303 April 1999 Q11 part (ii) We are given as the starting point an accident year loss ratio for accident year 1997, lots of other info, and asked to calculate the ULR on business written in July 99 (an underwriting year loss ratio) i would have thought the period for claims inflation would be from Jan 1997 to mid july 1999, based on the usual assumptions and converting everything to an inception rather than occurence basis. However, the solution starts in January 1998 and inflates to June of 1999 i have understood the rest of the question, but am gettng a different answer to the solutions because of this issue with the start and end points for claims inflation. The logic is sound, but it looks like the solutions are starting one year later and stopping one month earlier am i missing something here? or just being thick two weeks before the exam?
The solution isn't right. Not only does the month of writing not match up (in the question they say July, in the solution they say June), but also they've lost a year (in the question they say AY 97, in the solution they seem to have worked with AY 98). I find it easier to work on claims rather than policy inception - that way, you're inflating from claim payment date to claim payment date, and so will pick up the right inflation rates if they change (which they don't here). So the way I would do it is to assume that the average date of a claim in 1997 is mid-1997 (because it's accident year 97) and the average date of a claim of a policy written in July 1999 is 15/1/00. Therefore project for 30½ months. Same answer as you of course, but you've worked from inception to inception, which is also valid. We cover a simplified version of this question in the ST7 tutorials. Bear in mind that 1999 was a 'bad' year for Subject 303 - some very awkward questions. Hope this helps.
Ian - thank you for the speedy response - I understand it a lot better now - really appreciated. I'm relieved that its an error in the question - and am hopeful that this sort of paper isnt what I'm up against in two weeks time. One further question/observation though, You mentioned that you would have gone from paid to paid in this question. The reason I went from inception to inception is because the question asked for a loss ratio for business written in a month. But the starting point is a past accident year loss ratio. So in my mind, thats being asked to turn an accident year loss ratio into an underwriting year one, then update it with claims inflation and rate changes to the new rating period. I thought the conversion is crudely done by assuming AY 1997 claims happening in mid 1997 on average, and in turn arising from policies incepting on 1 jan 19997 on average. So you are saying this method would be OK, but i would get caught out if claims inflation had changed post June 1999? Is this what you meant? the only issue then is, if the premium rates had changed between inception and the average date of claim (in 1997), if you had gone from paid to paid, would this not have distorted your answer as well? I can imagine a situation where there was a premium index in the question - you might have to look at separate periods for the claims inflation and premium rate change parts of the loss ratio adjustment. This would be (average) inception to inception for the premium, and paid to paid for the claims inflation. The periods may be the same in terms of length, but the relative changes may be quite different depending. Any thoughts on this or general rules of thumb that may clear this up for me?
You're absolutely right - claims inflation rate changes messes up claims calcs whereas rate changes mess up premium calcs (both of which affect loss ratios of course). So you'd end up having to adjust any method used... I think it would be easy to waste an awful lot of time choosing a 'right' method. The examiners will be looking for any 'suitable justified approach', so as long as you make reasonable assumptions to allow for both inflation and rate changes, state them and run with them, they'd normally give you the marks. If you have a look at more recent questions covering this (eg ST3 April 2006 Q4) you'll see that they've been a lot more manageable, and not that complicated. Ian
