APV Premium Liabilities (Fall 2017 #15)
What do you do on the exam to calculate the APV of premium liabilities if they give you the discounted loss ratio instead of the undiscounted LR?
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What do you do on the exam to calculate the APV of premium liabilities if they give you the discounted loss ratio instead of the undiscounted LR?
Comments
It's hard to say in general because it would depend on what other information you're given.
The formula for PV assumes you've got the undiscounted loss ratio (or ELR, Expected Loss Ratio, as I've been calling it). Once you've got PV, you can calculate APV using the method discussed in the wiki article: https://battleactsmain.ca/wiki6c/CIA.PrLiabs
But if they give you the discounted loss ratio instead, one option is for them to also give you enough information to work backwards to the undiscounted loss ratio. You could then solve the problem as before. (Of course, you would have to know the formula for the discounted loss ratio, which is given at the bottom of the https://battleactsmain.ca/wiki6c/CIA.MfAD)
Another possibility is that all of the other formulas used in calculating APV could be adjusted to work using the discounted loss ratio. I haven't worked that out and I think it would be a real pain to do so, if it's even possible.
Your question is very reasonable because you're not always given the information the same way. Something tells me, however, they wouldn't change the problem in this way because calculating APV for premium liabilities is pretty hard anyway. If I were creating an exam question and wanted to create a variation on this APV problem, I would do it another way. For example, I might provide the undiscounted UCAE and the EP, and have you calculate the undiscounted loss ratio simply by dividing them. Granted, that would be a very easy variation, but I think more fair.
At the end of the sample answer it says "Note that there is no premium deficiency or DPAE for facility given that net unearned premium =
premium liabilities". What does this mean? Thanks.
I think you might be referring to a different exam question because 2017.Fall Q15 did not refer to facility. In any case, here's a brief review of the DPAE calculation.
After applying the basic formula:
the rule is:
Note that the basic formula is explained in: http://www.battleactsmain.ca/wiki6c/CIA.PrLiabs
Here is what's going on conceptually: If you look at the formula, you're really just calculating whether you have money (UPR + UEComm) to cover the future expected losses (PolLiabs(UPR) or policy liabilities related to the unearned premium). If the result is positive then you do have enough money, but if the result is negative then you don't. In that case you say there is a deficiency, or more specifically, a premium deficiency.
If the result is exactly 0, that means the UPR and UEComm exactly balanced the PolLiabs(UPR). This is great because it basically means the policies were priced perfectly. The money they generated was exactly equal to the losses they were intended to cover. In other words, there is neither a DPAE asset nor a premium deficiency liability.
Hi Graham,
I also saw the note mentionned by PeopleKnowMe.
In both sample answers of the examiner's report (Q15 Fall 2017) , there is a note that says: "Note that there is no premium deficiency or DPAE for facility given that net unearned premium =
premium liabilities".
I don't understand what that note refers to, any thoughts?
Thanks!
Ok, I see. The answer in the examiner's report does have that line at the end about facility. As far as I can tell, however, this is a typo. The old version of the DPAE calculation involved facility data (see 2015.Spring Q28). But there is nothing in the current DPAE paper about facility. I think you can just ignore that comment.
Hi,
When calculating the APV, why does their number for Gross PV of Loss &LAE give different number than doing Gross UPR *ELR+ULAE times the PV factor calculated?
I thought I read that I can calculate gross by just not adding any future reinsurance costs.
Thanks,
The ELR is probably different for gross. The ELR of 98% in the problem specifically refers to the net undiscounted loss ratio.
when calculate pfad for ceded reinsurance, the sample answer use (53000-49004) * mfad, but I think it should be (60,000-55,000) * 97% * mfad, am I correct?
you want to calculate the risk (or PfADs) in relation to expected claims from the premium not the premiums themselves. Claims are calculated as: (Premiums - Future.Re) x [Loss Ratio].
The exam confuses this particular question by using such a large loss ratio. Normally loss ratios will be in the 60-70% range (+32% expenses). There's no MfAD required for profits or expenses.
PfAD_ReIns = (PV_gross - PV_net) x MfAD
PV_gross (claims) = 53000 (given)
Net Claims = 98% (55000 - 6000) +2500
PV_net (claims) =
PfAD_ReIns = (53000 - 49005) x 1% = 40
Suggest working through Prm.Liabs practice problems especially the "123" calcualtion problems
Thx @chrisboersma. (The key is that the reinsurance MfAD should be applied to the ceded losses not the ceded premium. Good idea to review the "123" problems, both easy and hard versions for premium liabilities.)