FALL 2019, Q1
If the exposures are not uniform, then how are we supposed to derive the proportions for subparts 1a,c and d?
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If the exposures are not uniform, then how are we supposed to derive the proportions for subparts 1a,c and d?
Comments
This was a hard problem. The information you need on earning patterns is indirectly given in the table. And the information below the table is also important. For example, that all policies are annual and are written on the first day of each quarter.
Anyway, the earnings pattern as you have to use it is calculated as follows using the written and earned exposures given in the table:
Then you can use these proportions to calculate the answer to part (a) as follows, where I'm following sample answer 2 in the examiner's report:
If you add it all up, you get: 100 + 450 + 220 + 10 = 780.
This may help you understand the other parts of the problem better. If not, let me know.
Makes sense, thanks Graham!
Hi Graham - I have a theory question on part c which asks for the unearned exposure. In your wiki articles from Werner Chapter 4 (Exposures), you say that the reason we have to calculate the CY unearned exposure for groups (of policies) differently is because individual policies within a group all have different effective dates and expiration dates.
But in this particular exam question, it tells us that all policies are written on the first day of the quarter so that statement would seem to suggest we can use the individual policy approach to calculate CY unearned exposure since we don't have different effective dates within groups. However, I believe from practicing this problem that we have to use a grouped approach to solve it otherwise we will ignore the ending CY 2017 unearned exposures. But I'm trying to rationalize the why in my mind, is it because the policies across different groups have different effective and expiration dates and therefore we have to use a grouped method?
So in other words and going back to your original statement, the reason the aggregation formula is different is that individual policies within a group AND across groups may have different effective dates and expiration dates? Of course all of this pertains to CY aggregation because I know we don't run into this kind of issue with PY aggregation for unearned exposures. Thanks!
I would need to see your calculations to better comment on your proposed method. A couple of points however:
I like the second sample answer better because it makes it clear what's actually happening in terms of earnings.
Another way to look at the difference between the individual and aggregate formulas is that the individual policy formula holds for a specific point in time. But the aggregate formula deals with a specific period of time like a year.
I've attached my solution per your suggestion. So we can use the aggregate formula for CY unearned calculations independent of whether policies within a group have identical effective dates or not?
That certainly is an exhaustive solution! And now that the exam is given in Excel, you can actually solve it like that on the exam.
I want to say yes to your question about the aggregate formula. I only hesitate because who knows what kind of strange question they may come up with. It looks like you understand this very well now so I would suggest tailoring your approach to the specific question without a preconceived notion. Keep in mind the 2 approaches but also pay attention to the particular facts that you're given. You might sometimes even see a quick way to solve the problem that avoids a brute force calculation. In any case, you have more options now that you can set up your solution in Excel.