Variable Annuities in the Dutch Pension System

The risk-return trade-off for variable annuities in the retirement phase.

Recently, the Dutch senate passed a law that enables retirees to invest their pension wealth in risky assets. Before that law it was compulsory to convert pension wealth at retirement in a life-long fixed annuity. Under the new law, life-long variable annuities are allowed as well.

In the present paper we study the risk-return trade-off for variable annuities, focusing in particular on the choice of the assumed interest rate (AIR) and the effect of smoothing financial market shocks. We derive exact analytical expression for the distribution of pension payments at given horizons given a chosen assumed interest rate and possibly using the option to smooth financial market returns.

In particular we study the question of obtaining constant, in expected nominal terms, pension payments. In case of smoothing financial market returns that leads to the so-called BNW discount curve that we re-derive. In the setting of the new Dutch law, we translate this curve into a horizon- dependent “fixed decrease”.

The rest of this paper is organized as follows. In Section 2 we describe the Merton financial market that we consider. Section 3 considers the risk-return trade-off for variable annuities without smoothing. Subsequently, Section 4 considers the setting with smoothing of financial market shocks. Section 5 relates our paper to the Dutch institutional setting as it concerns the so-called “fixed decrease” (“vaste daling”). Section 6 concludes the paper. All numerical illustrations are based on an Excel spreadsheet that is available from the authors.

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