In the paper, we consider three quadratic optimization problems which are
frequently applied in portfolio theory, i.e, the Markowitz mean-variance
problem as well as the problems based on the mean-variance utility function and
the quadratic utility.Conditions are derived under which the solutions of these
three optimization procedures coincide and are lying on the efficient frontier,
the set of mean-variance optimal portfolios. It is shown that the solutions of
the Markowitz optimization problem and the quadratic utility problem are not
always mean-variance efficient. The conditions for the mean-variance efficiency
of the solutions depend on the unknown parameters of the asset returns. We deal
with the problem of parameter uncertainty in detail and derive the
probabilities that the estimated solutions of the Markowitz problem and the
quadratic utility problem are mean-variance efficient. Because these
probabilities deviate from one the above mentioned quadratic optimization
problems are not stochastically equivalent. The obtained results are
illustrated by an empirical study.Comment: Revised preprint. To appear in European Journal of Operational
Research. Contains 18 pages, 6 figure