TIA Additional Reserving Problem #1 (Cape Cod)

[nonactuarialactuary]

 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?

[Vorian Atreides]

When a filing requirement states that ECR needs to be at the same level as the losses being reserved.

[actuarialista]

Originally Posted by jts5009

 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.