Stress in SCR (Sept, 2021, Q1iii)

[studentactuary15]

Hi in this question, they say "property values have reduced so there is less stress". What does this "less stress" mean? How is this related to the magnitude of the SCR?

 

[Em Francis]

Hi in this question, they say "property values have reduced so there is less stress". What does this "less stress" mean? How is this related to the magnitude of the SCR?

If the absolute value of property has fallen then the stress will be applied to a lower absolute value, resulting in a lower SCR.

 

[studentactuary15]

If the absolute value of property has fallen then the stress will be applied to a lower absolute value, resulting in a lower SCR.

Thank you, so for an example, would we have something like this:

Say the stress test is 10% adverse movement in property (so reduction in 10%).
End of 2019, property is 200 => SCR = 0.1*200 = 20.
End of 2020, property is 150 => SCR = 0.1*150 = 15.

So the SCR decreases. Is this correct?

 

[studentactuary15]

If the absolute value of property has fallen then the stress will be applied to a lower absolute value, resulting in a lower SCR.

Sorry I think my previous post might not be too relevant. I assume we need to consider the components of actual SCR formula here?

SCR of risk i (SCR) = NAV in unstressed (best estimate) balance sheet (A) – NAV in stressed scenario of risk i (B),
The B component will depend on A => NAV stressed = NAV x (Adverse movement of say 10%).
(This formula is very informal)

Property value falls => NAV falls => NAV (property) stress falls.
Less annuities in force => less liabilities since less benefits to pay out => NAV falls => NAV (longevity) stress falls.
Interest rate is 0% => fixed interest assets more valuable => NAV rises => NAV (interest rate) stress rises.
Less term assurances in force => less mortality risk so less potential pay outs on death => NAV falls => NAV (mortality) stress falls.
Less policies in general => per policy expenses rises => NAV rises => NAV (per policy expense) stress rises.

Essentially the stressed NAV is positively correlated with the unstressed NAV, given the adverse movement component remains the same.

Is this okay? The Q does ask us about the magnitude of the SCR but the solutions doesn't even mention the direction of the SCR - it just mentions the directions of the stressed NAV. This is a bit confusing how they asked the question like that.

 

[Em Francis]

Sorry I think my previous post might not be too relevant. I assume we need to consider the components of actual SCR formula here?

SCR of risk i (SCR) = NAV in unstressed (best estimate) balance sheet (A) – NAV in stressed scenario of risk i (B),
The B component will depend on A => NAV stressed = NAV x (Adverse movement of say 10%).
(This formula is very informal)

Property value falls => NAV falls => NAV (property) stress falls.
Less annuities in force => less liabilities since less benefits to pay out => NAV falls => NAV (longevity) stress falls.
Interest rate is 0% => fixed interest assets more valuable => NAV rises => NAV (interest rate) stress rises.
Less term assurances in force => less mortality risk so less potential pay outs on death => NAV falls => NAV (mortality) stress falls.
Less policies in general => per policy expenses rises => NAV rises => NAV (per policy expense) stress rises.

Essentially the stressed NAV is positively correlated with the unstressed NAV, given the adverse movement component remains the same.

Is this okay? The Q does ask us about the magnitude of the SCR but the solutions doesn't even mention the direction of the SCR - it just mentions the directions of the stressed NAV. This is a bit confusing how they asked the question like that.

Hi

Yes, you are nearly there but you need to conclude what happens to the SCR component. And be careful when you say NAV stress falls - the stress applied to a smaller NAV will result in a smaller absolute stress and hence a smaller SCR (the difference between the unstressed NAV and stressed NAV will be smaller).

eg unstressed NAV = 100
20% stress applied
stressed NAV = 80
SCR = 20
Now:
unstressed NAV = 90
20% stress applied
stressed NAV = 72
SCR = 18


Likewise with a NAV stress rises - the stress applied to a bigger NAV will result in a bigger absolute stress and hence a bigger SCR (the difference between the unstressed NAV and stressed NAV will be bigger).

eg unstressed NAV = 100
20% stress applied
stressed NAV = 80
SCR = 20
Now:
unstressed NAV = 110
20% stress applied
stressed NAV = 88
SCR = 22

Does this make sense?
Thanks
Em

 

[studentactuary15]

Hi

Yes, you are nearly there but you need to conclude what happens to the SCR component. And be careful when you say NAV stress falls - the stress applied to a smaller NAV will result in a smaller absolute stress and hence a smaller SCR (the difference between the unstressed NAV and stressed NAV will be smaller).

eg unstressed NAV = 100
20% stress applied
stressed NAV = 80
SCR = 20
Now:
unstressed NAV = 90
20% stress applied
stressed NAV = 72
SCR = 18


Likewise with a NAV stress rises - the stress applied to a bigger NAV will result in a bigger absolute stress and hence a bigger SCR (the difference between the unstressed NAV and stressed NAV will be bigger).

eg unstressed NAV = 100
20% stress applied
stressed NAV = 80
SCR = 20
Now:
unstressed NAV = 110
20% stress applied
stressed NAV = 88
SCR = 22

Does this make sense?
Thanks
Em

This all makes perfect sense - thank you. Just one last thing. If less annuities are in-force, I'd first think that the NAV would actually increase - since NAV = assets - liabilities => liabilities go down but I wouldn't expect assets to change => NAV rises.

But I assume this is not the case, I assume when there are less annuities, there will be less liabilities yes, but also less backing assets since less policies are in-force => NAV falls - is this correct?

I was thinking of it like this:
Annuity 1 => NAV = 30 - 20 = 10
Annuity 2 => NAV = 30 - 20 = 10
Annuity 3 => NAV = 30 - 20 = 10
Hence, the total NAV for annuities is 30.

Then when number of annuities fall, we only have annuity 1 and 2 => total NAV is 20.

Is this correct?

 

[Em Francis]

This all makes perfect sense - thank you. Just one last thing. If less annuities are in-force, I'd first think that the NAV would actually increase - since NAV = assets - liabilities => liabilities go down but I wouldn't expect assets to change => NAV rises.

But I assume this is not the case, I assume when there are less annuities, there will be less liabilities yes, but also less backing assets since less policies are in-force => NAV falls - is this correct?

I was thinking of it like this:
Annuity 1 => NAV = 30 - 20 = 10
Annuity 2 => NAV = 30 - 20 = 10
Annuity 3 => NAV = 30 - 20 = 10
Hence, the total NAV for annuities is 30.

Then when number of annuities fall, we only have annuity 1 and 2 => total NAV is 20.

Is this correct?

Hi
I probably wouldn't think of it as NAV per annuity as there may not be excess assets over each policy.
Instead, think about a stress being applied to a lower inforce book, and then for longevity stress the impact on the liabilities will be lower if there are less liabilities inforce.

eg liabilities before fall in NB = 100
Longevity stress of 10% = 110

Liabilities after fall in NB = 80
Longevity stress of 10% = 88

So the increase in liabilities have fallen by 20% - resulting in a lower SCR.

Hope this helps.
Thanks
Em