Calculate written exposures by dividing the given written policies by 2. This is because the written policies are 6-month policies, so the total written exposures is half the written policies.
Step 2:
Apply this formula:
Earned Exposures = 0.75 * Current Year Written Exposures + 0.25 * Prior Year Written Exposures
But I assume it's that formula you're asking about.
The reason for the 0.75 factor is:
Since the policies are 6-month policies, 100% of the policies written in the first half of the year will be fully earned in the current year, but only 50% of the policies written in the second half of the year will be fully earned. If you combine these, you get that 75% of the written exposures from the current year will be earned in the current year.
The reason for the 0.25 factor is:
Half of the policies written in the second half of the prior year will be earned in the prior year, and half will be earned in the current year. Then half of the second half is one-quarter or 25%. This is the contribution to the current year from written exposures in the prior year.
To follow up on the explanation for the 0.75 factor, you mentioned only 50% of the policies written in the second half of the year will be fully earned. So for example, if 10 policies are written every month from July to December, then do you mean to say that 30 of those policies will be fully earned? A policy written in the month of August for example will only earn (5/6)th of the exposure by the end of the year.
Please correct me if I'm wrong, I have trouble understanding the picture behind the same.
Sorry, I didn't state it properly. I meant to say the amount earned for all policies written in the second half of the year would average to 50%. (The only policies that would be fully earned would be the ones written on July 1.)
Need clarification on the assumption behind Step 1:
Since the policies that were written were each for 1/2 a year, then the x number of policies written in year ABCD were each for 1/2 a car year, and thus the number of car-years being insured was x/2.
That's correct. The key is that the exposure base is car-years. So another way to say it is that each 6-month policy represents 1/2 a year of coverage so the insurer is exposed for only 1/2 year for each of these policies.
Comments
Step 1:
Step 2:
But I assume it's that formula you're asking about.
The reason for the 0.75 factor is:
The reason for the 0.25 factor is:
To follow up on the explanation for the 0.75 factor, you mentioned only 50% of the policies written in the second half of the year will be fully earned. So for example, if 10 policies are written every month from July to December, then do you mean to say that 30 of those policies will be fully earned? A policy written in the month of August for example will only earn (5/6)th of the exposure by the end of the year.
Please correct me if I'm wrong, I have trouble understanding the picture behind the same.
Thank you.
Sorry, I didn't state it properly. I meant to say the amount earned for all policies written in the second half of the year would average to 50%. (The only policies that would be fully earned would be the ones written on July 1.)
Need clarification on the assumption behind Step 1:
Since the policies that were written were each for 1/2 a year, then the x number of policies written in year ABCD were each for 1/2 a car year, and thus the number of car-years being insured was x/2.
Is that the way to interpret this?
Thanks,
Cj.
That's correct. The key is that the exposure base is car-years. So another way to say it is that each 6-month policy represents 1/2 a year of coverage so the insurer is exposed for only 1/2 year for each of these policies.