September 2018

[1495_sc]

Hello,

Need help in understanding Q1 part i) risk 'interest rates up'

As BEL for Solvency II SCR is calculated using risk-free rate as prescribed by EIOPA, why would there by any impact on valuation of liabilities?

It is assumed that matching adjustment is applicable for annuity and hence its a well matched portfolio. But, the answer also mentions that 'there should not be a significant impact from annuity business'. Should it not be 'no impact from annuity business'?

MA calculation = spread on matching assets - fundamental spread prescribed by EIOPA. Are we saying that the EIOPA risk free rate will also increase?

Similarly, why will the discount rate for non-unit reserve of unit linked liabilities change?

Please help. Thank you!

 

[1495_sc]

Continuation of the question-

How is 'diversified capital' calculated in this question from 'undiversified SCR'? In core reading, it is only mentioned that for each risk module, sub-risk module SCR is aggregated using specified correlation factors and matrix. This relates to part iv) How can capital be negative after diversification practically?

 

[1495_sc]

I need help with understanding part vi)

The question implies that company is reporting sensitivities on SCR and own fund. The sensitivities are given.

The sensitivities are applied on the balance sheet first. For example, 10% increase in equities.

Now, we need to comment on the impact on equity risk module, credit spread module and longevity module along with own capital.

For own capital , we need to consider only the sensitivity's impact but own capital also consists of SCR so it makes sense to talk about SCR risk modules first and then own capital.

Question- Can someone confirm if own capital= available capital= assets-technical provision- other liabilities?

For risk module impact, I need help with a numerical example.

Lets say, with 10% equity increase, the value of unit linked assets has increased from 100 to 110 and non-unit reserve liability has increased from 80 to 85.

Now, equity risk module SCR is calculated based on assets= 110, liability =85 and lets say other liabilities/equity=25.

How will risk module SCR be calculated using a numerical example?

 

[Em Francis]

Hello,

Need help in understanding Q1 part i) risk 'interest rates up'

As BEL for Solvency II SCR is calculated using risk-free rate as prescribed by EIOPA, why would there by any impact on valuation of liabilities?

It is assumed that matching adjustment is applicable for annuity and hence its a well matched portfolio. But, the answer also mentions that 'there should not be a significant impact from annuity business'. Should it not be 'no impact from annuity business'?

MA calculation = spread on matching assets - fundamental spread prescribed by EIOPA. Are we saying that the EIOPA risk free rate will also increase?

Yes, the question states that the interest rates are based on swap rates which are what EIOPA base their rates on.

Similarly, why will the discount rate for non-unit reserve of unit linked liabilities change?

Please help. Thank you!

Because of the change in discount rate.

 

[Em Francis]

Continuation of the question-

How is 'diversified capital' calculated in this question from 'undiversified SCR'? In core reading, it is only mentioned that for each risk module, sub-risk module SCR is aggregated using specified correlation factors and matrix. This relates to part iv) How can capital be negative after diversification practically?

All this is saying is following the stress, companies would hold less capital due to the impact from the longevity stress and the other non-interest rate stresses.

 

[Em Francis]

I need help with understanding part vi)

The question implies that company is reporting sensitivities on SCR and own fund. The sensitivities are given.

The sensitivities are applied on the balance sheet first. For example, 10% increase in equities.

Now, we need to comment on the impact on equity risk module, credit spread module and longevity module along with own capital.

For own capital , we need to consider only the sensitivity's impact but own capital also consists of SCR so it makes sense to talk about SCR risk modules first and then own capital.

Question- Can someone confirm if own capital= available capital= assets-technical provision- other liabilities?

I am assuming you are referring to 'own funds' which is, yes, assets minus technical provisions (and 'other' liabilities).

For risk module impact, I need help with a numerical example.

Lets say, with 10% equity increase, the value of unit linked assets has increased from 100 to 110 and non-unit reserve liability has increased from 80 to 85.

Now, equity risk module SCR is calculated based on assets= 110, liability =85 and lets say other liabilities/equity=25.

How will risk module SCR be calculated using a numerical example?

Before stress: Assets - liabilities = 100 - 80 = 20
After stress: Assets - liabilities = 110 - 85 = 25

This is a negative SCR of -5.

 

[1495_sc]

I am assuming you are referring to 'own funds' which is, yes, assets minus technical provisions (and 'other' liabilities).


Before stress: Assets - liabilities = 100 - 80 = 20
After stress: Assets - liabilities = 110 - 85 = 25

This is a negative SCR of -5.

Yes, was referring to own funds. Also, after revising surplus distribution, I realized that own funds= free assets= assets-liabilities. Is this equation always true?

Regarding the calculation, for each sensitivity in the question and corresponding risk module, can we use the following approach?
1. Consider the impact of sensitivity in on balance sheet
2. This impact will now be equal to the unstressed balance sheet which we will use for calculating new SCR
3. The SCR for risk modules in scope (equity, credit spreads, longevity) will be calculated as
(assets-BEL) in unstressed balance sheet from #2- (assets-BEL) in stressed balance sheet.

Now, for sensitivity= large increase in lapse; it affects only unit linked liabilities.

When we talk about credit spread risk module SCR now, the solution says it will not be affected as lapse doesn't affect annuity business. I understand that credit spread is relevant for annuity only but when we calculate the spread risk SCR, will we not consider the equation in #3 which will be affected because of lapse sensitivity anyway? The spread risk SCR would still include both annuity and unit linked business if I am not wrong? The simultaneous application of sensitivity and stress factors seems difficult to understand practically.
If there is another numerical example which you think might be helpful, please share.

Thanks a lot for helping all this while!

 

[Lindsay Smitherman]

Yes, was referring to own funds. Also, after revising surplus distribution, I realized that own funds= free assets= assets-liabilities. Is this equation always true?

The term 'own funds' is used under Solvency II to refer to assets in excess of technical provisions (and other misc liabilities) - as stated in Chapter 11.

Regarding the calculation, for each sensitivity in the question and corresponding risk module, can we use the following approach?
1. Consider the impact of sensitivity in on balance sheet
2. This impact will now be equal to the unstressed balance sheet which we will use for calculating new SCR
3. The SCR for risk modules in scope (equity, credit spreads, longevity) will be calculated as
(assets-BEL) in unstressed balance sheet from #2- (assets-BEL) in stressed balance sheet.

Yes, that works for this question

Now, for sensitivity= large increase in lapse; it affects only unit linked liabilities.
When we talk about credit spread risk module SCR now, the solution says it will not be affected as lapse doesn't affect annuity business. I understand that credit spread is relevant for annuity only but when we calculate the spread risk SCR, will we not consider the equation in #3 which will be affected because of lapse sensitivity anyway? The spread risk SCR would still include both annuity and unit linked business if I am not wrong? The simultaneous application of sensitivity and stress factors seems difficult to understand practically.

The increase in lapses will only impact the assets backing UL business and the technical provisions (TP) for the UL business - not the assets backing the annuity business or the TP for the annuity business (annuities don't lapse). So when applying the lapse increase sensitivity in step #1 above, the only components that will change are related to the UL business. The credit spread SCR stress will only impact the annuity business (since we are told that the UL assets are not invested in bonds). So because the assets and TP relating to annuity business haven't been changed by the sensitivity, the credit spread SCR component will also not change.

Hope that helps to clear this up.

 

[1495_sc]

Thank you, very helpful!

 

[Abcs]

What is the impact of interest rate increase on SCR ?
If interest rate increases then MV of bonds decreases and hence less exposure. Therefore less stress, so less SCR. But interest rates increase so discounting of BEL increase and hence lower BEL. Does this means than decrease in BEL > Decrease in MV of Bonds. Therefore more SCR required ?

 

[Lindsay Smitherman]

We need to be very careful here not to confuse two different types of question: (1) how the SCR components are calculated and (2) the impact of a particular event occurring on an existing SCR.

September 2018 Q1(i) is an example of type (1): it is asking about why certain stresses have generated an SCR component, including a change in interest rates. So we need to think about what the impact of the change is on the value of assets and the value of the BEL; specifically the impact on the value of {assets - BEL} under the stressed conditions relative to the base value of {assets - BEL}. For annuity business that is 'well matched by fixed interest assets' (as per the Q wording), the 'interest rate up' component of the SCR would need to reflect a lower value of assets and a lower value of BEL, and these should broadly offset each other, given the 'well matched' description. Hence that particular element of the SCR component might be relatively trivial. [If there is a slight mismatch, with the assets being of longer term than the liabilities, then there would be a small positive contribution to SCR.]

Your question 'What is the impact of interest rate increase on SCR?' sounds more like a type (2) question: if interest rates increase, what happens to the SCR? This is more complicated as we would have to think about what the implications of having a lower value of bonds and lower value of BEL would be for each of the SCR stresses. So, for example, having a lower value of bonds as the starting point would reduce the level of exposure to credit spread risk (to the extent that corporates are held), thus reducing that element of the SCR calculation.