Markowitz used mean-variance analysis to form efficient portfolios
, namely portfolios that provide the highest returns for a certain level of risk.
Under the assumption of the economic rationality, investors choose to keep efficient portfolios
, i.e., portfolios that maximize the return for a certain level of risk or that minimize the risk for a certain level of expected return.
Markowitz  first introduced the theory of mean-variance efficient portfolios
and also gave his critical line method for finding these.
Thus, investors seeking higher return must select higher risk but less efficient portfolios
. Utility maximization is troublesome because portfolio excess return per unit of risk is not constant because of the inability to short sell the risk-free asset.
In a next step, we calculate the corresponding market risk capital charges under the standard formula as well as the internal model to identify those efficient portfolios
that are attainable for an exogenously given amount of equity.
However, with the asset preselection process, the assets that may not be potentially included in the final portfolio are removed thereby reducing the computational time substantially while improving the quality of the generated efficient portfolios
within the same number of function evaluations.
Yu (2003) considers the question of choosing efficient portfolios
of energy and ancillary services sales by a generation owners able to sell in spatially distributed wholesale electricity markets.
Sarasin Systematic Efficient Approach is focused on constructing highly efficient portfolios
in a more robust way by addressing the stability problem of the Sharpe ratio through Sarasin & Partners' proprietary efficiency technique.
Alexander and Baptista (2004) rely on Merton (1972) when analyzing mean-VaR efficient portfolios
. In contrast, the present paper uses the computationally simple method of envelope portfolios developed by Black (1972) to derive the efficient frontier.
The firm offers a comprehensive suite of single-asset and multi-asset solutions designed to serve as powerful building blocks for smarter, more efficient portfolios
. Strategies are offered in the form of open- and closed-end funds and separately managed accounts.
(i) Efficient Portfolios
and Optimal Asset Allocations: