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#1




Tabular cost & Tabular interest
Can anyone explain what tabular cost & tabular interest mean?
Thanks. 
#2




context?

#3




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. 
#4




Quote:
a "balancing item"? 
#5




"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; 01152006 at 09:53 AM.. 
#6




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.

#7




Thanks to all, especially Steve White. It was really helpful.
Does any of you know how to derive the formula for calculating CI? 
#8




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 = (t1)V + P + i((t1)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*((t1)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*((t1)V + P)]  [q/2*(1tV)] 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*((t1)V + P) + i(tV + P)]  [q/2*(1tV) + 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*((t1)V + P)]  [q/2*(1tV)] 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; 01182006 at 01:15 PM.. 
#9




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.
__________________
Carol Marler, FSA, MAAA, A Former Actuary Dedicated to Retirement Just My Opinion (Although this statement is my opinion, and I am still listed as an actuary, it's still not a statement of actuarial opinion, and you really shouldn't rely on it.) 
#10




Quote:
I don't quite understand the equations below though: tV = t1V + P + i(t1V + 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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