Actuarial Funding

[Sisyphus]

Hopefully this is not a repeat of questions already asked. I think I understand the concept of actuarial funding, but there are a few issues around which I still have questions.

Firstly page 6 of Chapter 14 suggests we use a discount rate (d) equal to the fund management charge (m). I assume (m) here will be the excess of capital unit charges over accumulation unit charges. On page 9 the assurance function is used with interest rate (i) = (m). Strictly speaking, is it not the case that d = i/(1+i)?

Second, I am not sure I understand why we need to "buy back" units/rebuild the unit fund. Isn't the whole idea of actuarial funding, that the company deducts in advance, the fees it would otherwise deduct in the future? It is not borrowing the units so I don't understand why they would need to be put back (unless the mortality basis is strengthened in future). Is the "buy back" simply a notional action, in order to allow the full remaining capital unit charge to be deducted at the end of each year?

- (The post felt incomplete without a smiley face of some sort)

 

[morrisja]

The buy back is required because the policyholder is entitled to the full value of the units not the actuarially funded value (which is considerably less initially). Actuarial funding happens behind the scenes.. policyholders don't need to know that it is being used (other than the charging structure) as it doesn't affect their position.

Normally if full value of units aren't purchased then there would be a mismatch in the unit reserve as the shortfall would have to be covered from other assets.

The reason actuarial funding doesn't cause this mismatch is that the shortfall is initially covered through the Unit Linked surrender penalty and the charge (FMC) used to generate cash for purchasing the units to remove the shortfall is also fund related.


Also I believe discount rate and interest rate are used interchangeably in ST2 (and you'll never be asked to do the calculation for actuarial funding so there's no real need to worry about it).

 

[Sisyphus]

Thanks morrisja

I'm still not completely grasping this rebuilding concept, for the following reasons:

The policyholders entitlement to the full face value of units is contingent on them either dying first, or the policy maturing. If they surrender, any shortfall is matched (or exceeded) by the surrender penalty. It is because the claim on the unit fund is contingent, that actuarial funding can be applied in the first place. In a similar way, the policyholder of a term assurance is entitled to the full sum assured, but they have to die first to 'receive' it.

For those policyholders that do die, they receive the full face value of their units. A charge is deducted from the non-unit fund to cover the resulting expected death strain. Assuming death benefits are paid at the end of the year, surely there would be no need for mortality charges to be deducted, if the unit fund shortfall was being rebuilt anyway?

Lastly, I thought that with actuarial funding, the majority of the capital unit fee is deducted in advance, and used to finance initial expenses? If the rebuilding of units is a real transaction and not a notional one, is the company not taking on an investment risk? If not, then where does the money for the rebuilding come from?

 

[morrisja]

Money for rebuilding the units:
The money for rebuilding comes from the higher FMC (either on initial units or all units). This way it is matched because the FMC is a percentage of the fund and therefore will receive all the unit growth benefits, so there is no investment risk.

How initial expenses are paid
The capital unit fee is not taken in advance to pay the initial expenses (it's not possible to do this, the cashflows still arise as if they were normal FMC). It's the fact that the product design (high FMC and unit surrender penalty) exists that allows us to use actuarial funding. The actuarial funding allows us to purchase less units and this is where we get money to fund initial expenses. The capital requirements are reduced and money that otherwise would have been used to purchase units is now used to pay initial expenses.

Why rebuild the fund - generally
The fund needs to be rebuilt as it's only reasonable to hold the present value of the unit fund. This value will approach the face value of the unit fund as the funding term elapses and the discount factor increases towards 1.

Why rebuild the fund - surrender penalties
Surrender penalties in practice only last for a finite number of years after which the fund must hold the face value of the units or be exposed to persistency risk which can be hugely unpredictable as it's a policyholder option and in theory everyone could surrender at once.

Why rebuild the fund - maturity and matching
If the policy matures then we also need to have the full value of units available to pay for the maturity. It is imprudent and against the principles of reserving to have a strain at the end of the contract. While we could (in theory) hold non unit reserves for this purpose they will not match the unit fund payout as they will not be invested in the same way. In practice we couldn't use non unit reserves for this as regulations require unit linked liabilities to be matched exactly.

Why charge for death strain
We need to charge because if someone dies then we won't get the future FMC we have used to justify holding the actuarially funded value of units (the FMC that was supposed to pay for the difference between the fully funded and actuarially funded value over time). We charge because the death benefit is higher than the value of units actually held. The units are rebuilt over a period of years, not a single year, this is why we can wait on the FMC to emerge and use it to buy units. Eventually the units will be fully funded and we won't charge anymore as the strain will be gone.

Hopefully this is starting to make sense. If it still doesn't then keep asking!

 

[Lynn Birchall]

Thanks morrisja for that great, clear explanation. Very helpful

Lynn

 

[Sisyphus]

Yes, thanks morrisja! That clears that problem up quite nicely.