SA3 past exam question October 2007 Q3 parts (i), (ii) & (v)

[entact]

Hi

I've worked through the above question in detail with some assistence from the examiner's report but unfortunately the level of detail given in the examiner's report (in my opinion) is insufficient in the numeric parts to give me an indication of what is required to score high marks. I see how the figures have been calculated but It seems that a summary table was provided and the intermediate calculations were ommitted from the report.

To breakdown my query into smaller parts....

Part (i): the examiner's solutions give no assumptions - if this question came up again and I were to give the solution given in the examiner's report would I score full marks? Or would I need to give assumptions, show more intermediate calculations, give more explanation. I'm also not convinced by the reason to go with the chain ladder figure in 2004- the ULR is 113% by this method which is also out of line with experience to date.

Part (ii)

Even less explanation is given here - just a summary table. What additional information would need to be included here? The table shows 8 figures or the 'a priori' and 'BF ult', where 3 are only required - would any 3 suffice? Same comments as above re detail, assumptions etc.

Part (v)

The first part is given in the table in part (ii) solutions - again, my comments re detail apply.

The solution to part (b) is very difficult to follow - the calculation of the reserve deterioration. I'm not sure where they get the €90m or e justification or some of the assumptions.

Any help would be much appreciated.

 

[Katherine Young]

Part (i): the examiner's solutions give no assumptions - if this question came up again and I were to give the solution given in the examiner's report would I score full marks? Or would I need to give assumptions, show more intermediate calculations, give more explanation.

So long as you get the right answer you will score all the marks available for the calculation. It's always safer to give intermediate calculations thought isn't it, in case you make a mistake along the way.

As a general rule: When in doubt, state assumptions. There could easily be marks available for these in a future question.

I'm also not convinced by the reason to go with the chain ladder figure in 2004- the ULR is 113% by this method which is also out of line with experience to date.

You've been asked to carry out the BF estimates and the chain ladder estimates, so you need to do so. You’ve then been asked to comment on the figures in part (b), so you can easily bring up your ideas here. Indeed, even if the question did not ask you to do this, you should normally comment on the reasonableness of your answers.

Part (ii)

Even less explanation is given here - just a summary table. What additional information would need to be included here? The table shows 8 figures or the 'a priori' and 'BF ult', where 3 are only required - would any 3 suffice? Same comments as above re detail, assumptions etc.

You've been asked to "derive" 3 alternative loss ratios. There are several alternatives before you, and your calculations will be subjective. Therefore you need to explain why your 3 loss ratios are appropriate. If you like, you could calculate several loss ratios and then explain which 3 you have chosen. Or a simple justification of your choices would be fine too.

I make the same comments as above though; it's safer to give assumptions and intermediate calculations so the markers can follow your work.

A good answer might say something like:

"Rate reductions of 10% were observed according to the company pricing database. However, the ex-underwriter feels that a reduction of 1015% is more reasonable. He also tells us that there were some policies with wider coverage and so the effective rate reduction could well have been even greater.

These changes were since 2003, so perhaps 2003 is a better starting point, particularly given that 2004 is showing much worsening experience compared to the original a priori. However, either would be justified, as would any other starting point such as prior years’ chain ladder ultimates.

We can use the a priori for 2003 (ie 92%), adjusted for the factors above, to give three possible alternative a priori loss ratios, using say, the 10%, 15% and 20% rate reductions.

Three possible a priori loss ratios are therefore:

(1) 92/0.9=102.2%

(2) 92/0.85=108.2

(3) 92/0.8=115.0%

We can then substitute these values into the equation we used in part (i) to get three BF ultimate loss ratios:

(1) 34.6%+102.2%x69.6%=105.7%

(2) 34.6%+108.2%x69.6%=109.9%

(3) 34.6%+115.0%x69.6%=114.6%.

Then give a table of results.

Part (v)

The first part is given in the table in part (ii) solutions - again, my comments re detail apply.

You can select any a priori you calculated in part (ii), although given the concerns you will have identified in other parts of the question, you may be tempted to pick the most prudent one.

The calculation is reasonably straightforward, although the question isn’t quite clear about how the BF method is going to be used. The problem is how you interpret the director’s comment:

“…he intends to use the ultimate claims using the budgeted loss ratio in the BF calculation.”

Either this means that he intends to use the 85% loss ratio as the ultimate claims within the BF calculation, OR it means that he intends to use the 85% as the a priori within the BF calculation.

Given this confusion, you should score full marks if you use either interpretation.

The solution to part (b) is very difficult to follow - the calculation of the reserve deterioration. I'm not sure where they get the €90m or e justification or some of the assumptions.

We’ll select the a priori from part (ii) of 115%, which gave a BF ultimate loss ratio of 114.64%. This compares to the 93.7% BF ultimate loss ratio calculated in part (i).

With £20.1m of premium, the increase in reserves will therefore be:

20.1m x (114.64%-93.7%)=4.20m

The alternative approach would be to use the 85% as the ultimate loss ratio, giving the increase in claims as:

20.1m x (114.64%-85%)=5.95m

The total premium income for all years combined is around £90m, so given a previously-estimated ultimate loss ratio of 92%, the ultimate claims will be approximately:

90m x 92% = 83m

You are told that the mean term of paid claims is four years, so of this 83m, let’s assume 25% are paid claims, leaving around 62m in outstanding claims.

The increase in reserves of 4.2m calculated above therefore accounts for around 7% of the total reserves for this portfolio, which sounds material.

However, given that the company is large, this may not be material in the context of all business written by the company, so you would want to check the materiality of the size of this portfolio in relation to the rest of the business.

You would probably also want to check for possible mis-estimation of reserves in other lines of business we write, to make sure the same thing is not happening elsewhere.

 

[entact]

Hi Katherine

Many thanks for taking the time to respond to my query. I really appreciate it and you're comments are very helpful.

Regards

Matthew

 

[Katherine Young]

My pleasure.