Statistical Arbitrage

CHAPTER 1

Monte Carlo or Bust 1

Beginning 1

Whither? And Allusions 4

CHAPTER 2

Statistical Arbitrage 9

Introduction 9

Noise Models 10

Reverse Bets 11

Multiple Bets 11

Rule Calibration 12

Spread Margins for Trade Rules 16

Popcorn Process 18

Identifying Pairs 20

Refining Pair Selection 21

Event Analysis 22

Correlation Search in the Twenty-First Century 26

Portfolio Configuration and Risk Control 26

Exposure to Market Factors 29

Market Impact 30

Risk Control Using Event Correlations 31

Dynamics and Calibration 32

Evolutionary Operation: Single Parameter Illustration 34

CHAPTER 3

Structural Models 37

Introduction 37

Formal Forecast Functions 39

Exponentially Weighted Moving Average 40

Classical Time Series Models 47

Autoregression and Cointegration 47

Dynamic Linear Model 49

Volatility Modeling 50

Pattern Finding Techniques 51

Fractal Analysis 52

Which Return? 52

A Factor Model 53

Factor Analysis 54

Defactored Returns 55

Prediction Model 57

Stochastic Resonance 58

Practical Matters 59

Doubling: A Deeper Perspective 61

Factor Analysis Primer 63

Prediction Model for Defactored Returns 65

CHAPTER 4

Law of Reversion 67

Introduction 67

Model and Result 68

The 75 percent Rule 68

Proof of the 75 percent Rule 69

Analytic Proof of the 75 percent Rule 71

Discrete Counter 73

Generalizations 73

Inhomogeneous Variances 74

Volatility Bursts 75

Numerical Illustration 76

First-Order Serial Correlation 77

Analytic Proof 79

Examples 82

Nonconstant Distributions 82

Applicability of the Result 84

Application to U.S. Bond Futures 85

Summary 87

Appendix 4.1: Looking Several Days Ahead 87

CHAPTER 5

Gauss Is Not the God of Reversion 91

Introduction 91

Camels and Dromedaries 92

Dry River Flow 95

Some Bells Clang 98

CHAPTER 6

Interstock Volatility 99

Introduction 99

Theoretical Explanation 103

Theory versus Practice 105

Finish the Theory 105

Finish the Examples 106

Primer on Measuring Spread Volatility 108

CHAPTER 7

Quantifying Reversion Opportunities 113

Introduction 113

Reversion in a Stationary Random Process 114

Frequency of Reversionary Moves 117

Amount of Reversion 118

Movements from Quantiles Other Than

the Median 135

Nonstationary Processes: Inhomogeneous Variance 136

Sequentially Structured Variances 136

Sequentially Unstructured Variances 137

Serial Correlation 138

Appendix 7.1: Details of the Lognormal Case in Example 6 139

CHAPTER 8

Nobel Difficulties 141

Introduction 141

Event Risk 142

Will Narrowing Spreads Guarantee Profits? 144

Rise of a New Risk Factor 145