Rebasing of reserves

[KaustavSen]

Hi,

I have come across this term, "Rebasing of reserves" in work (mainly in the documentation pages of actuarial software). However, the explanation that they seem to provide is quite sparse without explaining what it truly means.

I intuitively think of "rebasing of reserves" as calculating the future projected reserves by allowing for the reserving probabilities (eg, in-force, death, surrender and maturity) to start from that future point in time ie, time t = 10 (say) reserves will be based on probabilities with the in-force probability being 1 at t = 10.

An alternative to "rebasing of reserves" would be to divide the "Reserves In-force" (the "rebased reserve" at t = 0) at future time-steps by the in-force probability to come up with the "Reserves Per Policy" (which will act as a proxy to the true "Rebased Reserve" at that point in time).

I am not sure if I am going on in the right direction. Can someone please confirm (and elaborate) on my understanding above?

Thanks,
Kaustav

 

[Lindsay Smitherman]

Hi - it sounds like you are thinking along the right lines.

In my experience, in the context of actuarial projection models, rebasing of reserves refers to the adjustments that are necessary due to the reserving and experience (or projection) bases differing.

For example, let's say that we want to project forward the non-unit reserve on a unit-linked policy. Our experience (or projection) basis might include the probability of the policy being in-force as 1 (at t=0), 0.9 (at t=1), 0.8 (at t=2) etc. However, let's say that the reserving basis has the probabilities as being 1 (at t=0), 0.8 (at t=1), 0.6 (at t=2) etc.

The model will calculate the non-unit reserve at time t=0 by projecting cashflows forward using the latter of these two sets of probabilities.

However, when we move on one year in the overall model projection to time t=1 and are now calculating the non-unit reserve at that point, we don't want to start from the time t=1 cashflows that have been multiplied by 0.8. We need to start from time t=1 cashflows that have been multiplied by 0.9, as per the experience basis - since this is what we are assuming is actually going to happen. But then the projection forward of those cashflows into times t=2 etc will need to use the reserving basis, in order to determine the non-unit reserve at time t=1.

In other words, when we are projecting what we expect future reserves to be, we are rebasing the calculations onto the experience basis - but only for the period up to the valuation date in each case.

[The same would be true for reserves on all other types of product.]

What it means is that projection model cannot just determine a single set of reserving cashflows and use those to determine the reserves in each future projection period. Instead, every time the model steps forward one projection period, a new set of reserving cashflows has to be produced - but this can often be done simply by 'rebasing' the original set according to the new in-force probabilities.

Does that make sense?

We meet a similar concept in the SP2 course (Chapter 18 Section 2.3), which explains the need for two separate bases for embedded value calculations: the projection / experience basis and the reserving basis.

 

[KaustavSen]

Hi Lindsay,

Thanks for the explanation. This is indeed very helpful and clears up a lot a grey areas.

I just have one follow up question here:

When you mention:

but this can often be done simply by 'rebasing' the original set according to the new in-force probabilities.

Are you referring to the approximate approach that I mentioned in my original post:

An alternative to "rebasing of reserves" would be to divide the "Reserves In-force" (the "rebased reserve" at t = 0) at future time-steps by the in-force probability to come up with the "Reserves Per Policy" (which will act as a proxy to the true "Rebased Reserve" at that point in time).

That is to say that:

• We will simply take the projected reserve (based on a reserving projection assumed throughout from t=0)
  
  
• Divide it by the In-Force probability (on a reserving basis) to arrive at a Per Policy figure; and then
  
  
• Multiply the resulting Per Policy figure by the corresponding In-Force probability (on an experience basis) to arrive at a proxy to the rebased reserve value.

Thanks again for such a prompt reply.

Thanks,
Kaustav

 

[Lindsay Smitherman]

So, the example that I used above only considered the in-force probabilities differing between the projection and reserving bases. A simple ratioing approach might work in that situation, but bear in mind that the company might also want to change its per policy expense assumptions under different projected numbers of in-force policies, to allow for the fixed expense spread. In which case, we can't just ratio the reserves.

Bear in mind also that there are other assumptions that can differ between the projection and reserving bases. For example, for non-unit reserves the unit growth rate assumption might well differ between the two bases. So we wouldn't be able to just proportion the non-unit reserves in the same way: some of the cashflows in the calculation will be impacted by the differing unit growth rate assumptions but others won't. So we need to 'rebase' the reserves fully to the t=1 position, allowing for experience to be as assumed under the projection (not reserving) basis up to that point, and then project forwards from there using the reserving basis in order to determine the cashflows that are needed then to determine the t=1 non-unit reserves. So the model can end up being relatively complex, with nested projections.

 

[KaustavSen]

Thanks again, Lindsay.

Agree with the points that you raise above regarding various other components of projection differing between the two bases (such as expenses, charges and fund growth rates).

And as you suggest, the model can end up being relatively complex, with nested projections. As an approximation, I thought (based on work experience) that insurers when modelling prorate using probabilities to arrive at a proxy to the true "rebased" reserve.

Once again, this discussion immensely helped me clearing this till now mysterious concept of rebasing of reserves

Cheers,

Kaustav

 

[Lindsay Smitherman]

Glad that helped.

Yes, sometimes taking pro-rata reserves will work & sometimes it won't. Personally, I think it is always worth looking to see whether there is a valid modelling short-cut that can be taken!