Odomirok.22-23-GAAP

Chapter 22 is about U.S. GAAP accounting. Chapter 23 is about Fair Value Under Purchase GAAP.

At some point you should definitely read the forum thread that discusses inconsistencies in the treatment of discounting on the balance sheet.

  Forum

Study Tips

There is a lot to learn in this chapter. There aren't as many calculations as in the RBC chapter but there are a lot of details memorize. The most commonly asked questions relate to differences between SAP and GAAP, so you have to know this very well, and be forewarned: It isn't enough just to have the "general idea". A good example of this is the accounting treatment of retroactive reinsurance. It's rather confusing the first time you read it but it has been asked more than once. You will have to drill yourself on this.

Here is a nice comparison table for SAP vs GAAP.  ← shout-out to CK1!

The differences between the previous and current editions of the source text are mainly in chapter 22:

• The old edition listed 10 differences between SAP and GAAP. The new edition lists 11. The new item is PDR or Premium Deficiency Reserves. The text includes a numerical example and that looks like a good candidate for a new type of exam question. The wiki includes Excel practice problems for this.
• The treatment of invested assets under SAP has changed.
• The new edition of the text has added a numerical example related to prospective reinsurance. This looks like another good exam question and there are Excel practice problems in the wiki.

The old exam problems should mostly still be valid. The only issue is that they wouldn't cover any of the new material, so the examiner's reports would not include all currently acceptable answers. This is minor however. The old exam questions and answers are still an excellent resource.

At some point you should definitely read the forum thread that discusses inconsistencies in the treatment of discounting on the balance sheet.

Estimated study time: 1 week (not including subsequent review time)

BattleTable

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

• SAP vs GAAP concepts
• SAP calculation - surplus, goodwill, admitted assets, liabilities, 10-year loss development (10K exhibit)
• GAAP calculation - surplus, goodwill
• other miscellaneous concepts: fair value, IFRS,...

Questions held out from Fall 2019 exam: #20, 21. (Skip these now to have a fresh exam to practice on later. For links to these questions, see Exam Summaries.) The examiners' report solution to E (2019.Fall #21) is outdated. For an explanation, see this forum discussion.

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #16)	GAAP: - FV(liabilities) components	GAAP: - FV(liabilities) methods
E (2019.Spring #17)	SAP vs GAAP: - discounting	SAP vs GAAP: - ceded resv (prosp. reins)	SAP vs GAAP: - ceded resv (retro reins)	SAP vs GAAP: DAC SAP vs GAAP: DTA
E (2018.Fall #19)	SAP vs GAAP: - intended user	SAP vs GAAP: - purpose	SAP vs GAAP: - differences on B/S	SAP vs GAAP: - differences on B/S 1
E (2018.Spring #19)	GAAP calculation: - surplus	SAP vs GAAP: - bonds/stocks	SAP: - bond treatment
E (2017.Fall #12)	SAP vs GAAP: - effects of reinsurance	SAP vs GAAP: - effects of reinsurance
E (2017.Fall #19)	GAAP: - FV(liabilities) components	SAP vs GAAP: - goodwill
E (2017.Fall #20)	SAP vs GAAP: - purpose	SAP vs GAAP: - various items
E (2016.Fall #18)	GAAP calculation: - goodwill	SAP calculation: - goodwill
E (2016.Spring #15)	SAP calculation: - admitted assets	SAP calculation: - liabilities	SAP vs GAAP: - various items
E (2014.Fall #15)	SAP calculation: - surplus (6 pts)
E (2014.Fall #19)	GAAP calculation: - surplus	SAP vs GAAP: - various items
E (2014.Spring #21)	SAP vs GAAP: - intended user	SAP vs GAAP: - DAC, loss discounting	SAP vs GAAP: - refer to (a) & (b)	general: - rent/buy furniture
E (2014.Spring #22)	fair-value reserves: - required adjustments	fair-value reserves: - versus SAP reserves
E (2014.Spring #23)	SAP calculation: - 10-yr loss development : 2	loss & DCC reserves: - accuracy
E (2012.Fall #23)	SAP vs GAAP vs IFRS: - reinsurance recoveries	SAP vs IFRS: - loss reserve discounting	SAP vs GAAP: - acquisition costs

¹ There is a forum thread that fills in some details missing from the examiner's report answer to part (d).

² Part (a) of this problem is outdated because the 10-year loss development exhibit has been removed from the syllabus.

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  Forum

In Plain English!

Intro

The difference between SAP (Statutory Accounting Principles) and GAAP (Generally Accepted Accounting Principles) is driven by the intended user. State regulators use SAP because it's focused on solvency and an insurer's ability to pay claims. All public companies use GAAP and SAP evolved from GAAP on a state by state basis. The SAP framework is considered to be more conservative due to its focus on solvency, versus the company as a going-concern.

Here's some super-basic info on SAP versus GAAP: (This topic was introduced briefly in SAP versus GAAP - Odomirok Chapter 8/9).

	SAP or (Statutory Accounting Principles)	GAAP (Generally Accepted Accounting Principles)
general comment	used only by insurance companies, evolved from GAAP	used by all U.S. public companies
objective	measure ability to pay claims (focus on solvency)	measure earnings
intended user	regulators	general audience: policyhoders, investors, public
oversight	individual states with assistance from NAIC	SEC (but SEC has delegated responsibility to FASB) 1

¹ SEC = Securities & Exchange Commission, FASB = Financial Accounting Standards Board

Memorize this table.

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SAP vs GAAP

Overview

There is a lot of material to cover before the next quiz (BattleQuiz #2) but the quiz provides a concise summary of the differences between SAP and GAAP so it might be helpful to skip ahead and take a look just so you know what's coming. The latest edition of the Odomirok source text also added an 11^th difference between SAP & GAAP (the PDR calculation) so make sure to pay attention to that.

This a heavily-tested section and will require significant effort to memorize:

Question: identify the 10+1 areas of difference between U.S. GAAP and U.S. SAP that actuaries should be familiar with [Hint: BASIC - D3NG + PDR]

Balance sheet presentation of reinsurance

Anticipated salvage/subrogation

Structured settlements

Invested assets   ← click Invested Assets for details on this confusing topic

Ceded reinsurance

–

DAC (Deferred Acquisition Expense)

DTA (Deferred Tax Asset)

Discounting loss reserves (See this forum discussion.)

Non-admitted assets

Goodwill

+

PDR (Premium Deficiency Reserve)   ← click PDR Calculation for a numerical example further down

I hope my memory trick helps you. Memory tricks are very personal and mine may not work for everyone. I reordered the list from the way Odomoirok did it so I could spell a word:

• BASIC

Then the leftover letters were D³NG and in my head, I hear this as:

• Da-Da-DiNG    Click if you love Beethoven!    (sing-out toSR! And let's also trumpet AveryN9!)

Then the newest edition of the source text added an 11th difference between GAAP & SAP:

• PDR or Premium Deficiency Reserve   ← click PDR Calculation for a numerical example further down

The old exam questions don't often ask you to list these areas. Rather, they list them for you and ask you to describe how each is treated in GAAP versus SAP. Take look at part (b) of:

E (2014.Fall #19)

It's a reasonable question, but the answer in the examiner's report is a bit ridiculous. It's a 2-point question, so each of the 4 parts (i), (ii), (iii), (iv) is 0.5 points each. To a reasonable person, that means stating briefly how the item is treated under SAP and how it's treated under GAAP. But the CAS answer is basically a copy/paste straight from Odomirok. Nobody would be able to provide that level of detail. The key to acing that type of question is boiling Odomirok's discussion down to its essentials. Here's how I did it:

item	SAP treatment	GAAP treatment
Structured settlements (when release from claimant not obtained)	record annuity cost as paid loss (disclose in Notes to Financial Statements)	record annuity cost as reinsurance (retain loss reserves & book payments as recoverables)
Discounting loss reserves (no discounting except in certain cases) (See this forum discussion.)	tabular discount rate - few state regulations non-tabular discount rate - formula-based & capped	options: use SAP rate or reasonable alternative
Ceded reinsurance    - retroactive reinsurance	record ceded reserves as negative write-in liability	record ceded reserves as reinsurance asset
DTAs (Deferred Tax Assets)	DTAs subject to strict admissibility test	DTAs fully recognized

There are lots more details in the BattleCards. (I don't normally put this much extra content only in the BattleCards, but the wiki would have become too cluttered otherwise.)

Here's a good exam question on SAP vs GAAP and also a related discussion in the forum. Parts (c) and (d) are good questions but they rely on information in the next BattleQuiz so you might want to take a second look after you do the quiz:

E (2018.Fall #19)

Here's another question below that we'll now look at in detail...

Ceded Reinsurance - Prospective

The latest edition of the source text added an example of SAP versus GAAP for prospective reinsurance. I've reproduced it below but with a few extra details. They didn't explain what they were doing and it took me a moment to understand it myself. Anyway, here it is, and then there are some Excel practice problems further down. It's sooooo simple. :-)

Here's the problem...

Here's the solution...

4 Excel practice problems...

Excel Practice: Odonirok.22-23 (005) - Prospective Reinsurance

Ceded Reinsurance - Retroactive: 2017.Fall Q12

To answer this question, you have to know the tiny details of SAP vs GAAP from the subsection on Ceded Reinsurance - Prospective & Retroactive. I thought this was worth a separate discussion. Here's a link to the question and answer in the examiner's report followed by my own answer:

E (2017.Fall #12)

First, you have to dissect the 2 paragraphs that discuss retroactive reinsurance. That's the key to this problem. Retroactive reinsurance is treated differently from prospective reinsurance. Prospective reinsurance is easy: SAP shows liabilities NET of prospective reinsurance, GAAP shows them GROSS. But retroactive reinsurance is treated as follow:

Retroactive reinsurance under SAP:

• undiscounted ceded reinsurance reserves are recorded as a negative write-in liability (or contra-liability)
• Schedule P is unchanged (shows gross of reinsurance)
• gain is recorded as a write-in gain [ note: gain = (negative write-in liability) – (cost of reinsurance) ]

   ==> goes into other income

   ==> no change to regular surplus because change goes into special surplus

Retroactive reinsurance under GAAP:

• ceded reinsurance reserves recorded as an asset
• gain is deferred (amortized over time)

   ==> no immediate impact on income

   ==> no immediate impact on surplus

The answer to the exam problem is just a rewording of this information:

effect of retroactive reinsurance under SAP on:

(i) loss reserves:

   - no change because ceded reserves go into a negative write-in liability (contra-liability), not into "normal" reserves

(ii) total liabilities:

   - decrease, since a negative liability will decrease liabilities

(iii) net income:

   - increase because other income increases

(iv) surplus:

   - increase, but this increase goes into special surplus

effect of retroactive reinsurance under GAAP on:

(i) loss reserves:

   - no change since ceded reserves are recorded as an asset

(ii) total liabilities:

   - increase, must establish a liability to offset the deferred gain in income (this was not explicitly stated in the text) ^footnote

(iii) net income:

   - no change (at least initially), gain is deferred

(iv) surplus:

   - no change (at least initially), surplus change is deferred

footnote

• Here's another way to think about the answer to part (b)(ii) regarding the effect on liabilities under GAAP. The liability that's created is similar to the UEP liability that's created when written premium comes through the door.

==> You can't recognize WP immediately as income

==> But over time, the written premium is earned and is permitted to flow into income

==> When this happens, the UEP liability decreases by the same amount

(You can think of written premium as a gain that's deferred but then "amortized" over time.)

• Well, the concept is the same with retroactive reinsurance. When retroactive reinsurance is purchased, any income gain is deferred then amortized. The way this is done on the books is to set up a liability and gradually decrease this liability as the gain is "earned".

PDR Calculation

The current edition of the Odomirok source text added a section on PDR (Premium Deficiency Reserve) and included a numerical example. That seems like a good candidate for an exam problem to see if people are paying attention. Don't worry, it's pretty easy. Below is a slightly expanded version of the text example and below that is an Excel file with randomized practice problems.

Under both GAAP and SAP, a PDR must be recognized with a charge to current operations when the unearned premium reserve (UPR) is insufficient to cover the anticipated costs. This must be done by policy grouping, and a premium deficiency from one grouping cannot be offset by expected profits from another grouping.

Question: identify the difference between GAAP & SAP regarding the premium deficiency calculation

• under SAP: commissions and other acquisition costs should not be included if those amounts have been expensed rather than established as an asset

Here's the problem...

Here's the solution...

4 Excel practice problems...

Excel Practice: Odonirok.22-23 (010) - PDR Calculation

Invested Assets

The difference in treatment of invested assets in SAP versus GAAP is highly technical, but it was asked in part (b) of this exam question:

E (2018.Spring #19)    (shout-out to KS!)

In particular, the question asked about treatment of:

(i) investment-grade bonds held to maturity (NAIC Class 1-2)

(ii) below investment-grade bonds available for sale (NAIC Class 3-6)

(iii) common stocks held for trading

The answer to this question is now partially outdated because the treatment of invested assets under SAP has changed a little bit. There are now 9 types of investments that are valued in SAP according to the table below. (Note: This table is inconsistent with the 1^st paragraph of the section on invested assets in the source text, but I believe the table is correct and the authors just forgot to update the paragraph text when the new edition was released in 2019.)

You would have to have memorized this table to be able to answer the exam question, which doesn't seem reasonable. If you love memorizing, then go for it. 😳 If not, here's a different strategy. Start by noticing that 3 of the investment types are valued the same way:

• fair value: common stocks, non-redeemable preferred stocks, SVO-identified investments (SVO = Securities Valuation Office)

Unfortunately, the other 6 investment types all have different values and I don't think I want to memorize all that. But I might go ahead and memorize how the 2 bond categories are valued since a large portion of most insurer's portfolios consists of bonds:

• amortized cost: investment-grade bonds (NAIC Class 1-2) long & short-term
• min(amortized cost, fair value) non-investment-grade bonds (NAIC Class 3-6) long & short-term

So you can remember 5 of the 9 categories without too much trouble. If the exam question asks anything other than these, just take an educated guess. There is a forum post with a trick for remembering the first 2 lines of the above table.  ← shout-out to Stowesam!

Finally, here's the quiz. I know you're super-excited. Make Alice proud.

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GAAP Surplus

This is the easiest calculation problem you will ever see on Exam 6. We covered SAP surplus in Odomirok.8-9-IS. Here are 2 old exam problems on GAAP surplus:

E (2018.Spring #19)

E (2014.Fall #19)

The examiner's report provided 2 sample answers, but the only formula you need to know is:

Formula used in this problem: 1    GAAP surplus    =    SAP surplus    +    (provision for reinsurance)    +    DAC

¹ There are other quantities (see above) that make GAAP surplus different from SAP surplus, but they were not provided in these problems. For example, if non-admitted assets were provided, you would have to include that in the sum on the right side of the equation. (Thx LK!)

The second sample answer excluded the term for provision for reinsurance, but I would go with the first answer. (The second answer seems to be saying that management's estimate of uncollectible reinsurance equals the provision for reinsurance, and this estimate is not included in GAAP surplus.)

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SAP Surplus (2014.Fall #15)

Fundamental Accounting Equation

We covered one way of calculating SAP surplus when we studied the income statement in chapter 8. Use the link to get a quick reminder of the formula we used. In this chapter, we'll see another version of calculating SAP surplus but here we use the Fundamental Accounting Equation. The wikipedia article uses the term equity but that's the same as surplus. In any case, we have:

Fundamental Accounting Equation:    surplus    =    assets    –    liabilities

This is the framework we'll use to solve the next problem. The solution consists of 3 separate calculations:

1. admitted assets
2. provision for reinsurance (part of liabilities)
3. liabilities

For step 2, you may need to review calculation of provision for reinsurance. We'll go over steps 1 & 3 below, but take a look at the problem first. (Don't panic when you see it! The solution in the examiner's report is well organized.)

E (2014.Fall #15)

Calculating the Admitted Assets

The key is being able to recognize which pieces of data are assets. They actually made it pretty easy for you because they put all the assets in the table at the top of the page, (except for the reinsurance recoverable, which is at the bottom.) Note however that not everything will be included. One of the items just doesn't count (goodwill, because it has been fully amortized) and one is a non-admitted asset (DAC, because this exists only in GAAP). Before going any further, it might be a good idea to review the asset side of the balance sheet in Elements of Financial Statements.

The solution is basically straightforward but there are lot of little details you have to remember:

• agents' balances > 90 days past due are not admitted
• how to calculate bond values - depends on the rating of the bond
• recalling that the amortization period for goodwill is at most 10 years
• DAC doesn't exist in SAP because SAP recognizes acquisition costs immediately (GAAP sets up an asset and amortizes the amount over the life of the asset)
• DTA must be netted out by subtracting DTL

If you put all this together, you'll get the correct answer of 61,900. This is one of those problems that's hard to get completely correct, but if you're well prepared you should get most of it.

Calculating the Liabilities

The hardest part of this problem is making sense of the large amount of information you're given. When you're asked to calculate liabilities for an insurance company, your mind should immediately go to loss & LAE reserves. That's always the biggest liability item on an insurer's balance sheet. That's where you'll need the Schedule P information. This is actually a very good problem for learning because it ties together so many different parts of the syllabus. The next thing you might notice is the third table on recoverables for an authorized reinsurer. Obviously they are setting up you to calculate the provision for reinsurance. This isn't too hard but you'll need information from the reinsurance chapter of Odomirok, Odomirok.14-F.

Beyond that, you just have to scan the given information for liability items to include. Recall the practice template from quiz 2 of Odomirok.8-9-IS where you had to state the location of line items from the financial statements. Part of the purpose of that exercise was so that you can immediately recognize that funds held and unearned premiums go into the liabilities bucket. Anyway, here's the list of liabilities that have to be included in the answer to this problem. You have to read the question very carefully to combine all the numbers correctly.

• loss reserves: 31,500 (= 19,000 + 20,000 - 7,500) ← from Schedule P info
• LAE reserves: 10,000 (= 3,500 + 4,000 + 2,500) ← from Schedule P info
• high deductible unpaid: 0 (this is a trick - the insured's losses are less than the deductible so the insurer pays nothing)
• UEP: 10,000 (= gross - ceded = 12,000 - 2,000)
• funds held: 180 (you just have to know this is a liability, as are ceded balances payable but those are 0 anyway)
• reinsurance provision: 60 (you had to calculate this like we did in Odomirok.14-F in the section calculation of provision for reinsurance)
• letters of credit: 0 (It didn't matter where you put this because it's 0 anyway. Note the definition of a letter of credit: a document sent from a bank or financial institute that guarantees that a seller will receive a buyer's payment on time and for the full amount. It guarantees a future liability so no specific liability is recognized on the balance sheet. Instead, a letter of credit is disclosed in the footnotes to the balance sheet.  ← shout-out to AS!)

The total is 51,740. You now have what you need to calculate the surplus using the Fundamental Account Equation.

Final Answer

This part is super-simple:

==> surplus    =    (admitted assets) – liabilities    =    61,900 – 51,740    =    10,160

Done!

SAP Surplus (2016.Spring #15)

Parts (a) & (b)

This problem is similar to the SAP surplus problem from above. A very good exercise is to do part (a) right now. Part (a) asks you to calculate the value of the admitted assets.

E (2016.Spring #15)

Once you've calculated the admitted assets, part (b) asks you to calculate the liabilities. The information is provided in a different format from the previous problem so you'll have to think through it. It's interesting they don't ask for the surplus, although that would be easy once you have the admitted assets and the liabilities. Anyway, give it a try on your own, then you can either check the examiner's report or read my explanation below.

In one sense calculating the liabilities is easier here than in the previous problem where you're given only loss & LAE (actually, DCC and A&O). There is no provision for reinsurance or anything else related to reinsurance aside from the ceded Schedule P amounts. In another sense, however, calculating the liabilities here is harder because they provide the Schedule P data differently. Let's think through it:

• Of course, the most important component of liabilities for an insurer is the loss & LAE reserves (DCC and A&O).
• At the very top, they tell you the company started operations in 2013. That seems like a throw-away piece of information but it's actually important. To calculate the loss reserves, you have to sum all AYs. You are given only AY 2013 and AY 2014, but that's all that exists if the company started in 2013.
• This problem provides Schedule P data just like on the real Schedule P: Years in Which Premiums Were Earned and Losses Were Incurred, except they don't provide totals across AYs. You have to sum AY 2013 and AY 2014. (Note that in the previous problem, they did provide the totals so you didn't have to worry about summing individual AYs.)

Once you realize all this, it isn't too hard. Aside from the UEP in the top table, you only need the lower part of the Schedule P table with the unpaid data:

==> net unpaid case loss & IBNR for AY 2013 & 2014:

= (100 + 120) - (10 + 15) + (150 + 200) - (5 + 20)

= 520

==> net unpaid DCC & IBNR for AY 2013 & 2014:

= (25 + 30) - (0.5 + 1) + (35 + 40) - (1.5 + 2)  ← shout-out to tubaguy!

= 125

==> net unpaid A&O (no IBNR) for AY 2013 & 2014:

= (12 + 18) - (0.1 + 0.2)

= 29.7

The UEP from the top table = 575. Summing these underlined values gives the total liabilities of 1,249.7.

Part (c)

I like part (c) of this problem. It's similar to other exam questions in that it asks you about differences between SAP and GAAP, but it doesn't specify which differences to discuss. That means you have to remember the 11 areas of difference [Hint: BASIC - D³NG + PDR], and select the ones that are most relevant to the information provided. For example, discussing how structured settlements are treated differently in SAP vs GAAP would not be a valid answer because this insurer did not have any structured settlements, at least as far as we know.

Here are a few examples of differences relevant to this insurer:

DAC: (this one is obvious!)

   - SAP does not have a DAC asset

   - GAAP does have a DAC asset (so the value of 32,500 would be included in GAAP assets)

non-admitted assets: (this one is obvious too!)

   - SAP did not admit agents' balances > 90 days past due

   - GAAP might admit this value of 1,800 if it is deemed collectible

balance sheet presentation of reinsurance:

   - SAP NETS OUT ceded reinsurance

   - GAAP does not (GAAP shows GROSS of reinsurance but has an offsetting asset for reinsurance recoveries)

anticipated salvage & subrogation: (this difference is less familiar)

   - we ignored salv/sub in our SAP calculation of liabilities

   - salv/sub must be netted out of reserves in GAAP

One of the other acceptable answers in the examiner's report was invested assets, bond valuation. This was a hard one, however, because you really had to know small details of how bonds & stocks can are valued in SAP vs GAAP.

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SAP 10K Exhibit (2014.Spring #23)

This was a very hard problem and it is probably the least likely problem to be asked from this chapter. If you're pressed for time, it may be wiser to skip ahead to Chapter 23 (see below) and return to this later.

Update: The 10-K Loss Development Table has been removed from the 2019 edition of Odomirok source text. That means this type of question should not appear on exams from 2021.Spring and later. Therefore you can ignore part (a) of this question. Click SAP 10K Exhibit for why the material on Exhibit 10-K is covered relatively lightly in the wiki.   (shout-out to KS!)

Here is the link to the problem:

E (2014.Spring #23)

Solution: 2014.Spring #23  ← Alice's awesome solution!

(The answer in the examiner's report is extremely unhelpful. It shows the answer but doesn't explain any of the steps.) They are asking you to reproduce the 10-year loss development table from the insurer's 10-K. If you look at the example exhibit in Odomirok, table 113, you'll see that it does indeed have 10 years of data. Luckily, the insurer in this 2014 exam problem started in 2009, so there's only 4 years of data here. Yay!

10-Year Loss Development Table    ← This exhibit has been removed from the current edition (2019) of Odomirok.

Anyway, let's start with part (b). Strictly speaking, you need the answer to part (a) to properly answer part (b), but we can still make a pretty good guess before doing the long calculation involved in part (a). You first have to remember a couple of things about Schedule P:

• Schedule P, Part 2 is labeled as incurred loss but it is really ultimate loss.
• Each row represents an AY
• Schedule P, Part 3 is just the normal cumulative paid (no tricks here.)

Part (b) of the question asks you to comment on the accuracy of the insurer's historical loss reserves. Well, it's pretty obvious they were initially over-reserved in AY 2009. Their initial estimate of ultimate loss was 16,500 and it decreased steadily over time so that 3 years later their estimate was only 13,000. If you do the same kind of simple analysis for AY 2010, you'll see they apparently over-corrected based on their AY 2009 experience. For AY 2010, their initial estimate of ultimate loss was 14,500 but this increased steadily over time so that 2 years later, it was 19,000. Ok, hold that thought.

Question: identify the purpose of the 10-year loss development table in the insurer's 10-K

• The 10-year loss development table provides information regarding the deficiency (redundancy) of initial AY reserves using subsequent experience.

It's like a report card for the reserving actuary. Alice thinks this exhibit should be part of the annual performance review for appointed actuaries, but she also knows this would not be a popular idea. TRUE STORY: I know someone who worked at a company where it came to light they were roughly $50 million under-reserved. This was based on $250 million of total reserves - not an insignificant amount. Needless to say, the chief actuary was fired. The problem was every quarter, the product managers would pressure the chief actuary to lower his estimates of ultimate loss for their state. (They wanted their bonuses.) Drip, drip, drip...but eventually the whole thing blew up.

Anyway, let's see if we can figure out how to construct this loss development table. Let's focus our attention on AY 2009 and make a few observations:

• The initial AY 2009 estimate of ultimate loss is 16,500 (from Schedule P, Part 2)
• The actual paid loss is 4,125 (from Schedule P, Part 3)
• You can then calculate the initial AY 2009 reserve as 16,500 - 4,125 = 12,375

Ok, pretty simple. Now observe that 1 year later, the estimate of ultimate for AY 2009 is 15,000. Presumably this is a better estimate because the AY is more mature. Here's the KEY to constructing this loss development table:

• what would the initial AY 2009 reserve have been if the initial estimate of ultimate had been 15,000 (instead of 16,500)

The answer is 15,000 - 4,125 = 10,875. The trick is that you always subtract the same paid loss of 4,125 because we want the improved estimate of ultimate applied to year-end 2009. Let's continue ahead 1 more year and see what happens. The estimate of ultimate for AY 2009 at the end of AY 2011 has dropped again to 13,500. This should be more accurate than the previous estimate of 15,000. Let's apply the KEY again:

• what would the initial AY 2009 reserve have been if the initial estimate of ultimate had been 13,500 (instead of 16,500)

The answer is 13,500 - 4,125 = 9,375. If you go forward 1 more year and apply the same reasoning, you'll get the value 13,000 - 4,125 = 8,875. Take another look at the solution in the examiner's report. We have done most of the calculations for the CY 2009 column. We have the first row, which they label as Initial and the last 4 rows, which they label as Cum Inc Re-Stated as of and Adv Dev. This last value 8,875 - 12,375 = -3,500 represents how much the reserves have decreased since the initial estimate at the end of CY 2009. Since it's a negative amount, we can say the initial reserves were redundant.

The other rows for the 2009 column, the rows labeled as Cum Paid as of...1-yr later, 2-yrs later, 3-yrs later are very easy:

• 1-yr(s) later: 6,750 - 4,125 = 2,625
• 2-yr(s) later: 10,100 - 4,125 = 5,975
• 3-yr(s) later: 11,700 - 4,125 = 7,575

Note that this paid information is not useful in evaluating deficiency (redundancy) of reserves.

Question: how do we construct the rest of the 10-year loss development table

I'm really glad you asked that question because I totally know the answer. It's conceptually the same as what we did above, but the calculations are a little messier because we have to combine AYs. Here's how you get all the numbers for the CY 2010 column as shown in the examiner's report:

• Initial

= [ (AY 2009 ultimate @ 2010) + (AY 2010 ultimate @ 2010) ] – [ (AY 2009 paid @ 2010) + (AY 2010 paid @ 2010) ]

= [ 15,000 + 14,500 ] – [ 6,750 + 3,300 ]

= 29,500 – 10,050

= 19,450

• Cum Incurred Re-Stated 1-yr Later (remember to subtract the same paid values every time)

= [ (AY 2009 ultimate @ 2011) + (AY 2010 ultimate @ 2011) ] – [ (AY 2009 paid @ 2010) + (AY 2010 paid @ 2010) ]

= [ 13,500 + 17,000 ] – [ 6,750 + 3,300 ]

= 30,500 – 10,050

= 20,450

• Cum Incurred Re-Stated 2-yr Later

= [ (AY 2009 ultimate @ 2012) + (AY 2010 ultimate @ 2012) ] – [ (AY 2009 paid @ 2010) + (AY 2010 paid @ 2010) ]

= [ 13,000 + 19,000 ] – [ 6,750 + 3,300 ]

= 32,000 – 10,050

= 21,950

• Adv Dev

= 21,950 – 19,450

= 2,500 (since this is positive, it's a deficiency)

As an exercise, complete the rest of the calculations. If you need a hint, see the link to Alice's awesome solution at the beginning of this section.

Question: if you're given a similar question on the exam, what should your general approach be

general approach: write out the structure of the exhibit

• write the relevant CYs at the top of your page - these are the column headings
• section 1: consists of 1 row labeled Initial
• section 2: Cum Pd consists of several rows labeled 1-yr later, 2-yr later,...
• section 3: Cum Inc Re-Stated as of consists of several rows labeled 1-yr later, 2-yr later,...
• Section 4: Adv Dev consists of 1 row - calculated as the last row of section 3 minus the Initial row

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Chapter 23 (U.S. Purchase GAAP)

Chapter 23 of Odomirok, (Fair Value Under Purchase GAAP) is an elaboration on the goodwill concept from earlier. Note that Purchase-GAAP or P-GAAP is a type of GAAP accounting that is used when one entity purchases another. It includes some intangible assets not normally recognized and measured under U.S. GAAP. I asked Alice if she could give me a simple explanation of goodwill, and she said,

Let's say you want to sell me your car, and that the fair market value of your car is $10,000. If I pay you $12,000 (because I like you!), the goodwill is $2,000.

It's the same when an entity buys an insurance company. Another way to think about it is that goodwill reflects the portion of a company’s value aside from cash or physical assets, like its reputation. Recall that under GAAP, if P = purchase price, then: (recall the SAP goodwill formula is slightly different)

Basic Formula:    GAAP goodwill    =    P    –    (net assets)    =    P    –    [ FV(assets)    –    FV(liabilities) ]

• if result > 0 → establish an asset equal to the amount of goodwill (for Alice's car example, the goodwill creates an asset worth $2,000 for the purchaser)
• if result < 0 → immediately recognize this amount as operating income gain (in this case, there is no goodwill)

Only the purchasing company recognizes goodwill. (Note that the limit on goodwill of 10% of the acquiring company's surplus applies only to SAP.) To calculate goodwill, we have to calculate the FV or Fair Value of the assets and liabilities of the company being acquired.

Question: define Fair Value according to U.S. Purchase GAAP

• Fair Value is the price at which an orderly transaction to sell the asset (or to transfer the liability) would take place between market participants at the measurement date under current market conditions.

We'll assume someone else calculates FV(assets) and that the actuary calculates the paid and unpaid loss & LAE component of FV(liabilities). Odomirok explains how this calculation is done and then provides a numerical example. Aha! This looks like a likely exam question. Fire up Excel and create a spreadsheet to follow along with the text example! But first let's look at a related non-numerical exam question:

E (2017.Fall #19)

The answer to part (a) of this question is the essence of Chapter 23.

Question: describe each component of FV(liabilities)* under GAAP purchase accounting and how to calculate each component

component #1: nominal future cash flows of liabilities

• calculate using LDFs

component #2: discounted component #1 + (load for illiquid nature of liabilities)

• calculate using risk-free rate

component #3: risk margin to compensate for uncertainty of liabilities

• calculate using cost-of-capital approach

^* Note that the exam problem should more accurately have stated FV(FAIR VALUE OF LOSS AND LAE RESERVES) rather than just FV(Liabilities), at least according to the first page of chapter 23 of Odomirok. The total FV(Liabilities) would also have to include liabilities other than loss & LAE reserves.

Now let's apply this knowledge to an actual problem. As always, Alice created her own nicely laid out solution in Excel, generated some similar random problems, then converted it all to PDFs for you guys, but here is the official version of the question and answer.

E (2016.Fall #18)

There is a formula for calculating component #3: (risk margin)

risk margin   =    (R - i)    x    Σ [ avg(Ct, Ct+1) / (1+i)t+1 ]

t = time (sum across t = 0, 1, 2,...)

R = pre-tax cost-of-capital (required return on capital by purchaser)

i = risk-free rate that includes illiquidity premium

C_t = capital carried at time to the support liability

Here is Alice's solution:

Solution to 2016.Fall #18

And here are 2 practice problems:

2 practice problems like 2016.Fall #18

And finally the last quiz...

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