TIA 5A Quiz 1 #4

[diputz42]

Calculate the 2007 on-level earned premium given the following information:

The calendar year 2007 earned premium = $1 million
20% of the premium is written on January 1.
10% of the premium is written on April 1.
The remainder of the premium is written uniformly throughout the year.
All policies are annual.

Rate change history:
7/1/06 +10%
4/1/07 -5%
4/1/08 +3%



Ken's solution assumes that the premium written on April 1 is split evenly between 4/1/06 and 4/1/07 and is therefore earned proportionally between the two. Meaning 25% earned in CY07 from 4/1/06, and 75% earned in CY07 from 4/1/07. But without explicitly stating how much was written on each date, this assumption becomes ambiguous.

Naturally, I made the assumption that all April 1 premium in this problem was written on 4/1/07 since the problem is about CY07. Is that a reasonable assumption to make on the exam if we're given a similar problem?

[doop]

since it doesn't specify a year it would be my intuition that it applies to all years. especially in a problem like this, where the whole point seems to be to address seasonality (which is usually predictable every year).

[Vorian Atreides]

I think an Exam problem will be a bit more specific as to which year(s) "4/1" will refer to. Especially since the premium written are at two different rate levels--so how is the 10% really interpreted? There's way too much wiggle room for assumptions to be made that I doubt that the graders will want to grade such a problem.

With that said, CY earned premium is generated from policies written in the given year and the prior year. Explicitly stating that the given info is in reference to 2007 is valid and working from there should be acceptable.

Also note that the use of the term "premium" in the second and third statements is also ambiguous, too. I would simplify your life and explicitly state that it's in reference to earned premium.

[Bobby]

Ken's solution assumes that the premium written on April 1 is split evenly between 4/1/06 and 4/1/07 and is therefore earned proportionally between the two. Meaning 25% earned in CY07 from 4/1/06, and 75% earned in CY07 from 4/1/07. But without explicitly stating how much was written on each date, this assumption becomes ambiguous.

Naturally, I made the assumption that all April 1 premium in this problem was written on 4/1/07 since the problem is about CY07. Is that a reasonable assumption to make on the exam if we're given a similar problem?

What did you believe the problem was stating? I interpreted it as this:

You write 10% of the premium from the current year on 4/1/07 and 75% of it is earned that calendar year.

Then you also have 10% of premium from the prior year, written on 4/1/06, and 25% of that it earned in the 2007 calendar year.

[diputz42]

Thanks for the replies.

After reading your guys' input, I agree with VA that this problem would have way to much room for interpretation on an actual exam.

@Bobby: 10% of the (earned) premium written on April 1. I interpreted this as $100,000 of the earned amount was written on 4/1/07. That would imply $133,333 was actually written on 4/1/07. (Of course I didn't think it through this much when I was actually doing the problem.)

[Vorian Atreides]

Note: it is possible that one like this could still slip through. I've noticed that the Exam (especially the last few years) have improved wrt ambiguity of the problem statement (at least, if one exists, there's only two or three valid interpretations of the ambiguity).

However, I don't think it very likely and spending time now trying to fuss/worry over such a problem isn't time well spent unless you feel you've mastered everyother aspect of the Exam.

If you happen to see one like this, go with what you think would be valid and easiest to solve the problem. If you have time at the end, make your assumptions explicit. While it's a pain, you can appeal your answer if the sample solutions don't recognize your interpretation and you received a fairly low score (25-49% range or lower).