Bubble Value at Risk

Max C.Y. Wong is a specialist in the area of risk modeling and Basel III. He started his career as a derivatives consultant at Credit Suisse First Boston in 1996. During the Asian crisis in 1998 he traded index futures at the open-outcry floor of SIMEX (now SGX). From 2003 to 2011, he worked for Standard Chartered Bank as a risk manager and senior quant. He is currently head of VaR model testing at the Royal Bank of Scotland. He has published papers on VaR models and Basel capital, recently looking at innovative ways to model risk more effectively during crises and to deal with the issues of procyclicality and Black Swan event in our financial system. He has spoken on the subject at various conferences and seminars. He holds a B.Sc. Physics from University of Malaya (1994) and a M.Sc. financial engineering from National University of Singapore (2004). He is an adjunct at Singapore Management University, a member of the editorial board of the Journal of Risk Management in Financial Institutions, and a member of the steering committee of PRMIA Singapore chapter.

About the Author xiii

Foreword xv

Preface xvii

Acknowledgments xxi

PART ONE Background

CHAPTER 1 Introduction 3

1.1 The Evolution of Riskometer 4

1.2 Taleb’s Extremistan 6

1.3 The Turner Procyclicality 7

1.4 The Common Sense of Bubble Value-at-Risk (BuVaR) 8

Notes 13

CHAPTER 2 Essential Mathematics 15

2.1 Frequentist Statistics 15

2.2 Just Assumptions 18

2.3 Quantiles, VaR, and Tails 26

2.4 Correlation and Autocorrelation 29

2.5 Regression Models and Residual Errors 35

2.6 Significance Tests 38

2.7 Measuring Volatility 41

2.8 Markowitz Portfolio Theory 45

2.9 Maximum Likelihood Method 48

2.10 Cointegration 50

2.11 Monte Carlo Method 52

2.12 The Classical Decomposition 55

2.13 Quantile Regression Model 58

2.14 Spreadsheet Exercises 62

Notes 64

PART TWO Value at Risk Methodology

CHAPTER 3 Preprocessing 67

3.1 System Architecture 67

3.2 Risk Factor Mapping 70

3.3 Risk Factor Proxies 75

3.4 Scenario Generation 76

3.5 Basic VaR Specification 79

Notes 81

CHAPTER 4 Conventional VaR Methods 83

4.1 Parametric VaR 84

4.2 Monte Carlo VaR 89

4.3 Historical Simulation VaR 93

4.4 Issue: Convexity, Optionality, and Fat Tails 96

4.5 Issue: Hidden Correlation 102

4.6 Issue: Missing Basis and Beta Approach 104

4.7 Issue: The Real Risk of Premiums 106

4.8 Spreadsheet Exercises 107

Notes 108

CHAPTER 5 Advanced VaR Methods 111

5.1 Hybrid Historical Simulation VaR 111

5.2 Hull-White Volatility Updating VaR 113

5.3 Conditional Autoregressive VaR (CAViaR) 114

5.4 Extreme Value Theory VaR 116

5.5 Spreadsheet Exercises 122

Notes 124

CHAPTER 6 VaR Reporting 125

6.1 VaR Aggregation and Limits 125

6.2 Diversification 126

6.3 VaR Analytical Tools 127

6.4 Scaling and Basel Rules 132

6.5 Spreadsheet Exercises 136

Notes 137

CHAPTER 7 The Physics of Risk and Pseudoscience 139

7.1 Entropy, Leverage Effect, and Skewness 140

7.2 Volatility Clustering and the Folly of i.i.d. 144

7.3 “Volatility of Volatility” and Fat Tails 145

7.4 Extremistan and the Fourth Quadrant 148

7.5 Regime Change, Lagging Riskometer, and Procyclicality 151

7.6 Coherence and Expected Shortfall 154

7.7 Spreadsheet Exercises 156

Notes 156

CHAPTER 8 Model Testing 159

8.1 The Precision Test 159

8.2 The Frequency Back Test 160

8.3 The Bunching Test 163

8.4 The Whole Distribution Test 165

8.5 Spreadsheet Exercises 167

Notes 167

CHAPTER 9 Practical Limitations of VaR 169

9.1 Depegs and Changes to the Rules of the Game 169

9.2 Data Integrity Problems 171

9.3 Model Risk 172

9.4 Politics and Gaming 174

Notes 175

CHAPTER 10 Other Major Risk Classes 177

10.1 Credit Risk (and CreditMetrics) 177

10.2 Liquidity Risk 182

10.3 Operational Risk 187

10.4 The Problem of Aggregation 190

10.5 Spreadsheet Exercises 195

Notes 195

PART THREE The Great Regulatory Reform

CHAPTER 11 Regulatory Capital Reform 199

11.1 Basel I and Basel II 199

11.2 The Turner Review 202

11.3 Revisions to Basel II Market Risk Framework (Basel 2.5) 206

11.4 New Liquidity Framework 211

11.5 The New Basel III 212

11.6 The New Framework for the Trading Book 214

11.7 The Ideal Capital Regime 215

Notes 217

CHAPTER 12 Systemic Risk Initiatives 221

12.1 Soros’ Reflexivity, Endogenous Risks 221

12.2 CrashMetrics 226

12.3 New York Fed CoVaR 230

12.4 The Austrian Model and BOE RAMSI 233

12.5 The Global Systemic Risk Regulator 238

12.6 Spreadsheet Exercises 240

Notes 241

PART FOUR Introduction to Bubble Value-at-Risk (BuVaR)

CHAPTER 13 Market BuVaR 245

13.1 Why an Alternative to VaR? 245

13.2 Classical Decomposition, New Interpretation 247

13.3 Measuring the Bubble 250

13.4 Calibration 254

13.5 Implementing the Inflator 257

13.6 Choosing the Best Tail-Risk Measure 259

13.7 Effect on Joint Distribution 262

13.8 The Scope of BuVaR 264

13.9 How Good Is the BuVaR Buffer? 265

13.10 The Brave New World 268

13.11 Spreadsheet Exercises 271

Notes 271

CHAPTER 14 Credit BuVaR 273

14.1 The Credit Bubble VaR Idea 273

14.2 Model Formulation 276

14.3 Behavior of Response Function 278

14.4 Characteristics of Credit BuVaR 280

14.5 Interpretation of Credit BuVaR 282

14.6 Spreadsheet Exercises 284

Notes 284

CHAPTER 15 Acceptance Tests 285

15.1 BuVaR Visual Checks 285

15.2 BuVaR Event Timing Tests 297

15.3 BuVaR Cyclicality Tests 304

15.4 Credit BuVaR Parameter Tuning 306

Notes 313

CHAPTER 16 Other Topics 315

16.1 Diversification and Basis Risks 315

16.2 Regulatory Reform and BuVaR 317

16.3 BuVaR and the Banking Book: Response Time as Risk 319

16.4 Can BuVaR Pick Tops and Bottoms Perfectly? 321

16.5 Postmodern Risk Management 321

16.6 Spreadsheet Exercises 323

Note 323

CHAPTER 17 Epilogue: Suggestions for Future Research 325

Note 327

About the Website 329

Bibliography 331

Index 337