2015 Fall 7
For question a, before reading the notes, I made a following guess.
15% correctly calculated as participation ratio.
But for LR, instead of taking 75015% as a part of premium, I directly took 50 as that is the amount this company put into RSP.
So I got LR = (100015%)/(50*125%) = 240%.
So if I understand correctly, the only thing differentiating the LR for each company on its share of RSP is the amount of expense allowance? But then again, I'm thinking why is the expense allowance being added to the portions of premiums? Doesn't that make everybody's LR on its share of RSP lower than it is? Like, sum of all the companies' LR's numerators or sum of all the companies' LR's denominator should give RSP LR, but since each company's expense allowance is added to the denominator, doesn't this lower the LR? Shouldn't the total expense allowance actually be subtracted from 750?
I think it should be like this
LR = (100015%)/[(750(1-25%)15%+5025%]
Comments
Let me start by writing out the formula used in the examiner's report: (BTW, the "*" in this editor's markup language means "italics". If you want to indicate "multiplication", you have to use "x". That's why your formulas came out funny and you have italics in your post.) Anyway...
If you use prem = 50 in the denominator, then to be consistent, you should use loss = 40 in the numerator because Co.IL(ceded) = 40. So if you agree with the 150 as losses in the numerator, then using prem = 50 in the denominator is logically inconsistent. Now let's address your other comment about how LRs can be different between companies.
There are 2 things (not just the expense allowance) that cause different companies to have different LRs:
If I'm reading your question correctly, you are asking:
I understand why you might have asked that because expenses are usually included with losses. But that's not the right thing to do here because it's not really an expense. Think about like this:
Getting back to one of the points you made in your original question, the expense allowance term in the denominator does indeed make the LR lower, but not in an "incorrect" way. It comes out of the "premium pot" so it should be included with whatever other premiums are being included in the the calculation, not with the losses.
I hope that helps. This is definitely a very confusing question exam problem.
In order to lower LR, we should cede risks with higher LR than the pool's average LR. However in this question,
Ceded business LR = 40/50 = 80%
Pool LR (with company A) = 1000/750 = 133.33%
Pool LR (w/o company A) = (1000-40)/(750-50) = 137.14%
Ceded LR is way lower than the pool average, and yet, company's total LR still goes down 3% (75% to 72%) after it cedes risks to the pool. Why is this happening?
That's a good observation. For part (d), it isn't quite so simple as sample answer 2 in the examiner's report implies.
When a company cedes business, there are several moving parts that have to be taken into account and neither the examiner's report nor the source text discuss this in sufficient detail.
In your example, the company is ceding business with a LR of 80% which is LESS than the pool average. You would think this would make the company's total LR worse because their "good" policies are now subsidizing the "bad" pool policies which have an average LR of 133.3%. But there's more going on...
These 2 items offset the penalty from ceding "good" policies to the pool. I suppose you could calculate the break-even point by solving these equations simultaneously. But there would be many more variables than equations because each policy could be ceded or not ceded. That means there would be 2^n combinations of policies (where n = # of policies). In other words there isn't a unique solution. That's probably why the examiner's report answer just simplifies the answer to the simpler statement:
If you ceded enough bad policies, you would definitely come out ahead.
If there were no limit to what you could cede, a sure-fire strategy might be to cede everything. Then your company PR=0 and you wouldn't be responsible for any pool losses. You would also have no retained losses so your company's entire income would be from reimbursement due to the PEA. (This is basically what a servicing carrier is for FARM.)
I will add a link in the wiki to this discussion thread. Thank you for your insightful observation.
I agree, there is definitely more to this actuarial game of musical chair than meets the eye, a game I hope I would get the chance to play one day for real.
Thanks Graham!
Hi @graham, I was reading the original post in this thread, and it seems like the question was actually slightly different than what you answered. I don't think the problem is with subtracting expense allowance from the numerator vs adding it to the denominator. The question is really about why the formula from the examiner's report for a single company doesn't work for all companies combined (i.e. LR for the entire pool).
Since the participation ratio of all companies combined is 100%, we would replace 15% in the problem with 100%. Then, since total ceded premium is 750, we would use that instead of 50, when determining the total expense allowance returned to all companies combined. As a result, we get (100% * 1000)/((750 * 100%) + 25% * 750) = 106.7% (not in line with the value of total RSP LR).
The question is: where are we getting these additional 25% of total ceded premium from?
I believe the answer is: instead of multiplying PR by the total ceded premium, we should really be multiplying it by the (total ceded premium less the expense allowance), because the expense allowance is automatically returned to the respective insurer regardless of their participation ratio.
So the formula for company A, as mentioned in the original post, would be (15% * 1000)/((750 * (1- 25%) * 15%) + 25% * 50) = 154.8%
Or if generalize:
[PR * Prov.IL(ceded)]/[[(Prov.EP(ceded) * (1-PEA) * PR] + PEA * Co.EP(ceded)]
If we substitute the values for all companies combined, we will get the same value as you provided for the total RSP LR:
(100% * 1000)/((750 * (1- 25%) * 100%) + 25% * 750) = 133.3%
You know what - I did misread the original question. I see now what the original poster was saying and it does make more sense than the answer in the examiner's report.
The answer in the examiner's report double-counts the expense allowance in the denominator. This causes the LR to be lower than it should be on Company A's share of the pool, 120%, instead of 154.8%, as you said.
I'm not sure what to suggest here because the source text does not properly explain how to do this calculation.
But as you and the original poster correctly pointed out, the problem is with the denominator of the LR formula
I appreciate you thinking through all this and I will put a link to your post in the wiki. I honestly don't think they will ask a question like this again because the source text for this material doesn't have any calculations. It's all conceptual and except for that one question from 2015.Fall, all exam questions have been essays not calculations. Still, I suppose you can't be totally sure.
Unfortunately, I put a question like this on the 2019.Fall practice exam and I used the method from the examiner's report. That means you will get a different answer when you do it. I think I will just remove this from future practice exams altogether.
HI @graham , to add on the discussion with @DulcineaDelCA above, the examiner's report also suggests that Company A should add more risks to the RSP since it is below the max limit.
My question is "How do we know Company A is below the max limit?"
The 8% limit is for New Brunswick. This exam problem is about Nova Scotia and there's (currently) no limit on the number of risks transferred for NS, although certain other limitations and conditions still apply.
Thank you very much @graham !
hi, for calculating participation ratio - should we always use formula (EE non ceded company/ EE non ceded province) -> or does this formula varies by province? If yes, do you know what would be the cases.
thanks
From the Dutil reading:
But this doesn't completely answer your question. The participation ratio is slightly different for Ontario, but you are not expected to go to the external source. For the purposes of the exam, you should assume the formula is the same for all RSPs.
Hi Graham, is it fair to say that a company is better off sharing its bad risk for the following 2 reasons:
Each insurer should be maximizing their RSP limit, right?
Points 1 and 2 are good rules of thumb:
Regarding whether each insurer should cede the maximum, I'm not sure that's true. An insurer would want to cede risks they think are worse than the pool. If the limit is 5% for example but only 4% of an insurer's risks are expected to be worse than the pool average, then they would only cede 4%. The other 1% would be better than the pool average and the insurer would end up paying more through sharing than if they had just kept that 1% themselves.
I don't think there's any foolproof way to calculate exactly how many risks, and which risks, should be ceded to the pool to exactly maximize profit (or whatever other metric you might want to maximize or minimize.) There are too many moving parts. But it should always have the effect of stabilizing or reducing the variability of an insurer's overall results from year to year.
If this question were to be a ON RSP, would we multiply the companies "share of pooled losses and premium" by 85%. So for part A, would it be 0.85x150/(0.85x750x0.15+Premium Expense Allowance=Premium Ceded x 0.85x Expense allowance %)?
Another question, correct me if I'm wrong, but the ceded premium to the pool is Net of acquisition expenses. The acquisition expenses for the premiums are approximated as the ceded premium x Expense allowance. So the Losses on their share of the RSP = Losses responsible for / Premium responsible for (including acquisition expenses) hence why the denominator adds the expense.
First question:
Second question: According to the source text: