regular adjustments for changes in longevity. The longevity adjustments are based on periodic estimates of longevity changes in the pool of annuitants that use a particular fund (relative to the longevity expectations factored in the setting of the initial benefit payments). Except for any guaranteed benefits, the providers do not bear the longevity risk, which is shared among all annuitants. The charges for expenses and longevity vary from year to year, affecting the net RIR and annuity payments. The providers are effectively allowed to make transfers from investment income to reserves to reflect changes in longevity. The CREF annuity represents an interesting approach to the treatment of longevity risk but it is notable that neither Canada nor the United Kingdom has authorized this type of annuity.

The **traditional participating annuities** that are found in continental Europe follow a broadly similar approach. These policies are usually offered with guaranteed minimum benefits and declare annual bonuses based on the results of investment performance and longevity experience. A key variable for these policies is the profit sharing rule, which allocates annual profits between shareholders and policyholders. Once the profit allocated to policyholders is determined, it is used to calculate the bonus rate that is credited to policyholders and the share of profits that is placed in the collective bonus reserve. A smoothing mechanism is normally used in order to avoid wide fluctuations in the level of annual bonuses, but these mechanisms lack transparency and generate concerns about the equity and appropriateness of the bonus crediting policies of different providers.

**Escalating participating annuities** aim to pay bonuses that increase at a more or less stable rate and incorporate such bonuses in the guaranteed benefits once they are declared. The initial payments are lower in these policies and the bonus rate is determined by taking into account the net investment performance and longevity experience of the fund as well as the need to build adequate reserves to enable the payment of rising guaranteed benefits. Annual bonuses may be suspended if net performance is very weak and threatens to undermine the adequacy of reserves. Such policies aim to replicate the benefits paid by fixed real annuities but without committing to do so. Because of this, they do not need to have access to an ample supply of inflation-linked securities.

The **PPM unit-linked annuities** follow a different approach in calculating subsequent annual benefit payments. The Swedish Pensions Agency maintains individual accounts that record changes in account balances. The end-of-year (EOY) balance in any one year is equal to the beginning-of-year (BOY) balance less the benefit payments made during the year, plus investment income, less operating fees, plus survival credits. Survival credits in any one year are determined by multiplying the average account balance during the year (which is given by the BOY balance less half the benefit payments during the year) by the economic mortality risk for the year<sup>16</sup> . Survival credits are given by the remaining balances in the accounts of deceased annuitants in any one year and for each age cohort. The BOY balance in the following year is divided by the new appropriate annuity factor to determine the annual benefits for that year. The annuity factor is based on the AIR, which may change from year to year, and expected mortality. The use of expected mortality protects pensioners in advanced ages from the declining cell numbers, while the small number of survivors does not affect the soundness of the program.

> 16 Half the annual benefits is taken into account because payments are made on a monthly basis.

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