Über die Autorin bzw. den Autor

Robert Engle is the Michael Armellino Professor in the Management of Financial Services at New York University's Leonard N. Stern School of Business. His books include Cointegration, Causality, and Forecasting. He was awarded the 2003 Nobel Prize in economics.

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"This book offers a comprehensive and thorough discussion of the Dynamic Conditional Correlation class of models. It presents things in an easy-to-read, coherent, and unified framework, and includes new and interesting empirical findings and economic insights.Anticipating Correlations should serve as the authoritative reference for this important class of models."--Tim Bollerslev, Duke University

"This is a timely volume about how to model the conditional correlations among asset returns. Engle has pioneered much of the field and the book is likely to be popular."--Neil Shephard, University of Oxford

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"This book offers a comprehensive and thorough discussion of the Dynamic Conditional Correlation class of models. It presents things in an easy-to-read, coherent, and unified framework, and includes new and interesting empirical findings and economic insights.Anticipating Correlations should serve as the authoritative reference for this important class of models."--Tim Bollerslev, Duke University

"This is a timely volume about how to model the conditional correlations among asset returns. Engle has pioneered much of the field and the book is likely to be popular."--Neil Shephard, University of Oxford

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Anticipating Correlations

Princeton University Press

Contents

Introduction......................................................................vii1 Correlation Economics..........................................................11.1 Introduction..................................................................11.2 How Big Are Correlations?.....................................................31.3 The Economics of Correlations.................................................61.4 An Economic Model of Correlations.............................................91.5 Additional Influences on Correlations.........................................132 Correlations in Theory.........................................................152.1 Conditional Correlations......................................................152.2 Copulas.......................................................................172.3 Dependence Measures...........................................................212.4 On the Value of Accurate Correlations.........................................253 Models for Correlation.........................................................293.1 The Moving Average and the Exponential Smoother...............................303.2 Vector GARCH..................................................................323.3 Matrix Formulations and Results for Vector GARCH..............................333.4 Constant Conditional Correlation..............................................373.5 Orthogonal GARCH..............................................................373.6 Dynamic Conditional Correlation...............................................393.7 Alternative Approaches and Expanded Data Sets.................................414 Dynamic Conditional Correlation................................................434.1 DE-GARCHING...................................................................434.2 Estimating the Quasi-Correlations.............................................454.3 Rescaling in DCC..............................................................484.4 Estimation of the DCC Model...................................................555 DCC Performance................................................................595.1 Monte Carlo Performance of DCC................................................595.2 Empirical Performance.........................................................616 The MacGyver Method............................................................747 Generalized DCC Models.........................................................807.1 Theoretical Specification.....................................................807.2 Estimating Correlations for Global Stock and Bond Returns.....................838 FACTOR DCC.....................................................................888.1 Formulation of Factor Versions of DCC.........................................888.2 Estimation of Factor Models...................................................939 Anticipating Correlations......................................................1039.1 Forecasting...................................................................1039.2 Long-Run Forecasting..........................................................1089.3 Hedging Performance In-Sample.................................................1119.4 Out-of-Sample Hedging.........................................................1129.5 Forecasting Risk in the Summer of 2007........................................11710 Credit Risk and Correlations...................................................12211 Econometric Analysis of the DCC Model..........................................13011.1 Variance Targeting...........................................................13011.2 Correlation Targeting........................................................13111.3 Asymptotic Distribution of DCC...............................................13412 Conclusions....................................................................137References........................................................................141Index.............................................................................151

Chapter One

1.1 Introduction

Today there are almost three thousand stocks listed on the New York Stock Exchange. NASDAQ lists another three thousand. There is yet another collection of stocks that are unlisted and traded on the Bulletin Board or Pink Sheets. These U.S.-traded stocks are joined by thousands of companies listed on foreign stock exchanges to make up a universe of publicly traded equities. Added to these are the enormous number of government and corporate and municipal bonds that are traded in the United States and around the world, as well as many short-term securities. Investors are now exploring a growing number of alternative asset classes each with its own large set of individual securities. On top of these underlying assets is a web of derivative contracts. It is truly a vast financial arena. A portfolio manager faces a staggering task in selecting investments.

The prices of all of these assets are constantly changing in response to news and in anticipation of future performance. Every day many stocks rise in value and many decline. The movements in price are, however, not independent. If they were independent, then it would be possible to form a portfolio with negligible volatility. Clearly this is not the case. The correlation structure across assets is a key feature of the portfolio choice problem because it is instrumental in determining the risk. Recognizing that the economy is an interconnected set of economic agents, sometimes considered a general equilibrium system, it is hardly surprising that movements in asset prices are correlated. Estimating the correlation structure of thousands of assets and using this to select superior portfolios is a Herculean task. It is especially difficult when it is recognized that these correlations vary over time, so that a forward-looking correlation estimator is needed. This problem is the focus of this book. We must "anticipate correlations" if we want to have optimal risk management, portfolio selection, and hedging.

Such forward-looking correlations are very important in risk management because the risk of a portfolio depends not on what the correlations were in the past, but on what they will be in the future. Similarly, portfolio choice depends on forecasts of asset dependence structure. Many aspects of financial planning involve hedging one asset with a collection of others. The optimal hedge will also depend upon the correlations and volatilities to be expected over the future holding period. An even more complex problem arises when it is recognized that the correlations can be forecast many periods into the future. Consequently, there are predictable changes in the risk-return trade-off that can be incorporated into optimal portfolios.

Derivatives such as options are now routinely traded not only on individual securities, but also on baskets and indices. Such derivative prices are related to the derivative prices of the component assets, but the relation depends on the correlations expected to prevail over the life of the derivative. A market for correlation swaps has recently developed that allows traders to take a position in the average correlation over a time interval. Structured products form a very large...