Sept 2013 q10

[r_v.s]

Why should we use the acpc? Is there a difference in trying to project expected number of claims and expected claims cost separately and projecting the acpc?

Specifically, I am unable to find out te mistake I'm making in using
Exposure * avg freq/ exposure * avg cost / exposure??

The answer is way off the mark

Would you pls explain the meaning of gross and net in part (ii)??
((

 

[Darren Michaels]

You are trying to estimate the (total claims cost / exposure).

This can be split into (no of claims / exposure) * (total claims cost / no of claims).

The first term is the frequency and the second the severity (acpc).

You need to consider them separately here because the question gives you information about the effect of changes made in years 4 and later on each part.

I can't quite tell what you have done so it is hard for me to comment on your mistake.

You need to allow for the different exposures in each year which projecting claim numbers and claim amounts separately does not do.


Gross/Net in part (ii) refers to commission.

 

[r_v.s]

I guess its because I divided by exposure twice!
Thanks for all your responses!

 

[Qayanaat]

Hi,

Why are we apply inflation to ACPC instead of inflating the total cost first, before calculating the ACPC?

Would alternative approaches have been awarded marks in the exam?

My approach was:
1. Apply claims inflation to the total claims amount.
2. Calculate claims frequency per vehicle year for each policy year ( #claims / vehicle years)
3. Calculate on-level claims frequency per vehicle year (i.e. by adjusting for the 5% reduction)
4. Calculate ACPC = Inflated total claims amount / #claims
5. RP per vehicle year = Freq * Severity
6. RP for year 6 = RP per vehicle year * year 6 exposure

For my step 5, I got RP per vehicle year = 196.81
For my step 6. I got the RP for year 6 = 600,271 (not too far off from solution 584,540, but unsure if I would have gotten marks for my method)

Thank you.

 

[Darren Michaels]

It shouldn't make any difference here whether you divide by the number of claims or multiply by the inflation adjustment first due to the order of operations (ie (a/b)*c is the same as (a*c)/b), so long as you multiply and divide by the correct numbers of course!

There is presumably another reason as to why you have come up with a different answer.

However, even if you do make an error on one stage of the calculation, then follow through marks are normally given if you complete the rest of the calculation correctly. You are only penalised once for an error in a calculation.

Be careful describing the adjustment in 3 as "on-levelling" as that normally refers to adjusting historical premiums for premium rate changes.

 

[Qayanaat]

Hi Darren,

Yes my bad, my ACPC and the solution's adjusted ACPC are the same.

Would different approaches to selecting next year's value get full marks? As far as I can see, there's so many different ways of selecting next year's estimate. Would any of the following methods be considered unreasonable and not given marks?

• Solution's approach

RP per vehicle year = ( RP per vehicle year * vehicle years ) / sum of all vehicle years

• Method 2

RP per vehicle year = Straight average of (RP per vehicle year)

• Method 3

Get a straight average of (Claim frequency per vehicle year, adjusted for economic effect)
Get a straight average of (ACPC, adjusted for inflation)
RP per vehicle year = Multiply the two

• Method 4

Subjective selections, e.g. take only year's 5 RP and provide some justifications (e.g. year's 5 RP good bit higher than the older year's, may be more representative for year 6) or take an average of last 3 years RP and provide some justifications (e.g. more recent years = more representative)

Thank you.

 

[Darren Michaels]

Any reasonable alternative approach provided that they are well explained and justified based on the data provided in the question should receive appropriate credit.

However, be careful to look out for any obvious trends or anomalies in the data provided and if there are any make sure your selected approach appropriately allows for these, otherwise you are likely to lose marks.

Given there weren't any clear trends in this question, your suggested approaches should have all been plausible as long as you justified them appropriately. Where there are no clear trends or outliers it is most common to use a weighted average as has been done in the Examiners' Report.

 

[Qayanaat]

Okay that's very clear thank you very much Darren.