Fall 2016, Q16 a i

danielle4nan

Hi, I'm having difficulty with how the reinsurer will never have a loss. This is how I've approach the problem:
First $3mln loss: 1st $1m paid by insurer as retention, $1m xs $1m paid by insurer in aggregate deductible, $1m xs $2m paid by reinsurer (but fully recovered in premiums collected.
Second $3mln loss: 1st $1m paid by insurer as retention, $1m xs $1m paid by reinsurer (since the insurer's aggregate deductible has already been paid and there remains $1m left of the $2m aggregate limit covered by the reinsurer according to the contract).

Therefore, the maximum reinsurer loss would be $1m. Does this make sense? Thanks!

graham

Yes, I believe you are correct. I will make a note of this in the wiki. It seems the examiner's report assumed only 1 loss and did not consider the possibility of a second loss in the same year. Thx!

danielle4nan

Perfect, thanks!

chrisboersma

That question was a straight copy from the text:

An extreme example would be a single doctor paying $1M for a $1M x $5M medical malpractice treaty with a $2M aggregate limit. This contract passes the established criteria for the risk transfer to be reasonably self-evident, but I think most would agree that not enough risk is transferred in this contract for it to qualify as reinsurance.

We also have a chance of a $0 net loss for 1 claim and a $1m net loss for 2 claims.

The supplied answer may not have been that great, but it doesn't mean the general answer was wrong:

No risk transfer

jptardif2

Hi Graham,

I think you will agree with me that this is a poorly asked question eh? Why would they give us aggregate limit and deductible if they only assume 1 loss?
Regardless, I still have a hard time deciding if risk transfer happened. We don't have enough information to calculate ERD or 10-10 rule. It doesn't seem reasonably self-evident if I have to post on the wiki, so that leaves us with the Substantially All rule. It doesn't seem like the reinsurer could assume a significant loss, so I would so no risk transfer happened, base on the Substantially All rule. Agree or disagree?

Thanks,

graham

You're correct that it isn't a great question. An aggregate limit doesn't mean anything if there's only 1 loss. They probably didn't intend to assume only 1 loss - they just didn't think through all the possibilities the situation allows for.

I think I would disagree with your reasoning though. The "substantially all" rule is used to prove that there is risk transfer. If you're trying to prove there isn't risk transfer, you have to use a different method.

The way I stated the ERD rule in the wiki is:

• ERD = (frequency) x (severity as a % of premium)
• if ERD > 1% then risk transfer has occurred

But you can't calculate ERD with this formula. If you look a little further down in the wiki article however, you still can calculate ERD using a more direct method. You have to analyze a couple of different scenarios so take a look at the solution in the wiki for the details.

Note that the self-evident test can be used to prove either the existence or non-existence of risk transfer whereas the substantially all rule is generally used only to prove existence. (And of course the ERD and 10-10 rules can also be used to prove it either way, existence or non-existence.)

exam6_pass

Hi Graham,

I'm having bit of a difficulty understanding 1st two rules - Please let me know if i'm thinking correctly:

1) risk transfer is "reasonable self evident" -> If significant loss possible (e.g. EQ, hurricane) OR Prob of loss is high (e.g. >20%)

2) "Substantially All" Exception -> If high % of loss assumed by reinsurer (e.g. >50%) or Quota share % is high or Reinsurance contract w/o LR cap

For Q16 a(i) -> is following correct to check "substantially all" condition:
1) max loss is 3M (agg limit + agg deductible) -> Reinsurer covers (3M - 1M (retention) - 1M (deductible) = 1M -> so reinsurer covers (1/3) = 33% of max loss -> so % of loss assumed by reinsurer is not high -> "substantially all" rule doesn't apply.

graham

Good morning,

1) Self-evident test:

• Since the "self-evident" risk transfer test is a qualitative test, it's hard to be specific because it depends on the situation. The things you mentioned are definitely considerations, but the key is that it should be obvious to a reasonable person that risk transfer exists. You shouldn't have to do much calculation when applying this test.
• Note that a probability of loss >20% might not be enough to prove risk transfer without more information. If a very high premium was charged then the insurer may still always make a profit even if there's a high probability of being subject to a loss. In that case, risk transfer may still not exist.

2) Substantially All test:

• Exam problems that use this test are generally situations where the reinsurance contract is quota-share. The percent that has to be transferred is not specified anywhere so it isn't clear if 50% is high enough. Maybe you need 75% or 90%. For the purposes of the exam, just make sure you explain enough so the grader knows you understand the concept.
• About your other example of a reinsurance contract without a cap: I think the key may be a low retention by the primary insurer rather than a contract without a cap. The idea is that the primary insurer must retain very little to no risk. Just having no cap wouldn't satisfy that if the retention level is still high.

Q16 (a)(i):

• I think you would probably get most or all of the credit for your answer. You are doing the right kind of reasoning but just be more careful. It isn't so much that the reinsurer pays out only 1/3 of the max loss, it's that the reinsurer pays out 1m max but they also took in 1m of premium so the reinsurer can never suffer a net loss. Check the wiki for a detailed solution.

Hope that helps.