Actuarial Funding (17) Flashcards
Purpose of Actuarial Funding
To reduce new business strain on certain types of unit-linked contracts by holding lower reserves (unit-fund)
For what kind of product design will actuarial funding be useful?
- Where (at least) one type of unit has relatively high fund management charges (used to recoup initial expenses)
- Usually no explicit initial charge, only level regular fund management charges
- surrender penalty would have to exist (at least for initial period of years)
- product may have capital and accumulation unit structure (initial premium allocated to capital units and subsequent to accumulation units)
- capital units would have higher fund management charge
The problem that would arise without Actuarial Funding
- mismatch between income and outgo by nature and timing
- large outgo at policy inception
- income received regularly over term of policy
- causing NBS
- charges are investment linked, as the are proportionate to the fund values
- therefore, amount of income received to pay for initial expenses are subject to investment risk
How does actuarial funding help
- increased positive net non-unit fund cashflows on early years’ premium allocations.
- significantly reduce the initial strain
- elimate investment risk caused by initial mismatch, since income is now in cash form
- income = premium - unit reserve (as result of allocation, and not subject to investment risk)
Conditions of actuarial funding
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- need a charging structure that has higher than normal levels of fund management charges
- Not all the future fund management charges can be actuarially funded
- unit-related surrender penalty, such that the unit reserve is not less than surrender value
- - acheived through capital / accumulation units
- - higher charges on all units
- Statutory constraints: Amount of actuarial funding that can take place
- unit fund must be contingent on death and (usually) survival for a minimum period of years
- prudently projected future net cashflows tot he insurer should remain positive (after AF)
Calculating the Actuarially funded reserves
- nature of contingent payment = discount unit fund benefits as an endowment assurance
- for a term equal to the residual survival period
- using a maximum theoretical discount rate = annual fund management charge
- required to cover ongoing expenses = discount rate < theoretical max
- where capital and acc units are used -> discount rate = charge on cap units - charge on acc units
What changes to net cashflows to the insurer occur as a result of actuarial funding?
- when premium is allocated, an increased net cashflow to the insurer will occur, because the cost of allocation has been reduced
- net cashflows during each subsequent year will be reduced since charge is based on smaller unit reserve
- net cashflow also reduced by the cost of rebuilding the unit reserve back towards face value
-** increase in cost will be spread** over all the remaining years of the funding period - on death, additional cost = face value - funded value of units
- expected death cost each year = (face value - funded value of units) * mortality rate
- on surrender, reduced net cashflow to the insurer compared with non-funded position
- profit on surrender = fund value of units - surrender value
- expected surrender profit = (fund value of units - surrender value)*surrender probability
How are the usual cashflow of management charges from the unit fund to the non-unit fund adjusted with actuarial funding
- cashflow from unit to non-unit = fully funded - actuarially funded units
- cashflow from unit to non-unit of the charge on the units
- cashflow from non-unit to unit to build up the increasing number of actuarially funded capital units required at year-end
- cashflow from non-unit when death ocures to meet the cost of excess of guarantee over units value
- cashflow to non-unit fun on surrender = fund value - surrender value
Advantages of Actuarial funding
For insurer
- Less capital needed to write new business
- Reduced cost of capital Improving profitability
- Higher volumes can be achieved without jeopardising solvency
- Reduced investment risk for company: A fixed initial expense is converted into a unit-linked expense. Which better matches the unit linked income. - MC
Disadvantages of Actuarial funding
for insurer
- Introduces mortality risk (disadvantage) and surrender risk if surrender penalty is insufficient
- Non unit reserve is bigger (disadvantage)
Advantages of Actuarial funding
for p/h
- Reduced charges (since charges based on fund, which is now smaller)
- Or larger maturity benefits
Actuarial Funding
Rationale and Formula
- Unit fund will only be required when contingent events occur.
- because liabilities are contingent, it is reasonable to hold the actuarial present value of unit-fund instead of its fully funded value
What should the maximum discount rate be?
Rate of annual fund management charge
- without discounting, company will hold assets equal to fund value
- fund management charge will be earned as interest on this amount each year
- the discount rate should be the proportion of the find management charge we wish to take advance credit for
