This edition first published 2017
© 2017 Paul Darbyshire and David Hampton

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ISBN 978-1-118-87957-3 (hbk) ISBN 978-1-118-87955-9 (ebk)
ISBN 978-1-118-87956-6 (ebk) ISBN 978-1-118-87954-2 (ebk)

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CONTENTS

Preface

C++ Source Code
Hypothetical Hedge Fund Data
Book Website

Chapter 1: Essential C++

1.1 A Brief History of C and C++
1.2 A Basic C++ Program
1.3 Variables
1.4 Operators
1.5 Input and Output
1.6 Control Structures
1.7 Arrays
1.8 Vectors
1.9 Functions
1.10 Object Oriented Programming
Notes

Chapter 2: The Hedge Fund Industry

2.1 What are Hedge Funds?
2.2 The Structure of a Hedge Fund
2.3 The Global Hedge Fund Industry
2.4 Specialist Investment Techniques
2.5 Recent Developments for Hedge Funds
Notes

Chapter 3: Hedge Fund Data Sources

3.1 Hedge Fund Databases
3.2 Major Hedge Fund Indices
3.3 Database and Index Biases
3.4 Benchmarking
Notes

Chapter 4: Statistical Analysis

4.1 The Stats Class
4.2 The Utils Class
4.3 The Import Class
4.4 Basic Performance Plots
4.5 Probability Distributions
4.6 Probability Density Function
4.7 Cumulative Distribution Function
4.8 The Normal Distribution
4.9 Visual Tests for Normality
4.10 Moments of a Distribution
4.11 Covariance and Correlation
4.12 Linear Regression
Notes

Chapter 5: Performance Measurement

5.1 The PMetrics Class
5.2 The Intuition Behind Risk-Adjusted Returns
5.3 Absolute Risk-Adjusted Return Metrics
5.4 The Sharpe Ratio
5.5 Market Models
5.6 The Minimum Acceptable Return
Notes

Chapter 6: Mean-Variance Optimisation

6.1 The Optimise Class
6.2 Mean-Variance Analysis
Notes

Chapter 7: Market Risk Management

7.1 The RMetrics Class
7.2 Value-at-Risk
7.3 Traditional VaR Methods
7.4 Modified VaR
7.5 Expected Shortfall
7.6 Extreme Value Theory
Notes

References

Index

EULA

List of Illustrations

Chapter 1

Figure 1.1 Schematic of a typical class hierarchy
Figure 1.2 Adding new functions to the derived class
Figure 1.3 Overriding base-class functions
Figure 1.4 The Generic C++ Class Wizard dialogue box

Chapter 2

Figure 2.1 A schematic of the typical structure of a hedge fund
Figure 2.2 Growth in the global hedge funds industry since 2000
Figure 2.3 Global hedge fund industry map as of first half 2015
Figure 2.4 Growth of the North American hedge fund industry since 2000
Figure 2.5 Growth of the European hedge fund industry since 2000
Figure 2.6 Growth of the Asian hedge fund industry since 1999
Figure 2.7 Growth in number of UCITS hedge funds since December 2007

Chapter 3

Figure 3.1 The Liquid Alternative Beta Index model
Figure 3.2 Hedge fund reallocation
Figure 3.3 Hypothetical performance of the CS LAB Index from Jan 1998 to Dec 2009 and actual historical performance from Jan 2010 through Feb 2016
Figure 3.4 A schematic of the CS LAB Index construction process
Figure 3.5 The growth of $1000 since inception of the HFRI Fund Weighted Composite Index and FoHFs Composite Index against the S&P 500
Figure 3.6 A dynamic, bottom-up approach to HFRX index construction
Figure 3.7 FTSE Hedge Index quantitative and qualitative index construction
Figure 3.8 The family of GAI Investable Indices
Figure 3.9 Schematic of the fund selection process
Figure 3.10 A schematic of te MSCI investable index construction methodology

Chapter 4

Figure 4.1 Using an array OFFSET to index between 1D and 2D arrays
Figure 4.2 Bar chart of the monthly returns for the CTA Index
Figure 4.3 The VAMI plot for the CTA Index of monthly returns
Figure 4.4 A histogram plot for the CTA Index of monthly returns
Figure 4.5 Several samples taken from the population of the data set
Figure 4.6 The PDF and interval [a, b]
Figure 4.7 The relationship between the PDF and CDF
Figure 4.8 The central limit theorem
Figure 4.9 The normal distribution
Figure 4.10 Empirical vs. normal distribution for the CTA Index
Figure 4.11 A normal probability plot for the CTA Index
Figure 4.12 Positive and negative skew
Figure 4.13 Positive, negative and zero kurtosis
Figure 4.14 Summary statistics for the CTA Index
Figure 4.15 An example output from the 10_hedge_funds.dat file
Figure 4.16 Some typical correlation plots
Figure 4.17 Simple linear regression
Figure 4.18 t-distribution vs. normal distribution
Figure 4.19 A residual plot
Figure 4.20 The linear regression plot for the Long-Short Index vs. S&P 500
Figure 4.21 Summary of the statistics from the regression analysis

Chapter 5

Figure 5.1 The first 18 values of the data file two_managers.dat
Figure 5.2 The VAMI for MgrA and MgrB
Figure 5.3 MgrA and MgrB in return/volatility space
Figure 5.4 10 hypothetical hedge fund monthly returns (first 18 only)
Figure 5.5 Annualised mean and standard deviation for each of the 10 hedge funds
Figure 5.6 The M1/M2 performance metric for each of the 10 hedge funds
Figure 5.7 The VAMI for each of the 10 hedge funds
Figure 5.8 Upside and downside volatility
Figure 5.9 Upside and downside volatility
Figure 5.10 The SML for two hedge funds A and B
Figure 5.11 Monthly returns for 10 hedge funds including the new global equity benchmark (SDX)
Figure 5.12 Relative directional exposure to a benchmark

Chapter 6

Figure 6.1 Annualised mean and standard deviation for each of the 10 hedge funds
Figure 6.2 Risk-return scatter plot for the 10 hedge funds
Figure 6.3 Equal weights for W and W^T
Figure 6.4 The annualised VCV matrix
Figure 6.5 Find x and y to maximise f(x, y) subject to a constraint g(x, y) = c
Figure 6.6 Amount of investment for each of the 10 hedge funds
Figure 6.7 Efficient frontier, minimum variance frontier and global minimum variance portfolio

Chapter 7

Figure 7.1 VaR at the 95% and 99% confidence levels
Figure 7.2 5% worse case losses for the hypothetical CTA index
Figure 7.3 Histogram showing monthly VaR using historic simulation
Figure 7.4 Histogram showing monthly VaR using the parametric method
Figure 7.5 Histogram plot showing monthly MVaR
Figure 7.6 Comparison of ES and VaR at the 95% confidence level
Figure 7.7 Monthly ES at 95% confidence level
Figure 7.8 The ‘child’ and ‘parent’ distributions
Figure 7.9 Hypothetical hedge fund losses over 100 days
Figure 7.10 The largest losses in each 10-day block
Figure 7.11 Losses over a threshold
Figure 7.12 The random variable X and threshold u

Preface

This book is a practical introduction to modelling and analysing hedge funds using the C++ programming language. The structure of the book is as follows. Chapter 1 gives an overview of the C++ syntax in enough detail to approach the material covered in the technical chapters. Chapter 1 also introduces the concept of object oriented programming which allow us to build large and complex programs that can be broken down into smaller self-contained reusable code units known as classes. We will develop a series of classes throughout the book to tackle many of the problems encountered. Please note that this book is not intended to be an exhaustive exploration of C++ to solve problems in modelling and analysing hedge fund data. In addition, C++ is used to facilitate the solution of such problems through object oriented programming methods and various details highlighted as and when necessary.

Chapters 2 and 3 give an update of the current state of the global hedge fund industry and a detailed look at the primary data sources available to hedge fund managers and analysts. With this fundamental knowledge in place, Chapters 4–7 cover the more quantitative and theoretical material needed to effectively analyse a series of hedge fund returns and extract the relevant information required in order to make critical investment decisions.

C++ Source Code

Throughout the book there are numerous C++ source boxes (e.g., Source 2.4) typically listing the AClass.h, AClass.cpp, and main.cpp files and a console window showing the results of the class implementation. For example, an extract from the Optimise class is shown in Source P.1.

Source P.1: A Sample C++ Source Code

Comment blocks, such as:

// ...
// main.cpp
// ...

are used to omit parts of the source code (above and below) when new code is added to existing definitions or implementations. As we progress through the book we will gradually reduce unnecessary overuse of comments (//) within source listings once we feel confident we have clearly defined such routines and concepts in previous listings.

Please note that we do not give any warranty for completeness, nor do we guarantee that the code is error free. Any damage or loss incurred in the application of the C++ source code, algorithms and classes discussed in the book are entirely the reader's responsibility. If you notice any errors in the C++ source code, algorithms or classes, or you wish to submit some new method as a C++ function, algorithm, class, model or some improvement of the method illustrated in the book, you are very welcome.

Hypothetical Hedge Fund Data

Throughout the book there is constant reference to many monthly hedge fund return series. The 10 hedge funds are all hypothetical and have been simulated by the authors as a unique data set for demonstration purposes only. The techniques and models used in the book can therefore be tested on the hypothetical data before being applied to real-life situations by the reader. The hypothetical data is nonetheless close to what would be expected in reality. The 10 funds are a mixture of several major hedge fund strategies i.e. Commodity Trading Advisor (CTA), Long/Short Equity (LS), Global Macro (GM) and Market Neutral (MN) strategies as described in Table P.1.

Table P.1 10 Hypothetical Hedge Funds

Hedge Fund	Abbreviation
Commodity Trading Advisor	CTA1, CTA2, CTA3
Long Short Equity	LS1, LS2, LS3
Global Macro	GM1, GM2
Market Neutral	MN1, MN2

All data files used throughout the book are identified in italics e.g. 10_hedge_funds.dat.

Book Website

The official website for the book is located at: www.darbyshirehampton.com

The website provides free downloads to all of the hypothetical data, C++ programs and classes, as well as many other useful resources.

The authors can be contacted on any matter relating to the book, or in a professional capacity, at the following email addresses:

Paul Darbyshire: pd@darbyshirehampton.com
David Hampton: dh@darbyshirehampton.com

Hedge Fund Modelling and Analysis

An Object Oriented Approach Using C++

Preface

C++ Source Code

Source P.1: A Sample C++ Source Code

Hypothetical Hedge Fund Data

Book Website