September 2022

[Lindsay Smitherman]

Q3, v) Can someone please help in understanding the impact of fall in interest rates to the proposed investment strategy with an example? Somehow I am finding it hard to understand the concept with change in economic conditions and its impact on the overall business (assets as well as liabilities).. For instance

"If the company invested assets longer than liabilities and interest rates were to fall, then the value of the assets would rise
resulting in additional capital if interest rates fall
So, with this strategy, the company would have to hold less required capital against the fall in interest rates risk"

Here they say, additional capital first but then say less capital required. So it is a bit confusing!

If assets are longer in duration than liabilities, then interest rates falling will mean that assets go up by more than liabilities go up, which basically means the company has made some profit (increased surplus) from this event and it has increased the available capital of the company. Since this event improves the capital position of the company, then it has to hold less required capital (since required capital protects against adverse events).

 

[Arush]

If assets are longer in duration than liabilities, then interest rates falling will mean that assets go up by more than liabilities go up, which basically means the company has made some profit (increased surplus) from this event and it has increased the available capital of the company. Since this event improves the capital position of the company, then it has to hold less required capital (since required capital protects against adverse events).

Thanks.

1. If the asset duration is increased, although the payout period is increased, doesn't the payout itself reduce so that the PV is still the same? Example, say 5% interest 10-year bond of 1000 would give roughly 50 per year and if the duration is increased to 20-years then the bond interest would halve to 2.5%? My point is that the initial invest of 1000 would remain just the duration is being increased and this might result in lower payouts to match liabilities. Or am I missing something here?

2. How does the available capital impact the required capital? If I look from a calculation point of the required capital, say of SCR, my understaning is that its derived by stressting the risk driver which usually would be claims. So where does the available capital come into the overall picture here?

 

[Lindsay Smitherman]

1. If the asset duration is increased, although the payout period is increased, doesn't the payout itself reduce so that the PV is still the same? Example, say 5% interest 10-year bond of 1000 would give roughly 50 per year and if the duration is increased to 20-years then the bond interest would halve to 2.5%? My point is that the initial invest of 1000 would remain just the duration is being increased and this might result in lower payouts to match liabilities. Or am I missing something here?

If we are holding 1000 in bonds and we sell them to buy bonds of a longer duration, we will still have (roughly) 1000 in bonds (in reality, a little less due to transaction costs). If our liabilities have a present value of 1000 and everything goes the way it is expected to in that valuation, then we still have enough bonds to meet those liabilities (ignoring the dealing costs).

 

[Arush]

If we are holding 1000 in bonds and we sell them to buy bonds of a longer duration, we will still have (roughly) 1000 in bonds (in reality, a little less due to transaction costs). If our liabilities have a present value of 1000 and everything goes the way it is expected to in that valuation, then we still have enough bonds to meet those liabilities (ignoring the dealing costs).

What about the matching concept though? Although the PV of assets = PV of liab, the expected liab outflow should also be matched by asset at each duration, isn't it? And with longer duration, the asset income available at each duration reduces, isn't it?

 

[Lindsay Smitherman]

2. How does the available capital impact the required capital? If I look from a calculation point of the required capital, say of SCR, my understaning is that its derived by stressting the risk driver which usually would be claims. So where does the available capital come into the overall picture here?

If required capital is determined using a VaR approach (as it is under Solvency II), then required capital for a given stress = {'base' available capital} minus }available capital under that stress}. [This is explained for Solvency II on page 18 of Chapter 10]

Also note that the risk driver will not always be 'claims' - it will depend on the stress (eg could be investment returns, expenses).

 

[Lindsay Smitherman]

What about the matching concept though? Although the PV of assets = PV of liab, the expected liab outflow should also be matched by asset at each duration, isn't it? And with longer duration, the asset income available at each duration reduces, isn't it?

The differing duration only matters when the stress is applied.

 

[ahtohallan]

It isn't the excess over BEL that would be deducted, it is the excess over asset share.

The asset share of an individual policy is the amount of money that the company has accumulated in respect of that policy. If it pays a death claim out on that policy which is higher than the asset share, it has used up more money than it was holding for that policy. That money has to come from somewhere, so the company may decide to charge it across all of the other WP policies. This is done by deducting a 'cost of life cover' charge from asset shares that is based on actual mortality experience.

Alternatively, the company could base its 'cost of life cover' charge deduction from asset shares on a notional (or 'smoothed') mortality rate. Then the extent to which actual experience is worse or better than that rate would fall to the estate.

Hi there,

When the cost of life cover is charged to the inforce asset shares, the overall CoG increase because the asset share at claim will now be lower than the guarantee at the point of claim. Does this increase in the overall guarantee lead to a further CoG charge to the asset shares?
I am trying to understand the relationship between the CoG that must be deducted from AS or estate (if AS< guarantee) and the charge to the asset shares for CoG. Please could this be explained?

Thank you!

 

[Lindsay Smitherman]

Yes, there is an element of circularity here. So the company might set the charge by modelling it as being a variable within the cost of guarantee projection / calculation, then solving to give the charge that equates to the expected guarantee cost within the model (and so the model would automatically take into account the impact that you describe).

However, bear in mind that what we are talking about here is making a reasonable deduction of charges from asset shares so that they are expected to broadly cover the actual cost of guarantees as and when such guarantees bite, and this will only ever be an approximation - so the company probably wouldn't over-engineer it.

 

[1495_sc]

Yes that's right - but spread risk is higher because there is no matching adjustment allowed in B, so a widening in credit spread would reduce the value of assets whilst the value of the BEL would remain unchanged.

The point about counterparty risk is really just saying that: if the company keeps all the business in Country A, there is no reinsurance in place. If it reinsures the business into the new subsidiary in Country B, there is now an (internal) reinsurance arrangement in place, which increases risk.

Regarding counterparty risk- will this not be higher for Country A as it is reinsuring its liabilities? Or would it be same for both countries? This seems like a very high level comment as I believe that both countries will be exposed to internal default risk.

 

[Lindsay Smitherman]

Yes I agree, I think it is just intended as a high-level comment: if the reinsurance goes ahead, there will be more counterparty risk relating to the operations as a whole (it's effectively a 'group risk' since it is an internal reinsurance arrangement).

 

[Arush]

Q1. iii) Why interest rate risk is future yields being lower than expected? The increase in BEL would be offset by the increase in assets. I thought it might be there other way around ie rise in future yields would reduce the BEL but reduce the assets more assuming there will be some assets as part of own funds. And in part v) it is mentioned that the interest risk is lower in B because of lower rates, so both statements sound conflicting.

In general, I am not able to follow the impact of interest rate and credit spread risks on SCR magnitude as well as in what direction the stress should be applied. If possible, a simple example will help.

 

[Arush]

The examiner remark says Q1. "(vi) This was answered best by candidates that recognised that the risk margin only covers non-hedgeable risks and that the reduction in interest rate would reduce the discounted value."

How would reduction in interest rate reduce the discounted value? is it a typo?

 

[Em Francis]

Q1. iii) Why interest rate risk is future yields being lower than expected? The increase in BEL would be offset by the increase in assets. I thought it might be there other way around ie rise in future yields would reduce the BEL but reduce the assets more assuming there will be some assets as part of own funds.

It is likely that the duration of the annuity liabilities is longer than that of available assets and so an interest rate fall will increase liabilities by more than the increase in assets.

And in part v) it is mentioned that the interest risk is lower in B because of lower rates, so both statements sound conflicting.

As the yield curve is higher under Company B, then the liabilities are lower in value so any stress will be smaller, hence lower risk.

 

[1495_sc]

Spread risk stress = widening of spreads
Higher spread -> higher matching adjustment (not by the full amount, but part of it)
So in Country A, could increase the matching adjustment under the stressed conditions, increasing the discount rate and reducing the BEL
In Country B, are not able to do this
Therefore higher spread risk component in Country B

Hi,

Sep'22 paper-

Just to clarify again, generally speaking, spread risk stress in Solvency II is a widening of spread as it reduces value of assets. It is onerous for insurer as it reduces value of corporate bonds. No impact on BEL. Hence, it increases SCR.

Now, if an insurer has applied matching adjustment, and we consider the same spread risk stress, BEL will also fall as higher MA will be applied and hence BEL is subject to higher discounting.

In this case, increase in SCR will be lower as both assets and liabilities will be impacted and the stressed net assets is higher.

Now in Apr'19 paper, Q1 iii) c), are we saying that credit spread widening is a "scenario" i.e sensitivity. Hence, is the spread risk stress (Where we are assuming that credit spread has widened) is applied to situation when credit spread has already widened (in reality)?

Hence, the value of corporate bonds has reduced due to this "Scenario" and the spread risk stress is applied to a lower value of corporate bonds. This in turn leads to a lower SCR.

Please confirm. Thank you so much!

 

[1495_sc]

Further, in Apr'19 question, shouldn't we again consider the impact of increase in credit spread risk on BEL as Matching Adjustment is applied by the company? In this case, market value of corporate bonds falls and BEL reduces. I believe we can assume that the "unstressed BEL" reduces due to higher MA. What about the "Stressed BEL"? Will it be subject to further stress as seen in the original stress outlined above (Sep22 paper) or will it remain same as the reduced unstressed BEL.
If stressed BEL= reduced unstressed BEL, the SCR will be only affected by fall in corporate bonds hence fall in SCR.

 

[1495_sc]

In this case, increase in SCR will be lower as both assets and liabilities will be impacted and the stressed net assets is higher.

Here, there is no change in value of unstressed assets and liabilities. The SCR impact is only driven by a change in stressed assets and stressed BEL.

 

[1495_sc]

Can someone please help with these queries?

 

[Em Francis]

Hi,

Sep'22 paper-

Just to clarify again, generally speaking, spread risk stress in Solvency II is a widening of spread as it reduces value of assets. It is onerous for insurer as it reduces value of corporate bonds. No impact on BEL. Hence, it increases SCR.

It reduces value of backing assets. There will be an impact on BEL if impact MA, as you say below.

Now, if an insurer has applied matching adjustment, and we consider the same spread risk stress, BEL will also fall as higher MA will be applied and hence BEL is subject to higher discounting.

In this case, increase in SCR will be lower as both assets and liabilities will be impacted and the stressed net assets is higher.

yes

Now in Apr'19 paper, Q1 iii) c), are we saying that credit spread widening is a "scenario" i.e sensitivity. Hence, is the spread risk stress (Where we are assuming that credit spread has widened) is applied to situation when credit spread has already widened (in reality)?

Hence, the value of corporate bonds has reduced due to this "Scenario" and the spread risk stress is applied to a lower value of corporate bonds. This in turn leads to a lower SCR.

yes

Please confirm. Thank you so much!

 

[Em Francis]

Further, in Apr'19 question, shouldn't we again consider the impact of increase in credit spread risk on BEL as Matching Adjustment is applied by the company? In this case, market value of corporate bonds falls and BEL reduces. I believe we can assume that the "unstressed BEL" reduces due to higher MA.

Yes, but the fall in corporate bonds would reduce by more than the fall in the BEL.

What about the "Stressed BEL"? Will it be subject to further stress as seen in the original stress outlined above (Sep22 paper) or will it remain same as the reduced unstressed BEL.
If stressed BEL= reduced unstressed BEL, the SCR will be only affected by fall in corporate bonds hence fall in SCR.

Not sure I fully understand the question, why would it be subject to further stresses?

 

[1495_sc]

Yes, but the fall in corporate bonds would reduce by more than the fall in the BEL.

Not sure I fully understand the question, why would it be subject to further stresses?

In usual credit spread stress, we agree that in the presence of MA, the stressed assets and stressed BEL is impacted. No impact on unstressed net assets. (1)

In the widening of spreads scenario, unstressed corporate bonds will fall and unstressed BEL will fall (due to MA).

Now, if we consider credit spread SCR stress, stressed corporate bonds will be lower than stressed corporate bonds in base scenario as the insurer has less exposure to corporate bonds.

As unstressed BEL also reduces, stressed BEL will be lower than stressed BEL in base scenario as insurer has lower BEL in this scenario.

Hence, the unstressed BEL is impacted. Stressed BEL is not simply equal to unstressed BEL, it is subject to further shock due to "widening of spread stress" [as seen in (1) above].
The combined impact is a lower SCR requirement due to impact on both assets and BEL. The SCR in this scenario would be slightly higher if there was no MA as BEL would not be impacted then.

Can you please confirm?

 

[Em Francis]

If the unstressed BEL is reduced then the impact of any stresses will reduce and hence the SCR will reduce.