# Risk Margin and SCR relationship

Discussion in 'SA2' started by Peter Arthur Doyle, Aug 20, 2018.

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1. ### Peter Arthur DoyleMember

Hi, currently looking at the risk margin, I was googling it and came across some articles that critise it for being far too high, especially for long term products such as annuities and whole life.
I can't see how this is, I've tried looking for an example but from my understanding of it, the risk margin is calculated using the cost of capital approach, so should its relationship to the SCR not be (roughly) 0.06 of it?
The article I was reading was from insurance Europe and cited some risk margins being 50% of the SCR? It explicitly mentioned the Risk margin being extremely high for funeral insureanc??
Could you shed light on the relationship between the SCR and the Risk margin and how the risk margin could climb so high?
I presume I'm not understanding something fundamental about either the calculation of the SCR or the Risk margin.
Thanks
Peter

Last edited by a moderator: Aug 20, 2018
2. ### Lindsay SmithermanActEd TutorStaff Member

Hi - yes, I think it's the nature of the calculation of the risk margin that has caused the confusion.

It is calculated from a series of amounts that are equal to 6% of the non-hedgeable part of the SCR (not the whole SCR - only that part which relates to non-hedgeable risks, with examples of such risks being given in the course notes) projected forwards for each future year and then discounted back at the risk-free rate. So the risk margin is the sum of all the individual {6% of part-SCR} amounts that have been projected in each of these future years, after each has been discounted back for the appropriate time period.

For a whole of life contract (such as an annuity or whole life assurance) the outstanding projection period can be significant.

Say that the non-hedgeable risks (eg mortality risk) account for 50% of the SCR and the average outstanding projection period is 20 years on a portfolio of such business.

Bearing in mind that the risk-free discount rate is likely to be pretty low, then adding up 20 years' worth of 6% x 50% x SCR could indeed equal 50% of SCR.

Has that helped?

3. ### Peter Arthur DoyleMember

Yes thanks you!

4. ### Tanay ChandraMade first post

Thanks Lindsay.

I also had a query on the calculation. To calculate Risk Margin (RM) we need capital projection for future year. Letâ€™s assume I use the approx run off from SAR or Reserves to project the future capital and hence calculate RM. Also to calculate Base SCR, I need to have stressed BEL (say for mortality shock), then my confusions are two:

1) when RM depends on SCR but SCR also depends on RM then how is this circularity broken?
2) under a Base scenario, what would be my TP? Will it only be BEL and RM is calculated under each stress scenario which will contribute to SCR?

5. ### Lindsay SmithermanActEd TutorStaff Member

Hi - yes good observation: you are correct that there is the potential for circularity here.

That is why a more practical approach tends to be taken, whereby the base scenario and stress scenario for the SCR are both calculated on {Assets - BEL} rather than {Assets - TP}. This is as mentioned in the following Core Reading found in Chapter 12, and we also cover it in Question 12.4 in the course notes:

The SCR for each individual risk is then determined as the difference between the net asset value (for practical purposes this can be taken as assets less best estimate liabilities) in the unstressed balance sheet and the net asset value in the stressed balance sheet.

Hope that helps.

6. ### Tanay ChandraMade first post

Thanks it does.

7. ### David ChisnallMade first post

Followup question: Does the risk margin include the cost of holding itself?

If RM is the cost of holding the SCR (and thus, the cost to a third party of taking on your BEL and having to hold the SCR), does the RM calculation also include the cost of holding the RM itself? (Because the RM is ALSO capital that a third party would have to hold if it were to take on the BEL).

8. ### Franners81Member

Yes, I believe it will. Remember the SII CoC approach is cyclical and so basing it on cost of holding SCR (for non-hedgeable risks) it will itself also depend on Risk margin (as SCR is unstressed net assets - stressed net assets).

Last edited by a moderator: Sep 10, 2018
9. ### MLCKeen member

Hi Lindsay,

I'm a little confused about what makes up the non-hedgeable risks part of the SCR when calculating the RM. The notes say that this is just reinsurance credit risk, insurance risk, op risk and residual market risk. However couldn't you hedge reinsurance credit risk by use of derivatives such as credit default swaps? Also, for mortality risk for example, couldn't you hedge this using standard reinsurance?

The notes also say that the RM is the theoretical amount in addition to the value of the BEL that an insurer would need to pay a third party in order for them to take responsibility for its liabilities. I'm not quite sure I see why this is the case.

Any help would be much appreciated!

Thanks,

Max

10. ### mugonoTon up Member

These are actually really good questions.

< couldn't you hedge reinsurance credit risk by use of derivatives such as credit default swaps? Also, for mortality risk for example, couldn't you hedge this using standard reinsurance? >

The answer to this question can be found at Article 77: Calculation of technical provisions in the Solvency II Directive (or equivalently, the Calculation of Technical Provisions part of the PRA Rulebook). This includes the following paragraph, included below for ease:

Article 77 of the SII Directive (paragraph 4 of my version )
"Insurance and reinsurance undertakings shall value the best estimate and the risk margin separately. However, where future cash flows associated with insurance or reinsurance obligations can be replicated reliably using financial instruments for which a reliable market value is observable, the value of technical provisions associated with those future cash flows shall be determined on the basis of the market value of those financial instruments. In this case, separate calculations of the best estimate and the risk margin shall not be required."

The key sentence phrase that is worth highlighting is this one: " [the (re)insurance obligations] can be replicated reliably using financial instruments for which a reliable market value is observable".

(i) Credit default swaps could satisfy the 'observable market value' criteria; however 1) not all reinsurers will have a CDS that would pay out were it to default; and 2) even if there was a CDS it may be illiquid, which would violate the 'can be replicated reliably' criteria.

However, I don't in principle (subject to the above criteria being satisfied) see why a CDS couldn't be used to argue that the contribution of reinsurance counterparty risk to this element of the risk margin calculation wasn't required. I think that the entire reinsurance contract would need to structured as a financial instrument (as opposed to an insurance contract) to fall outside the scope of Article 77 but I'm happy to hear others' views on the matter.

(ii) Standard reinsurance would be transacted 'over the counter' and so would fail the '[observable] market value' criteria.

<The notes also say that the RM is the theoretical amount in addition to the value of the BEL that an insurer would need to pay a third party in order for them to take responsibility for its liabilities.>

Solvency II is a market consistent regime, i.e. it values assets and liabilities at a level that knowledgeable third parties would transact at arms' length.

The BEL is an amount that would be required to meet claims and expenses. If actual experience followed the assumptions (best estimate) reflected in the BEL there would be nothing for a third party to earn as profit. You can think of the risk margin as the amount that a third party would require to be incentivised (assuming they are rationale and are in the business of generating a return for its owners :-0) to take on the business.

Hope that helps; oh and apologies for not being Lindsay

Last edited: Sep 8, 2019
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11. ### Lindsay SmithermanActEd TutorStaff Member

Brilliant response, thank you!

The basic point to remember is that we are trying to do a market-consistent valuation, but to be able to use values directly from 'the market' in order to do this, that market has to be sufficiently deep and liquid. Otherwise there will be distortions that don't give us a fair market-consistent valuation. The reinsurance market isn't sufficiently deep and liquid - and there aren't really observable market trade values, as explained so well above.