Pairs Trading E-Book

Ganapathy Vidyamurthy

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 321

Veröffentlichungsjahr: 2011

Beschreibung

The first in-depth analysis of pairs trading Pairs trading is a market-neutral strategy in its most simple form. The strategy involves being long (or bullish) one asset and short (or bearish) another. If properly performed, the investor will gain if the market rises or falls. Pairs Trading reveals the secrets of this rigorous quantitative analysis program to provide individuals and investment houses with the tools they need to successfully implement and profit from this proven trading methodology. Pairs Trading contains specific and tested formulas for identifying and investing in pairs, and answers important questions such as what ratio should be used to construct the pairs properly. Ganapathy Vidyamurthy (Stamford, CT) is currently a quantitative software analyst and developer at a major New York City hedge fund.

Leseprobe

Table of Contents

Title Page

Copyright Page

Preface

Acknowledgments

PART One - Background Material

CHAPTER 1 - Introduction

THE CAPM MODEL

MARKET NEUTRAL STRATEGY

PAIRS TRADING

OUTLINE

AUDIENCE

SUMMARY

FURTHER READING MATERIAL

APPENDIX

DEFINITIONS

FORMULAS

CHAPTER 2 - Time Series

OVERVIEW

AUTOCORRELATION

TIME SERIES MODELS

FORECASTING

GOODNESS OF FIT VERSUS BIAS

MODEL CHOICE

MODELING STOCK PRICES

SUMMARY

FURTHER READING MATERIAL

APPENDIX

CHAPTER 3 - Factor Models

INTRODUCTION

ARBITRAGE PRICING THEORY

THE COVARIANCE MATRIX

APPLICATION: CALCULATING THE RISK ON A PORTFOLIO

APPLICATION: CALCULATION OF PORTFOLIO BETA

APPLICATION: TRACKING BASKET DESIGN

SENSITIVITY ANALYSIS

SUMMARY

FURTHER READING MATERIAL

CHAPTER 4 - Kalman Filtering

INTRODUCTION

THE KALMAN FILTER

THE SCALAR KALMAN FILTER

FILTERING THE RANDOM WALK

APPLICATION: EXAMPLE WITH THE STANDARD & POOR INDEX

SUMMARY

FURTHER READING MATERIAL

APPENDIX

PART Two - Statistical Arbitrage Pairs

CHAPTER 5 - Overview

HISTORY

MOTIVATION

COINTEGRATION

APPLYING THE MODEL

A TRADING STRATEGY

ROAD MAP FOR STRATEGY DESIGN

SUMMARY

FURTHER READING MATERIAL

CHAPTER 6 - Pairs Selection in Equity Markets

INTRODUCTION

COMMON TRENDS COINTEGRATION MODEL

COMMON TRENDS MODEL AND APT

THE DISTANCE MEASURE

INTERPRETING THE DISTANCE MEASURE

RECONCILING THEORY AND PRACTICE

SUMMARY

FURTHER READING MATERIAL

APPENDIX: EIGENVALUE DECOMPOSITION

CHAPTER 7 - Testing For Tradability

INTRODUCTION

THE LINEAR RELATIONSHIP

ESTIMATING THE LINEAR RELATIONSHIP: THE MULTIFACTOR APPROACH

ESTIMATING THE LINEAR RELATIONSHIP: THE REGRESSION APPROACH

TESTING RESIDUAL FOR TRADABILITY

SUMMARY

FURTHER READING MATERIAL

CHAPTER 8 - Trading Design

INTRODUCTION

BAND DESIGN FOR WHITE NOISE

SPREAD DYNAMICS

NONPARAMETRIC APPROACH

REGULARIZATION

TYING UP LOOSE ENDS

SUMMARY

FURTHER READING MATERIAL

PART Three - Risk Arbitrage Pairs

CHAPTER 9 - Risk Arbitrage Mechanics

INTRODUCTION

HISTORY

THE DEAL PROCESS

TRANSACTION TERMS

THE DEAL SPREAD

TRADING STRATEGY

QUANTITATIVE ASPECTS

SUMMARY

FURTHER READING MATERIAL

CHAPTER 10 - Trade Execution

INTRODUCTION

SPECIFYING THE ORDER

VERIFYING THE EXECUTION

EXECUTION DURING THE PRICING PERIOD

SHORT SELLING

SUMMARY

FURTHER READING MATERIAL

APPENDIX - DINIC’S ALGORITHM FOR MAXIMUM FLOW IN A NETWORK

LAZY ALLOCATION ALGORITHM

CHAPTER 11 - The Market Implied Merger Probability

INTRODUCTION

IMPLIED PROBABILITIES AND ARROW-DEBREU THEORY

THE SINGLE-STEP MODEL

THE MULTISTEP MODEL

RECONCILING THEORY AND PRACTICE

RISK MANAGEMENT

SUMMARY

FURTHER READING MATERIAL

APPENDIX

CHAPTER 12 - Spread Inversion

INTRODUCTION

THE PREDICTION EQUATION

THE OBSERVATION EQUATION

APPLYING THE KALMAN FILTER

MODEL SELECTION

APPLICATIONS TO TRADING

SUMMARY

FURTHER READING MATERIAL

APPENDIX

Index

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Copyright © 2004 by Ganapathy Vidyamurthy. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Vidyamurthy, Ganapathy.

Pairs trading : quantitative methods and analysis / Ganapathy

Vidyamurthy. p. cm.

Includes bibliographical references and index.

ISBN 0-471-46067-2 (cloth)

1. Pairs trading. 2. Stocks. 3. Portfolio management. 4. Investment analysis. I. Title.

HG4661.V53 2004

332.64’524—dc22

2004005528

Preface

Most book readers are likely to concur with the idea that the least read portion of any book is the preface. With that in mind, and the fact that the reader has indeed taken the trouble to read up to this sentence, we promise to leave no stone unturned to make this preface as lively and entertaining as possible. For your reading pleasure, here is a nice story with a picture thrown in for good measure. Enjoy!

Once upon a time, there were six blind men. The blind men wished to know what an elephant looked like. They took a trip to the forest and with the help of their guide found a tame elephant. The first blind man walked into the broadside of the elephant and bumped his head. He declared that the elephant was like a wall. The second one grabbed the elephant’s tusk and said it felt like a spear. The next blind man felt the trunk of the elephant and was sure that elephants were similar to snakes. The fourth blind man hugged the elephant’s leg and declared the elephant was like a tree. The next one caught the ear and said this is definitely like a fan. The last blind man felt the tail and said this sure feels like a rope. Thus the six blind men all perceived one aspect of the elephant and were each right in their own way, but none of them knew what the whole elephant really looked like.

Oftentimes, the market poses itself as the elephant. There are people who say that predicting the market is like predicting the weather, because you can do well in the short term, but where the market will be in the long run is anybody’s guess. We have also heard from others that predicting the market short term is a sure way to burn your fingers. “Invest for the long haul” is their mantra. Some will assert that the markets are efficient, and yet some others would tell you that it is possible to make extraordinary returns. While some swear by technical analysis, there are some others, the so-called fundamentalists, who staunchly claim it to be a voodoo science. Multiple valuation models for equities like the dividend discount model, relative valuation models, and the Merton model (treating equity as an option on firm value) all exist side by side, each being relevant at different times for different stocks. Deep theories from various disciplines like physics, statistics, control theory, graph theory, game theory, signal processing, probability, and geometry have all been applied to explain different aspects of market behavior.

It seems as if the market is willing to accommodate a wide range of sometimes opposing belief systems. If we are to make any sense of this smorgasbord of opinions on the market, we would be well advised to draw comfort from the story of the six blind men and the elephant. Under these circumstances, if the reader goes away with a few more perspectives on the market elephant, the author would consider his job well done.

Acknowledgments

All of what is in the book has resulted from the people who have touched my life, and I wish to acknowledge them. First, I thank my parents for raising me in an atmosphere of high expectations: my dad, for his keen interest in this project and for suggesting the term stogistics, and my mom, for her unwavering confidence in my abilities. I also thank my in-laws for being so gracious and generous with their support and for sharing in the excitement of the whole process.

I greatly thank friends Jaya Kannan and Kasturi Kannan for their thoughtful gestures and good cheer during the writing process. Thanks to my brother, brother-in-law, and their spouses—Chintu, Hema, Ganesh, and Annie—for their kind and timely enquiries on the status of the writing. It definitely served as a gentle reminder at times when I was lagging behind schedule.

I owe a deep debt of gratitude to my teachers not only for the gift of knowledge but also for inculcating a joy for the learning process, especially Professor Narasimha Murthy, Professor Earl Barnes, and Professor Robert V. Kohn, all of whom I have enjoyed the privilege of working with closely.

The contents of Chapters 11 and 12 are an outcome of the many discussions with Professor Robert V. Kohn (Courant Institute of Mathematics, New York University). The risk arbitrage data were provided by Jason Dahl. The cartoon illustrations done by Tom Kerr are better than I could ever imagine. I thank all of them.

Professors Marco Avellaneda (Courant Institute of Mathematics), Robert V. Kohn (Courant Institute of Mathematics), Kumar Venkataraman (Cox School of Business Southern Methodist University), and professionals Paul Crowley, Steve Evans, Brooke Allen, Jason Dahl, Bud Kroll, and Ajay Junnarkar agreed to review draft versions of the manuscript. Many thanks to all of them. All mistakes that have been overlooked are mine.

I thank my editor, Dave Pugh, for ensuring that the process of writing was a smooth and pleasurable one. Also, thanks to the staff at John Wiley, including Debra Englander for their assistance.

I apologize for any persons left out due to my absentmindedness. Please accept my unspoken thanks.

Last, but most importantly, I wish to thank my wife, Lalitha, for all the wonderful years, for teaching me regularization and being able to share in the excitement of new ideas. Also, thanks to Anjali and Sandhya without whose help the project would have concluded a lot sooner, but would have been no fun at all. You make it all worth it.

PART One

Background Material

CHAPTER 1

Introduction

We start at the very beginning (a very good place to start). We begin with the CAPM model.

THE CAPM MODEL

CAPM is an acronym for the Capital Asset Pricing Model. It was originally proposed by William T. Sharpe. The impact that the model has made in the area of finance is readily evident in the prevalent use of the word beta. In contemporary finance vernacular, beta is not just a nondescript Greek letter, but its use carries with it all the import and implications of its CAPM definition.

Along with the idea of beta, CAPM also served to formalize the notion of a market portfolio. A market portfolio in CAPM terms is a portfolio of assets that acts as a proxy for the market. Although practical versions of market portfolios in the form of market averages were already prevalent at the time the theory was proposed, CAPM definitely served to underscore the significance of these market averages.

Armed with the twin ideas of market portfolio and beta, CAPM attempts to explain asset returns as an aggregate sum of component returns. In other words, the return on an asset in the CAPM framework can be separated into two components. One is the market or systematic component, and the other is the residual or nonsystematic component. More precisely, if is the return on the asset, is the return on the market portfolio, and the beta of the asset is denoted as β, the formula showing the relationship that achieves the separation of the returns is given as