Mean-variance Inefficiency Of CRRA And CARA Utility Functions For Portfolio Selection In Defined Contribution Pension Schemes

The authors 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) they first find the efficient frontier of portfolios in the Black-Scholes financial market. Then, using standard stochastic optimal control they find the optimal portfolios derived via expected utility for popular utility functions. As a main result, they prove that the optimal portfolios derived with the CARA and CRRA utility functions are not mean-variance efficient. As a corollary, they prove that this holds also in the standard portfolio selection problem.