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Cyclical risk exposure of pension funds: a theoretical framework

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  • Francesco Menoncin

Abstract

We study the asset allocation problem for a pension fund which operates in a PAYG system and periodically revises its investment strategies. If the optimal amount of wealth invested in risky assets is always positive, then during the management period the optimal portfolio is constantly riskier (less risky) than Merton’s portfolio when the growth rate of workers is higher (lower) than the growth rate of pensioners. In particular, there exists a time when the risk exposure is a maximum (minimum).

Suggested Citation

  • Francesco Menoncin, 2005. "Cyclical risk exposure of pension funds: a theoretical framework," Working Papers ubs0503, University of Brescia, Department of Economics.
  • Handle: RePEc:ubs:wpaper:ubs0503
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    References listed on IDEAS

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    1. Menoncin, Francesco, 2002. "Optimal portfolio and background risk: an exact and an approximated solution," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 249-265, October.
    2. Simon Babbs & K. Nowman, 1998. "Econometric Analysis of a Continuous Time Multi-Factor Generalized Vasicek Term Structure Model: International Evidence," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 159-183, May.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2007. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," Annals of Operations Research, Springer, vol. 152(1), pages 141-165, July.
    5. Charupat, Narat & Milevsky, Moshe A., 2002. "Optimal asset allocation in life annuities: a note," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 199-209, April.
    6. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    7. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
    8. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    9. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March.
    10. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2001. "Minimization of risks in pension funding by means of contributions and portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 35-45, August.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    12. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
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    Cited by:

    1. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2010. "Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates," European Journal of Operational Research, Elsevier, vol. 201(1), pages 211-221, February.
    2. Gabay, Daniel & Grasselli, Martino, 2012. "Fair demographic risk sharing in defined contribution pension systems," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 657-669.

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