## Mean-Variance Analysis in Portfolio Choice and Capital MarketsJohn Wiley & Sons, 15.02.2000 - 400 Seiten In 1952, Harry Markowitz published "Portfolio Selection," a paper which revolutionized modern investment theory and practice. The paper proposed that, in selecting investments, the investor should consider both expected return and variability of return on the portfolio as a whole. Portfolios that minimized variance for a given expected return were demonstrated to be the most efficient. Markowitz formulated the full solution of the general mean-variance efficient set problem in 1956 and presented it in the appendix to his 1959 book, Portfolio Selection. Though certain special cases of the general model have become widely known, both in academia and among managers of large institutional portfolios, the characteristics of the general solution were not presented in finance books for students at any level. And although the results of the general solution are used in a few advanced portfolio optimization programs, the solution to the general problem should not be seen merely as a computing procedure. It is a body of propositions and formulas concerning the shapes and properties of mean-variance efficient sets with implications for financial theory and practice beyond those of widely known cases. The purpose of the present book, originally published in 1987, is to present a comprehensive and accessible account of the general mean-variance portfolio analysis, and to illustrate its usefulness in the practice of portfolio management and the theory of capital markets. The portfolio selection program in Part IV of the 1987 edition has been updated and contains exercises and solutions. |

### Inhalt

PORTFOLIO SELECTION MODELS | 3 |

THE GENERAL MEANVARIANCE PORTFOLIO SELECTION MODEL | 23 |

CAPABILITIES AND ASSUMPTIONS OF THE GENERAL MODEL | 42 |

8 | 63 |

PROPERTIES OF FEASIBLE PORTFOLIO SETS | 73 |

15 | 80 |

Compact Sets | 86 |

20 | 87 |

EFFICIENT SETS FOR NONDEGENERATE MODELS | 161 |

28 | 182 |

GETTING STARTED | 184 |

DEGENERATE CASES | 199 |

ALL FEASIBLE MEANVARIANCE COMBINATIONS | 225 |

CANONICAL FORM OF THE TWODIMENSIONAL ANALYSIS | 243 |

CONICAL CONSTRAINT SETS AND THE EFFICIENCY OF THE | 275 |

PROGRAM DESCRIPTION BY G PETER TODD | 301 |

Unbounded Constraint Sets | 92 |

Conical Sets | 98 |

22858 | 102 |

Exercises | 105 |

σ along a Straight Line | 116 |

Exercises | 122 |

24 | 145 |

36 | 337 |

APPENDIX ELEMENTS OF MATRIX ALGEBRA AND VECTOR SPACES | 339 |

References | 361 |

362 | |

367 | |

368 | |

### Häufige Begriffe und Wortgruppen

a₁ a₂ affine hull affine transformation analysis assume assumption axis Black's model bm+1 chapter coefficient column compute cone constraint set convex set coordinate system corner portfolio covariance matrix critical line algorithm defined definition deleted dimensional efficient EV combinations efficient portfolios efficient set equation example exercise expected return feasible direction feasible portfolio feasible solution figure finite number given identically zero implies Integer intersect investors lemma linear programming linear subspace market portfolio Markowitz maximizing mean-variance minimizes minimum model of form nondegenerate nonsingular NumSecs obtainable EV combinations orthogonal parabola piecewise linear portfolio selection model portfolio selection problem Proof random variable satisfies sequence set of efficient set of feasible set of obtainable simplex algorithm singular slack variables space straight line subspace Suppose theorem Tobin-Sharpe-Lintner model upper bound V₁ variance vector vertex Vmin X'CX X₁ Y₁ Y₂ zero-variance direction