2018 Fall Q15 Premium Liabilities ex. PfAD

jaylow96

Hi, the sample answers for this question showed that the calculations for the premium liabilities are as follows:

(1) Net unearned premium = 85,000 + 0 – 2,500 = 82,500
(2) Undiscounted liabilities = (82,500 – 2,500) × 84% + 2,000 = 69,200
(3) PV(Loss+LAE) = 69,200 × (0.84 × 1.03-0.5 + 0.13 × 1.03-1.5 + 0.03 × 1.03-2.5) × 1.03(0.5 – 1/3) = 68,144
(4) Premium Liabilities ex. PfAD = 68,144 + 85,000 × 2.5% + 2,500 = 72,769

I know that the premium liabilities for insurance risk should be net of reinsurance and exclude PfAD (thats why we need to deduct 2500 in step (2) before discounting). However, in step (4), the maintenance expense and the expected reinsurance premium of 2500 are ADDED to the discounted premium liabilities. I would like to know whether premium liabilities excluding PfAD should include maintenance expense and expected reinsurance premium?

Thank you for your answers.

graham

The solution to this exam problem follows the standard formulas for calculating premium liabilities except you use PV (Present Value) instead of APV (Actuarial Present Value.) This is because, as you said, for the MCT ratio you should exclude PfADs. Anyway, this calculation is shown in detail in the wiki article for CIA.PrLiabs. The solution in the examiner's isn't as easy to follow as it should be however, because they don't actually write out the formulas.

• Step (1) is pretty easy. NEP is just direct EP minus ceded EP.
• Step (2) has nothing to do with PfADs however. The formula is:
• ==> undiscounted prem liab = (NEP - FutRe) x ELR + ULAE
• Then in Step (3), they take the result of Step (2) and multiply by the PVfctr (or Present Value Factor). Calculating PVfctr is a bit messy and I think that's the part most prone to a calculation error. (Note that when calculating DPAE or Deferred Policy Acquisition Expense, you DO have to include PfADs, so we would calculate APV or Actuarial Present Value, not just PV. But for the MCT ratio, we only need to calculate the PV, not the APV.)
• Step (4) is pretty easy. Just apply the standard formula, but insert PV instead of APV and note that contingent commissions is 0:
• ==> prem liab for MCT = PV + FutRe + maint + contingent commissions
• (Note that the examiner's report solution, they reversed the order of the terms in Step (4) and put "maint + FutRe" instead of "FutRe + maint".)

I hope that helps! Let me know if you have further questions about this.

jaylow96

Hi Graham,

Thank you for your explanation. Please correct me if I am wrong. When we are calculating the premium liabilities for insurance risk in MCT Ratio, we need to calculate PV not APV; while when we are calculating DPAE and the premium liabilities for interest rate risk in MCT Ratio, we need to calculate APV not PV. Is this right?

Thank you.

graham

Yup, correct!

victory1995

@graham would you be able to provide a holistic understanding of why exactly FutRe is deducted from NEP, just to be added back in at a later step? Would really appreciate it as it's confusing me. Thanks!

graham

Sure, no problem @victory1995:

The short answer is that we don't want to include FutRe (Future Reinsurance Premium) when calculating net premium liabilities for the primary insurer, but we do have to take the cost of FutRe into account somewhere in the calculation.

Ok, here's a slightly longer explanation: The formula where FutRe is subtracted is the net PV calculation:

• PV = [ ( UPR - FutRe ) x ELR + ULAE ] x PVfctr

FutRe has to be taken out of UPR for the net calculation because FutRe doesn't really belong to the primary insurer and they are not responsible for any future losses associated with it. FutRe belongs to the reinsurer as premium for the reinsurance policy. If FutRe was not subtracted, we would essentially be calculating gross PV for the primary insurer in this step.

Then the formula where FutRe is added back in is:

• PolLiabs(UPR) = APV + FutRe + maint + contingent commissions

This is because the total premium liabilities must include FutRe. It's kind of like a flat fee borne by the primary insurer. They pay this fee to the reinsurer to be relieved of responsibility for a portion of future losses.

Side note: The reinsurer would not have to subtract and add FutRe when calculating their own premium liabilities. This FutRe simply becomes the reinsurer's UPR and the reinsurer would have no FutRe of its own to pay (unless the reinsurer itself had reinsurance.)

victory1995

Thanks Graham!

sant93

Why do we need to apply the bolded piece below? what does it mean?
PV(Loss+LAE) = 69,200 × (0.84 × 1.03-0.5 + 0.13 × 1.03-1.5 + 0.03 × 1.03-2.5) × 1.03(0.5 – 1/3) = 68,144

graham

That factor is an adjustment that gets you from the PV(AY) to PV(UPR). The mathematical details come from Appendix A in the CIA Premium Liabilities reading. Given the following notation:

The appendix derives the formula below. You can see the 1.03^(0.5 - 1/3) factor at the end where in our case i = 3.0% but we always have x = (0.5 - 1/3):

You would not have to derive this formula on the exam. You just have to know how to do the calculation. It might be good to be able to say in words the reason for the adjustment however. The reason would be:

• to account for the difference in average accident between an accident year and the UPR.

adipelino

Hi, would this adjustment of 1.03^(.5-1/3) still be relevant for Fall 2022 now that the premium liabilities paper is removed?

I believe this formula [PolLiabs(UPR) = APV + FutRe + maint + contingent commissions
] is replaced by the methods to calculate "unexpired coverage" under GMA or PAA for reinsurance or insurance now.

Thanks!

Staff-T1

I don't think so because you are directly calculating the PV using first principles. @graham thoughts?

graham

That adjustment is no longer relevant. According to the reading CIA.IFRS17-LRC, average accident dates are calculated using integration which shouldn't appear on an Excel-based exam.