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Optimal time of annuitization in the decumulation phase of a defined contribution pension scheme

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  • Marina Di Giacinto

    (University of Cassino)

  • Bjarne Højgaard

    (Spar Nord Bank, Aalborg)

  • Elena Vigna

    (Università degli studi di Torino, CeRP and Collegio Carlo Alberto)

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    Abstract

    In this paper, we consider the problem of finding the optimal time of annuitization for a retiree of a defined contribution pension scheme having the possibility of choosing her own investment and consumption strategy. We exploit the model introduced by Højgaard - Vigna (2010), who formulate the problem as a combined stochastic control and optimal stopping problem. They select a quadratic loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We make extensive numerical investigations to address relevant issues such as optimal annuitization time, size of final annuity upon annuitization, extent of improvement when annuitization is not immediate and comparison between optimal annuitization and immediate annuitization. We find that the optimal annuitization time depends on personal factors such as the retiree's risk aversion and her subjective perception of remaining lifetime. It also depends on the financial market, via the Sharpe ratio of the risky asset. Optimal annuitization should occur a few years after retirement with high risk aversion, low Sharpe ratio and/or short remaining lifetime, and many years after retirement with low risk aversion, high Sharpe ratio and/or long remaining lifetime. Moreover, we show rigorously that with typical values of the model's parameters, a pension system where immediate annuitization is compulsory for all individuals is sub-optimal within this model. We measure the cost of sub-optimality in terms of loss of expected present value of consumption from retirement to death, and we find that the cost of sub-optimality, in relative terms, varies between 6% and 40%, depending on the risk aversion. This result gives an idea about the extent of loss in wealth suffered by a retiree who cannot choose programmed withdrawals, but is obliged to annuitize immediately on retirement all her wealth.

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    Bibliographic Info

    Paper provided by Universita' di Cassino, Dipartimento di Scienze Economiche in its series Working Papers with number 2010-08.

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    Length: 44 pages
    Date of creation: 26 Dec 2010
    Date of revision:
    Handle: RePEc:css:wpaper:2010-08

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    Postal: Dipartimento di Scienze Economiche Via S. Angelo Loc. Folcara 03043 Cassino (FR) - Italy
    Phone: +3907762994734
    Fax: +3907762994834
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    Web page: http://www.eco-giu.uniclam.it/Dipartimento/Info
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    Related research

    Keywords: De ned contribution pension scheme; decumulation phase; optimal annuitization time; cost of sub-optimality.;

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    1. Albrecht, Peter & Maurer, Raimond, 2001. "Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark," Sonderforschungsbereich 504 Publications 01-35, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    2. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
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