I'm having trouble understanding the "NET unearned premium" concept.
Could you give an example of when NUEP would be different from UEP?
I can't seem to figure out what item I could take out or add to from UEP to make it "net".
Thank you,
That's correct. It works the same way as losses when there is reinsurance. As chrisboersma indicated, the key formula is:
net = gross - ceded
For example, if an insurer has a 25% quota-share treaty with a reinsurer, and the insurer received a claim for $1000 then:
gross losses = $1000
net loss = $750
ceded loss = $250
If the customer premium paid to the insurer was $500, then:
gross premium = $500
net premium = $375
ceded premium = $125 (This is the reinsurer's share of the customer premium for servicing their 25% share of the losses. This is different from the premium the insurer would pay to the reinsurer for the basic reinsurance policy.)
At any given point during the policy term, part of the premium will be earned and the remainder will be unearned. If the policy is 20% of the way through the policy term, we would have:
You noted that the ceded premium of 125$ in your example is different from the premium the insurer would pay to the reinsurer for the basic reinsurance policy, but the 100$ paid at the beginning of the year in 2017 Fall 17 question be considered a ceded premium or the basic premium? It seems like the latter from your explanation, but in the examiner's report, it seems to consider it a part of ceded premium (when they subtracted 100 from 750 to get 650 - by the way, I think there would have been no discrepancy between both methods had they given EP of 850, is this correct?)
Yes, in 2017.Fall Q17b, the $100 in reinsurance premium was considered ceded premium. This assumes that reinsurance premiums come of out gross premium, but I don't know the specific accounting rules for how reinsurance premiums are actually paid. It seems possible that reinsurance premiums could be paid out of investment income, for example, in which case they might not be considered "ceded" premium.
Anyway, in my example above, I wanted to make things simple by ignoring the basic reinsurance premium. I could have just said the basic reinsurance premium = 0, and that the ceded premium covers the cost of the reinsurance treaty. That seems reasonable in a quota-share treaty because the reinsurance premium wouldn't depend on subsequent losses.
The exam problem was a little different because it was an excess-of-loss treaty versus quota-share. For an excess-of-loss treaty, you definitely have to have a basic reinsurance premium because you don't know how much loss (if any) will be ceded. There might not be any ceded losses for the year, so the insurer would still have to pay a basic reinsurance premium at the start of the year, otherwise the reinsurer wouldn't get paid for assuming the risk unless there were losses!
You're also correct that if EP = 850, both methods would agree. (I still don't think the data would be internally consistent but it probably isn't worth the time to figure all that out.)
In your explanation above, you have Net UEP = NWP - NEP
However, in the examiner's report for part (b) of F17Q17, it says that NUEP = NWP - NEP is not a correct formula. If we use this formula in this question, we have:
NWP = 1450
NEP = 650
**NUEP = 1450 - 650 = 800 ** which is different from the answer. Can you please clarify this?
The formula NUEP = NWP - NEP only works for 1 policy at a time. For a single policy, at a particular point in time, the sum of the earned premium and unearned premium must equal NWP. The example that I gave above was just for 1 policy.
This relationship breaks down however for a book of policies where policies all start and end at different times. Earned premium for a book would be evaluated over a period such as a year. In that case, you need the other formula NUEP = NWP - chg(NEP). (This formula also works for a single policy at a given point in time but the concept of earned and unearned is easier to understand with the other formula.)
You're correct that something is wrong here. The information provided in this problem is not internally consistent. This problem is solved in the wiki at the link below and there is a comment about this discrepancy.
Comments
Basic Reinsurance Accounting – Selected Topics [Blanchard & Klann]
See Unearned Premiums: Net, Gross, Ceded.
Spoiler alert = Net = Gross - Ceded .
OR Net Unearned Premiums = Gross Unearned Premiums - Ceded Unearned Premiums
[So unearned premiums with adjustments for reinsurance]
That's correct. It works the same way as losses when there is reinsurance. As chrisboersma indicated, the key formula is:
For example, if an insurer has a 25% quota-share treaty with a reinsurer, and the insurer received a claim for $1000 then:
If the customer premium paid to the insurer was $500, then:
At any given point during the policy term, part of the premium will be earned and the remainder will be unearned. If the policy is 20% of the way through the policy term, we would have:
Similarly:
Then for the ceded amounts:
Thanks Graham,
You noted that the ceded premium of 125$ in your example is different from the premium the insurer would pay to the reinsurer for the basic reinsurance policy, but the 100$ paid at the beginning of the year in 2017 Fall 17 question be considered a ceded premium or the basic premium? It seems like the latter from your explanation, but in the examiner's report, it seems to consider it a part of ceded premium (when they subtracted 100 from 750 to get 650 - by the way, I think there would have been no discrepancy between both methods had they given EP of 850, is this correct?)
Yes, in 2017.Fall Q17b, the $100 in reinsurance premium was considered ceded premium. This assumes that reinsurance premiums come of out gross premium, but I don't know the specific accounting rules for how reinsurance premiums are actually paid. It seems possible that reinsurance premiums could be paid out of investment income, for example, in which case they might not be considered "ceded" premium.
Anyway, in my example above, I wanted to make things simple by ignoring the basic reinsurance premium. I could have just said the basic reinsurance premium = 0, and that the ceded premium covers the cost of the reinsurance treaty. That seems reasonable in a quota-share treaty because the reinsurance premium wouldn't depend on subsequent losses.
The exam problem was a little different because it was an excess-of-loss treaty versus quota-share. For an excess-of-loss treaty, you definitely have to have a basic reinsurance premium because you don't know how much loss (if any) will be ceded. There might not be any ceded losses for the year, so the insurer would still have to pay a basic reinsurance premium at the start of the year, otherwise the reinsurer wouldn't get paid for assuming the risk unless there were losses!
You're also correct that if EP = 850, both methods would agree. (I still don't think the data would be internally consistent but it probably isn't worth the time to figure all that out.)
Hi Graham,
In your explanation above, you have Net UEP = NWP - NEP
However, in the examiner's report for part (b) of F17Q17, it says that NUEP = NWP - NEP is not a correct formula. If we use this formula in this question, we have:
NWP = 1450
NEP = 650
**NUEP = 1450 - 650 = 800 ** which is different from the answer. Can you please clarify this?
Thank you!
The formula NUEP = NWP - NEP only works for 1 policy at a time. For a single policy, at a particular point in time, the sum of the earned premium and unearned premium must equal NWP. The example that I gave above was just for 1 policy.
This relationship breaks down however for a book of policies where policies all start and end at different times. Earned premium for a book would be evaluated over a period such as a year. In that case, you need the other formula NUEP = NWP - chg(NEP). (This formula also works for a single policy at a given point in time but the concept of earned and unearned is easier to understand with the other formula.)
Hi Graham,
In Fall2017 Q17, the company started operating on Jan 1, 2017, that is, no unearned premium from prior years.
The gross written premium in 2017 was 1550, GEP was 750, GUEP = 700 as at 31 Dec, 2017.
GEP = GWP - Change of UEP = 1550- (700-0) = 850
the GEP given (750) doesn't sound right to me. where did the 100 difference go?
Thank you.
You're correct that something is wrong here. The information provided in this problem is not internally consistent. This problem is solved in the wiki at the link below and there is a comment about this discrepancy.