Professional perspectives on fixed income portfolio management volume 4

Contents FIXED INCOME ANALYSIS AND STRATEGIES Laurent Gauthier and Laurie Goodman Ludovic Breger William Lloyd, Bharath Manium, and Mats Gustavsson Antti Ilmanen and Roberto Fumagalli Th

Professional Perspectives on

Fixed Income Portfolio

Management

Volume 4

FRANK J FABOZZI

EDITOR

John Wiley & Sons, Inc.

Frontmatter-Prof Persp Page iii Thursday, July 24, 2003 10:09 AM

Professional Perspectives on

Fixed Income

Portfolio Management

Volume 4

Frontmatter-Prof Persp Page i Thursday, July 24, 2003 10:09 AM

THE FRANK J FABOZZI SERIES

Fixed Income Securities, Second Edition by Frank J Fabozzi

Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L Grant and James A Abate

Handbook of Global Fixed Income Calculations by Dragomir Krgin

Managing a Corporate Bond Portfolio by Leland E Crabbe and Frank J Fabozzi

Real Options and Option-Embedded Securities by William T Moore

Capital Budgeting: Theory and Practice by Pamela P Peterson and Frank J Fabozzi

The Exchange-Traded Funds Manual by Gary L Gastineau

Professional Perspectives on Fixed Income Portfolio Management, Volume 3

edited by Frank J Fabozzi

Investing in Emerging Fixed Income Markets edited by Frank J Fabozzi and Efstathia Pilarinu

Handbook of Alternative Assets by Mark J P Anson

The Exchange-Traded Funds Manual by Gary L Gastineau

The Global Money Markets by Frank J Fabozzi, Steven V Mann, and Moorad Choudhry

The Handbook of Financial Instruments edited by Frank J Fabozzi

Collateralized Debt Obligations: Structures and Analysis by Laurie S Goodman and Frank J Fabozzi

Interest Rate, Term Structure, and Valuation Modeling edited by Frank J Fabozzi

Investment Performance Measurement by Bruce J Feibel

The Handbook of Equity Style Management edited by T Daniel Coggin and Frank J Fabozzi

The Theory and Practice of Investment Management edited by Frank J Fabozzi and Harry M Markowitz

Foundations of Economic Value Added: Second Edition by James L Grant

Financial Management and Analysis: Second Edition by Frank J Fabozzi and Pamela P Peterson

Measuring and Controlling Interest Rate and Credit Risk: Second Edition by Frank J Fabozzi, Steven V Mann, and Moorad Choudhry

Frontmatter-Prof Persp Page ii Thursday, July 24, 2003 10:09 AM

Professional Perspectives on

Fixed Income Portfolio

Management

Volume 4

FRANK J FABOZZI

EDITOR

John Wiley & Sons, Inc.

Frontmatter-Prof Persp Page iii Thursday, July 24, 2003 10:09 AM

Copyright © 2003 by Frank J Fabozzi All rights reserved.

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

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Contents

FIXED INCOME ANALYSIS AND STRATEGIES

Laurent Gauthier and Laurie Goodman

Ludovic Breger

William Lloyd, Bharath Manium, and Mats Gustavsson

Antti Ilmanen and Roberto Fumagalli

The Euro Benchmark Yield Curve: Principal Component Analysis of

Lionel Martellini, Philippe Priaulet, and Stéphane Priaulet

Jeffrey Ho and Laurie Goodman

CREDIT RISK AND CREDIT DERIVATIVES

Valuing Corporate Credit: Quantitative Approaches versus Fundamental Analysis 141 Sivan Mahadevan, Young-Sup Lee, David Schwartz, Stephen Dulake,

and Viktor Hjort

Maturity, Capital Structure, and Credit Risk: Important Relationships for

Steven I Dym

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Ren-Raw Chen, Frank J Fabozzi, and Dominic O’Kane

Arthur Q Frank and James M Manzi

Sivan Mahadevan and David Schwartz

Preface

he articles in volume 4 of Professional Perspectives on Fixed Income

Anal-ysis and Strategies, Credit Risk and Credit Derivatives, and StructuredProducts

FIXED INCOME ANALYSIS AND STRATEGIES

In the lead article in this volume, “Risk/Return Trade-Offs on Fixed IncomeAsset Classes,” Laurent Gauthier and Laurie Goodman look at the risk/return characteristics of major fixed-income asset classes over time in order

to see if one asset class consistently outperforms another on a risk-adjustedbasis They first look at the Sharpe ratios for each asset class, and comparethose to the duration-adjusted excess returns The authors then use princi-pal components analysis to identify the factors that are important in deter-mining excess returns and duration-adjusted excess returns Finally,Gauthier and Goodman examine the performance by asset classes afterhedging out the market factors identified through the principal componentsanalysis The conclusions are quite robust: Overweighting spread productpays over time Within spread products, mortgages and asset-backed secu-rities tend to have a very favorable risk/return profile over time

The next four articles focus on the European fixed-income marketand European asset managers and traders In “Fixed Income Risk Mod-eling for Portfolio Managers,” Ludovic Breger discusses the importantsources of risk in European fixed-income securities and how to build areasonable risk model The author addresses challenges such as accom-modating different benchmarks and securities, or providing a wide cov-erage without compromising accuracy The risk characteristics of atypical euro investment-grade corporate index are roughly halfwaybetween the conservative and speculative ends of the risk spectrum.Although European fixed-income instruments are on average less riskythan their U.S dollar equivalent, this by no means implies that a soundrisk management is less relevant

T

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viii Preface

The growth in the popularity of total return management in theEuropean fixed-income market has led portfolio managers, consultants,and pension funds to increasingly focus on ex ante tracking error tomeasure the risk in their portfolios relative to a market index In

“Tracking Error,” William Lloyd reviews three different methodologiesfor calculating tracking error and the assumptions associated with them.While very convenient and conceptually straightforward, he concludesthat tracking error is not the best way to evaluate the relative risk in afixed-income portfolio Instead, Lloyd advocates the use of scenarioanalysis as a better method of determining the risk exposures in a fixed-income portfolio

Yield-seeking investment strategies are popular ways of trying toadd value in active portfolio management Most carry strategies—over-weighting high-yielding assets and underweighting low-yielding assets—are profitable in the long run, but some strategies appear more riskythan others Antti Ilmanen and Robert Fumagalli in their article “Con-sistency of Carry Strategies in Europe” show that carry strategies areespecially consistently profitable at short maturities Among variousstructural tilts that real-money investors can make in their portfolios,replacing short-dated government debt with safe credits seems to offerthe best reward for risk They find similar patterns in all markets theyexamine, presenting empirical results from European and U.S swap-government spread markets and credit markets However, they find theresults are more compelling for real-money investors than for leveragedinvestors because the latter need to factor in funding spreads Moreover,

as Ilmanen and Fumagalli note, the consistency of outperformancefound is not as robust when investors go further down the credit curvethan when they only shift from governments to highest-grade credits.The term structure of interest rates can take at any point in timevarious shapes and the key question from a risk management perspec-tive is to understand how the term structure of interest rates evolvesover time There have been several studies of the term structure for theU.S market In “The Euro Benchmark Yield Curve: Principal Compo-nent Analysis of Yield Curve Dynamics” Lionel Martellini, Philippe Pri-aulet, and Stéphane Priaulet present an empirical analysis of the termstructure dynamics in the euro-zone They study both the zero-couponeuro interbank yield curve, and zero-coupon Treasury yield curves fromfive individual countries (France, Germany, Italy, Spain, and the Nether-lands) Using principal components analysis, they find that three mainfactors typically explain more than 90% of the changes in the yieldcurve, whatever the country and the period under consideration Thesefactors can be interpreted as changes in the level, the slope, and the cur-vature of the term structure Martellini, Priaulet, and Priaulet also find

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Preface ix

strong evidence of homogeneity in the dynamics of the yield curve fordifferent countries in the euro-zone, signaling an increasing financialintegration

In “Dollar Rolling: Does It Pay?” Jeffrey Ho and Laurie Goodmanlook at the historical performance of a mortgage portfolio in which aninvestor holds a limited number of securities and dollar rolls these secu-rities This strategy is compared to the historical performance of a mort-gage index The authors show that on average, since 1992, rolling asmall portfolio of TBA (“To be Announced”) securities outperformed amortgage market index by 50 to 60 basis points Even so, there aretimes when dollar rolling just does not pay Generally, they find thatdollar rolling is the most profitable during prepayment waves, it is lessprofitable during periods of limited supply

CREDIT RISK AND CREDIT DERIVATIVES

Several major events in the credit markets have put a new focus on ing corporate credit What methodologies can be used to value corporatecredit? There are many potential answers to this question Quantitativeapproaches have gained popularity recently, particularly structural mod-els based on equity market inputs The traditional fundamental approach,used for decades by most credit analysts, requires company and industryknowledge In “Valuing Corporate Credit: Quantitative Approaches Ver-sus Fundamental Analysis” Sivan Mahadevan, Young-Sup Lee, DavidSchwartz, Stephen Dulake, and Viktor Hjort compare fundamentalapproaches to valuing corporate credit with quantitative approaches,commenting on their relative merits and predictive powers On the quan-titative front, they review structural models, such as KMV and Credit-Grades™ These models utilize information from the equity markets andcorporate balance sheets to determine default probabilities or fair marketspreads Then they describe reduced form models These models useinformation from the fixed-income markets to directly model defaultprobabilities Finally, the authors review simple statistical techniques such

valu-as factor models These models are helpful in determining relative value.With respect to fundamental approaches, they provide an in depth exami-nation of rating agency and credit analyst methodologies

Typical corporate bond pricing models simply add a risk premium tothe riskless government bond yield This fails to capture the diversity ofbond structures and attendant risk differentials The approach presented

by Steven Dym in “Maturity, Capital Structure, and Credit Risk: tant Relationships for Portfolio Managers” recognizes the distinct risk

Impor-Frontmatter-Prof Persp Page ix Thursday, July 24, 2003 10:09 AM

In the past few years, corporate bond investors have often observed

an inverse correlation between a company’s stock price and the spread

on its bonds The so-called “Merton approach” to credit risk, whichanalyzes a firm’s capital structure using contingent claims theory, pro-vides a theoretical explanation for this correlation Merton models havebecome increasingly popular in the banking industry, and are most oftenused to predict default probabilities In his article “Implications of Mer-ton Models for Corporate Bond Investors,” Wesley Phoa describes howequity-based credit risk models can be interpreted by corporate bondinvestors focused on mark-to-market returns rather than default rates.Credit default swaps provide an efficient means of pricing purecredit, and by definition are a measure of the credit risk of a specific ref-erence entity or reference asset Asset swaps are well-established in themarket and are used both to transform the cash flow structure of a cor-porate bond and to hedge against interest rate risk of a holding in such abond As asset swaps are priced at a spread over LIBOR, with LIBORrepresenting interbank risk, the asset swap spread represents in theorythe credit risk of the asset swap name By the same token, using the no-arbitrage principle it can be shown that the price of a credit default swapfor a specific reference name should equate the asset swap spread for thesame name However a number of factors, both structural and opera-tional, combine to make credit default swaps trade at a different level toasset swaps These factors are investigated by Moorad Choudhry in hisarticle “Some Issues in the Asset-Swap Pricing of Credit Default Swaps.”

He finds that the difference in spread, known as the default swap basis,can be either positive (the credit default swap trading above the assetswap level) or negative (trading below the asset swap)

Further discussion of the default swap basis is provided by ViktorHjort in “Exploring the Default Swap Basis.” He presents an overview

of the factors driving default swaps and analyzes the relationship

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Preface xi

between the cash and derivatives markets at the market, sector, andindividual credit level The default swap market is often perceived asdriven primarily by technical factors particular to this market only.Hjort finds little evidence to support this view Instead, the nature of themarkets argues for a close correlation and for the default swap marketeffectively being positively correlated with, but more volatile than, aversion of the underlying cash market—what the author defines as

“high beta.” In the author’s view, the investment implications are that(1) investors should aim to get exposure to credit in whichever market ischeaper, and (2) investors should use the high-beta character of thedefault swap market to position themselves for major rallies or sell-offs.Trading the basis can allow investors to accomplish the first objective bypicking up significant spread without changing the view on the credit.Hjort finds that being long the market that rallies the most can be asimportant as having the right call on the direction of the market itself sothat investors can achieve the second objective

There are two approaches to pricing credit default swaps: static lication and modeling Static replication is based on the assumption that

rep-if one can replicate the cash flows of a credit default swaps using a folio of tradable financial instruments, then the price of a credit defaultswap should equal the value of the replicating portfolio In situationswhere either the credit default swap cannot be replicated or one doesnot have access to prices for the financial instruments in the replicatingportfolio, it may become necessary to use a modeling approach Ren-Raw Chen, Frank J Fabozzi, and Dominic O’Kane focus on the model-ing approach In “The Valuation of Credit Default Swaps,” they explainhow to determine the premium or spread for a single-name creditdefault swap, what factors affect its pricing, and how to mark-to-mar-ket credit default swaps The authors show that this requires a modeland set out the standard model that is used by the market

port-STRUCTURED PRODUCTS

The largest sector of the U.S investment-grade market is the MBS/ABSsector The MBS market, which includes both residential and commercialMBS, continues to grow Agency MBS (which includes Ginnie Mae MBSand conventional MBS issuance by Fannie Mae and Freddie Mac) repre-sents between 35% to 38% of most U.S investment-grade broad-basedbond market indexes Add to this nonagency MBS and residential ABS,one realizes the importance of understanding these structured products

in order to effectively manage a bond portfolio While a much smaller

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xii Preface

sector compared to the mortgage sector, the has been the substantialgrowth in ABS and CDOs The list of products that have been securitizedand the collateral used for CDOs continues to grow The articles in thissection discuss structured products

The maturation of securitization combined with a dramatic growth

in consumer credit and a secular decline in interest rates fueled thedevelopment of nonconforming mortgage products such as home equityloans These nonconforming mortgage products supply the collateralbacking the residential ABS market John McElravey describes themajor features of the residential, or home equity loan, ABS market in

“Introduction to Residential ABS.” The intent of the article is to providethe reader with a foundation for understanding and analyzing residen-tial ABS collateral and structures as well as their investment attributes

An overview of nonagency prepayments and an introduction to thevaluation of nonagency securities is provided in Steve Bergantino’s article

“Nonagency Prepayments and the Valuation of Nonagency Securities.”The model, developed by Lehman Brothers, covers 15-and 30-year fixed-rate jumbos, jumbo alt-As, conforming balance alt-As, and jumbo relos,explicitly incorporating the effects on prepayments of loan size, borrowercredit quality, prepayment penalties, and geographic distribution

While the usage of mortgage insurance (MI) at the loan level toinsure high loan-to-value mortgage loans against losses is fairly com-mon, it is only recently that a variant of this technology, referred to as

“deep MI,” has been used in subprime structured transactions AnandBhattacharya and Jonathan Lieber in “The Role and Performance ofDeep Mortgage Insurance in Subprime ABS Markets” explain how theincorporation of deep MI into structured deals allows an issuer toobtain lower aggregate credit enhancement than other structured alter-natives, such as subordination of cash flows However, as with otheroptions, the continued usage of this technology in the structured mar-kets will be heavily determined by the cost of deep MI, which is a func-tion of the ability and willingness of insurance providers to continue tounderwrite this risk Bhattacharya and Lieber point out that althoughthe use of deep MI in the subprime ABS arena is relatively recent, theperformance of deep MI as a credit enhancement tool so far appears to

be quite promising

The GNMA multifamily mortgage market, also known as theproject loan market, has been growing in both size and number of insti-tutional investors involved Research support for this market sector isstill developing Art Frank in “Some Investment Characteristics ofGNMA Project Loan Securities” helps to close this research gap withanalysis of both recent and long-term default and prepayment trends forGNMA project loans

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Preface xiii

With the increased trading of collateralized debt obligations (CDOs)

in recent years, the topic of CDO pricing has become increasinglyimportant In “A Framework for Secondary Market CDO Valuation,”Sivan Mahadevan and David Schwartz describe three fundamentalapproaches for valuing CDO tranches: the rerating methodology, themarket value methodology, and the cash flow methodology Theapproaches vary considerably in terms of computational complexity andrequired market savvy, but each can be useful for investors trying toevaluate opportunities in the market

In “Understanding Commercial Real Estate CDOs,” Brian caster chronicles the rapid growth of the $13 billion commercial realestate (CRE) CDO market, the factors driving such growth, the market’sperformance, issuer motivations in sponsoring CRE CDOs, and key fac-tors for investors to consider in the purchase of CRE CDOs He alsoanalyzes the relative value of CRE CDOs versus other fixed-incomeinstruments, arguing that they benefit from the overly conservativenature of the rating agencies methodologies Finally, Lancaster stressesdifferent types of CRE CDOs in light of the historic performance of theCRE markets and in so doing provides the investor with a methodology

Lan-to discriminate among CRE CDOs

The market for aircraft ABS remains under severe stress due to thecombination of a weak U.S economy, the bankruptcy of several majorU.S carriers, the Iraq war of 2003, and SARS Pooled aircraft ABS secu-rities are suffering from a combination of lower cash flows and aircraftvaluations In “Aircraft Valuation-Based Modeling of Pooled AircraftABS,” Mark Heberle introduces a valuation-based model to provide amore robust means of analyzing pooled aircraft securitizations Thismethodology uses assumptions about an aircraft’s future value pros-pects to drive a forward-looking portfolio valuation and related leasecash flows The methodology presented by the author should help inves-tors in this asset class to develop a more complete understanding of thecorrelation between aircraft values, lease revenue, and deal structure

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Contributing Authors

Steve Bergantino Lehman Brothers

Anand K Bhattacharya Countrywide Securities Corporation

Ludovic Breger Barra, Inc.

Ren-Raw Chen Rutgers University

Moorad Choudhry Centre for Mathematical Trading and Finance,

CASS Business School, London Stephen Dulake Morgan Stanley

Steven I Dym Brocha Asset Management

Frank J Fabozzi Yale University

Arthur Q Frank Nomura Securities International, Inc.

Roberto Fumagalli Citigroup

Laurent Gauthier UBS Warburg

Laurie Goodman UBS Warburg

Mats Gustavsson Barclays Capital

Mark A Heberle Wachovia Securities, Inc.

Viktor Hjort Morgan Stanley

Jeffrey Ho UBS Warburg

Antti Ilmanen Citigroup

Brian P Lancaster Wachovia Securities

Young-Sup Lee Morgan Stanley

Jonathan Lieber Countrywide Securities Corporation

William Lloyd Barclays Capital

Sivan Mahadevan Morgan Stanley

Bharath Manium Barclays Capital

James M Manzi Nomura Securities International, Inc.

Lionel Martellini University of Southern California

and EDHEC Risk and Asset Management Research Center

John N McElravey Banc One Capital Markets, Inc.

Dominic O’Kane Lehman Brothers, Inc.

Wesley Phoa The Capital Group Companies

Philippe Priaulet HSBC-CCF

and University of Evry Val d’Essonne Stéphane Priaulet AXA Investment Managers

David Schwartz Morgan Stanley

Frontmatter-Prof Persp Page xiv Thursday, July 24, 2003 10:09 AM

Risk/Return Trade-Offs on Fixed Income Asset Classes

Laurent Gauthier, Ph.D.

DirectorUBS Warburg

Laurie Goodman, Ph.D.

Managing DirectorUBS Warburg

n fixed-income markets, investors often pay inadequate attention tothe historical risk/return characteristics of different asset classes Thus,for example, if one asset class consistently outperforms another on arisk adjusted basis, then total rate-of-return money managers (whoseperformance is measure against an aggregate fixed income index) shouldconsistently overweight that particular asset class

In this chapter, we look at the risk/return characteristics of majorfixed-income asset classes over time in order to see if such opportunitiesexist We will delve into Treasuries, noncallable Agency debentures,callable Agency debentures, mortgage-backed securities, asset-backedsecurities, and corporates (also referred to as “credit”) For robustness,

we use several risk/return measures, each valuable for different poses

pur-Our plan of attack is as follows We first focus on the Sharpe ratiosfor each asset class, then compare those to the duration-adjusted excessreturns (which are returns over the relevant benchmark Treasury securi-ties) In the second section, we run a principal components analysis toI

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2 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

identify the common factors in the performance of fixed income assetclasses In the final section, we review a regression analysis of thereturns over the risk-free rate

Our conclusion is that overweighting spread products over timepays Within spread products, mortgages and asset-backed securitiestend to have a very favorable risk/return profile over time

THE DATAFor this study, we used the total rate-of-return for the components ofthe SSB (Salomon Smith Barney) Broad Investment Grade (BIG) Index.1Monthly return data on the major asset classes of Treasuries, mort-gages, Agency debentures, and corporates is available going back wellinto the 1980s However data quality on the callable Agency serieslooked suspect in its early years, and data for asset-backed securitieswere not available prior to January 1992 As a result, we only used data

as far back as January 1992, and ran it up through March 2003, which

is the most recent available when we were writing this article

SSB also calculates a duration-adjusted excess return series for eachasset class in their index, which is available back to January 1995 Thatparticular return series is calculated by subtracting out the weightedreturns on each of the benchmark Treasuries that characterizes eachindex, with weightings determined by the partial effective durations

SHARPE RATIOS

We began our analysis by calculating the risk/return trade-off (theSharpe ratio) for each of the major assets classes This Sharpe ratio isgiven by the following equation:

where r a is the return on the asset class, and r f is the risk free rate

We used 1-month LIBOR as the risk-free rate for our analysis.Exhibit 1 shows our findings As can be seen, the average return (and

1 UBS, our employer, has licensed the SSB Yield Book and attendant data.

Sharpe RatioAverage excess return Standard deviation of return⁄

=

σ r( a–r f) -

=

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Risk/Return Trade-Offs on Fixed Income Asset Classes 3

average return over LIBOR) for noncallable Agencies and corporates ishigher than that for the other asset classes (callable Agencies, MBS,ABS, and Treasuries) However the standard deviation of the return forboth the credit and noncallable Agency categories is so much higherthan that on other asset classes, that their Sharpe ratios end up lower.Meanwhile, the ABS, MBS, and callable Agency categories have muchlower standard deviations than do the other asset classes Thus, theyend up with higher Sharpe ratios (0.27 on ABS, 0.24 on MBS, and 0.22

on callable Agencies.)

In fact, the standard deviation of returns is strongly related to theduration of a security That is, securities with higher durations will end uphaving higher returns when interest rates drop, and lower returns wheninterest rates rise compared to their shorter duration counterparts.Longer duration securities will have a higher standard deviation ofexcess returns, due to the historical volatility of interest rates

However, the problem with using Sharpe ratios as a guide to mance is that it assumes investors can leverage without limit, and thatmoney can be freely borrowed ad infinitum at the risk-free rate Thus alongthose theoretical lines investors should lever up shorter instruments ratherthan holding the longer duration instruments that constitute a chunk ofSSB’s BIG Index But in reality most total rate-of-return money managers

perfor-EXHIBIT 1 Historical Returns

Agency Callable

Agency Non-

Credit Callable

Credit Non- callable Nominal Monthly Returns (1/1992–3/2003)

Average 0.552 0.654 0.588 0.610 0.606 0.653 0.652 Standard dev 0.765 1.419 0.838 0.834 1.261 1.390 1.315

Excess Monthly Returns

(= Nominal return minus 1-month LIBOR, 1/1992–3/2003)

Average 0.167 0.269 0.202 0.225 0.221 0.268 0.267 Standard dev 0.756 1.414 0.828 0.834 1.258 1.387 1.313 Ratio 0.221 0.190 0.244 0.269 0.176 0.193 0.203

Duration-Adjusted Returns (1/1995–3/2003)

Average 0.030 0.055 0.068 0.074 0.022 0.000 0.042 Standard dev 0.225 0.273 0.306 0.251 0.074 0.968 0.774 Ratio 0.135 0.201 0.221 0.297 0.302 0.000 0.054 1-Gauthier/Goodman Page 3 Thursday, July 24, 2003 10:44 AM

4 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

do have leverage constraints and therefore cannot leverage without limit.Thus, while Sharpe ratios are certainly one good measure of risk/return,that should not be the only measure; as portfolios containing only theasset classes with the highest Sharpe ratios would require more leveragethan most portfolio managers are permitted Besides, most fixed incomeportfolio managers are unwilling to put on a huge curve bet, whichwould be implicit in buying leveraged short paper versus non-leveragedlonger paper

DURATION-ADJUSTED EXCESS RETURNS

the curve bet It essentially looks at the return on each asset class versuswhat a duration-equivalent portfolio of on-the-run Treasuries wouldhave provided The results of such an analysis are shown in the bottomsection of Exhibit 1 (with returns also on a monthly basis) For exam-ple, Exhibit 1’s Agency NC return of 0.0555 means that Agencies have,

on average, provided a duration-adjusted excess return of 5.5 basispoints/month Just as with the Sharpe ratio analysis the ABS and MBScategories provided the highest excess returns, while the noncallablecredit series provided returns similar to Agency debentures One inter-esting point about this analysis is that callable Agencies look worse thannoncallable Agencies, which is the opposite of results from using Sharperatios Also, the differential between MBS and Agency noncallables ismuch less pronounced than under Sharpe ratios

The reason for this point of interest is that OAS-based models areused in determining the partial durations implicit in duration-adjustedexcess return calculations To the extent that the market does notbehave according to how the models work—there will be a bias in dura-tion-adjusted excess returns

Let’s now attempt to quantify the effect of this bias that throwsawry the effective duration Exhibit 2 shows the average effective dura-tion of each of the indices over our 11 plus-year period, as well as thelatest duration Obviously, in the current low rate environment, dura-tions for the callable indices (Agency callables and mortgages) are con-siderably shorter than historical averages Agency bullets are also muchshorter than historically as the GSEs have altered their debt mix overthe last decade, and are now issuing more at the front end of the curve(where they fund more favorably relative to LIBOR) The third row ofExhibit 2 is the empirical duration of each of the indices over the period

we looked at It is calculated as minus the coefficient of the regression of

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Risk/Return Trade-Offs on Fixed Income Asset Classes 5

monthly returns over changes in 10-year Treasury yields Basically thismeasure shows the sensitivity of returns to interest rate levels Now wecould compare this empirical duration (Exhibit 2’s third row) to theexhibit’s first row (average effective duration) But since the interest rateenvironment has changed a great deal over the time period covered, andthere have been changes in the indices’ composition, such a juxtaposi-tion would not be very telling

To pinpoint directionality more accurately via a single numericalreading, we first constructed a specific measure for the discrepancybetween empirical and effective durations We used a 2-year rolling win-dow (12 months of data before the observation + 12 months of dataafter the observation) to obtain the empirical duration of returns, whichwas expressed as a percentage of the average effective duration over thesame period To get a specific measure of directionality of durations, wethen regressed the duration discrepancy over the 2-year average of 10-year Treasury yields, with our measure of directionality taken from theslope of that regression

Our results are shown in the bottom row of Exhibit 2, and we have

a handy intuitive interpretation that aids in understanding the results.For example, the coefficient for duration directionality on MBS is 12%,which suggests that a 100-basis-point rally would shorten the duration

by 12% more than would be suggested by option-adjusted spread (OAS)models Note that duration directionality is extremely low for bothAgency bullets and for Treasuries, as would be expected It is alsohigher for MBS and callable Agencies than for ABS The only surprisemay be the result listed for corporate bonds However, realize that peri-

EXHIBIT 2 Duration and Duration Directionality

a

Slope of the ratio of empirical to effective duration versus average 10-year Treasury yield (2-year rolling window).

Agency Callable

Agency Non- callable MBS ABS Treasury

Credit Non- callable

SSB Avg Duration

(1/1992–3/2003)

SSB Latest Duration 2.1 4.7 1.6 3.0 5.8 5.8 Empirical Index Duration

(1/1992–3/2003)

Measure of Index

Duration Directionality a 14% 0% 12% 7% 4% 25% 1-Gauthier/Goodman Page 5 Thursday, July 24, 2003 10:44 AM

6 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

ods of low rates tend to be correlated with times of crises, during whichcorporates typically underperform Thus, corporates should behave as ifthey have a shorter duration during time of low yields

This produces a bias in the average duration adjusted returns Sincethe market has rallied over the period under consideration, the SSBaverage duration adjusted excess returns on the sections with high dura-tion directionality are biased downward This helps explain the weakerperformance of ABS, MBS, and callable agencies on the durationadjusted excess return measures versus those using Sharpe ratios.The row just before the end of Exhibit 1 captures the standard devi-ation of excess returns The conclusions are somewhat obvious: Trea-suries have a very low standard deviation of excess returns (as we aresimply capturing the on-the-run versus off-the-run basis), while thecredit series has a very high standard deviation of excess returns (asduration alone is inadequate, since it only explains part of the returnvariability) The standard deviations for MBS, ABS, and callable andnoncallable Agency series lie between those two extremes

The last line of Exhibit 1 shows (duration-adjusted excess returns)/(standard deviation of these returns) We do not regard this number asparticularly useful, as it overstates the standard deviation of sectors withhigh duration directionality, and hence understates the attractiveness ofthese sectors Even so, some market participants do look at this measure

FIXED INCOME RETURNS, BY ASSET CLASS

To try to figure out what factors are important in determining excessreturns and duration-adjusted excess returns, we ran a principal compo-nents analysis The factors, or “components,” emerging from that pro-cess can then be matched to market factors to “explain” performance.Exhibit 3 shows the results of our principal component analysis

1 Let’s look first at the top part of the exhibit, which “explains” nominalreturns Note that the first component explains 92.7% of the variationand looks exactly like the exposure to interest rates (duration) Notealso that the order of magnitude of the coefficients on each of the indi-ces looks very much like the average duration given in Exhibit 2.Exhibit 4 confirms this, showing a scatter plot of the return on Factor 1versus the change in the 10-year Treasury yield Factor 1 has a veryclear linear relationship to changes in interest rates Identification isprovided in Exhibit 5, which looks at the correlation of each factor tovarious market measures (such as the slope of the 2–10 spread; 5-year

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Risk/Return Trade-Offs on Fixed Income Asset Classes 7

EXHIBIT 3 Principal Component Analysis

EXHIBIT 4 Relationship—Rates versus Nominal Return Factor #1

Component

Nominal Returns

Agy Callable 0.28 0.00 0.41 0.16 0.00 0.85 Agy NC 0.54 0.24 –0.20 0.60 0.46 –0.22 MBS 0.30 0.00 0.75 0.00 –0.34 –0.46 Credit 0.48 –0.82 –0.28 –0.11 0.00 0.00 ABS 0.31 0.15 0.19 –0.73 0.56 0.00 Treasury 0.47 0.49 –0.34 –0.25 –0.60 0.00 Factor contribution (%) 92.7 3.1 2.3 0.9 0.5 — Cumulative Importance (%) 92.7 95.8 98.1 99 99.5 1

Duration-Adjusted Returns

Agy Callable 0.18 0.28 0.76 –0.10 –0.53 –0.12 Agy NC 0.21 0.52 0.17 0.67 0.45

ABS 0.23 0.26 –0.58 0.32 –0.64 –0.18 Treasury 0.00 0.00 0.00 –0.22 0.97 Factor contribution (%) 80.3 12.1 2.9 2.5 1.8 — Cumulative importance (%) 80.3 92.4 95.3 97.8 99.6 1.0 1-Gauthier/Goodman Page 7 Thursday, July 24, 2003 10:44 AM

8 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

cap volatility, etc.) Looking across the row labeled “Factor 1,” we seethat the 10-year yield has a correlation of –89% to the first factor ofnominal returns

2 The second most important factor in “explaining returns” by assetclass is the credit specific factor This alone explains another 3.1% ofthe nominal returns, which brings the cumulative total part

“explained” up to 95.8% Our identification of this factor was tively easy—a high negative weighting on the credit index combinedwith a high positive weighting on Treasuries Exhibit 6 confirms thisidentification, showing a strong relationship between Factor 2 andthe S&P 500; and our correlation analysis in Exhibit 5 confirms thisintuition as well Factor 2 has a correlation of –50% to the S&P 500

EXHIBIT 5 Correlations—PCA Factors and Explanatory Variables

EXHIBIT 6 Relationship—S&P 500 versus Nominal Return Factor #2

Factor

Slope (2–10s)

10-yr Trsy

10-yr Swap Spd

5-yr Cap Vol

S&P 500

Nominal Return 1 4% –89% –15% 40% –9%

3 42% 13% –28% –27% 0% Duration-Adjusted

Return

3 16% 27% 4% –15% –3% 1-Gauthier/Goodman Page 8 Thursday, July 24, 2003 10:44 AM

Risk/Return Trade-Offs on Fixed Income Asset Classes 9

lower the S&P 500, the lower corporate bond returns will be, and

3 The third aspect explaining returns by asset class is very clearly an

have some optionality (callable Agencies, MBS, and ABS) is positive,while the coefficient on the noncallable series (Treasuries, noncallableAgencies, and credit) is negative Optionality actually involves severalmarket factors, such as the shape of the curve and volatility Exhibit 5shows that the optionality factor has a very positive correlation withcurve slope, but a negative relationship with 5-year cap volatility Thissuggests that the steeper the curve (the slope), the better a callableseries should do (as the options that have been implicitly written arenow more out-of-the-money) The higher the volatility, the lower thereturn on the callable series Exhibit 7 confirms the negative relation-ship between Factor 3 and volatility Because the shape of the curve isalso quite important, the relationship between volatility and Factor 3 isslightly less clear than it was between the first two factors But the sig-nificant point is that the three factors together—Treasury yields, credit,and volatility—explain 98.1% of the variation in nominal returns ofaggregate fixed-income indices

We now turn to explaining the duration-adjusted excess returns.These are actually much harder to “explain,” as we have already elimi-nated changes in interest rates (which we just showed to be the mostimportant factor, accounting for 92.7% of return variation)

EXHIBIT 7 Relationship—Cap Volatility versus Nominal Return Factor #3

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10 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

EXHIBIT 8 Relationship—Swap Spreads versus Duration-Adjusted Return Factor #1

1 Look first at the coefficients on Factor 1 in the bottom section ofExhibit 3 It is very clear from these that the most important factor isone governing all spread product Swap spreads are certainly a proxyfor this factor Exhibit 5 shows that the 10-year swap spread has a –63% correlation to Factor 1, which is far higher than that on anyother market variables Exhibit 8 confirms the strong relationshipbetween swap spreads and the duration-adjusted return Factor 1.Note that this factor explains 80.3% of the variation in this series

2 The second factor is a corporate-specific factor Corporates have anegative factor coefficient, while all other asset classes have a positivefactor coefficient Exhibit 5 shows that this second factor has a clearnegative relationship to the S&P 500 The relationship between Factor

2 and the S&P 500 is shown in Exhibit 9; it is quite a strong one ever Exhibit 5 also shows a negative relationship between 10-yearswap spreads and the second factor, indicating that the factor identifi-cation is not as clean as it otherwise could be Intuitively, the negativecorrelation between Factor 2 and swap spreads mitigates some of theeffect of the first factor This credit-specific factor (Factor 2) explainsanother 12.1% of the returns, bringing the total explanatory power to92.4% (Additional remaining factors are not easily identifiable.)

How-CAPTURING EXCESS RETURNS

Now that we have figured out the factors which fundamentally matter

in examining returns by fixed income asset class, we can look at using

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Risk/Return Trade-Offs on Fixed Income Asset Classes 11

these factors to capture excess returns by asset class That is, if a givenasset class still outperforms (after hedging out market factors), it sug-gests that over time, the asset class is a superior provider of excessreturns

We will now apply the specific market factors we have identified inthe prior section of our analysis We first set up a series of regressions

on nominal excess returns These regressions use the excess returns eachmonth as the dependent variable, with independent variables being thefundamental factors which we’ve discovered above that should matter—the level of Treasury rates, the shape of the Treasury curve, 10-yearswap spreads, 5-year cap volatility and the S&P 500 Exhibit 10 dis-plays the regression results

First look at Treasuries—for which the level of rates is the whelming factor powering the sector The S&P 500 has a low coeffi-cient, but it is significant and has the expected sign We had expectedthe shape of the curve to be important—but it was not Arguably, sincethe duration of the Treasury index is closer to the 10-year Treasury than

over-to anything else, the curve effect was muted Additionally, as explainedbelow, we have multicollinearity problems with this analysis

sig-nificant The S&P also enters significantly, with the expected sign, but isclearly less important than the level of rates or swap spreads The shape

of the curve and volatility are insignificant There are no surprises here.Now let’s move on to the callable instruments:

EXHIBIT 9 Relationship—S&P 500 versus Duration-Adjusted Return Factor #2

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12 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

EXHIBIT 10 Regression Results—Excess Returns

excepting the S&P 500 (as expected)

the slope of the curve is much less important; and in ABS, cap volatility

is not significant, as the option component of this index is small

Agency Callable

Agency Non- callable MBS ABS Treasury

Credit Callable

Credit Non- callable Coefficients

Intercept 0.080 0.095 0.118 0.123 0.058 0.080 0.094 Slope 0.690 –0.116 0.462 0.940 0.014 –1.071 –0.448 10-yr Treasury –2.427 –4.506 –2.485 –2.503 –3.973 –3.766 –3.986 10-yr Swap Spread –0.020 –0.036 –0.029 –0.023 –0.012 –0.051 –0.054 5-yr cap –0.049 0.006 –0.052 0.012 0.038 0.033 –0.013 S&P 500 –0.221 –2.555 –0.794 –1.381 –2.457 4.357 2.325

Standard dev of coefficients

Intercept 0.034 0.055 0.042 0.034 0.047 0.074 0.059 Slope 0.230 0.369 0.286 0.230 0.317 0.497 0.399 10-yr Treasury 0.139 0.222 0.172 0.139 0.191 0.300 0.241 10-yr Swap Spread 0.005 0.008 0.006 0.005 0.007 0.011 0.009 5-yr cap 0.023 0.037 0.028 0.023 0.032 0.049 0.040 S&P 500 0.774 1.239 0.960 0.771 1.066 1.668 1.340

T-statistics

Slope 3.0 –0.3 1.6 4.1 0.0 –2.2 –1.1 10-yr Treasury –17.5 –20.3 –14.4 –18.1 –20.8 –12.6 –16.6 10-yr Swap Spread –3.9 –4.4 –4.6 –4.6 –1.7 –4.7 –6.2 5-yr cap –2.1 0.2 –1.8 0.5 1.2 0.7 –0.3 S&P 500 –0.3 –2.1 –0.8 –1.8 –2.3 2.6 1.7 Resid St Dev 0.376 0.602 0.466 0.375 0.518 0.811 0.652 Original St Dev 0.756 1.414 0.828 0.834 1.258 1.387 1.313

Risk/Return Trade-Offs on Fixed Income Asset Classes 13

EXHIBIT 11 Correlation Matrix

S&P 500 matter (For the S&P 500, the coefficient is quite high, but thesignificance is less than we had hoped) Curve slope and volatility areinsignificant

Note that callable corporate bonds tend to be much less callable thantheir Agency counterparts That is they have long lock-outs before thecall, and many calls are at a premium Moreover, it is the volatility ofthe individual corporate/credit that matters more than implied interestrate volatility Given all the factors that go into pricing a callable corpo-rate, it is not surprising that 5-year cap volatility came in insignificant

It is important to realize that the coefficients on these regressionsshould not be regarded as gospel There is a fairly high correlationbetween the independent variables, as shown in Exhibit 11 As a result,the coefficients will be less meaningful.2

Now we will focus on two aspects of our results First, the interceptterm on the regression should measure the hedged excess return Notethat the intercept is highest and most significant for MBS and ABS ForMBS, the intercept is 0.12, with a t-statistic of 2.8 For ABS the intercept

is 0.12, with a t-statistic of 3.6 The intercepts for Agency and corporatepaper are similar to each other, but clearly lower than MBS and ABS.Treasury paper has the lowest intercept This indicates that after hedging,all spread product outperforms Treasuries Second, the residual standarddeviation (as shown in Exhibit 10) gives us some idea as to how much ofthe standard deviation of returns can be explained by market factors wehave discussed Note that for all asset classes, we “explained” from 41%

to 58% (roughly, about one-half) of the variation in excess returns

Slope

10-yr Trsy

10-yr Swap Spread

5-yr Cap

S&P 500

or-to interpret So we just acknowledge the issue and live with it.

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14 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

We can use these results to measure the risk/return trade-off of

“hedged excess returns” for various asset classes If we look at the

inter-cept divided by the residual standard deviation, then ordinal results

look roughly similar MBS and ABS look better than all other asset

classes Agencies look better than corporates or Treasuries, while

corpo-rates outshine Treasuries These results are shown in the bottom section

of Exhibit 10 Note that this particular ranking of returns by asset class

is very similar to the Sharpe ratios we obtained in the first section and

repeated for convenience in the bottom row of Exhibit 10

CONCLUSION

In this article we looked at the risk/return trade-offs of the various fixed

income asset classes We found consistent outperformance on the MBS

and ABS series Here’s a quick review of the evidence:

■ The Sharpe ratios and duration-adjusted excess returns both indicated

the superior performance of the ABS and MBS sectors

■ In addition, callable Agencies have done better (on a Sharpe ratio basis)

than noncallable Agencies

■ Credit asset classes fared much more poorly than either structured

products or callable agencies on a Sharpe ratio basis, but better than

Treasuries

■ Looking at the average duration-adjusted excess returns, the

noncall-able credit has done better than the callnoncall-able Agencies, but less well than

noncallable Agencies

■ Treasuries again fared the most poorly on a duration-adjusted basis

We then used a principal component analysis to examine the market

factors that mattered most for excess returns and duration-adjusted

excess returns We identified the usual suspects: the level of rates, the

shape of the curve, volatility, swap spreads and the S&P 500 We took

that one step further, and used regression analysis to determine how

much excess return and residual risk there was within each asset class

after hedging out the market factors we identified Again, ABS and MBS

remain the best performing asset classes, whether measured by the alpha

or the alpha divided by residual standard deviation Looked at in this

manner, the corporate series looks approximately as appealing as that

for Agency debentures Treasuries again were the poorest performer

Putting these results together, it appears that being overweighted in

spread product is a strategy that historically pays on a risk/return basis

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Risk/Return Trade-Offs on Fixed Income Asset Classes 15

(as Treasuries are consistently the poorest performer) Moreover, ABS

and MBS are consistently the best performing asset classes, regardless of

the risk/return measures used, suggesting total return managers should

have a consistent overweight to these sectors

1-Gauthier/Goodman Page 15 Thursday, July 24, 2003 10:44 AM

1-Gauthier/Goodman Page 16 Thursday, July 24, 2003 10:44 AM

Barra, Inc.

he European credit market, consisting mainly of euro and sterlingdenominated debt, is second only to the U.S domestic market interms of size, influence, and liquidity Not surprisingly, European securi-ties are becoming common in global portfolios The recent turmoil incredit markets has shown once again that understanding risk is orshould be a critical aspect of portfolio management However, as theEuropean credit market is a mosaic of widely different instruments,issuers, and currencies, identifying and forecasting the risk of Europeanfixed income securities is not a simple task

This article will take the reader through the process of building aEuropean risk model and discuss the important sources of risk in genericfixed income portfolios Our intention is not to cover the whole spectrum

of securities but to address some typical modeling challenges such asaccommodating different benchmarks and securities, and providing awide coverage without compromising accuracy With a general frame-work in place, the model can be easily extended to cover more markets orbond types

18 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

A FRAMEWORK FOR UNDERSTANDING AND MODELING RISKThis discussion covers the main factors affecting bond returns in theEuropean fixed income market, namely, the random fluctuations ofinterest rates and bond yield spreads, the risk of an obligor defaulting

on its debt, or issuer-specific risk, and currency risk There are alsoother, more subtle sources of risk Some bonds such as mortgage-backedand asset-backed securities are exposed to prepayment risk but suchinstruments still represent a small fraction of the total outstandingEuropean debt Bonds with embedded options are exposed to volatilityrisk However, it is not apparent that this risk is significant outsidederivatives markets

A detailed understanding of correlations between asset returns isrequired to accurately estimate the risk of a portfolio Unfortunately,estimating correlations directly is in practice impossible as unknownsseverely outnumber observations even in relatively small portfolios Thestandard solution is to decompose the portfolio’s vector of asset returnsusing market-wide common factors:1

(1)where

Decomposing returns is a key step in identifying, understanding,and modeling the sources of risk that are at work in the market It isalso crucial in understanding risk exposures

We begin our analysis by writing the excess returns of assets in aportfolio as

(2)where

1 For more information on factor models, see for instance Richard C Grinold and Ronald N Kahn, “Multiple Factor Models for Portfolio Risk,” John W Peavey III (ed.) A Practitioner’s Guide to Factor Models (Charlottesville, VA: AIMR, 1994).

X = the matrix of asset exposures

f = the vector of factor returns

rspecific = the vector of asset residual returns not explained by factors

or specific returns idiosyncratic to individual assets

rIR = the vector of returns due to changes in interest rates

rexcess = X f⋅ +rspecific

rexcess = (rIR+rcurr+rspread factor+rspecific)

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Fixed Income Risk Modeling for Portfolio Managers 19

Note that the decomposition implicitly ignores the predictable ponent of return that is irrelevant for risk modeling purposes.2 Thereturn common horizon will be one month in most cases Althoughdaily or even weekly returns would provide a much larger data set, theyare also on average much more sensitive to noise in bond data.3 We willalso see in what follows that it is sometimes possible to use returns over

com-a shorter time horizon

If the return factor model adequately accounts for common factors,then the specific returns are uncorrelated and we can write portfolio riskas

(3)with

(4)where

Equation (4) will yield active risk forecasts when h is a vector of activeholdings

The data that can go into computing factor returns will of coursedepend on what the factors are It can include bond and index level data

as well as currency exchange rates Assume that we have the factorreturn series To construct covariances, we could postulate that theunderlying random processes are time stationary and compute covari-ances using equally weighted factor returns We actually know that mar-

rcurr = the vector of returns due to changes in currency exchange

2 Some market idiosyncrasies such as settlement conventions are an important part

of a valuation model but irrelevant to a risk model.

3 For instance, short-horizons spread returns observed for high-grade corporate bonds are small and are typically very noisy

h = the vector of portfolio holdings

Σ = the covariance matrix of asset returns

Φ = the covariance matrix of factor returns

∆ = the diagonal matrix of specific variances

σ2 = T h⋅ ⋅Σ h

Σ = T X⋅ ⋅Φ X ∆+

2-Breger Page 19 Wednesday, July 23, 2003 10:21 AM

20 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

kets change over time and that recent data are more representative ofcurrent market conditions than are older data A simple method foraccommodating this fact consists in exponentially weighting factorreturns to calculate the covariance matrix The relative weight ofreturns from time τ in the past relative to the most recent returns is e–t/τ,where τ is a time-decay constant.4 The optimal time constant τ can beobtained empirically using, for instance, a maximum-likelihood estima-tor However, series that are particularly volatile may require a differenttreatment (see for instance Currency Returns section)

Much of the art of constructing a model goes in choosing relevantfactors Note that factors are descriptive and not explanatory In otherwords, they allow for forecasting risk without necessarily being linked

to the forces that really drive interest rates or returns Let’s now proceedwith a discussion of several classes of factors

INTEREST RATE RISK

Interest rate or term structure risk stems from movements in the mark interest rate curve Excluding exchange rate risk, it is the mainsource of risk for most investment-grade bonds Any reasonable modelwill include markets that are stable and actively traded A typical cover-age, taken from JP Morgan GBI Broad Index, is shown in Exhibit 1.Note the presence of two emerging markets

bench-Building a term structure risk model for the European marketinvolves choosing several benchmarks—at least one for each currency Arecent complication is that domestic government yields are no longerthe universal choice The LIBOR/swap curve has recently emerged as theeuro zone preferred benchmark due to the absence of a natural sover-eign yield curve and the growing liquidity and transparency of swap

Portugal Spain Sweden Switzerland United Kingdom 2-Breger Page 20 Wednesday, July 23, 2003 10:21 AM

Fixed Income Risk Modeling for Portfolio Managers 21

curves However, many markets continue to trade primarily with respect

to the government benchmark In some emerging markets, the absence

of a liquid market for sovereign debt makes the LIBOR/swap curve theonly available benchmark A simple approach used at Barra and whichpermits alternative views is to use the sovereign term structure as localbenchmark whenever possible and include a swap spread “intermedi-ate” factor that can be added to the sovereign-based interest rate factors

to allow interest rate to be expressed with respect with the swap curve.This swap spread factor will be described in more detail in the next sec-tion In markets where the benchmark is already the LIBOR/swap curve,there is obviously no need for a swap factor

The existence of a euro zone born from the union of several legacymarkets introduces an additional modeling challenge More than onedomestic government is issuing euro-denominated debt, and althoughyields have converged, some differences clearly remain that suggestbuilding a set of factors for each legacy market (See Exhibit 2 for someexamples of sovereign term structures within the euro zone.) Somebonds also need to be analyzed almost completely independently ofother assets This is the case for Inflation Protected Bonds (IPBs) denom-inated in euro or sterling, which offer investors a “real” inflation-adjusted yield Such securities are weakly correlated with other assetclasses and are exposed to a set of IPB-specific interest risk factors simi-

EXHIBIT 2 Examples of Sovereign Term Structures within the Euro Zone on July

31, 2002

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22 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

lar in nature to the conventional interest rate factors but derived fromIPB data and real yields

What should the interest rate factors be? Key rate durations, whichare rate changes at the term structure vertices, seem a natural and some-what appealing choice However, because rates for different maturitiesare highly correlated, using so many factors is unnecessary, and causesdifficulty with spurious correlations Anywhere from 90% to 98% ofterm structure risk can in fact be modeled using only three principalcomponents commonly referred to as shift, twist, and butterfly Theprincipal component analysis is now a fairly standard approach that wedescribe in more details in the Appendix to this article Exhibit 3 showsexamples of factor shapes Note how principal components derivedfrom Portuguese sovereign euro-denominated debt are very differentfrom the German shapes Such large differences within the euro zoneconfirm the need for a different set of factors in each legacy market Shift, twist, and butterfly volatilities are shown in Exhibit 4 Quasi-parallel shifts in the term structure are the dominant source of risk in allcases with volatilities ranging from 35 to 200 basis points per year Inspite of these large differences, term structure risk is relatively homoge-neous across most markets and in particular within the euro zone Note,

EXHIBIT 3 Examples of Shift, Twist and Butterfly Interest Risk Factors Shapes (Top) and Return Volatilities (Bottom) on July 31, 2002

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Fixed Income Risk Modeling for Portfolio Managers 23

again, that the differences in factor volatilities are sufficiently large to tify building separate legacy factors.5 As expected, the largest volatilitiesare observed for emerging market benchmarks, Czech Republic being theriskiest market And not surprisingly, real yields appear to be more stablethan their noninflation protected sovereign counterparts

jus-5 An alternative but less accurate approach would be to build a unique set of EMU terest rate factors and capture each legacy market idiosyncrasies with a spread factor

in-EXHIBIT 4 Interest Rate Factor Volatilities on July 31, 2002

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24 PROFESSIONAL PERSPECTIVES ON FIXED INCOME PORTFOLIO MANAGEMENT

EXHIBIT 5 Examples of Interest Rate Risk Breakdown

The interest rate risk of any given bond will depend on the bond’sexposures to the factors and on correlations between factors Exhibit 5gives detailed risk decompositions for three sovereign bonds The typi-cal annualized risk of a straight bond issued by the Federal Republic ofGermany varies from about 200 to 300 basis points to over 800 basispoints, depending on its duration At the other end of the spectrum, theinterest rate risk of a bond issued by the Czech Republic can reach asmuch as 3,000 basis points,6 which exceeds the risk of most speculativecorporate issues in developed markets Clearly, such extreme cases willrequire special attention when controlling risk

SPREAD RISK

Until fairly recently, outside the U.S., U.K., and Japan, there were tively few tradable nongovernment bonds The recent explosion of theglobal corporate credit market now provides asset managers with newopportunities for higher returns and diversification Unlike domesticgovernment debt, however, corporate debt is exposed to spread risk,which arises from unexpected yield spread changes For modeling pur-poses, such changes can again be decomposed into a systematic compo-nent that describes, for instance, a market-wide jump in the spread of A-rated utility debt and can be captured by common spread factors, and

rela-an issuer or bond-specific component This section discusses model ket-wide spread risk, while the next section will address issuer specificspread risk and default risk

mar-Data considerations are crucial in choosing factors The choice offactors will be somewhat limited in markets with little corporate debt.Spread factors should increase the investor’s insight and be easy to inter-pret Meaningful factors will in practice be somewhat connected to the

Shift Twist Butterfly Shift Twist Butterfly Total

Federal Republic of

Germany 8.5% 07/16/07

4.9 –0.3 –2.9 310 8 35 312 Federal Republic of

Germany 4.75% 07/04/28

10.8 18.7 10.6 680 490 130 850 Czeck Republic 6.95%