Risk sharing rules for longevity risk

Impact and wealth transfers

In this paper, we consider pension plans in which actuarial gains or losses at the fund level are covered by adjustments of the accrued rights of the surviving participants. At the level of the pension fund, an actuarial loss (gain) arises if the number of participants that survived during the year is higher (lower) than expected at the beginning of the year, and/or if “best-estimate” projections of future mortality rates are adjusted downwards (upwards). It is common practice that institutes such as the Dutch Actuarial Society (AG) or Statistics Netherlands (CBS) frequently revise best-estimate projections of future mortality rates. Such updates can lead to non-negligible changes in the best-estimate value of pen- sion liabilities.

We examine mechanisms by which actuarial gains and losses that arise due to longevity risk are neutralized via adjustment of the accrued rights of the participants. If more participants survived than expected, or if best-estimates of their future survival rates are adjusted upwards, the accrued

rights of the participants are adjusted downwards so as to keep the best-estimate value of the liabilities at fund level equal. When the value of accrued rights is expressed in real terms, such adjustments can (at least in part) be implemented via conditional indexation schemes. If the adjustment is immediate and complete, the mechanism implies that the funding ratio is unaffected by longevity risk. If in- stead the effect of a mortality shock on the value of the liabilities can be spread out over a period of, say, ten years, the adjustment mechanism mitigates, but does not fully eliminate, the effect of longevity risk on the funding ratio.

The current practice regarding adjustment rules (for example, conditional indexation rules) is that the adjustment factor is the same for every participant. The impact of updates in best-estimate future mortality rates on the value of pension annuities, however, can be very different de- pending on the age of the participant. This implies that an age-independent adjustment mechanism can lead to (unin- tended) wealth transfers between generations. The benefits and drawbacks of collective systems with risk sharing be- tween generations have been discussed intensively in the past few years (see, for example, Bonenkamp et al., 2013; Chen et al., 2014; Beetsma and Bucciol, 2015). Some suggest moving to a system with individual pension accounts, while still allowing for sharing of longevity risk, or so-called “biometric risk” (see, e.g., Bergamin et al., 2014; Boelaars et al., 2014; Bovenberg and Gradus, 2014). We consider a number of rules for sharing longevity risk that differ in the ex- tent to which longevity risk is shared within or over cohorts, and investigate the impact of each adjustment rule on the accrued rights of participants, and on wealth transfers be- tween generations.

The remainder of the paper is organized as follows. In Section 2, we discuss the setup of the analysis. In Section 3, we qyuantify the effect of micro- and macro-longevity risk on the aggregate value of the liabilities of all participants risk sharing rules for longevity risk 9 belonging to a certain cohort. We then use these results in Section 4 to determine the required adjustment to accrued rights to neutralize the effect of micro- and macro-longevity risk for a number of adjustment rules that differ in the extent to which micro- and macro-longevity risk is shared within or over cohorts. In Section 5 we show the effect of the adjust- ment rules on transfers of wealth between generations, and between survivors and non-survivors within generations. Section 6 concludes.

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