Hedge Fund Modelling and Analysis

Preface xi

CHAPTER 1 Essential C++ 1

1.1 A Brief History of C and C++ 1

1.2 A Basic C++ Program 2

1.3 Variables 4

1.3.1 Characters and Strings 5

1.3.2 Variable Declarations 8

1.3.3 Type Casting 9

1.3.4 Variable Scope 10

1.3.5 Constants 11

1.4 Operators 12

1.4.1 The Assignment Operator 12

1.4.2 Arithmetic Operators 14

1.4.3 Relational Operators 15

1.4.4 Logical Operators 16

1.4.5 Conditional Operator 17

1.5 Input and Output 18

1.6 Control Structures 21

1.6.1 Branching 21

1.6.2 Looping 25

1.6.3 The for Loop 25

1.6.4 The while Loop 27

1.6.5 The do...while Loop 29

1.7 Arrays 30

1.8 Vectors 31

1.9 Functions 33

1.9.1 Call-by-Value vs. Call-by-Reference 36

1.9.2 Overloading Functions 39

1.10 Object Oriented Programming 41

1.10.1 Classes and Abstract Data Types 42

1.10.2 Encapsulation and Interfaces 43

1.10.3 Inheritance and Overriding Functions 44

1.10.4 Polymorphism 45

1.10.5 An Example of a Class 46

1.10.6 Getter and Setter Methods 49

1.10.7 Constructors and Destructors 52

1.10.8 A More Detailed Class Example 55

1.10.9 Implementing Inheritance 61

1.10.10 Operator Overloading 64

CHAPTER 2 The Hedge Fund Industry 71

2.1 What are Hedge Funds? 71

2.2 The Structure of a Hedge Fund 74

2.2.1 Fund Administrators 74

2.2.2 Prime Brokers 75

2.2.3 Custodian, Auditors and Legal 76

2.3 The Global Hedge Fund Industry 77

2.3.1 North America 79

2.3.2 Europe 80

2.3.3 Asia 81

2.4 Specialist Investment Techniques 82

2.4.1 Short Selling 82

2.4.2 Leverage 83

2.4.3 Liquidity 84

2.5 Recent Developments for Hedge Funds 85

2.5.1 UCITS Hedge Funds 85

2.5.2 The European Passport 88

2.5.3 Restrictions on Short Selling 88

CHAPTER 3 Hedge Fund Data Sources 91

3.1 Hedge Fund Databases 91

3.2 Major Hedge Fund Indices 92

3.2.1 Non-Investable and Investable Indices 92

3.2.2 Dow Jones Credit Suisse Hedge Fund Indices (www.hedgeindex.com) 94

3.2.3 Hedge Fund Research (www.hedgefundresearch.com) 100

3.2.4 FTSE Hedge (www.ftse.com) 102

3.2.5 Greenwich Alternative Investments (www.greenwichai.com) 104

3.2.6 Morningstar Alternative Investment Center (www. morningstar.com/advisor/alternative-investments.htm) 108

3.2.7 EDHEC Risk and Asset Management Research Centre (www.edhec-risk.com) 112

3.3 Database and Index Biases 113

3.3.1 Survivorship Bias 113

3.3.2 Instant History Bias 115

3.4 Benchmarking 115

3.4.1 Tracking Error 116

CHAPTER 4 Statistical Analysis 119

4.1 The Stats Class 119

4.2 The Utils Class 120

4.3 The Import Class 123

4.4 Basic Performance Plots 127

4.4.1 Value Added Index 127

4.4.2 Histograms 130

4.5 Probability Distributions 131

4.5.1 Populations and Samples 132

4.6 Probability Density Function 133

4.7 Cumulative Distribution Function 134

4.8 The Normal Distribution 134

4.8.1 Standard Normal Distribution 136

4.9 Visual Tests for Normality 136

4.9.1 Inspection 136

4.9.2 Normal Probability Plot 137

4.10 Moments of a Distribution 138

4.10.1 Mean and Standard Deviation 138

4.10.2 Skew 141

4.10.3 Kurtosis 142

4.11 Covariance and Correlation 146

4.12 Linear Regression 158

4.12.1 Coefficient of Determination 163

4.12.2 Residual Plots 167

CHAPTER 5 Performance Measurement 173

5.1 The PMetrics Class 173

5.2 The Intuition Behind Risk-Adjusted Returns 174

5.2.1 Risk-Adjusted Returns 182

5.3 Absolute Risk-Adjusted Return Metrics 184

5.4 The Sharpe Ratio 187

5.5 Market Models 191

5.5.1 The Information Ratio 192

5.5.2 The Treynor Ratio 197

5.5.3 Jensen's Alpha 203

5.5.4 M-Squared 205

5.6 The Minimum Acceptable Return 207

5.6.1 The Sortino Ratio 207

5.6.2 The Omega Ratio 211

CHAPTER 6 Mean-Variance Optimisation 213

6.1 The Optimise Class 213

6.2 Mean-Variance Analysis 214

6.2.1 Portfolio Return and Variance 214

6.2.2 The Mean-Variance Optimisation Problem 229

6.2.3 The Global Minimum Variance Portfolio 244

6.2.4 Short Sale Constraints 246

CHAPTER 7 Market Risk Management 247

7.1 The RMetrics Class 247

7.2 Value-at-Risk 248

7.3 Traditional VaR Methods 251

7.3.1 Historical Simulation 251

7.3.2 Parametric Method 254

7.3.3 Monte-Carlo Simulation 261

7.4 Modified VaR 263

7.5 Expected Shortfall 266

7.6 Extreme Value Theory 271

7.6.1 Block Maxima 272

7.6.2 Peaks Over Threshold 272

References 277

Index 279