Hence, without knowing his exact utility function in terms of Von Neumann and Morgenstern (1944), an investor is likely to maximize the true expected utility when selecting his preferred

mean-variance efficient portfolio.

Since Equation (1') is the necessary and sufficient condition for the optimal portfolio solution [omega]* within the mean-variance framework, and Equation (1') mathematically equals (1), the unique [omega] in Equation (1) must be the optimal mean-variance efficient portfolio [omega]*.

In addition, the object of Equation (3) is the optimal mean-variance efficient portfolio for n securities rather than the market equilibrium.

In the model, when commissions are tied to returns and the reference portfolio is a

mean-variance efficient portfolio, optimal decisions by the funds would lead them closer to the efficient frontier with the ensuing benefits to the funds' affiliates.

The sampling error in estimates of

mean-variance efficient portfolio weights.

For example, the investor could use the Markowitz

mean-variance efficient portfolio approach; the Bayes-Stein shrinkage portfolio approach; or any of the 'data-and-model' approaches.

Thus, our simulation creates a situation where the market is indeed a

mean-variance efficient portfolio and all securities earn true returns in accordance with their betas.

If so, you still want to solve the mean-variance problem of figure 1, and you still want a

mean-variance efficient portfolio.

2) The term `market' here refers to the set of assets in the

mean-variance efficient portfolio.

This means that every

mean-variance efficient portfolio [[?

First, a good part of the better performance of portfolio-based models simply reflects Roll's [137] theorem: We can always construct a reference portfolio that perfectly fits all asset returns: the sample

mean-variance efficient portfolio.

From a theoretical perspective, the mean-variance framework which underlies the Sharpe-Lintner capital asset pricing model (CAPM) is predicated on certain assumptions required for rational agents to hold

mean-variance efficient portfolios.