April 2021

[1495_sc]

Q3. vi) Why would the new approach under which free capital is lower lead to insolvency of companies?

Regarding balance sheet disruption, I understand that required capital will be much higher under new regime hence reduce free capital.

As required capital is higher, companies would have to either hold higher assets or have lower liabilities in place.

Will the need to hold higher volume of assets cause insolvency? Please help in understanding in simple terms.

 

[1495_sc]

vii) Where is it mentioned in the Core Reading that the assets are expected to earn a risk free rate only? In the solution, we have considered that while calculating non unit reserve under SII like regime, the unit fund growth rate (for calculating charges) will be same as risk free rate.

Under Solvency II valuation of assets, for assets, we assume market value. Now, if we were to discount future cashflows from these assets to arrive at assets as at valuation date, are we saying that we will use risk free yield curve for discounting?

 

[1495_sc]

Continuation of vii) Contract boundary for UL in Solvency II like regime- how is it relevant ? The question mentions that the premium is not reviewable and cannot be altered. Which other policy feature makes CB relevant?

 

[Lindsay Smitherman]

Q3. vi) Why would the new approach under which free capital is lower lead to insolvency of companies?

Regarding balance sheet disruption, I understand that required capital will be much higher under new regime hence reduce free capital.

As required capital is higher, companies would have to either hold higher assets or have lower liabilities in place.

Will the need to hold higher volume of assets cause insolvency? Please help in understanding in simple terms.

Under the new approach, required capital is higher. A company which could only just cover its required capital previously (little free capital) could perform the calculations under the new approach and find that it is now insolvent (not enough available capital to cover the new, higher required capital). It wouldn't just be able to generate more assets from nowhere to cover this immediately, it would have to raise capital somehow - which could be difficult (particularly given its financial position) and take some time.

 

[Lindsay Smitherman]

vii) Where is it mentioned in the Core Reading that the assets are expected to earn a risk free rate only? In the solution, we have considered that while calculating non unit reserve under SII like regime, the unit fund growth rate (for calculating charges) will be same as risk free rate.

Under Solvency II valuation of assets, for assets, we assume market value. Now, if we were to discount future cashflows from these assets to arrive at assets as at valuation date, are we saying that we will use risk free yield curve for discounting?

The Core Reading states that Solvency II is a 'market-consistent' valuation and describes how the projected cashflows have to be discounted using risk-free rates. It must by definition therefore be a 'risk-neutral' market-consistent valuation, whereby all assets are expected to earn a risk-free return. Hence projected future investment returns should be based on risk-free rates.

If we had to model the valuation of an asset rather than taking its market value (say, if such a market value were not readily observable or the market were not sufficiently deep / liquid / efficient to be a 'fair value') then yes, we would use risk-free rates. This makes sense: let's say we are holding an equity that has an observable and 'fair' market value. if we project forward the cashflows arising from that equity, assuming it to earn the risk-free rate, and then discount those cashflows back also at the risk-free rate, we would get back to its current market value. Hence market-consistent.

 

[Lindsay Smitherman]

Continuation of vii) Contract boundary for UL in Solvency II like regime- how is it relevant ? The question mentions that the premium is not reviewable and cannot be altered. Which other policy feature makes CB relevant?

For unit-linked business, contract boundaries will also reflect the extent to which charges are reviewable. [The Core Reading mentions that contract boundaries relate to either premiums or benefits being reviewable, and charges directly impact the benefits under UL.]

 

[1495_sc]

The Core Reading states that Solvency II is a 'market-consistent' valuation and describes how the projected cashflows have to be discounted using risk-free rates. It must by definition therefore be a 'risk-neutral' market-consistent valuation, whereby all assets are expected to earn a risk-free return. Hence projected future investment returns should be based on risk-free rates.

If we had to model the valuation of an asset rather than taking its market value (say, if such a market value were not readily observable or the market were not sufficiently deep / liquid / efficient to be a 'fair value') then yes, we would use risk-free rates. This makes sense: let's say we are holding an equity that has an observable and 'fair' market value. if we project forward the cashflows arising from that equity, assuming it to earn the risk-free rate, and then discount those cashflows back also at the risk-free rate, we would get back to its current market value. Hence market-consistent.

Alright. I revised Core Reading again to look at the relevant part. It mentions mark to model as long as it is market consistent (which is risk free, as you said)

It also mentions fair value/economic value. Fair value would definitely not be risk free if my understanding is correct? Please help.

Reference below.

If such prices (market value) are not available then mark-to-model techniques can be used – provided these are consistent with the overall market-consistent (or ‘fair value’ or ‘economic value’) approach, ie the amount at which the assets could be exchanged between knowledgeable willing parties in an arm’s length transaction.

Thank you

 

[Lindsay Smitherman]

Fair value can be proxied through a market-consistent modelling approach, and the easiest way to model a market-consistent value is to use the risk-neutral approach.

 

[1495_sc]

Alright. For exam purpose, I will keep risk neutral/market consistent approach in mind when considering value of assets which don't have a readily available market value like equity. Hope it should be fine.

 

[1495_sc]

I just came across a similar question in September 2018. Q1, part i)

Interest rates up- the solution mentions following

For the unit-linked business the impact on the charges will depend on their
form (monetary or percentage of funds). If they are percentage of funds, then
their value will be unchanged

What does this mean? I thought as interest rate increases, unit fund growth rate would also increase and charges will increase. This will reduce the non unit reserve and the discounting rate for non unit reserve also increases so that would also contribute to fall in non unit reserve.

Are we not referring to same concept in Apr 2021 and this question?

 

[1495_sc]

Same question, credit spread increase part-

An increase in spreads will reduce the value of assets. Agree.
It is likely that there are significant bonds in the annuity matching adjustment
portfolio. Definitely

Not all of the spread will feed through to the BEL discount rate under stress. Why would this hold true? MA= spread on matching assets- fundamental spread (prescribed by EIOPA). Hence, why wouldn't spread on matching assets be adjusted completely when credit spread widens?

 

[Lindsay Smitherman]

I just came across a similar question in September 2018. Q1, part i)

Interest rates up- the solution mentions following

For the unit-linked business the impact on the charges will depend on their
form (monetary or percentage of funds). If they are percentage of funds, then
their value will be unchanged

What does this mean? I thought as interest rate increases, unit fund growth rate would also increase and charges will increase. This will reduce the non unit reserve and the discounting rate for non unit reserve also increases so that would also contribute to fall in non unit reserve.

Are we not referring to same concept in Apr 2021 and this question?

Let's say that one of the charges is z% of the unit fund value.

The present value of that charge expected to be incurred in year t = current fund value x z% x (1 + i)^t / (1 + r)^t
where i is the expected return on the unit fund and r is the discount rate.

Under a risk-neutral valuation, i = r, so those terms cancel out.

Therefore if the interest rate changes, both i and r will change in the formula above, but will still cancel each other out.

So the value of those charges is unchanged.

 

[Lindsay Smitherman]

Same question, credit spread increase part-

An increase in spreads will reduce the value of assets. Agree.
It is likely that there are significant bonds in the annuity matching adjustment
portfolio. Definitely

Not all of the spread will feed through to the BEL discount rate under stress. Why would this hold true? MA= spread on matching assets- fundamental spread (prescribed by EIOPA). Hence, why wouldn't spread on matching assets be adjusted completely when credit spread widens?

Simplistically, credit spread = liquidity risk premium + default risk premium

The MA represents only the liquidity risk premium component (and even then, only approximately; normally calibrated by EIOPA to be less than a best estimate of that component, through 'overstatement' of the fundamental spreads).

If the total credit spread increased by x%, only part of that increase would be to the liquidity risk premium, the rest being taken as an increase to the default risk premium (hence the fundamental spread would also increase).

So the MA would increase by < x%.

 

[1495_sc]

Let's say that one of the charges is z% of the unit fund value.

The present value of that charge expected to be incurred in year t = current fund value x z% x (1 + i)^t / (1 + r)^t
where i is the expected return on the unit fund and r is the discount rate.

Under a risk-neutral valuation, i = r, so those terms cancel out.

Therefore if the interest rate changes, both i and r will change in the formula above, but will still cancel each other out.

So the value of those charges is unchanged.

Alright. Makes sense. At an aggregate level, although there is no impact on charges, if interest rate increases, non unit reserve would still reduce due to fall PV of expenses and PV of benefits in excess of unit fund within non unit reserve. I believe there wouldn't be any exceptions to this?

 

[1495_sc]

Simplistically, credit spread = liquidity risk premium + default risk premium

The MA represents only the liquidity risk premium component (and even then, only approximately; normally calibrated by EIOPA to be less than a best estimate of that component, through 'overstatement' of the fundamental spreads).

If the total credit spread increased by x%, only part of that increase would be to the liquidity risk premium, the rest being taken as an increase to the default risk premium (hence the fundamental spread would also increase).

So the MA would increase by < x%.

In case there isn't any matching adjustment and say credit spread increases, will it still affect the valuation (risk free) interest rate? I don't think it should because this is EIOPA prescribed; unlike matching adjustment which has a 'spread' component based on insurer's assets portfolio. Can you please confirm?

 

[Lindsay Smitherman]

Alright. Makes sense. At an aggregate level, although there is no impact on charges, if interest rate increases, non unit reserve would still reduce due to fall PV of expenses and PV of benefits in excess of unit fund within non unit reserve. I believe there wouldn't be any exceptions to this?

Yes, but be a little careful: normally we would expect a (realistic) NUR to be negative, so it would become more negative. Also the value of the benefits in excess of unit fund could change if interest rates change, beyond just the impact on the discounting.

 

[Lindsay Smitherman]

In case there isn't any matching adjustment and say credit spread increases, will it still affect the valuation (risk free) interest rate? I don't think it should because this is EIOPA prescribed; unlike matching adjustment which has a 'spread' component based on insurer's assets portfolio. Can you please confirm?

If a company does not use a matching adjustment or a volatility adjustment, then it will be using the basic EIOPA risk-free rates for discounting. If risk-free rates don't change, the discount rates for that insurer would not change.

 

[Arush]

Q1. ii)

Why increase in interest and spread only impacts the fixed interest bonds in free assets and not the other ones like property? An increase in interest would generally reduce the value of other assets as well.

And why lapses up bite for UL, understand future charges will reduce although the BEL is unfavourable in the question so could higher lapses actually lead to less unfavourable or lower BEL?

iii) Why risk-free rate of 0% results in higher undiversified SCR? The answer only taks about increase in fixed interest assets but not of other assets or impact on BEL.

 

[Lindsay Smitherman]

I struggled to find the question reference here - is this now asking about the September 2021 paper? Assuming so then:

The SCR interest rate stress is a stress to interest rates and bond yields (since the two are intrinsically linked). Remember that the SCR stresses each consider a separate risk factor in isolation. Yes, interest rate movements and property / equity movements have a relationship with each other, but this is dealt with through the correlations assumed between the individual stresses when aggregating the individual SCR risk components.

Lapses up -> future profits down -> non-unit component of BEL up -> negative impact on balance sheet. [If a cohort of UL business were expected to be unprofitable and so had a positive non-unit component of BEL, then lapses up could be favourable for that cohort (assuming that surrender value paid < BEL) - but this is a much less likely scenario.]

(iii) Re other assets: see answer in first para above. Re BEL: remember that SCR = {base assets - base BEL} - {stressed assets - stressed BEL}. Both the base BEL and stressed BEL are now calculated using the lower risk-free rates, so this lower discount rate impact largely cancels out, and the BEL impact tends to be second order to the asset impact.

 

[Arush]

Thanks and apologies, yes I am referring to sep 21.
1. I still don’t follow the explanation. Why no correlation seen for fixed bonds but only for property or equity.

2. So a negative non-UL BeL suggests profitable business? But the overall BeL is still positive ie unfavourable, so why is the business profitable?

3. Why the asset impact doesn’t cancel out? Somehow I think I’m missing the basics here. An example will be very helpful maybe.

 

[Lindsay Smitherman]

Thanks and apologies, yes I am referring to sep 21.
1. I still don’t follow the explanation. Why no correlation seen for fixed bonds but only for property or equity.

Under Solvency II, an interest rate stress is a change in the risk-free yield curve, and hence is a change in risk-free bond yields. So interest rate stress -> bond movements.