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skaren9
04-12-2011, 04:11 PM
The loss cost for renewal is L(1-.1). Can somebody explain why it's not L/1.1? "loss costs for renewal are % lower than" was the same wording used in other exams yet only this problem computes L differently.

Thanks!

Scarlett5
04-27-2011, 05:12 PM
In that problem it says

"loss costs . . . are 10% lower . . . "

while in prior years they usually use the wording

"loss costs improve by x% . . ."

JasonScandopolous
04-27-2011, 05:26 PM
The loss cost for renewal is L(1-.1). Can somebody explain why it's not L/1.1? "loss costs for renewal are % lower than" was the same wording used in other exams yet only this problem computes L differently.

Thanks!

1-.1 is 10% lower... e.g. 10% lower than 100 is 90, not 90.90909.

Doc
04-27-2011, 05:49 PM
Here are two questions regarding a modification to losses and their method of determining the 2nd policy year losses:

2007 #28:

"average lost costs in any policy year are 3% lower than in the preceding policy year after adjustment for loss cost trend."
$900 x .75 x 1.07 / 1.03 = $701.21

2008 #44:

"Loss costs for renewal business are 10% lower than for new business."
$1000 x .9 = $900


The 2007 #28 question removes the 3% from the 7% trend growth. The 2008 #44 question directly lowers losses by 10%.

booyah81
04-28-2011, 06:36 AM
It's right. Divide by 1+% if lowering trend, and multiply by 1-% if lowering losses.

JasonScandopolous
04-28-2011, 10:02 AM
It's right. Divide by 1+% if lowering trend, and multiply by 1-% if lowering losses.

Hmm... not sure why this is the case? Specifically, the poster above you. I interpret the question to say: Looking at trended losses, losses decline by 3% every year.

Let's compare two years. Year 1 is this
Year 1: 100

Lets trend this to Year 2 (doesnt matter whether we are trending further than this, as year 1&2 would get the same trend and it'd cancel out in comparing the two):
Year 1 trended to year2: 100 * 1.07 = 107.00

"average lost costs in any policy year are 3% lower than in the preceding policy year after adjustment for loss cost trend."

Ok. I've adjusted for loss cost trend. For year 2, the previous average, adjusted-for-trend, loss cost is $107. Clearly, 107 * .97 gives you what they asked for, not 107 / 1.03. I'm not sure why the CAS solution did it the way they did... maybe it was a case of a non-perfect answer being given as the featured solution.

Edit: Maybe they are trying to imply that there's an exposure trend? Let me get the 3% from exposure trend and see what happens:

Yr1-Losses * 1.07 / Yr-1Exposures * X = Yr-1 Trended [X = exposure trend]
100 * 1.07 / X = Yr-1 Trended [100 given as yr 1 loss cost]
107 / X = Yr-1 Trended

Yr2-Losses / Yr2-Exposures is supposed to be 3% lower than Yr-1 Trended. If we assume an exposure trend of 3%, we get 107 / 1.03, which is essentially what the CAS answer did. But this is just a wrong as it was above in my post; this results in loss costs that are 2.9126% lower, not 3% lower. The exposure trend would need to be 1.030928 to achieve 3% lower loss costs.

Vorian Atreides
04-28-2011, 10:36 AM
I think when it comes Exam time, the graders aren't going to be overly concerned whether you multiplied by "0.97" or divided by "1.03" so long as you're making some sort of an appropriate adjustment using the info that is given.

If you really want to determine the "absolute correct way" look to W&M and other CAS publications (as well as experienced actuaries), not the CAS sample solutions. All you can really get from the CAS sample solutions is an idea of how sensitive the graders are to showing that you understand the process. As mentioned in the first paragraph, having the the adjustment factor is far more important to demonstrating that you understand the problem and the needed process to work it out than what that adjustment factor really is.

At this stage in the game, I would suggest just choosing which one makes most sense to you right now, and just go with it for the Exam. I'll bet that two students offering the exact same process but differ only in the "multiply by 0.97" vs. "divide by 1.03" will get the exact same score for that problem.

booyah81
04-28-2011, 11:05 AM
I'd go with what has been laid out in the original paper and on past exam problems. Exam writers have been consistent with how they treat lowering trend (divide by 1+%) versus lowering absolute dollar amounts (multiply by 1-%). At best you get the same points as what the exam solution says, at worst you get docked a quarter of a point.

JasonScandopolous
04-28-2011, 11:26 AM
I'd go with what has been laid out in the original paper and on past exam problems. Exam writers have been consistent with how they treat lowering trend (divide by 1+%) versus lowering absolute dollar amounts (multiply by 1-%). At best you get the same points as what the exam solution says, at worst you get docked a quarter of a point.

Looks like Vorian already answered this question better in 2010:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=191263&highlight=feldblum

quote from feldblum: "A 2% loss improvement factor may mean that de-trended losses in Year Y are 2% less than de-trended losses in Year Y-1, or that de-trended losses in Year Y are 2% more than de-trended losses in Year Y+1. If the exam problem is ambiguous, state your interpretation. We recommend the first interpretation."

When you say "loss improvement", I agree that there is some level of ambiguity. For some reason Feldblum thinks that multiplying by .98 is better and yet divided by 1.02 in his paper (page 222 of Feldblum) and basically caused all of this confusion to begin with.... But, ok, fine, either way is acceptable.

This only gives me more confidence, however, that the answer to 2007's problem is wrong. There, the question doesn't use the words "loss improvement", but explicitly state that loss costs are 3% lower than the previous year. With wording like that, the only correct answer is to multiply by .97. I agree that the graders probably didn't penalize this harshly or at all, but I hate when incorrect things are accepted just because they are conventional, which is why I wasted time on this. the tone of my post probably conveys my bad mood, sorry for that.

Vorian Atreides
04-28-2011, 12:21 PM
In some cases, "incorrect things" are accepted because the graders recognize that you're under time constraints and that the difference between the two doesn't invalidate that you understand the process.

In practice, you'll know how the "3% improvement" is calculated or how it's to be interpreted (this is often a measure of what's expected to happen when you re-underwrite your book) and how it relates to loss trends (which might be just an industry benchmark).