Risk-Return Analysis: The Theory and Practice of Rational Investing (Volume One), 1st Edition

Foreword xi
Preface xxi
Acknowledgments xxvii
Outline of Plans for Volumes II, III, and IV xxix

1. The Expected Utility Maxim 1
Introduction 1
Defi nitions 5
Uniqueness 10
Characteristics of Expected Utility Maximization 12
RDMs Versus HDMs 14
Allais’s Paradox 17
Weber’s Law and the Allais Paradox 21
The Axioms 24
Axiom I 25
Axiom II 26
Axioms III and III¿ 28
Bounded Versus Unbounded Utility of Returns 31
Postscript 34

2. Mean-Variance Approximations to Expected Utility 37
Introduction 37
Why Not Just Maximize Expected Utility? 41
Utility of Return Versus Utility of Wealth 44
Loistl’s Erroneous Analysis 47
Levy and Markowitz (1979) 48
Highly Risk-Averse Investors 53
Highly Risk-Averse Investors and a Risk-Free Asset 56
Portfolios of Call Options 58
Ederington’s Quadratic and Gaussian Approximations to Expected Utility 63
Other Pioneers 69
Conclusion 72

3. Mean-Variance Approximations to the Geometric Mean 73
Introduction 73
Why Inputs to a Mean-Variance Analysis Must Be Arithmetic Means 78
Six Mean-Variance Approximations to g 80
Observed Approximation Errors for Asset Classes 84
Relationships Among Approximation Methods 90
Twentieth-Century Real Equity Returns 97
Choice of Approximation 111
Recap 117
Technical Note: Selecting a Weighted Average of Approximations 118

4. Alternative Measures of Risk 123
Introduction 123
The Asset-Class Database 124
Comparisons 127
The DMS Database 137
Caveat and Conclusion 147

5. The Likelihood of Various Return Distributions (With Anthony Tessitore, Ansel Tessitore,and Nilufer Usmen) 149
Introduction 149
Bayes Factors 153
Transformed Variables 156
Compound Hypotheses 159
The Pearson Family 161
The DMS Database 169
Practically Normal Distributions 175
Illustrative Histograms 179
Near LH-Maximizing Distributions for the Ensemble 182
Transformed Country Distributions 186
Observations 190
Recommendation 192

Notes 195
References 209
Index 217