Spring - 2019 Question 4a
I'm curious how everyone would answer the above question. Specifically designed to calculate "proposed differentials" for Ontario filing. Remember that the KPMG doc allows for -10% to 0% per terr, the official simplified filing rules allows for -15% to 5% and a Major filing currently allows for +/- 10%. In theory any one of these answer could be correct as the question only asks for a "differential proposal that meets the requirements for approval". Part B of this question makes A seem to imply it was a simplified filing (as does the 0.0% overall indication). But a profit maximizing insurer should do a full filing to get as much rate in Terr 3 as possible (+10%). I don't believe full filing guidelines are part of 6C though.
Giving 5 points (1.25) for this problems suggests there is some calculations involved.
Competing problems:
1. Actuarially sound differentials (given regulatory constraints). - profit maximizing
2. Within guidelines (+/- amount correct).
3. Make sense (+0% overall)
I had to cycle through a number of different options as I did the problem as calculating a maxed differential that maximize the other differentials, but maintains a 0.00% increase is non-trivial. I got a sense that I made the question was much harder than it was supposed to be.
Comments
I just noticed the official solution is actually a rate decrease:
(0.7981/0.850 x 52 + 1.0088/1.000 x 36+ 1.1537/1.05 x 23) / 111 = 99.47%
or -0.53% decrease or $586,000 loss (profit loss)!
It didn't cross my mind until I compared my solutions rate change to the official rate change.
You're supposed to off-balance considering the impact of the current relativities themselves. I realize this is not really the point of this question - but considering no "steps" are provided this problem - is slightly concerning: did no student document their work. Or there were no accepted answers with clear documentation? There should be some sort of documentation for a perfect answer.
Note my goals when answering this question was:
1. maximize the 10% territory (to minimize loss / minimize competitiveness)
2. keep 0% rate increase (obviously!)
3. not rate decrease terr 1 (don't want off-balance to cause decrease in terr 1)
My perfect sample solution [done in excel after exam]:
OWA = One-Way Analysis indication
Unweighted = CurrEP/CurrDiff.
Proposed = capped
Best = selected answer (also off-balanced).
Cas [accepted] Solution:
What's bad about the cas solution:
1. does not get a 10% increase in terr 3
2. gets larger than a 6% decrease in terr 1
3. terr 2 therefor has the largest increase relative to indicated.
Thus, resulting in problems in all 3 territories.
Normalizing the CAS solution to remove the -0.53% error would result in overshooting territory 3 (10.46%). This is actually EXACTLY what happened to me in the exam. The quick solution was wrong. So I had to start trial and error to create a solution that met my goals from above.
Worst part for me I got between 50 - 100 out of 1.25 points or .75 - 1.25.
That's a very detailed analysis. I will need to set aside some time over the next few days to go over this.
Since this question was worth 1.25 points, you should plan to complete your answer in roughly 4-5 minutes. Recall that calculation questions on Exam 6 generally take longer than essay questions for the same points, but this wasn't intended to be a heavy calculation question.
I think you were right when you alluded to the notion that your answer above was for an extended version of this question versus the one that was asked on the exam.
I'd say you'd get 0.75 pts just for knowing the 3 requirements for territorial changes. Then 0.5 pts for applying the rules and doing the off-balance in a very simple way.
It's true that their answer had a larger than 6% decrease in territory 1 after the off-balance but they didn't appear to care about that (maybe they should have). That kind of thing is always potentially a problem when doing an off-balance to get back to a 0% overall change. To fix that, you could go back and propose a -5% change in territory 1 so that after the off-balance, the decrease would be a little more than -5% but still within the indicated level of -6%.
The only stipulation of the question was that the proposed changes meet the requirements for approval so there were many different possible answers.