303 Apr 99 Q9 (iv)

[entact]

I have worked through this question but I was hoping someone might be able to clarify something for me which I can't figure out.

In the last part of the question (at the beginning of the examiner's comments) the solution says that for Company A, reserves are 15 months claims whereas as company B(restated to A's basis) is 47 months claims. I'm not sure how these are calculated. I would calculate them as follows:

A's reserves (assuming they are referring to claims reserves only): 6000
Annual claims for A: 60%*(8000) = 4800
Ration of reserves to claims: 1.25 or 15 months which matches

B's reserves are 12496 (solution to part ii)
B's annual claims: 88%*3200 = 2816
Ration of reserves to claims: 4.43 or 53.25 months which does not match
Examiner's report has 47 months

Similarly, 'm not sure where they get the figures for the tails for A(9 months in examiner's report) and B(4 years in examines report)

 

[Katherine Young]

Hi Entact.

Q9 of April 99 is a pricing question. Could you look again?

 

[entact]

Hi Katherine, apologies it's sept 99 Q9 (iv)

Hi Entact.

Q9 of April 99 is a pricing question. Could you look again?

 

[entact]

Hi Katherine, apologies it's sept 99 Q9 (iv)

Hi Katherine

Have you had a chance to look at this?

Regards

Matthew

 

[Darren Michaels]

Hi Matthew

The Examiners' Report talks about the ratio of reserves to annual premiums. In the absence of any data on paid or incurred claims per year, they are using this as a very rough measure of the length of the tail.

For B this is 12,496/3,200 = 3.9 years (or 47 months)

This is where the 47 months that they talk about has probably come from.

If you do the same thing for A you get 6,000/8,000 = 0.75 years (or 9 months)

These are then the figures used for the tail in the next paragraph (as 47 months is virtually 4 years).

You have applied the loss ratio to the premiums as well.

In an exam, which ever approach you take would be ok for a question like this as they both demonstrate that B's business is much more longer tailed than A's (4 years versus 1 year).

 

[entact]

Hi Matthew

The Examiners' Report talks about the ratio of reserves to annual premiums. In the absence of any data on paid or incurred claims per year, they are using this as a very rough measure of the length of the tail.

For B this is 12,496/3,200 = 3.9 years (or 47 months)

This is where the 47 months that they talk about has probably come from.

If you do the same thing for A you get 6,000/8,000 = 0.75 years (or 9 months)

These are then the figures used for the tail in the next paragraph (as 47 months is virtually 4 years).

You have applied the loss ratio to the premiums as well.

In an exam, which ever approach you take would be ok for a question like this as they both demonstrate that B's business is much more longer tailed than A's (4 years versus 1 year).

Thanks Darren

That clears up my confusion regarding the length of the tail calculation but I'm still not sure why there is inconsistency regarding the calc of the "reserves as number of months claims" in the first paragraph of part iv) I'm referring to the 15 months vs 47 months.

Later on in he second paragraph they refer to 4 years vs 9 months which you have clarified (with my thanks)

Could you also confirm what the correct formula would be for tail length assuming all info was at hand?

 

[Darren Michaels]

Hi Matthew

I can understand why the inconsistency in the calculations in the first paragraph may appear somewhat confusing. However, the important thing to focus on for the exam is that whichever of the two approaches you use to guesstimate the tail for the two companies you will still reach the same conclusion that B's business is much more longer tailed than A's. I would not get too hung up on which method to use.

To investigate the length of the tail I would ideally use the sorts of ratios described in the "Claim Settlement Pattern" section of Chapter 25 (Interpreting Accounts). Specifically, the ratio of the total outstanding claims reserve to claims paid.