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On efficiency of mean-variance based portfolio selection in DC pension schemes

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  • Elena Vigna

Abstract

We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean-variance portfolio selection problem using the embedding technique pioneered by Zhou and Li (2000) and show that it is equivalent to a target-based optimization problem, consisting in the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk aversion coefficient into the easiest task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean-variance setting. We address the issue of comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of expected utility (EU). The two natural notions of Variance Inefficiency and Mean Inefficiency are introduced, which measure the distance of an optimal inefficient portfolio from an efficient one, focusing on their variance and on their expected value, respectively. As a particular case, we investigate the quite popular classes of CARA and CRRA utility functions. In these cases, we prove the intuitive but not trivial results that the mean-variance inefficiency decreases with the risk aversion of the individual and increases with the time horizon and the Sharpe ratio of the risky asset. Numerical investigations stress the impact of the time horizon on the extent of mean-variance inefficiency of CARA and CRRA utility functions. While at instantaneous level EU-optimality and efficiency coincide (see Merton (1971)), we find that for short durations they do not differ significantly. However, for longer durations - that are typical in pension funds - the extent of inefficiency turns out to be remarkable and should be taken into account by pension fund investment managers seeking appropriate rules for portfolio selection. Indeed, this result is a further element that supports the use of the target-based approach in DC pension schemes.

Suggested Citation

  • Elena Vigna, 2010. "On efficiency of mean-variance based portfolio selection in DC pension schemes," Carlo Alberto Notebooks 154, Collegio Carlo Alberto, revised 2011.
  • Handle: RePEc:cca:wpaper:154
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    File URL: http://www.carloalberto.org/assets/working-papers/no.154.pdf
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    References listed on IDEAS

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    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    2. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    3. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2010. "Constrained portfolio choices in the decumulation phase of a pension plan," Carlo Alberto Notebooks 155, Collegio Carlo Alberto.
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    More about this item

    Keywords

    Mean-variance approach; efficient frontier; expected utility maximization; defined contribution pension scheme; portfolio selection; risk aversion; Sharpe ratio;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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