17. Actuarial funding

Question 1

What is the purpose of actuarial funding?

Answer 1

• Reduce NBS on certain kinds of unit-linked contracts

Question 2

Describe the principles of actuarial funding?

Answer 2

• Method life insurance company can use to reduce size of “unit reserves” it needs to hold in respect of unit-linked business.
• Company effectively capitalises some or all of unit-related charges it expects to receive from units it has nominally allocated, with funding repaid from future charges as they are received.
• When associated with appropriate surrender penalties, enables company to:
  o Reduce financing requirements because initial expenses are
  matched in terms of time and nature.

Question 3

For what kind of product design will actuarial funding be useful?

Answer 3

• One type of unit has relatively high management charges, primarily used to recoup initial expenses
• There’d usually be no explicit initial charge …
• … just regular fund management charges
• SP would have to exist for initial period of years
• Product may have capital and accumulation unit structure with initial premium(s) allocated to capital units and …
• … subsequent premiums to accumulation units
• Capital units have much higher fund management charge
• Design not necessary …
  ….any design where fund management charges used to recoup initial E okay

Question 4

Explain the problem with this unit-linked design if actuarial funding isn’t used

Answer 4

• Mismatch between income and outgo
• Large outgo at start of policy, but income received regularly over term
• Produces large capital strain when policy sold
• Mismatch also by nature
• Fund management charges investment linked
• i.e, proportional to future fund values
• Amount of income received subject to investment risk

Question 5

How does atuarial funding reduce problems with unit-linked design?

Answer 5

• Much increased positive net non-unit fund cashflows on early years’ premium allocations
• Significantly reduces initial strain
• Eliminate investment risk caused by mismatch, income now in cash form
• Income = premium paid - unit reserve set up as a result of premium allocation which …
• … is not subject to investment risk

Question 6

What are the necessary conditions for actuarial funding to apply?

Answer 6

• Unit fund benefits must be contingent on death and usually survival for a minimum period of years
• Needs to be sufficient regular fund management charges available. The limiting condition is that, after actuarial funding, prudently projected future net cashflows to insurer remain positive
• Must be unit-related surrender penalty imposed, st.t unit reserve is not lower than surrender value payable

Question 7

How do you calculate actuarially funded unit reserves?

Answer 7

• Nature of contingent payment means we can discount unit fund benefits as endowment assurance.
• This can be done for a term equal to residual survival period.
• The maximum theoretical discount rate that can be used is the annual fund management charge.
• The requirement to cover ongoing cash outflows forces discount rate used to be lower than the theoretical maximum.
• If using capital and accumulation units are used, the rate may be the difference between the management charges on the two units.

Question 8

What changes to net cashflows to the insurer occur as a result of actuarial funding?

Answer 8

• When premium is allocated, an increased net cashflow occurs because cost of allocation has been reduced
• Cost of allocation- amount of additional unit reserve required on premium allocation
• Net cashflows to insurer during each subsequent year will be reduced because fund management charge is based on smaller unit reserve.
• Net cashflow to insurer each year will be reduced by cost of building the unit reserve back up towards face value.
• Increase in cost will be spread over all remaining years of funding period.
• On death:
  o Additional cost equal to face value less funded value of units will be
  incurred
  o Expected amount of cost in any year will be equal to this diff multiplied by the appropriate q_x
• On surrender:
  o Reduced net cashflow will be made compared to non-funded
  position.
  o Profit made on each surrender after actuarial funding, will = excess
  of funded value of units over surrender value at time of surrender.
  o Expected surrender profit per policy in force x probability of
  surrender.