Klann.ReinsComm

put summary here

Pop Quiz

Identify 6 functions of reinsurance. [Hint: cat-SWIGS] (Answer at bottom of this wiki article.)

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

reference	part (a)	part (b)	part (c)	part (d)
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	impact: on IRIS 3
E (2015.Fall #18)	RESTATE: triangles after commutation	calculate: IRIS 2, 7, 11	interpret: other related IRIS ratios
E (2015.Spring #26)	motivation: for a commutation (SEDR)	calculate: change in surplus	discuss: distortions to triangles
E (2013.Fall #29)	define: commutation	discuss: factors affecting pricing	discuss: factors affecting pricing	impact: on balance sheet

In Plain English!

Definition of Commutation

A reinsurance commutation is a way of ending a relationship between an insurer & reinsurer. Consider the following sequence of events:

1. A primary insurer buys a policy from the reinsurer A1-Re for price P.
2. During the 1st year, A1-Re assumes $1,000 in losses, makes payments of $100, and has year-end reserve of $900.
3. At year-end the primary insurer and A1-Re decide to end their relationship by commuting the remaining losses.
4. They decide on a fair price, let's say the present value of $900, the reinsurer's current reserve. (ignore tax effects)
5. 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)
6. 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!

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.

Klann commutation example

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)

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

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 small 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)

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 booked at their nominal (undiscounted) value, but for tax purposes, loss reserves are discounted

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!)

Canada: In Canada, reserves are booked at their discounted value. This includes both the time-value of money and something called margins for adverse deviations. The Canadian Institute of Actuaries provides detailed guidelines on this discounting process. If you ever do work in Canada, that is something you would definitely have to learn. (This is covered exhaustively in the Canadian version of BattleActs for Exam 6.)

Anyway, 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.

example

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 simple variables are:

price = commutation price

d₁ = discount factor for primary insurer

d₂ = discount factor for reinsurer

The complicated variables are for the different types of losses:

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	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

Here are 2 easy problems in calculating the change in taxable income for the primary insurer & reinsurer.

tax effect PRACTICE

One you understand the above problem, next is a harder version of that problem. It's harder 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.

2017.Spring #26b solution

Let's finish with a problem just like (2017.Spring #26b) but with different numbers so you can practice.

2017.Spring #26b 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 (2016.Fall #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 the provides a mutual benefit to both primary insurer & reinsurer [Difficulty: kind of hard]

Question: what are the steps in pricing a commutation [Hint: EDTU]

Let's go back to that example from an earlier section where the primary insurer estimated the value of the reserves at $100, and the reinsurer at $1,000.. These numbers are really simple, but it will aid your understanding. (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 on 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 – ( pR-c ) + ( pT ) > 0
...reinsurer benefit	– price + ( 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:

• _pT as the tax benefit to the primary insurer
• _reT as the tax benefit to the reinsurer

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 ).

See if you can solve (2016.Spring #27). It's not too hard if you know the formulas. (The source reading did not provide the formulas, so you had to come up with then on your own. That's what made the problem hard.)

BattleCodes

Memorize:

Conceptual:

Calculational:

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POP QUIZ ANSWERS

cat-SWIGS

cat: CATASTROPHE protection (a very large loss will be mostly absorbed by reinsurance)

S: STABILIZE loss experience (reinsurance 'cuts the right tail off' the loss distribution)

W: WITHDRAWAL from market is facilitated (off-loading risk to reinsurance is quicker than runoff)

I: INCREASE large-line capacity (but minimize associated risk)

G: GUIDANCE from reinsurer (with expertise in U/W & pricing for that particular line)

S: SURPLUS relief (reinsurance reduces net leverage ratio)