Fall 2019 Q16

Tony88pass

I'm confused why we have to reduce cash and bonds by the ceded premium, thought it was paid to reinsurer out of the gross premium already?

graham

Note that this isn't a quota-share treaty, so there isn't really any "ceded" premium. The cost of reinsurance is given as 5% of gross premium. The reinsurer then receives:

• 5% x 450,000 = 22,500

but again, this isn't "ceded" premium. It's just the cost of the reinsurance treaty.

If you're asking why bonds and cash are reduced to 700,000 and 100,000 when a catastrophe occurs, you just have to take this as a given. I assume the reduction is due to the insurer having to pay out a portion of the losses that fall below the threshold for reinsurance to kick in.

The rest of the solution as given in the examiner's report follows the formulas given here:

• https://battleactsmain.ca/wiki6c/CCIR.ARinstr#Other_Basic_Accounting_Formulas

If that doesn't answer your question, please let me know. Note also that the numbers given in exam problems aren't always internally consistent (unfortunately). You just have to work with what you're given as best you can.

Tony88pass

Hi Graham,

Sorry I wasn't clear enough. So based on the sample answer, they have already counted the cost of reinsurance when calculating the u/w income, in that case, why it comes into play again when calculating the investment income, that looks double counting to me.

graham

Oh, ok. I see what you mean:

• First, NEP is reduced by the cost of reinsurance. (That part is straightforward.)
• But this NEP has to be put somewhere, like cash, bonds, or stocks. If NEP is lower, then the corresponding value of cash/bonds/stocks is going to be lower by the same amount. The investment return rate must then be applied to this lowered amount.

So when your NEP is lower, your U/W income is lower, but it also has the knock-on effect of making your investment income lower because you now have less to invest.

Tony88pass

Oh so you meant the cash includes the NEP, I thought there were independent, make sense now. Thanks

Tony88pass

Hi Graham,

I came up with a few questions when reviewing your first response:

1. Is cost of reinsurance = ceded premium in a QS treaty?
2. In a UPR question, assuming XOL treaty, when calculating the NU using (Net UPR-FutRe)*ELR+ULAE, here in the formula, the Net UPR should be net of reinsurance already, why do we need to exclude the FutRe again?

Thanks,
Tony

graham

Hi Tony,

1. The answer depends on how the contract is written but I don't think you can assume the cost of a quota-share treaty equals the ceded premium. This isn't discussed in this reading, but there is likely a separate cost associated with the transfer of risk to the reinsurer that isn't covered by the ceded premium. Also, the reinsurer may price the risk differently from the primary insurer and that would also factor into the cost of the reinsurance policy.
2. See below for an excerpt from the NetPremLiab worksheet of the Excel appendix of the CIA Premium Liabilities reading. The ceded UPR in column (4) is different from the cost of reinsurance in column (6). In other words, net UPR has not already had the cost of reinsurance subtracted. The net UPR refers to the gross UPR with only the ceded UPR removed, not FutRe. I'm not absolutely certain this is true in all cases, but my guess is that for an XoL treaty, we would have gross UPR = net UPR.

Tony88pass

Thanks Graham, it makes a lot more sense to me now.

oxalis

Hi,

I'm not sure how the reinstatement premium provision for reinsurance works, we are told: treaty has a mandatory reinstatement premium provision, with the reinstatement premium due once the treaty attachment is reached on a paid basis. So my understanding is that the insurer only needs to pay additional premium to purchase more reinsurance if the previous reinsurance limit got exhausted by the paid loss, here for a $200k cat loss, the reinsurer only paid out for $110k, there's another $340k($450k-$110k) that should be covered under the reinsurance treaty?

Thanks,

graham

Your interpretation of when the reinstatement premium is due is not correct. This premium is due when paid losses by the primary insurer reach the attachment point. Now, the attachment point is 20% of gross earned premium or $90,000. That means as soon as the primary insurer has paid $90,000 to catastrophe claimants, they must then pay the reinstatement premium to the reinsurer.

Note also that this scenario is hypothetical and the solution assumes the primary insurer will have already paid $90,000 to claimants so this amount has to be taken into account in calculating the net income.

ibsy

Hello Graham,

I am coming back on the initial question of this thread, since I am still confused on why we have to reduce cash and bonds by the ceded premium, based on how the problem was written.

Indeed it says the following:

• "The following scenarios with and without a catastrophic event [...] as at December 31,2018"
• "below are the expected financial statements figures"
• "the treaty costs 5% [...] is paid in full at inception"

So what I understand is that the fin statement numbers in the "with catastrophic event" represent the scenario with cat (and therefore with reins) at the end of the year 2018, and that the reins costs are paid at the beginning year 2018: so doesn't that imply that Bonds and Cash (which are end of year 2018 numbers) already have the reins costs embedded in them?

I also have a follow-up question on how the inv yield is applied: since we are asked the income of 2018, shouldn't the inv yield be applied to the the Bonds and Cash amount of the beginning of the year 2018? While here, again I understand we are given the amounts of end of year: so aren't we calculating the inv income of 2019 in the examiner report solution?

Thanks.

graham

I had similar queries about this question and I emailed the 6C exam committee last year for clarification but I didn't think the answer I got back was entirely satisfactory.

This question is basically a harder version of the catastrophe scenario discussed in the Blanchard & Klann reading on reinsurance. The example in the Blanchard and Klann source text provided the investment income with and without cats so you didn't have to calculate it, unlike in this exam problem. The explanation I provided above was how I made sense of the solution in the examiner's report. I'm not 100% my explanation or the examiner's report solution is correct.

Regarding your second question about how to apply the 5% investment return given that you're trying to find the investment income for 2018 (not 2019): I wondered about that too. I think the problem just got the dates all mixed up.

Unfortunately, there are errors in the examiner's reports more often than you would think but there really isn't anything you can do about it. The best advice I can give you for this problem (or any exam problem) is write down as sensible an answer as you can based on what you know and what the problem is asking for. In this problem:

• write down the basic formulas for total income and U/W income
• then use the given information to plug numbers into these formulas in the most sensible way you can think of
• if you think something doesn't make sense in the problem, make a note of it so the graders know what you're thinking
• make sure you've used all the information in the problem, like the investment return rate, the details of the reinsurance treaty, and the costs associated with the treaty

If you do all that, you will get a significant proportion of the points on the problem even if you don't solve it completely. And probably most importantly, don't spend too long on the problem. (Past a certain point, you will be wasting your time without getting any more points.) Keep to your time management plan. You have to make sure you finish the exam and not leave blank questions at the end that might be easy.

You almost have to expect a couple of problems on every exam that are going to give you (and everyone else) trouble. When this happens, don't panic. Like I said, just do the best you can and move on.

ibsy

Makes senses, thanks for the tips!

suomi

Hi @graham. I don't understand the explanation for reinstatement premium. "This premium is due when paid losses by the primary insurer reach the attachment point". For an extreme example, lets say the the cat losses = attachment point, so insurer pays 90K, but would still have to pay a reinstatement premium, and reinsurer doesn't have to pay any losses because losses haven't reached past the attachment point. Seems odd to me.

I've always thought the reinstatement premium was paid when reinsurance coverage has been exhausted, so the insurer needs to pay a fee to replenish their coverage in case another cat occurs. In this example, the reinsurance coverage has not been exhausted so I'm confused as why the insurer would have to pay a reinstatement fee.

graham

I believe your reasoning is correct and the way the reinstatement premium is described here doesn't make sense. This is a poorly constructed exam problem but you just have to take the information provided "as is", even if it doesn't make sense.

If you get such a question on the exam where the given information doesn't make sense, just be sure to explain your reasoning.