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emg3000
04-24-2011, 10:31 PM
This problem states that 2003 Average Written Premium is $933.33. It also states that there was a rate decrease of 20% implemented on July 1, 2003. Calculating on-level premium is central to the problem. The official exam answers state that the on-level average written premium is $840. Exposures are written uniformly throughout the year.

From the official exam answers:
CAY 2003 Half of the written premium needs to be adjusted down by 20%. The adjusted CAY 2003 average written premium is
1⁄2(933.33) + 1⁄2(933.33)(0.8) = 840

Am I missing something? If the average written premium for the year was $933.33 but there was a rate change halfway through, does that not imply that half the exposures were written at a rate level greater than $933.33 and half written at some level below $933.33?

My calculation is as follows:
[(Rate)(0.5 Exposures)+(0.8 Rate)(0.5 Exposures)] /[Exposures] = 933.33

=> (0.9 Rate) = $933.33

=> Rate = $1037.03

=> On-level Rate = ($1037.03)(0.8) = $829.63

So, what's up with this?

booyah81
04-24-2011, 11:33 PM
I wouldn't worry about this question. I've found it's an exception and that after it all the questions about on-leveling premium are consistent. VA can correct me though...

Vorian Atreides
04-25-2011, 09:22 AM
http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=191627

And I would say that this question is still valid under W&M.

booyah81
04-25-2011, 09:52 AM
It's definitely still valid, but the way they on-level for 2003 is the exception. Problems since then have been very good about stating whether it's a rate change (earned proportionally to length of policy over time aka "diagonally") or a law amendment change (applies in force aka vertically).

gitmichaels
04-25-2011, 11:42 AM
It's definitely still valid, but the way they on-level for 2003 is the exception. Problems since then have been very good about stating whether it's a rate change (earned proportionally to length of policy over time aka "diagonally") or a law amendment change (applies in force aka vertically).

Hi,
I'd be careful with this diagonal generalization - remember that rate changes applied to written premium are also depicted as vertical lines. JS

booyah81
04-25-2011, 11:44 AM
If it's CY and not PY, right?

gitmichaels
04-25-2011, 01:10 PM
Yeah, that's a good point.

booyah81
04-25-2011, 01:26 PM
Gotta love these exams...

MeanMetalX
01-03-2015, 10:44 PM
I recently came across this problem. I agree with emg3000 that the solution is incorrect. It is not a question of diagonal versus vertical. It is a question of the average written date of a policy which contributed written premium to the time period in question. Under the assumption of policies be written uniformly, this is precisely 07/01/2003. Hence, the calculation should .8/(.5*1 + .5*.8) = 8/9. To see this another way, let W be the written premium for the year, R be the rate in effect on 01/01/2003, and E be the total number of written exposures for the year. Then the on-leveled written premium for the year would be .8ER. However, under the assumption of a uniform writing of policies W = .5ER + .5*.8ER = .9ER. Hence, the on level factor should be 8/9. If this reasoning is incorrect, please inform me.