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Portfolio Optimization
Michael J. Best
Contents
Preface
Acknowledgments
About the Author
Chapter 1 Optimization
1 . 1 Quadratic Minimization
1 . 2 Nonlinear Optimization .
1.3 Extreme Points . .
1.4 Computer Results .
1.5 Exercises . . . . . .
Chapter 2 The Efficient Frontier
2.1 The Efficient Frontier
2.2 Computer Programs
2.3 Exercises . . . . . . . .
Chapter 3 The Capital Asset Pricing Model
3.1 The Capital Market Line .
3.2 The Security Market Line
3.3 Computer Programs
3.4 Exercises . . . . . . . . . .
Chapter 4 Sharpe Ratios and Implied Risk Free Returns 59
4. 1 Direct Derivation . . . . 60
4.2 Optimization Derivation . . . . . . . . . . . . . . . 66
4.3 Free Problem Solutions . 73
4.4 Computer Programs 75
4.5 Exercises . . . . . . . . . 78
Chapter 5 Quadratic Programming Geometry 81
5. 1 The Geometry of QPs . . . . . . . . . . 81
5.2 Geometry of QP Optimality Conditions . 86
5.3 The Geometry of Quadratic Functions 92
5.4 Optimality Conditions for QPs 96
5.5 Exercises . . . . . . . . . . . . . . . 103
Chapter 6 A QP Solution Algorithm 107
6 . 1 QPSolver: A QP Solution Algorithm 108
6.2 Computer Programs 127
6.3 Exercises . . . . . . . . . . . . . . . . 136
Chapter 7 Portfolio Optimization with Constraints 139
7.1 Linear Ine quality Constraints: An Example . 140
7. 2 The General Case . 151
7.3 Computer Results . 159
7.4 Exercises . . . . . . 163
Chapter 8 Determination of the Entire Efficient Frontier 165
8 . 1 The Entire Efficient Frontier 165
8.2 Computer Results . 183
8.3 Exercises . . . . . . . . . . . 189
Chapter 9 Sharpe Ratios under Constraints, and Kinks 191
9 . 1 Sharpe Ratios under Constraints 191
9.2 Kinks and Sharpe Ratios 199
9.3 Computer Results . 2 1 1
9.4 Exercises . 213
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