Handbook of Fixed-Income Securities

A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities

Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape.

Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature:

• An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them

• Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments

• Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints

• The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility

• Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds

• Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing

• Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints

• Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises

A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering,

Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets.

Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.

• Language: English
• Publisher: Wiley
• Release date: Mar 23, 2016
• ISBN: 9781118709269

Book preview

Dedication

To Tommaso, Gabriele, Sofia, and Micaela.

Notes on Contributors

Yacine Aït-Sahalia is the Otto A. Hack ‘03 Professor of Finance and Economics at Princeton University. He served as the inaugural Director of the Bendheim Center for Finance from 1998 to 2014. He was previously an Assistant Professor (1993–1996), Associate Professor (1996–1998), and Professor of Finance (1998) at the University of Chicago’s Graduate School of Business. He is a Fellow of the Econometric Society, a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, an Alfred P. Sloan Foundation Research Fellow, a Fellow of the Guggenheim Foundation, and a Research Associate for the National Bureau of Economic Research (NBER). His research has been widely published in the leading academic journals in finance, econometrics, and statistics. He co-wrote the book High Frequency Financial Econometrics, published in 2014, with Jean Jacod. He is the recipient of the 1997 Michael Brennan Award, the 1998 Cornerstone Research Award, the 2001 FAME Research Award, and the 2003 Dennis J. Aigner Award. He recently served as the editor of the Review of Financial Studies and currently serves as the editor of the Journal of Econometrics. He received his PhD in Economics from the Massachusetts Institute of Technology in 1993 and is a graduate of France’s Ecole Polytechnique.

Pierluigi Balduzzi is Professor of Finance at the Carroll School of Management at Boston College, where he teaches Masters and PhD-level courses in Finance. His main area of research is empirical asset pricing, with a focus on the fixed-income markets. His research has appeared in leading finance and economic journals, such as the Journal of Finance, the Journal of Financial Economics, and the American Economic Review. He currently serves as an Associate Editor of the Journal of Business and Economic Statistics and the Journal of Financial Econometrics.

Jules van Binsbergen is an Associate Professor at the Wharton School of the University of Pennsylvania and conducts theoretical and empirical research in finance. His current work focuses on asset pricing, in particular the relationship between financial markets and the macroeconomy, and the organization, skill and performance of financial intermediaries. Some of his recent research focuses on measuring the skill of mutual fund managers, the term structure of cash flow growth and stock return predictability, and the implications of good-specific habit formation for asset prices. His research has appeared in leading academic journals, such as the American Economic Review, the Journal of Finance, the Journal of Financial Economics, and the Journal of Monetary Economics. He received his PhD from the Fuqua School of Business at Duke University. He previously taught at the Stanford Graduate School of Business and the Kellogg School of Management.

Michael W. Brandt is the Kalman J. Cohen Professor of Business Administration at the Fuqua School of Business of Duke University. He conducts empirical and theoretical research in finance. His current work focuses on quantitative portfolio management, risk management, currency and fixed-income markets, and financial econometrics. Professor Brandt’s research has appeared in leading academic journals, including the American Economic Review, Journal of Business, Journal of Finance, Journal of Financial Economics, Journal of Monetary Economics, and Review of Financial Studies. He has served as co-editor of the Review of Finance, the official journal of the European Finance Association, and as associate editor of the Journal of Finance, the official journal of the American Finance Association. He is also a Faculty Research Associate of the NBER. Before joining Fuqua in 2003, Professor Brandt was at the Wharton School of the University of Pennsylvania for 6 years.

Professor Damiano Brigo is Chair in Mathematical Finance and Stochastic Analysis at the Department of Mathematics at Imperial College London. Former roles include Gilbart Professor at King’s College London, Managing Director at Fitch Ratings, Director of the Capco Institute, and Head of Credit Models in Banca IMI. Dr Brigo published 80+ works in Quantitative Finance, Probability and Statistics, and field reference books in interest rate and credit modeling, and he is in the editorial board of several journals including Mathematics of Control, Signals and Systems and the International Journal of Theoretical and Applied Finance. Dr Brigo has been the most cited author in Risk Magazine in 2006, 2010, and 2012. His interests include valuation, funding, risk, credit, and stochastic differential geometry. Dr Brigo holds a PhD in Mathematics.

Andrea Buraschi is the Chair in Finance at Imperial College London and a research fellow at the Center for Economic and Policy Research. He has been a visiting professor at the University of Chicago Booth and Columbia University. He earned his PhD from the University of Chicago specializing in Financial Economics. His area of research is empirical asset pricing and general equilibrium models of bond and derivative markets. His work has appeared in several publications, including the Journal of Finance, the Journal of Financial Economics, Review of Financial Studies, Journal of Derivatives, European Financial Management, and the Journal of Banking and Finance. Prof. Buraschi is a recipient of several best paper and teaching awards and serves as Associate Editor for the Review of Finance.

Christopher Culp is a Senior Advisor with Compass Lexecon, Adjunct Professor at the Swiss Finance Institute, Research Fellow at the Johns Hopkins Institute for Applied Economics, and Honorarprofessor at Universität Bern in the Institut für Finanzmanagement. His research and teaching specializations include derivatives, structured finance, insurance, risk management, credit markets, and clearing/settlement, and he also provides advisory consulting services and testimonial expertise in these areas. He has written four books, co-edited two books (one with Merton Miller and the other with William Niskanen), and has authored numerous articles on the same topics. Dr Culp is on the editorial advisory boards of the Journal of Applied Corporate Finance, the Journal of Structured Finance, and Futures Industry magazine, and was previously on the editorial advisory boards of Derivatives Quarterly (where he was also co-editor), FMA Online, and the Journal of Risk Finance. He holds a PhD in finance from the University of Chicago’s Booth School of Business, where he was also an Adjunct Professor of Finance from 1998 to 2013.

Magnus Dahlquist is the Peter Wallenberg Professor of Finance at the Stockholm School of Economics (SSE). He is also a Research Fellow with the Centre for Economic Policy Research (CEPR), London, and with the Network for Studies on Pensions, Aging and Retirement (NETSPAR) in the Netherlands. Dahlquist’s research interests lie in asset management, asset pricing, and international finance. His current research focuses on (i) individuals’ and institutions’ investment behavior and the design of pension plans, (ii) trading strategies in the bond and currency markets and their relation to fundamentals, and (iii) performance evaluation and practical problems related to portfolio selection. Dahlquist has been an advisor to several financial institutions as well as government authorities.

Alexander David, PhD, is the Haskayne Research Professor of Finance at the Haskayne School of Business at the University of Calgary. Before joining Haskayne, he worked at the Federal Reserve Board in Washington DC as a staff economist and the Olin School of Business at Washington University in St Louis. He has taught classes in financial risk management, advanced corporate finance, options and futures, energy finance, investments, and asset pricing in the undergraduate, MBA, Executive MBA, and PhD programs. His main research interest is the modeling of changing investors’ uncertainty about the state of economic fundamentals and their impact on asset prices. His research has been published in leading academic journals such as the Journal of Political Economy, Journal of Finance, Review of Financial Studies, and Journal of Financial Economics.

Jens Dick-Nielsen is Associate Professor of Finance at the Center for Financial Frictions (FRIC), Department of Finance, Copenhagen Business School where he teaches Masters and Executive-level courses in finance and credit risk modeling. His research on credit risk and liquidity risk has impacted European Banking regulation and has been published among others in the Journal of Financial Economics and the Journal of Fixed Income.

Jefferson Duarte is the Gerald D. Hines Professor of Real Estate Finance at the Jesse H. Jones Graduate School of Business at Rice University. He is an expert on fixed-income and mortgage-backed securities. His research has received many awards including the prestigious Fama-DFA prize for the best asset pricing paper published in the Journal of Financial Economics. Dr. Duarte’s research has also been covered in United States and international media, including the following papers and magazines: The Wall Street Journal, Financial Times, and The Economist. Prior to joining academia, Dr. Duarte worked at the proprietary trading desk of JP Morgan Chase in New York as part of the group managing a multibillion dollar commercial mortgage-backed security (CMBS) portfolio.

Matthias Fleckenstein joined Cornerstone Research, a leading economic and financial consulting firm, after obtaining his PhD at UCLA in 2013. Matthias also has Masters’ degrees in Quantitative Finance, Business Administration, and Industrial Engineering and Management. Matthias has consulted on complex financial issues arising in litigation, including securities class actions and antitrust matters in derivatives markets. For joint work with Francis Longstaff and Hanno Lusting on TIPS markets, he received a Distinguished Paper award as part of the Amundi Smith Breeden Prize for the best paper in the Journal of Finance on capital markets.

Jean-Sébastien Fontaine is a principal researcher in the Financial Markets Department at the Bank of Canada. In this role, he studies the interaction between monetary policy and fixed-income markets. His research focuses on the effect of funding liquidity on asset prices; macrofinance models of the term structure of interest rates; and the information content of option prices. He holds a PhD from the Université de Montréal, and his research has been published in the Review of Financial Studies and the Review of Finance.

René Garcia holds a PhD in Economics from Princeton University. He is Chair Professor of Finance at EDHEC Business School in Nice (France). Formerly, he was a professor at University of Montreal, held the Hydro-Québec Chair in Risk Management, and was a Research Fellow of the Bank of Canada. He was also the scientific director of the Centre for Interuniversity Research and Analysis on Organizations (CIRANO). He is a co-founding editor of the Journal of Financial Econometrics, published by Oxford University Press and was Editor-in-Chief until June 2012. His recent research focuses on the evaluation of asset pricing models accounting for higher moments, long-run risk asset pricing models, and the funding liquidity premium in bonds and equities. His work has appeared in numerous publications, including the Journal of Finance, Review of Financial Studies, Econometrica, and Journal of Econometrics.

Henrik Hasseltoft is an Assistant Professor of Finance at the University of Zurich. He holds a PhD in Finance from the Stockholm School of Economics. Hasseltoft’s research on asset pricing lies in the intersection between finance and macroeconomics. His empirical research focuses on predictability of asset returns in equity, bond, and currency markets while his theoretical research focuses on understanding the time-series and cross-sectional aspects of asset prices using consumption-based models. Hasseltoft is affiliated with the Swiss Finance Institute.

Robert L Kimmel is an Associate Professor at the NUS Business School, and the Deputy Director of Research at the Risk Management Institute, at the National University of Singapore. He received his PhD in finance from the University of Chicago Graduate School of Business. Before joining NUS, Prof. Kimmel was at Princeton University, Ohio State University, and EDHEC Business School. His research focuses on the econometrics of continuous-time models for asset prices, and on methods for estimation and testing of linear factor models of asset returns.

David Lando is Professor of Finance at Copenhagen Business School and Director of the Center for Financial Frictions (FRIC) funded by the Danish National Research Foundation. He holds a Master’s degree from the joint Mathematics–Economics program at the University of Copenhagen and a PhD in Statistics from Cornell University. His main area of research in finance is credit risk modeling and risk management, and some of his work has appeared in Econometrica, Journal of Financial Economics, and Review of Financial Studies. He has been a visiting scholar at among other places Princeton University, the Federal Reserve Board in Washington, The Federal Reserve Bank of New York. Before joining the Copenhagen Business School, he was a professor at the Department of Applied Mathematics and Statistics at the University of Copenhagen.

Qing (Daphne) Liu is currently a PhD student in Mathematical Finance at Imperial College London under the supervision of Prof. Damiano Brigo. Her main research focus is on developing and studying a consistent derivative valuation framework incorporating counterparty credit risk, collateralization, and funding risk.

Hanno Lustig joined Stanford GSB in 2015. Prior to that, he taught at the University of Chicago, the UCLA Economics department, and UCLA’s Anderson School of Management. He graduated in 2002 from Stanford University with a PhD in economics. He has been awarded the JP Morgan Award for the Best Paper on Financial Institutions and Markets in 2012 as well as the NASDAQ OMX Award for the Best Paper on Asset Pricing in 2010. Lustig is a Faculty Research Fellow at the NBER and an associate editor at the Journal of Finance and Econometrica. Francis Longstaff and Lustig were also awarded a Distinguished Paper distinction as part of the Amundi Smith Breeden Prize for the best paper in the Journal of Finance on capital markets for their work on TIPS markets with Matthias Fleckenstein.

Professor Francis Longstaff, PhD, CPA, CFA, is the Allstate Professor of Insurance and Finance at the UCLA Anderson School. His research focuses primarily on fixed-income and derivatives markets, asset pricing, and the valuation of illiquid assets. He has published over 60 articles in top finance, economics, and science journals. He is a research associate of the NBER.

Gerardo Manzo is the Fama-Miller Center Postdoctoral Researcher at the University of Chicago Booth School of Business. He earned his PhD in Money and Finance at the University of Rome Tor Vergata in 2013 after an 18-month visiting scholar position at the Booth School of Business. Gerardo conducts research on asset pricing, credit risk, systemic risk, and macrofinance. He is the recipient of several academic awards, including the 2014 UniCredit & Universities Best PhD Thesis Award, the 2014 John A. Doukas Best PhD Paper Award, and the 2011 Orazio Ruggeri Best Master Thesis Award.

Doug McManus is the Director of Financial Research in the Office of the Chief Economist at Freddie Mac where he has worked on issues related to financial markets, credit scoring, credit loss forecasting, fair lending testing, and house price modeling. While at Freddie Mac, he has also served as an advisor to the US Treasury on housing and mortgage modification issues. Prior to joining Freddie Mac, he was at the Board of Governors of the Federal Reserve System where he conducted research on commercial bank risk management, capital requirements, and general econometric methodology. He has published articles in the Journal of Fixed Income, Journal of Banking and Finance, Real Estate Economics, and the Journal of Econometrics and has been issued many US patents in the area of house price forecasting and credit scoring. He received his PhD in Economics at the University of Pennsylvania in 1985.

Antonio Mele is a Senior Chair at the Swiss Finance Institute and a Professor of Finance at University of Lugano, after a decade spent as a tenured faculty at the London School of Economics. He is also a research fellow of the CEPR. He holds a PhD in Economics from the University of Paris. His work focuses on capital market volatility, interest rates and credit markets, macrofinance, and information in securities markets, and has appeared in journals such as the Journal of Financial Economics, the Review of Economic Studies, the Review of Financial Studies, and the Journal of Monetary Economics. His work outside academia includes developing fixed-income volatility indexes for Chicago Board Options Exchange. He is currently a member of the Securities and Markets Stakeholder Group of the European Securities Markets Authority (ESMA). At ESMA, he is also a member of the Group of Economic Advisers.

Fabio Moneta is an Assistant Professor of Finance at the Stephen J.R. Smith School of Business, Queen’s University, Canada. He received his PhD in Finance from the Carroll School of Management, Boston College. He also holds an MSc in Finance from CORIPE Piemonte (Turin, Italy) and a BA in Economics from the University of Pisa in Italy. His research interests concentrate on investments, institutional investors, mutual fund performance, and empirical asset pricing. He has presented his research at the American Finance Association and the European Finance Association meetings, as well as other conferences and universities in Europe and North America. He has published articles on mutual fund performance, forecasting, and international business cycle synchronization in a variety of journals.

Yoshiki Obayashi is a managing director at Applied Academics LLC in New York. The company specializes in developing and commercializing ideas emanating from a growing think tank of academic researchers selected on the basis of their work’s relevance to practice in the finance industry. His most recent projects range from running systematic trading strategies for funds to developing fixed-income volatility indexes for Chicago Board Options Exchange. Yoshiki Obayashi previously managed US and Asian credit portfolios for a proprietary fixed-income trading group at an investment bank. He holds a PhD in Finance and Economics from Columbia Business School.

Andrea Pallavicini is the head of equity, FX, and commodity models at Banca IMI, Milan, and visiting professor at the Department of Mathematics of Imperial College, London. He holds a PhD in Theoretical and Mathematical Physics from the University of Pavia for his research activity at CERN. Over the years, he published several papers in financial modeling, theoretical physics, and astrophysics. He is the author of the books Credit Models and the Crisis: a journey into CDOs, copulas, correlations and dynamic models, Wiley (2010), and Counterparty Credit Risk, Collateral and Funding with pricing cases for all asset classes, Wiley (2013).

Carolin Pflueger is an Assistant Professor of Finance in the Sauder School of Business at the University of British Columbia. She received her PhD in Business Economics from Harvard University in 2012. Her research focuses on asset pricing and macroeconomics, bond risks and returns, and monetary policy. Her work has appeared in the Journal of Finance, Journal of Monetary Economics, and Journal of Business and Economic Statistics.

Riccardo Rebonato is Professor of Finance at EDHEC Risk Institute and a Professorial fellow at the Edinburgh University. He was previously Global Head of Interest Rates and FX Analytics at PIMCO, a Visiting Lecturer at Oxford University (Mathematical Finance). He sits on the board of Trustees for GARP and was on the Board of ISDA for 11 years. He holds doctorates in Nuclear Engineering and in Condensed Matter Physics (Stony Brook University), and was a postdoctoral Research Fellow in physics at Oxford University (Corpus Christi) and Research Fellow at Brookhaven National Laboratory and Institut Laue Langevin (Grenoble). He is the author of several books in finance and of many papers in academic journals in the same area.

David Sloth is a quantitative strategist/structure in Rate Options and Inflation Trading at Danske Bank Markets, Copenhagen. He holds a PhD in Mathematical Finance from Aarhus University. His research focuses on derivatives pricing, trading strategies, counterparty credit and funding risk, and numerical methods. Dr. Sloth’s work has appeared in several publications, including Quantitative Finance.

Josephine M. Smith, PhD, is a Vice President in the Model Portfolios Solutions team at BlackRock, where she is responsible for the research, development, and management of strategic and tactical asset-allocation models. Before joining BlackRock, Dr. Smith was an assistant professor of finance at the New York University Stern School of Business, where she taught an advanced fixed income course to undergraduates and MBAs. Before this, she worked on various research projects at the Bureau of Labor Statistics, Federal Reserve Bank of San Francisco, and the Division of Monetary Affairs at the Federal Reserve Board in Washington, DC.

Oleg Sydyak is the Director of the Asset and Liability Strategy group at a major financial services company. Oleg has designed and implemented the firm’s strategic positioning and product offering for liability-driven investing (LDI) strategies and asset and liability management (ALM) studies. He is responsible for the ongoing development of LDI strategies and ALM studies, including analysis of the capital markets, modeling of asset and liability cash flows, and making asset allocation recommendations. Oleg regularly contributes to the firm’s thought leadership related to LDI strategies and ALM studies through writing white papers and developing and enhancing analytic capabilities.

Claudio Tebaldi is Associate Professor in quantitative methods for economics, finance, and insurance at the Department of Finance of L. Bocconi University, Milano. In March 2015, he received the national habilitation for full professorship. In 2004, he visited the Faculty of Finance, Anderson School of Management, UCLA. He owns a PhD in Statistical Mechanics, an MPhil in Complex Systems, Institute for Advanced Studies (SISSA) and a Master in Economics and Finance (Venice International University). His research has appeared in numerous publications, including the Review of Financial Studies and Mathematical Finance, among others.

Pietro Veronesi is the Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. His research focuses on asset pricing, and especially on stock and bond valuation, bubbles and crashes, return predictability, stochastic volatility, and recently, on the interaction between government interventions and asset prices. His work has appeared in leading academic journals, such as the Journal of Finance, Journal of Financial Economics, Review of Financial Studies, the Journal of Political Economy, the American Economic Review, and the Quarterly Journal of Economics. He is the recipient of several awards, including the 2015 AQR Insight award, the 2012 and 2003 Smith Breeden prizes from the Journal of Finance, the 2006 Fama/DFA prize from the Journal of Financial Economics, and the 1999 Barclays Global Investors/Michael Brennan prize from the Review of Financial Studies. In 2010, he wrote the popular textbook Fixed Income Securities, published by John Wiley and Sons. Veronesi is also a research associate of the NBER, a research fellow of the Center for Economic and Policy Research, and a former co-editor of the Review of Financial Studies. He received his PhD in Economics from Harvard University in 1997, his Master in Econometrics and Mathematical Economics from the London School of Economics in 1993, and is a graduate of Bocconi University.

Luis M. Viceira is the George E. Bates Professor at the Harvard Business School, where he has been in the faculty since 1998. He received his MA and PhD in Economics from Harvard University. He is a Research Associate in the NBER’s Program on Asset Pricing, a Research Fellow and member of the Scientific Council of Netspar, the Network for Studies on Pensions, Aging, and Retirement, a Fellow of the TIAA-CREF Institute, and a Public Governor of the Financial Industry Regulatory Authority. Viceira is a financial economist interested in the study of asset allocation models, with an emphasis on models that explore the asset allocation implications of empirical regularities in asset pricing and on life-cycle investing, asset pricing, with an emphasis on models of the term structure of interest rates, household finance, and international finance. His research has been published in the Journal of Finance, the Journal of Financial Economics, the Review of Financial Studies, the American Economic Review, the Quarterly Journal of Economics, and the Review of Finance, among others. He is also the author of the book Strategic Asset Allocation with John Y. Campbell. Viceira is also interested in the design of pension fund systems, the design of investment strategies for long-term investors, the management and organization of large institutional investors, and product innovation in the money management industry.

Paul Whelan is an Assistant Professor of Finance at Copenhagen Business School where he teaches asset pricing to MSc and PhD students. His research interests are in the areas of asset pricing and financial econometrics with a focus on fixed-income markets. Dr. Whelan has won several awards for his work, including the GARP Risk Management Research Award (2013), Carefin-Bocconi Research in Finance Grant Award (2012), and Q-Group Grant Award (2011).

Preface

Fixed income markets have been changing dramatically over the past few years, especially after the financial crisis. New regulation, aggressive monetary policy that led to zero nominal rates, large expansions of government debt, new empirical behavior of Treasury securities, appearance of new securities, and so on have been changing the way fixed income markets work. Old theories have been challenged and new ones have been proposed. Much new research has been poured into uncovering new empirical properties of fixed income securities. Many of us who teach fixed income courses have had to change substantial portions of class material as many old methodologies and formulas have become obsolete and to make space for new material. All these recent changes make the market for fixed income securities all the more exciting.

I accepted to be the editor of this handbook because I thought it was important to collect the new research and new methodologies all in one place. I tried to balance basic material with more advanced material so that even readers new to fixed income will be able to read and understand most of the chapters. Still, readers that are already well versed in the intricacies of fixed income markets will also find most of the handbook material interesting, both because most of the chapters contain novel research and because some of the chapters deal with very advanced new topics. Finally, I also tried to balance empirical evidence with methodology. Both types of chapters are very informative, and in fact, given the novelty of much of the material, they are complementary to each other and illuminating. Kudos to the contributors who took great effort and did a marvelous job in writing intriguing and engaging chapters.

The Handbook

I now describe the handbook and the topics in more detail.

The handbook is divided into eight parts that cover different topics. The first part is an overview of current fixed income markets, namely, U.S. Treasuries, money markets, and mortgage-related securities. More specifically, in Chapter 1, provide an overview of fixed income markets by discussing some recent developments, such as their growth, the recent aggressive monetary policy, and the puzzling behavior of bond betas in recent times. I also cover some of the terminologies, concepts, and methodologies that lay the foundations for many of the following chapters. In Chapter 2, Smith teaches us about money market instruments, an important market that played a special role during the financial crisis. In Chapter 3, Fleckenstein, Longstaff, and Lustig cover the U.S. Treasury inflation-protected securities and discuss the ways these securities can be combined with regular Treasury securities to learn about expected future inflation and the inflation risk premium. Finally, in Chapter 4, Duarte and McManus discuss the mortgage-backed securities (MBS) market. The MBS market has been especially affected by the crisis, as the two giant government-sponsored enterprises (GSEs) Fannie Mae and Freddie Mac needed to be placed under government conservatorship in 2008. Duarte and McManus walk us through the changes in the MBS market and the new pricing methodologies that make use of large datasets that are now available from the GSEs.

Part 2 of this handbook is about monetary policy and bond markets, a critical topic especially given the aggressive expansionary policy measures pursued by the Federal Reserve in the United States, the Bank of England in the United Kingdom, and the European Central Bank in Europe in the wake of the financial crisis. Treasury securities played the role of safe havens for investors during the crisis as risk-averse investors sold their holdings of risky securities and searched for safe investments. Numerous questions arise on the size (if any) of the impact of monetary policy on bond prices and the transmission channel through which monetary policy affects short- and long-term yields. In Chapter 5, Buraschi and Whelan discuss the channels through which conventional monetary policy affects interest rates and the evidence in favor of the effects. The empirical methodology exploits high-frequency data to identify the impact of monetary policy shocks on the term structure of interest rates. In Chapter 6, Buraschi and Whelan organize the recent evidence about unconventional monetary policy, that is, the exceptional measures taken by the Federal Reserve, Bank of England, and European Central Bank to cope with the 2008–2009 crisis, as well as the subsequent slow recovery and the (still ongoing) European debt crisis.

Part 3 covers interest rate risk management, with applications to asset–liability management (ALM). As the number of institutions issuing debt instruments and investing in fixed income securities around the world increases, the issue of interest rate risk management takes center stage. Indeed, as shown in Chapter 1, the size of the interest rate derivatives market increased 10-fold over the last 20 years, as the risk-management needs of institutions increased. Chapter 7, by Sydyak, covers the traditional tools of interest rate risk management, from the concept of duration and convexity to key-rate duration and factor analysis, and illustrates their use in ALM problems. In Chapter 8, Brandt and Van Binsbergen show how modern techniques of dynamic portfolio allocation with constraints can be profitably used to solve ALM problems for numerous types of constrained institutions, such as pension funds and insurance companies. Such modern techniques use advanced numerical methodologies, such as Monte Carlo simulations to identify the optimal strategies, and are becoming widely used in the industry to carry out interest rate riskmanagement.

Part 4 of this handbook deals with the predictability of bond returns, a hot topic that interests both practitioners who look for the best investment strategies and financial economists who try to understand what drives the variation of U.S. Treasury bond prices. In Chapter 9, Dahlquist and Hasseltoft review the empirical methodologies and the empirical evidence supporting the view that bond risk premia are time varying. The chapter does not limit itself to just a review of U.S. Treasuries but also considers other countries, such as the United Kingdom, Switzerland, and Germany. Interestingly, bond risk premia across countries display a strong comovement, which the authors identify with a global predicting factor. In Chapter 10, Pflueger and Viceira survey and provide novel evidence about the predictability of bond returns and especially focus the analysis on the returns of inflation-protected securities. This chapter contains a discussion of the liquidity premium that is apparent in inflation-protected bonds. Finally, in Chapter 11, Balduzzi and Moneta survey the literature that identifies bond risk premia using high-frequency data. This chapter contains an intriguing discussion of the evidence about time variation in risk premia at high frequencies and the impact of market microstructure effects, and it even touches upon the recent literature on high-frequency trading and its impact on bond returns.

Part 5 covers a number of advanced topics on fixed income models and their estimation. In Chapter 12, Rebonato discusses the popular class of affine term structure models. This chapter also covers the concept of market price of risk and the recent evidence about time-varying risk premia, now casted in fully fledged no-arbitrage term structure models. In Chapter 13, ït-Sahalia and Kimmel review several empirical methodologies used to estimate term structure models, with a detailed discussion of their pros and cons. In Chapter 14, Fontaine and Garcia focus on several recent models and evidence on old fixed income topics, including some new evidence about the expectations hypothesis, the importance of liquidity and liquidity premia, and, interestingly, the impact of the zero lower bound of nominal rates – that is, the fact that nominal interest rates cannot become negative – on term structure modeling. The latter issue is especially important in current markets with extremely low interest rates. Finally, in Chapter 15, David and Veronesi discuss the recent theories and evidence about the time-varying correlation of Treasury bond returns with stock market returns, a correlation that was very positive in the 1980s but became very negative in the 2000s. During this time span, U.S. Treasuries moved from being a risky investment (their prices drop together with the stock market) to being a hedging vehicle (their prices rise when the stock market drops). The question is why.

Part 6 focuses on derivative securities. The financial crisis spurred a large amount of new regulation on interest rate derivatives. In Chapter 16, Culp walks us through the new regulation that shapes the derivatives markets, both in the United States and in Europe. This chapter provides numerous statistics about the current state of derivatives markets and reviews the new infrastructure, such as the introduction of central counterparties (CCPs) to clear OTC derivatives and the electronic execution platforms (EEPs). In Chapter 17, Tebaldi and Veronesi introduce the pricing of derivatives in the familiar – and relatively simple – context of binomial trees. This chapter also provides several real-world examples by applying the binomial – and trinomial – tree methodology to real-world securities. In Chapter 18, discuss the impact of the crisis and new regulation on the pricing of plain vanilla derivatives and especially the use of double-curve pricing of London Interbank Offered Rate (LIBOR)-based derivatives. This chapter is introductory and mostly highlights the main changes that occurred after the crisis.

Part 7 of this handbook is about advanced topics in derivative pricing. The chapters included in this part of the handbook use rather advanced techniques, such as continuous time models, Monte Carlo simulations, and the like. More specifically, in Chapter 19, Tebaldi and Veronesi develop the pricing formulas for derivatives in continuous time, derive the risk-neutral pricing formulas, and show their implementation using Monte Carlo simulations. In Chapter 20, Mele and Obayashi provide a detailed review of modern derivative pricing techniques. They also focus on modeling and trading volatility, which is an important topic in current fixed income markets. Finally, in Chapter 21, Brigo, Liu, Pallavicing, and Sloth discuss recent modifications to derivative pricing formulas as security dealers and financial institutions were forced to rethink their pricing methodologies in the wake of the 2008–2009 financial crisis. Such adjustments – such as credit value adjustments, funding value adjustments, and so on – make the pricing of OTC derivatives very complex and the chapter covers the new methodologies in detail.

Finally, Part 8 of this handbook looks at another class of fixed income instruments, that is, corporate and sovereign bonds. The focus of this part of the handbook is on the impact of credit risk on the pricing of fixed income securities. In particular, in Chapter 22, Dick-Nielsen and Lando review and discuss the existing pricing methodologies for corporate bonds. The chapter covers both the Merton model and the intensity-based model and provides an overview of their performance when confronted with the data. In Chapter 23, Manzo and Veronesi cover sovereign default risk. After a discussion of the pricing methodology for sovereign bonds, most of the chapter is devoted to the empirical analysis of sovereign credit risk and the credit risk premium, with a special attention to emerging economies and the recent European debt crisis.

The handbook is finally complete. I have to very much thank all of the contributors to this handbook, who have generously contributed their time to write a chapter and make this handbook a reality. I hope – and I am sure – that readers will learn a good deal from these contributions about the new reality of fixed income markets.

Pietro Veronesi

Chicago

3 June, 2015

Part I

Fixed Income Markets

1

Fixed Income Markets: An Introduction

Pietro Veronesi

Booth School of Business, University of Chicago, Chicago, IL, United States

1.1 Introduction

The last decade witnessed a profound transformation of fixed-income markets, in no small part due to the 2008–2009 financial crisis. The transformation took different forms: first, in the aftermath of the crisis, a number of countries – and the United States, in particular – had to expand their borrowing capacity in order to stimulate the economy. Lower tax revenues due to the economic downturn and higher government spending resulted in a large increase in government debt. As an example, Panel A of Figure 1.1 plots the outstanding U.S. debt from 1985 to 2014, compared to the mortgage-backed securities market, the corporate debt market, and the money market, which include commercial paper, bankers’ acceptance, and large time deposits. The first obvious observation is that all debt markets have been trending upward. The second observation is that while the U.S. Treasury debt market was the largest market between 1985 and the late 1990s, by year 2000, it was surpassed in sheer size by two forms of private debt, namely, the mortgage-backed securities market (the mortgage-related debt of individual households) and the corporate debt market (the debt market of private corporations). The United States has steadily becoming more in debt, but until the mid-2000s, this new debt was mainly private debt. With the advent of the financial crisis, the U.S. debt started a quick ascent to then take over both the mortgage-backed securities market and the corporate debt market, both of which instead show no growth after the crisis.

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Figure 1.1 The outstanding amount of U.S. debt

Panel A shows the outstanding marketable U.S. debt, mortgage-backed securities, and corporate debt from 1985 to 2014. Panel B reports the same quantities rescaled by U.S. GDP for the same period.

Source: SIFMA and FRED at Federal Reserve Bank of St Louis.

Clearly, the trends in Panel A are partly misleading, as it is true that the United States increased its nominal debt levels considerably since 1985, but the U.S. economy itself also grew substantially over the past 30 years. To take this into account, Panel B plots the same quantities as in Panel A but as a percentage of the U.S. Gross Domestic Product (GDP). The normalized U.S. debt shows a much more stable path over the sample period, as it had been indeed decreasing as a percentage of GDP between 1995 and 2008. The last 4 years, however, have seen the debt-to-GDP ratio rise from 30% to 70%, a clear concern that even led the rating agency Standard & Poor to downgrade the U.S. debt to AA+ from AAA in August 2011. In contrast to the U.S. Treasury debt, both the mortgage-backed securities market and the corporate debt market have been declining in the last few years as percentage of U.S. GDP. Finally, the size of the money markets also reached its peak in 2007, at around 20% of GDP and has been declining ever since. Smith (2015, Chapter 2 in this handbook) covers in detail the recent trends in money markets.

Besides declining in size (relative to the GDP), the mortgage-backed securities market also underwent several transformations on its own during the crisis, starting with U.S. government placing the two mortgage giants Freddie Mac and Fannie Mae under conservatorship. Duarte and McManus (2015, Chapter 4 in this handbook) discuss the evolution of the mortgage-backed securities market after the crisis. In particular, after the crisis, large amounts of new data have become available, and Duarte and McManus discuss new methodologies to price mortgage-backed securities.

A second important change in the U.S. debt market is the unprecedented aggressive monetary policies adopted by the Federal Reserve. In 2008, the Federal Reserve slashed its main reference interest rates – the Federal funds rate – to essentially zero and then moved to the so-called unconventional monetary policies, which essentially entailed large purchases of U.S. government debt as well as mortgage-backed securities. Panel A of Figure 1.2 plots the Federal funds rate over time, which highlights its precipitous drop from 5.27% in July 2007, to 2% in June 2008, to 0.25% in November 2008. Panel B shows the entire term structure of interest rates over the same time period, with maturities ranging from 3 months to 30 years.¹ The short-term 3-month Treasury bill rate hit (almost) zero at about the same time as the Federal funds rate, while the long-term yields steadily decreased over time, with some ups and downs in the last few years. Several questions arise on the impact that the Federal Reserve actually has on the term structure of interest rates. Buraschi and Whelan (2015a, 2015b, Chapters 5 and 6 in this handbook) discuss the existing evidence as well as provide new evidence about the impact of monetary policy on the term structure of interest rates.

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Figure 1.2 Federal funds and U.S. Treasury yields

Panel A shows the Federal funds effective rate from 1954–2014 (Source: Federal Reserve Bank of New York website). Panel B plots the zero-coupon bond yields from 1952–2014.

Source: Yields up to 5 years are from the Center for Research in Security Prices (CRSP). Yields from 10 to 30 are from Gürkaynak, Sack, and Wright (2007), updated series.

Third, in the aftermath of the 2008–2009 financial crisis, governments around the world introduced substantial regulatory changes with the aim of regulating trading in derivatives markets and curbing the risk-taking behavior of a number of financial institutions (see Culp (2015, Chapter 16 in this handbook) for a detailed discussion of the new regulatory environment). Indeed, Figure 1.3 shows that the size of the global fixed-income derivatives market has been increasing steadily over the two decades preceding the financial crisis. Panel A shows the increase in the notional amount of Over-the-Counter (OTC) derivatives from June 1998 to June 2013, starting from about $50 trillion and increasing to over $560 trillion over the 15-year period.² The figure also shows that interest rate swaps comprise the lion’s share of the OTC fixed-income derivatives market. While the tenfold increase in the OTC market is impressive, the global economy also expanded considerably over the same period. Panel B of Figure 1.3 renormalizes the notional amount of OTC derivatives by world GDP. Even after normalization, the total notional of OTC fixed-income derivatives increased from about 1.5 times the global GDP in 1998 to 8 times the global GDP at the end of 2007 and then mildly declined to 7 times the global GDP level by the end of 2012, possibly due to the effects of the financial crisis and the new regulation on derivatives.

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Figure 1.3 The notional amount of over-the-counter derivatives. Panel A shows the notional amount of OTC fixed-income derivatives from June 1998 to June 2013. Panel B reports the notional amount of OTC derivatives rescaled by the world global GDP from 1998 to 2012. OTC derivatives data are from the Bank for International Settlements, while global GDP data are from the World Bank.

One additional important change that came with the new regulation, however, is that the pricing of derivative securities has became even more complex than ever before. Even relatively simple plain vanilla securities became challenging to price, as market participants now require (or are required to require) full collateralization of derivative positions, which entail additional costs from holding the positions open. Veronesi (2015, Chapter 18 in this handbook) and Brigo et al. (2015, Chapter 21 in this handbook) discuss a number of pricing issues that arise from the new regulation.

Finally, besides the level of interest rates and additional regulation, the last decade also witnessed substantial changes in the behavior of bond returns themselves. For instance, the left panel of Figure 1.4 shows the quarterly series of the covariance of 5-year U.S. bond returns with the returns of the S&P 500 index. The covariance is computed from daily returns in each quarter. Quite dramatically, the covariance turned from being mostly positive until about the year 2000 to being mostly negative since then. The right panel shows that the realized beta of bonds with respect to the S&P 500 index (i.e., the covariance divided by the variance of the S&P 500 index) also experienced a rather dramatic fall over the same period. That is, since 2000, bonds have become an important hedge against stock market fluctuations. But why were not bonds a hedge historically? What has changed recently? The answers to these questions have obvious first-order consequences for asset allocation between two of the largest financial asset classes. David and Veronesi (2015, Chapter 15 in this handbook) review the recent literature on the movement of stock-bond covariance over time.

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Figure 1.4 Stock-bond covariance and bond beta of 5-year treasury bonds

The left panel plots the quarterly covariance between the S&P 500 daily return and the 5-year bond return computed from daily returns. The right panel plots the quarterly beta of the 5-year bond with respect to the S&P 500 index. The vertical gray bars indicate U.S. recessions dated by the National Bureau of Economic Research.

Source: Stock data are from the Center for Research in Security Prices (CRSP) while 5-year zero-coupon bond data are from Gürkaynak, Sack, and Wright (2007, updated series).

This introduction only touched upon a few of the major changes that took place in the last 10–15 years. This handbook collects recent research on these and many more topics. Indeed, in addition to sheer changes to the markets, novel methodologies and new fixed-income instruments have been introduced to fixed-income markets, and the handbook covers such recent topics as well.

In this introductory chapter, I cover some basic notions of fixed-income securities and markets. In the next section, I briefly discuss the U.S. Treasury market. Section 1.3 introduces the notions of interest rate and risk-free discounting. Section 1.4 focuses on the term structure of interest rates and on the economic forces that affect its shape. A brief discussion of the expectations hypothesis as well as forward rates as predictor of future interest rates is included in this section. Section 1.5 discusses U.S. Treasury coupon bonds and notes, as well as the methodologies to estimate the zero-coupon bond curve from coupon bonds. Section 1.6 discusses the real term structure of interest rates, as extracted from the U.S. Treasury Inflation-Protected Securities (TIPS), while Section 1.7 contains a discussion of the pricing of Floating Rate Notes (FRNs), which the U.S. Treasury started issuing in January 2014. Section 1.8 concludes.

1.2 U.S. Treasury Bills, Notes, and Bonds

A cursory look at the U.S. Treasury website immediately shows the large number of different securities that are available to investors. These securities comprise Treasury bills, Treasury notes, Treasury bonds, TIPS, and FRNs.³

The U.S. Treasury conducts regular auctions according to a well-defined calendar in order to place such securities with the public, individual investors or institutional investors. Two types of bids are available: in a competitive bid, the investor quotes the (minimum) rate that he/she will be willing to accept. In a noncompetitive bid, the investor agrees to purchase some amount of securities at the rate that is set at the auction. The Treasury allocates the amount available at the auction to noncompetitive bids and then to competitive bids (from the lowest rate to the highest rate bid) up to the amount available for sale. All investors receive the highest rate bid. Each type of security auctioned off by the U.S. Treasury is normally available with different maturities. For instance, Treasury bills are regularly auctioned off with maturities of 4, 13, 26, and 52 weeks. Treasury notes, by contrast, are regularly auctioned off with maturities of 2, 3, 5, 7, and 10 years. Treasury bonds are now only sold with a maturity of 30 years.

Table 1.1 reports the breakdown of marketable U.S. Treasury securities on March 31, 2015.⁴ As can be seen, the majority of U.S. Treasury securities held by the public (65%) are in the form of Treasury notes and thus with maturity ranging between 1 and 10 years. Short-term Treasury bills and long-term Treasury bonds are of about equal size, at 12% and 13% of the total. Securities with floating rate coupons, either tied to inflation (TIPS) or tied to interest rates (FRNs) comprise together about 10% of the total U.S. marketable debt.

Table 1.1 Marketable U.S. Treasury Securities (Million of Dollars)

Source: U.S. Treasury website. https://www.treasurydirect.gov/govt/reports/pd/mspd/2005/2005_mar.htm.

1.3 Interest Rates, Yields, and Discounting

The concept of interest rates is ubiquitous to fixed-income securities. The problem is that the notion of an interest rate is not well defined without explicitly defining a compounding frequency, that is, the number of times within the year in which the interest accrues to the initial investment. For instance, 100,000 dollars invested at 10% annual rate for 10 years yields a final amount in 10 years that crucially depends on how many times per year the interest on the investment is calculated and accrued. If the interest accrues annually (annual compounding), then in 10 years we obtain (in thousands of dollar)

equation

If instead the interest accrues twice per year (semiannual compounding), then we receive c01-math-0002 every 6 months but 20 times (the number of 6 months in 10 years), obtaining

equation

If the interest accrues quarterly, then we will receive c01-math-0004 every 3 months 40 times, obtaining in 10 years

equation

In the limit, if the interest accrues daily, we receive a rate c01-math-0006 every day, 3650 times (approximately, because of leap years), obtaining in 10 years

equation

In all these cases, the quoted interest rate on the $100,000 investment is the same (10%), but the accrual convention makes a difference of over $12,000 between annual compounding and daily compounding.

The general formula for compounding frequency is the following: given a quoted (annualized) interest rate c01-math-0008 accrued c01-math-0009 times per year for c01-math-0010 years, the total amount at maturity from a $1 investment is equal to

(1.1) equation

It is often convenient to work with an extremely high compounding frequency, namely, continuous compounding, which is the limit of Equation 1.1 as c01-math-0012 becomes very large. Indeed, as c01-math-0013 goes to infinity, the right-hand side of Equation 1.1 converges to

(1.2) equation

where c01-math-0015 is the Euler number. The function c01-math-0016 is called the exponential function, and it is widely used in finance and fixed-income because of its convenient mathematical properties. One can safely think of continuous compounding to be the same as daily compounding frequency and thus that the continuous compounding formula (the exponential) is nothing more than a convenient tool to approximate daily compounding. Indeed, in the previous example, if we compute the total value c01-math-0017 using directly the number c01-math-0018 (available on any calculator), we obtain

equation

which is indeed very similar to the case with daily compounding in the preceding text.

Given an interest rate (and a compounding frequency), we can invert the relations in the preceding text and obtain the discount factors c01-math-0020 to discount dollars paid at time c01-math-0021 to dollars today. That is, how much are we willing to pay today to have $1 at time c01-math-0022 ? Given an interest rate c01-math-0023 that is compounded c01-math-0024 times per year, by inverting Equation 1.1, we obtain

equation

That is, c01-math-0026 is the amount that we have to invest today in order to receive $1 at c01-math-0027 , as c01-math-0028 . In the limit as c01-math-0029 diverges to infinity, we obtain the discount function

equation

I will mostly use continuous compounding in this chapter, except when other forms of compounding are required for clarity.

1.4 The Term Structure of Interest Rates

In general, when we discount future cash flows to the present, different discount rates apply for different maturities. It is customary to denote such discount rates by c01-math-0031 , where c01-math-0032 stands for yield. Therefore, we denote the discount factor today for a dollar to be received at time c01-math-0033 by

equation

The function c01-math-0035 (as a function of maturity c01-math-0036 ) is called zero-coupon discount function. Panel A of Figure 1.5 plots six discount functions at the end of January in 2007–2009, 2011, 2013, and 2015. The discount functions c01-math-0037 have been increasing during these years, meaning that the value of $1 to be received in the future has been increasing over the period.

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Figure 1.5 Zero-coupon bonds and yield curves

Panel A shows the zero-coupon bonds at the end of January in 2007–2009, 2011, 2013, and 2015. Panel B reports the corresponding yield curves against maturity. Yields are continuously compounded.

Source: Data are from Gürkaynak, Sack, and Wright (2007), updated series.

Panel B of Figure 1.5 plots the term structures of interest rate. In January 2007, the yields c01-math-0038 are essentially constant across maturities. The interest rate on a 1-year risk-free investment is the same as the (annualized) interest rate of a 15-year risk-free investment or a 30-year risk-free investment. However, things are very different in the other years. In 2008, short-term yields were already much lower than long-term yields, and long-term yields themselves also decreased compared to their values in 2007. From 2009 on, short-term rates were at very low levels, while long-term rates went down and up to finally drop dramatically by January 2015.⁵

1.4.1 The Economics of the Nominal Yield Curve

What economics forces affect the term structure of interest rates? While short-term rates may be believed to be greatly affected by monetary policy (but see, e.g., Fama (2013) and the related discussion in Buraschi and Whelan (2015b, Chapter 6 in this handbook)), a number of questions arise as to what factors affect long-term yields.

A standard decomposition of long-term nominal yields is revealing:

(1.3)

equation

Thus, a low nominal yield may be due to a low real yield, a low expected inflation, or a low risk premium (or any combination of those). We return to real yields in Section 1.6. What are the other two terms?

Expected inflation refers to the market expectation of average inflation over the life of the bond. Such expectations are time varying, depending on market conditions. Panel A of Figure 1.6 plots the realized inflation from 1952 to 2015 and the expected inflation from 1980 to 2015. Expected inflation is computed as the consensus inflation forecast from the Survey of Professional Forecasters available at the Federal Reserve Bank of Philadelphia. As can be seen, inflation expectations dropped substantially in the last 10 years, as inflation itself has decreased over time.

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Figure 1.6 Expected inflation and risk premium

Panel A shows the quarterly realized inflation rate (Consumer Price Index (CPI), dashed gray line) and the professional forecasters’ consensus forecast of future inflation with 2 years horizon (solid black line). CPI data are from the FRED database at the Federal Reserve Bank of St Louis, while consensus forecasts are from the Survey of Professional Forecasters from the Federal Reserve Bank of Philadelphia. CPI forecasts are only available from 1981 onward. Panel B reports the estimated expected excess return of a 5-year zero-coupon bond computed from the Cochrane and Piazzesi factor.

Source: Data for Panel B are from Fama–Bliss zero-coupon bond yields available at the Center for Research in Security Prices (CRSP).

Why does expected inflation affect long-term yields? Intuitively, with the exception of TIPS (see Section 1.6), U.S. Treasury securities’ promised payments are expressed in dollars. If investors expect a high rate of inflation over the life of the bond, they are not willing to pay much money today for a security that will pay deflated dollars in the future. That is, the price of the U.S. Treasury security will be low today, implying a high yield. Thus, the higher the expected inflation, the higher is the (nominal) yield that investors require to buy the U.S. Treasury securities.

The last term in Equation 1.3 is a risk premium that investors require for holding nominal bonds. What types of risks does an investor in long-term bonds actually bear? While U.S. Treasuries are often referred to as risk-free, what is really meant is default risk-free, in the sense that the investor who holds the U.S. Treasury bond to maturity will receive its promised payments with an extremely high probability. However, holding long-term bonds can be quite risky for other reasons. There are two important sources of risk in particular. First, there is an inflation risk: because nominal bonds promise coupons and final payoffs in dollars, if inflation unexpectedly increases over the life of the bond, the real value of these promised payments declines, and investors require a premium to hold a security with an uncertain real payoff.

The second source of risk in a long-term bond stems from interest rate risk: if the investor needs to sell the bond before maturity, he/she may suffer potentially severe capital losses if nominal interest rates increased in the meantime. To illustrate, Panel A of Figure 1.7 plots the life cycle of a 30-year coupon bond, issued on February 15, 1985, and maturing on February 15, 2015. The coupon rate of the bond is 11.25%. More specifically, Panel A plots the end-of-month price of the coupon bond (solid black line) together with the 1-month Treasury bill rate (dashed gray line). The price of the coupon bond shot up from its issue price of $100 in February 1985 to $140 by March 1986 and then dropped to $113 by September 1987.⁶ If an investor bought the bond at $140 in March 1986 but found it necessary to sell it in September 1987, he/she would have suffered a capital loss of 20%, which would have only partly be compensated from receiving the 11.25% coupon.

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Figure 1.7 The life cycle of a 30-year coupon bond

Panel A shows the monthly (clean) price of 11.25%, 30-year U.S. Treasury coupon bond issued on February 15, 1985, and expiring on February 15, 2015, alongside the 1-month Treasury bill rate. Panel B shows the monthly excess return of the coupon bond and its monthly volatility computed as the 3-year trailing standard deviation of excess returns. Panel C shows the monthly excess return of the S&P 500 index and its monthly volatility computed as the 3-year trailing standard deviation of excess returns.

Source: All data are from the Center for Research in Security Prices (CRPS).

Panel B of Figure 1.7 plots the total monthly return (capital gain plus accrued interest) in excess of the 1-month T-bill rate from investing in the 30-year bond (dashed gray line). Monthly excess returns of plus/minus 5% are not uncommon for the first half of the sample. Indeed, the solid black line in the figure reports the monthly standard deviation of excess bond returns estimated over the previous 3 years, and we find that such bond return volatility was as high as 4% at the beginning of the sample (equivalent to about 13.8% annualized), a sizable variation. Panel B shows that the volatility of bond returns also declines over time as we approach maturity: indeed, long-term bonds are far more volatile than short-term bonds, due to their higher duration (see, e.g., Sydyak (2015, Chapter 7 in this handbook)). In fact, in the very last part of the sample, the price declines almost deterministically (close to zero volatility) toward $100, which is the promised principal at maturity. The reason why the price declines so steeply is that these bonds carry a coupon of 11.25%. Because short-term interest rates were essentially zero in this period, the steep decline in the coupon bond price must compensate for the high 11.25% coupon for the total bond return to be approximately zero, that is, the same as the return on an alternative investment in Treasury securities with similar short maturity.⁷

For