Ch 17: Actuarial funding

Question 1

What is actuarial funding? (4)

Answer 1

1. A technique whereby life insurance companies can hold lower reserves for unit-linked contracts to which it can be applied, and thus can reduce new business strain
2. The company holds a smaller unit fund (reserve) at policy inception that would be expected to be bought for the given amount of premium, and then uses some of the future fund management charges to buy back the missing units over time.
3. By anticipating future management charges, bringing forward the positive cashflows, we produce a better match for the initial expenses.
4. Money saved can be used to cover intitial expenses.
5. Management charges should thus be greater than the actual fund management expenses.

Question 2

What are the requirements necessary for actuarial funding to work? (5)

Answer 2

1. Permitted by regs
2. Benefit contingent on death/survival
   
   • ​for minimum period of years, thus still some risk on death
3. Unit related charge
   
   • company hold less than full funded value
   • additional units purchased over lifetime (using unit related charges)
   • unit charge exactly sufficient (because charge is unit related, irrespective of any price movement)
4. Sufficient regular fund management charges
   
   • ​limiting condition is that after actuarial funding, prudently projected future net cashflow to insurer remain positive
   • shortfall capitalised in non-unit reserve
5. Unit-linked related surrender penalty
   
   • ​imposed such that unit reserve not lower than surrender value payable

Question 3

What common mechanisms can be used to implement actuarial funding? (2)

Answer 3

1. Higher fund managment charges
   
   • on all units
   • need sizeable quanity of fund management charges to pre fund
2. Capital/accumulation units (with different management charges)
   
   • capital units: attracts higher managment charge, typically allocated premiums used to buy during first few years
   • accumulation units: lower management charge, allocated premiums used to buy later on
   • however, has issues with transparency:
     
     • thus no longer really used in contract design
     • but because of long term nature, still many policies in force

Question 4

Actuarial funding factors

Answer 4

For endowment assurance at policy duration t allowing for contingency of death would be (using a suitably chosen basis):

• UF_t * A_(x+t:n-t), where
  
  • UF_t is the fully funded value of the unit fund at policy duration t
  • x is the entry age
  • n is the policy term
• Discount rate used should be proportion of fund management charge we wish to take advance credit for
  
  • considering the ability to cover renewal expenses

Question 5

What is the effect of actuarial funding on net cashflows from the unit fund? (5)

Answer 5

1. Creates extra cashflows to non-unit fund (funding factor)
   
   • to help reduce new business strains
   • net cashflow reduces since assurance factor increases with time
2. Reduces future managment charges
   
   • transferred from unit fund to non-unit fund, because charge is only levied on actual number of units purchase (which will now be less)
3. Additional charges/reduced credits
   
   • to non-unit fund will be much smaller than the additional credit as result of actuarial funding, providing AMC on units in unit fund is substantial
4. Creates additional liability on death
   
   • on non-unit fund, because death of policyholder because higher amount required to make up bid value of unit fund to guaranteed minimum sum assured
   • this expected additional death cost is a charge on non-unit fund at each year end
5. Swap high future managment charges for capitalised sum early
   
   • thus matched cashflows from policy with incidence of expenses

Question 6

Considerations to consider when applying actuarial funding? (2)

Answer 6

1. Don’t allow excess management charges in the calculation of non-unit reserves
   
   • only residual cashflows from unit fund can be counted towards future cashflow projections
     
     • full fund management charge is no longer available for this purpose
2. Unit fund should not be less than surrender value
   
   • thus, extent to which actuarial funding may be employed is restricted by amount of any surrender penalty (reduction in benefit from bid value of units) that company may impose.
   • too risky to deduct cost of additional benefit on surrender, because surrendering the policy is an option, it is quite feasible for all policies to surrender over a very short period of time.
   • would then have to find value of units almost immediately, and there’d be inadequate reserves

Question 7

Advantages of actuarial funding? (7)

Answer 7

1. Lower reserves
2. Reduce new business strain
3. Write more new business
4. More capital efficient
   
   • Charges/expenses well-matched, while also…
5. …allowing initial allocation (instead of zero allocation to match charges/expenses)
   
   • making product more marketable than if allocation was zero
6. Reduced investment/persistency risk
   
   • because charges/expenses more closely matched

Question 8

Disadvantages of actuarial funding? (5)

Answer 8

1. Regulatory restrictions
2. Can be complicated
   
   • particularly when used together with capital units
3. Issues because of complexity
   
   • reduced transparency
   • poor persistency because of selling to clients who don’t understand
   • restricts distribution channels
   • more effort required to sell
   • may restrict level of sales, depending on remuneration
4. Requires surrender penalty
   
   • which may be unattractive
5. Increase mortality risk
   
   • As sum at risk will be higher due to greater discrepency between reserves held and face value of units

(Just putting ideas out there: since FMC are higher it would be less marketable)

Question 9

Summary

Answer 9

• Flows from unit fund to non-unit fund
• Actuarially funded units cashflow of unit management charges from the unit fund to the non-unit fund will be adjusted. Calculated by (for first two points):
  
  • UF_(t-1) * F_(t-1) * (1+g) - UF_(t) * F_(t)
  • where UF_(.) is the face value of units at .
  • F_(.) is the actuarial funding factor at .
  • g is the unit growth over the year
• difference between fully and actuarially funded units
  
  • cashflow from unit fund to non-unit fund on each unit purchased
• charge on units
  
  • cashflow from unit fund to non-unit fund, followed at same time by cashflow from non-unit fund to unit fund to build up inreasing number of actuarially funded capital units required at year-end
• excess of value of units (actually held by company over surrender value granted)
• Flows from non-unit fund to unit fund
  
  • cost of excess guaranteed minimum sum assured on death
    
    • over the value of units actuallyp held by company