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  #1  
Old 01-13-2006, 07:53 PM
inhring inhring is offline
 
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Default Tabular cost & Tabular interest

Can anyone explain what tabular cost & tabular interest mean?
Thanks.
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  #2  
Old 01-13-2006, 08:40 PM
urysohn
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context?
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  #3  
Old 01-13-2006, 09:04 PM
Steve White Steve White is offline
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This is probably from the Life Insurance statutory statement, the Analysis of Increase in Reserves exhibit. The idea is that you demonstrate that, in some broad context, Opening Reserves + Net Premiums + Interest - Cost of Insurance (q times net amount at risk) - Reserves Released on deaths - Reserves released on other terminations (mainly surrenders) = Ending Reserves. There probably are other items, like something for disability, and there is a somewhat similar formula for annuities. As you complete the exhibit you end up to a very slight extent estimating Interest (called Tabular Interest in the exhibit) and Cost of Insurance (called Tabular Cost) is a balancing item. However, if you did a seriatim calculation of the Cost of Insurance, you should get something similar to the Tabular Cost.

Possibly, on UL or VUL with explicit COIs, a company could use that as Tabular Cost, with something else as a balancing item, if the NAIC instructions allow.
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Old 01-15-2006, 01:37 AM
inhring inhring is offline
 
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Quote:
Originally Posted by Steve White
This is probably from the Life Insurance statutory statement, the Analysis of Increase in Reserves exhibit. The idea is that you demonstrate that, in some broad context, Opening Reserves + Net Premiums + Interest - Cost of Insurance (q times net amount at risk) - Reserves Released on deaths - Reserves released on other terminations (mainly surrenders) = Ending Reserves. There probably are other items, like something for disability, and there is a somewhat similar formula for annuities. As you complete the exhibit you end up to a very slight extent estimating Interest (called Tabular Interest in the exhibit) and Cost of Insurance (called Tabular Cost) is a balancing item. However, if you did a seriatim calculation of the Cost of Insurance, you should get something similar to the Tabular Cost.

Possibly, on UL or VUL with explicit COIs, a company could use that as Tabular Cost, with something else as a balancing item, if the NAIC instructions allow.
Thanks for your reply. I know it sounds really stupid to ask this, but what is
a "balancing item"?
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  #5  
Old 01-15-2006, 09:50 AM
Steve White Steve White is offline
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"Balancing item" = what's necessary to make the two sides of the equation balance. We know that in principle it would be possible to calculate the ending reserve for a single policy from the beginning reserve and the activity (premiums, interest, etc), and that the reserve calculated that way should match reserves calculated other ways (e.g., by matching the policies with a factor tape of prospective reserves by plan, age, duration). In principle, if you could do it for one, you could do it for all. That's too much work for too little benefit.

Instead suppose you have equations of the form: A + B + C should equal D, which you are trying to apply in the aggregate to a huge block of business. By doing an exact calculation of some pieces (which would include opening and ending reserves in the tabular cost example) and trying to make good estimates of the others, you might get A = 1000, B = 600 C = -100, D = 1480. It's undesirable to show 1000 + 600 - 100 = 1480, and the reporting formats don't have a line for "approximation impact". You might choose to throw that difference in with the 600 and report 1000 + 580 - 100 = 1480. In that case, the 580 term would be your balancing item.

Note, in that same example, if you were always going to use that term as your balancing item, you aren't forced to estimate it in advance. If you've calculated or estimated the 1000, -100 and 1480, you can just calculate the 580 as "whatever makes it work".

If a company did calculate a balancing item as "whatever makes it work", it would be good to review trends - is the resulting value in line with recent years - and to make sure it's reasonable. For tabular cost, you can get a very good estimate of aggregate net amount at risk. For an established company, if tabular cost / aggregate net amount at risk turned out to be a mortality rate for a female nonsmoker age 20, something is very odd.

I suspect tabular cost as "whatever makes it work" is common. The degree to which any companies make estimates before calculating what makes the equation balance, or how much review of the result is made, will vary.

Last edited by Steve White; 01-15-2006 at 09:53 AM..
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  #6  
Old 01-15-2006, 11:12 AM
Chuck Chuck is offline
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In more general terms I think "tabular" generally means coming from or derived from a table or tabulated set of numbers. In life insurance context, tabular cost and tabular interest just means derived based on calculations using a mortality table.
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  #7  
Old 01-16-2006, 07:29 PM
inhring inhring is offline
 
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Thanks to all, especially Steve White. It was really helpful.
Does any of you know how to derive the formula for calculating
C-I?
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  #8  
Old 01-18-2006, 10:27 AM
Steve Grondin Steve Grondin is offline
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The following is taken from Life Insurance Accounting - Noback p 239 - 240

0M = reserve at 12/31/prev
1M = reserve at 12/31/curr
P = tabular net premiums during year
I = required interest for year
C = tabular cost of mort for year
VD = reserves released by death for year
VT = reserves released by termination other than death for year


For those inforce at both year ends:
Adding the three equalities
tV = (t-1)V + P + i((t-1)V + P) - q(1 - tV)
P = P
(t+1)V = tV + P + i(tV + P) - q(1 - (t+1)V)
and dividing by 2 gives
(t+1)M = tM + P + [i/2*((t-1)V + 2P + tV)] - [1/2*(q(1 - tV) + q(1- (t+1)V)]

The first item in brackets is I and the second is C, so it can rearranged
C - I = tM + P - (t+1)M
Noting that VD and VT is zero for this class, it matches the formula.

For those who die (using curtate assumptions):

Those who die before policy anniversary in year:
tVD = tM + [i/2*((t-1)V + P)] - [q/2*(1-tV)]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM - tVD
Remembering that P during the current year, (t+1)M and VT are all 0, it matches.

Those who die after policy anniversary in year:
(t+1)VD = tM + P + [i/2*((t-1)V + P) + i(tV + P)] - [q/2*(1-tV) + q(1 - (t+1)V]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM + P - (t+1)VD
Remembering that (t+1)M and VT are 0, it matches.

For those who surrender (curtate assumptions)
tVT = tM + [i/2*((t-1)V + P)] - [q/2*(1-tV)]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM - tVT
Remembering that P during the current year, (t+1)M and VD are all 0, it matches.

Last edited by Steve Grondin; 01-18-2006 at 01:15 PM..
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  #9  
Old 01-18-2006, 11:54 AM
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Noback was never my favorite, but this is good. Of course, the same formulas are also found in the instructions to the annual statement.

I always claimed that the analysis of increase in reserve would be far more meaningful if the tabular assumptions had somewhat greater relationship to reality.

I never could convince anyone that we should also do an analysis of increase in FAS 60 GAAP reserves, but at least FAS97 generates some sort of analysis of "expected" vs. actual.
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  #10  
Old 01-18-2006, 07:59 PM
inhring inhring is offline
 
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Quote:
Originally Posted by Steve Grondin
The following is taken from Life Insurance Accounting - Noback p 239 - 240

0M = reserve at 12/31/prev
1M = reserve at 12/31/curr
P = tabular net premiums during year
I = required interest for year
C = tabular cost of mort for year
VD = reserves released by death for year
VT = reserves released by termination other than death for year


For those inforce at both year ends:
Adding the three equalities
tV = (t-1)V + P + i((t-1)V + P) - q(1 - tV)
P = P
(t+1)V = tV + P + i(tV + P) - q(1 - (t+1)V)

and dividing by 2 gives
(t+1)M = tM + P + [i/2*((t-1)V + 2P + tV)] - [1/2*(q(1 - tV) + q(1- (t+1)V)]

The first item in brackets is I and the second is C, so it can rearranged
C - I = tM + P - (t+1)M
Noting that VD and VT is zero for this class, it matches the formula.

For those who die (using curtate assumptions):

Those who die before policy anniversary in year:
tVD = tM + [i/2*((t-1)V + P)] - [q/2*(1-tV)]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM - tVD
Remembering that P during the current year, (t+1)M and VT are all 0, it matches.

Those who die after policy anniversary in year:
(t+1)VD = tM + P + [i/2*((t-1)V + P) + i(tV + P)] - [q/2*(1-tV) + q(1 - (t+1)V]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM + P - (t+1)VD
Remembering that (t+1)M and VT are 0, it matches.

For those who surrender (curtate assumptions)
tVT = tM + [i/2*((t-1)V + P)] - [q/2*(1-tV)]
The first item in brackets is I and the second is C, so it can rearranged
C - I = tM - tVT
Remembering that P during the current year, (t+1)M and VD are all 0, it matches.
Wow.. This is really nice. Thanks.

I don't quite understand the equations below though:

tV = t-1V + P + i(t-1V + P) - q(1 - tV) <-- what is q? perhaps mortality rate?
then, why do we need to subtract tV from 1? Is tV the same as the reserve
at time t?

P = P
t+1 V = tV + P + i(tV + P) - q(1 - t+1V)
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