Exam 5 2005 #37

[emg3000]

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]

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]

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]

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]

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]

If it's CY and not PY, right?

[gitmichaels]

Yeah, that's a good point.

[booyah81]

Gotta love these exams...