Chapter 17

Question 1

What is the primary purpose and rationale behind using actuarial funding for unit-linked life insurance contracts?

Answer 1

◦ To reduce new business strain: Actuarial funding is a technique that enables life insurance companies to hold lower reserves for unit-linked contracts, thereby reducing the new business strain.
◦ To match cashflows with expenses: It allows the company to swap high future fund management charges for a capitalised sum early in the policy’s life, more closely matching the cashflows obtained from the policy with the incidence of its expenses.
◦ To anticipate future charges: By anticipating future management charges, positive cashflows are brought forward, which better matches the initial expenses incurred on the policy.
◦ To reduce cost of capital: This technique can reduce the cost of capital required to issue the policy.

Question 2

Describe how the technique of actuarial funding works to achieve its purpose of reducing new business strain.

Answer 2

◦ Lower Initial Unit Fund: At policy inception, the company holds a smaller unit fund (reserve) than would typically be purchased for the given premium.
◦ Covering Initial Expenses: The money “saved” by holding these lower reserves is then used to cover the high initial expenses incurred on day one of the policy.
◦ Future Purchase of Units: The “missing” unit funds are subsequently purchased later on from future management charges.
◦ Credit for Future Charges: In effect, the company takes credit at inception for some of the future charges by allocating less money to the policyholder’s unit account at the policy’s start.
◦ Extra Cashflow: This process creates an extra cashflow to the non-unit fund at early policy durations, which helps to reduce the strains on this fund resulting from high initial expenses.
◦ Investment and Reinvestment: The value of actuarially funded units will be invested by the company, and the excess management charges regularly accruing will be used to purchase additional units.

Question 3

What are the necessary conditions for actuarial funding to be workable and applied effectively?

Answer 3

◦ Higher Regular Fund Management Charges: For actuarial funding to be workable, the charging structure needs to have higher (than “normal”) levels of regular fund management charge.
◦ Sufficient Fund Management Charges: There must be a sizeable quantity of fund management charges available to pre-fund, making the technique worthwhile.
◦ Charging Structure Types: This can be achieved in two main ways:
▪ Capital/Initial Units: In the past, insurers used two types of units: “capital” or “initial” units (attracting higher management charges) and “accumulation” or “ordinary” units (with lower charges). Allocated premiums in early years would buy capital units. (Note: This approach is no longer popular due to transparency issues, but many such policies remain in force).
▪ Higher Charges on All Units: Alternatively, actuarial funding can be used on any kind of unit, provided there are substantial fund management charges.
◦ Surrender Value Limitation: The extent to which actuarial funding can be employed is restricted by the amount of any surrender penalty. It would not be prudent to hold a unit fund that is less than the amount required if the policyholder were to surrender immediately. The surrender value must not be higher than the funded value of units held.

Question 4

How are actuarially funded unit reserves calculated, and what is the significance of the Actuarial Funding Factor?

Answer 4

◦ Actuarial Present Value: Instead of the fully funded value, the actuarial present value of the unit fund is held because the liabilities are contingent upon certain events (e.g., death).
◦ Formula for Endowment Assurance: For a unit-linked endowment assurance at policy duration t, allowing for the contingency of death, the actuarial present value would be: (UF)t * A[x]:m|¬t.
▪ (UF)t represents the fully funded value of the unit fund at policy duration t.
▪ ‘x’ is the entry age, ‘m’ is the policy term.
◦ Actuarial Funding Factor: The assurance function, A[x]:m|¬t, is commonly referred to as the Actuarial Funding Factor.
◦ Discount Rate: The annual interest rate used for calculating the funding factors should approximate the amount of annual fund management charge the company wishes to pre-fund. This rate should not exceed the full fund management charge on the units and is typically less.

Question 5

Explain how actuarial funding affects the non-unit cashflows emerging in each policy year for the insurer.

Answer 5

◦ Initial Credit to Non-Unit Fund: At the outset, a cashflow equal to the difference between the fully funded value and the actuarially funded value of units is transferred from the unit fund to the non-unit fund. This is (UF)₀ * {1 - A[x]:m|¬₀}.
◦ Adjusted Management Charges: The usual cashflow of unit management charges from the unit fund to the non-unit fund is adjusted.
◦ Net Cashflow from Unit Fund: A net cashflow will emerge from the unit fund on allocation of each premium equal to the difference between the premium paid and the actuarially funded value of the units purchased.
◦ Ongoing Cashflow Adjustments:
▪ A cashflow from the unit fund to the non-unit fund, representing the charge on the units.
▪ Followed immediately by a cashflow from the non-unit fund to the unit fund to build up the increasing number of actuarially funded capital units required at the year-end.
▪ These two items can be neatly netted off using the formula: net cashflow = (UF)t-1 * Ft-1 * (1+g) - (UF)t * Ft.
◦ Reduced Future Credits: The initial transfer (or “saving”) reduces the future management charges transferred from the unit fund to the non-unit fund, as the charge is only levied on the actual number of units purchased.
◦ Increased Death Costs: An additional liability is created on the non-unit fund. On the death of the policyholder, the amount required to make up the bid value of the unit fund to the guaranteed minimum sum assured will be larger. This expected additional death cost becomes a charge on the non-unit fund at each year-end.
◦ Surrender Cashflow: A cashflow to the non-unit fund on surrender, equal to any excess of the value of units actually held by the company over the surrender value granted.