Optimal Portfolio Choice in Retirement With Participating Life Annuities

Abstract

This article derives optimal consumption, investment, and annuitization patterns for retired households that have access to German-style participating payout life annuities (PLAs), allowing for capital market risks as well as idiosyncratic and systematic longevity risks. PLAs provide guaranteed minimum benefits in combination with participation in insurers’ surpluses. Minimum benefits are calculated based on conservative assumptions regarding capital market and mortality developments, while surpluses distributed to annuitants bridge the gap between the insurers’ actual investment and mortality experiences and the projections used in pricing. Through the participation scheme, systematic longevity risk is shared between insurers and annuitants, as unanticipated longevity shocks result in benefit adjustments via the surplus mechanism. We show that the retiree draws substantial utility from access to PLAs, equivalent to 20% of initial wealth in the presence of systematic longevity risk. We also find that stochasticity in mortality rates only has minor impact on the appeal of PLAs to the retiree. Even if the interest rate guarantee is reduced to zero in adverse capital market environments, PLAs prove to provide substantial utility for retirees. Overall, the participating life annuity design produces substantial welfare gains over a no-annuity world, while being an effective setup that helps providers manage long-term risks that are difficult to hedge otherwise, such as systematic longevity risks.

ACKNOWLEDGMENTS

We thank Helmut Gründl, Raimond Maurer, Olivia S. Mitchell, and Sandy Bruszas for their helpful comments; also, we appreciate comments from participants at the Twelfth International Longevity Risk and Capital Markets Solutions Conference in Chicago, IL, as well as from an anonymous referee.

Notes

1 For a comprehensive overview of the literature on participating contracts see, for example, Jørgensen (2004), Bohnert and Gatzert (2012), and Eling and Holder (2013).

2 With respect to fixed-income investments, a typical approach in the literature on portfolio choice with annuities is to assume that bonds earn a constant real rate of return. Here, we allow for stochastic variation in fixed-income returns as these fluctuations play a major role in the surplus mechanism of the PLA. We focus on the long-term government bond yield and not on the return of a diversified bond portfolio, as the guaranteed interest rate, a central parameter in the PLA mechanics, is directly tied to the long-term yield. Moreover, we work under the simplifying assumption of normally distributed yields, as the standard approach of incorporating autoregressive yields or even a fully fledged term structure model is computationally infeasible due to the curse of dimensionality.

3 This calibration results in a small but nonzero probability for negative bond yields. In our simulation analyses we account for this by setting negative yield draws to zero.

4 More recently, yields on German government bonds have declined even further, resulting in substantial difficulties for insurers that previously sold policies with generous, irrevocable, lifelong return guarantees. These insurers currently struggle to find adequate new investment opportunities that generate returns sufficient to cover those guarantees with limited exposure to capital market risks. Despite these developments, we refrain from narrowing down our calibration period to the most recent years, as the unprecedented decline in yields was accompanied by substantial stock price increases. It is likely that these capital market developments cannot be sustained over a time period that corresponds with our long-term projection horizon.

5 Before 2016, the 60% rule was codified in the German Insurance Supervision Act (see, among others, Berdin and Gründl 2015). The revised act includes qualitatively comparable regulations without the explicit quantitative specification. For a discussion of how guaranteed interest rates in PLAs should optimally be set see Schmeiser and Wagner (2015).

Additional information

Funding

This research was supported by the Metzler Exchange Professor program.