# SCR/RM question

Discussion in 'SA2' started by Joseph Barnett, Apr 11, 2021.

Tags:
1. Hi,

My understanding of the SCR calculation is that it is the 99.5th VaR for own funds. Own funds = Assets - Technical Provisions = Assets - (BEL + RM). RM is a function of the future SCR run off, so this means that calculating the SCR and/or risk margin at t=0 gets exponentially more difficult the longer it takes the SCR to run off.

I was talking about this with a colleague recently and they said that in fact the risk margin is not stressed as part of the SCR calculation, which makes it a good deal easier to calculate.

I know there are a number of simplifications that are allowed for the risk margin calculation, on the basis that they appropriately approximate the "real" risk margin. My question is about whether my colleague was referring to a simplification for practicality's sake, or whether that is actually how the SCR is defined.

In other words if we suddenly found our computers were fast enough to calculate the SCR using a stressed risk margin tomorrow, would that be more faithful to the theory underlying the regulation? Or is there some theoretical reason why we shouldn't be stressing the risk margin in the SCR calculation?

Thanks

2. Including the risk margin within the calculation of the SCR introduces circularity. The risk margin is the discounted value of future SCRs discounted at the risk free rate and after multiplying by the cost of capital rate (currently 6% in SII).

How would you calculate a “stressed risk margin” as part of the SCR if you need the SCR to calculate the risk margin based on the current SII methodology...?

I suspect this is your colleague’s (implicit) point.

3. If RM(t) is computed using SCR(t+1) and onwards, then you could start at the end of the projection period T where SCR(T) = 0 and RM(T-1) = 0 and work backwards from there. So it wouldn't be entirely circular in this case but is practically impossible for anything more than a small value of T (as the number of calculations would increase exponentially).

4. The approach to calculating the risk margin is prescribed. My (and I suspect your colleagues) comment is in relation to where the current design of the risk margin interacts with reality , which would have likely considered (but not limited to) technical considerations.

5. From my understanding, the risk margin is stressed in theory. Why would it not be? Changes in the risk margin lead to changes in own funds for SCR calculating purposes, as the risk margin is present both on the opening balance sheet and the closing balance sheet after one year, unless all liabilities have run-off after one year (unlikely!).

There are certainly simplifications that happen including for practical reasons, but I'm not aware of saying the risk margin should not be stressed at all. For example the risk margin might be allowed to vary in line with the modelled BEL, or as some power of the BEL value. The opening risk margin put into the model might be determined via an alternative method or simplification rather than using the internal model, which avoids the circularity I think you're referencing.

This is my understanding but I'm by no means an expert on life insurance, so very happy to be corrected.

6. The SCR is defined as the change in basic own funds.

A number (dare I say, all...) of the Standard Formula demographic [sub]modules includes the phrase "Technical Provisions without the risk margin" when describing how to go about calculating the SCR.

The risk margin is not stressed. The actual legislative ([Commission Delegated Regulations]) text says:

1. insurers should not change the amount of the risk margin included in TPs when performing scenario based calculations [Article 83 of CDR.]

2. the change in liabilities denotes the increase in TPs less risk margin when calculating the non-life lapse risk sub-module [Article 118 of CDR]; mortality risk sub-module [Article 137 of CDR]; Longevity risk sub-module [Article 138 of CDR]; etc etc.

3. the current design of the prescribed time 0 risk margin includes the time 0 SCR. Stressing the time 0 risk margin in order to capture it within the SCR would introduce circularity.

Having a read of the CDR could clear up any [residual] misunderstandings.

Last edited: Apr 12, 2021
7. Thanks mugono for your response based around the standard formula. It's also been my experience using the standard formula that the risk margin isn't stressed, which as you point out is exactly in line with what the regulation says.

I understood this thread about being on the SCR / RM in general though, rather than only in the standard formula.
It isn't exactly that the time 0 risk margin is stressed in internal models, it's that the risk margin at time 1 is stochastic and the 99.5th percentile difference between the two gives the risk margin stress.

Joseph Barnett likes this.
8. Thanks both for your contributions - I think that clears it up for me. I should have mentioned that this originally came up in a standard formula context - so it would seem that not stressing the RM in this case actually follows the letter of the regulation and isn't a simplification. Was definitely interested beyond that as well though so thanks for the extra insights.

9. An internal model allows a firm to calculate the SCR using its own model, methodology, assumptions etc.

All firms (IM and SF) are bound by the prescriptive nature of the risk margin calculation - a component of technical provisions. So stressing the risk margin introduces a circularity regardless of whether the firm calculates its capital on an IM or SF basis.

The risk margin could be stressed in theory - though it isn't the only consideration.

The theory would need to be balanced against other considerations: ease of practical implementation, what stressing the risk margin is seeking to achieve, changing how the risk margin is defined in the legal text, political considerations etc.

Last edited: Apr 12, 2021
CapitalActuary likes this.