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Professional Perspectives on

Fixed IncomePortfolio

Management

Volume 4

FRANK J. FABOZZI

EDITOR

John Wiley & Sons, Inc.

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

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Management

Volume 4

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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, andMoorad Choudhry

The Handbook of Financial Instruments


Collateralized Debt Obligations: Structures and Analysis

by Laurie S. Goodman and Frank J. Fabozzi

Interest Rate, Term Structure, and Valuation Modeling


Investment Performance Measurement

by Bruce J. Feibel

The Handbook of Equity Style Management

edited by T. Daniel Coggin andFrank 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 andPamela P. Peterson

Measuring and Controlling Interest Rate and Credit Risk: Second Edition

byFrank J. Fabozzi, Steven V. Mann, and Moorad Choudhry

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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 JerseyPublished simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or oth-erwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rose-wood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Per-missions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, e-mail: [email protected].

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies con-tained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

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For more information about Wiley, visit our web site at www.wiley.com.

ISBN: 0-471-26805-4

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

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http://www.copyright.comhttp://www.wiley.com

v

Contents

Preface viiContributing Authors xiv

FIXED INCOME ANALYSIS AND STRATEGIES

Risk/Return Trade-Offs on Fixed Income Asset Classes 1Laurent Gauthier and Laurie Goodman

Fixed Income Risk Modeling for Portfolio Managers 17Ludovic Breger

Tracking Error 45William Lloyd, Bharath Manium, and Mats Gustavsson

Consistency of Carry Strategies in Europe 77Antti Ilmanen and Roberto Fumagalli

The Euro Benchmark Yield Curve: Principal Component Analysis ofYield Curve Dynamics 103

Lionel Martellini, Philippe Priaulet, and Stéphane Priaulet

Dollar Rolling—Does It Pay? 131Jeffrey Ho and Laurie Goodman

CREDIT RISK AND CREDIT DERIVATIVES

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

and Viktor Hjort

Maturity, Capital Structure, and Credit Risk: Important Relationships forPortfolio Managers 183

Steven I. Dym

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vi

Contents

A Unified Approach to Interest Rate Risk and Credit Risk of Cash andDerivative Instruments 197

Steven I. Dym

Implications of Merton Models for Corporate Bond Investors 211Wesley Phoa

Some Issues in the Asset Swap Pricing of Credit Default Swaps 229Moorad Choudhry

Exploring the Default Swap Basis 239Viktor Hjort

The Valuation of Credit Default Swaps 255Ren-Raw Chen, Frank J. Fabozzi, and Dominic O’Kane

STRUCTURED PRODUCTS

An Introduction to Residential ABS 281John N. McElravey

Nonagency Prepayments and the Valuation of Nonagency Securities 303Steve Bergantino

The Role and Performance of Deep Mortgage Insurance in Subprime ABS Markets 325Anand K. Bhattacharya and Jonathan Lieber

Some Investment Characteristics of GNMA Project Loan Securities 339Arthur Q. Frank and James M. Manzi

A Framework for Secondary Market CDO Valuation 365Sivan Mahadevan and David Schwartz

Understanding Commercial Real Estate CDOs 395Brian P. Lancaster

Aircraft Valuation-Based Modeling of Pooled Aircraft ABS 431Mark A. Heberle

Index 439

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Preface

he articles in volume 4 of

Professional Perspectives on Fixed IncomePortfolio Management

are grouped into three areas: 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 orderto 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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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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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 valu-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 suchas 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 presentedby Steven Dym in “Maturity, Capital Structure, and Credit Risk: Impor-tant Relationships for Portfolio Managers” recognizes the distinct risk

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Preface

profiles of senior and subordinated debt. Dym shows how to relatechanges in return on the firm’s physical assets to the prices, hence yields,of these instruments, and explains how maturity differences interact withseniority levels to produce important, albeit counterintuitive, price effects.

Bond portfolio managers are today faced with an almost bewilderingarray of instruments and associated risk profiles. In his article “UnifiedApproach to Interest Rate Risk and Credit Risk of Cash and DerivativeInstruments,” Steven Dym presents a unique, yet straightforward, way tothink about the main variables in these instruments—pure interest raterisk and credit risk. The intuitive approach applies to fixed couponbonds as well as to floating-rate notes, derivatives, and cash-derivativecombinations. In the process, Dym throws some light on a number ofcounterintuitive relationships in the fixed-income marketplace.

In the past few years, corporate bond investors have often observedan inverse correlation between a company’s stock price and the spreadon 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 overviewof the factors driving default swaps and analyzes the relationship

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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 rep-lication and modeling. Static replication is based on the assumption thatif one can replicate the cash flows of a credit default swaps using a port-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.

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 productsin order to effectively manage a bond portfolio. While a much smaller

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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 growthin 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 tobe 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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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 Lan-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 methodologyto 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 BrothersAnand K. Bhattacharya Countrywide Securities CorporationLudovic Breger Barra, Inc.Ren-Raw Chen Rutgers UniversityMoorad Choudhry Centre for Mathematical Trading and Finance,

CASS Business School, LondonStephen Dulake Morgan StanleySteven I. Dym Brocha Asset ManagementFrank J. Fabozzi Yale University Arthur Q. Frank Nomura Securities International, Inc.Roberto Fumagalli CitigroupLaurent Gauthier UBS WarburgLaurie Goodman UBS WarburgMats Gustavsson Barclays CapitalMark A. Heberle Wachovia Securities, Inc.Viktor Hjort Morgan StanleyJeffrey Ho UBS WarburgAntti Ilmanen CitigroupBrian P. Lancaster Wachovia SecuritiesYoung-Sup Lee Morgan StanleyJonathan Lieber Countrywide Securities CorporationWilliam Lloyd Barclays CapitalSivan Mahadevan Morgan StanleyBharath Manium Barclays CapitalJames 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 CompaniesPhilippe Priaulet HSBC-CCF

and University of Evry Val d’EssonneStéphane Priaulet AXA Investment ManagersDavid Schwartz Morgan Stanley

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1

Risk/Return Trade-Offs onFixed 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 pur-poses.

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 to

I

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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 DATA

For this study, we used the total rate-of-return for the components ofthe SSB (Salomon Smith Barney) Broad Investment Grade (BIG) Index.

1

Monthly 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 dataas far back as January 1992, and ran it up through March 2003, whichis 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⁄=

ra rf–

σ ra rf–( )-----------------------=


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 0.22on 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 perfor-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

EXHIBIT 1 Historical Returns

AgencyCallable

AgencyNon-

callable MBS ABS TreasuryCredit

Callable

CreditNon-

callable

Nominal Monthly Returns (1/1992–3/2003)

Average 0.552 0.654 0.588 0.610 0.606 0.653 0.652Standard 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 0.267Standard dev. 0.756 1.414 0.828 0.834 1.258 1.387 1.313Ratio 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 0.042Standard dev. 0.225 0.273 0.306 0.251 0.074 0.968 0.774Ratio 0.135 0.201 0.221 0.297 0.302 0.000 0.054


4


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

A

duration-adjusted excess return

removes both implicit leverage andthe 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 periodwe looked at. It is calculated as minus the coefficient of the regression of



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 havea 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 durationby 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 Treasuryyield (2-year rolling window).

AgencyCallable

AgencyNon-

callable MBS ABS Treasury

CreditNon-

callable

SSB Avg Duration(1/1992–3/2003)

3.1 6.0 3.1 3.0 5.3 5.5

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

(1/1992–3/2003)2.3 4.6 2.3 2.5 4.1 3.9

Measure of IndexDuration Directionalitya

14% 0% 12% 7% 4% 25%


6


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



7

EXHIBIT 3 Principal Component Analysis

EXHIBIT 4 Relationship—Rates versus Nominal Return Factor #1

Component

1 2 3 4 5 6

Nominal Returns

Agy. Callable 0.28 0.00 0.41 0.16 0.00 0.85Agy. NC 0.54 0.24 –0.20 0.60 0.46 –0.22MBS 0.30 0.00 0.75 0.00 –0.34 –0.46Credit 0.48 –0.82 –0.28 –0.11 0.00 0.00ABS 0.31 0.15 0.19 –0.73 0.56 0.00Treasury 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 –0.12Agy. NC 0.21 0.52 0.17 0.67 0.45MBS 0.23 0.65 –0.23 –0.66 0.21Credit 0.91 –0.40 0.00 0.12ABS 0.23 0.26 –0.58 0.32 –0.64 –0.18Treasury 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


8


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 rela-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.

Note:

The weight on the credit index is –0.82, indicating that the

EXHIBIT 5 Correlations—PCA Factors and Explanatory Variables

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

FactorSlope

(2–10s)10-yrTrsy

10-yrSwap Spd

5-yrCap Vol

S&P500

Nominal Return 1 4% –89% –15% 40% –9%2 15% –20% 38% 27% –50%3 42% 13% –28% –27% 0%

Duration-AdjustedReturn

1 –6% 36% –63% –43% 41%2 21% 1% –40% –11% –24%3 16% 27% 4% –15% –3%



9

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

vice versa

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

optionality factor

. Note that the coefficient on the assets classes thathave 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


10


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 Factor2 and the S&P 500 is shown in Exhibit 9; it is quite a strong one. How-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.)

CAPTURING EXCESS RETURNS

Now that we have figured out the factors which fundamentally matterin examining

returns

by fixed income asset class, we can look at using



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

For

noncallable Agencies

—the level of rates and swap spreads are 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 shapeof 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


12


EXHIBIT 10

Regression Results—Excess Returns

■

For

callable Agencies

—all of the variables we used were significant,excepting the S&P 500 (as expected).

■

MBS and ABS

look a lot like callable Agencies—except that with MBS,the slope of the curve is much less important; and in ABS, cap volatilityis not significant, as the option component of this index is small.

AgencyCallable

AgencyNon-

callable MBS ABS TreasuryCredit

Callable

CreditNon-

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

Intercept 2.3 1.7 2.8 3.6 1.2 1.1 1.6

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

% Explained 50% 43% 56% 45% 41% 58% 50%

Alpha/Residual St. Dev.

0.21 0.16 0.25 0.33 0.11 0.10 0.14

Sharpe ratio 0.22 0.19 0.24 0.27 0.18 0.19 0.20



13

EXHIBIT 11

Correlation Matrix

■

For

noncallable corporates

—the level of rates, swap spreads and theS&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.

■

For

callable corporates

—all factors except volatility are important.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 interceptis 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.

Slope10-yrTrsy

10-yrSwap Spread

5-yrCap

S&P500

Slope 100% 6% –36% 11% –20%10-yr Treasury 6% 100% –4% –48% 11%10-yr Swap Spread –36% –4% 100% 7% –12%5-yr cap 11% –48% 7% 100% –23%S&P 500 –20% 11% –12% –23% 100%

2

In regression-speak, we have a multicolinearity problem. We can solve that by or-thogonalizing the variables, but that leaves us with numbers that are more difficultto interpret. So we just acknowledge the issue and live with it.


14


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 resultslook roughly similar. MBS and ABS look better than all other assetclasses. Agencies look better than corporates or Treasuries, while corpo-rates outshine Treasuries. These results are shown in the bottom sectionof Exhibit 10. Note that this particular ranking of returns by asset classis very similar to the Sharpe ratios we obtained in the first section andrepeated for convenience in the bottom row of Exhibit 10.

CONCLUSION

In this article we looked at the risk/return trade-offs of the various fixedincome asset classes. We found consistent outperformance on the MBSand ABS series. Here’s a quick review of the evidence:

■

The Sharpe ratios and duration-adjusted excess returns both indicatedthe 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 structuredproducts or callable agencies on a Sharpe ratio basis, but better thanTreasuries.

■

Looking at the average duration-adjusted excess returns, the noncall-able credit has done better than the callable Agencies, but less well thannoncallable Agencies.

■

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

We then used a principal component analysis to examine the marketfactors that mattered most for excess returns and duration-adjustedexcess returns. We identified the usual suspects: the level of rates, theshape of the curve, volatility, swap spreads and the S&P 500. We tookthat one step further, and used regression analysis to determine howmuch excess return and residual risk there was within each asset classafter hedging out the market factors we identified. Again, ABS and MBSremain the best performing asset classes, whether measured by the alphaor the alpha divided by residual standard deviation. Looked at in thismanner, the corporate series looks approximately as appealing as thatfor Agency debentures. Treasuries again were the poorest performer.

Putting these results together, it appears that being overweighted inspread product is a strategy that historically pays on a risk/return basis


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