The theory and practice of investment management frank fabozzi harry markowitz

Performance measurement involves the calculation of the return realized by a portfolio manager over some time interval, which we refer to as the evaluation period.. Thus, the return can

The Theory and

Practice of Investment Management

Second Edition

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

The Handbook of Financial Instruments edited by Frank J Fabozzi

Collateralized Debt Obligations: Structures and Analysis by Laurie S Goodman and Frank J Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J Fabozzi

Investment Performance Measurement by Bruce J Feibel

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

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

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

Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J Fabozzi,

Steven V Mann, and Moorad Choudhry

Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J Fabozzi The Handbook of European Fixed Income Securities edited by Frank J Fabozzi and Moorad Choudhry The Handbook of European Structured Financial Products edited by Frank J Fabozzi and Moorad Choudhry The Mathematics of Financial Modeling and Investment Management by Sergio M Focardi and

Frank J Fabozzi

Short Selling: Strategies, Risks, and Rewards edited by Frank J Fabozzi

The Real Estate Investment Handbook by G Timothy Haight and Daniel Singer

Market Neutral Strategies edited by Bruce I Jacobs and Kenneth N Levy

Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J Fabozzi and Steven V Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T Rachev, Christian Menn, and

Frank J Fabozzi

Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J Fabozzi, Sergio M

Focardi, and Petter N Kolm

Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by

Frank J Fabozzi, Lionel Martellini, and Philippe Priaulet

Analysis of Financial Statements, Second Edition by Pamela P Peterson and Frank J Fabozzi

Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J Lucas, Laurie S

Goodman, and Frank J Fabozzi

Handbook of Alternative Assets, Second Edition by Mark J P Anson

Introduction to Structured Finance by Frank J Fabozzi, Henry A Davis, and Moorad Choudhry

Financial Econometrics by Svetlozar T Rachev, Stefan Mittnik, Frank J Fabozzi, Sergio M Focardi, and

Teo Jasic

Developments in Collateralized Debt Obligations: New Products and Insights by Douglas J Lucas,

Laurie S Goodman, Frank J Fabozzi, and Rebecca J Manning

Robust Portfolio Optimization and Management by Frank J Fabozzi, Petter N Kolm,

Dessislava A Pachamanova, and Sergio M Focardi

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T Rachev,

Stogan V Stoyanov, and Frank J Fabozzi

How to Select Investment Managers and Evaluate Performance by G Timothy Haight,

Stephen O Morrell, and Glenn E Ross

Bayesian Methods in Finance by Svetlozar T Rachev, John S J Hsu, Biliana S Bagasheva, and

John Wiley & Sons, Inc.

The Theory and

Practice of Investment Management

Second Edition

FRANK J FABOZZI HARRY M MARKOWITZ

EDITORS

Asset Allocation, Valuation,

Portfolio Construction,

and Strategies

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 ted in any form or by any means, electronic, mechanical, photocopying, recording, scan- ning, or otherwise, 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 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web

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Library of Congress Cataloging-in-Publication Data

The theory and practice of investment management / Frank J Fabozzi, Harry M Markowitz, editors.—2nd ed.

p cm.—(Frank J Fabozzi series)

Instruments, Asset Allocation,

CHAPTER 1

Frank J Fabozzi and Harry M Markowitz

CHAPTER 2

Asset Classes, Alternative Investments,

Investment Companies, and Exchange-Traded Funds 15

Mark J P Anson, Frank J Fabozzi, and Frank J Jones

CHAPTER 3

Frank J Fabozzi, Harry M Markowitz,

Petter N Kolm, and Francis Gupta

Questions 78

CHAPTER 4

Frank J Fabozzi and Harry M Markowitz

Questions 101

CHAPTER 5

Guofu Zhou and Frank J Fabozzi

Questions 124

CHAPTER 6

Dessislava A Pachamanova and Frank J Fabozzi

Geometric Random Walks 134

Asset Allocation and Portfolio Construction 159

Noël Amenc, Felix Goltz, Lionel Martellini, and Vincent Milhau

Asset Allocation and Portfolio Construction Decisions in the

Asset Allocation and Portfolio Construction Decisions in the

Dynamic Allocation Decisions to the Performance-Seeking and

Frank J Fabozzi, Frank J Jones,

Robert R Johnson, and Pamela P Drake

Earnings 208Dividends 210

Common Stock Portfolio Management Strategies 229

Frank J Fabozzi, James L Grant, and Raman Vardharaj

Tracking Error and Related Measures 233

Approaches to Common Stock Valuation 271

Pamela P Drake, Frank J Fabozzi, and Glen A Larsen Jr.

Questions 285

CHAPTER 11

Quantitative Equity Portfolio Management 287

Andrew Alford, Robert Jones, and Terence Lim

Traditional and Quantitative Approaches to

Bruce I Jacobs and Kenneth N Levy

Questions 325

CHAPTER 13

Frank J Fabozzi, Raman Vardharaj, and Frank J Jones

Bruce M Collins and Frank J Fabozzi

CHAPTER 15

Using Equity Derivatives in Portfolio Management 383

Bruce M Collins and Frank J Fabozzi

Federal Agency Securities 423

Frank J Fabozzi and Steven V Mann

Bond Portfolio Strategies for Outperforming a Benchmark 535

Bülent Baygün and Robert Tzucker

Questions 554

CHAPTER 20

The Art of Fixed Income Portfolio Investing 557

Chris P Dialynas and Ellen J Rachlin

Regulatory Changes, Demographic Trends, and

Volatility 574

CHAPTER 21

Multifactor Fixed Income Risk Models and Their Applications 585

Anthony Lazanas, António Baldaque da Silva,

Radu Gąbudean, and Arne D Staal

Questions 644

CHAPTER 23

Credit Default Swaps and the Indexes 647

Stephen J Antczak, Douglas J Lucas, and Frank J Fabozzi

Key Points 658Questions 658

Index 663

Frank J Fabozzi is Professor in the Practice of Finance in the Yale School of

Man agement Prior to joining the Yale faculty, he was a Visiting Professor

of Finance in the Sloan School at MIT He is a Fellow of the International Center for Finance at Yale University and on the Advisory Council for the Department of Operations Research and Financial Engineering at Prince-

ton University Professor Fabozzi is the editor of the Journal of Portfolio Management and an associate editor of the Journal of Fixed Income, Jour- nal of Asset Management, Review of Futures Markets, and Quantitative Finance He is a trustee for the BlackRock family of closed-end funds In

2002, he was inducted into the Fixed Income Analysts Society’s Hall of Fame and is the 2007 recipient of the C Stewart Sheppard Award given by the CFA Institute He has authored numerous books in investment man-agement Professor Fabozzi earned a doctorate in economics from the City University of New York in 1972 and earned the designation of Chartered Financial Analyst and Certi fied Public Accountant

Harry M Markowitz has applied computer and mathematical techniques

to various practical decision making areas In finance, in an article in 1952 and a book in 1959, he presented what is now referred to as MPT, “modern portfolio theory.” This has become a standard topic in college courses and texts on investments and is widely used by institutional investors for tacti-cal asset allocation, risk control, and attribution analysis In other areas,

Dr Markowitz developed “sparse matrix” techniques for solving very large mathematical optimization problems These techniques are now standard

in production software for optimization programs He also designed and supervised the development of the SIMSCRIPT programming language SIMSCRIPT has been widely used for programming computer simulations

of systems like factories, transportation systems, and communication works In 1989, Dr Markowitz received the John von Neumann Award from the Operations Research Society of America for his work in portfolio theory, sparse matrix techniques, and SIMSCRIPT In 1990, he shared the Nobel Prize in Economics for his work on portfolio theory

António Baldaque da Silva Barclays Capital

JLG Research

New York University Glen A Larsen, Jr Indiana University Kelley School of Business–

Indianapolis

South Carolina

Harry M Markowitz Consultant

Dessislava A Pachamanova Babson College

Then and Now in Investing, and Why Now Is So Much Better

Peter L Bernstein

This Foreword originally appeared in the first edition of The Theory and

Prac-tice of Investment Management Peter Bernstein passed away in June 2009

Ref-erences to the updated chapters mentioned in the Foreword are provided by the editors.

contrast between the investment world of today and what professional investing was like at the beginning of my career 50 years ago The revolu-tion in investing over the past half century has been far more remarkable than most people with a shorter memory bank can realize

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

of achieving what they hoped to accomplish Entire areas and techniques of investment management had yet to be discovered, many destined to appear only 20 or 30 years later The momentous Nobel-prize-winning theoreti-cal innovations that did develop during the 1950s—Markowitz’s prin-ciples of portfolio selection, Modigliani-Miller’s contribution to corporate finance and the uses of arbitrage, and Tobin’s insights into the risk–reward trade-off—trickled at a snail’s pace even into the academic world and were unknown to nearly all practitioners until many years later

We did understand the importance of diversification, in both individual positions and in asset allocation The diversification we provided, however, was determined by seat-of-the-pants deliberations, with no systematic eval-uation beyond hunch Although risk was an ever-present consideration, in

our shop at least, the idea of attaching a number to investment risk was inconceivable Performance measurement was a simple comparison to the Dow Jones Industrials Institutional and tax-free investors were few and far between Many of the individual clients who comprised our constituency kept their securities in safe deposit boxes instead of with brokers (risky) or custodian banks (costly), which was a major obstacle to making changes in portfolios, especially with bearer bonds.

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

“expensive,” but we worked without any explicit methodology for fying what those words meant The notion of growth as an investment con-sideration simply did not exist in the early 1950s, when stocks still yielded more than bonds Although I attracted some attention with an article on the

quanti-subject in the Harvard Business Review in 1956, growth as a central

ele-ment of equity investing did not gain any traction until well into the 1960s

We expected bond yields to rise and fall with business activity and stocks to do the opposite, which meant any suggestion of the two asset classes moving in tandem was unthinkable Credit risk and interest rate risk were the only kinds of fixed income risk we thought about; inflation played no part in decisions concerning asset allocation, market timing, or managing the bond portions of our portfolios Everybody knew long bonds were riskier than short-term obligations, but precisely how much riskier and the structure of risk and return in the bond market were never part of our deliberations The uses of the complex and fascinating mathematics 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 familiar today But that did not matter much because we acquired most of our clients’ bonds

on a buy-and-hold basis, as was the custom with all fixed income ties purchased by sober investors like insurance companies, college endow-ments, trustees for widows and orphans, and the small number of fee-only investment counsel firms like ours

securi-With the invention of the money market fund still some 20 years in the future, and Treasuries difficult to trade in small or odd amounts, cash man-agement consisted of advising clients to deposit or withdraw money from savings accounts Once in the savings account, the money became “their” money rather than “our” money And that meant we had to call even clients with discretionary accounts and engage in a debate whenever we wanted to make a purchase without an offsetting sale

The volume of information of interest to investors was infinitesimal from today’s vantage point At 10 minutes past every hour, a friendly broker would call on the phone to give us the latest hourly price of the Dow Jones

Industrials and a rundown on the stocks we followed most closely That was all we knew during the day about what was happening in the market The Standard & Poor’s averages were published only monthly because calculat-ing values for market-weighted indexes took too long for the result to be timely; searching the ticker tape for the 30 Dow stocks, jotting down their prices, adding them up, and then dividing 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 way ahead of its time in working off a disciplined valuation procedure (although the say-ing went that if the stock’s price did not move toward the Line after a while, the Line would manage to move toward the price) Wall Street research was spotty and superficial As we and other leading investment advisors insisted that our clients choose their own brokers in order to avoid any odor of conflicts of interest, soft dollar research in such a world was nonexistent

I need not elaborate on the difference the computer has made in ing timely and elaborate client valuations, in organizing data for research purposes, and in speedy communication But that was only the beginning: The computer has been the messenger of the investment revolution If the world’s stock of office equipment still consisted only of the slide-rules and hand-turned or electric (not electronic) desk-top calculators we used in the 1950s, the theories comprising the subject matter of this book, and that support today’s investment practices, would never have moved beyond their pages in scholarly journals into the real world of investing

To give you a flavor of the profound nature of the changes that have curred, I suggest you peek ahead to a few chapters in this book For ex-ample, skim through Chapter 3 on applying Markowitz’s mean-variance analysis, Chapters 5 and 6 on asset pricing models, Chapter 19 on fixed income portfolio strategies, and Chapter 7 on asset allocation Even a su-perficial view will reveal the radical difference between the way we managed portfolios in the 1950s and common practice today

oc-Markowitz won the Nobel Prize for his emphasis on two ancient lies—nothing ventured, nothing gained, but do not put all your eggs into one basket Markowitz’s memorable achievement was to transform these two basic investment guidelines into a rigorous analytical procedure for composing investment portfolios His primary innovation, in fact, was to distinguish between risk in a portfolio setting and the risk an investor faces

homi-in selecthomi-ing homi-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 of tional risk an investor must face in order to increase the portfolio’s expected

addi-return by a given amount Investors can now employ diversification uting the eggs in many baskets) to minimize the amount of “venture,” or risk, relative to a given amount of expected “gain,” or return Or, with the same process, the investor can choose to maximize the gain to be expected from a given amount of venture Markowitz characterizes such portfolios as

(distrib-“efficient,” because they optimize the combination of input (risk) per unit of output (return) This pioneering analysis was only a starting point, but it is still the inspiration for an extensive set of novel approaches for arriving at the most critical decisions in the portfolio-building process

Despite his contribution to the measurement and understanding of investment risk, Markowitz skipped over a full-dress definition of the other side of the equation—expected return Chapters 5 and 6 on asset pricing models detail striking advances in both defining and quantifying expected return Nevertheless, the methodology in these chapters is still a variation

on Markowitz’s theme, for risk continues to play a central role in the prices investors set on individual assets as they go about building their portfolios.This approach is a quantum leap from the way I used to guess whether

a security was “cheap” or “expensive.” We limited ourselves to trying to figure out what P/E or dividend yield was appropriate for each stock we considered, a judgment that ignored the correlations between that security and all the other securities in the portfolio or between that security and the market as a whole But Markowitz made it clear that the selection of issues for a portfolio is not the same thing as valuing individual securities Those choices must be set in terms of the interaction between each individual secu-rity and the rest of the portfolio; later variations by William Sharpe and others, also described in Chapters 4 and 5, emphasized the importance of the interaction between individual securities and the market as a whole Consequently, the models in Chapters 4 and 5 have an entirely different goal from the traditional valuation parameters covered in Chapter 10

This entire structure of portfolio formation is by no means limited to selecting stocks: It is equally important in the management of fixed-income portfolios Here, as you will see in Chapter 19, the many aspects of fixed-income strategies are even further removed from traditional investment practices than the modern approach to equity selections The proliferation

of new forms of fixed income instruments has joined with the conversion of buy-and-hold into a broad set of active bond management strategies, creat-ing a world of fixed-income investing unrecognizable to a Rip Van Winkle who went to sleep in the early 1950s and awoke in the early 2000s Indeed, today’s debt instruments are explicitly designed for agile and dynamic trad-ing; the sanctified practice of holding bonds to maturity that I once knew would be dangerously inappropriate in today’s world Fixed income instru-ments may still be less risky than equities, but they nevertheless offer an

immense and widening span of risk and return trade-offs The result is a significant increase in total portfolio expected returns relative to the risks incurred Here, too, portfolio efficiency can be enhanced.

Despite my enthusiasm for the whole long story within the covers of this book, I warn the reader against expecting magic potions showering instant riches on anyone who masters these lessons The future faced by investors

is just as unpredictable as it ever was Do not believe any boasts to the trary Risk is an inescapable companion in the investment process

con-But that is just the point By making risk an integral part of the sionmaking process, and by incorporating the rigor and discipline of quan-tification, modern theories and applications clarify as never before the mul-tifarious paths linking the risk of loss to opportunities for gain One of the most exciting features to me is how a few dominant principles can spawn

deci-an apparently unlimited supply of variations on the basic themes, opening investment possibilities we never dreamed of 50 years ago While this book does a great job of describing the cat, it also provides a broad menu of effec-tive methods to skin the cat

The transformation in investing over the past 50 years is comparable to

stepping from Charles Lindbergh’s Spirit of St Louis into a modern

com-mercial aircraft Lindbergh’s flight from New York to Paris made him a hero before the whole world A flight from New York to Paris now takes 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 A glance into the cockpit of a contemporary aircraft reveals a fantastic array of controls and instruments whose entire purpose is to prevent the kinds of crashes that were as routine in Lindbergh’s day as they are headline news in our own time—and to do so without any loss of speed The secret of success is in control of an airliner at altitudes and velocity Lindbergh never dreamed of.The metaphor is apt As this book makes abundantly clear, the strik-ing difference between today’s investment world and the world to which

I was 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 know enough

of what lies ahead to make greater wealth a certainty, but we can learn how

to increase the odds and—equally important, I assure you—we can avoid losing our shirts because of foolish decisions

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

Instruments, Asset Allocation, Portfolio Selection, and Asset Pricing

Edited by Frank J Fabozzi and Harry M Markowitz Copyright © 2011 John Wiley & Sons, Inc

Overview of Investment Management

Frank J Fabozzi, Ph.D., CFA, CPA

Professor in the Practice of FinanceYale School of Management

Harry M Markowitz, Ph.D.

Consultant

vehi-cles associated with investment management Investment management— also referred to as portfolio management and money management—requires

an understanding of:

whether or not a particular investment is fairly priced, underpriced, or overpriced

a specified investment objective

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

introductory chapter, we set forth in general terms the investment ment process This process involves the following five tasks:

manage-1 Setting investment objectives.

2 Establishing an investment policy.

3 Selecting an investment strategy.

Edited by Frank J Fabozzi and Harry M Markowitz Copyright © 2011 John Wiley & Sons, Inc

4 Constructing the portfolio.

5 Measuring and evaluating investment performance

SETTING INVESTMENT OBJECTIVES

Setting investment objectives, begins with a thorough analysis of the ment objectives of the entity whose funds are being managed These entities

invest-can be classified as individual investors and institutional investors Within

each of these broad classifications is a wide range of investment objectives.Institutional investors include:

associa-tions, and credit unions)

and health companies)

gov-ernment agencies

In general, we can classify institutional investors into two broad egories: those that must meet contractually specified liabilities and those that do not We can classify those in the first category as institutions with

cat-“liability-driven objectives” and those in the second category as institutions

with “nonliability driven objectives.” A liability is a cash outlay that must

be made at a specific time to satisfy the contractual terms of an issued

obli-gation An institutional investor is concerned with both the amount and timing of liabilities because its assets must produce the cash flow to meet

any payments it has promised to make in a timely way

Some institutions have a wide range of investment products that they offer investors, some of which are liability driven and others that are non-liability driven Once the investment objective is clearly defined, it will then be possible to (1) establish a “benchmark” by which to evaluate the performance

of the investment manager and (2) evaluate alternative investment strategies

to assess the potential for realizing the specified investment objective

ESTABLISHING AN INVESTMENT POLICY

Establishing an investment policy starts with the asset allocation decision That is, a decision must be made as to how the funds to be invested should

be distributed among the major classes of assets

Asset Classes

Throughout this book, we refer to certain categories of investment products

as an “asset class.” In the next chapter, we take a closer look at what is meant by an asset class From the perspective of a U.S investor, the conven-

tion is to refer to the following as traditional asset classes: U.S common

stocks, non-U.S (or foreign) common stocks, U.S bonds, non-U.S (or eign) bonds, cash equivalents, and real estate Common stock and bonds are further divided into different asset classes Cash equivalents are defined

for-as short-term debt obligations that have little price volatility In addition to the traditional asset classes, there are asset classes commonly referred to as

alternative assets or alternative investments Two of the more popular ones

are hedge funds and private equity In the next chapter, we review three popular alternative assets

In the development of an investment policy, the following factors must be considered: client constraints, regulatory constraints, and tax and accounting issues

Examples of client-imposed constraints would be restrictions that ify the types of securities in which a manager may invest and concentration limits on how much or little may be invested in a particular asset class or in

spec-a pspec-articulspec-ar issuer When spec-a benchmspec-ark is estspec-ablished, there mspec-ay be spec-a tion as to the degree to which the manager may deviate from some key characteristics of that benchmark

restric-There are many types of regulatory constraints These involve straints on the asset classes that are permissible and concentration limits

con-on investments Moreover, in making the asset allocaticon-on decisicon-on, ccon-onsid-eration must be given to any risk-based capital requirements For deposi-tory institutions and insurance companies, the amount of statutory capital required is related to the quality of the assets in which the institution has invested

consid-Tax considerations are important for several reasons First, certain tutional investors such as pension funds, endowments, and foundations are exempt from federal income taxation Consequently, the assets in which they invest will not be those that are tax-advantaged investments Second,

insti-there are tax factors that must be incorporated into the investment policy For example, although a pension fund might be tax-exempt, there may be certain assets or the use of some investment vehicles in which it invests whose earnings may be taxed

Generally accepted accounting principles (GAAP) and regulatory accounting principles (RAP) are important considerations in developing investment policies

SELECTING A PORTFOLIO STRATEGY

The next task in the investment management process is selecting a portfolio strategy that is consistent with the investment objectives and investment policy guidelines The selection can be made from a wide range of portfolio strategies In general, portfolio strategies 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 simply diversified broadly Essential to all active strategies are expectations about the factors that have been found to influence the performance of an asset

class A passive portfolio strategy involves minimal expectational input, and

instead relies on diversification to match the performance of some market index In effect, a passive strategy assumes that market prices impound all available information Between these extremes of active and passive strate-gies, several strategies have sprung up that have elements of both

Given the choice among active and passive strategies, which should be selected? The answer depends on (1) the client’s or money manager’s view of how “price-efficient” the market is; (2) the client’s risk tolerance; and (3) the nature of the client’s liabilities By “marketplace price efficiency,” we mean how difficult it would be to earn a greater return than passive management after adjusting for the risk associated with a strategy and the transaction costs associated with implementing that strategy

CONSTRUCTING THE PORTFOLIO

Once a portfolio strategy is selected, the next task is to construct the folio (i.e., select the specific assets to be included in the portfolio) It is in this phase of the investment management process that the investor attempts

port-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 risk for a given expected return

To construct an efficient portfolio, the investor must be able to quantify risk and provide the necessary inputs As explained in Chapter 3, there are three key inputs that are needed: future expected return (or simply expected return), variance of asset returns, and correlation (or covariance) of asset returns All of the investment tools described in the chapters that follow in this book are intended to provide the investor with information with which

to estimate these three inputs

MEASURING AND EVALUATING PERFORMANCE

Finally, there is the task of measuring and evaluating investment

perfor-mance Performance measurement involves the calculation of the return

realized by a portfolio manager over some time interval, which we refer to

as the evaluation period There are several important issues that must be

addressed in developing a methodology for calculating a portfolio’s return and we discuss them below

Performance evaluation is concerned with three issues: (1) determining

whether the portfolio manager added value by outperforming the lished benchmark; (2) identifying how the portfolio manager achieved the calculated return; and (3) assessing whether the portfolio manager achieved superior performance (i.e., added value) by skill or by luck There are two approaches that have been employed in evaluating the performance of port-folio managers: single-index performance measures and performance attri-bution models

estab-Despite their popularity, single-index performance measures do not specify how or why a portfolio manager may have outperformed or under-

information ratio These two ratios are return/risk ratios At this junction,

an explanation of the information ratio is not easy to understand but it will

be described in Chapter 9 The Sharpe ratio is equal to

The numerator of the Sharpe ratio is a measure of return It is not the raw return but the return in excess of what could have been earned by investing in a risk-free security The denominator is a measure of the risk associated with generating the portfolio return As explained in Chapter

3, the standard deviation is a commonly used measure of risk Thus, the

1William F Sharpe, “Mutual Fund Performance,” Journal of Business 39, S1 (1966):

119–138.

Sharpe ratio is a measure of the excess return relative to the variability of the portfolio return

Performance attribution models (also called return attribution models)

decompose the portfolio return so that a client can determine how the folio manager earned the return As we explain in later chapters, a portfolio manager seeking to outperform a designated benchmark can do so by con-structing a portfolio so that it differs from the risks embedded in the bench-mark Consequently, understanding the risk embedded in a benchmark are essential to understanding not only how to construct a portfolio, but also for employing return attribution models

port-Measuring Performance

The starting point for evaluating the performance of a portfolio manager is measuring return This might seem quite simple, but several practical issues make the task complex because one must take into account any cash distri-butions made from a portfolio during the evaluation period

The dollar return realized on a portfolio for any evaluation period (i.e.,

a year, month, or week) is equal to the sum of:

1 The difference between the market value of the portfolio at the end

of the evaluation period and the market value at the beginning of the evaluation period

2 Any distributions made from the portfolio

It is important that any capital or income distributions from the portfolio to

a client or beneficiary of the portfolio be taken into account

The rate of return, or simply return, expresses the dollar return in terms

of the amount of the market value at the beginning of the evaluation period Thus, the return can be viewed as the amount (expressed as a fraction of the initial portfolio value) that can be withdrawn at the end of the evaluation period while maintaining the initial market value of the portfolio intact

In equation form, the portfolio’s return can be expressed as follows:

MV

0where

MV0 = the portfolio’s market value at the beginning of the evaluation period

evaluation period

To illustrate the calculation of a return, assume the following tion for the portfolio manager of a common stock portfolio: The portfolio’s market value at the beginning and end of the evaluation period is $250 mil-lion and $280 million, respectively, and, during the evaluation period, $10 million is distributed to the client from investment income Therefore,

There are three assumptions in measuring return The first assumption

is that cash inflows (i.e., dividends and interest) into the portfolio during the evaluation period but are not distributed are reinvested in the portfolio For example, suppose that during the evaluation period, $20 million is received from dividends This amount is reflected in the market value of the portfolio

at the end of the period

The second assumption is that if there are distributions from the folio, they either occur at the end of the evaluation period or are held in the form of cash until the end of the evaluation period In our example,

port-$10 million is distributed to the client But when did that distribution ally occur? To understand why the timing of the distribution is important, consider two extreme cases: (1) the distribution is made at the end of the evaluation period, as is assumed in the return calculation; and (2) the dis-tribution is made at the beginning of the evaluation period In the first case, the portfolio manager had the use of the $10 million to invest for the entire evaluation period By contrast, in the second case, the portfolio manager loses the opportunity to invest the funds until the end of the evaluation period Consequently, the timing of the distribution will affect the return, but this is not considered in the return calculation above

actu-The third assumption is that there is no cash contributed to the lio by the client For example, suppose that sometime during the evaluation period, the client contributes $15 million to the portfolio manager to invest Consequently, the market value of the portfolio at the end of the evalua-tion period, $280 million in our example, would reflect the contribution of

portfo-$15 million The return calculation does not reflect that the portfolio’s ing market value is affected by the cash contributed by the client Moreover, the timing of this contribution will affect the calculated return.

end-Thus, while the return calculation for a portfolio can be evaluated for any length of time—such as one day, one month, five years—from a practi-cal point of view, the assumptions of this approach limit its application The longer the evaluation period, the more likely the assumptions will be violated For example, it is highly likely that there may be more than one distribution to the client and more than one contribution from the client

if the evaluation period is five years Therefore, a return calculation made over a long period of time, if longer than a few months, would not be very reliable because of the assumption underlying the calculations that all cash payments and inflows are made and received at the end of the period.Not only does the violation of the assumptions make it difficult to com-pare the returns of two portfolio managers over some evaluation period, but

it is also not useful for evaluating performance over different periods For example, the return calculation above will not give reliable information to compare the performance of a 1-month evaluation period and a 3-year eval-uation period To make such a comparison, the return must be expressed per unit of time, for example, per year

The way to handle these practical issues is to calculate the return for a short unit of time such as a month or a quarter We call the return so cal-

culated the subperiod return To get the return for the evaluation period,

the subperiod returns are then averaged So, for example, if the tion period is one year, and 12 monthly returns are calculated, the monthly returns are the subperiod returns, and they are averaged to get the 1-year return If a 3-year return is sought, and 12 quarterly returns can be calcu-lated, quarterly returns are the subperiod returns, and they are averaged

evalua-to get the 3-year return The 3-year return can then be converted inevalua-to an annual return by the straightforward procedure described later

Three methodologies have been used in practice to calculate the average

of the subperiod returns: arithmetic average rate of return, time-weighted rate

of return (also called the geometric rate of return), and dollar-weighted return

Arithmetic Average (Mean) Rate of Return

The arithmetic average (mean) rate of return is an unweighted average of

the subperiod returns The general formula is

N A

where

RA = the arithmetic average rate of return

N = the number of subperiods in the evaluation period

For example, if the portfolio returns were –10%, 20%, and 5% in months July, August, and September, respectively, the arithmetic average monthly return is 5%, as shown:

is then 25% Not a bad return! But think about this number The portfolio’s initial market value was $280 million Its market value at the end of two months is $280 million The return over this 2-month evaluation period is zero Yet the arithmetic average rate of return says it is a whopping 25%.Thus it is improper to interpret the arithmetic average rate of return as

a measure of the average return over an evaluation period The proper pretation is as follows: It is the average value of the withdrawals (expressed

inter-as a fraction of the portfolio’s initial market value) that can be made at the end of each subperiod while keeping the portfolio’s initial market value intact In our first example, in which the average monthly return is 5%, the investor must add 10% of the initial portfolio market value at the end of the first month, can withdraw 20% of the initial portfolio market value at the end of the second month, and can withdraw 5% of the initial portfolio market value at the end of the third month In our second example, the average monthly return of 25% means that 100% of the portfolio’s initial market value ($280 million) can be withdrawn at the end of the first month, and 50% must be added at the end of the second month

Time-Weighted Rate of Return

The time-weighted rate of return measures the compounded rate of growth

of the portfolio’s initial market value during the evaluation period, ing that all cash distributions are reinvested in the portfolio This return

assum-is also commonly referred to as the geometric mean return because it assum-is

computed by taking the geometric average of the portfolio subperiod turns The general formula is

Because the time-weighted rate of return is 4.3% per month, $1 invested in the portfolio at the beginning of July would have grown at a rate of 4.3% per month during the 3-month evaluation period

The time-weighted rate of return in the second example is 0%, as expected, as shown here:

In general, the arithmetic average rate of return will exceed the weighted average rate of return The exception is in the special situation where all the subperiod returns are the same, in which case the averages are identical The magnitude of the difference between the two averages is smaller the less the variation in the subperiod returns over the evaluation period For example, suppose that the evaluation period is four months,

and the time-weighted average rate of return is 2.46% Not much of a ference In our earlier example, in which we calculated an average rate of return of 25% but a time-weighted average rate of return of 0%, the large discrepancy is due to the substantial variation in the two monthly returns

dif-Dollar-Weighted Rate of Return

The dollar-weighted rate of return is computed by finding the interest rate

that will make the present value of the cash flows from all the subperiods

in the evaluation period plus the portfolio’s terminal market value equal to the portfolio’s initial market value The cash flow for each subperiod reflects the difference between the cash inflows due to investment income (i.e., divi-dends and interest) and to contributions made by the client to the portfolio and the cash outflows reflecting distributions to the client Notice that it is not necessary to know the portfolio’s market value for each subperiod to determine the dollar-weighted rate of return

The dollar-weighted rate of return is simply an internal rate of return

calculation, and, hence, it is also called the internal rate of return The

gen-eral formula for the dollar-weighted return is

R

C R

where

subperiod k, where k = 1, 2, , N

The dollar-weighted rate of return and the time-weighted rate of return will produce the same result if no withdrawals or contributions occur over the evaluation period and if all investment income is reinvested The prob-lem with the dollar-weighted rate of return is that it is affected by factors that are beyond the control of the money manager Specifically, any contri-butions made by the client or withdrawals that the client requires will affect the calculated return This may make it difficult to compare the performance

of two portfolio managers Despite this limitation, the dollar-weighted rate

of return does provide information about the growth of the fund This growth, however, may not be solely attributable to the performance of the portfolio manager when there are contributions and withdrawals

Annualizing Returns

The evaluation period may be less than or greater than one year Typically, return measures are reported as an average annual return This requires the

annualization of the subperiod returns The subperiod returns are usually calculated for a period of less than one year for the reasons described earlier The subperiod returns are then annualized using the following formula:

For example, suppose the evaluation period is three years, and a monthly period return is calculated Suppose further that the average monthly return

is 2% Then the annual return would be

KEY POINTS

objec-tives, establishing an investment policy, selecting an investment strategy, constructing the portfolio, and measuring and evaluating investment performance

across the major asset classes taking into consideration client-imposed and regulatory constraints

objectives, a client can select an active strategy or a passive strategy The selection of a strategy depends on the client’s view of the pricing efficiency of the market, as well as the client’s risk tolerance

cre-ate an efficient portfolio: a portfolio that provides the grecre-atest expected return for the target level of risk

This tool allows a client to understand why a portfolio manager may have underperformed or outperformed a benchmark

period

based on averaging subperiod returns are the arithmetic average rate of return, time-weighted rate of return, and dollar-weighted return The last two measures will produce the same result if no withdrawals or contributions occur over the evaluation period and if all investment income is reinvested

Asset Classes, Alternative Investments, Investment Companies, and

Exchange-Traded Funds

Mark J P Anson, Ph.D., JD, CPA, CFA, CAIA

Chief Investment Officer and Managing Partner

Oak Hill Investments

Frank J Fabozzi, Ph.D., CFA, CPA

Professor in the Practice of FinanceYale School of Management

Frank J Jones, Ph.D.

Professor, Accounting and Finance Department

San Jose State University

the various financial products available to investment managers Because the focus is on the two major asset classes, common stock and bonds, in this book, we do not discuss them in any in any detail here Instead, we pro-vide an overview of alternatives asset classes and two important financial products that can be used to obtain exposure to all asset classes, regulated investment companies and exchange-traded funds

referred to as asset classes? That is, how do we define an asset class? There

are several ways to do so The first is in terms of the investment attributes that the members of an asset class have in common These investment char-acteristics include:

and, as a result, correlate highly with the returns of each member included in the asset class

Based on this way of defining an asset class, the correlation between the turns of two different asset classes—the key statistical measure for success-ful diversification as will be explained in the next chapter—would be low.Mark Kritzman offers a second way of defining an asset class based simply on a group of assets that is treated as an asset class by asset manag-ers He writes:

re-[S]ome investments take on the status of an asset class simply cause the managers of these assets promote them as an asset class They believe that investors will be more inclined to allocate funds

be-to their products if they are viewed as an asset class rather than

Kritzman then goes on to propose criteria for determining asset class status which includes the attributes that we mentioned above and that will be de-scribed in more detail in later chapters

Based on these two ways of defining asset classes, the four major asset classes above can be extended to create other asset classes From the per-spective of a U.S investor, for example, the four major asset classes listed earlier have been expanded as follows by separating foreign securities from U.S securities: (1) U.S common stocks, (2) non-U.S (or foreign) common stocks, (3) U.S bonds, (4) non-U.S bonds, (5) cash equivalents, and (6) real estate

Common stocks and bonds are commonly further partitioned into more

asset classes For U.S common stocks (also referred to as U.S equities),

asset classes are based on market capitalization and style (growth versus value)

The market capitalization of a firm, commonly referred to as

“mar-ket cap,” is the total mar“mar-ket value of its common stock outstanding For

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

Invest-ments 2, no 1(1999): 79.

example, suppose that a corporation has 400 million shares of common stock outstanding and each share has a market value of $100 Then the mar-ket capitalization of this company is $40 billion (400 million shares times

$100 per share) The categories of common stock based on market

capital-ization are mega-cap (greater than $200 billion), large cap ($10 billion to

$200 billion), mid-cap ($1 billion to $10 billion), small cap ($300 million

to $1 billion), micro-cap ($50 million to $300 million), and nano-cap (less

than $50 million)

While the market cap of a company is easy to determine given the market price per share and the number of shares outstanding, how does one define “value” and “growth” stocks? How this is done is explained in Chapter 10

For U.S bonds, also referred to as fixed income securities, the

follow-ing are classified as asset classes: (1) U.S government bonds, (2) corporate bonds, (3) U.S municipal bonds (i.e., state and local bonds), (4) residen-tial mortgage-backed securities, (5) commercial mortgage-backed securities, and (6) asset-backed securities In turn, several of these asset classes are further segmented by the credit rating of the issuer For example, for corpo-rate bonds, investment-grade (i.e., high credit quality) corporate bonds and noninvestment-grade corporate bonds (i.e., speculative quality) are treated

as two asset classes

For non-U.S stocks and bonds, the following are classified as asset classes: (1) developed market foreign stocks, (2) developed market foreign bonds, (3) emerging market foreign stocks, and (4) emerging market foreign bonds The characteristics that market participants use to describe emerging markets is that the countries in this group:

political, economic, and financial market reforms in order to participate

in the global capital market

politi-cal risk and the unstable value of their currency

Loucks, Penicook, and Schillhorn describe what is meant by an ing market as follows:

emerg-Emerging market issuers rely on international investors for tal Emerging markets cannot finance their fiscal deficits domesti-cally because domestic capital markets are poorly developed and local investors are unable or unwilling to lend to the government Although emerging market issuers differ greatly in terms of credit

capi-risk, dependence on foreign capital is the most basic characteristic

The asset classes above are referred to as traditional asset classes Other asset classes are referred to as nontraditional asset classes or alternative asset classes They include hedge funds, private equity, and commodities

and are discussed later

Finally, real estate is not an alternative to stocks and bonds—it is a damental asset class that should be included within every diversified port-folio Alternative assets are meant to diversify the stock-and-bond holdings within a portfolio context

fun-What Is an Alternative Asset Class?

Part of the difficulty of working with alternative asset classes is defining them Are they a separate asset class or a subset of an existing asset class?

Do they hedge the investment opportunity set or expand it? That is, in terms

of Markowitz diversification that we describe in the next chapter, do they improve the efficient portfolio for a given level of risk? This means that for

a given level of risk, do they allow for a greater expected return than by just investing in traditional asset classes?

In most cases, alternative assets are a subset of an existing asset class This may run contrary to the popular view that alternative assets are sep-arate asset classes However, we take the view that what many consider separate “classes” are really just different investment strategies within an

2 Maria Mednikov Loucks, John A Penicook, and Uwe Schillhorn, “Emerging

Mar-kets Debt,” Chapter 31 in Frank J Fabozzi (ed.), Handbook of Finance: Vol I,

Financial Markets and Instruments (Hoboken, NJ: John Wiley, 2008): 340.

existing asset class In most cases, they expand the investment opportunity set, rather than hedge it Finally, with the exception of one alternative asset type, commodity futures, alternative assets are generally purchased in the private markets, outside of any exchange

Alternative assets, then, are just alternative investments within an ing asset class Specifically, most alternative assets derive their value from either the debt or equity markets For instance, most hedge fund strategies involve the purchase and sale of either equity or debt securities Addition-ally, hedge fund managers may invest in derivative instruments whose value

exist-is derived from the equity or debt market

Efficient versus Inefficient Asset Classes

Another way to distinguish alternative asset classes from traditional asset classes is based on the efficiency of the marketplace in which the assets trade The U.S public stock-and-bond markets are generally considered to

be the most price efficient marketplaces in the world Often, these markets are referred to as “semistrong efficient.” As explained in Chapter 9, this means that all publicly available information regarding a publicly traded corporation, both past information and present, is fully digested into the price of that company’s traded securities

Yet inefficiencies exist in all markets, both public and private If there were no informational inefficiencies in the public equity market, there would

be no case for pursuing a strategy that seeks to outperform the market

Such strategies are referred to as active management strategies Nonetheless,

whatever inefficiencies do exist, they are small and fleeting The reason is that information is easy to acquire and disseminate in the publicly traded securities markets Top-quartile portfolio managers who pursue active strat-egies in the public equity market earn returns in excess of their benchmark

of approximately 1% a year

In contrast, with respect to alternative assets, information is very ficult to acquire Most alternative assets (with the exception of commodi-ties) are privately traded This includes private equity and hedge funds The difference between top-quartile and bottom-quartile performance in private equity can be as much as 25%

dif-Consider venture capital, one subset of the private equity market Investments in start-up companies require intense research into the product niche the company intends to fulfill, the background of the management of the company, projections about future cash flows, exit strategies, potential competition, beta testing schedules, and so forth This information is not readily available to the investing public It is time consuming and expensive

to accumulate Furthermore, most investors do not have the time or the

talent to acquire and filter through the rough data regarding a private pany One reason why alternative asset managers charge large management and incentive fees is to recoup the cost of information collection.

com-This leads to another distinguishing factor between alternative asset classes and traditional asset classes: the investment intermediary Continu-ing with our venture capital example, most investments in venture capital are made through limited partnerships, limited liability companies, or spe-cial-purpose vehicles It is estimated that 80% of all private equity invest-ments in the United States are funneled through a financial intermediary.Investments in alternative assets are less liquid than their public market counterparts Investments are closely held and liquidity is minimal Further-more, without a publicly traded security, the value of private securities cannot

be determined by market trading The value of the private securities must be estimated by book value or appraisal, or determined by a cash flow model

Beta and Alpha Drivers

Two terms bandied about in asset management are “beta drivers” and pha drivers.” To understand these terms, we must understand what is meant

“al-by a market risk premium A market (or systematic) risk premium for an

asset class is the difference in the return on an asset class and the return fered on a risk-free asset such as a U.S Treasury security Investors seek to

of-capture that risk An excess return is the return earned on an asset class that

exceeds the return on a risk-free asset

In constructing a portfolio, an investor seeks the most efficient off between risk and return given a mix of asset classes In the context of Markowitz diversification discussed in the next chapter, an efficient port-folio is sought—the portfolio that maximizes the expected portfolio return for a given level of risk In this sense, the basic asset allocation is all about capturing the market risk premiums that exist for investing in different asset classes However, if additional asset classes can be added to the mix

trade-of potential investment opportunities in which an investor may invest, the efficient frontier can be improved so as to provide a greater range of risk and return opportunities for an investor Recall that in our earlier descrip-tion of an asset class, we explained that it had a low correlation of returns with other asset classes

Beta drivers capture market risk premiums in an efficient manner We have already discussed the notion or beta or systematic risk In contrast, alpha drivers seek pockets of excess return often without regard to benchmarks

It is useful to think of traditional and alternative assets within the text of beta and alpha drivers Alternative assets represent an alternative source of beta that is different from the mixture of traditional assets—