Fall 2018 Q25
The question states, "the reinsurer will pay all ceded losses in entirety on January 1, 2020"
How does this qualify for reinsurance accounting? It seems like a clear violation of timing risk, in which case there is no need to test for reasonable chance of significant loss.
Comments
You are correct. It was not a well constructed exam question.
The reason they told you the payment date is so you could discount the loss back to the contract effective date for use in the ERD forumla. It was just a way to make the question something you could easily do on the exam.
What they should have done is also give you a distribution for the timing of the losses. Then they could have said the reinsurer generally pays losses 12 months after the date of loss. It's reasonable to assume a lag between claim date and reinsurer reimbursement, but the reinsurer isn't allowed to specify a payment date before the loss even occurs. But that would have made the question more difficult.
A follow-up question...
Assuming we ignore the timing issue above, I wonder if the solution for a.ii is calculated incorrectly.
Examiner's report:
ERD = .05 * (16/1.05^2 – 5 – 5/1.05^0.5) = 0.23 million
0.23/(5 – 5/1.05^0.5) = 2.34%
Since ERD % > 1% qualifies for risk transfer
My calculation
ERD = .05 * (16/1.05^2 – 5 – 5/1.05^0.5) = 0.23 million
0.23/(5 + 5/1.05^0.5) = 3.14%
Since ERD % > 1% qualifies for risk transfer
Which one is correct? Thanks!
I think the final answer of 2.34% is correct, but as you said, the calculation should be:
If you punch into your calculator what's shown in the examiner's report, you get 198%. Your formula is correct, but I don't get 3.14%. I get 2.33% which is close (rounding?) to the examiner's report.
Do me a quick favor and double-check this. I've listed it as footnote 3 under the BattleTable in the Freihaut.Reins wiki article here:
Thanks!
Yes, I must have punched in something wrong.
I now get 2.34% if I carry the answer from the first line (it's not exactly 0.23).
Thanks!
Thx! I hope everything goes well tomorrow!
Another follow-up question...
Why we don't use 95% level Loss to calculate ERD? Is it because if we use the 95% level, then there is no risk transfer? Do we need to make an assumption?
It's because there is no reinsurance deficit with the $5M loss. So, zero takes 95% weight, and the alternative takes 5% weight, to give the expected RD.
So part b looks to incorporate the exact payment date into the answer, since there's no timing risk. I'm guessing we would get no credit for using that logic in part a, even though it technically disqualifies risk transfer for 10-10 rule and ERD method, right?
Also, assuming there was timing risk, would it be a fair question to ask if there was risk transfer when 10-10 says no but ERD says yes? Does one take priority? The "Casualty Actuarial Society E-Forum, Spring 2009" source seems to say ERD is preferred, but nothing definitive.
Part a is flawed: it should be asking whether the contract qualifies for underwriting risk transfer under either of the two methods, because that is what these two methods test.
Part b's question works, because there is decidedly no risk transfer due to absence of timing risk. But the examiner's answer is flawed: there are not two possible answers to risk transfer, because of the missing timing risk.
If, as you say, there was timing risk, you would have to specify the correct accounting treatment under the result of each test. I am not aware that one test is favored over the other.