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  #11  
Old 05-10-2007, 08:21 PM
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Sonny Sonny is offline
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cubs1908,

Good post. I just have a couple of comments.

1. In my simple example, you've basically got a list of three policies that renewed during the period, and you can calculate both the average expiring rate and the average renewal rate on each policy, as well as the % rate change. So the next challenge is to determine the overall renewal rate (per exposure) % change for the whole book for the period.

We discussed two ways to do this. First, you can determine a weighted average % change, using the expiring premium for each policy as the weight (as defined in the article you cited). The second method is as you defined it in your last post: Overall RRC = Average Renewal Rate Per Unit (on entire book) / Average Expiring Rate Per Unit (on entire book) - 1.

I just want to point out that these two methods are equivalent if the exposure distribution has not changed. In fact, provided the exposure distribution doesn't change drastically, the two methods should be very close.

The problem arises when the exposure distribution changes drastically, as it did in my contrived example (going from 6 to 8 total exposures with a big change in mix). In this case, the two methods will give very different answers.

The fundamental problem here all goes back to the fact that RRC reports simply don't work well when the mix changes. And that's really clear in my example, where the rates are generally increasing, but the average rate per exposure on the book has declined from $1917 to $1725, simply because one of the accounts added a low-valued unit at renewal. Ultimately, this is just one of the things that causes problems and makes RRC reports misleading and complicated.

2. I like your suggestion of weighting exposure changes by expiring premium -- because it is consistent w/ the way you are handling the rate per exposure changes and everything adds up pretty well.

3. I still don't understand what value you gain by incorporating the overall change in exposures and the overall change in premium on the renewal book. What does this tell you? It doesn't say anything about the premium growth or decline for the company, because you also have policies non-renewing and new policies being written. If I were you, I would stick to measuring the change in rate per exposure for the renewal policies. The other measures are not meaningful in any way.
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  #12  
Old 05-10-2007, 08:25 PM
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Originally Posted by Sonny View Post
cubs1908,

Good post. I just have a couple of comments.

1. In my simple example, you've basically got a list of three policies that renewed during the period, and you can calculate both the average expiring rate and the average renewal rate on each policy, as well as the % rate change. So the next challenge is to determine the overall renewal rate (per exposure) % change for the whole book for the period.

We discussed two ways to do this. First, you can determine a weighted average % change, using the expiring premium for each policy as the weight (as defined in the article you cited). The second method is as you defined it in your last post: Overall RRC = Average Renewal Rate Per Unit (on entire book) / Average Expiring Rate Per Unit (on entire book) - 1.

I just want to point out that these two methods are equivalent if the exposure distribution has not changed. In fact, provided the exposure distribution doesn't change drastically, the two methods should be very close.

The problem arises when the exposure distribution changes drastically, as it did in my contrived example (going from 6 to 8 total exposures with a big change in mix). In this case, the two methods will give very different answers.

The fundamental problem here all goes back to the fact that RRC reports simply don't work well when the mix changes. And that's really clear in my example, where the rates are generally increasing, but the average rate per exposure on the book has declined from $1917 to $1725, simply because one of the accounts added a low-valued unit at renewal. Ultimately, this is just one of the things that causes problems and makes RRC reports misleading and complicated.

2. I like your suggestion of weighting exposure changes by expiring premium -- because it is consistent w/ the way you are handling the rate per exposure changes and everything adds up pretty well.

3. I still don't understand what value you gain by incorporating the overall change in exposures and the overall change in premium on the renewal book. What does this tell you? It doesn't say anything about the premium growth or decline for the company, because you also have policies non-renewing and new policies being written. If I were you, I would stick to measuring the change in rate per exposure for the renewal policies. The other measures are not meaningful in any way.
Exposure change on renewing policies is a valid statistic that can be meaningful for other purposes, such as long term modeling of a book of business to determine lifetime value.
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  #13  
Old 05-03-2013, 01:01 PM
ExamTortoise ExamTortoise is offline
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Default Price Monitoring

I know I'm bumping this super-old thread, but have there been more recent threads on this subject?

We are engaged in the age-old debate of whether to weight renewal price changes by:

o Expiring Exposures
o Current Exposures
o Expiring Premium
o Renewal Premium
o Proxy Expiring Premium (i.e. Renewal Premium divided by price change)

If someone can point me to the definitive treatise, I'd be appreciative. I've got the Vaughn paper in front of me.
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  #14  
Old 05-03-2013, 02:35 PM
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Maphisto's Sidekick Maphisto's Sidekick is offline
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Originally Posted by ExamTortoise View Post
I know I'm bumping this super-old thread, but have there been more recent threads on this subject?

We are engaged in the age-old debate of whether to weight renewal price changes by:

o Expiring Exposures
o Current Exposures
o Expiring Premium
o Renewal Premium
o Proxy Expiring Premium (i.e. Renewal Premium divided by price change)
Ideally, you would weight by renewable annualized premium on the exposures at expiration (assuming that your base policy term is annual; if not adjust accordingly), if you're trying to generate figures like "exposure change", "rate change", "price change" overall for a product or a line.

Expriring premium will generally be a reasonable proxy in most normal circumstances.

If you think of renewal price changes as looking like the following function:

[$Expiring Premium] + [$ Premium Change due to exposure change] + [$ Premium Change due to limit/deductible/... change] + ... + [$ Premium Change due to rate change] = [$Renewal Premium]

...and you apply that function across all renewals for a line or a product, then the weighting by expiring premium just naturally arises from the algebra.
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  #15  
Old 05-03-2013, 02:48 PM
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I would argue price changes should be weighted on expiring exposures.

Think of it this way:


Premium Change = Renewal Premium/Expiring Premium

= (Renewal Exposure/Expiring Exposure) * (Renewal Base Rate/Expiring Base Rate) * (Renewal Coverage Factors/Expiring Coverage Factors) * (Renewal Experience Mod/Expiring Experience Mod) * (Renewal Schedule Mod/Expiring Schedule Mod)

I think the appropriate weighting factor for each of those percentages is the product of all the denominators before it. So for base rate, it's Expiring Exposure, but for the change in the average schedule mod, it's Expiring Premium before the application of Schedule Mod.
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  #16  
Old 05-03-2013, 03:22 PM
ExamTortoise ExamTortoise is offline
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Default valid, but...

Here is where that solution seems counter-intuitive (I've made an extreme example, just to make my point):

Assume, you have two classes (or lines of business, or segments, etc).

In the expiring year, the 99% of your exposure (and premium) is in class A. In the renewal year, the 99% of your exposure (and premium) is in class B.

Class A undergoes a 100% rate increase, Class B has a 50% rate decrease.

Using expiring premium method, we report almost 100% price increase on the book. Everyone puts on a party hat, starts blowing a kazoo and doing the limbo.

Then someone notices that we renewed virtually no business in class A, but class B had 100% renewal retention. People choke on their kazoos, the hats go in the garbage and people start cleaning out their desks.

Weighting it on renewal premium would result in a rate decrease of almost 50% which seems more indicative of the current book in the example I just created.
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  #17  
Old 05-03-2013, 03:30 PM
Mary Frances Mary Frances is offline
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Depends what question you want to answer:
(a) - what is the effect of the rate change on my expiring book, assuming that they all renew? This is what is normally expected by and filed with the regulators
(b) - what is the average effect on the insureds who stay with me? This may be far more interesting for planning purposes, but note that if you want to compare this with your indication, then you've got to adjust the indication for the changes in the mix from expiring to renewal as well
(c) - what's the percentage change in premium from expiring to renewal? This is the easiest to calculate, of course, but it also tells you the least
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  #18  
Old 05-03-2013, 05:55 PM
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Maphisto's Sidekick Maphisto's Sidekick is offline
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Quote:
Originally Posted by ExamTortoise View Post
Here is where that solution seems counter-intuitive (I've made an extreme example, just to make my point):

[...]

Weighting it on renewal premium would result in a rate decrease of almost 50% which seems more indicative of the current book in the example I just created.
Got it; and I'll revise my answer.

Here is a numeric example based roughly on the scenario you described:

Code:
             Expiring Term           Renewing Term
         Exposure Rate Premium   Exposure Rate Premium
Class A     99      2   198         1      4      4  
Class B     10      0.1   1       990      0.05  49.5

TOTAL                   199                      53.5
My premium change is obviously -73.1% = (53.5/199-1)

Class A and Class B exposure bases are not necessarily the same; it is not safe to assume that the exposure is additive across the classes. Therefore I need to do some kind of weighted average, and expiring premium makes the most sense to me.

So, my exposure change is -49.2% = [198*(1/99-1)+1*(990/10-1)]/[198+1]

In this example, premium = rate × exposure. So, (1+premium change) = (1+rate change)×(1+exposure change)

Therefore, my rate change is -47.0% = (-0.731+1)/(-0.492+1)-1

The expiring premium weighted average rate change would be 99.2% (math left as an exercise for the reader), which is clearly wrong and I stand corrected.

It's happy hour, so I'm not going to try to figure out what the rate change is weighted by. Premium change is pretty easy to capture, and exposure change isn't too bad to do if your source data is set up appropriately.

Changes due to limits, attachment, etc. are kind of like exposure, and I can do math to figure them out.

If the product/accounts in question have multiple exposure bases, working directly with rate can be messy...and that's OK, because if I know the renewal premium change and the other components of renewal premium change, then I can solve for rate change, avoiding that messiness.

Edit: I went to happy hour and the outstanding question killed my buzz, so I grabbed a cocktail napkin and worked it out. In the example above, to get the average rate change, you would weight by (renewed exposure×expiring rates). This corresponds to Mary Frances' option (b). That's also a rather ugly looking weighting to describe, which is probably why I prefer to just solve for rate change, rather than attempting to directly calculate the average.

Mary Frances' option (a) in my example would be the 99.2% weighted-by-expiring-premium figure (I guess this must be a deregulated market).

Now, if you want to make a few heads explode, let's say for the sake of argument that the profit margin on Class B's renewal rates is significantly greater than the profit margin on Class A's rates (expiring or renewing). If that's the case, then even though we have a decrease in the average rate, we are left in a better position profit-margin wise. Break out the kazoos; that -47% is good news!

Moral of the story: Numbers can be deceptive, unless there's context. Providing that context is the reason we get paid the big bucks.

Last edited by Maphisto's Sidekick; 05-03-2013 at 06:53 PM.. Reason: I should have ordered something more potent, to anesthetize that part of my brain which couldn't let the problem go.....
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  #19  
Old 05-03-2013, 06:42 PM
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Have you read Neil Bodoff's paper?
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  #20  
Old 05-03-2013, 07:14 PM
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Maphisto's Sidekick Maphisto's Sidekick is offline
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Have you read Neil Bodoff's paper?
It's far more fun to figure out the answer than to just read it in a paper.
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