Postmodern Portfolio Theory: Navigating Abnormal Markets and Investor Behavior (Quantitative Perspectives on Behavioral Economics and Finance)

This survey of portfolio theory, from its modern origins through more sophisticated, “postmodern” incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that more accurately describe abnormal markets and investor psychology, this book bifurcates beta on either side of mean returns. It then evaluates this traditional risk measure according to its relative volatility and correlation components. After specifying a four-moment capital asset pricing model, this book devotes special attention to measures of market risk in global banking regulation. Despite the deficiencies of modern portfolio theory, contemporary finance continues to rest on mean-variance optimization and the two-moment capital asset pricing model. The term postmodern portfolio theory captures many of the advances in financial learning since the original articulation of modern portfolio theory. A comprehensive approach to financial risk management must address all aspects of portfolio theory, from the beautiful symmetries of modern portfolio theory to the disturbing behavioral insights and the vastly expanded mathematical arsenal of the postmodern critique. Mastery of postmodern portfolio theory’s quantitative tools and behavioral insights holds the key to the efficient frontier of risk management. 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 26 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: Τέσσερα, Τέσσερα: 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 189 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- 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 This survey of portfolio theory, from its modern origins through more sophisticated, "postmodern" incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that more accurately describe abnormal markets and investor psychology, this book bifurcates beta on either side of mean returns. It then evaluates this traditional risk measure according to its relative volatility and correlation components. After specifying a four-moment capital asset pricing model, this book devotes special attention to measures of market risk in global banking regulation. Despite the deficiencies of modern portfolio theory, contemporary finance continues to rest on mean-variance optimization and the two-moment capital asset pricing model. The term postmodern portfolio theory captures many of the advances in financial learning since the original articulation of modern portfolio theory. A comprehensive approach to financial risk management must address all aspects of portfolio theory, from the beautiful symmetries of modern portfolio theory to the disturbing behavioral insights and the vastly expanded mathematical arsenal of the postmodern critique. Mastery of postmodern portfolio theoryĺls quantitative tools and behavioral insights holds the key to the efficient frontier of risk management Front Matter....Pages i-xx Finance as a Pattern of Timeless Moments....Pages 1-2 Front Matter....Pages 3-3 Modern Portfolio Theory....Pages 5-25 Postmodern Portfolio Theory....Pages 27-38 Front Matter....Pages 39-39 Seduced by Symmetry, Smarter by Half....Pages 41-58 The Full Financial Toolkit of Partial Second Moments....Pages 59-78 Sortino, Omega, Kappa: The Algebra of Financial Asymmetry....Pages 79-105 Sinking, Fast and Slow: Relative Volatility Versus Correlation Tightening....Pages 107-151 Front Matter....Pages 153-154 Time-Varying Beta: Autocorrelation and Autoregressive Time Series....Pages 155-172 Asymmetric Volatility and Volatility Spillovers....Pages 173-187 A Four-Moment Capital Asset Pricing Model....Pages 189-224 The Practical Implications of a Spatially Bifurcated Four-Moment Capital Asset Pricing Model....Pages 225-233 Front Matter....Pages 235-235 Going to Extremes: Leptokurtosis as an Epistemic Threat....Pages 237-245 Parametric VaR Analysis....Pages 247-259 Parametric VaR According to Student’s t-Distribution....Pages 261-279 Comparing Student’s t-Distribution with the Logistic Distribution....Pages 281-289 Expected Shortfall as a Response to Model Risk....Pages 291-305 Latent Perils: Stressed VaR, Elicitability, and Systemic Effects....Pages 307-325 Finance as a Romance of Many Moments and Plural Views....Pages 327-329 Back Matter....Pages 331-339 Annotation This survey of portfolio theory, from its modern origins through more sophisticated, 'postmodern' incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that more accurately describe abnormal markets and investor psychology, this book bifurcates beta on either side of mean returns