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Interest rate stress on non-unit reserve value

M

mw97

Keen member
I have a question regarding the impact of an interest rate stress on the non-unit reserve under SII standard formula, and how this varies whether the reserve is positive or negative.

My understanding is that an interest rate rise would have no effect on charges, as they roll up and discount at the same rate. But expenses would be reduced as they are now discounted at a higher rate. So overall own funds would increase.

This seems to be the argument put forward in September 2018 Q1 vi: "Unit linked assets and unit liabilities are unaffected ......but projected charges may be higher as the yield curve increases ......this is offset by the increased discount rate .......but expenses are also discounted at a higher rate ......so own funds increase" . Here it looks like they have assumed a negative non-unit reserve but I'm not 100% clear on that.

However in September 21 Q1 ii they say the chosen SCR stress for interest rates would be upwards, and as part of their justification say: "for the UL business, the non-unit reserves are negative, and these will be discounted at a higher rate"

To me these seem contradictory. On one side it seems if you consider the cashflows separately, regardless of whether the NUR is positive or negative, if charges remain the same level and expenses are reduced then own funds would increase. However on the other I can see that if you took the cashflow as a whole (expenses less charges) and discounted it then the effect would depend on whether that cashflow is positive or negative.

I'd appreciate any guidance on how the impact of an interest range change is calculated for a non-unit reserve and why these answers are set out differently.

Thanks!
 
Apologies but I'm not seeing the 'contradiction' here. It seems to be different ways of discussing the same basic idea.
It would normally be the case that non-unit reserves are negative, since you would expect future charges to be sufficient to cover future expenses + excess benefits and contribute to profit.
Bear in mind also that not all charges will be expressed as a % of fund. There could, for example, be a per policy admin charge.
 
Thanks Lindsay.

The way I am interpreting the answers are:

Sep 18: An interest rate rise is good because it makes the expenses lower but the charges are kept the same.

Sep 21: An interest rate rise is bad because my positive cashflows (charge received less expenses) are now discounted at a higher rate, so are lower.

Maybe I'm missing something fundamental here but it isn't quite making sense to me how they can both be true.
 
In both questions we are basically having to justify an increase in interest rates as being the adverse SCR stress:
  • in 2018 because that's what the question states
  • in 2021 because the mismatched annuity portfolio and assets backing own funds will be the key drivers and that's the direction that will adversely impact both of those
In both cases, the impact on the non-unit part of the BEL for UL business is second order and so shouldn't be the focal point of the answer. The impact on the value of bonds held within own funds (or surplus assets) and the bonds backing annuities (particularly where we are told there is mismatching) will be the key drivers of the SCR impact.

In the 2018 solution, I agree that it does make the point that charges might be unaffected (if expressed as a % of funds) but it doesn't say that will be the case for all charges. Indeed, the full solution does point out that the impact will depend on whether charges are expressed in monetary terms or % fund. I think perhaps the confusion comes from the 2018 Examiners' Report phrase 'The value of charges less expenses will be discounted at a higher rate and this will result in a decrease in the BEL', which feels like it might be over-simplifying and trying to cover too much in one sentence. After all, we are trying to justify a positive SCR impact (as per the following solution line) and that would be driven by an increase in BEL ... or perhaps it isn't being clear enough about whether it means a decrease in absolute value terms (if negative). To the extent to which charges are expressed in monetary terms, the value of these will also reduce when the discount rate increases - and this would contribute towards increasing the BEL.

What actually happens to the NUR part of the BEL overall will depend on the balance between monetary charges, % fund charges, monetary additional benefits, % fund additional benefits and expenses within the cashflows. But this is likely going into too much detail on what is (as mentioned above) not the key SCR driver. If you look at our ASET for the 2021 question, you can see that we only cover the impacts relating to own funds and annuities in our full solution, relegating the NUR considerations to the 'Additional points' section. (There was no ASET written for 2018 papers but we would likely have done the same then.)

So what would have been important would have been to demonstrate your understanding that we need to consider both charges and expenses, and the fact that the discount rate would increase and therefore reduce present values.
 
Thanks Lindsay this is really helpful insight. I'm still not 100% clear on why in question vi it states that own funds would increase based on the interest rate increase (if the earlier statement that BEL reducing part was with reference to its absolute value then this means own funds would reduce?). But I completely take your point regarding the relative importance of this impact compared to other areas that would be affected.
 
Yeah agreed - this would have to be based on an (unstated) assumption that all charges were % fund and therefore unaffected. Since there are so many permutations around these NUR impacts, I would be inclined to focus on the line below it: credit being given for sensibly constructed arguments (which would hold whether you were considering +ve or -ve NURs).

In a way it is a shame that we don't have an ASET for this paper as we would have attempted to untangle all of this and express it a bit more clearly. On the other hand, that might have been quite hard work for us! :)
 
Apologoes , but coming up with hypothetical question.
If let's assume, the unit linked are all invested in bonds and we are required to evaluate how interest rate can be a biting scenario and lead to SCR.
FFthen is the following holds true?


If unit funds are invested in bonds and interest rate rises, then value of assets will fall. This way unit funds and the charge(which is percentage of funds) will fall.

Fall in charges lead to increase in BEL. ......(a)

Now this increased BEL (we know BEL is pv of expenses minus pv of charges) is discounted at higher interest rate .....(b)

Now,
case 1.
If the BEL is positive, then discounting will offset some of the impact seen in (a)
But overall the BEl will increase.

Case 2.
if the BEL is negative, then discounting will support the direction of impact as seen in (a)
And BEL will increase.

As BEl has ultimately increased due to rising interest rates, it will contribute to SCR.
 
Last edited:
mw97 said:
1 vi: "Unit linked assets and unit liabilities are unaffected ......but projected charges may be higher as the yield curve increases ......this is offset by the increased discount rate .......but expenses are also discounted at a higher rate ......so own funds increase
Click to expand...


How the projected cashflows for charges impacted by interest rate movement , question mentions that investment is in equity and property ?
 
prachi said:
How the projected cashflows for charges impacted by interest rate movement , question mentions that investment is in equity and property ?
Click to expand...

If a charge is expressed as a % of fund value (ie annual management charge) then we need to project forwards the unit fund value in order to determine the size of these future charges for the non-unit part of the BEL calculation. Solvency II is a risk-neutral market-consistent valuation, so all assets are expected to earn the risk-free rate. Interest rates up -> risk-free rates up -> projected returns on unit fund value up.

However, the discount rate will also increase (since discounted at risk-free rates). Since we are rolling up and discounting back at the same rates, the present value of these % of fund value charges is not impacted by any change in interest rates within the BEL calculation.
 
prachi said:
Apologoes , but coming up with hypothetical question.
If let's assume, the unit linked are all invested in bonds and we are required to evaluate how interest rate can be a biting scenario and lead to SCR.
FFthen is the following holds true?


If unit funds are invested in bonds and interest rate rises, then value of assets will fall. This way unit funds and the charge(which is percentage of funds) will fall.

Fall in charges lead to increase in BEL. ......(a)

Now this increased BEL (we know BEL is pv of expenses minus pv of charges) is discounted at higher interest rate .....(b)
Click to expand...

Yes, this all broadly sounds OK.

If the funds were invested in bonds then yes, an increase in interest rates would mean a fall in bond values and hence lower charges if these are expressed as a % of fund ... and therefore would lead to a higher BEL.

However, bear in mind that your point about the discounting is irrelevant to those charges, because the projection forward and discounting at higher rates will offset against each other, as per my post above.

The higher discount rate is only relevant to any fixed per policy charges and to the expenses. The impact overall will therefore depend on the weighting between each of the components.

Normally the non-unit part of the BEL would be expected to be negative. Higher discount rate -> smaller absolute value, ie a less negative non-unit part of the BEL, which would increase the BEL - and this supports the same direction as the other impact (as you say).
 
Lindsay Smitherman said:
If the funds were invested in bonds then yes, an increase in interest rates would mean a fall in bond values and hence lower charges if these are expressed as a % of fund ... and therefore would lead to a higher BEL
Click to expand...
Through this, we concluded that increase in interest rates cause decrease in charges used to compute.

Lindsay Smitherman said:
If a charge is expressed as a % of fund value (ie annual management charge) then we need to project forwards the unit fund value in order to determine the size of these future charges for the non-unit part of the BEL calculation. Solvency II is a risk-neutral market-consistent valuation, so all assets are expected to earn the risk-free rate. Interest rates up -> risk-free rates up -> projected returns on unit fund value up
Click to expand...
Through this, we concluded that increase in interest rate cause increase in charges.

Apologies i am still bit confused like why two things are contradictory.
 
I think you are leaving out the discounting impact here.

Lower unit fund value at start of projections -> lower % fund charges (than before the stress is applied)

All else being equal, higher interest rates in projections -> higher projected % fund charges, but this is exactly offset by the higher discount rate applied to those projected % fund charges.
 
Thanks Lindsay, I think you rightly said in conversation that impact on BEL would depend on multiple assumptions like.. NUR is positive or negative
or Fund charges are percatge or fixed....and also there are vauous type of charges as well , all these combinations result in different answers.

If question do not specify the details, shall we write the assumptions and explain our point..would that make sense to do in exam ?

Here I understand various things and trying to summarize
Eg, if we take interest rate up shock
Then
1. Assumptions is AMC are percentage of funds.

After shock BEL would decrease ( does not matter if before stress BEL was positive or negative)
- The projection of unit funds would be high so projexted charges will be high.
- these charges discounted at higher rates
- so no impact on charges
- expenses are discounted at higher rates so expense ( outgo) will fall.
- so BEL would decrease.

Case 2. Assumption is that fund charges are fixed And before stress BEL is negative
- No impact of charges from any changes in unit fund side
- BEL after shock would increase as negative BEL is is discounted at higher discounted rate and become less negative.

Case 3. Assumption is that fund charges are fixed And before stress BEL is positive.
- No impact of charges from any changes in unit fund side
- BEL after shock would decrease as positive BEL is discounted at higher discounted rate and become less positive.
 
prachi said:
If question do not specify the details, shall we write the assumptions and explain our point..would that make sense to do in exam ?
Click to expand...
Yes that might be helpful, but do be careful to keep an eye on the number of available marks, the command verb and the number of other things that would need to be covered within the solution (eg if there aren't many marks available and there are other angles that need to be covered, not a good idea to go down this particular avenue in a lot of depth and detail).
 
prachi said:
Eg, if we take interest rate up shock
Then
1. Assumptions is AMC are percentage of funds.

After shock BEL would decrease ( does not matter if before stress BEL was positive or negative)
- The projection of unit funds would be high so projexted charges will be high.
- these charges discounted at higher rates
- so no impact on charges
- expenses are discounted at higher rates so expense ( outgo) will fall.
- so BEL would decrease.

Case 2. Assumption is that fund charges are fixed And before stress BEL is negative
- No impact of charges from any changes in unit fund side
- BEL after shock would increase as negative BEL is is discounted at higher discounted rate and become less negative.

Case 3. Assumption is that fund charges are fixed And before stress BEL is positive.
- No impact of charges from any changes in unit fund side
- BEL after shock would decrease as positive BEL is discounted at higher discounted rate and become less positive.
Click to expand...

These sound broadly OK, just bear in mind that:
  • All of the above refers to just the impact on the non-unit part of the BEL, not to the BEL in total. The unit part of the BEL would fall if any of the unit funds held were invested in bonds, and this would need to be taken into consideration in the overall movement in BEL.
  • Under Case 1, the above-mentioned impact on the size of the unit funds (if some are held in bonds) would impact the size of the % fund charges, and this would have the opposite impact to what you have described, since lower fund values -> lower charges -> higher non-unit part of BEL
  • In reality, companies typically have both fixed and % fund charges in place, rather than having one or the other
 
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