The handbook of equity style management third edition by t daniel coggin and frank j fabozzi

The Handbook of Equity Style

Management
Third Edition

T. DANIEL COGGIN
FRANK J. FABOZZI
EDITORS

John Wiley & Sons, Inc.


Copyright © 2003 by Frank J. Fabozzi. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Printed in the United States of America
10 9 8 7 6 5 4 3 2 1



Contents

About the Editors
Preface
Overview of the Book
Contributing Authors
CHAPTER 1
Style Analysis: Asset Allocation and Performance Evaluation
Arik Ben Dor and Ravi Jagannathan
CHAPTER 2
The Many Elements of Equity Style: Quantitative Management of
Core, Growth, and Value Strategies
Robert D. Arnott and Christopher G. Luck
CHAPTER 3
Models of Equity Style Information
Robert C. Radcliffe

ix

xi
xiii
xv

1

47

75

CHAPTER 4
Style Analysis: A Ten-Year Retrospective and Commentary
R. Stephen Hardy

109

CHAPTER 5
More Depth and Breadth than the Style Box: The Morningstar Lens
Paul D. Kaplan, James A. Knowles, and Don Phillips

131

CHAPTER 6
Using Portfolio Holdings to Improve the Search for Skill
Ronald J. Surz

159

v

vi

Contents

CHAPTER 7
Are Growth and Value Dead?: A New Framework for Equity Investment Styles
Lawrence S. Speidell and John Graves

171

CHAPTER 8
The Style of Investor Expectations
Hersh Shefrin and Meir Statman

195

CHAPTER 9
The Effects of Imprecision and Bias on the Abilities of Growth and
Value Managers to Outperform their Respective Benchmarks
Robert A. Haugen
CHAPTER 10
Style Return Differentials: Illusions, Risk Premiums, or
Investment Opportunities
Richard Roll
CHAPTER 11
The Persistence of Equity Style Performance:
Evidence from Mutual Fund Data
Ronald N. Kahn and Andrew Rudd

219

229

259

CHAPTER 12
How the Technology Bubble of 1999–2000 Disrupted Equity Style Investing
Kari Bayer Pinkernell and Richard Bernstein

273

CHAPTER 13
Multistyle Equity Investment Models
Parvez Ahmed, John G. Gallo, Larry J. Lockwood, and Sudhir Nanda

293

CHAPTER 14
A Comparison of Fixed versus Flexible Market Capitalization Style Allocations:
Don’t Be Boxed in by Size
315
Marc R Reinganum
CHAPTER 15
A Plan Sponsor Perspective on Equity Style Management
Keith Cardoza

333

Contents

vii

CHAPTER 16
An Analysis of U.S. and Non-U.S. Equity Style Index Methodologies
H. David Shea

359

CHAPTER 17
Country-Level Equity Style Timing
Clifford Asness, Robert Krail, and John Liew

407

CHAPTER 18
Value Investing and the January Effect: Some More International Evidence
Bala Arshanapalli, T. Daniel Coggin, and William Nelson

419

CHAPTER 19
Exploring the Mathematical Basis of Returns-Based Style Analysis
Thomas Becker

435

CHAPTER 20
Trading (and Investing) in “Style” Using Futures and Exchange-Traded Funds

Joanne M. Hill

455

INDEX

483



About the Editors

T. Daniel Coggin, Ph.D. is a nationally recognized investment management consultant with over 25 years experience in investment management
and consulting. Dr. Coggin is a frequent speaker at investment industry
conferences, has co-edited three books and written numerous articles and
book chapters on quantitative investment management. He earned his
Ph.D. in political science from Michigan State University in 1977 with an
emphasis on econometrics and quantitative methods.
Frank J. Fabozzi, Ph.D. 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 of funds and the BlackRock complex of funds. He earned a
doctorate in economics from the City University of New York in 1972
and in 1994 received an honorary doctorate of Humane Letters from
Nova Southeastern University. Dr. Fabozzi is a Fellow of the International Center for Finance at Yale University. He is an Advisory Analyst
for Global Asset Management (GAM) with responsibilities as Consulting Director for portfolio construction, risk control, and evaluation.

ix

Preface

Since the publication of the second edition of this book in 1997, equity
style management has strengthened its position as a key component of
domestic and foreign equity analysis and portfolio management. Much like
the period leading up to the publication of the second edition, many important developments have occurred prior to the publication of this edition. In
fact, of the 20 chapters in this edition, 17 are new.
We are again fortunate to have gathered together some of the key
innovators and practitioners of equity style management from academia
and the investment profession. These 35 experts combine to provide the
most up-to-date treatment available of the key issues and developments in
this rapidly evolving field. Readers of the book will find it a valuable aid
to improving their understanding of the theory and practice of equity
style management.

xi



Overview of the Book

Chapter 1 by Dor and Jagannathan begins with a brief overview of portfolio-based style analysis and then provides a detailed treatment of returnsbased style analysis, including some common pitfalls. Included in this chapter is an example of the use of returns-based style analysis to analyze hedge
funds. Chapter 2 by Arnott and Luck discusses the various definitions of
equity style and their use in quantitative investment management. An overview of the various models of equity style measurement is provided by Radcliffe in Chapter 3, where he suggests that all models add important
information to the equity management process. Chapter 4 by Hardy provides an extensive discussion of returns-based style analysis and how it can
be used to dissect equity portfolios. In Chapter 5 Kaplan, Knowles, and
Phillips unveil a new portfolio-based style model used by Morningstar to
analyze mutual funds. Following the advice given in Chapter 3, Surz demonstrates in Chapter 6 how to combine returns-based with holdings-based
style analysis to sort out luck from skill in equity portfolio management.

Chapter 7 by Speidell and Graves suggests that the current definitions
of “growth” and “value” are no longer appropriate and presents a new
framework for defining these key terms. In Chapter 8, Shefrin and Statman apply the new tools of behavioral finance to the analysis of equity
style. A framework for understanding the periodic disparities in the performance of value and growth managers is provided by Haugen in Chapter 9. In Chapter 10, Roll presents empirical evidence that shows how the
major equity style descriptors (size, earnings/price and book/market) have
different risk profiles, and demonstrates that the Capital Asset Pricing
Model and Arbitrage Pricing Theory cannot fully explain disparities in
equity style performance. Chapter 11 by Kahn and Rudd presents evidence that past returns are not a good predictor of future returns for
equity style mutual funds, using data collected over three time periods.
Details of how the “Technology Bubble” of the late 1990s disrupted the
“normal” cycle of equity style performance are described by Pinkernell
and Bernstein in Chapter 12. In Chapter 13, Ahmed, Gallo, Lockwood
and Nanda discuss how rotation among the various equity styles has the
potential to greatly enhance portfolio returns. Chapter 14 by Reinganum

xiii


xiv

Overview of the Book

presents a “style allocation” model that adds substantial value to forecasts of small cap and large cap portfolio returns.
Chapter 15 by Cardoza discusses how a large state retirement fund
uses equity style to manage its equity portfolio. In Chapter 16, Shea provides a detailed analysis of the major domestic and foreign equity style
index portfolios. In Chapter 17, Asness, Krall, and Liew shows how a
simple measure of the value-growth spread can enhance the success of
international value investment strategies. Chapter 18 by Arshanapalli,
Coggin, and Nelson offer new evidence on the January effect and its
impact on international value investment strategies. In Chapter 19,

Becker derives the mathematical basis of returns-based style analysis. We
believe that this is the first time this has been made available to a broad
audience. Chapter 20 by Hill presents a detailed treatment of equity style
index futures and equity style exchange-traded funds (ETFs), the latest
addition to the list of equity style investment vehicles.
As a final note, we ask the reader to keep in mind that (as with the
first two editions) there is still some variation in the terminology used in
equity style management. For example, some authors abbreviate returnsbased style analysis “RBSA,” while some others use “RBS.” Similarly,
some authors use the term “portfolio-based style analysis,” while some
others substitute “holdings-based style analysis. This should not be a
source of concern.
T. Daniel Coggin
Frank J. Fabozzi


Contributing Authors

Parvez Ahmed
Robert D. Arnott
Bala Arshanapalli
Clifford Asness
Thomas Becker
Richard Bernstein
Keith Cardoza
T. Daniel Coggin
Arik Ben Dor
John G. Gallo
John Graves
R. Stephen Hardy
Robert A. Haugen

Joanne M. Hill
Ravi Jagannathan
Ronald N. Kahn
Paul D. Kaplan
James A. Knowles
Robert Krail
John Liew
Larry J. Lockwood
Christopher G. Luck
Sudhir Nanda
William Nelson
Don Phillips
Kari Bayer Pinkernell
Robert C. Radcliffe
Marc R Reinganum
Richard Roll
Andrew Rudd
H. David Shea
Hersh Shefrin
Lawrence S. Speidell
Meir Statman
Ronald J. Surz

University of North Florida
First Quadrant, LP and Research Affiliates, LLC
Indiana University Northwest
AQR Capital Management, LLC
Zephyr Associates, Inc.
Merrill Lynch
Boeing Company

Charlotte, North Carolina
Northwestern University
Navellier & Associates
Nicholas-Applegate Capital Management
Zephyr Associates, Inc.
Haugen Custom Financial Systems
Goldman, Sachs & Co.
Northwestern University
Barclays Global Investors
Morningstar, Inc.
York Hedge Fund Strategies Inc.
AQR Capital Management, LLC
AQR Capital Management, LLC
Texas Christian University
First Quadrant, LP
T. Rowe Price Associates, Inc.
Indiana University Northwest
Morningstar, Inc.
Merrill Lynch
University of Florida and PI Style Analytics, Inc.
Oppenheimer Funds
University of California, Los Angeles and
Roll and Ross Asset Management Corporation
BARRA, Inc.
Citigroup Asset Management
Santa Clara University
Nicholas-Applegate Capital Management
Santa Clara University
PPCA, Inc.

xv


CHAPTER

1

Style Analysis: Asset Allocation
and Performance Evaluation
Arik Ben Dor
Lecturer
Kellogg School of Management
Northwestern University
Ravi Jagannathan, Ph.D.
Chicago Mercantile Exchange Distinguished Professor of Finance
Kellogg School of Management
Northwestern University

everal changes have taken place in the past three decades in the U.S.
capital markets. An important one among them is the reduction in
the direct holdings of corporate equities by individual investors and a
corresponding increase in institutional holdings. The growth of mutual
funds and pension funds during this period has been the primary cause
of the sharp increase in the institutional holdings of equities in the U.S.
Whereas mutual funds and pension funds held only 14% of all U.S. corporate equities in 1970, they held almost 40% by 2001.1 While holding
equities through money management institutions has made it possible
for individual investors to reap diversification benefits and plan sponsors to benefit from specialization, it has not been without cost. Individual investors as well as pension plan sponsors who invest through

S

1

Based on the Flow of Funds Accounts of the U.S., Board of Governors of the Federal
Reserve System.

1


2

THE HANDBOOK OF EQUITY STYLE MANAGEMENT

professional money managers need to monitor their actions and evaluate their performance and this introduces invisible agency costs.
For example, consider a large plan sponsor who allocates the funds
across several money managers based on each manager’s unique investment style. How can a plan sponsor verify that the investment decisions
taken by the manger and the securities he or she purchased are consistent with the assigned investment style? How can a plan sponsor ensure
that the bets taken by different external managers do not offset each
other? Furthermore, external money mangers are compensated based on
their performance. In many cases an active investment manger’s performance is assessed in terms of her ability to “beat a benchmark.”2 How
can the pension fund manger evaluate the nature of the risk the manager
undertook in order to attain a performance that is superior to that of
the benchmark? These problems are not unique to plan sponsors, but
are also of considerable concern to individual investors who own
actively managed mutual funds.
Return-based style analysis provides a way of identifying the asset
mix of the fund manager and comparing it with the asset mix of the performance benchmark. This enables the plan sponsor to understand the
nature of the style and selection bets taken by an active manager. The
correlation structure among the type of bets taken by different active
managers provides a plan sponsor or an individual investor with valuable insights regarding the extent to which the bets cancel or reinforce
each other. This chapter provides a comprehensive description of how

return-based style analysis can be used to analyze the investment style of
professional money mangers and examine their relative performance.
After a brief overview of portfolio-based style analysis, we describe the
methodology and the mechanics of return-based style analysis with several examples using mutual funds data. We also discuss several common
pitfalls in implementing the technique and how it can used to analyze
the style of hedge fund managers.3
2

An example would be a management fee of 10 basis points (0.10%) of assets under
management plus an additional 15 basis points for each 1% of performance over the
benchmark such as the S&P 500. Typically the fees are determined from time to time
through negotiation between the manger and the pension plan
3
The section “Return-Based Style Analysis” follows closely the exposition in William Sharpe, “Asset Allocation, Management Style, and Performance Measurement,”
Journal of Portfolio Management, 18 (1992), pp. 7–19. The section “Style Analysis
of Hedge Funds” follows closely the exposition in William Fung and David Hsieh,
“Empirical Characterization of Dynamic Trading Strategies: The Case of Hedge
Funds,” Review of Financial Studies, 10 (1997), pp. 275–302, and William Fung and
David Hsieh, “The Risks in Hedge Fund Strategies: Theory and Evidence from Trend
Followers,” Review of Financial Studies, 14 (2001), pp. 313–341.


3

Style Analysis: Asset Allocation and Performance Evaluation

EXHIBIT 1.1

An Example of Portfolio Based Analysis for a Global Manager
(January 2001 through December 2001)

Japan
Europe and U.S.
Emerging Markets
Overall

Manager
Holdings

Benchmark
Composition

Difference
in weights

65%
20%
15%
100%

40%
30%
30%
100%

25%
–10%
–15%
—

Total difference in returns
Attributed to country-weighting
Return due to selection

Return
8%
5.5%
3%
—

Total
Effect
2.0%
–0.55%
–0.3%
1.15%
1.65%
1.15%
0.50%

PORTFOLIO-BASED STYLE ANALYSIS
The performance of money managers is often evaluated by comparing the
performance of the managed portfolio against the performance of a particular manager-specific passive benchmark (e.g., S&P 500 for a Large
Cap Core manager). Performance attribution seeks to explain the sources
of the difference between the manager’s performance and that of the specified benchmark. In other words, once it is clear what the results were, the
goal is to find out why they were what they were. One commonly used
approach is to examine the composition of the manager’s portfolio and
compare the characteristics or attributes of the securities the manager has
invested in with the characteristics of the securities that make up the performance benchmark. Some of the common characteristics that are often
used in such comparisons include: market cap, book-to-market ratio, historic earnings growth rate, dividend yield and for fixed income securities

attributes such as duration, rating, etc. The attributes are averaged across
securities and the returns associated with each attribute are determined.
Exhibit 1.1 provides a simple example of a global manager that outperformed his benchmark during 2001 by 165 basis points (1.65%).
The analysis shows that of the total difference, 115 basis points could
be attributed to the portfolio “tilt” toward investing in Japanese stocks
during a period in which Japanese stocks outperformed stocks of firms
from other developed countries and emerging markets countries. The
remaining 50 basis points could then be associated with the manger’s
ability to select “winners” within the various regions.
As mentioned earlier the use of portfolio-based style analysis
requires knowledge of the composition of the managed portfolio as well
as the performance benchmark at the time of the analysis. In the case of


4

THE HANDBOOK OF EQUITY STYLE MANAGEMENT

a pension plan sponsor the money manger typically would provide the
necessary information to the pension plan for performing the analysis.
In the case of mutual funds, the investor can obtain this information
from quarterly filings. Some Web sites also provide information on
mutual fund characteristics computed using portfolio-based style analysis and classify the funds they cover into various categories.
Exhibit 1.2 displays information available from the Morningstar
Web site (www.morningstar.com), for the Goldman Sachs Growth and
Income Fund as of January 2002. Panel a displays the equity characteristics of the fund portfolio and a comparison to the S&P 500 Index. The
portfolio attributes represent an aggregation of the individual securities
comprising the fund portfolio (the top 25 holdings are shown in Panel
b). The fund invests in only 95 stocks with no bonds, and also maintains
some exposure to foreign markets (roughly 5%). The companies owned

by the fund are much smaller than those included in the S&P 500 (the
median firm size is roughly $28 billion versus $58 billion in the S&P
500) and the industry weightings differ substantially (see Panel c). The
fund has a somewhat higher average price-to-book ratio, but a lower
price-to-earnings ratio. This is probably because the stocks owned by
the fund experienced a higher earning growth relative to price in the
past than the stocks comprising the benchmark. The difference in
returns between the fund and the benchmark that may arise may be
attributed to the characteristics bets the fund took relative to the performance benchmark. For example, the difference in industry weighting
between the fund and the benchmark, coupled with the returns for each
industry can be used to calculate the contribution of ‘industry bias’ to
the overall return difference as shown in Exhibit 1.1.
EXHIBIT 1.2

Portfolio-Based Analysis for Goldman Sachs Growth and
Income Fund, Based on Morningstar Data as of 01/31/2002
Panel a. Equity Characteristics

Number of Stocks
Median Market Cap
Price/Earnings Ratio
Price/Book Ratio
Price/cash flow
Earnings Growth Rate
Bond holding
Foreign Holdings
Turnover Rate (Fiscal Year)
Cash Investments

Growth and Income Fund

S&P 500

95
$27.84B
25.1×
4.2×
13.2×
16.2%
0%
4.93%
40.0%
0.1%

500
$58.0B
30.3×
3.7×
18.85×
14.2%
—
—
—
—


5

Style Analysis: Asset Allocation and Performance Evaluation

EXHIBIT 1.2 (Continued)
Panel b. Portfolio Stock Composition

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

Name of

Holding

Sector

P/E

YTD
Return %

% Net
Assets

ExxonMobil
Citigroup
ChevronTexaco
Bank of America
ConAgra
Merck
Philip Morris
Freddie Mac
Heinz HJ
XL Cap Cl A
Kimberly-Clark
U.S. Bancorp
SBC Comms
PPL
KeyCorp
Alliance Cap Mgmt Hldg
Wells Fargo
Anheuser-Busch

Energy East
PNC Finl Svcs Grp
Keyspan
Aon
Deere
Motorola
Intl Paper

Energy
Financial
Energy
Financial
Staples
Health
Staples
Financial
Staples
Financial
Industrial
Financial
Services
Utility
Financial
Financial
Financial
Staples
Utility
Financial
Energy
Financial

Industrial
Technology
Industrial

17.64
16.00
26.54
12.36
18.71
19.51
13.43
11.18
28.99
23.48
20.38
22.24
17.39
26.66
78.00
20.57
23.32
25.53
11.98
29.22
20.16
45.35
—
—
—

–0.19
–13.50
–8.00
–2.81
–0.66
4.18
13.35
–3.44
1.53
3.04
4.26
–6.50
–4.80
–6.69
–0.66
–9.20
6.33
7.14
2.81
0.09
–10.42
–1.01
3.28
–17.64
6.82

3.35
3.32
2.87
2.70

2.46
2.43
2.26
2.18
2.08
2.05
2.04
1.74
1.70
1.61
1.52
1.46
1.43
1.34
1.33
1.27
1.24
1.21
1.21
1.19
1.13

Portfolio-based style analysis requires information on portfolio
composition, which may be difficult to obtain. Further the classification
of individual securities into slots based on characteristics can involve
substantial amount of judgment. For example, a conglomerate firm
would typically have operations in several different sectors of the economy and it may be difficult to identify how much of the firm goes into
each sector. In addition, portfolio compositions may change over time.
Point in time categorization may result in significant style “drift.” Such
“drift” would render long-term style comparisons not very meaningful.

One solution is to calculate these characteristics at different points in
time and use multiple portfolios to classify the investment manger.


6

THE HANDBOOK OF EQUITY STYLE MANAGEMENT

EXHIBIT 1.2 (Continued)
Panel c. Industry Weightings
Sector Diversification
(% of Common Stocks)
Utilities
Energy
Financials
Industrials
Durables
Staples
Services
Retail
Health
Technology

Growth and
Income Fund

S&P 500
Index

Difference

6.40
10.00
36.20
10.40
0.70
11.00
10.80
1.00
6.30
7.30

2.89
6.42
17.78
11.06
2.82
8.92
4.86
13.56
14.90
16.80

3.51
3.58
18.42
–0.66
–2.12
2.08
5.94

–12.56
–8.60
–9.50

Another problem arises from simply calculating portfolio characteristics based on the portfolio holdings. A domestic equity mutual fund
investing in domestic stocks that derive a majority of their revenue from
sales abroad will clearly be influenced by factors in foreign economies.
If the foreign economies go into recession, the fund will be affected. In
this way, the fund, although domestic, responds to factors in foreign
economies with a manner similar to an international equity fund. An
investor interested in foreign exposure may be able to obtain it through
investing in such a domestic fund. In William Sharpe’s often-quoted
words, what is important here is that “If it acts like a duck, assume it’s a
duck.” One advantage of the approach however, is that it provides
updated information on the money manger investment strategy and
asset allocation.

RETURN-BASED STYLE ANALYSIS
While it is possible to determine a fund’s investment style from a
detailed analysis of the securities held by the fund, a simpler approach
that uses only the realized fund-returns is possible. Return-based style
analysis, requires only easily obtained information, while portfoliobased style analysis requires knowledge of the actual composition of the
portfolio.


7

Style Analysis: Asset Allocation and Performance Evaluation

Relation to Multifactor Models

Multiple factor models are commonly used to characterize how industry
factors and economy wide pervasive factors affect the return on individual securities and portfolios of securities. In such models a portfolio of
factors is used to replicate the return on a security as closely as possible.
Equation (1) gives a generic n-factor model that decomposes the return
on security i into different components:
˜ i, t = β F˜ + β F˜ + … + β F˜ + ε˜
R
i, 1 1, t
i, 2 2, t
i, n n, t
i, t

t = 1, 2, 3, …, T (1)

˜ i, t is the return on security i in period t; F˜ 1 represents the value
where R
of factor 1; F˜ 2 the value of factor 2; F˜ n the value of the nth factor and
ε˜ i is the “nonfactor” component of the return. The coefficients
β i, 1, β i, 2, …, β i, n represent the exposure of security i to the different set
of industry and economy-wide pervasive factors.
The expression
β i, 1 F˜ 1, t + β i, 2 F˜ 2, t + … + β i, n F˜ n, t + ε˜ i, t
is the particular combination (portfolio) of factors that best replicates
˜ i, t . In factor models the portfolio weights, β , β , …, β
the return R
i, 1 i, 2
i, n
need not sum to 1; and a factor, F˜ k, t , need not necessarily be the return
on a portfolio of financial assets.
Sharpe’s return-based style analysis can be considered a special case

of the generic factor model.4 In return-based style analysis we replicate
the performance of a managed portfolio over a specified time period as
best as possible by the return on a passively managed portfolio of style
benchmark index portfolios. The two important differences when compared to factor models are: (i) Every factor is a return on a particular
style benchmark index portfolio, and (ii) the weights assigned to the factors sum to unity. Rewriting equation 1 yields
˜
˜
R
p, t = [ δ 1, p x 1, t + δ 2, p x 2, t + … + δ n, p x n, t ] + ε t, p

t = 1, 2, 3, …, T (2)

˜
where R
p, t represents the managed portfolio return at time t and x1,t, x2,t,
…, xn,t are the returns on the style benchmark index portfolios. The slope
coefficients, δ1,p, δ2,p, …, δn,p, also referred to as style asset class exposures,
represent the average allocations among the different style benchmark
4

W. Sharpe, “Asset Allocation: Management Style and Performance Measurement,”
Journal of Portfolio Management, 18 (1992), pp. 7–19; and “Determining a Fund’s
Effective Asset Mix,” Investment Management Review, 2 (December 1988), pp. 59–
69.


8

THE HANDBOOK OF EQUITY STYLE MANAGEMENT

index portfolios during the relevant time period. The sum of the terms in
the square brackets is that part of the managed portfolio return that can be
explained by its exposure to the different style benchmarks and is termed
the style of the manger. The residual component of the portfolio return,
ε˜ t, p , reflects the manager decision to deviate from the benchmark composition within each style benchmark asset class. This is the part of return
attributable to the manager stock picking ability and is termed selection.
Given a set of monthly returns for a managed fund, along with comparable returns for a selected set of style benchmark index portfolios (asset
classes), the portfolio weights, δ1,p, δ2,p, …, δn,p, in equation (2) can be
estimated using multiple regression analysis. However, in order to get coefficients’ estimates that closely reflect the fund’s actual investment policy, it
is important to incorporate restrictions on the style benchmark weights.
For example, the following two restrictions are typically imposed:
δ j, p ≥ 0

∀j ∈ { 1, 2, …, n }

δ 1, p + δ 2, p + … + δ n, p = 1

(3)
(4)

The first restriction corresponds to the constraint that the fund manager is not allowed to take short positions in securities. The second restriction imposes the requirement that we are interested in approximating the
managed fund return as closely as possible by the return on a portfolio of
passive style benchmark indexes. The “no short-sale constraint” is standard for pension funds and mutual funds. For funds that employ some
leverage, short-selling, or derivatives (such as hedge funds discussed later
in this chapter), other bounds may be invoked.5
As before, the objective of the analysis is to select a set of coefficients that minimizes the “unexplained” variation in returns (i.e., the
variance of ε˜ t, p ) subject to the stated constraints. The presence of inequality constraints in (3) requires the use of quadratic programming to
estimate the parameters since standard regression analysis packages typically do not allow imposing such restriction. Writing equation (2) in
vector form and rearranging the terms yields
E p = R p – X∆ p

5

(5)

The Investment Company Act of 1940 requires mutual funds to state their likely
use of derivatives in their prospectuses. Although most of the mutual funds do explicitly state so in their prospectuses, they rarely use derivatives. See J.L. Koski and
J. Pontiff, “How Are Derivatives Used? Evidence from the Mutual Fund Industry,”
Journal of Finance, 54 (1999), pp. 791–816. They find that only 20% of the mutual
funds in their sample of 675 equity mutual funds invest in derivatives.


Style Analysis: Asset Allocation and Performance Evaluation

9

where X is the T × n matrix of asset classes returns, Rp is the T × 1 vector of portfolio returns and ∆p is the n × 1 vector of slope coefficients δ1,
δ2, …, δn. The term on the left Ep is the T dimensional vector [ε1,p, …,
εT,p]′ of differences between the returns on the fund and the returns on
the portfolio of passive benchmark style indexes corresponding to the n
dimensional vector ∆p of style benchmark portfolio weights (also
referred to as asset class exposures).
The goal of return-based style analysis is to find the set of nonnegative, style-asset class exposures, ∆' p = δ1,p, δ2,p, …, δn,p, that sum to 1
and minimize the variance of ε˜ t, p , referred to as fund’s tracking error
over the style benchmark. The objective of this analysis is to infer as
much as possible about a fund’s exposures to variations in the returns of
the given style benchmark asset classes during the period of interest.
The mathematics of this procedure is fully explained in Chapter 19 in
this book by Thomas Becker.
The style asset class exposures, referred to hereafter as style, identified
by return based style analysis represent the average style over the period

covered when style varies over time. The return on the portfolio of passive
benchmark style indexes is commonly referred to as the style benchmark
return for the fund. In any given month the return on the fund will in general be different from the style benchmark return. That may be due to style
rotation, i.e., time variations in the style of the fund and selection of securities within asset classes in a way that is different from the composition of
the securities that make up the primitive style indexes used in the analysis.

Active Versus Passive Management
The decomposition of a managed portfolio return into two components,
style and selection, provides a natural distinction between “active” and
“passive” managers. An “active” manager is looking for ways to improve
performance by investing in asset classes as well as individual securities
within each asset classes that she considers underpriced. She will therefore deviate from the style of the performance benchmark index (i.e., tilt
towards style benchmarks that she considers undervalued and away from
style benchmarks she considers overvalued), and select individual securities within each style benchmark asset class that she considers as being
good buys. Hence she will typically have different exposure to the style
benchmark asset classes when compared to her performance benchmark.
She will also be holding a different portfolio of securities within each style
benchmark asset class. She may also be holding securities that fall outside
the range of asset classes spanned by the style benchmarks.
As a result, the benchmarks will have a lower explanatory power and
the residual terms ε˜ i will be larger in absolute value for the managed
funds when compared to their respective performance benchmarks. In