Gross Premium Reserves

Question 1

Why hold reserves?

Answer 1

• In many life insurance contracts, the expected cost of paying benefits increases over the term of the contract as the life ages and the probability of a claim by death increases
• the premiums which pay for these benefits are usually level. This means that premiums received in the early years of a contract are more than enough to pay the expected benefits that fall due in those early years, but in the later years the premiums are too small to pay for the expected benefits.
• It is prudent for the premiums which are not required in the early years of a contract to be set aside, or reserved, to fund the shortfall in the later years. While funds are reserved, they are invested so that interest also contributes to the cost of benefits.

Question 2

Prospective reserve

Answer 2

• The expected present value of the future outgo less the expected present value of the future income
• the company holds funds equal to the reserve and the future experience follows the reserve basis, then, averaging over many policies, the combination of reserve and future income will be sufficient to pay the future liabilities

Question 3

Valuation of the policy

Answer 3

The minimum funds the company needs to hold at any point during the term of the contract

Question 4

Retrospective reserves

Answer 4

The accumulated value allowing for interest and survivorship of the premiums received to date
less
the accumulated value allowing for interest and survivorship of the benefits and expenses paid to date

Question 5

Conditions for equality of prospective and retrospective reserves

Answer 5

If:
1. the retrospective and prospective reserves are calculated on the same basis, and
2. this basis is the same as the basis used to calculate the premiums used in the reserve calculation,
then the retrospective reserve will be equal to the prospective reserve.

Question 6

Why do the conditions for equality of the prospective and retrospective reserve rarely hold?

Answer 6

1. the assumptions that are appropriate for the retrospective calculation are not generally appropriate for the prospective calculation. The conditions experienced over the duration of the contract up to the valuation date may no longer be suitable assumptions for the remainder of the policy term.
2. The assumptions considered appropriate at the time the premium was calculated may not be appropriate for either the retrospective or prospective reserve some years later.
   • The number of people who actually die will differ from the number expected.
   • Investment returns will not exactly match what was assumed.
   • We may have had margins in our assumptions.
   • The actuary’s expectation of future interest rates may have changed

Question 7

The differences between the net premium reserve and the gross premium reserve for any conventional without-profit contract:

Answer 7

1. all expenses are ignored; and
2. the premium used in the reserve calculation is the net premium, as defined below.
   The net premium reserve is the prospective reserve, where we make no allowance for future expenses, and where the premium used in the calculation is a notional net premium. This net premium is calculated using the equivalence principle and using the same assumptions as the reserve basis, and again making no allowance for future expenses.

Question 8

Explain why a life insurance company will need to set up reserves for the single premium life annuity contracts it has sold.

Answer 8

• Benefits are paid until death i.e. an uncertain date, however the only premiums received is at outset.
• If the premium that was not required to pay benefits early in the contract were spent by the company, on dividends for example, then later in the contract, if the policyholder was still alive, the company may not be able to find funds to pay the benefits.