Advanced bond portfolio management best practices in modeling and strategies

In particular, they demonstrate how activebond portfolio managers can optimize in a relative risk-return space theallocated active risk budget through the use of a factor analysis of dev

Bond Portfolio Management

Best Practices in Modeling and Strategies

FRANK J FABOZZI LIONEL MARTELLINI PHILIPPE PRIAULET

EDITORS

John Wiley & Sons, Inc.

ffirst.frm Page iii Monday, November 21, 2005 1:15 PM

Bond Portfolio Managementffirst.frm Page i Monday, November 21, 2005 1:15 PM

THE FRANK J FABOZZI SERIES

Grant and James A Abate

by Frank J Fabozzi

Efstathia Pilarinu

Moorad Choudhry

and Frank J Fabozzi

Frank J Fabozzi

Harry M Markowitz

Pamela P Peterson

Frank J Fabozzi, Steven V Mann, and Moorad Choudhry

by Frank J Fabozzi

Moorad Choudhry

Fabozzi and Moorad Choudhry

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Bond Portfolio Management

Best Practices in Modeling and Strategies

FRANK J FABOZZI LIONEL MARTELLINI PHILIPPE PRIAULET

EDITORS

John Wiley & Sons, Inc.

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Copyright © 2006 by John Wiley & Sons, Inc All rights reserved

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Contents

Leland E Crabbe and Frank J Fabozzi

CHAPTER 3 Portfolio Strategies for Outperforming a Benchmark 43 Bülent Baygün and Robert Tzucker

PART TWO

CHAPTER 4 The Active Decisions in the Selection of Passive Management and

Chris P Dialynas and Alfred Murata

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CHAPTER 7 Understanding the Building Blocks for OAS Models 131 Philip O Obazee

CHAPTER 8

Ludovic Breger and Oren Cheyette

CHAPTER 9 Multifactor Risk Models and Their Applications 195 Lev Dynkin and Jay Hyman

PART FOUR

CHAPTER 10 Measuring Plausibility of Hypothetical Interest Rate Shocks 249 Bennett W Golub and Leo M Tilman

CHAPTER 11 Hedging Interest Rate Risk with Term Structure Factor Models 267 Lionel Martellini, Philippe Priaulet, Frank J Fabozzi, and Michael Luo

CHAPTER 12 Scenario Simulation Model for Fixed Income Portfolio Risk Management 291 Farshid Jamshidian and Yu Zhu

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Contents vii

PART FIVE

CHAPTER 13 Valuing Corporate Credit: Quantitative Approaches versus

Sivan Mahadevan, Young-Sup Lee, Viktor Hjort, David Schwartz, and Stephen Dulake

CHAPTER 14

Donald R van Deventer

CHAPTER 15

Donald R van Deventer

CHAPTER 16 Implications of Merton Models for Corporate Bond Investors 389 Wesley Phoa

Srichander Ramaswamy and Robert Scott

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Preface

onds, also referred to as fixed income instruments or debt instruments,have always been and will likely remain particularly predominant ininstitutional investors’ allocation because they are typically the asset classmost correlated with liability structures However, they have evolved fromstraight bonds characterized by simple cash flow structures to securitieswith increasingly complex cash flow structures that attract a wider range ofinvestors In order to effectively employ portfolio strategies that can controlinterest rate risk and enhance returns, investors and their managers mustunderstand the forces that drive bond markets, and the valuation and riskmanagement practices of these complex securities

In the face of a rapidly increasing complexity of instruments andstrategies, this book aims at presenting state-of-the-art of techniquesrelated to portfolio strategies and risk management in bond markets.(Note that throughout the book, we use the terms “fixed income securi-ties” and “bonds” somewhat interchangeably.) Over the past severalyears, based on the collective work of numerous experts involved inboth practitioner and academic research, dramatic changes haveoccurred in investment best practices and much progress has been made

in our understanding of the key ingredients of a modern, structured,portfolio management process In this book, these ingredients that con-tinue to shape the future of the bond portfolio management industrywill be reviewed, with a detailed account of new techniques involved inall phases of the bond portfolio management process This includes cov-erage of the design of a benchmark, the portfolio construction process,and the analysis of portfolio risk and performance

The book is composed of six parts

Part One provides general background information on fixed incomemarkets and bond portfolios strategies Chapter 1 by Frank Jones pro-vides a general classification of bond portfolio strategies, emphasizingthe fact that bond portfolio strategies, just like equity portfolio strate-gies, can be cast within a simple asset management setup, or alternativelyand arguably more fittingly, cast within a more general asset-liabilitymanagement context The chapter not only covers standard active andB

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x Preface

passive bond portfolio strategies; it also provides the reader with anintroduction to some of the new frontiers in institutional portfolio man-agement, including an overview of the core-satellite approach as well as

an introduction to portable alpha strategies

In Chapter 2, Leland Crabbe and Frank Fabozzi offer a thorough anddetailed analysis of liquidity and trading costs in bond markets Whileactive trading is meant to generate outperformance, it can also result inefficiency loss in the presence of market frictions Because it is quite oftenthat the presence of such frictions may transform a theoretically soundactive bond portfolio decision into a costly and inefficient dynamic trad-

of bond portfolio management decisions is of an importance equal to

present in Chapter 2 are useful ingredients in a bond portfolio tion process that accounts for the presence of trading costs

optimiza-A first view on the fundamental question of the design of fixedincome benchmarks in the context of active bond portfolio strategies isprovided by Bülent Baygün and Robert Tzucker in Chapter 3 Theybegin by explaining how different methods can be used in the process ofbenchmark construction, with a key distinction between rule-basedmethods meant to ensure that the benchmark truthfully represents agiven sector of the market, and optimization methods to ensure that thebenchmark is an efficient portfolio They then explore various aspects ofthe active portfolio management process, which allows managers totransform their view on various factors affecting bond returns intomeaningful and coherent portfolio decisions

Part Two is entirely devoted to the first, and perhaps most important,phase in the bond portfolio management process: the design of a strategybenchmark In Chapter 4 Chris Dialynas and Alfred Murata presents auseful reminder of the fact that existing commercial indices containimplicit allocation biases; they then explore the market conditions andfactors that result in outperformance of one versus another bond index.Overall, the chapter conveys the useful message that selecting a bench-mark accounts for most of the eventual portfolio performance

Lev Dynkin, Jay Herman, and Bruce Phelps revisit the question ofbond benchmarks from a liability-based standpoint in Chapter 5 Exist-ing commercial indices are not originally designed to serve as properbenchmarks for institutional investors; instead they are meant to repre-sent specific given sectors of the bond markets Because commercialindices are inadequate benchmarks for institutional investors, the ques-tion of the design of customized benchmarks that would properly repre-sent the risks faced by an institution in the presence of liabilityconstraints is a key challenge Dynkin, Herman, and Phelps introducefpref.frm Page x Monday, November 21, 2005 1:18 PM

Preface xi

the modern techniques involved in the design of such customized marks with an emphasis on liability-matching though the presentation

bench-of conceptual underpinnings as well as practical illustrations

Risk budgeting in a fixed income environment process is explained

in Chapter 6 by Frederick Dopfel; he carefully explains how investorsmay usefully implement an optimal allocation of resources across man-agers based on efficient spending of an active risk budget perceived asthe maximum amount of deviation between the manager’s benchmarkand the actual portfolio A key distinction is made between style risk on

and the benchmark return that is caused by different strategic factorexposures in the manager’s portfolio with respect to the benchmark

manager’s portfolio and the benchmark return that is due to securityselection and/or factor timing skills exercised by the manager

The presentation of the toolbox of the modern bond portfolio ager is the subject of Part Three In particular, this part of the book cov-ers various aspects of fixed income modeling that will provide keyingredients in the implementation of an efficient portfolio and risk man-agement process In this respect, the chapters in this part of the book setforth critical analytical concepts and risk concepts that will be used inthe last three parts of the book Chapters in those parts provide a moredetailed focus on some of the risk factors introduced in there In the firstchapter in Part Three, Chapter 7, Philip Obazee presents a detailedintroduction to option-adjusted spread (OAS) analysis, a useful analyti-cal relative value concept employed in the context of security selectionstrategies, particularly in analysis of securities backed by a pool of resi-dential mortgage loans (i.e., residential mortgage-backed securities) Chapter 8 offers a thorough account of the design of factor modelsused for risk analysis of bond portfolios, with an emphasis not only onindividual risk components but also on how they relate to each other.The authors, Ludovic Breger and Oren Cheyette, provide as an illustra-tion an application in the context of risk analysis of several well-knownbond indices

man-In Chapter 9, Lev Dynkin and Jay Hyman follow up on this tion by exploring how such factor models can be used in the context ofbond portfolio strategies In particular, they demonstrate how activebond portfolio managers can optimize in a relative risk-return space theallocated active risk budget through the use of a factor analysis of devi-ations between a portfolio and a benchmark portfolio

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xii Preface

Part Four focuses on interest rate risk management, arguably thedominant risk factor in any bond portfolio The main object of attentionfor all bond portfolio managers is the time-varying shape of the termstructure of interest rates In Chapter 10, Bennett Golub and Leo Tilmanprovide an insightful discussion of how to measure the plausibility, interms of comparison with historical data, of various scenarios about thefuture evolution of the term structure They use principal componentanalysis of past changes in the term structure’s shape (level, slope, andcurvature) as a key ingredient for the modeling of future changes

In Chapter 11, the coeditors along with Michael Luo build on such

a factor analysis of the time-varying shape of the term structure toexplain how bond portfolio managers can improve upon duration-basedhedging techniques by taking into account scenarios that are not limited

to changes in interest rate level, but instead account for general changes

in the whole shape of the term structure of interest rates Farshid

analysis of interest rate risk and present an introduction to modelingtechniques used in the context of stochastic simulation for bond portfo-lios, with an application to Value-at-Risk and stress-testing analysis The focus in Part Five is on the question of credit risk management,another dominant risk factor for the typical bond portfolio managerswho invests in spread products In Chapter 13, Sivan Mahadevan,Young-Sup Lee, Viktor Hjort, David Schwartz, and Stephen Dulake pro-vide a first look at the question of credit risk management emphasizingthe similarities and differences between quantitative approaches tocredit risk analysis and more traditional fundamental analysis By com-paring and contrasting fundamental credit analysis with various quanti-tative approaches, they usefully prepare the ground for subsequentchapters dedicated to a detailed analysis of various credit risk models

In Chapter 14, Donald van Deventer begins with a thorough sion of both structural models and reduced form models, emphasizingthe benefits of the latter, more recent, approach over Merton-basedcredit risk models In Chapter 15, he explains how these models can beused for the pricing and hedging of credit derivatives that have become

discus-a key component of the fixed income mdiscus-arket

Wesley Phoa revisits structural models in Chapter 16 These modelsare the most adapted tools for an analysis of the relationship betweenprices of stock and bonds issued by the same company In Chapter 17,David Soronow concludes this analysis of credit risk with a focus on theuse of credit risk models in the context of bond selection strategies Heprovides convincing evidence of the ability for a portfolio manager toadd value in a risk-adjusted sense on the basis of equity-implied riskmeasures, such as those derived from structural models

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Preface xiii

After these analyses of interest rate and credit risk analysis in thecontext of bond portfolio management, the last part of this book, PartSix, focuses on additional risk factors involved in the management of aninternational bond portfolio Lee Thomas in Chapter 18 makes a strongcase for global bond portfolio management, with a detailed analysis ofvarious bond markets worldwide, and a discussion of the benefits thatcan be gained from strategic as well as tactical allocation decisions tothese markets

The specific challenges involved in the management of a rency portfolio and the related impacts in terms of benchmark designand portfolio construction are covered in Chapter 19 The chapter,coauthored by Srichander Ramaswamy and Robert Scott, also providesdetailed discussion of the generation of active bets based on fundamen-tal macro and technical analysis, as well as a careful presentation of theassociated portfolio construction and risk analysis process In Chapter

multicur-20, Maria Mednikov Loucks, John A Penicook, and Uwe Schillhornconclude the book with a specific focus on emerging market debt Onceagain, the reader is provided with a detailed analysis of the various ele-ments of a modern bond portfolio process applied to emerging marketdebt investing, including all aspects related to the design of a bench-mark, the portfolio construction process, as well as the analysis of riskand performance

Overall, this book represents a collection of the combined expertise

of more than 30 experienced participants in the bond market, guidingthe reader through the state-of-the-art techniques used in the analysis ofbonds and bond portfolio management It is our hope, and indeed ourbelief, that this book will prove to be a useful resource tool for anyonewith an interest in the bond portfolio management industry

The views, thoughts and opinions expressed in this book should not

in any way be attributed to Philippe Priaulet as a representative, officer,

or employee of Natexis Banques Populaires

Frank FabozziLionel Martellini Philippe Priauletfpref.frm Page xiii Monday, November 21, 2005 1:18 PM

fpref.frm Page xiv Monday, November 21, 2005 1:18 PM

About the Editors

the School of Management at Yale University Prior to joining the Yalefaculty, he was a Visiting Professor of Finance in the Sloan School at MIT.Professor Fabozzi is a Fellow of the International Center for Finance at

He earned a doctorate in economics from the City University of NewYork in 1972 In 1994 he received an honorary doctorate of Humane Let-ters from Nova Southeastern University and in 2002 was inducted intothe Fixed Income Analysts Society’s Hall of Fame He earned the designa-tion of Chartered Financial Analyst and Certified Public Accountant

Business and the Scientific Director of Edhec Risk and Asset ManagementResearch Center A former member of the faculty at the Marshall School ofBusiness, University of Southern California, Dr Martellini is a member of

asset management and derivatives valuation which has been published inleading academic and practitioner journals and has coauthored books ontopics related to alternative investment strategies and fixed income securi-ties He holds master’s degrees in Business Administration, Economics, Sta-tistics and Mathematics, as well as a Ph.D in Finance from the HaasSchool of Business, University of California at Berkeley

Popu-laires Related to fixed-income asset management and derivatives pricingand hedging, his research has been published in leading academic and prac-titioner journals He is the coauthor of books on fixed-income securitiesand both an associate professor in the Department of Mathematics of theUniversity of Evry Val d’Essonne and a lecturer at ENSAE Formerly, hewas a derivatives strategist at HSBC, and the head of fixed-income research

in the Research and Innovation Department of HSBC-CCF He holds a ter’s degrees in business administration and mathematics as well as a Ph.D

mas-in fmas-inancial economics from the University Paris IX Dauphmas-ine

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Contributing Authors

Stephen Dulake

Twente

Securities Exchange

David Schwartz

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xviii Contributing Authors

and Fore Research & Management, LPflast.frm Page xviii Monday, November 21, 2005 1:19 PM

Part1 Page 2 Monday, October 3, 2005 1:51 PM

San Jose State University

andVice Chairman, Board of DirectorsInternational Securities Exchange

his chapter provides a general overview of fixed income portfoliomanagement More specifically, investment strategies and portfolioperformance analysis are described A broad framework is providedrather than a deep or exhaustive treatment of these two aspects of fixedincome portfolio management

A discussion of the risks associated with investing in fixed incomesecurities is not provided in this discussion They are, however, provided

in other chapters of this book Exhibit 1.1, nonetheless, provides a mary of the risk factors that affect portfolio performance

sum-FIXED INCOME INVESTMENT STRATEGIES

Fixed income investment strategies can be divided into three approaches.The first considers fixed income investment strategies that are basicallythe same as stock investment strategies This is a pure asset management

T

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4 BACKGROUND

Risk Factors

Risk Factor Measurement

Market Changes that Affect Risk Factors

Change in Yield Curve Yield Curve

Risk

Convexity/Distribution of Key Rate Durations (Bullet, Barbell, Lad- der, et al.)

Change in Slope and Shape of Yield Curve

Exposure to Market Volatility

Convexity

• Negatively convex assets (e.g., callables)/portfolios are adversely affected by volatility

• Positively convex assets (e.g., putables)/portfolios are benefited

Allo-Percent allocation to each sector, microsector, and security and the option-adjust spread (OAS) of each

macro-Change in option-adjusted spreads (OAS) of macrosectors, microsec- tors, and individual securities Credit Risk Average credit rating of portfolio

and its sectors

Changes in credit spreads (e.g., spread between Treasuries versus AAA corporates; or spread between AAA corporates versus BBB corporates); also specific company rating changes Liquidity

Risk

Typically measured by the bid/ask price spread—that is, the differ- ence between the price at which a security can be bought and sold

at a point in time The liquidity of a security refers to both it marketability (the time it takes to sell a security at its mar- ket price, e.g., a registered corpo- rate bond takes less time to sell than a private placement) and the stability of the market price

Different securities have inherently different liquidity (e.g., Treasuries are more liquid than corporates) The liquidity of all securities, par- ticularly riskier securities, decreases during periods of mar- ket turmoil.

Exchange Rate Risk

Changes in the exchange rate between the U.S dollar and the currency in which the security is denominated (e.g., yen or euro)

Volatility in the exchange rate increases the risk of the security For a U.S investor, a strengthen- ing of the other currency (weak- ening of the U.S dollar) will be beneficial to a U.S investor (neg- ative to a U.S investor) who holds a security denominated in the other currency

1-Jones-Fixed Income Investment Page 4 Monday, October 3, 2005 2:01 PM

Overview of Fixed Income Portfolio Management 5

considers features unique to bonds—that is, fixed coupons and a definedtime to maturity and maturity value, which relates these cash flows tomany of the liabilities or products of an institution We refer to this

first two types It represents a surplus optimization strategy that, as cussed, includes both beta and alpha management We refer to this asthe unified approach

dis-Total Return Approach

TRR are the income component and the capital gains component.Despite the different risks associated with these two components of theTRR, they are treated fungibly in TRA

TRR strategies for bonds, as well as stocks, are based on their ownrisk factors In the TRR approach, the TRR for the fixed income portfo-lio is compared with the TRR of a benchmark selected as the basis forevaluating the portfolio (discussed in more detail below) The risk fac-tors of the benchmark should be similar to those of the bond portfolio.Overall, however, two different portfolios, or a portfolio and abenchmark that have different risk factors, will experience differentTRRs due to identical market changes A portfolio manager should cal-

dif-ferential response to the relevant market change or, if this response isunacceptable to the portfolio manager, to alter the exposure to the riskfactor by portfolio actions

Thus, changes in market behavior may affect the performance of theportfolio and the benchmark differently due to their differences in riskfactors The specification measurement of a portfolio’s risk factors andthe benchmark’s risk factors are critical in being able to compare theperformance of the portfolio and benchmark due to market changes.This is the reason the risk factors of a bond portfolio and its benchmarkshould be very similar A methodology for doing so is described inChapter 9

Having selected a benchmark, being aware of the risk factors of theportfolio, and having calculated the risk factors for the benchmark, aportfolio manager must decide whether he or she wants the portfolio to

Litterman of Goldman Sachs Asset Management.

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6 BACKGROUND

replicate the risk factors of the benchmarks or to deviate from them

That is, a portfolio manager could be passive with respect to somerisk factors and active with respect to others—there is a large number ofcombinations given the various risk factors Passive strategies require noforecast of future market changes—both the portfolio and benchmarkrespond identically to market changes Active strategies are based on aforecast, because the portfolio and benchmark will respond differently

to market changes In an active strategy, the portfolio manager mustdecide in which direction and by how much the risk factor value of theportfolio will deviate from the risk factor value of the benchmark on thebasis of expected market changes

Consequently, given multiple risk factors, there is a pure passivestrategy, and there are several hybrid strategies that are passive on somerisk factors and active on others

Exhibit 1.2 summarizes the passive strategy and some of the mon active strategies The active strategies relate to various fixedincome risk factors An active fixed income manager could be active rel-ative to any set of these risk factors, or all of them This chapter doesnot provide a thorough discussion of any one of these strategies How-ever, some stylized comments on some of the common strategies are pro-vided

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Overview of Fixed Income Portfolio Management 7

Trades

Replicate duration of the benchmark, but vary the convexity and yield curve exposure by varying the com- position of key rate durations

Bullets outperform during yield curve steepenings; barbells out- perform during yield curve flatten- ings

microsec-• Macro—overall sectors ies; agencies; corporates; MBS;

(Treasur-ABS; Municipals)

• Microcomponents of a macrosector (e.g., utilities versus industrials in corporate sector)

• weight individual securities in a microsector (e.g., Florida Power and Light versus Niagara Mohawk

Securities—overweight/under-in corporate utility sector)

Deviations based on adjusted spread (OAS) of sectors, subsectors and securities relative

option-to hisoption-torical averages and mental projection; can use break- even spreads (based on OAS) as a basis for deviations

funda-On overweights, spread tightening produces gain; spread widening produces losses; and vice versa

Credit Risk

Allocations

Deviate from average credit rating of macrosector or microsectors and composites thereof

Credit spreads typically widen when economic growth is slow or negative

Credit spread widening benefits higher credit rating, and vice versa Can use spread duration as basis for deviations

Trading Short-term changes in specific

securi-ties on the basis of short-term price discrepancies

Often short-term technicals, ing short-term supply/demand factors, cause temporary price dis- crepancies

includ-1-Jones-Fixed Income Investment Page 7 Monday, October 3, 2005 2:01 PM

8 BACKGROUND

Market Timing

Few institutions practice market timing by altering the duration of theirportfolio based on their view of yield changes Few feel confident thatthey can reliably forecast interest rates A common view is that markettiming adds much more to portfolio risk than to portfolio return, andthat often the incremental portfolio return is negative The duration oftheir portfolio may, however, inadvertently change due to yield changesthrough the effect of yield changes on the duration of callable or pre-payable fixed income security, although continual monitoring andadjustments can mitigate this effect

Credit Risk Allocations

Institutions commonly alter the average credit risk of their corporate bondportfolio based on their view of the credit yield curve (i.e., high quality/lowquality yield spreads widening or narrowing) For example, if they believethe economy will weaken, they will upgrade the quality of their portfolio.Sector Rotation

Institutions may rotate sectors, for example, from financials to als, on the basis of their view of the current valuation of these sectorsand their views of the prospective economic strength of these sectors.Security/Bond Selection

industri-Most active institutional investors maintain internal credit or fundamentalbond research staffs that do credit analysis on individual bonds to assesstheir overevaluation or underevaluation A portfolio manager would havebenefited greatly if they had avoided Worldcom before the bankruptcyduring June 2002 (at the time Worldcom had the largest weight in the Leh-man Aggregate) or General Motors or Ford before downgraded to junkbond status in June 2005 Security/bond selection can also be based onrich/cheap strategies (including long-short strategies) in Treasury bonds,mortgage-backed securities or other fixed income sectors

Core Satellite Approach

As indicated above, the active/passive decision is not binary A passiveapproach means that all risk factors are replicated However, an activeapproach has several subsets by being active in any combination of riskfactors There is another way in which the active/passive approach isnot binary

An overall fixed income portfolio may be composed of several cific fixed income asset classes The overall portfolio manager may1-Jones-Fixed Income Investment Page 8 Monday, October 3, 2005 2:01 PM

spe-Overview of Fixed Income Portfolio Management 9

choose to be passive in some asset classes, which are deemed to be veryefficient and have little potential for generating alpha Other assetclasses, perhaps because they are more specialized, may be deemed to beless efficient and have more potential for generating alpha For example,the manager may choose to use a “core” of U.S investment-grade bondspassively managed via a Lehman Aggregate Index and “satellites” ofactively managed bonds such as U.S high-yield bonds and emergingmarket debt Such core satellite approaches have become common withinstitutional investors

These and other fixed income investment strategies are commonlyused by institutional investors Note, however, that the TRR approachrelates to an external benchmark, not to the institution’s internal liabili-ties or products That is why the TRR approach is very similar forbonds and stocks

Now consider evaluating an institution’s investment portfolio tive to its own liabilities or products Because the cash flows of these lia-bilities or products are more bond-like than stock-like, bond investmentstrategies assume a different role in this context

rela-Liability Funding Approach

The benchmark for the TRR approach is an external fixed incomereturn average Now consider a benchmark based on an institution’sinternal liabilities or products Examples of this would be a defined ben-efit plan’s retirement benefit payments; a life insurance company’s actu-arially determined death benefits; or a commercial bank’s payments on abook of fixed-rate certificate of deposits (CDs) In each case, the pay-ments of the liability could be modeled as a stream of cash outflows.Such a stream of fixed outflows could be funded by bonds which pro-vide known streams of cash outflows, not stocks that have unknownstreams of cash flows Consider the investment strategies for bonds forfunding such liabilities

The first such strategy would be to develop a fixed income portfoliowhose duration is the same as that of the liability’s cash flows This is

matches of the liability due to market risks only for parallel shifts in theyield curve If the yield curve steepens (flattens), however, the immu-nized portfolio underperforms (outperforms) the liability’s cash flows

A more precise method of matching these liability cash flows is todevelop an asset portfolio which has the same cash flows as the liability

more constraints than an immunized portfolio and, as a result, has alower return Its effectiveness, however, is not affected by changes in the1-Jones-Fixed Income Investment Page 9 Monday, October 3, 2005 2:01 PM

10 BACKGROUND

slope of the yield curve But if non-Treasury securities are included inthe portfolio, this strategy as well as the immunization strategy, areexposed to credit risk

planning Assume an investor with $900,000 available for retirement is

60 years old, plans to retire at age 65, and wants to have funds for 10years The investor could buy $100,000 (face or maturity value) each ofzero-coupon bonds maturing in 5, 6, 7…, and 14 years Thus, indepen-dent of changes in yields and the yield curve during the next 10 years, theinvestor will have $100,000 of funds each year To continue this approachfor after age 75, the investor could buy a new 10-year bond after eachbond matures These subsequent investments would, of course, depend onthe yields at that time This sequence of bonds of different maturities,which mature serially over time, is a laddered portfolio (Some analystsliken a laddered portfolio to a stock strategy called dollar-cost averaging.)

(ignor-ing the optionality of the GIC) would depend on the difference betweenthe yield on the asset invested against these products (such as 6-monthcommercial paper or 6-month fixed-rate notes) and the yield paid on theproducts by the institution Spread management is managing the profit-ability of a book of such products based on the assets invested in tofund these products In the short term, profitability will be higher if lowquality assets are used; but over the longer run, there may be defaultswhich reduce the profitability

Overall, while both bonds and stocks can be used for the TRR egy, only bonds are appropriate for many liability funding strategiesbecause of their fixed cash flows, both coupon and maturity value.Unified Approach2

strat-A recent way of considering risk and corresponding return is by gregating risk and the corresponding return into three components Lit-terman calls this approach “active alpha investing.”

to investors, Goldman Sachs Asset Management (three-part series).

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Overview of Fixed Income Portfolio Management 11

The first type is the risk and desired return due to the institution’s orindividual’s liabilities A portfolio is designed to match the liabilities ofthe institution whose return matches or exceeds the cost of the liabili-ties Typically, liabilities are bond-like and so the matching portfolio istypically a fixed income portfolio Examples of this are portfoliosmatching defined benefit pensions, whole life insurance policies, andcommercial bank floating-rate loans

The second risk/return type is a portfolio that provides market risk:either stock market risk (measured by beta) or bond market risk (mea-sured by duration) The return to this portfolio is the stock marketreturn (corresponding to the beta achieved) or the bond market return

could also be, rather than a pure beta or duration portfolio, a tion of a beta portfolio for stocks and a duration portfolio for bonds;that is, an asset allocation of market risk In practice, the beta portfolio

combina-is typically achieved by an S&P 500 product (futures, swaps, etc.) for abeta of one, and the duration portfolio by a Lehman Aggregate product(futures, swaps, etc.) for a duration equal to the duration of the LehmanAggregate These betas or duration could also be altered from these baselevels by additional (long or short) derivatives

sophisticated risk-factor models have been used to adjust for other types

of risk beyond market risk in determining alpha (e.g., two-, three-, andfour-factor alphas) For now, we will assume that the beta or durationreturn on the one hand and alpha return on the other hand go together ineither a stock portfolio or a bond portfolio singularly That is, by selecting

a passive (or indexed) stock where the market return for stocks is the S&P

500 return and for bonds is the Lehman Aggregate return, one obtainseither the stock market beta return or bond return duration and no alpha.Selecting an active stock portfolio, one has both the stock market beta andthe prospects for an alpha, either positive or negative Similarly for activefixed income funds and bond market duration and alpha returns

So far, we have considered the market return (associated with beta

or duration) as being part of the same strategy as the alpha return.There are two exceptions to this assumption The first is market neutralfunds Market neutral funds are usually hedge funds which achieve mar-ket neutrality by taking short positions in the stock and/or bond mar-

3

For a stock portfolio: Alpha = Portfolio return – Beta (Market return – Risk-free return) For a bond portfolio: Alpha = Portfolio return – Duration (Market return – Risk-free return).

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12 BACKGROUND

kets Thus, they have no market return and their entire return is analpha return By being market neutral, they have separated marketreturn (beta or duration) from alpha return

The second exception is an extension of market-neutral hedge fundsand is discussed in the next section

Portable Alpha

We have assumed that for stock and bond portfolios, the market return(due to beta or duration) is part of the same strategy as the alpha return.But market neutral hedge funds separate the market return from thealpha return by taking short and long positions in the markets via deriv-atives However, portfolio managers could also separate the marketreturn from the alpha return by taking short positions in the market viaderivatives

To understand how, consider the following example Assume thatthe chief investment officer (CIO) of a firm faces liabilities that require abond portfolio to fund liabilities Further assume that the CIO considersthe firm’s bond portfolio managers to be not very talented In contrast,the firm has stock managers who the CIO considers to be very talented.What should the CIO do? The CIO should index the firm’s bond portfo-lio, thereby assuring that the untalented bond managers do not generatenegative alpha, while providing the desired overall bond market returns

By using long positions in bond derivatives (e.g., via futures, swaps, orexchange-traded funds), the untalented bond managers could be elimi-nated The CIO could then permit the firm’s talented stock managers torun an active stock portfolio, ideally generating a positive alpha Inaddition, at the CIO level, the CIO could eliminate the undesired stockmarket risk by shorting the stock market (e.g., via S&P 500 futures,swaps, or exchange-traded funds) The CIO could then “port” the stockportfolio alpha to the passive bond portfolio and achieve excess returns

on the firm’s passive bond portfolio The final overall portfolio wouldconsist of a long bond position using bond derivatives, an active stockportfolio, and a short S&P 500 position using derivatives This is the

“search for alpha.”

The opposite could also be the case for the CIO with an equity date (for example, the manager of a P&C insurance company portfolio

man-or an equity indexed annuity pman-ortfolio): an untalented stock managersand a talented bond managers In this case, the CIO could index thefirm’s stock portfolio, let the bond managers run an active portfolio,eliminate the stock managers, hedge the market risk of the bond portfo-1-Jones-Fixed Income Investment Page 12 Monday, October 3, 2005 2:01 PM

Overview of Fixed Income Portfolio Management 13

lio at the CIO level with short bond derivatives and “port” the bondportfolio alpha to an indexed stock portfolio

The portable alpha concept is a natural extension of advances indisaggregating overall returns into liability matching returns, marketreturns, and alpha returns and has provided considerable additionalflexibility to asset managers Specifically, a CIO can search for alpha inplaces that are not associated with beta The beta portfolio is typicallydetermined by the type of institution (e.g., pension fund, insurance com-pany or endowment) However, alpha—in a market-neutral portfolio—can be obtained anywhere such as in stocks, bonds, hedge funds, realestate, and the like

The total return approach is typical for portfolios with no clear bility such as mutual funds Bonds are often used in the total returnapproach for a pure active portfolios, a pure passive portfolio or a com-bination as in the core satellite approach The liability fundingapproach is typical for portfolios which have specific liabilities such aspension funds or, to a lesser extent, insurance companies Bonds are typ-ically used in the liability funding approach because some institutionshave liabilities which are similar to bonds These approaches are thetwo traditional portfolio investment approaches

Litter-man) begins with, in effect, the liability funding approach, using thisapproach to fund an institution’s liabilities Having funded the liabili-ties, the unified approach disaggregates the market (or beta) risk and thealpha risk using derivatives (long and short) to achieve an excess returnover the liability funding return The beta and alpha returns are essen-tially surplus optimization strategies The unified approach, as with theliability funding approach, applies to institutions whose liabilities areknown In addition to pension funds and insurance companies, it couldapply to foundations and endowments

The role of bonds in the unified approach is varied Certainly, bondsare used to fund liabilities In addition, passive bond portfolios could be

alpha portfolio, for example fixed income market-neutral hedge funds,high-yield bonds, or emerging market bonds

Overall the total return approach and the liability funding approachare the traditional approaches The unified approach (or active alphaapproach) is more recent, more flexible, and requires liquid derivativesinstruments It may also provide more latitude and more responsibility

to the CIO and portfolio mangers Managing market risk should be easyand cheap Managing alpha risk may be difficult and more expensive.1-Jones-Fixed Income Investment Page 13 Monday, October 3, 2005 2:01 PM

14 BACKGROUND

EX POST PORTFOLIO EVALUATION ANALYSIS

Assume that a portfolio has been developed corresponding to a specifiedinvestment strategy Time has passed and the portfolio has performed.The portfolio and its performance must now be evaluated The analysis

There are three parts of the portfolio evaluation: selection of a mark, evaluation of returns, and evaluation of risks as measured interms of tracking error

bench-Selection of a Benchmark

Before one can evaluate how a portfolio did, one has to know what itwas supposed to do Suppose a portfolio manager says, “My portfolioreturned 6.5% in 2004 Wasn’t that good?” In 2004 a 6.5% return wasexcellent for a short-term bond fund but terrible for a high-yield bondfund To answer the question posed by the portfolio manager, one needs

a benchmark for comparison That is, one needs to know “what” theportfolio manager was trying to do

Answering the “what” question involves selecting a benchmark,that is a portfolio—actual or conceptual—whose return can be used as abasis of comparison In the above example, it could be a short-term,investment-grade bond portfolio, a high-yield bond portfolio, or abroad taxable, investment-grade bond portfolio

There are three fundamentally different kinds of benchmarks Thefirst kind is a market index or market portfolio In this case a sponsor of

an index—such as Standard and Poor’s, Lehman Brothers, or DowJones—specifies an initial portfolio and revises it according to somerules or practices and periodically or continually calculates the marketcapitalization-weighted (usually) prices and returns on the portfolio.This is a simulated portfolio, not an actual portfolio and, thus, has noexpenses or transaction costs associated with it The Lehman BrothersAggregate Index, High Yield Index, Municipal Index, and IntermediateTerm Index are examples of bond market indexes

The second kind of benchmark is managed portfolios that are actualportfolios whose actual returns—usually after expenses and transactioncosts—are collected and averaged for similar types of actual portfolios.For example, Morningstar and Lipper categorize fixed income mutualfunds into cells, collect return data on these funds, and average thereturns for funds in a cell on a market capitalization-weighted basis andthen report these averages Examples of such managed portfolio indexesare Morningstar’s short-term, high-quality bond index; intermediate-1-Jones-Fixed Income Investment Page 14 Monday, October 3, 2005 2:01 PM

Overview of Fixed Income Portfolio Management 15

term, low-quality bond index; and intermediate-term, ity bond index—all averages of mutual funds with these characteristics.Instead of using asset portfolios as a benchmark, the liabilities orproducts of an institution may be used as the basis of the benchmark.This is the third kind of benchmark The liabilities are specified, thereturns on the liabilities are determined, and the marked capitalization-weighted return on the liabilities is used as a benchmark With the poorperformance of defined benefit pension plan since 2000, plan sponsorsare beginning to use the calculated return on their pension liabilities as abenchmark or basis of comparison for their investment portfolios used

intermediate-qual-to fund these pension benefits

Finally, consider a fairly recent type of investment strategy that has

beta of zero That is, it responds to neither the overall bond market norstock market It achieves these characteristics, typically by taking shortpositions As a frame of reference, a short-term interest rate—such as

benchmark for absolute return strategies

Evaluation of Return: Attribution Analysis

benchmark has been specified, one of the three types of benchmarksspecified in the previous section—and consider the portfolio’s return rel-ative to its benchmark The return on the portfolio minus the return on

portfolio return has been adjusted for risk because the benchmarkshould have approximately the same risk as the portfolio if the bench-mark has been selected correctly

If the excess return on the portfolio is positive, the portfolio has

outperfor-mance and underperforoutperfor-mance is used, not only to evaluate the portfolio,

in general, but to compensate portfolio managers in particular

The next question is how the outperformance or underperformanceoccurred Was it due to market timing, that is taking a market bet,either bull or bear? Was it due to sector selection? Was it due to securityselection?

Does it make any difference what the reason for outperformance orunderperformance was? Yes it does If the outperformance was due tomarket timing, the positive performance may not continue Many—1-Jones-Fixed Income Investment Page 15 Monday, October 3, 2005 2:01 PM

16 BACKGROUND

including this author—believe that returns due to market timing are lesspersistent (that is, more of a gamble) than other types of returns Out-performance due to individual bond selection may be preferable sincesuch positive returns may be more persistent In this case, with respect

to compensation, the CIO may want to give the firm’s fundamentalbond analysts responsible for the outperformance an additional bonus.Another reason that the source of the return makes a difference isthat many portfolio managers have limitations on different sources ofreturn (e.g., credit risk, duration mismatches, etc.) that are specified intheir investment guidelines or prospectuses

If knowledge of the causes of the outperformance or mance of a portfolio is important, how are these causes determined? To

underperfor-be specific, one tries to “attribute” the excess return (positive or tive) to specific risk factors, or deviations from the benchmark This is

excess return of a portfolio was 1.5%, the attribution analysis mightconclude that 0.6% was due to market timing, 0.2% to sector selection,and 0.7% to security selection In practice, one might also be interested

in which particular sector and security overweights and underweightswere responsible for these returns A more detailed attribution analysiscould answer these questions as well

Risk: Tracking Error

In the previous section, in calculating excess return relative to a mark, we implicitly assumed that the managed portfolio and the bench-mark had the same total risk That is, it is assumed that theoutperformance or underperformance was due to manager skill in devi-ating from various risk factors, not to differences in overall risk Butthis is not usually the case The total risk of the portfolio is typically dif-

Excess Return

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Overview of Fixed Income Portfolio Management 17

ferent from that of the benchmark How different are the risks? What is

the metric for measuring this difference?

To answer these questions, consider a simple example While there

have been various measures of risk proposed in the literature, risk is

20% Is the incremental risk of the managed portfolio the excess of the

calcula-tion ignores the fundamental result of Markowitz diversificacalcula-tion—it

ignores the effect of diversification In this case, taking the differences of

the risk ignores the relationship of the return pattern of the portfolio

and the return pattern of the benchmark Are these return patterns

per-fectly correlated, in which case the benchmark is a good one? Or are the

return patterns very imperfectly correlated, in which case the

bench-mark is not a good one?

So what is the best way to determine the risk of a portfolio’s return

R(B)] This construct, that is, the standard deviation of the difference in

the portfolio return and the benchmark return, is called tracking error

(TE) of the portfolio’s return relative to the benchmark’s return.

A second way to determine the tracking error is to use the statistical

equation for the risk a portfolio of two or more securities that requires

the correlation coefficient of the returns on these securities In this

con-text, the portfolio would consist of a 100% long position (+100%) in

the managed portfolio and a 100% short position (–100%) in the

benchmark Examples of this method are considered in the appendix to

this chapter These two approaches are perfectly statistically equivalent

Both start with the returns of the portfolio and benchmark over time

The first approach—the approach usually used in practice—calculates

the differences in return over time and then calculates the mean and SD

of these differences The second approach calculates the mean of each

return, the correlation between these returns, and then the standard

deviation of the difference from the standard statistical equation used in

the appendix at the end of this chapter

Overall, the standard deviation of the difference in returns is called

the tracking error of the return of a managed portfolio relative to its

benchmark Thus, the standard deviation of the difference in the returns

of the managed portfolio and the benchmark, not the difference in the

1-Jones-Fixed Income Investment Page 17 Monday, October 3, 2005 2:01 PM

18 BACKGROUND

standard deviations of the returns on the managed portfolio and the

benchmarks is a metric for the relative risk of a managed portfolio tive to its benchmark

rela-Exhibit 1.4 provides general guidelines for the magnitude of thetracking error and the degree of active risk of a portfolio relative to its

benchmarks Thus, a tracking error (standard deviation) of 0%

indi-cates an indexed portfolio; a tracking error of 2% indiindi-cates a portfolio,which has little tracking risk relative to its benchmark; and a trackingerror of 6% indicates a significant amount of tracking risk Returning to

a previous concept, the greater the tracking error, the greater the tial for alpha (either positive or negative) Thus, a portfolio with atracking error of 0% has no potential for alpha generation

poten-CONCLUSION

The fundamentals of fixed income investment strategies include many ofthe same elements of stock investment strategies, but also some uniquefeatures These unique features are due to the different cash flows forbonds, specifically their defined coupons and maturity values Therehave been advances in the concepts and practices for both fixed incomeand stock investment strategies, and these advances have tended tounify the treatment of fixed income and stock investment strategies.Nevertheless, there are unique aspects of fixed income investment strat-egies due to their exact coupon and maturity cash flows Fixed incomeinvestment strategies are myriad and have many applications

Tracking Error (TE) for Degree of Activity of an Active Portfolio

Note: TE measured in terms of the number of standard deviations.

TE Strategy

Overview of Fixed Income Portfolio Management 19

APPENDIX

Equation for Alternative Method for Computing Tracking

Error

The tracking error of a portfolio (P) relative to a benchmark (B) can be

calculated from the standard equation for the risk of a combination of

variables This equation for two asset types, P and B, is

where W(.) is the weight of the asset type in the portfolio, SD(.) is the standard deviation of the asset type, and CORR is the correlation coef-

ficient between the two asset types

In this application of a managed portfolio, P, and a benchmark, B,

W(P) = +1 and W(B) = –1 Also, SD (P, B) is the tracking error (TE) of P

relative to B.

The following table shows the tracking error of P relative to B for two different combinations of risks of P and B (20%/18% and 18%/18%) and three different correlation coefficients (CORRs) between P and B:

Note that for a perfect benchmark (CORR = +1), the tracking error

is equal to the difference between SD(P) and SD(B) (0% in A and 2% in B) But for CORR(P, B) less than +1, the tracking error becomes greater than this difference as CORR (P, B) decreases.