Accident Year Reserving

[RedCoat]

Hey,

Possibly a stupid question - sorry! The Core Reading says

"Where a reserving exercise is completed on an accident year basis, it will produce an estimate of the earned reserves.
Where a reserving exercise is completed on an underwriting year basis, it will produce an estimate of the earned and unearned reserves combined. A separate exercise is then required to determine the earned reserves."

I'm struggling a little bit with this concept on the AY basis. So I get that if it's 2018 and you're reserving for the 2017 AY then all of those accidents have already occurred, or been earned. But what if it's 2019 Q2 and you're reserving for the 2019 AY? Are you not then making some estimate of unearned reserves, occurring during the rest of the year?

And then I think I get it on UWY basis but please correct if not - it's earned/unearned because if it's 2018 and you're reserving for 2017, there may be policies which incepted at the end of 2017 and are still in force etc so there's some unearned?

 

[Jammy]

Hello RedCoat,

Using the example you used:

AY: If you're reserving in 2019Q2, you cannot possibly reserve for the entire 2019 AY. You may still reserve on an accident year basis, where all years prior to 2019 will be entire accident years, but AY 2019 will implicitly refer only to the portion of AY 2019 that has already been earned as at valuation date.

UWY: Yes I believe your understanding is correct.

 

[Darren Michaels]

Jammy is correct here.

Worth noting that also with underwriting year approach if you carry the exercise out at 2019 Q2 then similarly you will only estimate reserves in respect of policies that have been written up to and including 2019 Q2 - it wont cover the policies written later in 2019.

 

[Delvesy888]

I have also been trying to understand this exact same point by RedCoat, and I'm not sure I'm any wiser..

Using the example provided, reserving in 2019 Q2, and suppose I have an AY triangle, with quarterly development.
The quarterly link ratios inferred from prior years between Development Quarter 1 and Development Quarter 4 will include the fact that business is actively written during all of those quarters and accidents happen throughout all of those quarters.

When using the Chain Ladder on the 2019 AY, I will also be projecting losses for business yet to be written and for accidents yet to have occurred (e.g. policy written in 2019 Q3, with a loss occurring in that quarter, too, if that's what happened in prior years).

I understand that at 2019 Q2 we only can reserve for the earned portion of the 2019 AY, but the methodology will fall over, surely, unless an adjustment is made based on amount of business anticipated to be written, and accidents anticipated to happen, for the rest of the year?

Thanks for any further assistance.

 

[Delvesy888]

Jammy is correct here.

Worth noting that also with underwriting year approach if you carry the exercise out at 2019 Q2 then similarly you will only estimate reserves in respect of policies that have been written up to and including 2019 Q2 - it wont cover the policies written later in 2019.

Hi Darren, this is where I have some confusion. On an underwriting year basis, the quarterly link ratios from prior years will include the fact that business is written throughout the entire year.
Therefore, if I use the Chain Ladder method on the 2019 UWY, surely it will implicitly include reserves for policies yet to be written?

 

[Darren Michaels]

Presumably you are suggesting using underwriting years down the left hand side and development quarters across the top.

If so then you are effectively assuming that the business is written evenly throughout the underwriting year.

By definition the triangle at 2019 Q2 can only include claims that have already arisen on business written to date, and by using the above assumption, we are assuming that the pattern applied is appropriate to develop that business and it should not make any allowance for business written subsequently.

If the assumption is not appropriate, perhaps you should use quarterly / quarterly triangles instead, which is more commonly done in practice and I think should resolve your concerns.

 

[Delvesy888]

Presumably you are suggesting using underwriting years down the left hand side and development quarters across the top.

If so then you are effectively assuming that the business is written evenly throughout the underwriting year.

By definition the triangle at 2019 Q2 can only include claims that have already arisen on business written to date, and by using the above assumption, we are assuming that the pattern applied is appropriate to develop that business and it should not make any allowance for business written subsequently.

If the assumption is not appropriate, perhaps you should use quarterly / quarterly triangles instead, which is more commonly done in practice and I think should resolve your concerns.

Thanks Darren.
Yes, I am assuming that we have a triangle with underwriting years down the LHS and quarterly development periods (very common), and, yes, I am assuming that business is written evenly throughout the year (extremely common).

Of course, the triangle at 2019 Q2 will only include claims from business written to date, but, without adjustment, you will be applying a factor to those 2019 UWY claims (in our example) that includes the fact that business is written throughout the year. That factor will likely be greater than a factor where all the business is written in the first quarter. Hence it must implicitly include reserves for business yet to be written. (Therefore I disagree with the closing statement of your third paragraph.)

Yes, if the valuation date falls on an exact quarter, then having underwriting quarters down the LHS solves this, but I would then argue the case of a valuation date not falling on an exact quarter and hence implicitly allowing for business yet to be written. The answer then being that you need to re-jig the triangle so the LHS aligns with your valuation date (unlikely to happen in practice).

Basically I don't think it can be claimed that projecting on an underwriting year basis will project reserves for business written to date, only, without further expansion.

Do you agree? I'm not sure if I'm missing something fundamental or if I'm just not understanding correctly, but I would appreciate any further clarification.

Kind regards

 

[Darren Michaels]

All prior underwriting years, excluding 2019 will be complete underwriting years, so the link ratios calculated from them will be based on projecting the claims in the first column of the triangle to ultimate, where this includes all claims from business written up to the end of each underwriting year. The figure in the first column in each of those rows represents the claims (paid or incurred) to date from the business written to date in the underwriting year.

All other factors being equal, the first entry in the row for the "2019Q2 underwriting year" will be much lower than it would be for a full underwriting year, so when you apply the development pattern from derived from the complete underwriting years, you will get a much lower answer than you would if this figure represented a full underwriting year, hence implicitly you are only estimating the reserves required for business written up to the end of 2019Q2.

 

[Delvesy888]

Thanks Darren,

That does make sense of course, and I now appreciate the angle you are coming from.
I would, however, be hesitant using a CDF factor inferred from prior "complete" years to a year that is not complete. But I guess this is then your point around changing the triangle if that is of concern.

Thanks a lot for the discussion, much appreciated.