investment assumptions to offset any under-estimation of longevity. One possible explanation for the lack of concern about potential adverse selection may well be the relatively low volume of VPA business. If demand for VPAs, i.e., if use of the annuitization option, were to increase to represent a large part of the business of providers, it is likely that policies would be adopted to prevent exposure to the adverse effects of self selection.

A low AIR implies relatively low initial payments but allows future payments to keep pace with inflation. Thus, a variable payout annuity with a low AIR may achieve the same objective as a fixed escalating annuity. This implies that the AIR should be close to the long-term real rate of interest. An AIR that is significantly lower than this level would create distortions in the pattern of real (i.e., inflation-adjusted) benefit payments among annuitants with different longevity prospects, favoring long-lived individuals at the expense of short-lived ones.

The choice of mortality table is a thorny issue in all types of annuity products. In general, annuity providers adopt conservative assumptions by factoring in projected improvements in mortality. They have a stronger incentive for this in contracts where they assume the longevity risk. It is notable that the Swedish Pensions Agency in Sweden uses a significantly more conservative mortality table for the calculation of the guaranteed benefits of the PPM participating annuities than it does for the benefit payments of both the unit-linked annuities and the regular payments of the participating annuities.

# **2.3 The Setting of Benefit Payments in Subsequent Years**

Differences arise among the different types of annuities in the setting of subsequent benefit payments. Starting with the simpler and more transparent case, the **standard unit-linked VPA** , the annual payment in year t is equal to the annual payment in the preceding year (t-1) multiplied by the ratio of (1+RIR)(t-1)/(1+AIR).<sup>13</sup> The RIR (the realized investment rate of return by the relevant fund or funds)<sup>14</sup> is determined after deducting from gross investment income the charge for expenses and longevity risk. The charge is stipulated in the contract and providers are not allowed to increase it over the life of each unit-linked contract.<sup>15</sup> Providers are required to create a mortality fluctuation reserve and to make transfers from surplus to ensure its adequacy when longevity assumptions are exceeded. They are of course free to make transfers in the opposite direction when assumptions are overstated. Any overrun (or under-estimation) of expenses affects the profits of providers. If they are offered with guaranteed minimum rates of return or guaranteed minimum benefits, then these would be used to determine the annual benefit payments. The offer of guarantees is covered by fees that are included in the stipulated annual charge. Providers are required to incorporate in their reserves the need to cover their guarantees or to use appropriate hedging facilities for their risk exposure.

The same approach in setting annual payments in subsequent years is also followed in **CREF unit-linked annuities** , but with one major difference. In CREF annuities the providers do not make a stipulated annual charge for expenses and longevity risk but are allowed to deduct from the gross investment income the actual expenses incurred in administering the contract as well as

> 13 The derivation of this simple formula is shown in Annex A.

> 14 The RIR is the realized investment return by the relevant fund. It is not the market investment rate of return, which is given by the average return of all funds in the market.

> 15 The charge for expenses and longevity risk may vary depending on the level of the AIR.

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