With-profits EV

[Mbotha]

It may help to think of calculating the PVIF as follows:

Allocate assets to the reserve (this may be BEL only if the Risk Margin is allowed for in the required capital (and modelled separately) as part of EV or could be the Technical Provisions (TP) if otherwise). As an approximation to BEL, the asset share could be used plus any with-profits guarantees).

Having allocated assets, the assets and in-force business are projected forward on an actively-reviewed, broadly realistic basis.

If it is a 90:10 fund, shareholder transfers made are one-ninth of the cost of bonuses (RB and TB) and therefore projected future bonus rates are required.

The excess of projected assets over projected BEL (or TP) are the shareholder transfer each year. These transfers are discounted back at a suitable risk discount rate (RDR) and it is this that equals the PVIF component of the EV calculation.
Em

I was hoping to get some help on this but thought I'd start a new thread. I'm struggling to grasp the way it's explained above given that
PVIF = PV(shareholder cashflows) + PV(change in reserves)

My understanding is:

1. The projected assets would also include:

(charges for cost of smoothing, capital, guarantees)
- actual cost of smoothing, capital guarantees
+ (charges for expenses - actual expenses) if asset shares deduct charges for expenses
- (expenses not charges to asset shares) in the case where actual expenses are deducted from asset shares
- claims in excess of assets shares
+ investment income
+ 1/9th of the cost of future bonuses (in a 90/10 fund)
These are the shareholder cashflows that we're projecting. Is that right?

2. Future bonus rates are needed for the BEL calculation and, because shareholder transfers are 1/9th of the cost of bonuses in the BEL, this is where we'd get the last item in the list above from.

3. I'm not sure I understand how the shareholder transfers are the "excess of projected assets over projected BEL?

4. My feeling is that there would always be a PVIF component iro WP business because we're comparing shareholder cashflows with policyholder liabilities - which is not 'like-for-like' as in the case of without profits business. Is that right?​

 

[Lindsay Smitherman]

3. I'm not sure I understand how the shareholder transfers are the "excess of projected assets over projected BEL?​

Hi - yes, I agree - I don't think this is the best way to think about shareholder transfers, particularly as in a 90:10 fund you would need to take into account the fact that shareholders have only a 10% share of surpluses. It is much easier to think about WP s/h transfers in terms of 1/9 cost of bonus, assuming that we are talking about a 90:10 fund.

I'm struggling to grasp the way it's explained above given that
PVIF = PV(shareholder cashflows) + PV(change in reserves)

Although your expression here works for without-profits business, this isn't so helpful for with-profits business. A better starting point would be PVIF = PV(shareholder profits). For without-profits business, s/h profit = increase in assets minus increase in liabilities, which ties in with your expression. However, for with-profits business (assuming a 90:10 WP Fund), s/h profit = s/h transfer = 1/9 cost of bonus. The only way that the shareholders can get their hands on any profits from the WP fund is when a bonus is declared (RB) or paid out (TB), at which point they gain 1/9 of that amount. Hence PV of future shareholder profits = PV of these 1/9 cost of bonus amounts.

Therefore, in order to calculate PVIF for WP business, we need to project forward future RB declarations and future TB payments. For RB, this requires us to project forwards the benefits on which the RB declarations will be made (allowing for decrements etc), and to make assumptions about future RB rates. Such assumptions should be consistent with PRE (particularly past practice), TCF, PPFM, assumed future investment conditions etc. For each projection year, we would then calculate the cost of the RB declaration in that year, and add the discounted value of 1/9 of that cost into our PVIF.

For TB, this requires us to project forwards the asset shares, since TB for a policy that becomes a claim is calculated as (smoothed) asset share minus guaranteed benefit. This would involve projecting forwards the current asset shares, plus premiums and investment return, minus deductions for expenses and cost of life cover etc. In our projection model, every time we are assuming that a claim happens (death, surrender, maturity), the model needs to calculate what TB (if any) is paid on that claim and then 1/9 of that amount can be discounted and added into our PVIF.

If there is without-profits business written within the WP Fund, then 10% of the profits arising on that business are also attributable to the shareholder, so this should also be added into the PVIF. This can either be done explicitly (ie just add 10% of PV future profits on the without-profits business into the PVIF for the WP Fund), or by adding 100% of those profits (as they arise in each modelled period) into the projected asset shares described above, so that they then automatically become part of bonus payments and are thus allowed for in PVIF through the 1/9 cost of bonus calculations described above.

In order to complete the EV calculation for the WPF, we need to add in the shareholders' share (likely 10%) of the free surplus (or estate) within the fund. [This value would need to be adjusted to allow for any cost of guarantees biting, particularly if the EV is being calculated on a market-consistent basis.]

Hope that helps with the basic WP EV calculation approach. I will pick up your other points separately.

 

[Lindsay Smitherman]

My understanding is:

1. The projected assets would also include:

(charges for cost of smoothing, capital, guarantees)
- actual cost of smoothing, capital guarantees
+ (charges for expenses - actual expenses) if asset shares deduct charges for expenses
- (expenses not charges to asset shares) in the case where actual expenses are deducted from asset shares
- claims in excess of assets shares
+ investment income
+ 1/9th of the cost of future bonuses (in a 90/10 fund)
These are the shareholder cashflows that we're projecting. Is that right?​

As described above, normally in a 90:10 fund only the final point on that list (1/9 cost of bonus) comprises shareholder profit and would therefore be directly allowed for in the PVIF.

It may be the case that the shareholders have made an arrangement with the 90:10 WP Fund to accept charges from WP p/hs in return for the shareholders paying the actual expenses. This might, for example, be the case in a closed fund where there are concerns about the increasing burden of overheads on a per policy basis. In that case, the PVIF (which of course represents the present value of shareholder profits) would also have to include the expected present value of the excess of charges over expenses - but this is an exception rather than the normal scenario. This type of expense deal is mentioned in Section 3.1 of Chapter 22.

Normally in a 90:10 fund any excess of actual expenses (and actual cost of benefits) over what is charged to asset shares is met in the first instance by the WP Fund estate, not by the shareholders.

 

[Lindsay Smitherman]

I should also add that the course mentions another type of WP Fund arrangement, whereby policyholders gain 100% of investment surplus and shareholders gain 100% of other surplus, eg for UWP business.

The PVIF for such business would be calculated in basically the same way as it would for unit-linked business, since the shareholder profits arising in both cases will be the excess of charges received over {expenses incurred and benefits paid in excess of asset share or unit fund} [plus investment return on non-unit reserves and plus release of non-unit reserves].

 

[Lindsay Smitherman]

4. My feeling is that there would always be a PVIF component iro WP business because we're comparing shareholder cashflows with policyholder liabilities - which is not 'like-for-like' as in the case of without profits business. Is that right?​

I am not sure that I understand your point about comparing s/h cashflows with p/h liabilities, but I would agree that there will normally be a PVIF component for WP business. This is because it is generated by future bonuses, rather than under without-profits business where it is generated by the release of prudential margins in the liabilities. Future bonuses will (normally) happen, since these bonuses are generated by future investment returns and by having held back the distribution of some of the surplus that has already arisen.

 

[Mbotha]

Lindsay, thank you so so much! This really helps.

Therefore, in order to calculate PVIF for WP business, we need to project forward future RB declarations and future TB payments. For RB, this requires us to project forwards the benefits on which the RB declarations will be made (allowing for decrements etc), and to make assumptions about future RB rates. Such assumptions should be consistent with PRE (particularly past practice), TCF, PPFM, assumed future investment conditions etc. For each projection year, we would then calculate the cost of the RB declaration in that year, and add the discounted value of 1/9 of that cost into our PVIF.

For TB, this requires us to project forwards the asset shares, since TB for a policy that becomes a claim is calculated as (smoothed) asset share minus guaranteed benefit. This would involve projecting forwards the current asset shares, plus premiums and investment return, minus deductions for expenses and cost of life cover etc. In our projection model, every time we are assuming that a claim happens (death, surrender, maturity), the model needs to calculate what TB (if any) is paid on that claim and then 1/9 of that amount can be discounted and added into our PVIF.

So, we basically project the benefits part of the WP BEL (= benefits + expenses - premiums) and then take 1/9th of the cost of those bonuses and discount them? As is the case with the BEL, we would thus need a stochastic model for projecting the asset shares - is that right?

In order to complete the EV calculation for the WPF, we need to add in the shareholders' share (likely 10%) of the free surplus (or estate) within the fund. [This value would need to be adjusted to allow for any cost of guarantees biting, particularly if the EV is being calculated on a market-consistent basis.]

Am I right in saying that an alternative approach would be to model bonus rates (for the PVIF) that are higher - i.e. Bonus rates that are such that the aim is to exstinguish the estate?

How would we allow for the releases in risk margin in your PVIF approach outlined above (i.e. If the RM isn't included in the required capital component of the EV)?

I am not sure that I understand your point about comparing s/h cashflows with p/h liabilities

Don't worry about this, you've cleared up my confusion - thank you!

I should also add that the course mentions another type of WP Fund arrangement, whereby policyholders gain 100% of investment surplus and shareholders gain 100% of other surplus, eg for UWP business.

The PVIF for such business would be calculated in basically the same way as it would for unit-linked business, since the shareholder profits arising in both cases will be the excess of charges received over {expenses incurred and benefits paid in excess of asset share or unit fund} [plus investment return on non-unit reserves and plus release of non-unit reserves].

Oh, I see. So, this could be viewed in the same light as without-profits business, namely?

PVIF = PV(shareholder profits) - PV(change in reserves)
= PV (increase in assets) - PV(increase in liabilities)​

On a slightly different note, the % of fund charges modelled in the BEL (UL product) require projection of the unit fund value. Does the unit fund need to be projected stochastically (to model different investment scenarios and hence charges)? And if not, why?

Thanks again for your detailed responses!! You've really helped me!

 

[Lindsay Smitherman]

You're very welcome!

So, we basically project the benefits part of the WP BEL (= benefits + expenses - premiums) and then take 1/9th of the cost of those bonuses and discount them? As is the case with the BEL, we would thus need a stochastic model for projecting the asset shares - is that right?

It is easier to think in terms of projecting asset shares rather than the BEL, because we need to project future bonuses, which are set using asset shares.
A stochastic model would be needed in order to determine those scenarios where the guarantees bite (and so no TB is paid). However, a more straightforward approach would be to do the PVIF projections on a deterministic basis first, and then make an adjustment for the s/h's share of the time value of those guarantees, where this would have to be done on a stochastic (or option pricing) calculation basis. As I mentioned above, though, you could just deduct the time value of guarantees from the estate before taking 10% of it into the EV, which would give the same overall effect.

 

[Lindsay Smitherman]

Am I right in saying that an alternative approach would be to model bonus rates (for the PVIF) that are higher - i.e. Bonus rates that are such that the aim is to exstinguish the estate?

Yes - that is indeed an alternative acceptable approach. You would basically allocate ALL of the assets in the WPF into the asset shares (deducting what is needed to cover the time value of guarantees and options first, if the PVIF projection will be deterministic; also deducting assets backing without-profits business written in the fund if you are valuing these separately) and project these higher asset shares forwards. That way, the estate emerges as future bonus and the shareholder share is taken into PVIF via the 1/9 cost of bonus route. This gives roughy the same overall answer, albeit with timing differences.

How would we allow for the releases in risk margin in your PVIF approach outlined above (i.e. If the RM isn't included in the required capital component of the EV)?

The assets backing the risk margin are effectively just part of the estate: you can add 10% of the risk margin (minus a deduction for cost of holding, if appropriate) into the EV or alternatively treat it as you have suggested above and add it into asset shares in order to be distributed as bonus, with 10% of it thus emerging via the PVIF.

 

[Lindsay Smitherman]

Oh, I see. So, this could be viewed in the same light as without-profits business, namely?

PVIF = PV(shareholder profits) - PV(change in reserves)
= PV (increase in assets) - PV(increase in liabilities)​

Yep - you've got it

 

[Lindsay Smitherman]

On a slightly different note, the % of fund charges modelled in the BEL (UL product) require projection of the unit fund value. Does the unit fund need to be projected stochastically (to model different investment scenarios and hence charges)? And if not, why?

No it doesn't need to be modelled stochastically because the distribution of outcomes is (broadly speaking) symmetric. If you projected the unit fund forward stochastically over 10,000 simulations and took the average charge across the 10,000 simulations, it would be the same as the charge that would be obtained on the average investment return. So a deterministic projection (using the average investment return) would give you the same result - hence no need for a stochastic approach.

Stochastic modelling adds value where the outcome is asymmetric, such as for a guarantee. On a deterministic projection using the average expected future investment return, the cost of a guarantee which is currently out-of-the-money would be zero. On a stochastic projection, there would still be a zero cost for the majority of the simulations, but a positive cost under some of them (those with poorer investment returns). So the average across all simulations is non-zero, hence giving a different result than under a deterministic run.

 

[abcdeqwer]

Hello, thanks a lot for the discussion in this thread - very helpful for my understanding of WP and EV.

Just a bit unclear about how this ties in with the EV under Solvency II. From page 12 of chapter 18 (EV) of the course notes, it says (in relation to with-profits):

"Even where no prudential margins are expected to emerge on a supervisory valuation basis, the insurance company may still determine a PVIF in relation to future shareholder transfers in respect of with-profits business to the extent that these are not already allowed for within 'own funds' (e.g. may include the value of shareholder transfers in relation to a future distribution of the estate which has not yet been formally approved by the regulator)"

Based on the replies above, it seems like the helpful way to think about PVIF for WP is in terms of PV(shareholder profits), where shareholders get 1/9 the cost of bonus (hence we need to project forwards the asset shares, benefits etc to obtain the future bonus cashflows).

So I'm a little confused: could I understand how future shareholder transfers can be allowed for in the 'own funds'? Are the shareholder transfers referred to in the replies above already allowed for in the own funds, such that there would be no more PVIF under SII for WP (unless there are exceptional cases of one-off distributions, for example)?

Sorry if this has been covered elsewhere in another thread too.

Thanks a lot!

 

[Lynn Birchall]

Hello

Yes, a helpful way to think about PVIF for WP is in terms of PV(shareholder profits), where shareholders get 1/9 the cost of bonus (hence need to project forwards the asset shares etc).

For Solvency II technical provisions for WP, the BEL does not include this PV(shareholder profits). To tie back to the Solvency II Core Reading, Chapter 11, page 8 says:

The BEL for with-profits business should not include the value of shareholder transfers in respect of future bonus declarations. These are not included as a liability, but should be valued separately (to the extent that such transfers relate to future discretionary benefits recognised in the BEL).

So, this separate value of shareholder transfers is already allowed for in own funds. The only reason we’d get additional WP PVIF in EV under Solvency II would be, as you say, for something such as an estate distribution not reflected in the Solvency II value.

Hope this helps
Lynn

 

[abcdeqwer]

Hi Lynn,

Thanks a lot for the quick reply! So given that the PV(shareholder profits) are already part of own funds, could I just clarify if that means that most of the discussion betwen Mbotha and Lindsay (i.e. those about the 'normal' RB and TB distributions, save for the parts on estate) is not exactly applicable under SII, where WP PVIF would only arise for something like estate distributions?

I am not sure that I understand your point about comparing s/h cashflows with p/h liabilities, but I would agree that there will normally be a PVIF component for WP business. This is because it is generated by future bonuses, rather than under without-profits business where it is generated by the release of prudential margins in the liabilities. Future bonuses will (normally) happen, since these bonuses are generated by future investment returns and by having held back the distribution of some of the surplus that has already arisen.

I still can't exactly wrap my head around this concept and how it ties in with what Lindsay mentioned (in bold) above. I am guessing it's something along the lines of 'normal, expected RB/TB is already reflected in own funds, so only the unexpected / yet to be approved distributions will end up in PVIF.' Am I getting the correct idea here?

Thanks once again for your help.

 

[Lindsay Smitherman]

Hi - let me try to untangle this a bit more, although I realise that this runs the risk of making it sound more complicated. This is a tricky area ...

In terms of the original post, what we were getting at was:
- For without-profits business, PVIF = release of prudential margins in reserves. So if there are no prudential margins, PVIF = 0.
- For with-profits business, PVIF = PV future shareholder transfers.

For 90:10 additions to benefits business, for example, future s/h transfers are generated by future declared / paid bonuses. 10% of profits go to shareholders and 90% go to policyholders through bonuses. So shareholder transfer = 1/9 cost of bonus. So PVIF for with-profits business is generated by future bonuses, not by the release of prudential margins.

Hence, even though we have a basic best estimate liability under Solvency II, there are still future shareholder transfers that have to be included in the EV for with-profits business: those that are generated by future bonuses.

That's what the discussion back in 2018 was covering.

As Lynn says, PV future s/h transfers (in relation to future bonuses that are valued within the BEL) has to be calculated under Solvency II but is not part of BEL or TP. Therefore, by definition, it is part of own funds. Let's call this PVST.

For a 90:10 WP fund, we have to be careful when valuing own funds (within that fund) for EV purposes. 100% of the part of own funds that is the PVST should be included in the EV, since fully shareholder-owned. But potentially only 10% of the remainder of own funds (within the 90:10 WP fund) should be counted within EV: this is basically the shareholders' share when this 'estate' is eventually distributed. So the two parts do need to be considered separately. A company might include both the PVST and the latter in its 'PVIF' as part of its EV presentation, or it might choose a different presentation.

For example, a Solvency II company might fundamentally determine its EV as 'own funds + some PVIF-type adjustments'. In which case, the PVST part might be presented as part of the 'own funds' component and s/h transfers generated from distribution of the estate might be treated in the 'some PVIF adjustments' component. Or they might both be included in the 'own funds' bit (albeit with different multipliers).

So the bullet point you are referring to is basically saying:
- If you are a Solvency II company, you already have a calculation for the PVST in relation to {the future bonuses expected to be declared / paid out as per what is included in the BEL} so you can just add that into the EV
- But then don't forget to include the value of future shareholder transfers that aren't included within PVST, particularly the shareholders' share of a future estate distribution ... and you might include that in your PVIF

Apologies if that sounds more complicated, but bear in mind that there aren't 'rules' as such about what goes where. This is about what might be included in the PVIF.

 

[abcdeqwer]

Thank you so much Lindsay (and Lynn)! That was incredibly helpful.