Friedland06.Diagnostics

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

Chapter 6: The Development Triangle as a Diagnostic Tool

Pop Quiz

What are the 3 dimension of an accident year development triangle? Click for Answer 

Study Tips

VIDEO: F-06 (001) Diagnostics → 3:00 Forum

Chapter 6 in Friedland has an extremely detailed example demonstrating how diagnostic triangles can be used in a reserve analysis but it's probably more than you need at this point. There are 2 things however that you should start getting familiar with – how to use diagnostic triangles to see evidence of:

• case reserve adequacy changes
• claims settlement rate changes

We'll cover these 2 items fairly quickly so don't worry if not everything sinks in on your first pass. We're going to return to these ideas frequently in subsequent chapters.

Estimated study time: 2 days (not including subsequent review time)

BattleTable

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

• using diagnostics to analyze data and make decisions regarding reserving methods in situations that may include...

- settlement rate changes

- case reserve adequacy changes

- other operational changes

- combining data

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #17)	operational changes: - provide examples	operational changes: - suggest diagnostics
E (2017.Spring #15)	paid/rptd claims ratio: - interpretation	paid/rptd counts ratio: - interpretation
E (2016.Fall #16)	Friedland05.Triangles	Friedland05.Triangles	settlement rate change: - suggest diagnostic	Friedland07.Development Friedland13.BerqSherm
E (2016.Spring #21)	case reserve adequacy: - suggest diagnostic	Friedland13.BerqSherm
E (2015.Spring #16)	operational change: - suggest diagnostic	Friedland07.Development Friedland13.BerqSherm
E (2014.Fall #14)	Friedland05.Triangles	operational change: - suggest diagnostic
E (2013.Fall #15)	SOP.UnpaidClms	combining data: 1 - suggest diagnostics	combining data: - argue for or against	combining data: - argue for or against

¹ Parts (b), (c), (d) of this question require a synthesis of knowledge from several different chapters. You can look at it now but you may not be able to answer all of it until you've covered the chapters on different reserving methods.

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In Plain English!

Diagnostics

When doing a reserve analysis, here's the type of data you'd like to have: (Note that you might not always have all of this for smaller companies.)

• paid claims, reported claims
• paid counts, reported counts
• Earned Premiums, average annual rate changes

For reference, here are the diagnostic triangles discussed in the source text that you can calculate from the above data:

Diagnostic	Also Called...
paid claims (loss) / EP	- paid claims ratio - paid loss ratio
reported claims / EP	- reported claims ratio - reported loss ratio
(paid claims) / (reported claims)	- paid-to-reported ratio
(paid counts) / (reported counts)	- paid-to-reported counts ratio
(paid claims) / (paid counts)	- average paid claim - average paid loss - paid severity
(reported claims) / (reported counts)	- average reported claim - average reported loss - reported severity
(reported claims) – (paid claims) (reported counts) – (paid counts)	- average case outstanding - case O/S severity

Background Information

The 2 most important operational changes within an insurance company that are discussed in the text are:

• case reserve adequacy changes
• claim settlement rate changes

We need to cover a little background information on these concepts and operational changes in general.

Question: why is it important for a reserving actuary to be aware of operational changes within a company

• operational changes can distort the data and cause reserving methods to give inaccurate results

Question: how can a reserving actuary become informed regarding operational changes within a company

• asking questions of management → see Chapter 4 - Meetings with Management
• examining the data, including diagnostic triangles

Question: what can the actuary do upon becoming aware of material operational changes

• select a method that is not affected by the particular operational change
• modify a standard method to adjust for the operational change

In this chapter, we begin learning how to use triangles to see evidence of operational changes. This primarily includes changes in case reserve adequacy and changes in settlement rate of claims. The example in the source text also covers 2 external regulatory events that can impact the data: caps on awards and mandatory rate reductions, but I felt it would be too confusing to include these in the present discussion. We'll come back to them as required. (They are of lesser importance in subsequent chapters anyway.)

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Changes in Case Reserve Adequacy

Suppose an insured reports a minor auto physical damage claim. Claims adjusters often use tables to set the initial reserve for these types of common claims. Suppose,

• the table of initial case reserves lists $800 as the standard initial case reserve for this type of claim
• most minor auto physical damage claims settle for $1,000 on average

We say the strength of this case reserve is $800/$1,000 = 80% or that it has 80% adequacy. So on average, this company's reserves are deficient (too low). But let's say the company updates their tables of initial case reserves:

• the new table of initial case reserves lists $1,100 as the standard initial case reserve for this type of claim

The strength of the new case reserve amount is $1,100/$1,000 = 110%. This company's reserves are now redundant (too high).

Here is the million-dollar quesiton:

Question: how do changes in case reserve adequacy affect the data

• if case reserve adequacy strengthens → the reported claims (reported loss) triangle will show an increase along diagonals
• if case reserve adequacy weakens → the reported claims (reported loss) triangle will show a decrease along diagonals

These changes in the reported claims (reported loss) triangle will obviously affect any diagnostics that use the reported claims data. Note that paid claims (paid loss) is not affected.

VIDEO: F-06 (010) Diagnostics - Changes in Case Reserve Adequacy → 4:00

Alice took some notes on the video to help you out...

Alice's Video Notes: Case Reserve Adequacy Changes

• Scenario 0 is the stable base case. In each triangle all the rows are the same. We start with the stable base case so we can easily see what happens when the case reserve adequacy increases.
• Scenario 3 is a modification of the base case where the case reserve adequacy increased by 20% in CY 2023 and remained at that level.

→ only claims reported in CY 2023 and later will be affected (their case reserve will be at the higher level)

• the effect will be visible starting with the CY 2023 diagonal

→ claims already reported will not be affected (they have already been reserved at the lower level)

• this means the upper left portion of the triangle above the CY 2023 diagonal will not be affected

• Comparing scenario 3 to the base case shows changes in 5 of the 11 triangles: (increases in green, decreases in red)

→ reported loss along diagonals starting with AY/CY 2023

→ reported loss ratio along diagonals starting with AY/CY 2023

→ paid/reported loss along diagonals starting with AY/CY 2023

→ average reported loss along diagonals starting with AY/CY 2023 (also called reported severity)

→ average case O/S loss along diagonals starting with AY/CY 2023 (also called case O/S severity)

• These changes represent the genetic marker for increases in case reserve adequacy.
• If the case reserve adequacy decreases, then these same triangles will change but the changes will be in the opposite direction.

Alice's warning: Interpreting triangles can be tricky and the changes noted above were all relative to a stable base case. In real-life, the reported loss triangle might not always be a good indicator of an increase in case reserve adequacy because the insurer's operations might not have been stable to begin with. In the above example, we did see a raised diagonal for reported losses, but what if overall losses had already been significantly decreasing year-over-year. We might then see general decreases in reported loss as we look down columns, even if case reserve adequacy were increasing. If you are asked to provide a diagnostic for changes in case reserve adequacy, it's safer to use paid/reported loss, average reported loss or average case O/S loss. (This shows just how hard it can be to interpret real-life triangles. There are so many moving parts and it's hard to separate everything out.)

Pop Quiz A!    :-o

• Can you explain the changes you see in the triangles when there is an increase in case reserve adequacy? Hint: It isn't hard if you just think through it using the formulas for the diagnostic triangles. Click for Answer 

Here's the pdf version for easy access and printing:

Demo F-06 (010): Diagnostics - Changes in Case Reserve Adequacy

And here's the Excel version:

Excel Demo F-06 (010): Diagnostics - Changes in Case Reserve Adequacy

Final Comment: Real-life is never as tidy as the above example. Your data will always have noise which obscures underlying patterns. Also, there is rarely ever just 1 change at a time. Usually there are several changes to an insurer's operations happening simultaneously and it can be difficult in practice to isolate effects of individual changes. Nevertheless, you need to start with a clear understanding of the effects of simple changes to have any hope at all of discerning more complex patterns in messy real-life data.

Changes in Settlement Rate

Note: Often the terms paid and closed mean the same thing because usually when a claim has been paid it is considered settled and therefore closed. This ignores the possibility of partial payments however. That's when a payment is made for less than the final settlement amount, but for the present discussion, I'll use paid and closed as synonyms.

Suppose there are 12 claims in AY 2023 and suppose they're normally paid (closed) according to this pattern:

CY 2023 (12 months): 6 claims

CY 2024 (24 months): 3 claims

CY 2025 (36 months): 2 claims

CY 2026 (48 months): 1 claims

Suppose management decides they want to settle claims faster. To do this, they hire more claims staff and as a result, claims are paid 12 months earlier:

CY 2023 (12 months): 9 claims = 6 + 3 (3 claims from CY 2024 were moved forward to CY 2023)

CY 2024 (24 months): 2 claims (2 claims from CY 2025 were moved forward into CY 2024)

CY 2025 (36 months): 1 claims (1 claim from CY 2026 was moved forward to CY 2025)

CY 2026 (48 months): 0 claim (all claims have now been paid by the end of CY 2025 or 36 months so there's nothing left to pay in CY 2026 for AY 2023)

So the 3 claims that would have been paid in CY 2024 are now paid in CY 2023. That means a total of 6 + 3 = 9 claims are now paid in CY 2023. Similarly, the 2 claims that would have been paid in CY 2025 are now paid in CY 2024 instead. And the 1 claim that would have been paid in CY 2026 is now paid in CY 2025.

Pop Quiz B!    :-o

• How would the the payment pattern for AY 2021 change (thx CG!) if a 12-month speed-up in settlement was implemented in CY 2023? Click for Answer 

You might notice that every AY is affected differently. Speeding up settlement rates is a calendar year change so the effect is along diagonals.

VIDEO: F-06 (020) Diagnostics - Changes in Settlement Rates → 5:00

Alice took some notes on the video to help you out...

Alice's Video Notes: Settlement Rate Changes

• Scenario 0 is the stable base case. In each triangle all the rows are the same. We start with the stable base case so we can see easily see what happens when the settlement rate changes.
• Scenario 8 is a modification of the base case where the settlement rate of claims sped up by 12 months in CY 2023 and remained at that level.

→ only claims paid in CY 2024 and later will be moved forward (the speed-up occurred in CY 2023 but you can't magically go back in time and pay CY 2023 claims in CY 2022)

• the effect will be visible starting with a bump in the CY 2023 diagonal

→ claims already paid, and claims that were originally scheduled to paid in CY 2023 will not be affected

• this means the upper left portion of the triangle above the CY 2023 diagonal will not change

• Comparing scenario 8 to the base case shows changes in 6 of the 11 triangles: (increases in green, decreases in red)

→ paid loss along diagonals starting with AY/CY 2023

→ paid count along diagonals starting with AY/CY 2023

→ paid loss ratio along diagonals starting with AY/CY 2023

→ paid/reported loss along diagonals starting with AY/CY 2023

→ paid/reported counts along diagonals starting with AY/CY 2023

→ average case O/S loss drops to 0 because claims are closed earlier along diagonals starting with CY 2023 at age 24 months (also called case O/S severity)

• These changes represent the genetic marker for increases in settlement rates.
• If the settlement slows down, then these changes will be in the opposite direction.

Alice's warning: (This is essentially the same warning as given in the previous section.) Interpreting triangles can be tricky and the changes noted above were all relative to a stable base case. In real-life, the paid loss triangle might not always be a good indicator of an increase in settlement rate because the insurer's operations might not have been stable to begin with. In the above example, we did see a raised diagonal for paid losses, but what if overall losses had already been significantly decreasing year-over-year. We might then see general decreases in paid loss as we look down columns, even if settlement rates were increasing. If you are asked to provide a diagnostic for changes in settlement rates, it's safer to use paid/reported loss, paid/reported counts or average case O/S loss which drops to 0 along the diagonal because claims are closed earlier. (This shows just how hard it can be to interpret real-life triangles. There are so many moving parts and it's hard to separate everything out.)

Make sure you understand the logic behind why these changes occur. The diagnostics are created with formulas using paid & reported loss, paid & reported counts, and earned premiums. If you understand why those given data triangles change they way they do, the reasoning for the other diagnostics is similar to Pop Quiz A from the previous section. But if it doesn't completely make sense right now, don't worry too much because we'll return to these ideas many times in subsequent chapters.

Here's the pdf version for easy access and printing:

Demo F-06 (020): Diagnostics - Changes Settlement Rate

And here's the Excel version:

Excel Demo F-06 (020): Diagnostics - Settlement Rate Changes

Final Comment: In the above example, all claims were settled faster. But what often happens in a real claims department is that small claims are settled faster. In that case, you would also see a drop in average paid loss and a jump in average case O/S loss early on. And it's actually even more complicated than that as you can see in this forum discussion. But for now, I just wanted to keep things simple.

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10 Diagnostic Scenarios (Book of Triangles)

For each set of triangles from the Book of Triangles below, find the best matching interpretation from the list below: Click for Answer 

Problem F-06 (030): Diagnostic Scenarios (Book of Triangles)

Hint: You can do these without calculations. Don't overthink it, but be observant.

A: stable operations

B: large loss in AY 2023

C: deteriortating loss ratio AY 2020 to AY 2025

D: insurer entered a new region in CY 2023

E: settlement rate increase of 12 months at CY 2022

F: settlement rate increase of 12 months at CY 2023

G: case reserve adequacy +20% at CY 2023

H: case reserve adequacy -15% at CY 2023

J: case reserve adequacy +20% at CY 2024

K: case reserve adequacy +10% at CY 2023

A few more exam problems where you have to use diagnostics...(the problem from 2013 is really hard)...

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POP QUIZ ANSWERS

Each cell in an accident year triangle is identified by 3 dimensions:

1. The row labels are Accident Years and you'll often see the abbreviation AY.
2. The column labels are Development Period or Age. Those terms are interchangeable. In this triangle the periods are months and that's very common.
3. The skew diagonals represent Calendar Year, abbreviated CY

Go back

Pop Quiz A - Answer

Here's the reasoning:

• It's self-evident that the reported loss triangle will increase if the case reserve adequacy increases. The reason diagonals are affected is that increases in case reserves affect only newly reported claims. (Claims already reported have been reserved at the previous level and won't change.) So, the effect of the increase begins in CY 2023, and geometrically, CY 2023 is a diagonal starting on the row for AY 2023.
• It's also self-evident that the paid loss triangle will not change. Claims should settle for the same amounts as before regardless of the initial case reserve.
• Neither the paid count or reported count triangles will change because an increase in case reserve adequacy is a dollar-amount and can only affect dollar-based triangles.
• The earned premium did not change compared to the base case because reserves don't directly affect premium.
• All other diagnostics are calculated from these amounts so any increases or decreases follow directly from the formulas. For example, the reported loss ratio diagnostic triangle shows increases along diagonals starting with AY/CY 2023 because the reported loss triangle increased and the earned premiums didn't change. (If the numerator increases but the denominator stays the same, the ratio will increase.)
• The other changes can be explained similarly by simple logic using the formulas for those triangles.

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Pop Quiz B - Answer

First, here's the normal payment pattern for AY 2021:

CY 2021 (12 months): 6 claims

CY 2022 (24 months): 3 claims

CY 2023 (36 months): 2 claims

CY 2024 (48 months): 1 claims

Then if a 12-month speed-up is implemented in CY 2023, the accelerated pattern would look like this:

CY 2021 (12 months): 6 claims (no change because speed-up doesn't happen until the beginning of CY 2023)

CY 2022 (24 months): 3 claims (no change because speed-up doesn't happen until the beginning of CY 2023)

CY 2023 (36 months): 3 claims = 2 + 1 (the 2 claims paid in CY 2023 on the original schedule are still paid in CY 2023, but the 1 claim originally paid in CY 2024 is now paid 12 months earlier in CY 2023)

CY 2024 (48 months): 0 claims (the 1 claim paid in CY 2024 on the original schedule will now be paid in CY 2023)

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Diagnostic Scenarios Answers

A: Scenario 0 (stable operations)

B: Scenario 5 (large loss in AY 2023)

C: Scenario 6 (deteriortating loss ratio AY 2020 to AY 2025)

D: Scenario 7 (insurer entered a new region in CY 2023)

E: Scenario 10 (settlement rate increase of 12 months at CY 2022)

F: Scenario 8 (settlement rate increase of 12 months at CY 2023)

G: Scenario 3 (case reserve adequacy +20% at CY 2023)

H: Scenario 2 (case reserve adequacy -15% at CY 2023)

J: Scenario 4 (case reserve adequacy +20% at CY 2024)

K: Scenario 1 (case reserve adequacy +10% at CY 2023)

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