The theory and practice of investment management

4 FOUNDATIONS OF INVESTMENT MANAGEMENTStep 3: Selecting an investment strategy Step 4: Selecting the specific assets Step 5: Measuring and evaluating investment performance STEP 1: SETT

The Theory and Practice of

The Theory and Practice of

investment management

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 Handbook of Financial Instruments edited by Frank J Fabozzi

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

Moorad Choudhry

The Theory and Practice of

investment management

FRANK J FABOZZI HARRY M MARKOWITZ

EDITORS

John Wiley & Sons, Inc.

Copyright © 2002 by Frank J Fabozzi All rights reserved.

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

Published 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: permcoordinator@wiley.com.

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 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,

con-or other damages.

For general information on our other products and services, or technical support, please tact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002.

con-Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books.

ISBN: 0-471-22899-0

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

Frank J Fabozzi, Francis Gupta, and Harry M Markowitz

Frank J Fabozzi and James L Grant

Traditional Fundamental Analysis III:

Earnings Analysis, Cash Analysis, Dividends, and Dividend Discount Models 275 Pamela P Peterson and Frank J Fabozzi

CHAPTER 12

James A Abate and James L Grant

CHAPTER 13

Frank J Fabozzi, Frank J Jones, and Raman Vardharaj

CHAPTER 14

Bruce M.Collins and Frank J Fabozzi

CHAPTER 15

Equity Derivatives II: Portfolio Management Applications 409 Bruce M.Collins and Frank J Fabozzi

Frank J Fabozzi and Steven V Mann

CHAPTER 19

Frank J Fabozzi and Steven V Mann

CHAPTER 20

Frank J Fabozzi and Steven V Mann

CHAPTER 21

Frank J Fabozzi and Steven V Mann

CHAPTER 22

Frank J Fabozzi

CHAPTER 23

Lev Dynkin, Jay Hyman, and Vadim Konstantinovsky

CHAPTER 24

Multi-Factor Fixed-Income Risk Models and Their Applications 665 Lev Dynkin and Jay Hyman

about the editors

Frank J Fabozzi is editor of the Journal of Portfolio Management and an

adjunct professor of finance at Yale University’s School of Management

He is a Chartered Financial Analyst and a Certified Public Accountant

Dr Fabozzi is on the board of directors of the Guardian Life family offunds and the BlackRock complex of funds He earned a doctorate ineconomics from the City University of New York in 1972 and in 1994received an honorary doctorate of Humane Letters from Nova South-eastern University Dr Fabozzi is a Fellow of the International Center forFinance at Yale University He is an Advisory Analyst for Global AssetManagement (GAM) with responsibilities as Consulting Director forportfolio construction, risk control, and evaluation

Harry M Markowitz has applied computer and mathematical niques to various practical decision making areas In finance, in an arti-cle in 1952 and a book in 1959 he presented what is now referred to asMPT, “modern portfolio theory.” This has become a standard topic incollege courses and texts on investments, and is widely used by institu-tional investors for tactical asset allocation, risk control, and attributionanalysis In other areas, Dr Markowitz developed “sparse matrix” tech-niques for solving very large mathematical optimization problems Thesetechniques are now standard in production software for optimizationprograms He also designed and supervised the development of the SIM-SCRIPT programming language SIMSCRIPT has been widely used forprogramming computer simulations of systems like factories, transporta-tion systems, and communication networks

tech-In 1989, Dr Markowitz received The John von Neumann Awardfrom the Operations Research Society of America for his work in portfo-lio theory, sparse matrix techniques, and SIMSCRIPT In 1990, he sharedthe Nobel Prize in Economics for his work on portfolio theory

contributing authors

James A Abate Global Asset Management (U.S.A.)

Mark J P Anson CalPERS

Robert D Arnott First Quadrant LP

Bruce M.Collins QuantCast LLC

Lev Dynkin Lehman Brothers

Frank J Fabozzi Yale University

Bruce Feibel Eagle Investment Systems

Gary L Gastineau ETF Advisors, LLC

James L Grant JLG Research/Baruch College (CUNY)

Francis Gupta Credit Suisse Asset Management

Susan Hudson-Wilson Property & Portfolio Research, LLC

Robert R Johnson Association for Investment Management and Research Frank J Jones The Guardian Life Insurance Company of America Vadim Konstantinovsky Lehman Brothers

Steven V Mann University of South Carolina

Harry M Markowitz Consultant

Pamela P Peterson Florida State University

Raman Vardharaj The Guardian Life Insurance Company of America

While sophisticated investors back then understood a few of the basicideas and principles that drive today’s investment practices, their methodswere crude, undisciplined, purely intuitive, and wildly inaccurate in terms

of achieving what they hoped to accomplish Entire areas and techniques ofinvestment management had yet to be discovered, many destined to appearonly twenty or thirty years later The momentous Nobel-prize-winning the-oretical innovations that did develop during the 1950s—Markowitz’sprinciples of portfolio selection, Modigliani-Miller’s contribution to corpo-rate finance and the uses of arbitrage, and Tobin’s insights into the risk/reward tradeoff—trickled at a snail’s pace even into the academic worldand were unknown to nearly all practitioners until many years later

We did understand the importance of diversification, in both vidual positions and in asset allocation The diversification we provided,

indi-A

xiv Foreword

however, was determined by seat-of-the-pants deliberations, with nosystematic evaluation beyond hunch Although risk was an ever-presentconsideration, in our shop at least, the idea of attaching a number toinvestment risk was inconceivable Performance measurement was asimple comparison to the Dow Jones Industrials Institutional and tax-free investors were few and far between Many of the individual clientswho comprised our constituency kept their securities in safe depositboxes instead of with brokers (risky) or custodian banks (costly), whichwas a major obstacle to making changes in portfolios, especially withbearer bonds

We bought and sold stocks on the basis of their being “cheap” or

“expensive,” but we worked without any explicit methodology forquantifying what those words meant The notion of growth as aninvestment consideration simply did not exist in the early 1950s, whenstocks still yielded more than bonds Although I attracted some atten-

tion with an article on the subject in the Harvard Business Review in

1956, growth as a central element of equity investing did not gain anytraction until well into the 1960s

We expected bond yields to rise and fall with business activity andstocks to do the opposite, which meant any suggestion of the two assetclasses moving in tandem was unthinkable Credit risk and interest raterisk were the only kinds of fixed-income risk we thought about; inflationplayed no part in decisions concerning asset allocation, market timing, ormanaging the bond portions of our portfolios Everybody knew longbonds were riskier than short-term obligations, but precisely how muchriskier and the structure of risk and return in the bond market were neverpart of our deliberations The uses of the complex and fascinating mathe-matics of fixed-income securities were still largely undeveloped

In any case, the fixed-income universe available to us consisted only

of Treasuries, corporates, and municipals; many of the corporates traded

on the Big Board instead of in the dealer markets that are so familiartoday But that did not matter much, because we acquired most of our cli-ents’ bonds on a buy-and-hold basis, as was the custom with all fixed-income securities purchased by sober investors like insurance companies,college endowments, trustees for widows and orphans, and the smallnumber of fee-only investment counsel firms like ours

With the invention of the money market fund still some twenty years

in the future, and Treasuries difficult to trade in small or odd amounts,cash management consisted of advising clients to deposit or withdrawmoney from savings accounts Once in the savings account, the moneybecame “their” money rather than “our” money And that meant we had

to call even clients with discretionary accounts and engage in a debatewhenever we wanted to make a purchase without an offsetting sale

Foreword xv

The volume of information of interest to investors was infinitesimalfrom today’s vantage point At ten minutes past every hour, a friendlybroker would call on the phone to give us the latest hourly price of theDow Jones Industrials and a rundown on the stocks we followed mostclosely That was all we knew during the day about what was happening

in the market The Standard & Poor’s averages were published onlymonthly, because calculating values for market-weighted indexes tooktoo long for the result to be timely; searching the ticker tape for thethirty Dow stocks, jotting down their prices, adding them up, and thendividing by the divisor was a dreary task, but it could be accomplished

in just a few minutes

Research consisted primarily of the Value Line, which was wayahead of its time in working off a disciplined valuation procedure(although the saying went that if the stock’s price did not move towardthe Line after a while, the Line would manage to move toward theprice) Wall Street research was spotty and superficial As we and otherleading investment advisors insisted that our clients choose their ownbrokers in order to avoid any odor of conflicts of interest, soft dollarresearch in such a world was nonexistent

I need not elaborate on the difference the computer has made in paring timely and elaborate client valuations, in organizing data forresearch purposes, and in speedy communication But that was only thebeginning: The computer has been the messenger of the investment rev-olution If the world’s stock of office equipment still consisted only ofthe slide-rules and hand-turned or electric (not electronic) desk-top cal-culators we used in the 1950s, the theories comprising the subject mat-ter of this book, and that support today’s investment practices, wouldnever have moved beyond their pages in scholarly journals into the realworld of investing

pre-■ ■ ■

To give you a flavor of the profound nature of the changes that haveoccurred, I suggest you peek ahead to a few chapters in this book Forexample, skim through Chapter 3 on applying Markowitz’s mean-varianceanalysis, Chapter 4 on asset pricing models, Chapter 22 on fixed-incomeportfolio strategies, and Chapter 31 on active asset allocation Even asuperficial view will reveal the radical difference between the way we man-aged portfolios in the 1950s and common practice today

Markowitz won the Nobel prize for his emphasis on two ancienthomilies—nothing ventured, nothing gained, but do not put all your eggsinto one basket Markowitz’s memorable achievement was to transformthese two basic investment guidelines into a rigorous analytical procedure

xvi Foreword

for composing investment portfolios His primary innovation, in fact, was

to distinguish between risk in a portfolio setting and the risk an investorfaces in selecting individual security positions

Markowitz uses his quantitative definition of risk to provide a means

of calculating—in hard numbers—the price of risk, or the amount ofadditional risk an investor must face in order to increase the portfolio’sexpected return by a given amount Investors can now employ diversifi-cation (distributing the eggs in many baskets) to minimize the amount of

“venture,” or risk, relative to a given amount of expected “gain,” orreturn Or, with the same process, the investor can choose to maximizethe gain to be expected from a given amount of venture Markowitzcharacterizes such portfolios as “efficient,” because they optimize thecombination of input (risk) per unit of output (return) This pioneeringanalysis was only a starting point, but it is still the inspiration for anextensive set of novel approaches for arriving at the most critical deci-sions in the portfolio-building process

Despite his contribution to the measurement and understanding ofinvestment risk, Markowitz skipped over a full-dress definition of theother side of the equation—expected return In Chapter 4 on asset pric-ing models, Fabozzi details striking advances in both defining and quan-tifying expected return Nevertheless, the methodology in Chapter 4 isstill a variation on Markowitz’s theme, for risk continues to play a cen-tral role in the prices investors set on individual assets as they go aboutbuilding their portfolios

This approach is a quantum leap from the way I used to guesswhether a security was “cheap” or “expensive.” We limited ourselves totrying to figure out what P/E or dividend yield was appropriate for eachstock we considered, a judgment that ignored the correlations betweenthat security and all the other securities in the portfolio or between thatsecurity and the market as a whole But Markowitz made it clear that theselection of issues for a portfolio is not the same thing as valuing individ-ual securities Those choices must be set in terms of the interactionbetween each individual security and the rest of the portfolio; later varia-tions by William Sharpe and others, also described in Chapter 4, empha-sized the importance of the interaction between individual securities andthe market as a whole Consequently, the models in Chapter 4 have anentirely different goal from the traditional valuation parameters covered

in Chapters 9 through 11

This entire structure of portfolio formation is by no means limited toselecting stocks: It is equally important in the management of fixed-income portfolios Here, as you will see in Chapter 22, the many aspects

of fixed-income strategies are even further removed from traditionalinvestment practices than the modern approach to equity selections The

Foreword xvii

proliferation of new forms of fixed-income instruments has joined withthe conversion of buy-and-hold into a broad set of active bond manage-ment strategies, creating a world of fixed-income investing unrecogniz-able to a Rip Van Winkle who went to sleep in the early 1950s andawoke in the early 2000s Indeed, today’s debt instruments are explicitlydesigned for agile and dynamic trading; the sanctified practice of holdingbonds to maturity that I once knew would be dangerously inappropriate

in today’s world As Fabozzi makes clear in this chapter, fixed-incomeinstruments may still be less risky than equities, but they neverthelessoffer an immense and widening span of risk and return tradeoffs Theresult is a significant increase in total portfolio expected returns relative

to the risks incurred Here, too, portfolio efficiency can be enhanced.Arnott’s analysis of active asset allocation in Chapter 31 is also along way from the intuitive approaches I was taught We made changes

in asset allocation based roughly on our forecast of the evolving businesscycle, and that was the end of it Arnott, on the other hand, begins bydistinguishing between two types of allocation decisions: those designedfor long-run considerations, which relate to an investor’s risk aversionand the return required to achieve appointed goals over the long run,versus shorter-term allocation decisions designed to take advantage ofcontinuing shifts in the valuation of one major asset class such as stocks,relative to another major asset class, such as bonds Here, too, variety isthe spice of life, for Arnott supplies the reader with an enticing assort-ment of solutions to these problems Furthermore, most of these systemsreplace conventional asset return forecasts with the many devices of risk/return analysis displayed in the earlier chapters

■ ■ ■

Despite my enthusiasm for the whole long story within the covers ofthis book, I warn the reader against expecting magic potions showeringinstant riches on anyone who masters these lessons The future faced byinvestors is just as unpredictable as it ever was Do not believe anyboasts to the contrary Risk is an inescapable companion in the invest-ment process

But that is just the point By making risk an integral part of the making process, and by incorporating the rigor and discipline of quantification,modern theories and applications clarify as never before the multifariouspaths linking the risk of loss to opportunities for gain One of the mostexciting features to me is how a few dominant principles can spawn anapparently unlimited supply of variations on the basic themes, openinginvestment possibilities we never dreamed of fifty years ago While this

decision-xviii Foreword

book does a great job of describing the cat, it also provides a broad menu

of effective methods to skin the cat

The transformation in investing over the past fifty years is ble to stepping from Charles Lindbergh’s Spirit of St Louis into a moderncommercial aircraft Lindbergh’s flight from New York to Paris made him

compara-a hero before the whole world A flight from New York to Pcompara-aris nowtakes place without notice every hour of the day and into the night But it

is not only distance and time that modern technology has conquered Aglance into the cockpit of a contemporary aircraft reveals a fantasticarray of controls and instruments whose entire purpose is to prevent thekinds of crashes that were as routine in Lindbergh’s day as they are head-line news in our own time—and to do so without any loss of speed Thesecret of success is in control of an airliner at altitudes and velocity Lind-bergh never dreamed of

The metaphor is apt As this book makes abundantly clear, the ing difference between today’s investment world and the world to which Iwas introduced is in control over the consequences of decision-making,under conditions of uncertainty, without any loss of opportunity Indeed,the opportunity set has been greatly expanded We will never knowenough of what lies ahead to make greater wealth a certainty, but we canlearn how to increase the odds and—equally important, I assure you—wecan avoid losing our shirts because of foolish decisions

strik-The ideas in this book comprise a rich treasure How I wish I had had

it in my hands when I first entered the challenging world of investing back

in 1951!

one

Foundations of Investment Management

CHAPTER 1

3

Investment Management

Frank J Fabozzi, Ph.D., CFA

Adjunct Professor of FinanceSchool of ManagementYale University

Harry M Markowitz, Ph.D.

Consultant

he purpose of this book is to describe the activities associated with

investment management Investment management—also referred to

as portfolio management and money management—requires an

under-standing of:

1 how investment objectives are determined

2 the investment products to which an investor can allocate funds

3 the way investment products are valued so that an investor can assesswhether or not a particular investment is fairly priced

4 the investment strategies that can be employed by an investor to ize a specified investment objective

real-5 the best way to construct a portfolio, given an investment strategy

6 the techniques for evaluating the performance of an investor

In this book, the contributors will explain each of these activities In

this introductory chapter, we set forth in general terms the investment

management process This process involves the following five steps: Step 1: Setting investment objectives

Step 2: Establishing an investment policy

T

4 FOUNDATIONS OF INVESTMENT MANAGEMENT

Step 3: Selecting an investment strategy

Step 4: Selecting the specific assets

Step 5: Measuring and evaluating investment performance

STEP 1: SETTING INVESTMENT OBJECTIVES

The first step in the investment management process, setting investmentobjectives, begins with a thorough analysis of the investment objectives

of the entity whose funds are being managed These entities can be

clas-sified as individual investors and institutional investors Within each of

these broad classifications is a wide range of investment objectives.The objectives of an individual investor may be to accumulatefunds to purchase a home or other major acquisition, to have sufficientfunds to be able to retire at a specified age, or to accumulate funds topay for college tuition for children An individual investor may engagethe services of a financial advisor/consultant in establishing investmentobjectives

Institutional investors include

■ regulated investment companies (mutual funds)

■ endowments and foundations

■ treasury department of corporations, municipal governments, and ernment agencies

gov-In general we can classify institutional investors into two broad egories—those that must meet contractually specified liabilities andthose that do not We can classify those in the first category as institutionswith “liability-driven objectives” and those in the second category as

cat-“non-liability driven objectives.” Some institutions have a wide range ofinvestment products that they offer investors, some of which are liabil-ity driven and others that are non-liability driven Once the investmentobjective is understand, it will then be possible to (1) establish a “bench-mark” or “bogey” by which to evaluate the performance of the investmentmanager and (2) evaluate alternative investment strategies to assess thepotential for realizing the specified investment objective

A liability is a cash outlay that must be made at a specific time to

satisfy the contractual terms of an issued obligation An institutional1-Fabozzi/Markowitz Page 4 Thursday, July 25, 2002 12:29 PM

Investment Management 5

investor is concerned with both the amount and timing of liabilities,

because its assets must produce the cash flow to meet any payments ithas promised to make in a timely way

STEP 2: ESTABLISHING AN INVESTMENT POLICY

The second step in the investment management process is establishingpolicy guidelines to satisfy the investment objectives Setting policybegins with the asset allocation decision That is, a decision must bemade as to how the funds to be invested should be distributed amongthe major classes of assets

Asset Classes

Throughout this book we refer to certain categories of investment ucts as an “asset class.” From the perspective of a U.S investor, the con-

prod-vention is to refer the following as traditional asset classes:

U.S common stocks

Non-U.S (or foreign) common stocks

Large capitalization stocks

Mid capitalization stocks

Small capitalization stocks

Growth stocks

Value stocks

By “capitalization,” it is meant the market capitalization of the pany’s common stock This is equal to the total market value of all ofthe common stock outstanding for that company For example, supposethat a company has 100 million shares of common stock outstandingand each share has a market value of $10 Then the capitalization of

com-6 FOUNDATIONS OF INVESTMENT MANAGEMENT

this company is $1 billion (100 million shares times $10 per share) Themarket capitalization of a company is commonly referred to as the

“market cap” or simply “cap.”

While the market cap of a company is easy to determine given the marketprice per share and the number of shares outstanding, how does one define

“value” and “growth” stocks? We’ll see how that is done in Chapter 8.For U.S bonds, also referred to as fixed-income securities, the fol-lowing are classified as asset classes:

U.S government bonds

Investment-grade corporate bonds

High-yield corporate bonds

U.S municipal bonds (i.e., state and local bonds)

Mortgage-backed securities

Asset-backed securities

All of these securities are described in Chapters 16 and 17, where what ismeant by “investment grade” and “high yield” are also explained Some-times, the first three bond asset classes listed above are further divided into

“long term” and “short term.”

For non-U.S stocks and bonds, the following are classified as assetclasses:

In addition to the traditional asset classes, there are asset classes

commonly referred to as alternative investments Two of the more

pop-ular ones are hedge funds and private equity Hedge funds are covered

in Chapter 29 and private equity is the subject of Chapter 30

How does one define an asset class? One investment manager, MarkKritzman, describes how this is done as follows:

some investments take on the status of an asset class simplybecause the managers of these assets promote them as an assetclass They believe that investors will be more inclined to allocatefunds to their products if they are viewed as an asset class ratherthan merely as an investment strategy.1

He then goes on to propose criteria for determining asset class status

We won’t review the criteria he proposed here They involve concepts

Developed market foreign stocks Developed market foreign bondsEmerging market foreign stocks Emerging market foreign bonds

1Mark Kritzman, “Toward Defining an Asset Class,” The Journal of Alternative

In-vestments (Summer 1999), p 79.

Investment Management 7

that are explained in later chapters After these concepts are explained itwill become clear how asset class status is determined However, itshould not come as any surprise that the criteria proposed by Kritzmaninvolve the risk, return, and the correlation of the return of a potentialasset class with that of other asset classes

Along with the designation of an investment as an asset class comes

a barometer to be able to quantify performance—the risk, return, andthe correlation of the return of the asset class with that of another assetclass The barometer is called a “benchmark index,” “market index,” orsimply “index.” For example, listed below are the most popular indexesused to represent the various asset classes that fall into the equity area:

For the U.S fixed income (bond) asset class, the two commonly usedindexes are the Lehman Brothers Aggregate Bond Index and theSalomon Brothers Broad Index

As other asset classes are described in later chapters, the index used

as a proxy for that asset class will be discussed

If an investor wants exposure to a particular asset class, an investormust be able to buy a sufficient number of the individual assets compris-ing the asset class Equivalently, the investor has to buy a sufficientnumber of individual assets comprising the index representing that assetclass This means that if an investor wants exposure to the U.S largecap equity market and the S&P 500 is the index (consisting of 500 com-panies) representing that asset class, then the investor can’t simply buythe shares of a handful of companies and hope to acquire the desiredexposure to the large cap equity market For institutional investors,acquiring a sufficient number of individual assets comprising an assetclass is often not a serious problem and we will see how this can be done

in later chapters However, for individual investors, obtaining exposure

U.S Equity Wilshire 5000, Frank Russell 3000

U.S Large Cap Equity Standard & Poor’s (S&P) 500

U.S Large Cap Value Frank Russell 1000 Value, S&P/Barra 500 Value U.S Large Cap Growth Frank Russell 1000 Growth, S&P/Barra 500 Growth U.S Mid Cap Equity Frank Russell Mid Cap

U.S Small Cap Equity Frank Russell 2000

U.S Small Cap Value Frank Russell 2000 Value

U.S Small Cap Growth Frank Russell 2000 Growth

International Equity Morgan Stanley Capital International (MSCI) EAFE

Salomon Smith Barney International, MSCI All Country World (ACWI) ex U.S.

Emerging Markets MSCI Emerging Markets

8 FOUNDATIONS OF INVESTMENT MANAGEMENT

to an asset class by buying individual assets is not simple How can vidual investors accomplish this?

indi-Fortunately, there is an investment vehicle that can be used toobtain exposure to asset classes in a cost effective manner The vehicle is

a regulated investment company, more popularly referred to as a mutualfund This investment vehicle is the subject of Chapter 26 For now,what is important to understand is that there are mutual funds thatinvest primarily in specific asset classes Such mutual funds offer aninvestor the opportunity to gain exposure to an asset class without theinvestor having expertise in the management of the individual assets inthat asset class and by investing a sum of money that in the absence of amutual fund would not allow the investor to acquire a sufficient number

of individual assets to obtain the desired exposure

Constraints

There are some institutional investors that make the asset allocationdecision based purely on their understanding of the risk-return charac-teristics of the various asset classes and expected returns The asset allo-cation will take into consideration any investment constraints orrestrictions Asset allocation models are commercially available forassisting those individuals responsible for making this decision Chapter

31 describes one such model

In the development of an investment policy, the following factorsmust be considered:

spec-For example, in later chapters of this book the concepts of the beta

of a common stock portfolio and the duration of a bond portfolio will

be discussed These risk measures provide an estimate of the exposure of

a portfolio to changes in key factors that affect the portfolio’s value—the market overall in the case of a portfolio’s beta and the general level1-Fabozzi/Markowitz Page 8 Thursday, July 25, 2002 12:29 PM

Investment Management 9

of interest rates in the case of a portfolio’s duration Typically, a clientwill not set a specific value for the level of risk exposure Instead, theclient restriction may be in the form of a maximum on the level of therisk exposure or a permissible range for the risk measure relative to thebenchmark For example, a client may restrict the portfolio’s duration

to be +0.5 or −0.5 of the client-specified benchmark Thus, if the tion of the client-imposed benchmark is 4, the manager has the discre-tion of constructing a portfolio with a duration between 3.5 and 4.5

con-to how sensitive the asset or portfolio is con-to changes in interest rates Thegreater the sensitivity, the higher the statutory capital required

Tax and Accounting Issues

Tax considerations are important for several reasons First, certain tutional investors such as pension funds, endowments, and foundationsare exempt from federal income taxation Consequently, the assets inwhich they invest will not be those that are tax-advantaged investments.Second, there are tax factors that must be incorporated into the invest-ment policy For example, while a pension fund might be tax-exempt,there may be certain assets or the use of some investment vehicles inwhich it invests whose earnings may be taxed

insti-Generally accepted accounting principles (GAAP) and regulatoryaccounting principles (RAP) are important considerations in developinginvestment policies An excellent example is a defined benefit plan for acorporation GAAP specifies that a corporate pension fund’s surplus isequal to the difference between the market value of the assets and thepresent value of the liabilities If the surplus is negative, the corporatesponsor must record the negative balance as a liability on its balancesheet Consequently, in establishing its investment policies, recognition1-Fabozzi/Markowitz Page 9 Thursday, July 25, 2002 12:29 PM

10 FOUNDATIONS OF INVESTMENT MANAGEMENT

must be given to the volatility of the market value of the fund’s portfoliorelative to the volatility of the present value of the liabilities Considerthis In 1994 the return on the S&P 500 and the Lehman BrothersAggregate Bond Index was 1.29% and −2.92%, respectively Interestrates rose in 1994 In 1995, the return on the S&P 500 was 37.52% and18.47% on the Lehman Brothers Aggregate as a result of a decline ininterest rates.2 Most pension plans allocate the bulk of their funds tocommon stocks and bonds Which was the best year for pension funds?

It would seem that 1995 was the best year Yet, The Pension BenefitGuaranty Corporation stated that underfunding by pension fundsincreased in 1995 but decreased in 1994 The reason is that the decline

in interest rates increased the present value of liabilities in 1995 anddecreased liabilities in 1994 due to a rise in interest rates Thus, it is notjust the performance of the assets that affects the performance of a pen-sion fund but the relative performance of assets versus liabilities

STEP 3: SELECTING A PORTFOLIO STRATEGY

Selecting a portfolio strategy that is consistent with the investmentobjectives and investment policy guidelines of the client or institution isthe third step in the investment management process Portfolio strate-gies can be classified as either active or passive

An active portfolio strategy uses available information and

forecast-ing techniques to seek a better performance than a portfolio that is ply diversified broadly Essential to all active strategies are expectationsabout the factors that have been found to influence the performance of

sim-an asset class For example, with active common stock strategies thismay include forecasts of future earnings, dividends, or price-earningsratios With bond portfolios that are actively managed, expectationsmay involve forecasts of future interest rates and sector spreads Activeportfolio strategies involving foreign securities may require forecasts oflocal interest rates and exchange rates

A passive portfolio strategy involves minimal expectational input,

and instead relies on diversification to match the performance of somemarket index In effect, a passive strategy assumes that the marketplacewill reflect all available information in the price paid for securities.Between these extremes of active and passive strategies, several strategieshave sprung up that have elements of both For example, the core of aportfolio may be passively managed with the balance actively managed

2 The relationship between changes in interest rates and bond prices will be explained

in Chapter 21.

1-Fabozzi/Markowitz Page 10 Thursday, July 25, 2002 12:29 PM

Investment Management 11

In the bond area, several strategies classified as structured portfolio

strategies have been commonly used A structured portfolio strategy is

one in which a portfolio is designed to achieve the performance of somepredetermined liabilities that must be paid out These strategies are fre-quently used when trying to match the funds received from an invest-ment portfolio to the future liabilities that must be paid

Given the choice among active and passive management, whichshould be selected? The answer depends on (1) the client’s or moneymanager’s view of how “price-efficient” the market is, (2) the client’srisk tolerance, and (3) the nature of the client’s liabilities By market-place price efficiency we mean how difficult it would be to earn a greaterreturn than passive management after adjusting for the risk associatedwith a strategy and the transaction costs associated with implementingthat strategy

STEP 4: SELECTING THE SPECIFIC ASSETS

Once a portfolio strategy is selected, the next step is to select the specificassets to be included in the portfolio It is in this phase of the investment

management process that the investor attempts to construct an efficient

portfolio An efficient portfolio is one that provides the greatest

expected return for a given level of risk, or equivalently, the lowest riskfor a given expected return

Inputs Required

To construct an efficient portfolio, the investor must be able to quantifyrisk and provide the necessary inputs As will be explained in the nextchapter, there are three key inputs that are needed: future expectedreturn (or simply expected return), variance of asset returns, and correla-tion (or covariance) of asset returns All of the investment toolsdescribed in the chapters that follow in this book are intended to providethe investor with information with which to estimate these three inputs.There are a wide range of approaches to obtain the expected return

of assets Investors can employ various analytical tools that will be cussed throughout this book to derive the future expected return of anasset For example, we will see in Chapter 4 that there are various assetpricing models that provide expected return estimates based on factorsthat historically have been found to systematically affect the return onall assets Investors can use historical average returns as their estimate

dis-of future expected returns Investors can modify historical averagereturns with their judgment of the future to obtain a future expected

12 FOUNDATIONS OF INVESTMENT MANAGEMENT

return Another approach is for investors to simply to use their intuitionwithout any formal analysis to come up with the future expected return

In the next chapter, the reason why the variance of asset returnsshould be used as a measure of an asset’s risk will be explained Thisinput can be obtained for each asset by calculating the historical vari-ance of asset returns There are sophisticated time series statistical tech-niques that can be used to improve the estimated variance of assetreturns but they are not covered in this book Some investors calculatethe historical variance of asset returns and adjust them based on theirintuition

The covariance (or correlation) of returns is a measure of how thereturn of two assets vary together Typically, investors use historicalcovariances of asset returns as an estimate of future covariances Butwhy is a covariance of asset returns needed? As well be explained in thenext chapter, the covariance is important because the variance of a port-folio’s return depends on it and the key to diversification is the covari-ance of asset returns

Approaches to Portfolio Construction

Constructing an efficient portfolio based on the expected return for aportfolio (which depends on the expected return of all the asset returns

in the portfolio) and the variance of the portfolio’s return (whichdepends on the variance of the return of all of the assets in the portfolioand the covariance of returns between all pairs of assets in the portfolio)

is referred to as “mean-variance” portfolio management The term

“mean” is use because the expected return is equivalent to the “mean”

or “average value” of returns This approach also allows for the sion of constraints such as lower and upper bounds on particular assets

inclu-or assets in particular industries inclu-or sectinclu-ors The end result of the sis is a set of efficient portfolios—alternative portfolios from which theinvestor can select that offer the maximum expected portfolio return for

analy-a given level of portfolio risk

There are variations on this approach to portfolio construction.Mean-variance analysis can be employed by estimating risk factors thathistorically have explained the variance of asset returns The basic princi-ple is that the value of an asset is driven by a number of systematic factors(or, equivalently, risk exposures) plus a component unique to a particularcompany or industry A set of efficient portfolios can be identified based

on the risk factors and the sensitivity of assets to these risk factors Thisapproach is referred to the “multi-factor risk approach” to portfolio con-struction and is explained in Chapter 13 for common stock portfoliomanagement and Chapter 24 for fixed-income portfolio management

The second variation is one in which the input used to measure risk

is the tracking error of a portfolio relative to a benchmark index, ratherthan the variance of the portfolio return By a benchmark index it ismeant the benchmark that the investor’s performance is comparedagainst As explained in Chapter 7, tracking error is the variance of thedifference in the return on the portfolio and the return on the bench-mark index When this “tracking error multi-factor risk approach” toportfolio construction is applied to individual assets, the investor canidentify the set of efficient portfolios in terms of a portfolio thatmatches the risk profile of the benchmark index for each level of track-ing error Selecting assets that intentionally cause the portfolio’s riskprofile to differ from that of the benchmark index is the way a manageractively manages a portfolio In contrast, indexing means matching therisk profile “Enhanced” indexing basically means that the assetsselected for the portfolio do not cause the risk profile of the portfolioconstructed to depart materially from the risk profile of the benchmark.This tracking error multi-factor risk approach to common stock andfixed-income portfolio construction will be explained and illustrated inChapters 13 and 24, respectively

At the other extreme of the full mean-variance approach to portfoliomanagement is the assembling of a portfolio in which investors ignore all

of the inputs—expected returns, variance of asset returns, and ance of asset returns—and use their intuition to construct a portfolio

covari-We refer to this approach as the “seat-of-the-pants approach” to lio construction In a rising stock market, for example, this approach istoo often confused with investment skill It is not an approach we rec-ommend

portfo-STEP 5: MEASURING AND EVALUATING PERFORMANCE

The measurement and evaluation of investment performance is the laststep in the investment management process Actually, it is misleading tosay that it is the last step since the investment management process is anongoing process This step involves measuring the performance of theportfolio and then evaluating that performance relative to some bench-mark

14 FOUNDATIONS OF INVESTMENT MANAGEMENT

Although a portfolio manager may have performed better than abenchmark, this does not necessarily mean that the portfolio managersatisfied the client’s investment objective For example, suppose that afinancial institution established as its investment objective the maximi-zation of portfolio return and allocated 75% of its funds to commonstock and the balance to bonds Suppose further that the managerresponsible for the common stock portfolio realized a 1-year return thatwas 150 basis points greater than the benchmark.3 Assuming that therisk of the portfolio was similar to that of the benchmark, it wouldappear that the manager outperformed the benchmark However, sup-pose that in spite of this performance, the financial institution cannotmeet its liabilities Then the failure was in establishing the investmentobjectives and setting policy, not the failure of the manager

SUMMARY

The overview of the investment management process described in thischapter should help in understanding the activities that the portfoliomanager faces and the need for the analytical tools that are described inthe chapters that follow in this book

3 A basis point is equal to 0.0001 or 0.01% This means that 1% is equal to 100 basis points.

CHAPTER 2

15

Portfolio Selection

Frank J Fabozzi, Ph.D., CFA

Adjunct Professor of FinanceSchool of ManagementYale University

Harry M Markowitz, Ph.D.

Consultant

Francis Gupta, Ph.D.

Vice PresidentCredit Suisse Asset Management

his chapter is an introduction to the theory of portfolio selection,which together with asset pricing theory, discussed in Chapter 4, pro-vides the foundation and the building blocks for the management of port-folios The goal of portfolio selection is the construction of portfolios thatmaximize expected returns consistent with individually acceptable levels

of risk Using both historical data and investor expectations of futurereturns, portfolio selection uses modeling techniques to quantify “expectedportfolio returns” and “acceptable levels of portfolio risk,” and providesmethods to select an optimal portfolio

The theory of portfolio selection presented in this chapter, popularly

referred to as mean-variance portfolio analysis or simply mean variance

analysis, is a normative theory A normative theory is one that describes

a standard or norm of behavior that investors should pursue in structing a portfolio, in contrast to a theory that is actually followed Inthe next chapter we illustrate how mean-variance analysis is applied inpractice

con-T

16 FOUNDATIONS OF INVESTMENT MANAGEMENT

Asset pricing theory goes on to formalize the relationship thatshould exist between asset returns and risk if investors behave in ahypothesized manner In contrast to a normative theory, asset pricingtheory is a positive theory—a theory that hypothesizes how investorsbehave rather than how investors should behave Based on that hypoth-esized behavior of investors, a model that provides the expected return(a key input into constructing portfolios based on mean-variance analy-

sis) is derived and is called an asset pricing model.

Together, portfolio selection theory and asset pricing theory provide

a framework to specify and measure investment risk and to develop tionships between expected asset return and risk (and hence between riskand required return on an investment) However, it is critically important

rela-to understand that portfolio selection theory is a theory that is dent of any theories about asset pricing The validity of portfolio selec-tion theory does not rest on the validity of asset pricing theory

indepen-It would not be an overstatement to say that modern portfolio ory has revolutionized the world of investment management Allowingmanagers to quantify the investment risk and expected return of a port-folio has provided the scientific and objective complement to the subjec-tive art of investment management More importantly, whereas at onetime the focus of portfolio management used to be the risk of individualassets, the theory of portfolio selection has shifted the focus to the risk

the-of the entire portfolio This theory shows that it is possible to combinerisky assets and produce a portfolio whose expected return reflects itscomponents, but with considerably lower risk In other words, it is pos-sible to construct a portfolio whose risk is smaller than the sum of all itsindividual parts!

Though practitioners realized that the risks of individual assets wererelated, prior to modern portfolio theory they were unable to formalizehow combining them into a portfolio impacted the risk at the entireportfolio level, or how the addition of a new asset would change thereturn/risk characteristics of the portfolio This is because practitionerswere unable to quantify the returns and risks of their investments Fur-thermore, in the context of the entire portfolio, they were also unable toformalize the interaction of the returns and risks across asset classes andindividual assets The failure to quantify these important measures andformalize these important relationships made the goal of constructing anoptimal portfolio highly subjective and provided no insight into thereturn investors could expect and the risk they were undertaking Theother drawback before the advent of the theory of portfolio selection andasset pricing theory was that there was no measurement tool available toinvestors for judging the performance of their investment managers

Portfolio Selection 17

SOME BASIC CONCEPTS

Portfolio theory draws on concepts from two fields: financial economictheory and probability and statistical theory This section presents theconcepts from financial economic theory used in portfolio theory Whilemany of the concepts presented here have a more technical or rigorousdefinition, the purpose is to keep the explanations simple and intuitive

so the reader can appreciate the importance and contribution of theseconcepts to the development of modern portfolio theory

Utility Function and Indifference Curves

In life there are many situations where entities (i.e., individuals andfirms) face two or more choices The economic “theory of choice” usesthe concept of a utility function to describe the way entities make deci-

sions when faced with a set of choices A utility function assigns a

(numeric) value to all possible choices faced by the entity The higherthe value of a particular choice, the greater the utility derived from thatchoice The choice that is selected is the one that results in the maxi-mum utility given a set of constraints faced by the entity.1

In portfolio theory too, entities are faced with a set of choices ferent portfolios have different levels of expected return and risk Also,the higher the level of expected return, the larger the risk Entities arefaced with the decision of choosing a portfolio from the set of all possi-ble risk/return combinations, where when they like return, they dislikerisk Therefore, entities obtain different levels of utility from differentrisk/return combinations The utility obtained from any possible risk/return combination is expressed by the utility function Put simply, theutility function expresses the preferences of entities over perceived riskand expected return combinations

Dif-A utility function can be expressed in graphical form by a set of

indifference curves Exhibit 2.1 shows indifference curves labeled u1, u2,

and u3 By convention, the horizontal axis measures risk and the cal axis measures expected return Each curve represents a set of portfo-lios with different combinations of risk and return All the points on agiven indifference curve indicate combinations of risk and expectedreturn that will give the same level of utility to a given investor For

verti-example, on utility curve u1, there are two points u and u ′, with u

hav-1

The origins of utility theory date back to the 18th century But it was not until 1944 that utility theory was formalized in a set of necessary and sufficient axioms by von Neumann and Morgenstern and applied to decision-making under risk and uncer-

tainty See J von Neumann and Oskar Morgenstern, Theory of Games and

Eco-nomic Behavior (Princeton, NJ: Princeton University Press, 1944)

2-F/M/G-PortSelect Page 17 Friday, July 26, 2002 9:42 AM

18 FOUNDATIONS OF INVESTMENT MANAGEMENT

ing a higher expected return than u′, but also having a higher risk.Because the two points lie on the same indifference curve, the investorhas an equal preference for (or is indifferent to) the two points, or, forthat matter, any point on the curve The (positive) slope of an indiffer-ence curve reflects the fact that, to obtain the same level of utility, theinvestor requires a higher expected return in order to accept higher risk.For the three indifference curves shown in Exhibit 2.1, the utilitythe investor receives is greater the further the indifference curve is fromthe horizontal axis, because that curve represents a higher level ofreturn at every level of risk Thus, for the three indifference curves

shown in the exhibit, u3 has the highest utility and u1 the lowest

The Set of Efficient Portfolios and the Optimal Portfolio

Portfolios that provide the largest possible expected return for given

lev-els of risk are called efficient portfolios To construct an efficient

portfo-lio, it is necessary to make some assumption about how investors behavewhen making investment decisions One reasonable assumption is that

investors are risk averse A risk-averse investor is an investor who, when

faced with choosing between two investments with the same expectedreturn but two different risks, prefers the one with the lower risk

EXHIBIT 2.1 Indifference Curves

2-F/M/G-PortSelect Page 18 Friday, July 26, 2002 9:42 AM

Portfolio Selection 19

In selecting portfolios, an investor seeks to maximize the expectedportfolio return given his tolerance for risk.2 Given a choice from the set

of efficient portfolios, an optimal portfolio is the one that is most

pre-ferred by the investor

Risky Assets versus Risk-Free Assets

A risky asset is one for which the return that will be realized in the future isuncertain For example, an investor who purchases the stock of Pfizer Cor-poration today with the intention of holding it for some finite time does notknow what return will be realized at the end of the holding period Thereturn will depend on the price of Pfizer’s stock at the time of sale and onthe dividends that the company pays during the holding period Thus,Pfizer stock, and indeed the stock of all companies, is a risky asset

Securities issued by the U.S government are also risky For example,

an investor who purchases a U.S government bond that matures in 30years does not know the return that will be realized if this bond is heldfor only one year This is because changes in interest rates in that yearwill affect the price of the bond one year from now and that will impactthe return on the bond over that year

There are assets, however, for which the return that will be realized

in the future is known with certainty today Such assets are referred to

as risk-free or riskless assets The risk-free asset is commonly defined as

a short-term obligation of the U.S government For example, if aninvestor buys a U.S government security that matures in one year andplans to hold that security for one year, then there is no uncertaintyabout the return that will be realized The investor knows that in oneyear, the maturity date of the security, the government will pay a specificamount to retire the debt Notice how this situation differs for the U.S.government security that matures in 30 years While the 1-year and the30-year securities are obligations of the U.S government, the formermatures in one year so that there is no uncertainty about the return thatwill be realized In contrast, while the investor knows what the govern-ment will pay at the end of 30 years for the 30-year bond, he does notknow what the price of the bond will be one year from now

MEASURING A PORTFOLIO’S EXPECTED RETURN

We are now ready to define the actual and expected return of a riskyasset and a portfolio of risky assets

2 Alternatively stated, an investor seeks to minimize the risk that he is exposed to

giv-en some target expected return.

20 FOUNDATIONS OF INVESTMENT MANAGEMENT

Measuring Single-Period Portfolio Return

The actual return on a portfolio of assets over some specific time period

is straightforward to calculate using the following:

R p = w1R1 + w2R 2 + + w G R G (1)where,

In shorthand notation, equation (1) can be expressed as follows:

(2)

Equation (2) states that the return on a portfolio (R p ) of G assets is

equal to the sum over all individual assets’ weights in the portfolio times

their respective return The portfolio return R p is sometimes called the

holding period return or the ex post return.

For example, consider the following portfolio consisting of threeassets:

The portfolio’s total market value at the beginning of the holding period

is $25 million Therefore,

R p = rate of return on the portfolio over the period

R g = rate of return on asset g over the period

w g = weight of asset g in the portfolio (i.e., market value of asset g

as a proportion of the market value of the total portfolio) atthe beginning of the period

G = number of assets in the portfolio

Asset

Market value at the beginning of holding period

Rate of return over holding period

w 1 = $6 million/$25 million = 0.24, or 24% and R 1 = 12%

w 2 = $8 million/$25 million = 0.32, or 32% and R 2 = 10%

w 3 = $11 million/$25 million = 0.44, or 44% and R 3 = 5%