Freihaut.Reins

Reading: “Common Pitfalls and Practical Considerations in Risk Transfer Analysis,” Casualty Actuarial Society E-Forum, Fall 2009.

• Appendices A and B are for information only and will not be directly tested.

Author: Freihaut, D. and Vendetti, P.

Forum

BA Quick-Summary: Risk Transfer Analysis This reading provides an overview of risk transfer analysis, highlighting nuances that can challenge actuaries. It covers common pitfalls and practical considerations. The paper includes examples and simulations to illustrate these points, emphasizing the importance of accurate documentation and analysis in determining risk transfer. It aims to open further discussion on unresolved issues in the field.

Study Tips

Freihaut & Vendetti covers several methods for assessing whether risk transfer from insurer to reinsurer has occurred. The existence (or non-existence) of risk transfer has important accounting implications. The main thing you have to do is practice the different methods for assessing risk transfer. A smaller portion of the tested material concerns pitfalls and practical considerations in risk transfer tests. There are a lot of BattleCards for this reading, but most of them are quite easy once you understand how to apply the risk transfer testing methods.

Estimated study time: several days (not including subsequent review time)

BattleTable

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

• ERD method for testing risk transfer
• 10-10 rule for testing risk transfer
• reinsurance accounting - determining if a contract qualifies
• discount rate selection considerations
• practical considerations in risk transfer analysis: parameter selection & risk, pricing assumptions, commutation clause
• pitfalls in risk transfer analysis: profit commission, reinsurer expenses,... [PRICE – P]
• general concepts in risk transfer testing: determining most appropriate test, determining whether risk transfer is self-evident

Questions held out from Fall 2019 exam: #27. (Skip these now to have a fresh exam to practice on later. For links to these questions, see Exam Summaries.)

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #23)	pitfalls: - in risk transfer test	NAIC.SSAP-62R
E (2018.Fall #25)	10-10 rule, ERD method: - test risk transfer 2,3	reinsurance accounting: - conditions to qualify	compare methods: 1 - advantage of 10-10 rule	compare methods: 1 - advantage of ERD method
E (2018.Spring #26)	10-10 rule: - test risk transfer	'substantially all' rule: - test risk transfer	ERD method: - test risk transfer
E (2017.Spring #27)	ERD method: - test risk transfer	pitfalls: - in risk transfer test	discount rate: - selection considerations
E (2016.Fall #25)	any method: - test risk transfer	any method: - test risk transfer	any method: - test risk transfer
E (2016.Spring #26)	10-10 rule: - test risk transfer	see Odomirok.19-RBC	ERD method: - test risk transfer
E (2015.Fall #26)	self-evident?: - test risk transfer	reinsurance accounting: - conditions to qualify	pitfalls: - in risk transfer test
E (2015.Spring #25)	10-10 rule: - test risk transfer	ERD method: - test risk transfer	see Odomirok.19-RBC
E (2014.Spring #27)	describe 2 tests: - for risk transfer	is 1 test better: - in a certain scenario	required data: - for risk transfer test	(d) practical considerations in a risk transfer test (e) reinsurance accounting vs risk transfer
E (2013.Fall #28)	ERD method: - test risk transfer	reinsurance accounting: - conditions to qualify	practical considerations: - in risk transfer test
E (2012.Fall #31)	Scenario: - risk transfer concerns	discount rate: - selection considerations

¹ The answers to part (c) & (d) in the examiner's report are wrong. Most of the advantages listed for the ERD method over the 10-10 rule are not valid. It lists advantages of the ERD method as being able to incorporate discounting, modeled loss distributions, simulation, and variation or parameters, but these items can also be incorporated into the 10-10 rule. (See the 10-10 rule practice template ) The larger issue is that there is no explicitly defined procedure underlying application of either method.

² This is a defective question. An explanation is given in this brief forum discussion

³ The ERD calculation for part (a)(ii) shown in the examiner's has a typo. The calculation shows:

• 0.23 / (5 – 5/1.05²)

but the "–" in the denominator should be a "+". The correct expression is:

• 0.23 / (5 + 5/1.05²)

(Note that the final answer of 2.34% is correct however.)

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  Forum

In Plain English!

Intro

This is a well-organized paper, and I'd suggest reading Section 1. It's short, but provides a nice introduction. The main question that's addressed is:

How can an actuary determine when risk transfer has (or has not) occurred?

But even before trying to answer that, another reasonable question is:

Why do we care whether risk transfer has taken place?

• One obvious reason is that a reinsurer cannot properly price a reinsurance contract without knowing how much risk they've taken on.
• Another reason is that when a contract qualifies as reinsurance, the cedant may use reinsurance accounting treatment, which is more favorable than the alternative (deposit accounting)

Question: identify 2 conditions for a contract to receive reinsurance accounting treatment

1. requires that significant insurance risk is assumed by reinsurer (under reinsured portion of contract)
2. requires that a significant loss to the reinsurer is reasonably possible

A related concept concerns the components of insurance risk. It's generally understood that insurance risk must include:

• U/W risk (there must be uncertainty in the $-value of loss)
• timing risk (refers to timing of claims payments - there should not be any sort of predetermined payment schedule)

Now that we know the conditions & components necessary for reinsurance account, this raises the following question:

Question: what are the implications for an insurer's balance sheet if they cannot use 'reinsurance accounting' (must use 'deposit accounting' instead)

It's simple: the insurer cannot show reserves as 'net' of reinsurance recoverables (in other words, they get no capital credit for having reinsurance)

The concepts covered above are basic to an understanding of risk transfer. Learn them well!

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Risk Transfer Testing

Background

When testing risk transfer, you must assess whether the 2 conditions and 2 components of risk transfer are present. (These were described above.) Below are some specific methods for doing this. (There are other pitfalls and considerations that we'll cover later, but this is a good place to start.)

Method 1: Qualitative

• Is transfer of risk self-evident? (Maybe the reinsurance premium is very low, or the potential loss is very high, like with hurricanes or earthquakes - either way, it should be obvious that the reinsurer has a significant chance of a significant loss.)
• Sometimes you might see reasonably self-evident characterized as: (i) transaction is done at arms-length, (ii) no risk-limiting features.
• If there is some sort of predetermined payment pattern or if it's obvious there is no U/W risk, then it is self-evident that there's no risk transfer.

Method 2: Qualitative

• "Substantially All" exception: IF (significant loss NOT reasonably possible) BUT (reinsurer assumes "substantially all" risk) THEN (risk transfer may still exist)
• (Often applies to quota-share contracts with a high % transferred)

Method 3: Quantitative

• Calculate ERD (Expected Reinsurer Deficit): ERD = prob(NPV reinsurer loss) x NPV(reinsurer loss) / (reinsurance premium)
• If ERD > 1% then there has been transfer of risk
• click for ERD Example.

Method 4: Quantitative

• 10-10 rule: IF reinsurer has ≥10% chance of ≥10% U/W loss THEN the contract has transferred risk
• 2 practice problems on the 10-10 rule

Note that these practice problems on the 10-10 rule involve discounting, but most of the old exam problems on the 10-10 rule do not have a discounting component.

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Example 1

• Given the following info, explain whether there is risk transfer. Assume there can be at most 1 loss in the coverage period. (An excess-of-loss treaty with $A excess of $B means the reinsurer is liable for loss events falling in the range $B → $B + $A.)

excess of loss treaty	$2M excess of $1M
aggregate limit	$2M
aggregate deductible	$1M
reinsurance premium	$1M

• Let's step through the methods in order:

• Is risk transfer self-evident?

• If you have to think about this for more than just a few seconds, then it is not self-evident.
• (Method 1 inconclusive.)

• Does the "substantially all" rule apply?

• No, this doesn't apply either because the maximum reinsurer liability is only $2M, and the deductible and premium together sum to $2M. (It seems closer to "substantially nothing" than substantially all!)
• (Method 2 inconclusive.)

• Calculate ERD

• We don't have any data on frequency and severity, but we can still deduce the ERD from the given info:

• max loss = 3M THEREFORE max reinsurer payout = 1M (because retention = 1M and deductible = 1M) THEREFORE max reinsurer loss = 1M - (premium of 1M) = 0
• BINGO! The reinsurer can't lose. Therefore there has been no transfer of risk.

• (Method 3 provided the answer.)

• Note: Do you see the reason for assuming there is only 1 loss in the coverage period? If there was a second loss of 3m, the insurer would then suffer a loss of 1m. The reasoning is that for the second 3m loss, 1m is retained by the insured as before, but the aggregate deductible of 1m was reached on the first loss and there's still 1m left in the aggregate limit. So, the insurer would have to pay 1m. The answer to whether there has been true transfer of risk would not be so clear now.

Example 2

• Given the following info, explain whether there is risk transfer.

quota share %	90%
ceding commission	20%
ERL (expected LR)	40%
reinsurance expenses	5%

• If you remember that the "substantially all" rule applies to quota-share reinsurance, then you can immediately conclude that there is risk transfer under this contract. (Method 2 provided the answer.)
• (The text says that the 'substantially all' applies to quota-share with a high percentage transfer, but they don't tell you what 'high' means. Is 80% high enough? 70%?)

Example 3

• Given the following info, explain whether there is risk transfer.

excess of loss (earthquake)	$300M excess of $50M
reinsurance premium	$5M
100-year PML	$50M
200-year PML	$200M
500-year PML	$350M

• This is the easiest of the 3 problems. It's tempting to try to calculate ERD because we're given information about both the frequency and severity, but since it's earthquake reinsurance, there is potential for a catastrophic loss in any year.
• We can immediately invoke Method 1 to conclude that there is self-evident risk transfer under this contract.

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Section 3ab & 4: Pitfalls & Practical Considerations in Reinsurance

The first thing you should do is study the 2 examples in the source reading at the beginning of Section 3.

Contract 1 is an example of a quota-share contract:

• quota share contract (with profit commission LR @ 66%) and one-for-one profit swing up to 5% below an LR of 66%.

Contract 2 is an example of an excess-of-loss contract:

• excess-of-loss (with optional commutation after 5 yrs) and swing-rated where provisional the reinsurance premium rate of 8.5% varies between 6%-11% based on LR of 75%

These examples are used to illustrate the pitfalls and practical considerations discussed in this section, but also that if you get another problem like the one linked to below, you'll be familiar how quota-share, and excess-of-loss reinsurance contracts work.

E (2015.Fall #26)

This section is fairly straightforward memorization. The first list you must memorize is:

Question: identify the pitfalls in a risk transfer test [Hint: PRICE – P]

Profit commission

Reinsurer expenses

Interest rates

Commutation timing

Evaluation date

    –

Premiums

See details in mini BattleQuiz.

mini BattleQuiz 4

The second list you must memorize is:

Question: identify the practical considerations in a risk transfer test [Hint: parameter(selection, risk).Pr(ass).Comm]

Parameter selection (interest rate, payment-pattern, loss distribution)

Parameter risk

Pricing assumptions

Commutation clause

See details in mini BattleQuiz. Note that the source text contains a contradiction: Friehaut says that ceding commission should be excluded from a risk transfer analysis, but the example in Appendix A includes ceding commission. Since the CAS syllabus states that Appendix A is for informational purposes only (I guess that means you don't have to study it?) You should assume that ceding commissions are indeed excluded from premiums in a risk transfer analysis. (shout-out to forum-user RISQ for noticing this! See forum thread.)

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Note :There is a lot to memorize in these sections on pitfalls and practical considerations, and you can see from the BattleTable that there's about a 50-50 chance to be asked. The questions on discount rate would also be included here. I cannot emphasize enough that if you want to memorize something reliably, you have to do the BattleCard 10-20 times.

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Final Thoughts

I mentioned in the introduction at the very top of this wiki article that it seems like there's a lot of memorization, especially in the sections on pitfalls and practical considerations. But many of the BattleCards are actually quite easy if you've simply memorized the 2 lists and have some general sense for how risk transfer works. The main thing from this reading is developing the skill for assessing the existence of risk transfer. For this, you have several different standard methods. It's just practice.

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