With-profits technical provisions

[Mbotha]

I'm struggling to understand how the technical provisions for with-profits policies are calculated.

The BEL for a with-profits product allows for both guaranteed (ie. including bonuses declared to date) and discretionary benefits (ie. future reversionary and terminal bonuses), where the BEL is calculated separately for each (according to the Solvency chapters).

• What is the significance of calculating these separately? Isn't the total BEL the sum of the two anyway?
• Ch21 pg7 states "...a bonus strategy with a greater weighting towards terminal rather than reversionary bonus will allow the company to hold lower reserves or technical provisions (due to lower guaranteed benefits)". If discretionary benefits (terminal bonuse in this case) are included in the BEL, I'm not sure I understand why this is the case?
• Ch21 pg 7 states "...as they [special reversionary bonuses] aren't included in reserves (technical provisions) until the point at which they're expected to be declared...". Again, similarly to the previous point, I don't understand why they'd be excluded if the BEL allows for discretionary benefits?
• With respect to the last two points, am I looking at it from the wrong perspective - are the suggested impacts on the risk margin rather than the BEL?

Any help would be appreciated. Thanks!

 

[Lindsay Smitherman]

Hi

You don't need to worry too much about the separation of the calculation - it is for disclosure/presentation purposes.

The discretionary benefits include both terminal bonus and future reversionary bonuses. Once declared, future reversionary bonuses will increase the guarantee under the product - and so will increase the cost of guarantee within the BEL (it is a market consistent valuation of the liabilities, so will need to include the time value of the guarantees). However, terminal bonuses are not guaranteed and so do not increase the cost of guarantee element of the BEL. Hence a bonus strategy which is more weighted towards terminal rather than (future) reversionary bonus will accrue lower additional guaranteed benefits in future. Hence the cost of guarantees under that product will be lower than if there was a higher expected weighting towards reversionary bonus, and therefore the BEL (which includes the cost of guarantees) will be lower.

A special bonus is normally a one-off which arises due to a specific situation, e.g. as a result of an estate distribution exercise. The company does not have to include anything in the BEL for such a bonus until the time at which it decides that it is going to declare one. But as soon as it decides that it is going to declare a special bonus at some point in the future, it needs to include that in its BEL.

Hope that makes things clearer? Do of course come back and post again if you need more help.

 

[ActuaryLad]

Hi

I just wanted to chip in with respect to your first bullet point.

• What is the significance of calculating these separately? Isn't the total BEL the sum of the two anyway?

Insurers must calculate the value of future discretionary benefits separately as it is a regulatory requirement under Article 25 of the Commission Delegated Regulation.

The value of future discretionary benefits is also needed from a practical perspective when calculating the SCR under the standard formula. The standard formula SCR calculation allows insurers to take credit for the loss absorbing capacity of technical provisions. (The management actions an insurer would take to reduce the impact of stress events e.g. reducing bonuses in a market crash.). The total loss absorbing capacity of technical provisions, after diversification is taken into account, is not allowed to be greater than the value of future discretionary benefits.

Thanks
Amit

 

[Lindsay Smitherman]

Thanks Amit - agreed: nice point!

Also: companies have to perform a separate calculation of the present value of shareholder transfers that relate to future (discretionary) bonus declarations, and this value then forms a separately identified part of "own funds" (as mentioned in Section 2.1 of Chapter 12). Again looking from the practical perspective, this calculation can be made easier through having a separate valuation of the future discretionary bonuses.

[Bear in mind that you are not expected to know factual points of detail that are not included in the Core Reading.]

 

[Mbotha]

Thanks so much Lindsay and ActuaryLad! This has really helped a lot.

Another thing that I'm struggling with is the relationship between reserves (BEL) and asset share as well as the relationship between assets and asset share - and the movements in these components over the duration of a WP policy. My thinking is as follows:

1. Once a policy is sold, the BEL is set up (using pricing assumptions for future discretionary bonuses?) and you would need appropriate backing assets
2. Not too long thereafter, you would have to determine the regular bonus payable (by equating projected asset share to projected maturity values in order to determine the maximum sustainable regular bonus rate)
   1. Alternatively (according to the notes), by comparing asset share to a gross premium valuation. Please can you help me understand how these two investigations are the same?
3. As time progresses and the BEL is recalculated (before having declared any bonus) you would expect surplus to arise:
   1. If all assumptions are borne in practice, surplus may arise out of assets and liabilities not being perfectly matched
   2. If not, surplus may arise from actual experience being different to expected (in the period between valuations)
   3. Surplus may also arise from changes in assumptions
   4. Ch21 pg states that "Surpluses which are expected to arise fairly regularly (eg. From releases of explicit bonus loadings on CWP business, or from a relatively stable level of investment return)..." - can you please explain how these two sources of surplus work and fit in with the above?
4. Now that we know what bonus we can pay out (point 2) and the surplus that has arisen (point 3), how do we link the two (how do they fit in with each other)?

• At some stage, regular bonus would be declared and these would be included in the BEL as a guarantee (and no longer in the discretionary element of the BEL)

1. Given the guaranteed nature, I would expect the BEL to increase (?)
2. This declared bonus would also now form part of the asset share calculation (in the cost of providing life cover component) and so would reduce the asset share (?)
3. What is the impact if we now had to repeat point 2 (and specifically point 2.1)?

• Where in this process are assets (and the inherited estate) impacted?

Any help in understanding this process would be appreciated! Thank you.

 

[Viki2010]

Hello, great topic.

So in practice if TB is decided only at maturity of the contract, how does an insurer know what to reserve for in its BEL for future discretionary benefits - TB portion?

 

[Lindsay Smitherman]

Another thing that I'm struggling with is the relationship between reserves (BEL) and asset share as well as the relationship between assets and asset share - and the movements in these components over the duration of a WP policy. My thinking is as follows:

1. Once a policy is sold, the BEL is set up (using pricing assumptions for future discretionary bonuses?) and you would need appropriate backing assets

The total BEL for a with profits policy will very basically be the asset share (which includes accrued terminal bonus) plus the cost of inherent guarantees (and with adjustment as necessary to allow for smoothing). The cost of guarantees element is typically determined using a stochastic modelling approach and will need to reflect future expected reversionary bonus (RB) declarations (which will add to future guarantees) and not just guarantees that have already built up. Therefore an assumption will need to be made about future RB rates. These are likely to be set to vary dynamically within the stochastic model, i.e. lower RB rates in the simulations which have poor investment returns.

Not too long thereafter, you would have to determine the regular bonus payable (by equating projected asset share to projected maturity values in order to determine the maximum sustainable regular bonus rate) Alternatively (according to the notes), by comparing asset share to a gross premium valuation. Please can you help me understand how these two investigations are the same?

Comparing projected asset share to projected maturity value is about comparing values as at the maturity date. Comparing asset share to a GPV is about comparing values now. They are doing the same thing, just at different points in time. [Broadly speaking, the first comparison is {asset share now + future premiums - future expenses + future investment return} v {maturity value}. The second comparison is {asset share now} v. {maturity value + future expenses - future premiums - future investment return (due to discounting)}. So they are equivalent.]

As time progresses and the BEL is recalculated (before having declared any bonus) you would expect surplus to arise:

1. If all assumptions are borne in practice, surplus may arise out of assets and liabilities not being perfectly matched
2. If not, surplus may arise from actual experience being different to expected (in the period between valuations)
3. Surplus may also arise from changes in assumptions
4. Ch21 pg states that "Surpluses which are expected to arise fairly regularly (eg. From releases of explicit bonus loadings on CWP business, or from a relatively stable level of investment return)..." - can you please explain how these two sources of surplus work and fit in with the above?

The "surplus" which we refer to when talking about bonus declaration basically arises due to the components which increase an asset share (in practice it's a little more complicated than that, but hopefully this simplification makes it easier to understand). As an asset share increases, we need to get that increase to the policyholder somehow (since the asset share represents what the policyholder is entitled to) - and the only way to do this is via bonus (either now via RB or in the future via TB). So investment return (net of charges/expenses etc) increases the asset share, generates "surplus" (in this context) and then needs to be allocated to the policyholder via a combination of regular and terminal bonus. [Asset shares increase by premiums too, of course, but these are (partly) needed to pay for the underlying guaranteed benefit, so only the "explicit bonus loading" part would fall into the "surplus" that is used for bonus distribution.]

 

[Lindsay Smitherman]

Now that we know what bonus we can pay out (point 2) and the surplus that has arisen (point 3), how do we link the two (how do they fit in with each other)?

The supportability investigations are used by companies to determine the maximum levels of RB rates that they can expect to sustain throughout the remaining lifetime of the policies, and this helps them to decide on an appropriate level - as policyholders will prefer RB rates not to change too frequently. TB rates are set using the process described in Section 5.4 of Chapter 21, i.e. basically set in order to pay out asset share. Considering the source of the "surpluses" arising would be one factor that the company would consider when deciding on its RB rate, alongside others (including the supportability investigation mentioned here). The RB allocates to the policyholder some of the "surplus" each year, the rest is allocated at the time of claim via the TB.

 

[Lindsay Smitherman]

• At some stage, regular bonus would be declared and these would be included in the BEL as a guarantee (and no longer in the discretionary element of the BEL)

1. Given the guaranteed nature, I would expect the BEL to increase (?)
2. This declared bonus would also now form part of the asset share calculation (in the cost of providing life cover component) and so would reduce the asset share (?)
3. What is the impact if we now had to repeat point 2 (and specifically point 2.1)?

• Where in this process are assets (and the inherited estate) impacted?

The BEL already includes allowance for the future bonuses, and any guarantees relating to them. Therefore, if the RB is declared at the same rate as was expected in the previous BEL calculation there would be no change (ignoring the impact of rolling forward by one period of course). If the declared RB is lower than that expected, the BEL would reduce (lower cost of guarantees) and vice versa if higher than that expected.

Yes, a declared bonus could increase the amount payable on death and hence increase the deduction made to asset share for the cost of life cover, but bear in mind that this is a relatively small amount since is multiplied by a mortality rate (or, equivalently, the amounts paid out to those who have died are spread out over the much larger number of in-force surviving policies).

If you performed another sustainability investigation then the outcome would depend on things like what the investment return had been over the period since the previous investigation. The act of declaring a RB in itself would not impact the outcome of the investigation, provided the rate is broadly in line with the sustainable rate.

Apologies but I am not quite sure that I understand your final question. The asset share represents the accumulation of assets in respect of each policy. The inherited estate increases(+)/decreases(-) as a result of investment return on the assets in which it is invested (+), any expenses/tax which the company requires the estate to support (-), charges taken from asset shares (+), enhancements to asset shares (-) and the cost of paying benefits in excess of asset share (-).

Hope that helps & sorry if I have misunderstood anything.

 

[Lindsay Smitherman]

Hello, great topic.

So in practice if TB is decided only at maturity of the contract, how does an insurer know what to reserve for in its BEL for future discretionary benefits - TB portion?

Hi Viki: asset share

 

[Viki2010]

Lindsay, so the calculation would be: BEL for discretionary benefits = Asset share?
or would Asset share = BEL for guaranteed benefits + BEL for discretionary benefits.
Or would you estimate both portions of BEL via stochstic model projections.

 

[Lindsay Smitherman]

Lindsay, so the calculation would be: BEL for discretionary benefits = Asset share?
or would Asset share = BEL for guaranteed benefits + BEL for discretionary benefits.
Or would you estimate both portions of BEL via stochstic model projections.

Hi - might be worth stepping back a bit from this and thinking about what the basic calculation is: a valuation of the expected (projected) future liabilities. The easiest way to determine the two components of a with profits BEL is to start by calculating the total BEL.

The basic calculation for the total BEL would be the present value of expected total future benefits (i.e. both those that are currently guaranteed and discretionary future benefits) + expenses - premiums. Expected total future benefits would, for a with profits product, be based on the higher of smoothed asset share and the underlying guaranteed benefits at the time of claim (e.g. at maturity). Or in other words, on smoothed asset share + cost of guarantee, with the latter being defined in terms of the excess of guaranteed benefits over asset share. Because you need to model the probability of the guarantee biting, a stochastic model would normally be used.

To calculate the BEL for guaranteed benefits only, you do the same as above but only for the guaranteed benefit element - and so you would not necessarily have to use a stochastic model. The BEL for discretionary benefits is then the difference between these two calculations.

Bear in mind that future discretionary benefits can include future reversionary bonus, which will contribute to the cost of guarantees element once declared, and that asset share covers both guaranteed benefits awarded to date and accrued (discretionary) terminal bonus. So you cannot simply split asset share & cost of guarantee elements into guaranteed & discretionary elements.

Hope that helps give a little more clarity?

[Note that the precise treatment of future reversionary bonuses within the split of guaranteed and discretionary benefits is one area of evolving industry practice under Solvency II, with different companies currently taking different approaches, so you would not be expected to have a detailed knowledge of this for the exam.]

 

[Mbotha]

Hope that helps & sorry if I have misunderstood anything.

Thanks so much, Lindsay. I think I've got it now.

 

[Mbotha]

Just to come back to this on one point...

The discretionary benefits include both terminal bonus and future reversionary bonuses. Once declared, future reversionary bonuses will increase the guarantee under the product - and so will increase the cost of guarantee within the BEL (it is a market consistent valuation of the liabilities, so will need to include the time value of the guarantees).

So, within the discretionary element of the BEL, there is no "cost of guarantee" element until the reversionary bonuses are declared at some point in future (at which point they contribute to the guaranteed element of the BEL, and we include the cost of guarantee)?

The BEL already includes allowance for the future bonuses, and any guarantees relating to them.

Or is this saying that both the guaranteed and discretionary BEL elements include a cost of guarantee - for both declared, guaranteed reversionary bonuses (guaranteed BEL) and guarantees associated with future expected reversionary bonus declarations (discretionary BEL)?

 

[Lindsay Smitherman]

Hi - yes, your second point is correct (not your first one).

The guarantees provided by the basic sum assured and regular bonuses which have been declared up to the valuation date may "bite" at the claim date, and this forms part of the (market consistent) "cost of guarantees" element of the BEL.

And then future regular bonus becomes guaranteed once declared, and this also has to be allowed for in the BEL - so further increases the "cost of guarantees" within the BEL.

Hope that helps.

 

[Mbotha]

Hi Lindsay

I have another question but relating to AWP. Sorry, this is the longest thread ever - I know!

How do we value these in terms of the BEL?

• In the case where regular bonus rates are not guaranteed, do we use the current fund value as the benefit and project this to grow at the expected bonus rate (but there's no cost of guarantee element)?
• In the case of a 0% bonus rate guarantee (i.e. no "negative growth" on premiums already invested), do we:
  • Value premiums to date in the gauranteed element of the BEL (including cost of guarantees)
  • Value expected bonus rates (subject to a minimum of zero) in the discretionary element of the BEL?

Thanks again!

 

[ActuaryLad]

Hi

How do we value these in terms of the BEL?

To answer this its worth reviewing what we already know about the calculation of the BEL. In particular:

The basic calculation for the total BEL would be the present value of expected total future benefits (i.e. both those that are currently guaranteed and discretionary future benefits) + expenses - premiums. Expected total future benefits would, for a with profits product, be based on the higher of smoothed asset share and the underlying guaranteed benefits at the time of claim (e.g. at maturity). Or in other words, on smoothed asset share + cost of guarantee, with the latter being defined in terms of the excess of guaranteed benefits over asset share. Because you need to model the probability of the guarantee biting, a stochastic model would normally be used.

The approach for an AWP product follows the same approach:

• BEL = smoothed asset share + cost of guarantees

The cost of guarantee arises when the fund value that the policyholder sees (or the death/maturity/surrender benefit if higher) is greater than smoothed asset share at the time of claim/maturity/surrender.

When calculating the cost of guarantees you should project the fund value that the policyholder sees using best estimate future bonus assumptions. This assumption should have due consideration of PRE/TCF and allow for the stochastic scenario being modelled. Any guarantees on the bonus rate are allowed for in this future bonus rate assumption. So, in your example of a "no negative growth" guarantee, you should ensure that future bonuses are floored by 0% in your projections, regardless of how poor the investment returns are in any particular stochastic scenario.

Hope this helps
Amit

 

[Lindsay Smitherman]

Hi - this sounds broadly correct, since AWP will be valued as for any other type of with-profits business.

If there are no guarantees at all, then the benefits part of the BEL will be based simply on smoothed asset share and, as you say, there is no "cost of guarantee" element. Projecting forward the smoothed asset share will allow the company to model the expected future bonuses that would be added to the current benefit.

Where (as is more typical) there is an inherent guarantee, then benefits will normally be based on the higher of the guaranteed amount and the smoothed asset share (other than at points in time when an MVR can be applied).

The benefits that have built up to date form the guaranteed element of the BEL (this is not quite the same thing as valuing "premiums to date", as it also needs to take into account bonuses declared to date and charges deducted).

The discretionary element reflects the future bonuses that are projected to be added, and most companies include both future regular and future terminal bonus in this element. Bear in mind that future regular bonuses normally add to the inherent guaranteed benefit level, and so there is an extra "cost of guarantee" part of the discretionary element of the BEL.

And finally, future premiums (and the benefits relating to them) would be allowed for in the BEL if the contract boundary has not yet been reached.

 

[gruhaa]

Hi - yes, your second point is correct (not your first one).

The guarantees provided by the basic sum assured and regular bonuses which have been declared up to the valuation date may "bite" at the claim date, and this forms part of the (market consistent) "cost of guarantees" element of the BEL.

And then future regular bonus becomes guaranteed once declared, and this also has to be allowed for in the BEL - so further increases the "cost of guarantees" within the BEL.

Hope that helps.

Hi lindsay
is the cost of guarantee you mentioned above is time value of guarantee?
suppose i did 100 simulation of asset share for a business portfolio for 1year(assuming one year is left for the business portfolio). For each simulation, payouts are determined assuming 100% of projected asset share(no smoothing) . Now in 100 simulation, 50 projected asset share are less than the guarantee built up till valuation date such that average of difference between guarantee sum assured minus projected asset shares over 100 simulation is positive.
So the bel would be the average asset share plus cost of guarantee(with one year of discounting at risk free rate).
Is my calculation right?
If yes, i have three questions:
1. should i take BEC(Bonus earning capacity) rate as reversionary bonus for the left one year, before comparing with projected asset share ?
2.the cost ot guarantee calculated above is intrinsic value of guarantee or time value of guarantee ? i believe it is intrinsic value because is the best estimate(average) . if you agree, then should time value be somewhat greater than average value, say 75th percentile of the cost distribution ?
2. given the valuation is under SII, should the asset share in stochastic model be projected under risk free rate(as it is the assumed investment return under sii) ?

 

[Lindsay Smitherman]

The cost of guarantee you mentioned above is time value of guarantee?

It means the total value of the guarantee, both intrinsic and time value.

suppose i did 100 simulation of asset share for a business portfolio for 1year(assuming one year is left for the business portfolio). For each simulation, payouts are determined assuming 100% of projected asset share(no smoothing) . Now in 100 simulation, 50 projected asset share are less than the guarantee built up till valuation date such that average of difference between guarantee sum assured minus projected asset shares over 100 simulation is positive.
So the bel would be the average asset share plus cost of guarantee(with one year of discounting at risk free rate).
Is my calculation right?

Yes except that the company would be projecting the smoothed asset share as this is what payouts are based on if the guarantee doesn't bite. [The overall BEL should also reflect cost of smoothing.]

 

[Lindsay Smitherman]

1. should i take BEC(Bonus earning capacity) rate as reversionary bonus for the left one year, before comparing with projected asset share ?

Yes, or you could assume that it is the same as in the previous year (as companies try not to change RB rates too frequently). More normally, the RB rate would be programmed into the stochastic model so that it would vary appropriately in each future projection time period according to the conditions under each simulation, and according to whatever management action rules the company would normally apply to its RB rates.