Actuarial Outpost > CAS TIA Additional Reserving Problem #1 (Cape Cod)
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

#1
05-02-2011, 01:58 PM
 nonactuarialactuary Member Join Date: May 2008 Posts: 1,332
TIA Additional Reserving Problem #1 (Cape Cod)

Code:
``` AY     EP     ADJ EP   RPT   %RPT
2007   6000     8000   5000   87.5%
2008   7500     8000   4000   75.0%
2009   9000    10000   4000   50.0%
2010  10000    10000   2000   30.0%```
Part A of this problem is a pretty standard Cape Cod problem. They give you earned premium, onlevel earned premium, reported loss, and % reported for AY2007-2010, and ask for the Cape Cod ELR. Sum reported losses, and divide this total by the sumproduct of onlevel earned premium and % reported, and you get an expected loss ratio of 71.43%. Pretty straightforward.

Part B threw me a bit though. Part B asks for the unadjusted expected claim ratio for AY2008. To do this, I calculated the ultimate losses for AY2008:

=Reported+Expected Unreported
=Reported+[Selected ELR * Onlevel EP * % Unreported]
=4000+(0.7143*8000*(1-0.75))
=5428.57

Fikes' solution multiplies the ECR by the onlevel factor:

=71.43%*8000/7500
=76.19%

I dug into this a bit further, and I think I understand where this comes from now. Fikes' answer says:

So, first back out any differences to loss. In this case, no loss trend rates or tort reform factors were considered, so no adjustments need to be made. Second, back out any differences for premium:

The above is Fikes' answer, 76.13%. If we wanted ultimate claims, we could apply this to the unadjusted earned premium, similar to what I did above:

AY08 Ult Loss
=Reported+Expected Unreported
=Reported+[Unadjusted ELR * EP * % Unreported]
=4000+(0.7619*7500*(1-0.75))
=5428.57

Ultimate claims are the same in both calculations (5428.57). Other than having an exam problem specifically ask for it, is there ever any need to calculate these unadjusted expected claim ratios? On an exam, it seems like I can get to ultimate and unpaid claim totals using just the onlevel earned premium and adjusted ECR calculated in Part A. Where will the unadjusted ECRs help out?
#2
05-02-2011, 03:10 PM
 Vorian Atreides Wiki/Note Contributor CAS Join Date: Apr 2005 Location: Garroting Deep Studying for CAS Exam 7 College: Hard Knocks Favorite beer: Sam Adams Cherry Wheat Posts: 27,757

When a filing requirement states that ECR needs to be at the same level as the losses being reserved.
__________________
The Search is about to begin . . . There is still time left to join.

I find your lack of faith disturbing.

Wait until you have kids.

Freedom of speech is not a license to discourtesy
#3
05-02-2011, 08:36 PM
 actuarialista Member Join Date: Nov 2010 Posts: 165

Quote:
 Originally Posted by jts5009 Code: ``` AY EP ADJ EP RPT %RPT 2007 6000 8000 5000 87.5% 2008 7500 8000 4000 75.0% 2009 9000 10000 4000 50.0% 2010 10000 10000 2000 30.0%``` Part A of this problem is a pretty standard Cape Cod problem. They give you earned premium, onlevel earned premium, reported loss, and % reported for AY2007-2010, and ask for the Cape Cod ELR. Sum reported losses, and divide this total by the sumproduct of onlevel earned premium and % reported, and you get an expected loss ratio of 71.43%. Pretty straightforward. Part B threw me a bit though. Part B asks for the unadjusted expected claim ratio for AY2008. To do this, I calculated the ultimate losses for AY2008: =Reported+Expected Unreported =Reported+[Selected ELR * Onlevel EP * % Unreported] =4000+(0.7143*8000*(1-0.75)) =5428.57 I then said that the unadjusted expected loss ratio was this 5428.57 divided by the unadjusted earned premium of 7500, producing a loss ratio of 72.38%, which is the wrong answer. Fikes' solution multiplies the ECR by the onlevel factor: =71.43%*8000/7500 =76.19% I dug into this a bit further, and I think I understand where this comes from now. Fikes' answer says: Adj ECR = Loss/Adj Premium So, first back out any differences to loss. In this case, no loss trend rates or tort reform factors were considered, so no adjustments need to be made. Second, back out any differences for premium: Unadjusted ECR = Loss / [Adj Premium * (1/onlevel factor)] = Loss / [Adj Premium * 1/(8000/7500)] = Loss / [Adj Premium * (7500/8000)] = [Loss / Adj Premium] * (8000/7500) = Adj ECR * 8000/7500 The above is Fikes' answer, 76.13%. If we wanted ultimate claims, we could apply this to the unadjusted earned premium, similar to what I did above: AY08 Ult Loss =Reported+Expected Unreported =Reported+[Unadjusted ELR * EP * % Unreported] =4000+(0.7619*7500*(1-0.75)) =5428.57 Ultimate claims are the same in both calculations (5428.57). Other than having an exam problem specifically ask for it, is there ever any need to calculate these unadjusted expected claim ratios? On an exam, it seems like I can get to ultimate and unpaid claim totals using just the onlevel earned premium and adjusted ECR calculated in Part A. Where will the unadjusted ECRs help out?
Actually yes, I think that in Cape Cod problems where the claims are adjusted (for trend etc.), you do have to calculate the unadjusted ECR. See TIA, New Problems for Friedland Part III, #1.c. and #2.b. In these problems you cannot get ultimate losses by taking ECR*on-level prem*pctg unreported. You must first "unadjust" the ECR (by backing out claims and prem trend) to the right level for each AY. Then multiply by original prem and pctg unreported. Or, I suppose another method would be to "unadjust" the ECR for claims only and then multiply by on-level prem and pctg unreported.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 11:22 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top