April 2007 Question1 part iv

Hi,

Sorry for the extremely long post (and maybe rant)... but this question has basically driven me up the wall. I've spent the better part of the day trying to understand the assumptions and I've basically given up and am hoping someone better than me can help me here.

The essence of this question is basically around calculating loss ratios for covers that are changing. However, i have queries on some of the assumptions that have been made in the answer script (which does not sit well with me).

The WP and LR data is given for FY 2000 (with the year ending 31st march) through to FY 2007 (which is projected). the question mentions the following:
1. Coverage for the policy changed on 01/10/2003
2. There was an extreme heat wave in 2004 and
3. July 2006 was the hottest month on record

The question is to establish an estimate of the loss ratio.

A fundamental question
The examiner basically converts the losses that have been incurred after the coverage has changed to what would have been under the same cover.

A fundamental question I have here is why are we doing this? Would it not be easier to change the years prior to 2003 (and more sensible)? The insurer here has changed the coverage and is now operating under new policy terms and conditions... so shouldn't any comparison be on the new coverage terms and not the old coverage terms?

Usage of 87.5% for claims impact
The examiner assumes that the change in cover kicked in halfway through 2003 (no questions here).

But then, the examiner goes on to assume that the impact of claims for 2003/04 for the new cover was only 12.5%. How was this 12.5% figure arrived at? I cannot figure this out for the life of me honestly.

Assumption on influx of claims
The examiner has given "However, changes in cover on foundations brought in before the likely influx in claims due to adverse weather conditions, so potential impact of hot summer should be mitigated on a greater percentage of incurred claims. Say 15% (though anything up to, say, 25% may also be considered reasonable)."

My question here is how was this assumption arrived at? also if possible... why was this assumption arrived at because the question does not have this information

2005 claims

The examiner report then says "Likewise, some claims in 2005 will have originated from the original policy wording. So the impact may be assumed to affect 87.5% of claims."

But how is this possible? If we assume that the company stopped selling policies with old wordings on 30/09/2003, then the last policy (assuming annual policies) will expire on 29/09/2004. So any claims for subsidence (for which I am assuming reporting delays would be negligible) would be from the new policy wordings... in this case, how is it accurate to make such an assumption?


Final figures

So I had made some of the assumptions here (but not all of the assumptions) and had arrived at a LR of 120%. In a realistic exam setting, would that be accepted? (the answer has 112%).

I know this question is a little ambigious... what I meant here was will i get the majority of the marks as long as my assumptions make sense?

 

Hi

1. The question discusses the claims inflation of 10% with no change in cover. I assume that the assumption here is 10% if the old terms remain the same therefore you need to have your claims in old cover terms to apply the claims inflation.

2. There are other ways to explain how they got it but the best way I know is the parallelogram rule. If you represent the policies on an x-y plane. The x plane is the calendar time and the y is the policy term. for the 2003-4 year this represents a 1 x 1 (this represents all policies) square based on the assumptions. A policy starting at the midpoint will have a term of half a year in the 2003-4 year. All policies after that are therefore in the area in the bottom 0.5 x 0.5 triangle. The area of the triangle is 0.5*0.5*0.5 =0.125. Expressed as a percentage of the whole 1 x 1 area it's 12.5%.

3. Based on the above you would expect 112.5% of the claims to be based on the new terms for 2004 however because of how the date fo the event is defined it is likely to affect claims before 1 October meaning we need an assumption higher than 12.5% but not higher than 25%.

4. Using the same logic as point 2 above the top 12.5% of the 2005 year will be on old terms and therefore 87.5% will be on the new terms. However because the of the definition of the claim event likely more claims will be affected by the new terms so they moved to 95% of claims on new terms.

5. A tutor can give better advice on the issue of how they handle these issues but all I can say is a large amount of this is about the justification. In some instances, there are obvious oversights, in others you may have taken an alternative view.

 

Hi @Busy_Bee4422 ,

Thanks for the clarity on point 1. But shouldn't the answer then convert the final numbers to the new cover? I agree with your points entirely on claims inflation... but I somehow feel that showing the claim numbers in the old wordings is still somewhat an incorrect way to go about things... given that this is an SA paper... If I were an actuary who asked my subordinate to do this analysis, I would expect the analysis to be in the new wordings and not the claims in the old wordings... is this line of thinking off?

w.r.t point 2, this was my logic - And I think your explanation now matches up with my logic:

let us assume that we split 2003 into two halves (first half for policies issued with the old wordings and second half with the policy issued with the new wordings. So in this case, policies with the old wordings would have an average starting point of 01/07/2003 while policies with the new wordings will have an average starting of 01/12/2003

So in the year 2003, policies with the old wordings would have constituted 75% of the earned premium and policies with new wordings would have constituted 25% of the earned premiums.

In 2004, this would be flipped (i.e., 25% of the earned premiums come from old wordings while 75% of the earned premium cokmes from new wordings).

In 2005, the policies with the old wordings would have been completely earned and thus would contribute to 0% of the earnings.

If we assume that policies on average have a 3 month delay in claims reporting, then I suppose this means that 12.5% of the claims would constitute the claims from the new wordings... and this 12.5% would then seep into the 2005 year... is my thinking here correct?


>4. However because the of the definition of the claim event likely more claims will be affected by the new terms so they moved to 95% of claims on new terms.

But how can we make this assumption because the question does not give this data right? In fact, isn't it the opposite of what the question says (which effectively says the new terms reduce the incurred amounts)? Shouldnt more claims come from the old terms and not the new terms? So in my thinking, there should be a greater amount of claims in 2005 due to the contribution of the old claims... At this point I start going into a loop...get a nose bleed... and give up