Pairs
Trading
Quantitative Methods
and Analysis
GANAPATHY VIDYAMURTHY

Copyright ? 2004 by Ganapathy Vidyamurthy. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.

Contents
Prefaceix
Acknowledgmentsxi
PART ONE
Background Material
CHAPTER 1
Introduction3
The CAPM Model3
Market Neutral Strategy5
Pairs Trading8
Outline9
Audience10
CHAPTER 2
Time Series14
Overview14
Autocorrelation15
Time Series Models16
Forecasting24
Goodness of Fit versus Bias25
Model Choice26
Modeling Stock Prices30
CHAPTER 3
Factor Models37
Introduction37
Arbitrage Pricing Theory39
The Covariance Matrix42
Application: Calculating the Risk on a Portfolio44
Application: Calculation of Portfolio Beta47
Application: Tracking Basket Design49
Sensitivity Analysis50
v

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vi CONTENTS
CHAPTER 4
Kalman Filtering52
Introduction52
The Kalman Filter54
The Scalar Kalman Filter57
Filtering the Random Walk60
Application: Example with the Standard & Poor Index64
PART TWO
Statistical Arbitrage Pairs
CHAPTER 5
Overview73
History73
Motivation74
Cointegration75
Applying the Model80
A Trading Strategy82
Road Map for Strategy Design83
CHAPTER 6
Pairs Selection in Equity Markets85
Introduction85
Common Trends Cointegration Model87
Common Trends Model and APT90
The Distance Measure93
Interpreting the Distance Measure94
Reconciling Theory and Practice97
CHAPTER 7
Testing for Tradability104
Introduction104
The Linear Relationship106
Estimating the Linear Relationship: The Multifactor
Approach107
Estimating the Linear Relationship: The Regression Approach108
Testing Residual for Tradability112
CHAPTER 8
Trading Design118
Introduction118

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Contents vii
Band Design for White Noise119
Spread Dynamics122
Nonparametric Approach126
Regularization130
Tying Up Loose Ends135
PART THREE
Risk Arbitrage Pairs
CHAPTER 9
Risk Arbitrage Mechanics139
Introduction139
History140
The Deal Process141
Transaction Terms142
The Deal Spread145
Trading Strategy147
Quantitative Aspects149
CHAPTER 10
Trade Execution151
Introduction151
Specifying the Order152
Verifying the Execution155
Execution During the Pricing Period161
Short Selling166
CHAPTER 11
The Market Implied Merger Probability171
Introduction171
Implied Probabilities and Arrow-Debreu Theory173
The Single-Step Model175
The Multistep Model177
Reconciling Theory and Practice180
Risk Management184
CHAPTER 12
Spread Inversion189
Introduction189
The Prediction Equation190
The Observation Equation192

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viii CONTENTS
Applying the Kalman Filter193
Model Selection194
Applications to Trading197
Index205

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