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

Elena Vigna

No 108, Carlo Alberto Notebooks from Collegio Carlo Alberto

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.

Keywords: Mean-variance approach; efficient frontier; expected utility maximization; defined contribution pension scheme; portfolio selection; risk aversion; Sharpe ratio (search for similar items in EconPapers)
JEL-codes: C61 D81 G11 G23 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2009, Revised 2009
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:cca:wpaper:108

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