Portfolio Optimization

by Best; Michael J.

• ISBN13: 9781420085846
• ISBN10: 1420085840
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-03-09
• Publisher: Chapman & Hall/

Summary

Eschewing a more theoretical approach, this text provides a practical introduction to basic portfolio optimization models. It focuses on Markowitz mean-variance portfolio optimization. The first chapters include coverage on the derivation of the classical unconstrained efficient frontier, the capital market line, Sharpe ratios, and implied risk-free rates. The author then discusses quadratic and parametric quadratic programming, which is used to implement the theory in practice. MATLAB ® is included throughout the text in various realistic examples and then employed in the presented problem sets to help with calculations.

Table of Contents

Preface	p. ix
Acknowledgments	p. xii
About the Author	p. xii
Optimization	p. 1
Quadratic Minimization	p. 1
Nonlinear Optimization	p. 8
Extreme Points	p. 12
Computer Results	p. 15
Exercises	p. 18
The Efficient Frontier	p. 21
The Efficient Frontier	p. 21
Computer Programs	p. 33
Exercises	p. 36
The Capital Asset Pricing Model	p. 41
The Capital Market Line	p. 41
The Security Market Line	p. 51
Computer Programs	p. 54
Exercises	p. 58
Sharpe Ratios and Implied Risk Free Returns	p. 59
Direct Derivation	p. 60
Optimization Derivation	p. 66
Free Problem Solutions	p. 73
Computer Programs	p. 75
Exercises	p. 78
Quadratic Programming Geometry	p. 81
The Geometry of QPs	p. 81
Geometry of QP Optimality Conditions	p. 86
The Geometry of Quadratic Functions	p. 92
Optimality Conditions for QPs	p. 96
Exercises	p. 103
A QP Solution Algorithm	p. 107
QPSolver: A QP Solution Algorithm	p. 108
Computer Programs	p. 127
Exercises	p. 136
Portfolio Optimization with Constraints	p. 139
Linear Inequality Constraints: An Example	p. 140
The General Case	p. 151
Computer Results	p. 159
Exercises	p. 163
Determination of the Entire Efficient Frontier	p. 165
The Entire Efficient Frontier	p. 165
Computer Results	p. 183
Exercises	p. 189
Sharpe Ratios under Constraints, and Kinks	p. 191
Sharpe Ratios under Constraints	p. 191
Kinks and Sharpe Ratios	p. 199
Computer Results	p. 211
Exercises	p. 213
Appendix	p. 215
References	p. 217
Index	p. 221
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