Adjusted Earned Premium, Paid Loss & DCC, and Reported Loss & DCC

[tpgrove]

Hey, I am a newbie to the P & C industry and I am looking through a rate change filing and trying to make sense of it. This form lists actual earned premium, paid loss % DCC, reported loss & DCC. It also has the "adjusted value" for these categories for each year. How do they arrive at the adjusted value? I do not know what factor or method they apply and am only told that it is "adjusted for past rate changes and expected changes in the amount of exposure". Any help?

Thanks

[Vorian Atreides]

Might also look at CAS Exam 5 book on Ratemaking . . . but a few things to consider:

Ratemaking is prospective in nature, so you need to consider what things are going to look like in the time period you're estimating the rate need for.

One assumption that is often used is "Current rates are adequate and not excessive".

However, you may historical premiums that are not based on current rates; so what you do is adjust those premiums to reflect what would've been collected had the current rates been in effect throughout the past time period.

Also, you adjust losses to reflect changes over time. Inflation is one driver (what cost $1 three years ago now cost $1.05); but also changes in the exposure. For example, your book might shift from a predominate low-value homes (say average value of $150k) three years ago to a predominate intermediate value homes (say average value of $300k) more recently. This would lead to an increase in losses that's not accounted for by inflation, so you might need to adjust historical losses to reflect this change in your book.

All of these are based on actual information, but they're adjusted. The labeling of the data is just indicating that if someone (like a regulator) tries reconcile your information with a financial statement, they're not going to match because you've made adjustments to the data.

[tometom]

VA, as always an excellent explanation. Just to add.

Somewhere within that filing you should probably find the factors they used to adjust the data. At least in my experience, the states want to know how you calculated the factors.

[tpgrove]

After looking at it longer I noticed the other exhibits did explain how they were adjusted. I got confused again when they took the cumulative rate level change for the previous 3 years of a specific year and multiplied it by it's "area", these three products were added to get the ARLF they took the current rate index over that to get the current rate level factor for that year. Can anyone explain to me where this "area" comes from?

[tometom]

Just find someone with a ratemaking book for that exam as VA suggests.

this explains it: http://jofap.org/documents/vol10/v10_scollnik2.pdf

Basically, since your Earned Premium is for a Calendar Year and that contains written premium for a two year period. If there was a rate change at a particular date, then a portion of that EP needs adjusted to the revised rates. The paper gives the drawings an shows how there are different "areas" with different rates.

[Vorian Atreides]

Look at Chapters 4 and 5 (especially 5) of the following text from the Exam 5 syllabus:

http://www.casact.org/pubs/Werner_Modlin_Ratemaking.pdf

The most important aspect is the assumption that you're book is written uniformly over the year (that is, premium intake is the same no matter what day you look at).

[Vorian Atreides]

Originally Posted by tometom

VA, as always an excellent explanation. Just to add.

Somewhere within that filing you should probably find the factors they used to adjust the data. At least in my experience, the states want to know how you calculated the factors.

Thanks for the compliment.

[tpgrove]

OK thanks a ton for all your help, that did a lot of good in helping to sort through this filing. I have one final question. It gives a loss frequency table in one of the exhibits. It has the Actual Frequency listed and then a 5 point fitted and 4 point fitted frequency. How do you arrive at those numbers?

[Vorian Atreides]

Linear regression using the last x points.

Note that it might also be an exponential fit (take the (natural) logs of the frequency points, do a linear regression, the take e^(answer you get)).