April 2012 Question 4

[Maria Pizpiki]

Hello,

I have a few questions on this past exam Q.

Based on the notes the Solvency Ratio is the division of free reserves and net written premium. However I understand that in this question the premiums taken are gross and not net. Is it because by net we mean net of reinsurance and not net of acquisition costs?

I have an additional question regarding the Claims ratio. I see that the incurred claims taken in order to calculate the claim ratio is: claims paid+change in O/S reserve, where change in O/S reserve is (O/S reserve cf- O/S reserve bf). I would like to ask why do we take the change in O/S reserve and not the O/S reserve cf instead.

Final question, is regarding the UPR. I understand why GEP=GWP as we implicitly assume that the business is on a steady state. However, I'd like to understand why GWP=2*UPR when we assume uniform risk distribution and that policies are written uniformly over the year. I will give an example:
Assume that in total we write 120 euros in a given year. Given the assumptions above this would equate to writing 10 euros per month (2nd assumption). We now assume that we earn every month's 10 euros uniformly. Hence, the gross earned premium for policies written in this year would be:

(12+11+10+9+8+7+6+5+4+3+2+1)*10/12=65. The UPR then would be GWP-UPR=55. Why don't get that GWP=2*UPR? Is there something wrong in the above calculations?

Thanks in advance for your help.

Maria

 

[Jammy]

Final question, is regarding the UPR. I understand why GEP=GWP as we implicitly assume that the business is on a steady state. However, I'd like to understand why GWP=2*UPR when we assume uniform risk distribution and that policies are written uniformly over the year. I will give an example:
Assume that in total we write 120 euros in a given year. Given the assumptions above this would equate to writing 10 euros per month (2nd assumption). We now assume that we earn every month's 10 euros uniformly. Hence, the gross earned premium for policies written in this year would be:

(12+11+10+9+8+7+6+5+4+3+2+1)*10/12=65. The UPR then would be GWP-UPR=55. Why don't get that GWP=2*UPR? Is there something wrong in the above calculations?

Hi Maria,
I'm not clear what the numbers represent in your brackets i.e. (12+11+...1).
These cannot be GWP in each month, as GWP is 10 per month in your example.

I would calculate it this way:
GWP each month = 10. Assume written mid-way through each month.
So, GWP written in Jan will be earned for 11.5 months.
Hence, GEP will be 11.5/12 of GWP of Jan
Similarly, 10.5/12 of Feb Gwp....and 0.5/12 of Dec GWP.
So, you end up with {(11.5+ 10.5+...+0.5)/12} x 10 = 6 x 10 = 60.
UPR c/f = GWP - GEP = 120-60 = 60 in your example, and hence GWP = 2*UPR

 

[Maria Pizpiki]

Hi Maria,
I'm not clear what the numbers represent in your brackets i.e. (12+11+...1).
These cannot be GWP in each month, as GWP is 10 per month in your example.

I would calculate it this way:
GWP each month = 10. Assume written mid-way through each month.
So, GWP written in Jan will be earned for 11.5 months.
Hence, GEP will be 11.5/12 of GWP of Jan
Similarly, 10.5/12 of Feb Gwp....and 0.5/12 of Dec GWP.
So, you end up with {(11.5+ 10.5+...+0.5)/12} x 10 = 6 x 10 = 60.
UPR c/f = GWP - GEP = 120-60 = 60 in your example, and hence GWP = 2*UPR

Hi Jammy,

Thanks a lot for your response ! My numbers in the brackets are same as your (11.5+ 10.5+...+0.5). The difference between my and your calculation is that I essentially assume that policies incept at the beginning of each month and not at the mid-point as you do, and that's why I get these extra 5 in my earned premium. Now it's all clear-many thanks!

 

[Maria Pizpiki]

Hello,

I have a few questions on this past exam Q.

Based on the notes the Solvency Ratio is the division of free reserves and net written premium. However I understand that in this question the premiums taken are gross and not net. Is it because by net we mean net of reinsurance and not net of acquisition costs?

I have an additional question regarding the Claims ratio. I see that the incurred claims taken in order to calculate the claim ratio is: claims paid+change in O/S reserve, where change in O/S reserve is (O/S reserve cf- O/S reserve bf). I would like to ask why do we take the change in O/S reserve and not the O/S reserve cf instead.

Final question, is regarding the UPR. I understand why GEP=GWP as we implicitly assume that the business is on a steady state. However, I'd like to understand why GWP=2*UPR when we assume uniform risk distribution and that policies are written uniformly over the year. I will give an example:
Assume that in total we write 120 euros in a given year. Given the assumptions above this would equate to writing 10 euros per month (2nd assumption). We now assume that we earn every month's 10 euros uniformly. Hence, the gross earned premium for policies written in this year would be:

(12+11+10+9+8+7+6+5+4+3+2+1)*10/12=65. The UPR then would be GWP-UPR=55. Why don't get that GWP=2*UPR? Is there something wrong in the above calculations?

Thanks in advance for your help.

Maria

I think I understand the reason of taking the change in O/S reserve for the claim ratio. Am I correct if I generally think that the accounting ratios are calculated based on a profit and loss point of view?

 

[Darren Michaels]

In the solvency ratio net, means net of reinsurance.

The definition of the claims (loss) ratio is incurred claims / earned premiums.

The incurred claims in the period for which you are calculating the claims ratio are calculated as paid claims + (OCR c/f - OCR b/f).

 

[Maria Pizpiki]

Thank you a lot both!