Actuarial Outpost Loss triangle: calendar year vs accident year
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#1
06-13-2013, 03:26 AM
 Wile E Coyote Non-Actuary Join Date: Jun 2013 Posts: 5
Loss triangle: calendar year vs accident year

Hi,

I am not an actuary so pls don't mind if I ask something trivial . Searching the forum didn't help so far and another acturary couldn't really help me so it might not be that trivial after all.

Say I am given a loss triangle from a US P&C insurance. I attached one from Chubb as an example, some figures might help for this exercise. My understanding is that loss triangles are shown in calendar years (in this case from 2002 to 2012) and that conversion from calendar years into accident years is pretty much a no-brainer. So far I didn't figure out how to do it so I would be glad if someone could help me out.

As a sidenote, could it be that reporting in Europe (esp Germany) is different from reporting in the US ? The guy I asked is German and he couldn't really make head or tail of it, saying this is non-standard (according to his standards at least).

Wile E Coyote
Attached Images
 CB_10-K_2012_LossTriangle.pdf (27.8 KB, 1129 views)
#2
06-13-2013, 07:21 AM
 MountainHawk Member CAS AAA Join Date: Dec 2001 Location: Salem, MA Studying for Nothing!!!! College: Lehigh University Alum Favorite beer: Yuengling Posts: 64,850

It looks like those are accident years in the columns. The first row is the amount that the company incurred at the end of the initial calendar year, that is, 20XX as of 12/31/20XX. The next row is the incurred as of 20XX+1, and so on.

It's inverted from a standard triangle, but otherwise the same thing.

Calendar Years aren't reevaluated, so I don't think they can be CY like you originally interpreted them to be.
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#3
06-13-2013, 08:53 AM
 MightySchoop Member CAS AAA Join Date: Aug 2009 Location: Insula Primalis Posts: 6,740

Quote:
 Originally Posted by MountainHawk It looks like those are accident years in the columns. The first row is the amount that the company incurred at the end of the initial calendar year, that is, 20XX as of 12/31/20XX. The next row is the incurred as of 20XX+1, and so on. It's inverted from a standard triangle, but otherwise the same thing. Calendar Years aren't reevaluated, so I don't think they can be CY like you originally interpreted them to be.
Alternatively, it could be "policy year" or "report year." Accident year is by far the most common way to arrange data in a loss triangle, but sometimes these other methods are used -- usually when some feature of the data makes them more meaningful than accident year.
#4
06-13-2013, 09:01 AM
 Ganymede Member Join Date: Mar 2007 Posts: 155

I don't think you can reliably translate calendar year incurred losses into accident year incurred losses. Calendar year incurred means losses paid during the calendar year plus the change in outstanding losses. The losses (either paid or change in outstanding) could come from any accident year.

Accident year triangles are much better for loss reserve analysis. With accident year triangles you can make use of the fact that exposure should not change as you go forward in the development years.
#5
06-13-2013, 09:10 AM
 Ron Weasley Member CAS AAA Join Date: Oct 2001 Studying for naught. Favorite beer: Butterbeer Posts: 8,623

If the triangles are based on incurred losses, then the sum of the differences along the diagonals should yield the calendar year incurred losses, so long as all historical years with changes during the calendar year are represented.
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#6
06-13-2013, 10:39 AM
 MountainHawk Member CAS AAA Join Date: Dec 2001 Location: Salem, MA Studying for Nothing!!!! College: Lehigh University Alum Favorite beer: Yuengling Posts: 64,850

Quote:
 Originally Posted by MightySchoop Alternatively, it could be "policy year" or "report year." Accident year is by far the most common way to arrange data in a loss triangle, but sometimes these other methods are used -- usually when some feature of the data makes them more meaningful than accident year.
I would expect those in reinsurance, but in primary insurance it would be odd, though yes, it could be.
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#7
06-13-2013, 12:06 PM
 3.14 Member CAS Join Date: Sep 2005 Posts: 955

Quote:
 Originally Posted by Ron Weasley If the triangles are based on incurred losses, then the sum of the differences along the diagonals should yield the calendar year incurred losses, so long as all historical years with changes during the calendar year are represented.
This.
#8
06-13-2013, 12:19 PM
 yoyo Member CAS Join Date: Dec 2001 Posts: 21,450

This is what you have.

The first row of dollar amounts shows the ending liability as of 12/31 for 2002, 2003, ..., 2012. For a US P&C insurance company, this is sum of lines 1 and 3 on page 3 (the liability page of the balance sheet) of the annual statement as of 12/31 for each year. The unpaid liability for all accident years 2002 and prior is \$12,642 (in millions) as of 12/31/2002. The next number to the right (\$14,521) is the unpaid liability for all accident years 2003 and prior as of 12/31/2003, and so on.

The section below that row shows a reestimation of liabilities. If the actuary knew at 12/31/2002 what he knew at 12/31/2003, he would have estimated a liability of \$13,039 instead of \$12,642 for the 12/31/2002 liability. This means that the actuary strengthened reserves relating to accident years 2002 and prior by \$397 (= 13,039 - 12,642) during 2003. If the actuary knew at 12/31/2002 what he knows at 12/31/2012, the actuary would have estimated the liability to be \$15,362 at 12/31/2002 instead of his original estimate of \$12,642.

The total cumulative net deficiency embeded in the original liability estimate for all accident years 2002 and prior on 12/31/2002, as reestimated on 12/31/2012, is \$2,720 (= 15,362 - 12,642).

Note that the sum of the Total Cumulative Net Deficinecy (Redundancy) row is NOT income statement effect over the years related to reserve increases/decreases. The income statement effect over 10 years related to the annual reestimation of liabilities is:

(13,039-12,642) + (14,848-14,521) + ... + (20,715-21,329).
#9
06-13-2013, 12:24 PM
 Wile E Coyote Non-Actuary Join Date: Jun 2013 Posts: 5

Thanks you all for the replies so far.

The background of my question was indeed that I want to analyse the loss reserves to see whether the reserving is close to sensible. My understanding so far was that loss triangles are (usually) shown in calendar year format. I will check with their IR department but MountainHawk's point about reevaluation of calendar years makes sense to me .

Since we are at it... I wanted to check the reserving with a simple chain ladder method. Now I read somewhere about another method that should do a better job than chain ladder but don't remember the name. It was neither Bornhuetter-Ferguson nor Brosius, I think it started with "C". Does that ring a bell ?
#10
06-13-2013, 12:26 PM
 Wile E Coyote Non-Actuary Join Date: Jun 2013 Posts: 5

Yoyo, thanks a ton. I will take your post together with the figures and see where I end up.

 Tags loss triangle