Klann.ReinsComm
Reading: Reinsurance Commutation, 2013
Author: Klann, J.
| Certain facts presented in this reading are outdated. It was published in 2013 and the tax code has since changed. The official CAS syllabus instructs candidates to refer to the most recent version of the Odomirok text for current information. |
| BA Quick-Summary: Reinsurance Commutations
A reinsurance commutation is an agreement that terminates the relationship between an insurer and a reinsurer by settling all obligations with an immediate payment. Commutations can occur for various reasons, such as:
This process involves complex considerations in pricing, reserving, and accounting, and can significantly affect both parties' financial statements. The document delves into these aspects, particularly focusing on the accounting and taxation implications of commutations. |
Contents
Pop Quiz
Identify 6 functions of reinsurance. [Hint: F-cat-SWIPLES] (Answer at bottom of this wiki article. This question comes from Cedar.ReinsAccting which you probably haven't covered yet.)
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- motivation for a commutation
- how to RESTATE loss triangles after a commutation has taken place
- how to calculate the change in taxable income due to a commutation (and change in tax)
- how to calculate the price of a commutation
- impact on IRIS ratios
- distortions to LDFs due to commutation
Questions held out from Fall 2019 exam: #26. (Skip these now to have a fresh exam to practice on later. For links to these questions, see Exam Summaries.)
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reference part (a) part (b) part (c) part (d) E (2019.Spring #24) calculate: commutation price motivation: for a commutation (SEDR) E (2018.Fall #26) define: commutation motivation: for a commutation (SEDR) E (2017.Fall #27) calculate: commutation price that cancels tax RESTATE: triangles after commutation motivation: for a commutation but for only 1 policy year (variation on SEDR) E (2017.Spring #26) motivation: for a commutation (SEDR) calculate: change in taxable income E (2016.Fall #26) RESTATE: triangles after commutation calculate: change in taxable income motivation: for a commutation (SEDR) impact: financial instability & commutation price E (2016.Spring #27) calculate: commutation price impact: on IRIS 1 2 impact: on IRIS 3 E (2015.Fall #18) RESTATE: triangles after commutation calculate: IRIS 2, 7, 11 1 interpret: other related IRIS ratios E (2015.Spring #26) motivation: for a commutation (SEDR) calculate: change in surplus 3 discuss: distortions to triangles E (2013.Fall #29) define: commutation discuss: factors affecting pricing discuss: factors affecting pricing impact: on balance sheet
- 1 There is a typo in the examiner's report solution to part (b) where they calculate IRIS 11. The answer should be +22.07%. (The solution shows –22.07%)
- 2 I believe the surplus calculation shown in the examiner's report should have included the tax benefit of the 2M commutation price. In this case the tax benefit would be: (3M x 0.85 - 2M) x 0.35 = 0.1925. It isn't enough to offset the difference between the commutation price and the undiscounted ceded reserves, but you wouldn't know unless you calculated it.
- 3 Further explanation of the solution to part (b), calculating the change in surplus due to the commutation, is discussed further in the forum.
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In Plain English!
Definition of Commutation
Reinsurance commutation can be a confusing topic although the general concept is easy enough: Commutation of a reinsurance contract means that the primary insurer and reinsurer have ended their relationship. It's the calculations that are hard. Calculation of the commutation price is confusing and the Klann reading, although well written, does not provide a good numerical example. Actually, I find all the numerical problems from this reading pretty confusing. You will have to practice the calculations many times for each type of problem if you want to be confident on the exam.
A reinsurance commutation is a way of ending a relationship between an insurer & reinsurer. Consider the following sequence of events:
- A primary insurer buys a policy from the reinsurer A1-Re for price P.
- During the 1st year, A1-Re assumes $1,000 in losses, makes payments of $100, and has year-end reserve of $900.
- At year-end the primary insurer and A1-Re decide to end their relationship by commuting the remaining losses.
- They decide on a fair price, let's say the present value of $900, the reinsurer's current reserve. (ignore tax effects)
- A1-Re then sells the losses back to the primary insurer by paying them the present value of $900. (It's the seller who pays because the reserves are a liability)
- A1-Re's reserves decrease by $900, and the primary insurer's reserves increase by $900. (The primary insurer's paid losses also increase by the selling price, but we'll cover that later.)
At this point, the commutation is complete, and A1-Re no longer has any liability for these losses. The precise definition of commutation is as follows:
A commutation agreement is an agreement between a ceding insurer and the reinsurer that provides for the valuation, payment, and complete discharge of all obligations between the parties under a particular reinsurance contract.
That's a mouthful! I just like to think of it as a way of ending the insurer-reinsurer relationship where the reinsurer sells the remaining losses back to the original insurer. This reading discusses the accounting & taxation of commutations.
Motivation for a Commutation
Now that you have a basic idea of how a commutation works, let's look at why the parties to a contract might want to execute a commutation.
Question: identify reasons for a commutation to occur [Hint: SEDR, sounds like ceder]
- SOLVENCY: primary & reinsurer may have concerns about each other's solvency
- EXIT: commutation provides a way for the reinsurer (& primary insurer) to exit a particular market
- DISPUTES: primary & reinsurer may want to end their relationship because of disputes (Ex: over contract provisions)
- RESERVES: primary & reinsurer may disagree over the value of the ceded/assumed reserves (both may think they're getting a good deal under the commutation)
- You should also be able to provide details for these reasons. You can refer to p1 of the source reading for this, or study the BattleCards in the mini BattleQuiz below. (I just didn't want to clutter up this wiki article.) If you refer to the source reading, note that I listed the reasons in a different order. That was to make the memory trick SEDR work. Remember, it sounds like ceder - that's how you know it has something to do with reinsurance! (Note that sometimes a commutation clause is written into the original contract. In that case the "motivation" for the commutation would simply be to comply with contractual obligations.)
- A simple example for the RESERVES reason: (again, let's ignore tax effects for simplicity)
- suppose the primary insurer values the ceded/assumed reserves at $100, but the reinsurer values them at $1,000 (Very different!)
- suppose they agree on a commutation price of $450
- the primary insurer would believe they're making a profit of ($450 – $100) = $350
- the reinsurer would believe they're making a profit of ($1,000 - $450) = $550
- Both are happy! (At least until the real value of the claims becomes known – then only 1 of them will be happy.)
| Pop Quiz! :-o |
- Question: In the above example, if the final settlement value of all the claims was $300, who who would be happy and who would be bummed?
- Answer: The primary insurer would be happy because their final profit from the commutation would be ($450 – $300) = $150. The reinsurer would be bummed because they paid $450 to get rid of $300 worth of claims, meaning they lost $150 on the deal.
Related Exam Questions
- E (2017.Fall #27c) was about motivations for a commutation but they threw in a twist. They specified 1 policy year only. Answering with SEDR didn't get you credit. You had to think more carefully to come up with an acceptable answer.
- E (2017.Spring #26a) was an easy question. The answer is SEDR, but you didn't even have to provide all 4 reasons, just 2.
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Accounting Treatment of a Commutation
We're skipping the section on pricing a commutation but will return to it later. Let's highlight some basic facts on accounting treatment of a commutation.
Question: who is the buyer in a reinsurance commutation: primary insurer or reinsurer
- The primary insurer is the buyer because they are receiving the item in question. (The item in question is the collection of unpaid claims being commuted.)
- Normally, the buyer is also the payer, but here it's reversed because the item in question is a liability. That means the reinsurer gives money to the primary insurer.
A commutation can be very complicated if it applies to multiple policy years, or applies only to specific lines of business or claims. However, the example in the text on pages 3-6 is greatly simplified. It shows loss triangles for the primary insurer & reinsurer before & after the commutation, but the commutation applies to only 1 policy year, 2013,and occurs at the end of 2015.
Here is a link to the example from the Klann reading, but with highlighted cells to indicate the changes due to the commutation in the triangles on page 5.
You're going to have to read the example on pages 3-6 very carefully. There is a lot of information there, but for now just focus on understanding the adjustments to the triangles. Here are some facts to keep in mind as you're going through the example:
Question: which cells in the loss triangle change due to the commutation (pertains to text example)
- In the loss triangles for the primary insurer, the only cells that change due to the commutation are policy year 2013 @ 36 months:
- paid loss (ceded): PY 2013 @ 36 increases by the commutation price of $400 (because of the payment the reinsurer had to make)
- paid loss (net): PY 2013 @ 36 decreases by the commutation price of $400 (to balance the ceded triangle)
- reserves (ceded): PY 2013 @ 36 decreases from 500 to 0 (this is whole point of the commutation!)
- reserves (net): PY 2013 @ 36 increases by 500 (to balance the decrease in the ceded triangle)
- In the loss triangles for the primary insurer, the only cells that change due to the commutation are policy year 2013 @ 36 months:
- The reinsurer's loss triangles are simpler because there is only grosss (no net or ceded).
- paid loss (gross): PY 2013 @ 36 increases by the commutation price of $400 (because of the payment the reinsurer made to the primary insurer to get rid of the claims)
- reserves (gross): PY 2013 @ 36 decreases from 550 to 0 (this is whole point of the commutation!) 1
- The reinsurer's loss triangles are simpler because there is only grosss (no net or ceded).
- 1 Note that the reduction in reserves for the reinsurer was 550 versus the reduction for the primary insurer, which was only 500. This is because the primary insurer and reinsurer had valued those claims differently.
I've reworked the solution to part (b) from the examiner's report for: (See table below for the link to the reworked solution.)
- E (2017.Fall #27)
Study how this works, then do the practice problems. (Note the potential distortions a commutation can produce on LDF triangles)
| Note: There is a forum discussion with an alternate (easier?) solution to this problem than the one shown below. |
exam solution practice 1 practice 2 2017.Fall #27b solution 2017.Fall #27b PRACTICE 1 2017.Fall #27b PRACTICE 2
Ok, now you're ready to slay the mini BattleQuiz!
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Tax Effect of a Commutation
This is an easy section to read but the exam problem we're going to cover is quite hard:
- E (2017.Spring #26b)
But first, here is something you should know:
Fact: statutory loss reserves are generally1 booked at their nominal (undiscounted) value, but for tax purposes, loss reserves are discounted
- 1 Statement of Statutory Accounting Principles (SSAP) 65 indicates that except for certain workers compensation and long-term disability claims with fixed and reasonably determinable payments, property/casualty loss reserves cannot be discounted.
Outdated statement: Since time-discounted reserves are lower than nominal reserves, manipulating the payment pattern and discount rate is a way insurers can reduce their taxable income. (I'm sure nobody has ever done this!) ← see new tax information for how this has changed.
Getting back to the exam problem, we'll first cover an easy version of the problem. Click the green link below for an example. I had to invent notation to help me understand how the problem works. The notation seems complicated for this easy example, but it will make the hard version of the problem easier to understand.
The main formulas used in the example were: (See further down for an explanation of the notation.)
FORMULAS for change in taxable income after commutation for... ...primary insurer = price – ( pR-c ) x d1 ...reinsurer = ( reR-g ) x d2 – price
- The only way I could make sense out of this problem is to invent some good notation. The variables in the above formulas are:
- price = commutation price
- d1 = discount factor for primary insurer
- d2 = discount factor for reinsurer
- pR-c = undiscounted reserve amount that primary insurer cedes to reinsurer
- reR-g = undiscounted reserve amount that reinsurer assumes from primary insurer.
- You might think the red and green amounts above should be the same because they represent reserve amounts for the same set of claims. The reason they're not is that the actuary for the primary insurer may have valued them differently versus the actuary for the reinsurer. (They could be the same, but they don't have to be.)
Here are 2 more practice problems for the easy version of calculating the change in taxable income. (There's also a practice template for this in the mini BattleQuiz.)
For the hard version of this problem we'll need some more notation:
symbols meaning p, re primary insurer, reinsurer P, R, U Paid, Reserve, Ultimate -, + before & after commutation n, c, g net, ceded, gross1
- 1 Something that bothers me in this problem is that they give you the primary insurer's direct losses instead of calling it gross losses. Normally, gross = direct + assumed so the assumption appears to be that there are no assumed losses. It just seems confusing to use the terminology "direct" rather than "gross". For that reason, I'm going to shift to using "gross" instead of "direct" for the primary insurer in this problem.
- There are 2 x 3 x 2 x 3 = 36 different possible combinations of these symbols. Here are the symbols we need for the hard version of the problem:
symbol pre-subscript type of loss post-subscript comment pR-g primary insurer (Reserve) before commutation gross given (used in easy version) pU-g primary insurer (Ultimate Loss) before commutation gross given pR-c primary insurer (Reserve) before commutation ceded step 1 of calculation (used in easy version) reR-g reinsurer (Reserve) before commutation gross step 2 of calculation (used in easy version) pP-n primary insurer (Paid Loss) before commutation net step 3 of calculation pP-c = reP-g 2 primary insurer (Paid Loss) before commutation ceded step 4 of calculation reU-g reinsurer (Ultimate Loss) before commutation gross step 5 of calculation reU+g reinsurer (Ultimate Loss) after commutation gross Step 6 of calculation
- 2 reP-g is the reinsurer's GROSS PAID LOSS before commutation and is equal to the primary insurer's CEDED PAID LOSS before commutation. (Unlike the ceded and assumed reserve amounts, the paid amounts are not actuarial estimates so the primary insurer and reinsurer will record the same amount.)
Once you understand the easy version of this tax problem, try the hard version. It's hard because they don't give you the commutation price - they make you calculate it. The solution in the examiner's report wasn't very clear. Click the green link for a pdf with a better organized solution.
Even after you're able to follow the steps in the above solution, calculating the commutation price still probably confusing. You'll have to practice it a bunch of times, but here's a hack. When I solve this problem, I work backwards. I start with the formula for the commutation price then fill in the missing pieces. In other words, this is the step-by-step process I use:
step term formula comment 1 commutation price = reU+gross – reP-gross the commutation price is the leftover amount 2 reP-gross = pP-gross x qs%
= ( pU-gross – pR-gross ) x qs%just apply the qs% to the primary insuer's gross paid loss 3a reU+gross = reU-gross x ( 1 + increase in reinsurer's ultimate after commutation ) this increase is directly related to the commutation price the primary insurer & reinsurer agreed to 3b reU-gross = reR-gross + reP-gross ultimate = reserve + paid 3c reR-gross = pR-gross x ( 1 + increase in reinsurer's carried ) x qs% we're told the reinsurer has initially valued the ceded reserves higher by a given percentage
Let's finish with a problem just like (2017.Spring #26b) but with different numbers so you can practice.
One final thing, and it's very easy, is how you calculate the actual change in tax (versus taxable income). You have to know the tax rate, which could be different for the primary insurer & reinsurer. All you do is multiply (change in taxable income) by (tax rate). It couldn't possibly be any simpler! This comes up in a few places in the old exam problems.
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Pricing a Commutation
As of Spring.2018, there had been 3 calculation problems where you had to figure out the commutation price. (The links are given in the BattlePlan at the top of this wiki article, but I've also put them below for your convenience. You're welcome!) I think these problems were a little unfair because there was nothing in Jimmy Klann's nice article to prepare you for it. He provides a clear explanation of the general procedure, but no actual example.
- E (2017.Fall #27)
- (a) calculate a commutation price that so that the insurer pays no tax [Difficulty: not too hard]
- E (2017.Spring #26) [Difficulty: pretty hard]
- (b) calculate the change in taxable income for the primary insurer & reinsurer (they didn't explicitly ask you to calculate the commutation price, but you had to do it as an intermediate step in finding the change in taxable income) We covered this problem in the section on taxation and the practice problems provided.
- E (2016.Spring #27)
- (a) calculate a commutation price that provides a mutual benefit to both primary insurer & reinsurer [Difficulty: kind of hard]. There is a forum discussion on this, but this question is more closely related to a reading that is no longer on the syllabus. Alice says they really shouldn't ask a question like this again. If they do, and they don't give you the value for economic discounting, then you should just use statutory discounting.
- ==> Part (b) of this question is very tricky. See this forum post for an explanation.
| Question: what are the steps in pricing a commutation [Hint: EDTU] |
- Let's go back to my made-up example from an earlier section where the primary insurer estimated the value of the reserves at $100, and the reinsurer at $1,000.. My made-up numbers are not calculated using real data, but it will aid your understanding when you do a real problem using the actual formulas. (The old exam problems above are much harder.)
- Step 1: Estimate the claim payments that would be made in the absence of a commutation
- for the insurer, these payments are reinsurance recoverables: $100
- for the reinsurer, these payments are their loss reserves: $1,000
- Step 2: Discount the estimates (Recall that losses are booked on a nominal basis, but commutation price uses discounted values.)
- obviously you need a payment pattern and discount factor, which again will probably be different for the insurer and reinsurer.
- insurer's discounted value: $80
- reinsurer's discounted value: $820
- Step 3: Tax effects:
- Using these discounted values and any effects on taxation, the insurer and reinsurer would try to agree on a price that is mutually beneficial
- insurer's tax benefit: $10
- reinsurer's tax benefit: – $60 (it's actually a tax loss because they are losing the reserve liability deduction)
- Step 4: Unique considerations:
- there may be unique considerations (possibly qualitative) that affect the price in a particular situation.
- for example, the reinsurer may be desperate (for whatever reason) to exit the market and may accept a higher selling price. (Recall that the reinsurer is the seller, but since the losses are a liability, the seller is the party that pays.)
| FORMULAS for pricing a commutation for mutual benefit... | |
|---|---|
| ...primary insurer benefit | price – ( economic-discounted pR-c ) + ( pT ) > 0 |
| ...reinsurer benefit | – price + ( economic-discounted reR-g ) + ( reT ) > 0 |
- Recall:
- pR-c = primary insurer's RESERVES before commutation on a ceded basis
- reR-g = reinsurer's RESERVES before commutation on a gross basis
- And define: (note that the primary insurer & reinsurer might use different discount rates for the tax-discounting of the commuted reserves)
- pT as the tax benefit to the primary insurer
- = (tax rate for primary insurer) x (decrease in taxable income for primary insurer) = (tax rate for primary insurer) x (add the tax-discounted reserves commuted and subtract the commutation price)
- reT as the tax benefit to the reinsurer
- = (tax rate for reinsurer) x (decrease in taxable income for reinsurer) = (tax rate for reinsurer) x (subtract the tax-discounted reserves commuted and add the commutation price)
- Now solve each inequality for P:
- The overlap provides a range for a mutually beneficial price P. (Of course, there is no guarantee that the insurer and reinsurer will agree on a price. If not, the commutation cannot take place.)
- The acceptable range for our example is: ( $70 , $760 ).
Pop Quiz! :-o
- Will the quantity pT usually be positive or negative? Explain.
- Will the quantity reT usually be positive or negative? Explain.
Pop Quiz Answers! :-D
- Revised answer (Apr 9, 2023) Click for Klann Pop Quiz Old Answer
- Here's the quick answer: The commuted discounted reserve reduces the primary insurer’s income, while the price increases it. In the case where price is greater than the commuted discounted reserve, income, and tax on income, increases. The effect is reversed for the reinsurer.
- → pT should be negative
- → reT should be positive
- Here is the detailed explanation:
- There are numerous factors that result in differences between the nominal reserves, expected payment patterns, discount rates, and tax rates of the primary insurer and the reinsurer engaging in a commutation, for the same commuted liability. Nevertheless, both parties must agree on a single price for the commutation to take hold. It is reasonable to assume that parties will come to an agreement on a price, only if that price makes the commutation beneficial for both sides.
- That being said, to answer this question in a general sense, we need to assume that the said differences do not exist. Under this assumption, we have a single commuted discounted reserve amount for both parties, for the purpose of calculating tax.
- The price under these conditions will likely be greater than the discounted reserve amount. This is because there is uncertainty as to whether claims will ultimately pay out for the stated reserve amount. This uncertainty will be built in as a margin to price.
- See if you can solve (2016.Spring #27). It's not too hard if you know the formulas, but you first spend 5 minutes reading economic versus tax discounting. (The source reading did not provide the formulas, so you had to come up with them on your own. That's what made the problem hard.)
Here's my solution to that problem:
And here are 4 practice problems with randomized inputs:
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Remaining Exam Questions
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POP QUIZ ANSWERS
Question: identify 9 functions of reinsurance [Hint: F-cat-SWIPLES] or see this forum post for an alternate hint
- (9) → Fronting arrangements
- –
- (2) → catastrophe protection
- –
- (3) → Surplus relief & capital efficiency
- (6) → Withdrawal from market
- (8) → Internal reinsurance transactions
- (7) → Pools - mandatory & voluntary
- (1) → Large line capacity
- (5) → Enter market and/or U/W guidance
- (4) → Stabilize results
- (9) → Fronting arrangements
The numbers preceding the bullet points refer to the numbering used in the Cedar & Thompson source text. I changed the order so the hint, F-cat-SWIPLES, would spell a word, sort of. Sometimes people post better hints in the forum. If you come up with something better, please go ahead and post! I will link to it from here. This reordering doesn't change the content of course, but it might be slightly confusing if you try to read the source text.
