![]() In general, the matrix is positive semidefinite, but we will assume that it is positive definite. On the other hand, the risk is measured by, where is the covariance matrix. Most portfolio selection models are based on the original Markowitz model, in which the expected return of a given portfolio is measured by, where is the vector of mean returns of the assets and contains the weight of each asset in the portfolio. The portfolio selection problem consists of finding an efficient portfolio in the sense of obtaining a tradeoff between the expected return and the risk of the investment. The procedure has been implemented in Mathematica. ![]() Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. ![]() The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. ![]() An easy-to-use procedure is presented for improving the -constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints.
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