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Optimal annuity portfolio under inflation risk

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Abstract

The paper investigates the importance of inflation-linked annuities in retirement planning. Given nominal, inflation-linked, and variable annuities, as well as bonds and stocks, we search for optimal consumption and investment decisions under two different objective functions: (1) maximization of expected utility of real consumption, and (2) minimization of expected deviations from an inflation-adjusted target. When optimizing the objective, we allow for rebalancing the portfolio during retirement by buying additional annuities and by trading bonds and stocks. To find the optimal solution, we apply a multi-stage stochastic programming approach. Our findings indicate that independently of the considered objective function, real annuities are a crucial asset in every portfolio. In addition, without investing in real annuities, the retiree has to rebalance the portfolio more frequently, and still obtains a lower and more volatile real consumption.

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Notes

  1. We use British mortality tables for males based on 2000–2006 experience from UK self-administered pension schemes. Source: http://www.actuaries.org.uk/research-and-resources/documents/s1pml-all-pensioners-excluding-dependants-male-lives.

  2. We normalize the inflation index by assuming that \(I_{0}=1\).

  3. http://www.ons.gov.uk/.

  4. While in \({{\mathrm{\varvec{\xi }}}}\) realized inflation and stock returns are on a monthly basis, \({{\mathrm{\varvec{\zeta }}}}_\tau \) cumulates \(\tau \) monthly rates. The Nelson/Siegel parameter vector is the same for \({{\mathrm{\varvec{\xi }}}}\) and \({{\mathrm{\varvec{\zeta }}}}\).

  5. http://www.bankofengland.co.uk/statistics/pages/yieldcurve/default.aspx.

  6. Gilli et al. (2010) point out that estimation through OLS might be prone to a collinearity problem for certain values of \(\lambda ^i\). Therefore, we restrict \(\lambda ^i\) such that the correlation between the second and third factor loading is in the interval [\(-\)0.7, 0.7]. For nominal yields, the restriction turns out to be non-binding. For real yields, however, the optimal \(\lambda ^R\) is at the upper end of its admissible range.

  7. The analyzed historical data show that the average realized inflation rate has been higher than the break-even inflation, \({{\mathrm{\mathbb {E}}}}[rpi_t]=3.92\,\%\), which is common during the periods of relative illiquidity of inflation-linked bonds, see, e.g., Durham (2006). Nevertheless, recent years show that the inflation risk premium fluctuates around zero within \(\pm \)50 basis points, see, e.g., Christensen et al. (2010), therefore for our study we choose \({{\mathrm{\mathbb {E}}}}[rpi_t]={{\mathrm{\mathbb {E}}}}[bei]\).

  8. The inflation target range of the Bank of England is between 1 and 3 %, see http://www.bankofengland.co.uk/monetarypolicy/Pages/framework/framework.aspx.

  9. Note that the coefficients \(\alpha _t^{j,0}\) and \(\alpha _t^{j,i}\) differ for the purchases and sales.

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Authors and Affiliations

  1. DTU Management Engineering, Management Science, Technical University of Denmark, Produktionstorvet 426, 2800 Kgs., Lyngby, Denmark

    Agnieszka Karolina Konicz, David Pisinger & Alex Weissensteiner

  2. School of Economics and Management, Free University of Bolzano/Bozen, Universitätsplatz 1, 39100, Bolzano, Italy

    Alex Weissensteiner

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  1. Agnieszka Karolina Konicz
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  2. David Pisinger
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  3. Alex Weissensteiner
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Correspondence to Agnieszka Karolina Konicz.

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Konicz, A.K., Pisinger, D. & Weissensteiner, A. Optimal annuity portfolio under inflation risk. Comput Manag Sci 12, 461–488 (2015). https://doi.org/10.1007/s10287-015-0234-1

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