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September 2015 Q7 (iv)

T

TurnipKing

Member
Hi,

First let me apologize as I'm aware this has been asked before but the provided answers are not making sense to me. In the titled question I don't understand why we go through all the trouble of deriving % reported figures for each development month just to apply them to an ultimate loss figure that was gained through applying (earned premium)*(expected loss ratio) for each month. Could we not have just subtracted the incurred figure of 10m from 0.9*(earned premium for year) and arrived at a very similar answer that is equally if not more valid since the answer in the exam solution (and by extension ASSET pack) require additional assumptions on the loss ratio applying to each month of earnings as opposed to overall.

Thanks
 
Your answer would be similar yes, but different because the earning patterns and the claims reporting patterns are different. You have effectively assumed that they are the same, which the detailed workings set out in the Examiners Report and the ASET show is not the case.

You are unlikely to have obtained full credit for this in the exam as you have not used all of the information provided to you in the question (ie the incurred claims data broken down by monthly reporting delay) which along with the fact that the question was worth 8 marks should have been a clue that a more complicated approach was required.
 
Darren Michaels said:
Your answer would be similar yes, but different because the earning patterns and the claims reporting patterns are different. You have effectively assumed that they are the same, which the detailed workings set out in the Examiners Report and the ASET show is not the case.
Click to expand...

Thank you very much for your response. The above is what I don't feel like I'm understanding, can you give more detail on how am I assuming the same pattern? Am I not just ignoring claims patterns altogether as opposed to making assumptions on it? I just cannot get my head around it.

For instance in the ASET pack for delay month 1 it calculates an ultimate of 2.25m, which is below the incurred figure given in the question of 3.5m. Does this not contradict the information in the question?
 
The two tables you are referring to are looking at slightly different things and hence they do not necessarily contradict each other.

The one in the question shows the claims incurred by reporting delay. Hence it is saying that £3.5m has been incurred from claims that were reported within 1 month of the event happening, so this could be from events happening in January that were reported by February, events happening in February that were reported by March and so on.

The table on page 36 of the ASET shows the earned (and then ultimate) premiums by delay month as at 31 December 2014. So there is £2.5m of premium that has been earned in the last month (ie December 2014) made up of £0.21m written in each month from January to December, £2.29m of earned premium from November (so is at 2 months delay by the year end) made up of £0.21m written in each month from January to November, and so on. This comes from the triangle on page 33 of the ASET.

Thus you cannot readily compare the tables in the way that you have above.

Because you are doing everything in aggregate in your approach you are ignoring any differences between the claims reporting pattern and the premiums earnings pattern. The claims reporting pattern is derived in the table on page 35 of the ASET. You can work out the premium earning pattern by extending the triangle on page 33 of the ASET for the full 2 years.
 
Can someone explain how the "unreported amount" came about in the examiner's report under basic method? I'm still confused how the IBNR was derived in the end.
 
Thanks!
The table in the question - incurred amounts: do they refer to reported amounts?

When we use incurred claims in reserving, similarly does it refer to reported claims?
 
Yes in the question incurred claims means reported claims.

The Glossary has 2 definitions for incurred claims. The first one is akin to reported claims and is the definition typically used in a reserving context. The second definition is akin to ultimate claims and therefore includes IBNER/IBNR and is more commonly used in annual accounting.
 
Thanks!
I am curious about one thing - do reserves for unexpired risks only apply to underwriting year?
 
When you project a triangle using an accident year cohort, you need to estimate a separate reserve for unexpired risks. However, when you project a triangle using an underwriting year cohort the estimate obtained will include an allowance for unexpired risks.
 
I am not entirely sure what you have done, but you need to do the following to get the number the examiners have come up with:

1. Apply the loss ratio to the earned premiums by delay months (not written premiums which it looks like you have used)
2. Adjust the reporting pattern to allow for the fact that the exposure is not uniform by each month of delay as the insurer only started writing the business at the start of 2014.

You can find a detailed solution / explanation in the ASET.
 
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