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Pairs
Trading
Quantitative Methods
and Analysis
GANAPATHY VIDYAMURTHY
John Wiley & Sons, Inc.
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Contents
Preface ix
Acknowledgments xi
PART ONE
Background Material
CHAPTER 1
Introduction 3
The CAPM Model 3
Market Neutral Strategy 5
Pairs Trading 8
Outline 9
Audience 10
CHAPTER 2
Time Series 14
Overview 14
Autocorrelation 15
Time Series Models 16
Forecasting 24
Goodness of Fit versus Bias 25
Model Choice 26
Modeling Stock Prices 30
CHAPTER 3
Factor Models 37
Introduction 37
Arbitrage Pricing Theory 39
The Covariance Matrix 42
Application: Calculating the Risk on a Portfolio 44
Application: Calculation of Portfolio Beta 47
Application: Tracking Basket Design 49
Sensitivity Analysis 50
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vi CONTENTS
CHAPTER 4
Kalman Filtering 52
Introduction 52
The Kalman Filter 54
The Scalar Kalman Filter 57
Filtering the Random Walk 60
Application: Example with the Standard & Poor Index 64
PART TWO
Statistical Arbitrage Pairs
CHAPTER 5
Overview 73
History 73
Motivation 74
Cointegration 75
Applying the Model 80
A Trading Strategy 82
Road Map for Strategy Design 83
CHAPTER 6
Pairs Selection in Equity Markets 85
Introduction 85
Common Trends Cointegration Model 87
Common Trends Model and APT 90
The Distance Measure 93
Interpreting the Distance Measure 94
Reconciling Theory and Practice 97
CHAPTER 7
Testing for Tradability 104
Introduction 104
The Linear Relationship 106
Estimating the Linear Relationship: The Multifactor
Approach 107
Estimating the Linear Relationship: The Regression Approach 108
Testing Residual for Tradability 112
CHAPTER 8
Trading Design 118
Introduction 118
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Contents vii
Band Design for White Noise 119
Spread Dynamics 122
Nonparametric Approach 126
Regul