The purpose of this article is to illustrate how the pension benefits a pension saver will (expect to) receive will depend on the type of pension scheme chosen. We compare three widely different pension savings products: the “traditional” with-profits scheme involving bonus entitlement (average interest rate product), a market-based Unit Link scheme and, finally, a formula based smoothed investment-linked annuity scheme – TimePension in short – which is on many points a cross between the two prior-mentioned types of savings products.The three product types mentioned above have been analysed in previous literature, but those comparisons were based almost entirely on the values of pension savings accounts at the expiry of the accumulation period. This article will include the payout phase (decumulation phase) in the analysis, enabling us to analyse the size of paid-out pension benefits themselves as well as the possibilities of adjusting these benefits periodically. Compared to earlier articles, we have also improved the underlying model for the uncertainty of the underlying financial market.The article demonstrates that expected pension benefits from the three schemes are an increasing function of the allocation to shares in the underlying investment portfolios. TimePension involves the highest allocation to shares and therefore offers, on average, the highest pension benefits, followed by the Unit Link scheme. In the third and last place comes the traditional with-profits scheme, which has a relatively low allocation to shares, but which, in return, also provides relatively safe and stable pension benefits. We also show, however, that the stability of pension benefits from a TimePension scheme is completely level with the stability of benefits from the traditional scheme. Unit Link-based pension benefits, on the other hand, vary far more, and pension savers in this product segment will experience much higher annual adjustments – in a both negative and positive direction – than savers in the other product segments.

P. LINNEMANNLinnemann P. Valuation of participating life insurance liabilities. Scand. Actuarial J. 2004; 2: 81 -104.Surrender and paid-up states are incorporated in the valuation of guaranteed benefits and payments of a level premium paying life insurance policy.We present different valuation methods and examine to what extent they avoid capitalizing and releasing future loadings which are associated with the payment of future premiums.We demonstrate how to avoid capital being required in the future to cover valuation strains. The paid-up benefit valuation method is being extended so that it does not require the premium basis to be on the safe-side of the valuation basis. We obtain a unification and integration of the level premium and paid-up valuation principles.

This paper is a continuation of and a supplement to the paper by Jørgensen & Linnemann. Both papers deal with TimePension – a (formula-based) smoothed investment-linked annuity pension scheme. Both papers compare TimePension with other pension savings products using stochastic financial simulation. TimePension as well as the financial model and simulation concept being used in both papers were introduced in the paper op cit.Jørgensen & Linnemann compare TimePension with a traditional with-profits scheme involving bonus entitlement and an investment-linked Unit Link scheme with a fixed proportion of assets invested in equities and other so-called risky assets. Here, TimePension is compared with two investment-linked life-cycle (target date) products. The focus is especially on the decumulation period, and we show that despite the fact that the life-cycle products reduce investment risk in retirement (compared with TimePension’s fixed proportional allocation of assets), the year-over-year stability in benefits provided by TimePension cannot be matched. Even though the overall investment risk on accumulated benefits is at the same level, TimePension provide year-over-year stability, also in case of sharp price changes in the financial market.Our results show that not only investment profiles define the stability of annuity benefits over time. In addition, more fundamental elements of the product design are important. The perspective on product design and development is Danish, but two of the compared products are generic life-cycle products that exist in equivalent forms in many countries. Similarly, the smoothed income annuities could also become an alternative product design in an international perspective.

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