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  #1  
Old 06-27-2020, 09:21 PM
mischiefmanaged28 mischiefmanaged28 is offline
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Default Calendar Year vs Accident Year vs Policy Year

So I've been given explanations about the three different types of calendar year aggregation by different people. I've also read the definitions from exam 5 werner modlin manual but I'm still really confused about the differences between the three...

Could someone provide me a general explanation of the way the three are different?

From what I understand, it looks like calendar year and accident year treat premium similarly, but the losses differently (how though?).

And I'm guessing for the policy year; we're going to look at policies that were written in that specific year and the premiums that were received and if losses that were paid.
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Old 06-28-2020, 12:21 AM
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when we say premium is on a calendar year basis, it means policy year. Premium is always collected upfront, so this is easy to do.

Losses are different. Losses are unknown, that's why we use triangles. The question is then how long you want to wait to be able to fill this triangle out?

A claim emergence process for the company, if it happens, goes like this
policy written => accident happens => accident reported

if your losses are on a policy year basis, you're going to have to wait a long time, because you have to wait for accidents to happen, and then wait for them to be reported.

if your losses are on an accident year basis, you just need to wait for claims to be reported, but not when they happen. In doing so, the claims that you assign to the specific accident year don't line up perfectly with the premium written in that policy year.

if your losses are on a policy year basis, you don't need to wait for anything. There's no IBNR, because the claims in each report year are already reported, by definition. But boy, these reported years REALLY don't line up with your premium written years.
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Old 06-28-2020, 01:01 AM
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I'm writing from a North American background; I wouldn't expect what follows to vary internationally, but...that's not something I've looked at before.

So, you asked about three kinds of years:

Policy Year = Premiums and Losses are segmented based upon the year in which the associated policies were written

Calendar Year = Premiums and Losses are segmented based upon the year in which the transaction occurred.

Accident Year = Losses are segmented based upon the year in which the claim occurred. In this simple example, accident year premiums = calendar year premiums.

Be aware that that's a simplification. There are a few other kinds of years out there, that you'll run into if you get into certain types of work (reinsurance, claims-made business, etc.)...but for this explanation, let's ignore them.


So...let's say that we have a one-year policy that has an effective date of 2 July 2020, and its premium is $2000, collected on the effective date. During the life of this policy, there are two claims:
  • The first claim occurs on 1 September 2020:
    • $400 is reported and paid on 1 October 2020
    • Another $600 is reported and paid on 1 February 2021
  • The second claim occurs on 1 March 2021. $750 is reported and paid on 1 March 2021

So, when we look back at this policy at year-end 2021, we will see the following:

(AY="accident year", CY="calendar year", PY="policy year")

Premium written
PY2020 =$2000 / PY2021 = $0
CY2020 =$2000 / CY2021 = $0
AY2020 =$2000 / CY2021 = $0
...because the premium was written in 2020. There are situations where PY written premium can vary from CY/AY, but they're beyond the scope of this write-up.

Premium earned
PY2020 =$2000 / PY2021 = $0
CY2020 =$1000 / CY2021 = $1000
AY2020 = $1000 / AY2021 = $1000
...the policy was written half-way through 2020; assuming exposure is earned evenly through the year, half the exposure occurs in AY/CY20 and half the exposure occurs in AY/CY21. but since the policy effective date was in 2020, the premium is simply associated with PY2020.

Reported loss and paid loss
PY2020 = $1750 / PY2021 = $0
...because all of the losses ($400+$600+$750) are associated with a policy with an effective date in 2020.

AY2020 = $1000 / AY2021 = $750
...because the first loss ($400+600) occurred in 2020, and and the second loss ($750) occurred in 2021.

CY2020 = $400 / CY2021 = $1350
...because the first report/payment ($400) was made in 2020, and the 2nd and 3rd reports/payments ($600+$750) were made in 2021.


Now, as to why we keep track of all these different kinds of years (and again, this is simplified):

For pricing analyses, we traditionally/mostly prefer to use accident years. On an accident year basis, the losses are associated with the earned premiums associated with the exposures from whence those losses come, and with a bit of math, we can say things like "if we do nothing, our loss ratio next year will probably be x%, but we need y% to make our required profit, so we need to increase/decrease rates by z% to hit that target".

For reserving analyses, we traditionally use triangles where the vertical axis is accident year, and the horizontal axis is (calendar year-accident year). When loss data is displayed in this way, we can observe how quickly/slowly losses take to emerge, and set aside money for those losses that we think will eventually show up, but haven't yet been reported or paid.

For certain kinds of analysis (both reserving and pricing) it can be useful to group data on a policy year basis, rather than an accident year basis. If the law has changed on the what kinds of benefits must be provided under a workers comp policy, or if there was a major change in our contracts that impact premiums or losses, it might be easier to account for such in our analyses if we can separate (policies written before the change) from (policies written after the change).

And then, if you are working on financial reporting or things related to financial reporting, much of your work is done on a calendar year basis...because that's mostly how data is reported to the outside world (investors, regulators).

Last edited by Maphisto's Sidekick; 06-28-2020 at 01:05 AM..
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  #4  
Old 06-28-2020, 08:37 AM
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Quote:
Originally Posted by Maphisto's Sidekick View Post
I'm writing from a North American background; I wouldn't expect what follows to vary internationally, but...that's not something I've looked at before.

So, you asked about three kinds of years:

Policy Year = Premiums and Losses are segmented based upon the year in which the associated policies were written

Calendar Year = Premiums and Losses are segmented based upon the year in which the transaction occurred.

Accident Year = Losses are segmented based upon the year in which the claim occurred. In this simple example, accident year premiums = calendar year premiums.

Be aware that that's a simplification. There are a few other kinds of years out there, that you'll run into if you get into certain types of work (reinsurance, claims-made business, etc.)...but for this explanation, let's ignore them.


So...let's say that we have a one-year policy that has an effective date of 2 July 2020, and its premium is $2000, collected on the effective date. During the life of this policy, there are two claims:
  • The first claim occurs on 1 September 2020:
    • $400 is reported and paid on 1 October 2020
    • Another $600 is reported and paid on 1 February 2021
  • The second claim occurs on 1 March 2021. $750 is reported and paid on 1 March 2021

So, when we look back at this policy at year-end 2021, we will see the following:

(AY="accident year", CY="calendar year", PY="policy year")

Premium written
PY2020 =$2000 / PY2021 = $0
CY2020 =$2000 / CY2021 = $0
AY2020 =$2000 / CY2021 = $0
...because the premium was written in 2020. There are situations where PY written premium can vary from CY/AY, but they're beyond the scope of this write-up.

Premium earned
PY2020 =$2000 / PY2021 = $0
CY2020 =$1000 / CY2021 = $1000
AY2020 = $1000 / AY2021 = $1000
...the policy was written half-way through 2020; assuming exposure is earned evenly through the year, half the exposure occurs in AY/CY20 and half the exposure occurs in AY/CY21. but since the policy effective date was in 2020, the premium is simply associated with PY2020.

Reported loss and paid loss
PY2020 = $1750 / PY2021 = $0
...because all of the losses ($400+$600+$750) are associated with a policy with an effective date in 2020.

AY2020 = $1000 / AY2021 = $750
...because the first loss ($400+600) occurred in 2020, and and the second loss ($750) occurred in 2021.

CY2020 = $400 / CY2021 = $1350
...because the first report/payment ($400) was made in 2020, and the 2nd and 3rd reports/payments ($600+$750) were made in 2021.


Now, as to why we keep track of all these different kinds of years (and again, this is simplified):

For pricing analyses, we traditionally/mostly prefer to use accident years. On an accident year basis, the losses are associated with the earned premiums associated with the exposures from whence those losses come, and with a bit of math, we can say things like "if we do nothing, our loss ratio next year will probably be x%, but we need y% to make our required profit, so we need to increase/decrease rates by z% to hit that target".

For reserving analyses, we traditionally use triangles where the vertical axis is accident year, and the horizontal axis is (calendar year-accident year). When loss data is displayed in this way, we can observe how quickly/slowly losses take to emerge, and set aside money for those losses that we think will eventually show up, but haven't yet been reported or paid.

For certain kinds of analysis (both reserving and pricing) it can be useful to group data on a policy year basis, rather than an accident year basis. If the law has changed on the what kinds of benefits must be provided under a workers comp policy, or if there was a major change in our contracts that impact premiums or losses, it might be easier to account for such in our analyses if we can separate (policies written before the change) from (policies written after the change).

And then, if you are working on financial reporting or things related to financial reporting, much of your work is done on a calendar year basis...because that's mostly how data is reported to the outside world (investors, regulators).


I would add that there are additional complicating aspects on CY vs AY losses when you start including case and bulk reserves into your analysis.

The concepts presented hold up, with the underlying principle being:
CY: year accounting transaction took place
AY: year when the accident (exposure to Ioss) took place
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  #5  
Old 06-28-2020, 09:52 AM
mischiefmanaged28 mischiefmanaged28 is offline
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Quote:
Originally Posted by Maphisto's Sidekick View Post
I'm writing from a North American background; I wouldn't expect what follows to vary internationally, but...that's not something I've looked at before.

So, you asked about three kinds of years:

Policy Year = Premiums and Losses are segmented based upon the year in which the associated policies were written

Calendar Year = Premiums and Losses are segmented based upon the year in which the transaction occurred.

Accident Year = Losses are segmented based upon the year in which the claim occurred. In this simple example, accident year premiums = calendar year premiums.

Be aware that that's a simplification. There are a few other kinds of years out there, that you'll run into if you get into certain types of work (reinsurance, claims-made business, etc.)...but for this explanation, let's ignore them.


So...let's say that we have a one-year policy that has an effective date of 2 July 2020, and its premium is $2000, collected on the effective date. During the life of this policy, there are two claims:
  • The first claim occurs on 1 September 2020:
    • $400 is reported and paid on 1 October 2020
    • Another $600 is reported and paid on 1 February 2021
  • The second claim occurs on 1 March 2021. $750 is reported and paid on 1 March 2021

So, when we look back at this policy at year-end 2021, we will see the following:

(AY="accident year", CY="calendar year", PY="policy year")

Premium written
PY2020 =$2000 / PY2021 = $0
CY2020 =$2000 / CY2021 = $0
AY2020 =$2000 / CY2021 = $0
...because the premium was written in 2020. There are situations where PY written premium can vary from CY/AY, but they're beyond the scope of this write-up.

Premium earned
PY2020 =$2000 / PY2021 = $0
CY2020 =$1000 / CY2021 = $1000
AY2020 = $1000 / AY2021 = $1000
...the policy was written half-way through 2020; assuming exposure is earned evenly through the year, half the exposure occurs in AY/CY20 and half the exposure occurs in AY/CY21. but since the policy effective date was in 2020, the premium is simply associated with PY2020.

Reported loss and paid loss
PY2020 = $1750 / PY2021 = $0
...because all of the losses ($400+$600+$750) are associated with a policy with an effective date in 2020.

AY2020 = $1000 / AY2021 = $750
...because the first loss ($400+600) occurred in 2020, and and the second loss ($750) occurred in 2021.

CY2020 = $400 / CY2021 = $1350
...because the first report/payment ($400) was made in 2020, and the 2nd and 3rd reports/payments ($600+$750) were made in 2021.


Now, as to why we keep track of all these different kinds of years (and again, this is simplified):

For pricing analyses, we traditionally/mostly prefer to use accident years. On an accident year basis, the losses are associated with the earned premiums associated with the exposures from whence those losses come, and with a bit of math, we can say things like "if we do nothing, our loss ratio next year will probably be x%, but we need y% to make our required profit, so we need to increase/decrease rates by z% to hit that target".

For reserving analyses, we traditionally use triangles where the vertical axis is accident year, and the horizontal axis is (calendar year-accident year). When loss data is displayed in this way, we can observe how quickly/slowly losses take to emerge, and set aside money for those losses that we think will eventually show up, but haven't yet been reported or paid.

For certain kinds of analysis (both reserving and pricing) it can be useful to group data on a policy year basis, rather than an accident year basis. If the law has changed on the what kinds of benefits must be provided under a workers comp policy, or if there was a major change in our contracts that impact premiums or losses, it might be easier to account for such in our analyses if we can separate (policies written before the change) from (policies written after the change).

And then, if you are working on financial reporting or things related to financial reporting, much of your work is done on a calendar year basis...because that's mostly how data is reported to the outside world (investors, regulators).
Thank you so much, this was so incredibly helpful!!! I totally understand it now. I really appreciate the explanation since I just started a role in pricing and I see these terms all the time.
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Old 07-03-2020, 12:46 AM
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Quote:
Originally Posted by John S. Mill View Post

Premium is always collected upfront, so this is easy to do.
Even this is a bit of a simplification.

For most policies, premium is more or less set/known upfront, but it may be paid over time. If you have a mortgage, your HO insurance will be paid upfront. But many people pay monthly on their auto insurance. Even then, it's timing of the payment, but the amount is relatively certain at inception (barring a new vehicle, new driver, etc.). Many companies treat premium as written when it's billed, so if you have installments, your premium is not all written upfront. Also, sometimes premium is paid in installments, but via a premium finance company, which is a different legal entity from the insurance company. I don't have a lot of experience with those, so I can't get into much detail, but the short version is that the premium finance company pays the premium up front, and the insured pays the PF company, so from the point of view of the insurance company, the premium is collected up front.

But Work Comp is a different beast. Written premium continues to change throughout the life of the policy, and even after until the final audit is done. So, we (a WC carrier) also monitor something called EAP -- Estimated Annual Premium. This is the amount we expect to collect on a policy, based on what we think we know about the subject payroll. But it can vary DRAMATICALLY, with COVID being an extreme example. On average, we take in an additional $10M per year of audit premiums, which is about 4-5% of our annual premium.

So, premium can be almost as complicated as losses when comparing AY, PY and CY.
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Old 07-04-2020, 02:19 PM
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If you're a reinsurer, you might also wonder about underwriting year. Depending on the underlying and if the basis is risks attaching or losses occurring, losses and premiums can be a real challenge to estimate.
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Old 07-05-2020, 12:42 AM
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Maphisto's Sidekick Maphisto's Sidekick is offline
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Of course, by the time an actuarial student needs to know about installment premiums that vary by exposure, or reinsurers' underwriting years, or extended reporting period coverage, or policies that are fully earned upon exhaustion of limits, or the treatment of claims-made losses...you probably already have the basic concepts of accident/calendar/policy years sufficiently understood.

So, for this kind of question, it's probably best to oversimplify the general explanation.
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Old 07-06-2020, 10:53 AM
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Quote:
Originally Posted by Maphisto's Sidekick View Post

Of course, by the time an actuarial student needs to know about installment premiums that vary by exposure, or reinsurers' underwriting years, or extended reporting period coverage, or policies that are fully earned upon exhaustion of limits, or the treatment of claims-made losses...you probably already have the basic concepts of accident/calendar/policy years sufficiently understood.

So, for this kind of question, it's probably best to oversimplify the general explanation.
Yeah, my concern was the blanket statement that all premium is always paid upfront. I don't think the OP needs to know all of the exceptions now, but they should know that there are exceptions that they will likely learn about later.
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