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Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes

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  • Elena Vigna

    (University of Turin and CeRP-Collegio Carlo Alberto, Turin)

Abstract

We consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the mean-variance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li (2000) we first find the efficient frontier of portfolios in the Black-Scholes financial market. Then, using standard stochastic optimal control we find the optimal portfolios derived via expected utility for popular utility functions. As a main result, we prove that the optimal portfolios derived with the CARA and CRRA utility functions are not mean-variance efficient. As a corollary, we prove that this holds also in the standard portfolio selection problem. We provide a natural measure of inefficiency based on the difference between optimal portfolio variance and minimal variance, and we show its dependence on risk aversion, Sharpe ratio of the risky asset, time horizon, initial wealth and contribution rate. Numerical examples illustrate the extent of inefficiency of CARA and CRRA utility functions in defined contribution pension schemes.

Suggested Citation

  • Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    • Handle: RePEc:crp:wpaper:89
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    References listed on IDEAS

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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;
    All these keywords.

    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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