Postmodern Portfolio Theory (eBook)

James Ming Chen holds the Justin Smith Morrill Chair in Law at Michigan State University, USA. He teaches, lectures, and writes widely on law, economics, and regulation. His books, Disaster Law and Policy and Postmodern Portfolio Theory, cover a broad range of issues concerning extreme events and risk management, from natural to financial disasters. He is of counsel to the Technology Law Group of Washington, D.C.; a public member of the Administrative Conference of the United States; and an elected member of the American Law Institute. A magna cum laude graduate of Harvard Law School and a former editor of the Harvard Law Review, Chen also served as a clerk to Justice Clarence Thomas of the Supreme Court of the United States.

Acknowledgments 10
Contents 12
List of Figures 18
List of Tables 20
Chapter 1: Finance as a Pattern of Timeless Moments 22
1.1 Introduction 22
Part 1: Perpetual Possibility in a World of Speculation: Portfolio Theory in Its Modern and Postmodern Incarnations 24
Chapter 2: Modern Portfolio Theory 25
2.1 Mathematically Informed Risk Management 25
2.2 Measures of Risk the Sharpe Ratio
2.3 Beta 26
2.4 The Capital Asset Pricing Model 29
2.5 The Treynor Ratio 30
2.6 Alpha 32
2.7 The Efficient Markets Hypothesis 33
2.8 The Efficient Frontier 35
Notes 37
Chapter 3: Postmodern Portfolio Theory 46
3.1 A Renovation Project 46
3.2 An Orderly Walk 47
3.3 Roll’s Critique 48
3.4 The Echo of Future Footsteps49 50
Notes 52
Part 2: Bifurcating Beta in Financial and Behavioral Space 58
Chapter 4: Seduced by Symmetry, Smarter by Half 59
4.1 Splitting the Atom of Systematic Risk 59
4.2 The Catastrophe of Success 62
4.3 Reviving Beta’s Dead Hand 63
4.4 Sinking, Fast and Slow 65
Notes 67
Chapter 5: The Full Financial Toolkit of Partial Second Moments 77
5.1 A History of Downside Risk Measures 77
5.2 Safety First 78
5.3 Semivariance, Semideviation, and Single-Sided Beta 80
5.4 Traditional CAPM Specifications of Volatility, Variance, Covariance, Correlation, and Beta 82
5.5 Deriving Semideviation and Semivariance from Upper and Lower Partial Moments 85
Notes 90
Chapter 6: Sortino, Omega, Kappa: The Algebra of Financial Asymmetry 97
6.1 Extracting Downside Risk Measures from Lower Partial Moments 97
6.2 The Sortino Ratio 98
6.3 Comparing the Treynor, Sharpe, and Sortino Ratios 99
6.4 Pythagorean Extensions of Second-Moment Measures: Triangulating Deviation About a Target Not Equal to the Mean 103
6.5 Further Pythagorean extensions: Triangulating Semivariance and Semideviation 105
6.6 Single-Sided Risk Measures in Popular Financial Reporting 107
6.7 The Trigonometry of Semideviation 109
6.8 Omega 112
6.9 Kappa 113
6.10 An Overview of Single-Sided Measures of Risk Based on Lower Partial Moments 115
6.11 Noninteger Exponents Versus Ordinary Polynomial Representations 117
Notes 119
Chapter 7: Sinking, Fast and Slow: Relative Volatility Versus Correlation Tightening 124
7.1 The Two Behavioral Faces of Single-Sided Beta 124
7.2 Parameters Indicating Relative Volatility and Correlation Tightening 128
7.3 Relative Volatility and the Beta Quotient 132
7.4 The Low-Volatility Anomaly and Bowman’s Paradox 133
7.5 Correlation Tightening 137
7.6 Correlation Tightening in Emerging Markets 139
7.7 Isolating and Pricing Correlation Risk 143
7.8 Low Volatility Revisited 146
7.9 Low Volatility and Banking’s “Curse of Quality” 148
7.10 Downside Risk, Upside Reward 149
Notes 150
Part 3: ???????, ???????: Four Dimensions, Four Moments 169
Chapter 8: Time-Varying Beta: Autocorrelation and Autoregressive Time Series 171
8.1 Finding in Motion What Was Lost in Time 171
8.2 The Conditional Capital Asset Pricing Model 173
8.3 Conditional Beta 174
8.4 Conventional Time Series Models 176
8.5 Asymmetrical Time Series Models 178
Notes 180
Chapter 9: Asymmetric Volatility and Volatility Spillovers 189
9.1 The Origins of Asymmetrical Volatility the Leverage Effect
9.2 Volatility Feedback 190
9.3 Options Pricing and Implied Volatility 192
9.4 Asymmetrical Volatility and Volatility Spillover Around the World 193
Notes 195
Chapter 10: A Four-Moment Capital Asset Pricing Model 204
10.1 Harbingers of a Four-Moment Capital Asset Pricing Model 204
10.2 Four-Moment CAPM as a Response to the Fama–French–Carhart Four-Factor Model 205
10.3 From Asymmetric Beta to Coskewness and Cokurtosis 207
10.4 Skewness and Kurtosis58 211
10.5 Higher-Moment CAPM as a Taylor Series Expansion 213
10.6 Interpreting Odd Versus Even Moments 217
10.7 Approximating and Truncating the Taylor Series Expansion 219
10.8 Profusion and Confusion Over Measures of Coskewness and Cokurtosis 220
10.9 A Possible Cure for Portfolio Theory’s Curse of Dimensionality: Relative Lower Partial Moments 225
Notes 228
Chapter 11: The Practical Implications of a Spatially Bifurcated Four-Moment Capital Asset Pricing Model 240
11.1 Four-Moment CAPM Versus the Four-­Factor Model 240
11.2 Correlation Asymmetry 241
11.3 Emerging Markets 242
11.4 Size, Value, and Momentum 243
Notes 246
Part 4: Managing Kurtosis: Measures of Market Risk in Global Banking Regulation 249
Chapter 12: Going to Extremes: Leptokurtosis as an Epistemic Threat 250
12.1 VaR and Expected Shortfall in Global Banking Regulation 250
12.2 Leptokurtosis, Fat Tails, and Non-Gaussian Distributions 253
Notes 255
Chapter 13: Parametric VaR Analysis 259
13.1 The Basel Committee on Bank Supervision and the Basel Accords 259
13.2 The Vulnerability of VaR Analysis to Model Risk 261
13.3 Gaussian VaR 263
13.4 A Simple Worked Example 264
Notes 266
Chapter 14: Parametric VaR According to Student’s t-Distribution 272
14.1 Choosing Among Non-Gaussian Distributions 272
14.2 Stable Paretian Distributions 273
14.3 Student’s t-Distribution 275
14.4 The Probability Density and Cumulative Distribution Functions of Student’s t-Distribution 277
14.5 Adjusting Student’s t-Distribution According to Observed Levels of Kurtosis 279
14.6 Performing Parametric VaR Analysis with Student’s t-Distribution 281
Notes 284
Chapter 15: Comparing Student’s t-Distribution with the Logistic Distribution 291
15.1 The Logistic Distribution 291
15.2 Equal Kurtosis, Unequal Variance 294
Notes 298
Chapter 16: Expected Shortfall as a Response to Model Risk 300
16.1 VaR Versus Expected Shortfall 300
16.2 The Incoherence of VaR 301
16.3 Extrapolating Expected Shortfall from VaR 305
16.4 A Worked Example 307
16.5 Formally Calculating Expected Shortfall from VaR under Student’s t-Distribution 308
16.6 Expected Shortfall Under a Logistic Model 311
Notes 312
Chapter 17: Latent Perils: Stressed VaR, Elicitability, and Systemic Effects 315
17.1 Additional Concerns 315
17.2 Stressed VaR 316
17.3 Expected Shortfall and the Elusive Ideal of Elicitability 318
17.4 Systemic Risk 320
17.5 A Dismal Forecast 323
Notes 326
Chapter 18: Finance as a Romance of Many Moments and Plural Views 334
Notes 335
Index 337