Friedland15.Evaluation

Reading: Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.

Chapter 15: Evaluation of Methods

Pop Quiz

Ian-the_Intern has a collision deductible of $100 and yesterday he backed into a fire hydrant causing $600 worth of damage to his car. His auto insurer has a 60% quota-share reinsurance treaty. What is his insurer's loss net of all deductibles and reinsurance? Click for Answer 

Study Tips

This is a really great chapter because it ties together concepts from all previous chapters. The only thing that's totally new is a formula for calculating expected emergence. There are 2 versions and they are both pretty easy:

• expected emergence of reported losses
• expected emergence of paid losses

Most of the exam questions from this chapter ask you to do one or more of the following:

• evaluate the accuracy of an estimate from a given reserving method
• identify a scenario that explains differences in estimates between different accident years
• identify a scenario that explains differences in estimates between different reserving methods
• identify a scenario that explains changes in estimates for a given reserving method between successive evaluation dates
• suggest an adjustment or alternate method to improve accuracy of estimates

The best way to get the hang of answering these types of questions is to go through all old exam problems. There are a lot but don't let that scare you – many of them don't take long to do. It's a heavily tested chapter and is an excellent way to review concepts related the reserving methods from previous chapters.

Estimated study time: several days (not including subsequent review time)

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• emergence

- calculate expected emergence for paid or reported claims or claim counts, with interpolation if necessary

- compare expected emergence to actual emergence and decide whether to revise estimate of ultimate

• impact of operational and external changes on reserving methods and estimates of ultimates
• assess validity of reserve estimates or methods in various situations
• identify scenario that is consistent with given information or explains differences between methods

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #25)	emergence: - of losses	emergence: - actuary's decision
E (2018.Spring #24)
E (2018.Spring #26)
E (2017.Fall #27)	assess method: - paid & rptd devlpt	assess method: - Freq-Sev, rptd BF	assess method: - paid devlpt, paid BF
E (2017.Fall #28)	assess CDFs: - devlpt, BF, Freq-Sev	assess ECR: - BF method
E (2017.Spring #21)	identify scenario: - consistent with results	identify scenario: - to explain difference	alternate method: - for part (a)	alternate method: - for part (b)
E (2017.Spring #26)	assess ECR: - BF method	method comparison: - to Benktander	investigating results: - questions for mgmt 1
E (2016.Fall #16)	Friedland05.Triangles	Friedland05.Triangles	Friedland06.Diagnostics	select method: - settlement rate change
E (2016.Fall #18)	BF ECR: - calculate	select method: - calculate unpaid	assess method: - ECR, paid BF, paid devlpt
E (2016.Fall #27)	emergence: - counts	emergence: - limitations
E (2016.Spring #24)	emergence: - losses	emergence: - actuary's decision
E (2016.Spring #25)	identify scenario: - to explain difference	identify scenario: - to explain difference
E (2015.Fall #19)	assumptions: - recommend changes	revise: - estimates	assess: - revised estimates
E (2015.Fall #22)	impact / solution: - long development pattern	impact / solution: - tort reform	impact / solution: - higher deductibles	impact / solution: - faster claims processing
E (2015.Fall #25)	emergence: - losses based on devlpt	emergence: - losses based on selected	emergence: - actuary's decision
E (2014.Fall #19)	impact / solution: - increasing case strength	impact / solution: - premium growth	impact / solution: - higher limits
E (2014.Fall #22)	emergence: - of losses	emergence: - linear interpolation issues
E (2014.Fall #24)	select method: - that will be accurate	select method: - that will over-estimate	select method: - that will under-estimate
E (2014.Spring #17)	impact (case strength): - on rptd development	impact (case strength): - on ECR method	impact (case strength): - on rptd BF method	impact (case strength): - on Cape Cod method
E (2014.Spring #22)	emergence: - of losses	emergence: - of losses	identify scenario: - re: actuary's decision	identify scenario: - re: actuary's decision
E (2013.Fall #18)
E (2013.Fall #24)
E (2013.Spring #21)
E (2013.Spring #22)
E (2013.Spring #26)

¹ See Friedland04.Meetings for potential questions.

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In Plain English!

Selecting a Final Estimate

Suppose you get to the end of your reserve analysis as of Dec 31, 2025 and have estimates of ultimates from several different methods:

AY	Paid Development	Reported Development	Paid Berquist-Sherman	Reported Berquist-Sherman
2020	1,000	1,000	1,000	1,000
2021	1,000	1,000	1,000	1,000
2022	1,000	1,000	1,000	1,000
2023	1,000	1,050	1,000	1,000
2024	1,000	1,125	1,000	1,000
2025	1,000	1,300	1,000	1,000

Here are some typical questions:

• identify a scenario that explains differences in estimates between different accident years
• identify a scenario that explains differences in estimates between different reserving methods

To answer these, you need to make a few observations:

• paid development and both Berquist-Sherman methods show an estimate of 1,000 for all AYs
• reported development starts the same as the others but begins increasing at AY 2023

Let's consider the following potential explanations for a rise in the estimate for reported development:

• loss ratio is deteriorating (which is the same as saying the loss ratio is increasing)
• change in settlement rate of claims
• change in case reserve strength
• large loss or losses in AYs 2023, 2024, 2025
• change in mix of business
• court decision

It probably isn't a deterioration in the loss ratio because that would have affected the paid development method also. You have to pick something that would specifically affect only reported development. The best option from this list is a change (increase) in case reserve strength. We know from previous chapters that an increase in case strength causes reported development to over-estimate. The reason, of course, is that historical LDFs were taking lower case reserves to ultimate so if we suddenly increase case strength, these historical LDFs will overshoot.

Side note: If I asked you when the increase in case strength occurred, the answer is not CY 2023. You know that because an increase in CY 2023 would affect unreported claims from AY 2023 and prior, but AY 2022 is accurate. (How far back the effect goes depends on the length of the development tail.) Actually, you can't tell from the given data exactly when the case strengthening occurred, but a better guess would be the beginning of CY 2025. All AY 2025 claims would then be reserved at the higher level. The effect would be less noticeable for AY 2024 because only claims reported after 12 months would be at the higher level. (AY 2024 claims reported within the first 12 months would be reserved at the lower level so the distortion is less pronounced for AY 2024 versus AY 2025.) Similarly, even fewer claims from AY 2023 would still be unreported and receive the higher case reserves at the beginning of AY 2025. Since AY 2022 is accurate, it appears that all AY 2022 claims were reported by the beginning of CY 2025.

But getting back to the original questions: The scenario that explains the differences in estimates is most likely an increase in case reserve adequacy:

• it explains the increase in the reported development estimates starting in AY 2023
• it explains why paid development and paid Berquist-Sherman are accurate (an increase in case strength doesn't affect paid data)
• it explain why the reported Berquist-Sherman method is accurate for all AYs (reported BS corrects for changes in case strength)

I made my example very simple to illustrate the point. Below is a harder exam problem for you to try. In an exam situation you would only have about 8 minutes to solve it and write out your answer, but for learning it's worth spending a couple of hours. You may have to go back and review details of different methods from previous chapters.

E (2016.Spring #25)

Here are a few more similar exam problems in the quiz.

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Emergence Patterns

expected reported losst→t+1    = (current unreported)t x [ (%reportedt+1 - %reportedt) / %unreportedt ]

• formula...
• limitations of using emergence... see 2016.Fall #27

• non-linear emergence (linear interpolation of annual pattern to quarterly may not be accurate but quarterly to monthly may be ok solution use shorter time frames)
• if ultimate is not based on a development method then the CDFs from a development may not appropriate (use paid or reported divided ultimate to get pattern instead of CDFs)
• doesn't account for operational changes (Exs: change in mix of business, settlement rate, case strength) since projected emergence is based on historical patterns solution investigate operation changes then either select data that isn't affected or make adjustments to affected data to correct for distortions caused by operational changes

observation: paid and reported losses are generally skewed towards beginning of year because %paid and %reported curves are generally concave downward functions

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Retroactive Testing

mentioned on p345, 348

High White: p352

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POP QUIZ ANSWERS

• The insurer's loss net of Ian's deductible is $500.
• After the 60% quota-share reinsurance treaty is applied, the insurer's loss net of deductibles and reinsurance = 500 x 60% = $300

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