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

Chapter 6 in Friedland has an extremely detailed example demonstrating how diagnostic triangles can be used in a reserve analysis. I think it's way too complicated given that none of the standard methods for reserving have even been discussed yet. The 2 things you have to get familiar with however are how to use diagnostic triangles to see evidence of:

• case reserve adequacy changes
• claims settlement rate changes

We will cover these 2 items as efficiently as possible so you can keep forward moving through the material.

Estimated study time: 1 day (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...

- combining data

- settlement rate changes

- case reserve adequacy changes

- other operational changes

reference	part (a)	part (b)	part (c)	part (d)
E (2017.Spring #15)	paid/rptd claims ratio: - interpretation	paid/rptd counts ratio: - interpretation
E (2016.Spring #21)	case reserve adequacy: - suggest diagnostic	Friedland13.BerqSherm
E (2016.Fall #16)	Friedland05.Triangles	Friedland05.Triangles	settlement rate change: - suggest diagnostic	Friedland07.Development 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.

In Plain English!

Diagnostics

When doing a reserve analysis, here's the type of data you'd like to have: (might not always have all of it 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	common names	useful for investigating...
claims / EP	- claims ratio - loss ratio	...
(paid claims) / (reported claims)	- paid-to-reported ratio	changes in:    - case reserve adequacy    - settlement rates
(paid counts) / (reported counts)	- paid-to-reported counts ratio	...
(paid claims) / (paid counts)	- average paid claim - paid severity	...
(reported claims) / (reported counts)	- average reported claim - reported severity	...
(reported claims) – (paid claims) (reported counts) – (paid counts)	average case outstanding	...

Background Information

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

• case reserve adequacy changes
• claims 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 question 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

Changes in Case Reserve Adequacy

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

• the table of initial case reserves lists $800 as the standard initial case reserve for this type of claim
• 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 see 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.
• 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.

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.

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

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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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