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.
Table of Contents
The Efficient Frontier
The Efficient Frontier
The Capital Asset Pricing Model
The Capital Market Line
The Security Market Line
Sharpe Ratios and Implied Risk-Free Returns
Free Solutions to Problems
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
Portfolio Optimization with Linear Inequality Constraints
The General Case
Determination of the Entire Efficient Frontier
PQPSolver: Generates the Entire Efficient Frontier
Sharpe Ratios under Constraints and Kinks
Sharpe Ratios under Constraints
Kinks and Sharpe Ratios
Exercises appear at the end of each chapter.
Michael J. Best is a professor in the Department of Combinatorics and Optimization at the University of Waterloo in Ontario, Canada. He received his Ph.D. from the Department of Industrial Engineering and Operations Research at the University of California, Berkeley. Dr. Best has authored over 37 papers on finance and nonlinear programming and co-authored a textbook on linear programming. He also has been a consultant to Bank of America, Ibbotson Associates, Montgomery Assets Management, Deutsche Bank, Toronto Dominion Bank, and Black Rock-Merrill Lynch.
Michael Best’s book is the ideal combination of optimization and portfolio theory. Mike has provided a wealth of practical examples in MATLAB to give students hands-on portfolio optimization experience. The included stand-alone MATLAB code even provides its own quadratic solver, so that students do not need to rely on any external packages.
—David Starer, Stevens Institute of Technology
Overall, this is a nice book that would be ideal as a textbook for one-semester portfolio optimization courses. It can also be good as a supplementary text for courses in operations research and/or financial engineering. The book is self-contained enough to be used as study material for those who want to teach themselves portfolio optimization and related computer programming, be they advanced undergraduate students, graduate students, or financial practitioners.
—Youngna Choi, Mathematical Reviews, Issue 2012a
… an excellent companion text for the course ‘Discrete-Time Models in Finance’ that I have been teaching in the past years. … I think adding your text can make the course more lively. This is what I plan to do in the coming (fall) semester.
—Edward P. Kao, University of Houston, Texas, USA
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