Fixed Income Relative Value Analysis + Website E-Book

Doug Huggins

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

Veröffentlichungsjahr: 2024

Beschreibung

An invaluable guide for fixed income practitioners, fully updated to incorporate the shift from LIBOR to SOFR Since its first edition in 2013, Fixed Income Relative Value Analysis: A Practitioner's Guide to the Theory, Tools, and Trades has become the gold standard for guides linking financial theories with practical analysis tools. The newly revised second edition reflects both the progress in statistical tools over the last decade and the impact of the transition to SOFR on swap spreads. You'll find a set of statistical and financial tools, a multitude of actual trades resulting from the application of these tools, as well as access to a companion website featuring spreadsheets illustrating some of the models contained in the book. This book covers: * Statistical models for quantitative market analysis, in particular mean reversion models and principal component analysis, now including the multivariate Ornstein-Uhlenbeck model. * An in-depth approach to understanding swap spreads in theory and practice. * A comprehensive discussion of the various basis swaps and their combinations. * The incorporation of credit default swaps in yield curve analysis. * A classification of option trades into three types and the appropriate analysis tools. * Fitted curve techniques for identifying relative value among different bonds. * A multi-factor delivery option model for bond future contracts. Fixed Income Relative Value Analysis has proven to be an indispensable desk reference for buy- and sell-side fixed income professionals, including traders, quantitative analysts, portfolio managers, financial engineers, fixed income salespeople with sophisticated clientele and risk managers.

Leseprobe

Table of Contents

Cover

Table of Contents

Title Page

Copyright

Preface to the Second Edition

NEW REFERENCE RATES

INCREASING DEFAULT RISK OF GOVERNMENTS

REGULATION AND CAPITAL CONSTRAINTS

COMPUTATIONAL ACCESS TO COMPLEX MODELS

NOTE

CHAPTER 1: Relative Value

THE CONCEPT OF RELATIVE VALUE

THE SOURCES OF RELATIVE VALUE OPPORTUNITIES

THE INSIGHTS FROM RELATIVE VALUE ANALYSIS

THE APPLICATIONS OF RELATIVE VALUE ANALYSIS

THE CRAFT OF RELATIVE VALUE ANALYSIS

SUMMARY OF CONTENTS

NOTE

PART I: Statistical Models

CHAPTER 2: Mean Reversion

WHAT IS MEAN REVERSION AND HOW DOES IT HELP US?

DIAGNOSTICS FOR MODEL SELECTION

MODEL ESTIMATION

CALCULATING CONDITIONAL EXPECTATIONS AND PROBABILITY DENSITIES

CALCULATING CONDITIONAL, EX ANTE RISK-ADJUSTED RETURNS

ASSESSING AND OPTIMIZING EXECUTION STRATEGIES

A PRACTICAL EXAMPLE INCORPORATING ALL THE IDEAS

CONCLUSION

NOTES

CHAPTER 3: Principal Component Analysis

INTRODUCTION: GOAL AND METHOD

AN INTUITIVE APPROACH TO PCA

FACTOR MODELS: GENERAL STRUCTURE AND DEFINITIONS

PCA: MATHEMATICS

PCA AS A FACTOR MODEL

INSIGHT INTO MARKET MECHANISMS THROUGH INTERPRETATION OF THE EIGENVECTORS

APPLYING EIGENVECTOR INTERPRETATION IN DIFFERENT MARKETS

DECOMPOSING MARKETS INTO UNCORRELATED FACTORS

EMBEDDING PCA IN TRADE IDEAS

APPROPRIATE HEDGING

ANALYZING THE EXPOSURE OF TRADING POSITIONS AND INVESTMENT PORTFOLIOS

PCA AS A TOOL FOR SCREENING THE MARKET FOR TRADE IDEAS

EXAMPLE OF A PCA-BASED TRADE IDEA

PROBLEMS AND PITFALLS OF PCA 1: CORRELATION BETWEEN FACTORS DURING SUBPERIODS

PROBLEMS AND PITFALLS OF PCA 2: INSTABILITY OF EIGENVECTORS OVER TIME

NOTES

CHAPTER 4: Multivariate Mean Reversion

INTRODUCTION

EXAMPLES

EUR 5Y5Y AND GBP 5Y5Y IMPLIED VOLATILITIES

CONCLUSIONS AND IMPLICATIONS

NOTES

PART II: Financial Models

CHAPTER 5: Some Comments on Yield, Duration, and Convexity

INTRODUCTION

SOME BRIEF COMMENTS ON THE YIELD OF A COUPON-PAYING BOND

A BRIEF COMMENT ON DURATION

A COMMON MISAPPLICATION OF CONVEXITY

NOTE

CHAPTER 6: Some Comments on Yield Curve Models

INTRODUCTION

REMARKS ABOUT MIXED JUMP-DIFFUSION MODELS

REMARKS ABOUT SHADOW RATE MODELS

NOTES

CHAPTER 7: Bond Futures Contracts

FUTURES PRICE AND DELIVERY OPTION

ONE-FACTOR DELIVERY OPTION MODELS

THE NEED FOR MULTI-FACTOR DELIVERY OPTION MODELS

A FLEXIBLE MULTI-FACTOR DELIVERY OPTION MODEL

NOTES

CHAPTER 8: Fitted Bond Curves

INTRODUCTION

FRAMEWORK OF ANALYSIS

SPECIFYING A FUNCTION FOR DISCOUNT FACTORS

WEIGHTS

SETTING UP THE OPTIMIZATION

CONCLUSIONS

NOTES

CHAPTER 9: An Analytic Process for Government Bond Markets

INTRODUCTION

STEP 1: FITTED CURVES

STEP 2: PCA FOR MATURITY SELECTION AND CURVE TRADES

STEP 3: FITTED CURVES FOR BOND SELECTION

CHAPTER 10: Overview of the Following Chapters

NOTE

CHAPTER 11: Reference Rates

OVERVIEW OF GLOBAL REFERENCE RATES

OVERVIEW OF THE REPO MARKET

REPO RATES IN GREATER DETAIL

SOFR

DRIVING FORCES OF THE SPREAD BETWEEN DIFFERENT REFERENCE RATES

THE SPREAD BETWEEN SECURED AND UNSECURED LOANS AS DRIVEN BY CAPITAL REQUIREMENTS

THE SPREAD BETWEEN UNSECURED O/N AND TERM RATES AS DRIVEN BY CREDIT EXPOSURE

COMBINING THE DRIVING FORCES CAPITAL REQUIREMENTS AND CREDIT EXPOSURE INTO A MODEL FOR THE REPO–LIBOR SPREAD

NOTES

CHAPTER 12: Asset Swaps

GENERAL CONCEPT

APPLICATION OF THE GENERAL CONCEPT TO PRICE THE THREE TYPES OF ASSET SWAPS

TERM STRUCTURE OF SWAP SPREADS

CYCLICALITY OF SWAP SPREADS

DRIVING FORCES OF SWAP SPREADS CAPTURED IN OUR MODEL

DRIVING FORCES OF SWAP SPREADS NOT CAPTURED IN OUR MODEL

NOTES

CHAPTER 13: Credit Default Swaps

INTRODUCTION

STRUCTURE OF A CDS

OTHER APPLICATIONS OF CDS: TRADING CDS VERSUS OTHER CDS AND VERSUS BONDS

A PCA ON THE CDS CURVE

A PCA ON THE EUR SOVEREIGN CDS UNIVERSE

A PCA ON RISK-FREE BOND YIELDS

PITFALLS

CONCLUSION

NOTES

CHAPTER 14: Intra-Currency Basis Swaps

DEFINITION

PRICING OF ICBS

ROLE AS BUILDING BLOCKS

CHAPTER 15: Cross-Currency Basis Swaps

DEFINITION

APPLICATIONS OF THE CCBS

CONSTRUCTING ANY REFERENCE RATE FROM ANY OTHER

ISSUING FOREIGN BONDS WITHOUT FX EXPOSURE

INVESTING IN FOREIGN BONDS WITHOUT FX EXPOSURE

PRICING OF THE CCBS

THE IMPACT OF THE TRANSITION TO NEW REFERENCE RATES ON THE CCBS

NOTES

CHAPTER 16: Combinations and Mutual Influences of Asset, Basis, and Credit Default Swaps

INTRODUCTION

CALCULATING USD SWAP SPREADS FOR FOREIGN BONDS

THE EQUILIBRIUM BETWEEN ASSET AND BASIS SWAPS

ARBITRAGE EQUALITY BETWEEN USD ASW AND CDS

ARBITRAGE INEQUALITY BETWEEN USD ASW AND CDS

THE EQUILIBRIUM BETWEEN ASSET, BASIS, AND CREDIT DEFAULT SWAPS

THE EQUILIBRIUM FOR BUNDS (LOW-RISK BONDS)

THE EQUILIBRIUM IN CASE OF JGBS (RISKY BONDS)

NOTES

CHAPTER 17: Global Bond RV Via Fitted Curves and Via SOFR Asset Swap Spreads

INTRODUCTION

SOFR SWAP SPREADS AS A GLOBAL RELATIVE VALUE INDICATOR FOR BONDS

PROBLEMS WITH THE USE OF SWAP SPREADS AS RELATIVE VALUE INDICATOR FOR BONDS

CONCLUSION

NOTES

CHAPTER 18: Other Factors Affecting Swap Spreads

INTRODUCTION

HAIRCUTS AND MARGINS

REGULATORY CONSIDERATIONS

NOTES

CHAPTER 19: Options

INTRODUCTION

A BRIEF REVIEW OF OPTION PRICING THEORY

CLASSIFICATION OF OPTION TRADES

OPTION TRADE TYPE ➀: SINGLE UNDERLYING

OPTION TRADE TYPE ➀: TWO OR MORE UNDERLYINGS

OPTION TRADE TYPE ➁: SINGLE UNDERLYING

OPTION TRADE TYPE ➁: TWO OR MORE UNDERLYINGS

OPTION TRADE TYPE ➂: FACTOR MODEL FOR THE VEGA SECTOR

PITFALLS OF OPTION TRADES OF TYPE ➂

CONCLUSION: SUMMARY OF OPTION TRADE TYPES AND THEIR DIFFERENT EXPOSURE

SOME REMARKS ABOUT ASIAN OPTIONS

NOTES

CHAPTER 20: Relative Value in a Broader Perspective

INTRODUCTION

THE MACROECONOMIC ROLE OF RELATIVE VALUE ANALYSIS AND TRADING

ARBITRAGEURS AND POLITICIANS

THE MISREPRESENTATION OF ARBITRAGE BY POLITICIANS

CONCLUSION: POLITICAL IMPLICATIONS OF RELATIVE VALUE

NOTES

Bibliography

Index

End User License Agreement

List of Tables

Chapter 3

TABLE 3.1 Correlations of the First Three Factors of a PCA on the Bund Yield...

TABLE 3.2 Correlations of the First Three Factors of a PCA on Currencies ver...

Chapter 8

Table 8.1 Deliverable Issues into March 2013 Futures Contracts

Table 8.2 Bund Regression Coefficients

Chapter 11

Table 11.1 Most Common Reference Rates in the Major Markets

Chapter 12

Table 12.1 Driving Factors of the Different Types of Asset Swap Spreads

Chapter 13

Table 13.1 Correlation between Different Points on the Yield Curve and the F...

Chapter 16

Table 16.1 Risk Exposure of a Bond Together with Different Combinations of S...

Chapter 18

Table 18.1 Federal Reserve Haircut Schedule

Table 18.2 Bank of England Haircut Schedule

Table 18.3 ECB Haircut Schedule

Chapter 19

Table 19.1 Correlation of the First Three Factors of a PCA on the Vega Secto...

List of Illustrations

Chapter 2

FIGURE 2.1 Simulated random walk.

FIGURE 2.2 Simulated mean-reverting process.

FIGURE 2.3 Simulated mean-reverting process: faster mean reversion.

FIGURE 2.4 Simulated mean-reverting process: even faster mean reversion.

FIGURE 2.5 Spot price of gold in US dollars since January 1975.

FIGURE 2.6 Realized volatility of 10Y US Treasury bond yield (bp/year).

FIGURE 2.7 2/5/10 butterfly spread along USD swap curve since 1988.

FIGURE 2.8 Daily moves of the swaption volatility difference EUR 5Y5Y – GBP ...

FIGURE 2.9 Examples of drift coefficients.

FIGURE 2.10 Diagnostic tool for drift coefficient.

FIGURE 2.11 Target drift coefficient.

FIGURE 2.12 Diagnostic graph for drift coefficient.

FIGURE 2.13 Histogram of simulated values.

FIGURE 2.14 Nonparametric kernel densities with different bandwidths.

FIGURE 2.15 Nonparametric kernel density and histogram.

FIGURE 2.16 Nonparametric kernel density and histogram.

FIGURE 2.17 EUR and GBP 5Y5Y implied swaption volatilities.

FIGURE 2.18 Swaption volatility difference: EUR 5Y5Y – GBP 5Y5Y.

FIGURE 2.19 Daily change in swaption volatility difference series.

FIGURE 2.20 First-order nonparametric estimate of drift coefficient.

FIGURE 2.21 First-order nonparametric estimate of diffusion coefficient.

FIGURE 2.22 Unconditional and conditional densities for the volatility sprea...

FIGURE 2.23 First passage time density of volatility spread from 12.35 to 7....

FIGURE 2.24 First passage time density of volatility spread from 12.35 to 1....

Chapter 3

FIGURE 3.1 Structure of point cloud of 2Y and 10Y Bund yields.

FIGURE 3.2

Cov

and examples for its two eigenvectors.

FIGURE 3.3 Covariance across the Bund yield curve.

FIGURE 3.4 Scaled eigenvalues of a PCA on the Bund yield curve.

FIGURE 3.5 First three eigenvectors of a PCA on the Bund curve.

FIGURE 3.6 First eigenvector of a PCA on the Bund curve with data from 1993 ...

FIGURE 3.7 Second eigenvector of a PCA of the vega sector of the JPY implied...

FIGURE 3.8 Example for a cluster analysis of the whole JPY volatility surfac...

FIGURE 3.9 First three eigenvectors of a PCA on 5Y CDS for core Eurozone sov...

FIGURE 3.10 Scaled eigenvalues of a PCA on the soy market.

FIGURE 3.11 Eigenvectors of a PCA on the soy market.

FIGURE 3.12 Historical evolution of the first and second factors of a PCA on...

FIGURE 3.13 History of the first three factors of a PCA on the Bund yield cu...

FIGURE 3.14 Driving forces of a BPV-neutral and a PCA-neutral 2Y-5Y-7Y butte...

FIGURE 3.15 Two-factor residuals.

FIGURE 3.16 Two-factor residuals of a PCA on consecutive one-year forward EU...

FIGURE 3.17 One-factor residuals.

FIGURE 3.18 PCA-neutral 2Y-5Y-7Y butterfly.

FIGURE 3.19 PCA-neutral 2Y-5Y-7Y Bund butterfly and its future path as model...

FIGURE 3.20 First passage time density for the PCA-neutral 2Y-5Y-7Y butterfl...

FIGURE 3.21 Performance of Bund butterfly after entry compared to OU model f...

FIGURE 3.22 PCA-neutral 2Y-10Y Bund steepening position.

FIGURE 3.23 PCA-neutral steepener versus factor 1.

FIGURE 3.24 Evolution of the first eigenvector for US Treasuries since 1978....

FIGURE 3.25 Evolution of the first eigenvector for US Treasuries since 2015....

FIGURE 3.26 Scaled eigenvalues of a PCA on currencies.

FIGURE 3.27 Eigenvectors of a PCA on currencies.

FIGURE 3.28 Factors of a PCA on currencies.

FIGURE 3.29 Factor 3 of a PCA on currencies versus the S&P500 index.

FIGURE 3.30 Regression of factor 3 of the PCA on currencies versus the S&P50...

FIGURE 3.31 Two-factor residuals of a PCA on currencies.

FIGURE 3.32 Residual of a regression between a PCA-neutral portfolio of curr...

FIGURE 3.33 Actual performance of the trade versus the OU model forecast....

Chapter 4

FIGURE 4.1 Expected values over time.

FIGURE 4.2 Expected spread over time.

FIGURE 4.3 Expected values over time, given different half-lives.

FIGURE 4.4 Expected spread over time, given different half-lives.

FIGURE 4.5 Expected values over time, given different half-lives and a one-w...

FIGURE 4.6 Expected spread over time, given different half-lives and a one-w...

FIGURE 4.7 Vector field corresponding to the transition matrix.

FIGURE 4.8 Correlation as a function of horizon.

FIGURE 4.9 Correlation as a function of horizon with opposite reactions to c...

FIGURE 4.10 Yields of BTP 1.65% Mar-32, BTP 2.25% Sep-36, and BTP 5% Sep-40....

FIGURE 4.11 Butterfly spread and average yield.

FIGURE 4.12 Correlation as a function of horizon.

FIGURE 4.13 Correlation coefficient: estimated from data and fitted by MVOU ...

FIGURE 4.14 EUR and GBP 5Y5Y implied swaption volatilities.

FIGURE 4.15 Swaption volatility difference: EUR 5Y5Y – GBP 5Y5Y.

FIGURE 4.16 Estimated correlation coefficient as a function of horizon.

FIGURE 4.17 Expected values as a function of time.

FIGURE 4.18 Expected spread as a function of time.

FIGURE 4.19 Standard deviation of the spread as a function of time.

Chapter 6

FIGURE 6.1 Evolution of the O/N Shadow Rate implied by the EUR yield curve....

Chapter 7

FIGURE 7.1 CTD situation as a function of the yield level.

FIGURE 7.2 Fair futures price as a function of the yield level.

FIGURE 7.3 Results of a Monte Carlo simulation of the CTD situation at deliv...

FIGURE 7.4 Evolution of the yield spread volatility between CTD candidates a...

Chapter 8

FIGURE 8.1 Bund yields as of 7 Dec 2012.

FIGURE 8.2 Bund regression residuals expressed in EUR.

FIGURE 8.3 Bund regression residuals expressed in basis points.

Chapter 9

FIGURE 9.1 Combination of models into a possible analytic process for govern...

Chapter 10

FIGURE 10.1 Driving factors of asset swap spreads.

FIGURE 10.2 Mutual influences between the driving factors of asset swap spre...

Chapter 11

FIGURE 11.1 Evolution of the USD reference rate.

FIGURE 11.2 SOFR calculation.

FIGURE 11.3 Evolution of the USD reference rate used by most market particip...

Chapter 12

FIGURE 12.1 Conceptual approach to asset swap pricing.

FIGURE 12.2 Historical average for the GC–repo basis swap for different EUR ...

FIGURE 12.3 Integration of SOFR into a term rate in the US future, swap and ...

FIGURE 12.4 Actual SOFR–ASW of 5Y US Treasuries versus the model forecast....

FIGURE 12.5 Schematic relationship between the three asset swap spread curve...

Chapter 13

FIGURE 13.1 Cash flows in an investment into a 5Y asset&basis swapped and de...

FIGURE 13.2 Scaled eigenvalues of a PCA on the Italian CDS curve.

FIGURE 13.3 First three eigenvectors of a PCA on the Italian CDS curve....

FIGURE 13.4 First three factors of a PCA on the Italian CDS curve.

FIGURE 13.5 Scaled eigenvalues of a PCA on CDS quotes for EUR sovereigns....

FIGURE 13.6 First three eigenvectors of a PCA on CDS quotes for EUR sovereig...

FIGURE 13.7 Scaled eigenvalues of a PCA on CDS quotes for core EUR sovereign...

FIGURE 13.8 First three eigenvectors of a PCA on CDS quotes for core EUR sov...

FIGURE 13.9 First three factors of a PCA on CDS quotes for core EUR sovereig...

FIGURE 13.10 Current 1-factor residuals of a PCA on CDS quotes for core EUR ...

FIGURE 13.11 Scaled eigenvalues of a PCA on the risk-free BTP yield curve in...

FIGURE 13.12 First factor of a PCA on the risk-free BTP yield curve in compa...

FIGURE 13.13 Second factor of a PCA on the risk-free BTP yield curve in comp...

FIGURE 13.14 Correlation between factors 1 and 2 in the subperiod since 2010...

FIGURE 13.15 One-factor residuals of the PCA on risk-free BTP yields....

Chapter 14

FIGURE 14.1 5Y basis swap spread between 3M EURIBOR and 6M EURIBOR.

FIGURE 14.2 EUR exchange rate and 5Y basis swap spread between 3M EURIBOR an...

FIGURE 14.3 5Y basis swap spread between 3M EURIBOR and 6M EURIBOR and 5Y ba...

FIGURE 14.4 Regression of the 3M SOFR versus Eurodollar future spread agains...

Chapter 15

FIGURE 15.1 The 2Y JPY CCBS in 2002 and 2003 as a function of the ASW differ...

FIGURE 15.2 Factor 1 of a PCA on the JPY CCBS since 2010 as a function of th...

FIGURE 15.3 5Y basis swaps: EUR/USD and JPY/USD.

FIGURE 15.4 5Y EUR/USD CCBS versus the EUR/USD spot FX rate

.

Chapter 16

FIGURE 16.1 USD LIBOR swap spreads of US Treasuries, Bunds, and JGBs as of 2...

FIGURE 16.2 USD swap spread history of the 5Y US Treasury, Bund, and JGB....

FIGURE 16.3 USD ASW of JGBs versus the Japanese CDS of the same maturity as ...

FIGURE 16.4 USD ASW of the Korean government bond 5.75% 09/18 versus the 10Y...

FIGURE 16.5 Local and USD ASW of 5Y Bunds versus the 5Y EUR CCBS.

FIGURE 16.6 Local and USD ASW of 5Y JGBs versus the 5Y JPY CCBS.

FIGURE 16.7 5Y JPY CCBS versus the USD ASW of 5Y JGBs and the 5Y Japanese CD...

Chapter 17

FIGURE 17.1 Richness and cheapness of global bonds swapped into EUR versus t...

FIGURE 17.2 SOFR–ASW curves of global (basis swapped) bonds.

Chapter 18

FIGURE 18.1 Effect of ECB haircut schedule on German and Italian zero-coupon...

Chapter 19

FIGURE 19.1 Delta of an option as a function of the difference between the p...

FIGURE 19.2 Price of an option as a function of the difference between the p...

FIGURE 19.3 Theta of an ATM option as a function of the time to expiry (sche...

FIGURE 19.4 Delta of an option as a function of the difference between the p...

FIGURE 19.5 Classification of the volatility surface into a sector suitable ...

FIGURE 19.6 Breakeven curves for 1Y ATMF straddles on different maturities o...

FIGURE 19.7 Breakeven curves for 1Y ATMF payer swaptions on different maturi...

FIGURE 19.8 Breakeven curves for 1Y ATMF receiver swaptions on different mat...

FIGURE 19.9 Option market-implied evolution of the CPI as calculated through...

FIGURE 19.10 P&L from a 2Y-10Y curve-flattening position with swaps and with...

FIGURE 19.11 Premium pick-up/payment versus stability of directionality for ...

FIGURE 19.12 History of implied US bond futures option volatility versus imp...

FIGURE 19.13 5Y JPY swaption volatility (normal): History of realized versus...

FIGURE 19.14 Realized 10Y JPY swap volatility, calculated with a 3M and a 6M...

FIGURE 19.15 Realized 10Y JPY swap volatility, calculated with a 3M rolling ...

FIGURE 19.16 Realized 10Y JPY swap volatility, calculated with exponentially...

FIGURE 19.17 Current realized and implied volatility across the JPY curve....

FIGURE 19.18 History of 2Y-5Y JPY realized volatility curve steepness versus...

FIGURE 19.19 History of non-directional 2Y-5Y JPY realized volatility curve ...

FIGURE 19.20 First eigenvector of a PCA on the whole JPY volatility surface....

FIGURE 19.21 First eigenvector of a PCA on the vega sector of the JPY volati...

FIGURE 19.22 Scaled eigenvalues of a PCA on the vega sector of the JPY volat...

FIGURE 19.23 Second eigenvector of a PCA on the vega sector of the JPY volat...

FIGURE 19.24 Third eigenvector of a PCA on the vega sector of the JPY volati...

FIGURE 19.25 First three factors of a PCA on the vega sector of the JPY vola...

FIGURE 19.26 1-factor residuals of a PCA on the vega sector of the JPY volat...

FIGURE 19.27 Factor 2 as a function of the 5Y swap rate.

Guide

Cover

Table of Contents

Title Page

Copyright

Preface to the Second Edition

Begin Reading

Bibliography

Index

End User License Agreement

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Fixed Income Relative Value Analysis

A Practitioner’s Guide to the Theory, Tools, and Trades

DOUG HUGGINS

CHRISTIAN SCHALLER

Second Edition

This edition first published 2024

© copyright 2024 by Doug Huggins and Christian Schaller.

First edition © 2013 by John Wiley & Sons

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Preface to the Second Edition

Some important changes have occurred in the fixed income markets since we published the first edition of Fixed Income Relative Value Analysis in 2013, many of these due to the eventual policy response to the great financial crisis of 2008–2009: new reference rates, increasing default risk of governments, more regulation and capital constraints.

NEW REFERENCE RATES

Probably the most important effect of the great financial crisis from the viewpoint of relative value analysts and hence of this book was the transition away from LIBOR to other reference rates. After central banks largely disintermediated the interbank lending markets1 that had been the lifeblood of the money markets, it was only natural that banks would prefer to borrow from and lend to a central bank rather than another commercial bank. But as a result of this change, the liquidity in the interbank market declined considerably, casting suspicion on interbank lending reference rates, such as LIBOR. The final straw for the LIBOR market was the rate rigging scandal that encompassed a number of large banks, starting in 2008. In response to these issues, central banks in a number of jurisdictions pushed market participants away from LIBOR and toward reference rates of their own design, such as SOFR in the US. In fact, the move to SOFR was the impetus for our recent book, SOFR Futures and Options (Huggins and Schaller, 2022).

Since SOFR differs from LIBOR in a number of important ways, the SOFR swaps market differs from the LIBOR swaps market in a number of important respects. For example, LIBOR references unsecured transactions, whereas SOFR references secured transactions. This change alone has a material effect on valuations, particularly on the relative valuations between swaps and bonds.

On one hand, the multitude of reference rates (Chapter 11 provides an overview) for swaps has complicated the already complex relationships between asset, basis, and credit default swaps further. On the other hand, the transition from LIBOR to SOFR has eliminated the unsecured–secured basis in the asset swap spreads of government bonds, which has had several welcome effects:

Asset swap spreads versus SOFR can be modified to become suitable rich/cheap indicators for all bonds worldwide (

Chapter 17

). We have therefore reviewed the strong statement of the first edition that asset swap spreads should never be used to assess the RV between bonds. While it is still true for swap spreads versus LIBOR and OIS, par asset swap spreads versus SOFR can be modified to become a reasonable alternative to fitted curves.

Asset swap spreads versus SOFR can rather easily be linked with the credit risk of the sovereign issuer. Hence, the first hurdle facing an arbitrage equality between swap spreads and CDS, which occupied many pages of the first edition due to the correlation between credit risk and the unsecured–secured basis, now has a straightforward solution (

Chapter 16

).

A less welcome consequence of the transition to SOFR are the structural breaks in time series, for example, for cross-currency basis swaps between EURIBOR and USD LIBOR, which switched to USD SOFR. This is a general problem for analysts requiring long-term time series as input variables for their models. For the most basic of those time series, interest rates, we propose the solution of using constant maturity par yields from a fitted curve on government bonds (Chapter 8) rather than swap rates. And it is also a specific problem for this book, written shortly after the transition and hence with too little data for swaps with new reference rates to present meaningful case studies. We have therefore decided to keep many of the case studies of the first edition, which cover the subprime and euro crises and thus remain of interest, though this means that we need to carry some “historical ballast” and speak from time to time of (basis) swaps with USD LIBOR as the reference rate. Apart from these case studies, we have aimed for a complete update to the current reference rate situation.

INCREASING DEFAULT RISK OF GOVERNMENTS

The implementation of zero or even negative policy rates posed a challenge to analysts – as does its unwinding, which occurs at the same time as budget deficits and bond issuance soared, in part as a consequence of the fiscal response to the COVID-19 pandemic. An immediate implication for modeling government bonds is that the formerly common simplifying assumption that certain government bonds were default-free is less justifiable these days. As a result, incorporating credit considerations into the analysis of government bonds has become increasingly important. We have responded to this development by adding a term for credit difference to the term for funding difference in our swap spread model. While the sovereign CDS was already treated extensively in the first edition, it remained an external addition to the relationship between bonds and swaps, into which it has now been integrated (Chapter 12).

On the other hand, moves in rates and volatility even to unprecedented levels are the sorts of changes for which most good relative value models are well-suited or can be adapted. We provide a study of the impact of zero-interest rate policy on PCA eigenvectors in Chapter 3 and offer some remarks about Shadow Rate Models in Chapter 6. If those were the only changes occurring in the fixed income markets, the need for a second edition of Fixed Income Relative Value Analysis would be less clear.

But the move from LIBOR to overnight reference rates, non-negligible default risk of government bonds, and tighter regulation are the sorts of changes that require us to review and partly modify our approaches. The basic economics underlying our models are the same. They are still predicated on the principles that arbitrage opportunities are unsustainable and that instruments with similar risks should be expected to generate similar returns (Chapter 1). But the application of these principles via models needs to change as the structure of the market changes. And that's the primary motivation behind this second edition of the book.

REGULATION AND CAPITAL CONSTRAINTS

The Basel III process has culminated in quite a number of additional regulations designed to improve the safety and soundness of the world's banks, especially the largest institutions that tend to dominate the fixed income markets. One effect of these regulations is that bank balance sheets face many more constraints now than they did a decade ago. And the effect of these constraints is that the relevant cost for a bank contemplating a new position is no longer the marginal cost of funds in the market, such as interest rates paid on retail or commercial deposits. Rather, it's the shadow cost of the least onerous constraint currently binding the bank's balance sheet. For example, if a bank needs to shed an asset currently generating a return on capital of 7% in order to make room for another asset, then 7% is the relevant hurdle for the new asset, even if retail deposits cost the bank much less.

The presence of so many binding constraints on bank balance sheets has a number of important implications for the fixed income markets, two of which are discussed in Chapter 18. First, relative value analysts must incorporate these shadow costs into their analysis as and when these constraints are binding on the balance sheets of the firms for which they work. Second, analysts must incorporate the fact that traders at other firms will often face the same sorts of shadow costs and that these generally won't be observable in the market. In the old days, it wasn't difficult to produce a reasonable estimate of the marginal costs that other market participants faced when analyzing certain trades. These days, we typically have very little understanding of the shadow costs faced by traders at the largest banks.

As a result, it has become more difficult for relative value analysts to produce useful forecasts about the eventual richening or cheapening of various instruments. Given that the problem of unobservable input variables exists independently of the sophistication of the model, the analytic ideal to explain and predict all pricing relationships via no-arbitrage models needs to be reviewed. While these relationships continue to provide important insights, their influence on market prices on a given day depends on the unobservable shadow cost of arbitrage capital of the marginal market participant.

Chapter 18 highlights one of the more notable instances of this phenomenon: the repo spike of September 2019. As Jamie Dimon later stated publicly, JP Morgan wasn't in a position to satisfy the demand for cash against collateral that day, due to binding regulatory constraints on its balance sheet. He also noted that this was a change for the bank and that the bank had provided additional funds in similar situations prior to these additional regulations. We presume other banks faced similar constraints on their balance sheets at the same time. Repo rates are fundamental to a large number of relative value trades, and all of these are affected in some way when repo rates spike as high as they did that day. Relative value analysts have no choice but to grapple with these shadow costs and their effects on pricing in the fixed income markets, despite the fact that it can be a difficult task.

COMPUTATIONAL ACCESS TO COMPLEX MODELS

Beside these policy-related changes, over the last decade, even more computational capabilities have become available to the average market participant. Much of these have been directed at machine learning and artificial intelligence, including efforts to find attractive opportunities in fixed income markets. As far as we are aware, the widespread benefits of these approaches are still uncertain. We have heard reports of some firms generating attractive returns with these approaches and have been pleased with a few of our own ventures in this area. But, in general, we're still unclear whether the benefits of mass adoption of these approaches in the fixed income markets will produce the results for which so many analysts are working.

On the other hand, we have also used the enhanced computational capabilities available these days to make use of statistical models that may have been too slow or cumbersome for the average analyst in the past. One of these is the multivariate Ornstein–Uhlenbeck (MVOU) process – a generalization of the univariate Ornstein–Uhlenbeck process discussed in the first edition of this book and appearing again in Chapter 2 of this edition. The MVOU process has some distinct benefits when applied to financial markets, but it also comes with some distinct costs. In particular, it involves numerical optimizations over a larger number of parameters, which can take some time. But as computational speeds improve, the times required to perform these optimizations decrease, particularly when making use of the shortcuts we discuss in Chapter 4 for initializing the optimization algorithm with a guess that is likely to be in the vicinity of the optimized parameter estimates.

With change comes opportunity. But to benefit from opportunity, we need to respond effectively to change. This second edition of Fixed Income Relative Value Analysis represents our response to the changes that have occurred in the markets in recent years. We hope that readers are able to use the ideas in this edition to profit from the opportunities afforded by these changes.

NOTE

1

   Central banks not only have disintermediated the money markets in some jurisdictions, they have also disintermediated some of the bond markets. For example, the buying of JGBs by the official sector in that market has reduced the liquidity of the world's largest bond market at times to a trickle.

CHAPTER 1Relative Value

THE CONCEPT OF RELATIVE VALUE

Relative value is a quantitative analytical approach toward financial markets based on two fundamental notions of modern financial economics.

Proposition 1: If two securities have identical payoffs in every future state of the world, then they should have identical prices today.

Violation of this principle would result in the existence of an arbitrage opportunity, which is inconsistent with equilibrium in financial markets.

This proposition seems relatively straightforward now, but this wasn't always the case. In fact, Kenneth Arrow and Gérard Debreu won Nobel prizes in economics in 1972 and 1983 in part for their work establishing this result. And Myron Scholes and Robert Merton later won Nobel prizes in economics in 1997 for applying this proposition to the valuation of options. In particular, along with Fischer Black, they identified a self-financing portfolio that could dynamically replicate the payoff of an option, and they were able to determine the value of this underlying option by valuing this replicating portfolio.

Most of the financial models discussed in this book are based on the application of this proposition in various contexts.

Proposition 2: If two securities present investors with identical risks, they should offer identical expected returns.

This result may appear intuitive, but it's somewhat more difficult to establish than the first result. Of particular interest for our purposes is that the result can be established via the Arbitrage Pricing Theory, which assumes the existence of unobservable, linear factors that drive returns.

In this case, it's possible to combine securities into portfolios that expose investors to any one of the risk factors without involving exposure to any of the other risk factors. In the limit, as the number of securities in the portfolio increases, the security-specific risks can be diversified away. And in this case, any security-specific risk that offered a non-zero expected return would present investors with an arbitrage opportunity, at least in the limit, as the remaining risk factors could be immunized by creating an appropriate portfolio of tradable securities.

For our purposes, this is a powerful result, as it allows us to analyze historical data for the existence of linear factors and to construct portfolios that expose us either to these specific factors or to security-specific risks, at our discretion. In fact, principal component analysis (PCA) can be applied directly in this framework, and we'll rely heavily on PCA as one of the two main statistical models we discuss in this book.

THE SOURCES OF RELATIVE VALUE OPPORTUNITIES

From these two propositions, it's clear that the absence of arbitrage is the assumption that drives many of the models we use as relative value analysts. This should come as no surprise, since one of the main roles of a relative value analyst is to search for arbitrage opportunities.

But for some people, this state of affairs presents a bit of a paradox. If our modeling assumptions are correct about the absence of free lunches, why do analysts and traders search so hard for them?

This apparent paradox can be resolved with two observations. The first is the recognition that arbitrage opportunities are rare precisely because hardworking analysts invest considerable effort trying to find them. If these opportunities could never be found, or if they never generated any profits for those who found them, analysts would stop searching for them. But in this case, opportunities would reappear, and analysts would renew their search for them as reports of their existence circulated.

The second observation that helps resolve this paradox is that even seemingly riskless arbitrage opportunities carry some risk when pursued in practice. For example, one of the simpler arbitrages in fixed income markets is the relation between bond prices, repo rates, and bond futures prices. If a bond futures contract is too rich, a trader can sell the futures contract, buy the bond, and borrow the purchase price of the bond in the repo market, with the bond being used as collateral for the loan. At the expiration of the contract, the bond will be returned to the trader by his repo counterparty, and the trader can deliver the bond into the futures contract. In theory, this would allow the trader to make a riskless arbitrage profit. But, in practice, there are risks to this strategy.

For example, the repo counterparty may fail to deliver the bonds to the trader promptly at the end of the repo transaction, in which case the trader may have difficulty delivering the bonds into the futures contract. Failure to deliver carries significant penalties in some cases, and the risk of incurring these penalties needs to be incorporated into the evaluation of this seemingly riskless arbitrage opportunity.

These perspectives help us reconcile the existence of arbitrage opportunities in practice with the theoretical assumptions behind the valuation models we use. But they don't explain the sources of these arbitrage or relative value opportunities, and we'll discuss a few of the more important sources here.

Demand for Immediacy

In many cases, relative value opportunities will appear when some trader experiences an unusually urgent need to transact, particularly in large size. Such a trader will transact his initial business at a price that reflects typical liquidity in the market. But if the trader then needs to transact additional trades in the same security, he may have to entice other market participants to provide the necessary liquidity by agreeing to transact at a more attractive price. For example, he may have to agree to sell at a lower price or to buy at a higher price than would be typical for that security. In so doing, this trader is signaling a demand for immediacy in trading, and he's offering a premium to other traders who can satisfy this demand.

The relative value trader searches for opportunities in which he can be paid attractive premiums for satisfying these demands for immediacy. He uses his capital to satisfy these demands, warehousing the securities until he can liquidate them at more typical prices, being careful to hedge the risks of the transactions in a cost-effective and prudent manner.

Because these markets are so competitive, the premiums paid for immediacy are often small relative to the sizes of the positions. As a result, the typical relative value fund will be run with leverage that is higher than the leverage of, say, a global macro fund. Consequently, it's important to pay attention to small details and to hedge risks carefully.

Misspecified Models

It sometimes happens that market participants overlook relevant issues when modeling security prices, and the use of misspecified models can result in attractive relative value opportunities for those who spot these errors early.

For example, until the mid-1990s, most analysts failed to incorporate the convexity bias when assessing the relative valuations of Eurodollar futures contracts and forward rate agreements. As market participants came to realize the importance of this adjustment, the relative valuations of these two instruments changed over time, resulting in attractive profits for those who had identified this issue relatively early.

In recent years, as credit concerns have increased for many governments, it has become increasingly important to reflect sovereign credit risk as an explicit factor in swap spread valuation models, and we discuss this issue in considerable detail in this book.

Regulatory Arbitrage

The fixed income markets are populated by market participants of many types across many different regulatory jurisdictions, and the regulatory differences between them can produce relative value opportunities for some.

For example, when thinking about the relative valuations of unsecured short-term loans and loans secured by government bonds in the repo market, traders at European banks will consider the fact that the unsecured loan will attract a greater regulatory charge under the Basel accords. On the other hand, traders working for money market funds in the US won't be subject to the Basel accords and are likely to focus instead on the relative credit risks of the two short-term deposits. The difference in regulatory treatment may result in relative valuations that leave the European bank indifferent between the two alternatives but that present a relative value opportunity for the US money market fund.

THE INSIGHTS FROM RELATIVE VALUE ANALYSIS

In some sense, relative value analysis can be defined as the process of gaining insights into the relationships between different market instruments and the external forces driving their pricing. These insights facilitate arbitrage trading, but they also allow us more generally to develop an understanding of the market mechanisms that drive valuations and of the ways seemingly different markets are interconnected.

As a consequence, relative value analysis, which originated in arbitrage trading, has a much broader scope of applications. It can reveal the origins of certain market relations, the reasons a security is priced a certain way, and the relative value of this pricing in relation to the prices of other securities. And in the event that a security is found to be misvalued, relative value analysis suggests ways in which the mispricing can be exploited through specific trading positions. In brief, relative value analysis is a prism through which we view the machinery driving market pricing amidst a multitude of changing market prices.

As an example, consider the divergence of swap spreads for German Bunds and US Treasuries during the financial crisis, which might appear inextricable without considering the effects of cross-currency basis swaps (CCBS), intra-currency basis swaps (ICBS), and credit default swaps (CDS).

In this case, CCBS spreads widened as a result of the difficulties that European banks experienced in raising USD liabilities against their USD assets. On the other hand, arbitrage between Bunds, swapped into USD, and Treasuries prevented an excessive cheapening of Bunds versus USD LIBOR. As a consequence, Bunds richened significantly against EURIBOR (see Chapter 16 for more details).

However, given the relationship between European banks and sovereigns, the difficulties of European banks were also reflected in a widening of European sovereign CDS levels. Hence, Bunds richened versus EURIBOR at the same time as German CDS levels increased.

An analyst who fails to consider these interconnected valuation relations may find the combination of richening Bunds and increasing German CDS opaque and puzzling. But a well-equipped relative value analyst can disentangle these valuation relations explicitly to identify the factors that are driving valuations in these markets. And armed with this knowledge, the analyst can apply these insights to other instruments, potentially uncovering additional relative value opportunities.

THE APPLICATIONS OF RELATIVE VALUE ANALYSIS

Relative value analysis has a number of applications.

Trading

One of the most important applications of relative value analysis is relative value trading, in which various securities are bought and others sold with the goal of enhancing the risk-adjusted expected return of a trading book.

Identifying relatively rich and relatively cheap securities is an important skill for a relative value trader, but additional skills are required to be successful as a relative value trader. For example, rich securities can and often do become richer, while cheap securities can and often do become cheaper. A successful relative value trader needs to be able to identify some of the reasons that securities are rich or cheap in order to form realistic expectations about the likelihood of future richening or cheapening. We discuss this and other important skills throughout this book.

Hedging and Immunization

Relative value analysis is also an important consideration when hedging or otherwise immunizing positions against various risks. For example, consider a flow trader who is sold a position in ten-year (10Y) French government bonds by a customer. This trader faces a number of alternatives for hedging this risk.

He could try to sell the French bond to another client or to an interdealer broker. He could sell another French bond with a similar maturity. He could sell Bund futures contracts or German Bunds with similar maturities. He could pay fixed in an interest rate swap. He could buy payer swaptions or sell receiver swaptions with various strikes. He could sell liquid supranational or agency bonds issued by entities such as the European Investment Bank. Depending on his expectations, he might even sell bonds denominated in other currencies, such as US Treasuries or UK Gilts. Or he might choose to implement a combination of these hedging strategies.

In devising a hedging strategy, a skilled trader will consider the relative valuations of the various securities that can be used as hedging instruments. If he expects Bunds to cheapen relative to the alternatives, he may choose to sell German Bunds as a hedge. And if he believes Bund futures are likely to cheapen relative to cash Bunds, he may choose to implement this hedge via futures contracts rather than in the cash market.

By considering the relative value implications of these hedging alternatives, a skilled flow trader can enhance the risk-adjusted expected return of his book. In this way, the value of the book reflects not only the franchise value of the customer flow but also the relative value opportunities in the market and the analytical skills of the trader managing the book.

Given the increasing competitiveness of running a fixed income flow business, firms that incorporate relative value analysis as part of their business can expect to increase their marginal revenues, allowing them to generate higher profits and/or to offer liquidity to customers at more competitive rates.

Security Selection

In many respects, a long-only investment manager faces many of the same issues as the flow trader in the previous example. Just as a flow trader can expect to enhance the risk-adjusted performance of his book by incorporating relative value analysis into his hedging choices, a long-only investment manager can expect to enhance the risk-adjusted performance of his portfolio by incorporating relative value analysis into his security selection process.

For example, an investment manager who wants to increase his exposure to the 10Y sector of the EUR debt market could buy government bonds issued by France, Germany, Italy, Spain, the Netherlands, or any of the other EMU member states. Or he could buy Bund futures or receive fixed in a EURIBOR or ESTR interest rate swap. Or he might buy a US Treasury in conjunction with a cross-currency basis swap, thereby synthetically creating a US government bond denominated in euros.

An investment manager who incorporates relative value analysis as part of his investment process is likely to increase his alpha and therefore over time to outperform an otherwise similar manager with the same beta who doesn't incorporate relative value analysis.

THE CRAFT OF RELATIVE VALUE ANALYSIS

Relative value analysis is neither a science nor an art. Rather, it's a craft, with elements of both science and art. For a practitioner to complete the journey from apprentice to master craftsman, he needs to learn to use the tools of the trade, and in this book we introduce these tools along with their foundations in the mathematical science of statistics and in the social science of financial economics.

We also do our best to explain the practical benefits and potential pitfalls of applying these tools in practice. In the development of an apprentice, there is no substitute for repeated use of the tools of the trade in the presence of a master craftsman. So we make every effort in this book to convey the benefit of our experience over many years of applying these tools.

Since financial and statistical models are the tools of the trade for a relative value analyst, it's important that the analyst chooses these tools carefully, with an eye toward usefulness, analytical scope, and parsimony.

Usefulness

In our view, models are neither right nor wrong. Pure mathematicians may be impressed by truth and beauty, but the craftsman is concerned with usefulness. To us, various models have varying degrees of usefulness, depending on the context in which they're applied.

As Milton Friedman reminds us in his 1966 essay “The Methodology of Positive Economics,” models are appropriately judged by their implications. The usefulness of a particular model is not a function of the realism of its assumptions but rather of the quality of its predictions.

For relative value analysts, models are useful if they allow us to identify relative misvaluations between and among securities, and if they improve the quality of the predictions we make about the future richening and cheapening of these securities.

For example, we agree with critics who note that the Black–Scholes model is wrong, in the sense that it makes predictions about option prices that are in some ways systematically inconsistent with the prices of options as repeatedly observed in various markets. However, we've found the Black–Scholes model to be useful in many contexts, as have a large number of analysts and traders. It's important to be familiar with its problems and pitfalls, and like most tools it can do damage if used improperly. But we recommend it as a tool of the trade that is quite useful in a number of contexts.

Analytical Scope (Applicability)

For our purposes, it's also useful for a model to have a broad scope, with applicability to a wide range of situations. For example, principal component analysis (PCA) has proven to be useful in a large number of applications, including interest rates, swap spreads, implied volatilities, and the prices of equities, grains, metals, energy, and other commodities. As with any powerful model, there is a cost to implementing PCA, but the applicability of the model once it has been built means that the benefits of the implementation tend to be well worth the costs.

Other statistical models with broad applicability are those that characterize the mean-reverting properties of various financial variables. Over considerable periods of time, persistent mean reversion has been observed in quite a large number of financial variables, including interest rates, curve slopes, butterfly spreads, term premiums, and implied volatilities. And in the commodity markets, mean reversion has been found in quite a number of spreads, such as those between gold and silver, corn and wheat, crack spreads in the energy complexes, and crush spreads in the soybean complex.

The ubiquity of mean-reverting behavior in financial markets implies that mean reversion models have a tremendous applicability. As a result, we consider them some of the more useful tools of a well-equipped relative value analyst, and we discuss them in some detail in this book.

Parsimony

From our perspective, it's also useful for a model to be parsimonious. As Einstein articulated in his 1933 lecture “On the Method of Theoretical Physics,” “It can scarcely be denied that the supreme goal of all theory is to make irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.”

In our context, it's important to note the relative nature of the word “adequate.” In most circumstances, there is an inevitable tradeoff between the parsimony of a model and its ability to represent experience. The goal of people developing models is to improve this tradeoff in various contexts. The goal of people using models is to select those models that offer the best tradeoff between costs and benefits in specific applications. And it's in that sense that we characterize the models in this book as being useful in the context of relative value analysis.

SUMMARY OF CONTENTS

Relative value analysis models can be divided into two categories: statistical and financial. Statistical models require no specific knowledge about the instrument that is being modeled and are hence universally applicable. For example, a mean reversion model only needs to know the time series, not whether the time series represents yields, swap spreads, or volatilities, nor what drives that time series.

Financial models, on the other hand, give insight into the specific driving forces and relationships of a particular instrument (and are therefore different for each instrument). For example, the specific knowledge that swap spreads versus LIBOR include the unsecured–secured basis can explain its statistical behavior.