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

  • Elena Vigna

    ()

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

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    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.

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    Paper provided by Center for Research on Pensions and Welfare Policies, Turin (Italy) in its series CeRP Working Papers with number 89.

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    Length: 40 pages
    Date of creation: Sep 2009
    Date of revision:
    Handle: RePEc:crp:wpaper:89
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