The Effect of the Assumed Interest Rate and Smoothing on Variable Annuities

Abstract

In this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant relative risk aversion preferences. We investigate the utility loss due to deviations from this. Finally, we show analytically how habit-formation-type smoothing of financial market shocks over the remaining lifetime leads to smaller year-to-year volatility in pension payouts, but to increases in the longer-term volatility.

Variability in pension products: a comparison study between The Netherlands and Denmark

“…The law Improved Defined Contribution Scheme Act (“Wet Verbeterde Premieregeling” in Dutch, abbreviated as WVP) serves as a pioneer in the movement towards a more flexible pension system. In Balter and Werker (2019), the technical impact of the assumed interest rate and of smoothing financial shocks on the expected pension payments is analysed. The remainder of the paper focusses on the DC plans.…”

“…In Figure 1, the expected pension payments for an individual who currently attains the pension age of 67 is depicted. The calculations underlying the figure are based on the Black-Scholes/Merton model and described in Balter and Werker (2019).

Figure 1.Expected pension payments.

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New Dutch pension contracts and lessons for other countries

“…The maximum annual income that can be withdrawn is determined in such a way that the expected (nominal) income level does not decline during the rest of life. This is achieved by imposing that the Assumed Interest Rate (AIR) that determines the initial payout (see Horneff et al 2010 or Balter and Werker 2016) cannot exceed the expected return on the investment portfolio. This expected return is derived from the actual allocation in risky investments and legislative assumptions on the risk premium.…”

“…The core properties of the new rules for decumulation of DC capital can be illustrated numerically. A technical explanation that contains the assumptions behind the numerical illustration is provided in Balter and Werker (2016). In this example, the interest rate is 1%, the equity premium 4%, the volatility of equity returns 20% and (for simplicity) the rather extreme survival table is used that imposes a deterministic date of death 20 years after retirement.…”