Actuarial Outpost Loss Ratio
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#1
10-19-2018, 07:49 AM
 breader21 Non-Actuary Join Date: Sep 2018 Posts: 4
Loss Ratio

May I ask for a bit of input in respect of loss ratios?

The formula I have is incurred claims / earned premium.

I only have access to revenue account and balance sheet data, which includes claims paid, claims reserves, gross premium and unearned premium reserves.

Using this information, how can I obtain the correct numerator and denominator to calculate the loss ratio?

So in other words how do I convert paid claims to incurred claims? And how also do I convert gross premium to earned premium?

Kind regards,

BR
#2
10-19-2018, 08:06 AM
 Abelian Grape Meme-ber                         Meme-ber CAS Join Date: Jul 2014 Favorite beer: Allagash Curieux Posts: 42,093

Paid Claims + Claims Reserves = Incurred Claims

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#3
10-19-2018, 08:25 AM
 breader21 Non-Actuary Join Date: Sep 2018 Posts: 4

Thank you.

Incurred claims = paid claims + change in claims reserve.

Is this also correct?

Why is it correct (if it is correct)?

Regards,

Ben
#4
10-19-2018, 08:45 AM
 SlowMotionWalter Member CAS Join Date: Jun 2013 Posts: 13,478

https://www.casact.org/library/study...Ratemaking.pdf

pp 42-44, 91-94
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#5
10-19-2018, 09:24 AM
 CuriousGeorge Member CAS SOA Join Date: Dec 2005 Posts: 1,408

Quote:
 Originally Posted by breader21 Thank you. Yes I mean gross premium = written premium. I read somewhere the following: Earned premium = written premium - change in unearned premium reserve. Incurred claims = paid claims + change in claims reserve. Is this also correct? Why is it correct (if it is correct)? Regards, Ben
Grape's formulas are fine if you are looking at inception to date, i.e. beginning reserve and UPR is zero, or looking at the entire history of an accident year.

Your formulas should be used if you are dealing with calendar period data.
#6
10-19-2018, 09:29 AM
 Marcie Member CAS Join Date: Feb 2015 Posts: 9,656

Quote:
 Originally Posted by CuriousGeorge Grape's formulas are fine if you are looking at inception to date, i.e. beginning reserve and UPR is zero, or looking at the entire history of an accident year. Your formulas should be used if you are dealing with calendar period data.
breader's formulas could be used for inception-to-date as well.
#7
10-19-2018, 10:53 AM
 therealsylvos Member CAS Join Date: Mar 2014 Posts: 17,601

Quote:
 Originally Posted by breader21 Thank you. Yes I mean gross premium = written premium. I read somewhere the following: Earned premium = written premium - change in unearned premium reserve. Incurred claims = paid claims + change in claims reserve. Is this also correct? Why is it correct (if it is correct)? Regards, Ben
From a CY perspective:

Year 1:

Beginning UPR = 0
Beginning Claims Reserve = 0

Company opens for Business in July, and writes one anuual policy 7/1 for 100 dollars. They experience a claim initially reserved for 75 dollars, of which they pay 15 dollars on 12/1, and decrease the outstanding reserve correspondingly to 60 dollars.

Year Ending UEPR = 100/2 = 50
Year 1 WP = 100
Year 1 EP = (100-(50-0)) = 50

Year Ending Claims Reserve = 60
Year 1 Paid Claims = 15
Year 1 incurred loss = 15 + (60-0) = 75

Year 1 Loss Ratio = 75/50 = 1.5

Year 2:

Beginning UEPR = 50
Beginning Claims Reserve = 60

The company decides to double their premium to account for the poor Loss Ratio in the prior year. The 7/1 policy renews at 200 dollars. They pay the remaining 60 dollars and close the original claim (reserve set to 0). They get a new claim of 80 dollars and they pay 35 of it on 12/1.

Ending UEPR = 100
Year 2 WP = 200
Year 1 EP = 200 - (100-50) = 150 (50 dollars from last years policy and 100 dollars from this years)

Ending Claims Reserve = 45
Year 2 Paid claims = 60 + 35 = 95
Year 2 Incurred Loss = 95 + (45 - 60) = 80

Year 2 loss ratio = 80/150 = .533
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