Friedland16.ALAE

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

Chapter 16: Estimating ALAE (Allocated Claim Adjustment Expenses)

Pop Quiz

Suppose your reserve analysis used the 4 reserving methods: paid development, reported development, paid Berquist-Sherman, reported Berquist-Sherman. Suppose also that 3 of the 4 methods produced exactly the same estimates of ultimate for all accident years, but that the reported development was significantly lower for the previous 3 accident years. What is the most likely explanation for this discrepancy? Click for Answer 

Study Tips

VIDEO: F-16 (001) ALAE → 4:00 Forum

This chapter is pretty easy. Practice the calculations and memorize the advantages/disadvantages of each method. There aren't that many old exam problems so it's probably a good idea to run through all of them.

Estimated Study Time: 2-3 days (not including subsequent review time)

BattleTable

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

• multiplicative method - a ratio method for calculating ultimate ALAE
• additive method - a ratio method for calculating ultimate ALAE
• advantage/disadvantage - of ALAE ratio methods
• ALAE ratio methods - additive versus multiplicative method

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #24)	multiplicative method: - ultimate	ALAE ratio methods: - additive vs multiplicative	advantage/disadvantage: - of ALAE ratio methods
E (2018.Spring #25)	paid ALAE development: - ultimate	additive method: - ultimate	justify final selection: - ultimate
E (2017.Spring #25)	paid ALAE development: - ultimate (with large loss)	multiplicative method: - ultimate (with large loss)
E (2016.Spring #23)	additive or multiplicative: - ultimate	advantage/disadvantage: - of ALAE ratio methods
E (2015.Fall #24)	multiplicative method: - ultimate	additive method: - ultimate	justify final selection: - ultimate
E (2014.Spring #21)	paid ALAE development: - challenges	ALAE ratio methods: - challenges	frequency-severity: - for legal expenses

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In Plain English!

What is ALAE & ULAE

LAE (Loss Adjustment Expense) used to be simple. They are the costs incurred by a company during the claim settlement process. There was "Allocated" LAE (ALAE) and "Unallocated" LAE (ULAE). The key difference is that ALAE was tied to a particular claim whereas ULAE was not. Examples include:

ALAE: attorneys, experts, investigators, independent adjusters,...

ULAE: general overhead expenses such as salaries, rent, computer systems,...

ALAE has a loss date and a report date so you can create a triangle from ALAE data. But since ULAE is not tied to a particular claim, there is no associated loss date or report date and you cannot create a ULAE triangle. This is covered in more detail in Friedland17.ULAE.

Anyway, it's important for you as an actuary to understand the ALAE data you're given. This isn't discussed in detail in the source text, but here are a few things to keep in mind if you're ever asked to calculate ultimate or unpaid ALAE:

• attorney fees and court costs represent the biggest subcategory of ALAE (often treated separately)
• ALAE data is often combined with claims data (but be careful as ALAE development patterns may differ from claims development patterns)
• some companies track only paid ALAE (they don't even bother estimating case outstanding ALAE)

Note that in the United States 1998, the historic categorization of LAE into ALAE & ULAE was changed to:

DCC: Defense & Cost Containment (all defense litigation and medical cost containment expenses regardless of whether internal or external to the insurer)

A&O: Adjusting and Other (all claims adjusting expenses, whether internal or external to the insurer)

Insurers still generally use ALAE & ULAE but financial statements use DCC & A&O. There is a rough, but not exact, correspondence between the 2 sets of terms. You can see from the BattleTable however that old exam questions generally provide the data and all you have to do is perform the ALAE & ULAE calculations according to standard methods.

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Calculating Ultimate ALAE

Let's take a quick look at a very simple concept. Suppose you have a development triangle as follows: (thx MPT!)

AY	12	24	36
2018	15	20	22
2019	16	21
2020	15

The standard way of calculating link ratios is to form the quotient of a given value with the value in the previous column. This is multiplicative development:

AY	12-24	24-36
2018	1.33	1.10
2019	1.31
2020

But another way of calculating link ratios is to form the difference of those same values. This is additive development:

AY	12-24	24-36
2018	5.0	2.0
2019	5.0
2020

The multiplicative method is commonly used for estimating ultimate claims when we're given a paid claim or reported claim triangle. We call that paid loss development and reported loss development. The additive method works exactly the same way except wherever you would multiply or divide, you now add or subtract.

The additive method would be terrible for developing claim amounts however. The reason is that it doesn't take into account differences in claim volume between accident years. But if you apply the additive method to ratios rather than directly to amounts, then it often works pretty well. In fact the ratio methods, either multiplicative or additive, are common methods for estimating ultimate ALAE.

Question: identify 3 common methods used to estimate ultimate ALAE

• development of paid claims & paid ALAE triangle to ultimate in the standard way (ALAE is not separated from claims for development)

(may not work well if claims & ALAE have very different development patterns)

• development of paid ALAE triangle to ultimate in the standard way (ALAE is separated from claims)

(may not work well because ALAE data is often thin compared to claims data)

• ratio methods: uses triangle of (paid ALAE $s) / (paid claim $s)

   - may be developed multiplicatively (as in the standard development method)

   - may be developed additively (link ratios are calculated as a difference instead of a quotient)

(assumes the ratio is stable over the experience period)

Here's a good problem that illustrates the multiplicative version of the ratio method:

E (2019.Spring #24)

And here's Alice's nifty solution:

Solution: 2019.Spring #24 (ALAE Multiplicative Ratio Method)

Since Alice is very curious, she wondered what answer you'd get if you used the additive ratio method instead. It turns out that for this problem, the answer is not very different. The multiplicative method gave 595.7; the additive method, 597.6.

Solution: 2019.Spring #24 (ALAE Additive Ratio Method)

A good question is part (b) of (2019.Spring #24). The answer is given in the examiner's report and in the BattleCard quiz but the answer is simple. If the (paid ALAE)/(paid claims) ratio is small then multiplicative factors could be highly leveraged. Additive development would likely be less leveraged and more stable.

Here are a few practice problems with both the multiplicative and additive ratio methods:

Practice: 4 ALAE practice problems

Challenge Question

Use the data from (2019.Spring #24) to calculate ultimate ALAE using these alternate techniques and comment on how the results compare to the ratio methods:

• development of (paid ALAE) only
• development of (paid claims + paid ALAE)

Alice will post and give a shout-out to the first few answers she receives!

• Update: submission received Oct 20, 2020 (shout-out to MG!)

ALAE Concepts

You can see from the BattleTable that this next question is something you need to be able to answer:

Question: describe advantages & disadvantages of using ratio methods to estimate ultimate ALAE

advantages of ratio methods:

• ratios recognize the relationship between loss & ALAE
• ratios provide diagnostics (individual AYs can be excluded if unreasonable)
• ratios are more stable than developing ALAE directly (ALAE can be small & highly leveraged, especially at early maturities)

disadvantages of ratio methods:

• inaccurate ultimate loss estimates may cause inaccurate ALAE estimates
• large ALAE expense but claim settles with no payment (causes distortions in ratio triangle)
• timing of ALAE payments may differ from timing of loss payments (causes distortions in ratio triangle)
• trend for ALAE payments may differ from trend for loss payments (causes distortions in ratio triangle)

That's about it for ALAE. Alice now invites you to enter the wonderful & wacky world of ULAE. Calm down Alice, you're overselling it. :-)

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More Exam Problems

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POP QUIZ ANSWERS

• The most likely explanation for the reported development method to be lower for the previous 3 accident years is a decrease in case reserve adequacy.

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