Cost of guarantee and smoothing

[gruhaa]

Hi

Please I need a confirmation on my understanding on cost of guarantee and smoothing:
Suppose, in YE 2017, guaranteed benefit for a policy is 107(basic sum assured plus declared RB) and asset share as on YE 17 is 100(guarantee biting may be due to asset share has fallen during 2016-17). the policy is due to mature next year(and thus there is no other decrement, ignoring death).

If company expect to earn 5% investment return and smoothing payout policy is say 1% of YE17 asset share( £1) which makes unsmooth earned asset share to 105 but payout to 106.

Thus, at YE18, it is expected that
Guarantee benefit: 107
Smooth AS:106
Unsmooth AS: 105
Assuming 0 TB is acceptable

Then, should be I correct in saying that there will be no cost of smoothing and £2(107 - 105) is cost of guarantee?

If smoothing policy were such that smooth asset share would be 109 and thus payout will be 109 then 109 minus 107 would be cost of smoothing? Can I also say that 2/107 is the TB rate declared by the company during 2017-18?

 

[Lindsay Smitherman]

Hi

There aren't specific definitions of "cost of guarantees" and "cost of smoothing" which separate these two components definitively: different companies take different approaches.

So yes, your calculations make sense under one possible approach to this separation - and it looks like what you have done is consistent with the example definitions presented in Q1 on the April 2014 exam paper.

However, other possible splits could reasonably be used (which is why the exam paper had to define the ones that they wanted you to use for that question!).

For example, under your first case, rather than COG = 2 and COS = 0 you could have COG = 1 and COS = 1, by defining COS as the difference between smoothed and unsmoothed asset share, and the COG as the bite of the guarantee in excess of smoothed asset share. For your second example, I think that this would then give a split of COG = 0, COS = 4 (rather than COG = 2, COS = 2). It basically boils down to whether you look at the guarantee first and then the smoothing or vice versa.

And, yes, the TB rate would be 2/107 for that particular policy and situation (assuming that the company was able to set its TB rates so that it could target smoothed asset share exactly, which in practice doesn't tend to be the case due to approximations / practicalities / smoothing across model points).