate level adjustment factors then you may have to calculate OLEP yourself, but it would be very easy.
CY EP rate level
adjustment
factorOLEP 2023 700 1.2 700 x 1.2 = 840 2024 740 1.3 740 x 1.3 = 962 2025 770 1.0 770 x 1.0 = 770
They could make it slightly more complicated by providing average annualized rate changes instead of the rate level adjustment factors as in the above table. In that case, you would have to calculate the adjustment factors yourself, but this is unlikely for a question on the reserving material. Note that the rate level adjustment factor should always be 1.0 for the most recent year because that's the level everything else is adjusted to.
ECR Method Concepts
The key assumption of the ECR method as stated in the source text is not terribly clear. It says:
ECR Method Key Assumption: the actuary can better estimate total unpaid claims based on an a priori (or initial) estimate than from claims experience observed to date
When they say a-priori estimate they mean an estimate that isn't based on claims data for that AY. In the examples we looked at above, the ECR was derived using claims data from all other AYs . Then you multiplied the ECR by the premium for the AY we were interested in to get the a-priori estimate of ultimate for that year. Let's look at a simple example to try to make sense of this. Suppose:
- estimated ultimate from reported development method for AY 2025 = 750
- → this estimate used claims activity from AY 2025 and all prior AYs
- estimated ultimate from ECR method as discussed above = ECR2025 x EP2025 = 73.9% x 1,000 = 739 (this is the a-priori estimate)
- → this estimate didn't use claims activity from AY 2025
- reported claims for AY 2025 = 500
Then we can calculate the unreported or IBNR amount in 2 different ways:
- IBNR = 750 - 500 = 250 ← based on reported development method
- IBNR = 739 - 500 = 239 ← based on a-priori estimate
The key assumption above essentially says that the estimate of 239 (which didn't use claims data from AY 2025) is better than the estimate of 250 (which did use claims data from AY 2025). Of course, this will only be true in certain specific situations.
Question: in what situations is the key assumption for the ECR method more likely to be satisfied [Hint: NODD]
- New line or territory (where data is thin)
- Operational changes (historical data may no longer be relevant)
- Development method may not work well for less mature periods (LDFs could be highly leveraged, especially for lines with longer emergence and settlement patterns)
- Data unavailable for other methods
- You should NODD your head in agreement that the ECR method is good for these situations.
Let's pause for just a moment and think about the key assumption in a slightly different way that's probably more useful.
Alternate Version of ECR Method Key Assumption: claims experience reported to date may provide little information about ultimate claims, especially when compared to the a priori estimate
All the NODD examples are just specific situations where the claims experience to date provides little information about ultimate claims. Next is something very important because it helps you decide which reserving method to choose in a particular situation.
Responsiveness versus Stability: comment on the development method & the ECR method regarding responsiveness & stability
- the development method is more responsive and less stable
- the ECR method is more stable and less responsive
Of course, the 2 bullet points above are just different ways of saying the same thing. Do you understand why they are true?
- The ECR method is based entirely on data from prior years. It will produce the same result for the current AY regardless of actual losses in the current AY. This can be good if it's a new line with low volume. There could be large random fluctuations in the reported losses for the 1st development period of the current year and the development method could cause wild swings in your estimate of ultimate.
- But what if conditions really did change in the current AY? Unlike the development method, the ECR method can't respond to that. The development method uses losses from the current AY so if conditions changed, the development method estimate can indeed reflect that.
Ok, we're almost done now with the chapter but remember that coming up with the ECR is the most important element of the ECR method. In our examples, we got our ECR using trended claims from other AYs, adjusted for tort reform if applicable, and OLEPs (On-Level Earned Premiums). But the source text also mentions a couple of other ways to come up with the ECR:
- just use whatever claims ratio the pricing department used in their rate filing (lazy much?!)
- create a complex simulation model (that sounds like way too much work - you might do that for a unique line of business where credible data is not available)
If you understand the ECR method, then chapters 9 & 10 on the Bornhuetter-Ferguson method and Cape Cod method should go fairly quickly.
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Influence of a Changing Environment
Recall we studied the Influence of a Changing Environment in detail for the development method in chapter 7. In particular, we looked at the following scenarios:
- steady-state (this is the base used to compare against)
- increasing AY loss ratios
- increasing case O/S stength
- changing mix of business
We're going to do the same thing for the ECR but we're going to wait until we've also covered Chapter 9: Bornhuetter-Ferguson Method, and Chapter 10: Cape Cod Method. That's because all 3 methods are closely related.
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POP QUIZ ANSWERS
- yes, there is most likely further development given an LDF of 1.5 for 48-60 months
- auto physical damage (auto liability is not generally considered a long-tail line but it has a longer tail than auto physical damage which is very short)
Pop Quiz A - Answer
- AY 2020 & 2021: adjustment = 0.9
- AY 2022: adjustment = 0.9 / (average level for AY 2022) = 0.9 / [(1/3 x 1.0) + (2/3 x 0.9)] = 0.9 / 0.933 = 0.965
- AY 2023 & 2024: adjustment = 1.0
Pop Quiz B - Answer
- Use the adjusted ultimate claims ratios for AY 2025, 2023, 2022 (exclude AY 2024)
- ECR = (75% + 75% + 71.8%)/3 = 73.9%
- Note that you don't use the 3 years immediately prior to AY 2024 (which would have been AY 2023, 2022, 2021) because those are not the 3 most recent available years.
