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ST7 - April 2013, Q.5 (ii)

J

Jhanani

Member
Hi Friends!

I have a doubt in ST7 - April 2013, Q.5 (ii)
It deals with discounting of reserves.
I could get to the point of finding the % of outstanding reserves from the PAid link ratios.
I could not understand how the discounted reserves are calculated from the % of outstanding reserves.
Would be great if any of you can help!

Thanks in Advance,
Best Regards
Jhanani.M
 
Its probably easier to just look at the incremental % developed row, which basically tells you how the reserve will be paid out over time.

So for example, 2009 is at development year 4 at 31/12/2012. So its 38.9% developed. The remaining 61.1% will be paid out in the proportions 32.1% in the next year (ie 2013), 20.3% in 2014 and 8.7% in 2015. Assuming that the payments are made evenly over each year (and therefore on average happen in the middle of each year), we can then multiply the undiscounted reserve for 2009 by these percentages and apply the appropriate discount factor. You then need to divide by the sum of the proportions (61.1%) as the weights don't add up to 100%.
 
Thanks a tonne for the explanation!I could clearly understand the logic.
I got another doubt (quite difficult to put it in words!) : we start with 0-1 , 1-2, 2-3 etc for the link ratios. So for UW 2009, at the end of 2012, it would be till stage 2-3. So should we not consider the cumulative % of paid development as 13.8% & the OS as 86.2% instead to 61.1%? Ideally for 2009, 3-4 paid development would never have actually happened as at 31 Dec 2012.
Sorry if I'm confusing. Request you to please help me with this doubt.

Thanks!
Jhanani
 
It just depends on whether you start counting from 1 as effectively I have done or 0 as you have done. It boils down to a labelling difference. Either way around the 2009 year will be 38.9% developed as at 31/12/2012.

The successive development percentages derived from the link ratios in the question are:

1.3% 6.4% 13.8% 38.9% 71.1% 91.3% 100.0%

so the 2012 year is 1.3% developed as at 31/12/2012, the 2011 year 6.4% and so on.
 
Hi, what's the rationale for knowing to use the paid link ratios in calculating reserves here, as opposed to the incurred link ratios provided?

Is it that the claims experience has been volatile over time (adverse experience in 2010 & 2011), so we use Paid for a more stable projection?
 
In this question we are given the undiscounted reserves, so we aren't necessarily using the paid link ratios to calculate the reserves. We don't actually know how the undiscounted reserves have been calculated.

We are asked to discount the undiscounted reserves that we have been given.

Discounting is all about the time between when the reserves are held and when they will be paid out, so we need to use the paid link ratios for this purpose.
 
Hello,

I also have a question on this: I can't seem to work out how 1.3% has been derived. I understand the subsequent % developed, but I don't see where 1.3% comes from.
 
This is the percentage developed using the paid chain ladder method at development year 1.

It is calculated in the normal way by taking the reciprocal of the corresponding cumulative development factor, ie (5*2.165*2.825*...)^-1
 
Darren Michaels said:
It just depends on whether you start counting from 1 as effectively I have done or 0 as you have done. It boils down to a labelling difference. Either way around the 2009 year will be 38.9% developed as at 31/12/2012.

The successive development percentages derived from the link ratios in the question are:

1.3% 6.4% 13.8% 38.9% 71.1% 91.3% 100.0%

so the 2012 year is 1.3% developed as at 31/12/2012, the 2011 year 6.4% and so on.
Click to expand...

The above implies that the information given in the Qn (and soln) starts counting from 1. eg: 2012 is 0-1 dvpt year for UWY 2012.
This helps me understand the rows relating to cum and incremental % developed.

However, I am then confused how the development factor of 5.000 is calculated for 0-1 ?
Because I would assume you can only calculate link ratios from 1-2 onwards in the labelling convention described above.

Thanks!
 
In the question and solution in the Examiners' Report they actually start from development period 0. Hence at the end of 2009 the 2009 underwriting year is at development period 0 and so on.

So per my post above at the end of each successive year, the 2009 underwriting year is 1.3% 6.4% 13.8% 38.9% 71.1% 91.3% 100.0% developed respectively and so on for each other underwriting year.
 
Darren Michaels said:
In the question and solution in the Examiners' Report they actually start from development period 0. Hence at the end of 2009 the 2009 underwriting year is at development period 0 and so on.

So per my post above at the end of each successive year, the 2009 underwriting year is 1.3% 6.4% 13.8% 38.9% 71.1% 91.3% 100.0% developed respectively and so on for each other underwriting year.
Click to expand...

Thanks for responding, Darren.

The solution states that the 'Cumulative % developed' is 38.9% below dvpt period 3-4.
If 2009 is 38.9% developed at end of 2012, this means that the row 'Cumulative % developed' should be interpreted as to 'Cum % developed at beginning of the dvpt period' (Here, at beginning of period 3-4, which is 31/12/2012 for the 2009 UWY).

If this is true, I'm confused how 25.2% is the 'incremental % developed' mentioned below period 3-4? It corresponds to the increment in dvpt period 2-3 (Here, the period from 01/01/2012 to 31/12/2012 for the 2009 UWY.)

Am I missing something?
 
Again, it's really just naming convention. Incremental % developed is just the increase over the previous % developed. So for the first 'period' it's 1.3%. For the second 'period' it's the difference between 6.4 and 1.3, ie 5.1%. Etc. Don't get too hung up over what you're calling these things, it's more important that you just use them correctly to get reserves (or whatever else you're using them for).
 
Hi,
Can someone please explain calculation behind Sp7 April 2013 Question 5(ii).
I’m unable to understand how cumulative % developed is calculated.

Thank you!
 
Hi Rishita

As mentioned by Ian and Darren above, it is just a naming convention thing. If you do the calculations from first principles, you will still get to the reserves. So, the way I'd do it:
  • Derive the CDF from the individual DF
  • Calculate the % developed and the % incremental to get to the payment pattern.
Let's calculate for DY 0 - 1 and 1 - 2 for example:
DY 0 - 1
IDF: 5.000
CDF: 5.000 * 2.165 * 2.825 * 1.825 * 1.285 * 1.095 * 1.000 = 78.528
% Developed: 1/78.528 = 1.27%

DY 01- 2
IDF: 2.165
CDF: 2.165 * 2.825 * 1.825 * 1.285 * 1.095 * 1.000 = 15.706
% Developed: 1/15.706 = 6.37%

You can use the analogy of the above to calculate the rest of the numbers. Don't get bogged down with the examiners' report, as long as fundamentally you are doing what needs to be done to get to the reserves, you will be awarded marks.

Hope this helps.
 
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