The second book in Darbyshire and Hamptons Hedge Fund Modelling and Analysis series,Hedge Fund Modelling and Analysis Using MATLAB® takes advantage of the huge library of built-in functions and suite of financial and analytic packages available to MATLAB®. This allows for a more detailed analysis of some of the more computationally intensive and advanced topics, such as hedge fund classification, performance measurement and mean-variance optimisation. Darbyshire and Hamptons first book in the series,Hedge Fund Modelling and Analysis Using Excel& and VBA, is seen as a valuable supplementary text to this book.

Starting with an overview of the hedge fund industry the book then looks at a variety of commercially available hedge fund data sources. After covering key statistical techniques and methods, the book discusses mean-variance optimisation, hedge fund classification and performance with an emphasis on risk-adjusted return metrics. Finally, common hedge fund market risk management techniques, such as traditional Value-at-Risk methods, modified extensions and expected shortfall are covered.

The books dedicated website, www.darbyshirehampton.com provides free downloads of all the data and MATLAB® source code, as well as other useful resources.

Hedge Fund Modelling and Analysis Using MATLAB® serves as a definitive introductory guide to hedge fund modelling and analysis and will provide investors, industry practitioners and students alike with a useful range of tools and techniques for analysing and estimating alpha and beta sources of return, performing manager ranking and market risk management.

Paul Darbyshire gained his PhD in Theoretical Physics from Kings College London and then began his career working has a Quantitative Analyst and Trader at HSBC on the Exotic Derivatives and Structured Products desk. He has subsequently been involved in the development and implementation of a variety of trading and risk management platforms for a number of major investment banks around the globe. Since 2005, Paul has been responsible for the analysis and design of cutting-edge algorithms in the development of behavioural finance and decision making models at the University of Oxford. Paul also provides many private equity firms, hedge funds and investment management companies with senior consultancy in areas such as dynamic portfolio optimisation, trading platform design, software engineering and risk management.

David Hampton gained his PhD in Electrical Engineering from the Queens University of Belfast and an international MBA from Institut Superieur de Gestion in Paris, New York and Tokyo before joining Bank of America Capital Markets in London. David was previously an Adjunct Finance Professor at Skema Business School in Sophia Antipolis where he taught Financial Engineering and Excel/VBA Programming at the MSc level.  At EDHEC Business School in Nice, he was responsible for managing their range of five MSc courses as Assistant Dean of the Financial Economics Track. An NFA registered CTA since 1996, David has been active as a consultant to the hedge fund community and as a Hedge Fund Manager with particular expertise in Global Macro Managed Futures and Long Short Equity investment styles.

Both David and Paul are Directors of darbyshirehampton; an innovative quantitative research, advisory, and consultancy firm specialising in hedge funds and the alternative investment industry. Website: www.darbyshirehampton.com.

Preface xi

1 The Hedge Fund Industry 1

1.1 What are Hedge Funds? 1

1.2 The Structure of a Hedge Fund 4

1.2.1 Fund Administrators 4

1.2.2 Prime Brokers 5

1.2.3 Custodian, Auditors and Legal 6

1.3 The Global Hedge Fund Industry 6

1.3.1 North America 8

1.3.2 Europe 9

1.3.3 Asia 10

1.4 Specialist Investment Techniques 10

1.4.1 Short Selling 10

1.4.2 Leverage 12

1.4.3 Liquidity 13

1.5 New Developments for Hedge Funds 14

1.5.1 UCITS III Hedge Funds 14

1.5.2 The European Passport 17

1.5.3 Restrictions on Short Selling 17

2 Hedge Fund Data Sources 19

2.1 Hedge Fund Databases 19

2.2 Major Hedge Fund Indices 20

2.2.1 Non-Investable and Investable Indices 20

2.2.2 Dow Jones Credit Suisse Hedge Fund Indices 22

2.2.3 Hedge Fund Research 28

2.2.4 FTSE Hedge 32

2.2.5 Greenwich Alternative Investments 33

2.2.6 Morningstar Alternative Investment Center 35

2.2.7 EDHEC Risk and Asset Management Research Centre 39

2.3 Database and Index Biases 39

2.3.1 Survivorship Bias 40

2.3.2 Instant History Bias 41

2.4 Benchmarking 42

2.4.1 Tracking Error 43

3 Statistical Analysis 45

3.1 Basic Performance Plots 45

3.1.1 Value Added Index 45

3.1.2 Histograms 47

3.2 Probability Distributions 49

3.2.1 Populations and Samples 51

3.3 Probability Density Function 52

3.4 Cumulative Distribution Function 53

3.5 The Normal Distribution 54

3.5.1 Standard Normal Distribution 55

3.6 Visual Tests for Normality 56

3.6.1 Inspection 56

3.6.2 Normal Probability Plot 56

3.7 Moments of a Distribution 58

3.7.1 Mean and Standard Deviation 58

3.7.2 Skew 60

3.7.3 Kurtosis 62

3.8 Covariance and Correlation 63

3.9 Linear Regression 67

3.9.1 Coefficient of Determination 69

3.9.2 Residual Plots 69

3.9.3 Jarque-Bera Test 73

4 Mean-Variance Optimisation 77

4.1 Portfolio Theory 77

4.1.1 Mean-Variance Analysis 77

4.1.2 An Optimisation Problem 81

4.1.3 Sharpe Ratio Maximisation 85

4.2 Efficient Portfolios 87

5 Performance Measurement 97

5.1 The Intuition Behind Risk-Adjusted Returns 97

5.1.1 Risk-Adjusted Returns 99

5.2 Absolute Risk-Adjusted Return Metrics 103

5.2.1 The Sharpe Ratio 105

5.2.2 The Modified Sharpe Ratio 106

5.2.3 The Maximum Drawdown Ratio 107

5.3 Market Model Risk-Adjusted Return Metrics 110

5.3.1 The Information Ratio 111

5.3.2 The Treynor Ratio 113

5.3.3 Jensens Alpha 118

5.3.4 GH1 Metric 119

5.3.5 The M2 Metric 120

5.3.6 The GH2 Metric 123

5.4 MAR and LPM Metrics 125

5.4.1 The Sortino Ratio 125

5.4.2 The Omega Ratio 127

5.4.3 The Upside Potential Ratio and Group Rankings 129

5.5 Multi-Factor Asset Pricing Extensions 131

5.5.1 The Choice of Factors 133

6 Hedge Fund Classification 137

6.1 Financial Instrument Building Blocks and Style Groups 137

6.2 Hedge Fund Clusters and Classification 138

6.2.1 Metric Definitions 140

6.2.2 Creating Dendrograms 140

6.2.3 Interpreting Dendrograms 141

7 Market Risk Management 155

7.1 Value-at-Risk 155

7.2 Traditional VaR Methods 159

7.2.1 Historical Simulation 159

7.2.2 Parametric Method 161

7.2.3 Monte-Carlo Simulation 162

7.3 Modified VaR 165

7.4 Expected Shortfall 166

7.5 Extreme Value Theory 172

7.5.1 Block Maxima 174

7.5.2 Peaks Over Threshold 174

References 179

Index 183