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

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 method	Friedland09.BornFerg
E (2016.Spring #16)	unpaid claims: - ECR method	Friedland07.Development	Friedland09.BornFerg
E (2015.Fall #17)	Friedland07.Development	ultimate claims: - ECR method + trend
E (2015.Spring #18)	ultimate claims: - ECR method + trend
E (2014.Fall #15)	IBNR: - ECR method + trend/tort
E (2014.Spring #19)	ultimate claims: - ECR method + trend

In Plain English!

Example A: Intro to ECR Method

Recall that LR normally stands for Loss Ratio, and that this is the same things as CR or Claims Ratio. Let ECR stand for Expected Claims Ratio (this is an ultimate value) 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 of the ECR method. Suppose you're given:

ECR₂₀₂₅ = 75% (based on historical CRs from AY 2020 to 2024 which were all 75%)

EP₂₀₂₅ = 1,000

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 = 600

reported loss = 850

Then using Alice's Pro Tip & Mega-Useful Formulas we can calculate the following:

IBNR = (ultimate loss) – (reported loss) = 1,000 – 850 = 150

case O/S = (reported loss) – (paid loss) = 850 – 600 = 250

Then it's an easy matter to get:

total unpaid = (case O/S) + (IBNR) = 250 + 150 = 400

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.

E (2017.Spring #18)

E (2016.Spring #16)

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 claims	ultimate claims ratio
2020	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 talbe, 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 loss trend = 2%

Then we can insert 2 columns into the table for the trend factor and trended ultimate claims.

AY	OLEP	ultimate claims	trend factor 2	trended ultimate claims 3	trended ultimate claims ratio
2020	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 exponentes 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, apply 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 section.

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, 2020 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.

AY	OLEP	reported claims	CDF to ultimate	tort reform adjustment	adjusted ultimate claims 4	adjusted ultimate claims ratio
2020	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 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 to calculate 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!

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 unpaid amount in 2 different ways:

• unpaid = 750 - 500 = 250 ← based on reported development method
• unpaid = 739 - 500 = 239 ← based on a-priori estimate

The key assumption 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 is 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.

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, 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)

POP QUIZ ANSWERS

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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

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Pop Quiz B - Answer

• Use the adjusted ultimate claims ratios for AY 2025, 2023, 2022 (exclude AY 2024)

ECR = (75% + 75% + 71.8%) = 73.9%

• Note that you don't use AY 2023, 2022, 2021 as those are not the 3 most recent available years.

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