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Financial markets respond to information virtually instantaneously. Each new piece of information influences the prices of assets and their correlations with each other, and as the system rapidly changes, so too do correlation forecasts. This fast-evolving environment presents econometricians with the challenge of forecasting dynamic correlations, which are essential inputs to risk measurement, portfolio allocation, derivative pricing, and many other critical financial activities. In Anticipating Correlations, Nobel Prize-winning economist Robert Engle introduces an important new method for estimating correlations for large systems of assets: Dynamic Conditional Correlation (DCC). Engle demonstrates the role of correlations in financial decision making, and addresses the economic underpinnings and theoretical properties of correlations and their relation to other measures of dependence. He compares DCC with other correlation estimators such as historical correlation, exponential smoothing, and multivariate GARCH, and he presents a range of important applications of DCC. Engle presents the asymmetric model and illustrates it using a multicountry equity and bond return model. He introduces the new FACTOR DCC model that blends factor models with the DCC to produce a model with the best features of both, and illustrates it using an array of U.S. large-cap equities. Engle shows how overinvestment in collateralized debt obligations, or CDOs, lies at the heart of the subprime mortgage crisis--and how the correlation models in this book could have foreseen the risks. A technical chapter of econometric results also is included. Based on the Econometric and Tinbergen Institutes Lectures, Anticipating Correlations puts powerful new forecasting tools into the hands of researchers, financial analysts, risk managers, derivative quants, and graduate students.
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Anticipating Correlations This page intentionally left blank Anticipating Correlations A New Paradigm for Risk Management Robert Engle Princeton University Press Princeton and Oxford Copyright © 2009 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved ISBN: 978-0-691-11641-9 (alk. paper) Library of Congress Control Number: 2008939934 British Library Cataloging-in-Publication Data is available This book has been composed in LucidaBright using TEX Typeset and copyedited by T&T Productions Ltd, London Printed on acid-free paper ∞ press.princeton.edu Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Contents Introduction vii 1 Correlation Economics 1.1 Introduction 1.2 How Big Are Correlations? 1.3 The Economics of Correlations 1.4 An Economic Model of Correlations 1.5 Additional Influences on Correlations 1 1 3 6 9 13 2 Correlations in Theory 2.1 Conditional Correlations 2.2 Copulas 2.3 Dependence Measures 2.4 On the Value of Accurate Correlations 15 15 17 21 25 3 Models for Correlation 3.1 The Moving Average and the Exponential Smoother 3.2 Vector GARCH 3.3 Matrix Formulations and Results for Vector GARCH 3.4 Constant Conditional Correlation 3.5 Orthogonal GARCH 3.6 Dynamic Conditional Correlation 3.7 Alternative Approaches and Expanded Data Sets 29 30 32 33 37 37 39 41 4 Dynamic Conditional Correlation 4.1 DE-GARCHING 4.2 Estimating the Quasi-Correlations 4.3 Rescaling in DCC 4.4 Estimation of the DCC Model 43 43 45 48 55 5 DCC Performance 5.1 Monte Carlo Performance of DCC 5.2 Empirical Performance 59 59 61 6 The MacGyver Method 74