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Optimal portfolio choice with tontines under systematic longevity risk

Published online by Cambridge University Press:  13 July 2020

Irina Gemmo ,
Ralph Rogalla  and
Jan-Hendrik Weinert
Irina Gemmo*
Affiliation:
Chair of Integrative Risk Management and Economics, D-MTEC, ETH Zurich, Zurich, Switzerland
Ralph Rogalla
Affiliation:
Greenberg School of Risk Management, Insurance and Actuarial Science, Tobin College of Business, St John’s University, New York City, NY, USA
Jan-Hendrik Weinert
Affiliation:
Viridium Group, Neu-Isenburg, Germany
*
*Corresponding author. E-mail: igemmo@ethz.ch
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Abstract

We derive optimal portfolio choice patterns in retirement (ages 66–105) for a constant relative risk aversion utility maximising investor facing risky capital market returns, stochastic mortality risk, and income-reducing health shocks. Beyond the usual stocks and bonds, the individual can invest his assets in tontines. Tontines are cost-efficient financial contracts providing age-increasing, but volatile cash flows, generated through the pooling of mortality without guarantees, which can help to match increasing financing needs at old ages. We find that a tontine invested in the risk-free asset dominates stock investments for older investors without a bequest motive. However, with a bequest motive, it is optimal to replace the tontine investment over time with traditional financial assets. Our results indicate that early in retirement, a tontine is only an attractive investment option, if the tontine funds are invested in a risky asset. In this case, they crowd out stocks and risk-free bonds in the optimal portfolios of younger investors. Over time, the average optimal portfolio weight of tontines decreases. Introducing systematic mortality risks noticeably reduces the peak allocation to tontines.

Keywords

TontinesMortalitySystematic longevity riskRetirement planningD14E21G22J10
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 302 - 315
Copyright
© Institute and Faculty of Actuaries 2020

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