Best Portfolio Optimization

1. Auflage 2011
ISBN: 978-1-4398-8273-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 238 Seiten

Eschewing a more theoretical approach, Portfolio Optimization shows how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz "budget constraint only" model to a linearly constrained model.

Only requiring elementary linear algebra, the text begins with the necessary and sufficient conditions for optimal quadratic minimization that is subject to linear equality constraints. It then develops the key properties of the efficient frontier, extends the results to problems with a risk-free asset, and presents Sharpe ratios and implied risk-free rates. After focusing on quadratic programming, the author discusses a constrained portfolio optimization problem and uses an algorithm to determine the entire (constrained) efficient frontier, its corner portfolios, the piecewise linear expected returns, and the piecewise quadratic variances. The final chapter illustrates infinitely many implied risk returns for certain market portfolios.

Drawing on the author’s experiences in the academic world and as a consultant to many financial institutions, this text provides a hands-on foundation in portfolio optimization. Although the author clearly describes how to implement each technique by hand, he includes several MATLAB® programs designed to implement the methods and offers these programs on the accompanying CD-ROM.

Autoren/Hrsg.

Best, Michael J.

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Optimization
Quadratic Minimization
Nonlinear Optimization
Extreme Points
Computer Results
The Efficient Frontier
The Efficient Frontier
Computer Results
The Capital Asset Pricing Model
The Capital Market Line
The Security Market Line
Computer Results
Sharpe Ratios and Implied Risk-Free Returns
Direct Derivation
Optimization Derivation
Free Solutions to Problems
Computer Results
Quadratic Programming Geometry
Geometry of Quadratic Programs (QPs)
The Geometry of QP Optimality Conditions
The Geometry of Quadratic Functions
Optimality Conditions for QPs
A QP Solution Algorithm
QPSolver: A QP Solution Algorithm
Computer Results
Portfolio Optimization with Linear Inequality Constraints
An Example
The General Case
Computer Results
Determination of the Entire Efficient Frontier
PQPSolver: Generates the Entire Efficient Frontier
Computer Results
Sharpe Ratios under Constraints and Kinks
Sharpe Ratios under Constraints
Kinks and Sharpe Ratios
Computer Results
Appendix
References
Exercises appear at the end of each chapter.