Active Investing versus Index Investing:
An Evaluation of Investment Strategies
A Study Project presented to the
Graduate School of Business of the University of Stellenbosch
In partial fulfilment of the requirements for the degree of
Master of Business Administration
By
Daniel Rossouw Wessels
Study Leader:
Prof JD Krige
Degree of Confidentiality:
A
ii
Declaration
Hereby I, Daniel Rossouw Wessels, declare that this study project is my own original
work and that all sources have been accurately reported and acknowledged, and that
this document has not previously in its entirety or in part been submitted at any
university in order to obtain an academic qualification.
Daniel R Wessels
30 September 2004
iii
Preface and Acknowledgements
At the outset I set myself the goal to research a topic that would be enriching, far
more than just to obtain a formal qualification that would contribute to my overall
qualities as a professional investment advisor.
Starting off with the help and guide of my study leader, Professor Niel Krige, I did not
realise, nor have the expectation that the research topic of active versus index
investing would match my personal goals and ambitions. Yet, I soon discovered that
this journey I embarked upon had many twists in the tale. There were many truths to
uncover, back-to-basic disciplines to be studied and then maybe the topic was just
controversial enough to trigger my real enthusiasm for the task at hand.
Professional investors and consultants I came across either hated or loved index
investing (mostly the former), few had a moderate view. Looking back I understand
their perspectives, either they did not do similar in-depth studies or they simply
represented active management companies. They were probably not supposed to
question alternative strategies, besides the fact that they are ultimately investors too.
The sole focus of the study was done as seen from an investor’s perspective, which is
and should be relevant for the investment advisor. This study is an independent view,
not supporting or necessarily being supported by any particular interest group. It is not
about whether one advocates or promotes the interest of active management versus
index investing or vice versa. The story line of this study begins with the classical
active versus passive debate, and ends with an active and passive argument, which I
believe will be in the best interest of investors.
iv
I owe my sincere gratitude to the following institutions and individuals:

The University of Stellenbosch Business School for using their resources;

Personnel at the Library of the University of Stellenbosch Business School for
their professional assistance;

My study leader, Professor Niel Krige, for his sincere advice, guidance and
willingness in the planning and completion of my study;

Dr Martin Kidd at the Centre for Statistical Consultation at the University of
Stellenbosch, for his help in developing a useful database;

Professors Eon Smit and Wim Gevers at the University of Stellenbosch
Business School for listening to my ideas and giving advice;

Friends like Mr Johan Adler and Ms Estelle Du Toit, who regularly kept me
on my toes and pushed (or pulled!) me towards the completion of my studies;

My parents who convinced me to walk the extra mile in starting the study;

Last, my dear family whose patience has been tested and re-tested. It would
not have been possible without their understanding and sacrifice.
v
Opsomming
Die twee verskillende beleggingsbenaderings, naamlik aktiewe en passiewe (indeks)
beleggingsbestuur, is beoordeel deur die gemiddelde opbrengste van die aktiefbestuurde fondse in die algemene aandeelkategorie van die Suid-Afrikaanse
effektetrustbedryf met hul beleggingsmaatstaf, die ALSI indeks, te vergelyk.
Verskillende vergelykende metodes is in die ontleding gebruik wat die oorsigtydperk
1988-2003 gedek het.
Indien aanvangskoste by die aktief-bestuurde fondse buite rekening gelaat word, het
hul gemiddelde opbrengs oor die algemeen die opbrengste van die indeks oorskry.
Wanneer dié koste wel in ag geneem word, het die indeks egter die gemiddeld van die
aktief-bestuurde fondse geklop. Soortgelyk, het die indeks beter as die gemiddelde
van die risiko-aangepaste opbrengste van die aktief-bestuurde fondse vertoon.
‘n Indeksbenadering sou ten spyte van sy beter opbrengste oor die algemeen nie ‘n lae
risiko strategie verteenwoordig nie en beleggers sou wisselvallige opbrengste
ondervind het. ‘n Indeksbenadering en aktiewe bestuur het mekaar oor die verloop
van tyd herhaaldelik afgewissel as die dominante beleggingstrategie. ‘n Eensydige
benadering ten opsigte van enige van die strategieё sal nie deug nie en dit word eerder
voorgehou dat ‘n integrasie van beide strategieё in die verlede die hoogste opbrengs
per risiko-eenheid sou opgelewer het.
Deur verskillende kombinasie-moontlikhede oor verskillende beleggingsperiodes te
toets, is bevind dat die hoogste opbrengs per risikovlak verkry word deur die
indeksbenadering te verhoog met ‘n toename in die beleggingshorison. Eenvoudig
gestel, hoe langer die beleggingstermyn, hoe meer passiewe bestuur moet in die
beleggingsportefeulje gevolg word.
Hierdeur kan aangevoer word dat aktiewe bestuur oor die langer termyn moeilik die
mark gaan uitpresteer. Indien ‘n belegger in die langtermyn doeltreffendheid van die
mark glo, behoort die beleggingstrategie dienooreenkomstig daarby aangepas te word
en nie volgens die korttermyn prestasies van aktiewe bestuurders nie.
vi
Abstract
The two investment strategies, active and passive (index) investing, were evaluated by
comparing the average performance of actively managed funds in the general equity
category of the South African unit trust sector with its benchmark, the ALSI index.
Various comparative methodologies were followed in the analysis and covered the
period 1988-2003.
When the upfront costs applicable to the active funds were excluded it was found that
active funds on average outperformed the index benchmark. However, when including
these costs the index outperformed the average of active fund returns. Similarly, on a
risk-adjusted basis the index benchmark fared better than the average of actively
managed funds.
Index investing, despite its superior performance on average, would not have been a
low risk strategy and investors would have experienced volatile returns. Over time
index investing and active management repeatedly replaced one another as the
dominant investment strategy. A fundamentalist approach about any one of the
strategies is not prudent and it is argued that an integration approach of both strategies
would have yielded the highest reward per unit risk, based on past experience.
When following a strategy of combining both strategies in various combinations over
different investment periods, it was found that the highest reward to risk ratio was
attained by increasing index investing relative to active investing with an increase in
the investment horizon. Simply put, the longer one’s investment term, the more index
investing should be followed.
Hereby it can be argued that over the long run it is difficult for active management to
consistently beat the market. Therefore, investment strategies should be aligned with
one’s faith in the efficiencies of markets over time and not be overly influenced by
short-term performance records of active managers.
vii
Table of Contents
Declaration .....................................................................................................................ii
Preface and Acknowledgements ...................................................................................iii
Opsomming .................................................................................................................... v
Abstract ......................................................................................................................... vi
List of Tables ................................................................................................................ ix
List of Figures ..............................................................................................................xii
List of Appendices ...................................................................................................... xvi
CHAPTER 1:
INTRODUCTION & PROBLEM FORMULATION ....................... 1
1.1
Introduction .................................................................................................... 1
1.2
Setting the Context of the Study .................................................................... 2
1.3
Defining the Framework of the Study ........................................................... 3
1.4
Aim and Objectives of the Study ................................................................... 4
1.5
Methodology .................................................................................................. 4
1.6
Outline of the Study ....................................................................................... 6
CHAPTER 2:
THE THEORETICAL FRAMEWORK ............................................ 7
2.1
Arguments for Passive and Active Investing ................................................. 7
2.2
The Active/Passive Debate: Facts and Fallacies .......................................... 10
2.3
Synopsis of the Active/Passive Debate ........................................................ 14
2.4
Complexities facing Active and Passive Investment Strategies .................. 17
2.4.1
Tracking the Index ............................................................................... 17
2.4.2
Beating the Index ................................................................................. 18
2.5
Summary ...................................................................................................... 23
CHAPTER 3:
THE INTERNATIONAL EXPERIENCE ....................................... 24
3.1
Comparative Studies: Active versus Passive ............................................... 24
3.2
The Interpretation of Comparative Studies: Caveats ................................... 26
3.3
Alternative Performance Measurement: Return-based Style Analysis ........ 28
3.4
The Impact of Costs on Performance ........................................................... 29
3.5
The Effect of Survivorship Bias .................................................................. 30
3.6
The Capitalisation-Weighted Comparison ................................................... 30
3.7
Summary ...................................................................................................... 32
CHAPTER 4: THE SOUTH AFRICAN EXPERIENCE: ACTIVE INVESTING
VERSUS PASSIVE INVESTING ....................................................... 33
viii
4.1
Comparison on a Before- and After-Cost Basis .......................................... 33
4.1.1
Methodology ........................................................................................ 33
4.1.2
Analysis of Results .............................................................................. 37
4.2
Comparison on a Risk-adjusted Basis.......................................................... 54
4.2.1
Methodology and Explanation of Terminology ................................... 54
4.2.2
Analysis of Results .............................................................................. 57
4.3
Summary ...................................................................................................... 84
CHAPTER 5: THE PERSISTENCE OF ACTIVE MANAGEMENT
PERFORMANCE ................................................................................ 85
5.1
Review of International Studies ................................................................... 85
5.2
The South African Experience: Persistence in Fund Performance .............. 89
5.3
Persistence Analysis ..................................................................................... 90
5.3.1
Methodology ........................................................................................ 90
5.3.2
Results .................................................................................................. 91
5.4
Summary .................................................................................................... 104
CHAPTER 6:
TOWARDS AN OPTIMAL COMBINATION SOLUTION ........ 105
6.1
The Question .............................................................................................. 105
6.2
Theoretical Framework .............................................................................. 106
6.3
Developing an Optimal Allocation Model ................................................. 112
6.4
Results from the Optimal Allocation Model .............................................. 115
6.5
The Quest for an Optimal Solution ............................................................ 120
CHAPTER 7:
THE ROAD AHEAD: APPLYING PASSIVE STRATEGIES .... 127
CHAPTER 8:
ANSWERING THE SCEPTICS................................................... 130
CHAPTER 9:
CONCLUSIONS AND RECOMMENDATIONS ........................ 131
9.1
Conclusions ................................................................................................ 131
9.2
Recommendations for Implementing Investment Strategies ..................... 134
9.3
Recommendations for Future Research ..................................................... 135
LIST OF SOURCES .................................................................................................. 137
APPENDICES ........................................................................................................... 142
ix
List of Tables
Table 2.1:
The Probabilities of Active Management Outperforming an Index….11
Table 2.2:
Perceived Opportunity versus Effective Opportunity………………..20
Table 2.3:
Relative Performance in Different Markets……………………….....22
Table 3.1:
Capitalisation-weighted versus Equally-weighted Performances……27
Table 4.1:
The Cost Structure of Actively Managed Funds in the
General Equity Unit Trust Sector……………………………………35
Table 4.2:
The Performance Record of Actively Managed Funds versus the
Index on a Cumulative Return Basis…………………………………38
Table 4.3:
Random Sampling:
Comparison between Active and Passive Investing……………….....41
Table 4.4:
Comparison between Active and Passive Investing over
Rolling Three-, Five-, and Ten-year Periods…………………………47
Table 4.5:
Risk Data of Actively Managed Funds over
Rolling 36-month Investment Periods………………………………..58
Table 4.6:
Risk Data of Actively Managed Funds over
Rolling 60-month Investment Periods………………………………..59
Table 4.7:
Risk Data of Actively Managed Funds over
Rolling 120-month Investment Periods………………………………60
Table 4.8:
Statistical Significance of Sharpe Ratios……………………………..65
x
Table 4.9:
Statistical Significance of Treynor Ratios……………………………69
Table 4.10:
Value Added by Actively Managed Funds over
Rolling 36-month Investment Periods………………………………..74
Table 4.11:
Value Added by Actively Managed Funds over
Rolling 60-month Investment Periods………………………………..75
Table 4.12:
Value Added by Actively Managed Funds over
Rolling 120-month Investment Periods………………………………75
Table 5.1:
Percentile Ranking of Actively Managed Funds over
Rolling 36-month Investment Periods……………………………......96
Table 5.2:
Percentile Ranking of Actively Managed Funds over
Rolling 60-month Investment Periods………………………………..97
Table 5.3:
Percentile Ranking of Actively Managed Funds over
Rolling 120-month Investment Periods………………………………97
Table 5.4:
Consistency of Actively Managed Funds in Beating the
ALSI Index…………………………………………………………...98
Table 5.5:
Relative Movement of Actively Managed Funds between
Deciles over Different Forward-looking Periods…………………...100
Table 6.1:
Example of Optimal Manager Allocations…………………….........111
Table 6.2:
Risk Data and Ranking of Actively Managed Funds over
Rolling 60-month Investment Periods………………………………112
Table 6.3:
Data input of the Optimal Allocation Model………………….…….115
xi
Table 6.4:
Optimising Results with 70th Percentile
Active Investment Performance…………………………………….116
Table 6.5:
Optimising Results with 75th Percentile
Active Investment Performance…………………………………….117
Table 6.6:
Optimising Results with 80th Percentile
Active Investment Performance…………………………………….118
Table 6.7:
Optimal Allocation between Active and Passive Strategies
at an expected 0.6% per month Excess Return……….……………..121
Table 6.8:
Return and Risk Measures for Active and Index Investing…………122
xii
List of Figures
Figure 4.1:
Impact of Initial Charges on Investment Performance over Time…...36
Figure 4.2:
Cumulative Performance of Active versus Passive Investing
(1988-2003)…………………………………………………………..39
Figure 4.3:
Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Three Years…………...43
Figure 4.4:
Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Five Years……………..44
Figure 4.5:
Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Ten Years……………..45
Figure 4.6:
Active versus Passive Investing over
Rolling 36-month Investment Periods………………………………..49
Figure 4.7:
Active versus Passive Investing over
Rolling 60-month Investment Periods……………………………….50
Figure 4.8:
Active versus Passive Investing over
Rolling 120-month Investment Periods………………………………51
Figure 4.9:
Beating the Index over Rolling 36-month Investment Periods………52
Figure 4.10:
Beating the Index over Rolling 60-month Investment Periods………53
Figure 4.11:
Beating the Index over Rolling 120-month Investment Periods…......53
xiii
Figure 4.12:
Return/Risk Profile of Actively Managed Funds and Index over
Rolling 36-month Investment Periods………………………………..62
Figure 4.13:
Return/Risk Profile of Actively Managed Funds and Index over
Rolling 60-month Investment Periods………………………………..63
Figure 4.14:
Return/Risk Profile of Actively Managed Funds and Index over
Rolling 120-month Investment Periods………………………………64
Figure 4.15:
Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 36-month Investment Periods………………………......66
Figure 4.16:
Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 60-month Investment Periods………………………......67
Figure 4.17:
Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 120-month Investment Periods…………………………68
Figure 4.18:
Treynor Ratio of Active versus Passive Investing over
Rolling 36-month Investment Periods……………………………......70
Figure 4.19:
Treynor Ratio of Active versus Passive Investing over
Rolling 60-month Investment Periods………………………………..71
Figure 4.20:
Treynor Ratio of Active versus Passive Investing over
Rolling 120-month Investment Periods………………………………72
Figure 4.21: Alpha/Active Risk Profile of Actively Managed Funds over
Rolling 36-month Investment Periods………………………………..77
Figure 4.22:
Alpha/Active Risk Profile of Actively Managed Funds over
Rolling 60-month Investment Periods………………………………..78
xiv
Figure 4.23:
Alpha/Active Risk Profile of Actively Managed Funds over
Rolling 120-month Investment Periods………………………………79
Figure 4.24: Average Information Ratio over Rolling 36-month
Investment Periods…………………………………………………...81
Figure 4.25:
Average Information Ratio over Rolling 60-month
Investment Periods…………………………………………………...82
Figure 4.26:
Average Information Ratio over Rolling 120-month
Investment Periods…………………………………………………...83
Figure 5.1:
Quartile Ranking of Actively Managed Funds over
Rolling 36-month Investment Periods………………………………..92
Figure 5.2:
Quartile Ranking of Actively Managed Funds over
Rolling 60-month Investment Periods………………………………..93
Figure 5.3:
Quartile Ranking of Actively Managed Funds over
Rolling 120-month Investment Periods………………………………94
Figure 5.4:
Tendency of Actively Managed Funds to Move between Deciles
on a Month-to-Month basis…………………………………………102
Figure 5.5:
Tendency of Actively Managed Funds to Move between Deciles
on a Quarterly basis…………………………………………………102
Figure 5.6:
Tendency of Actively Managed Funds to Move between Deciles
on a Yearly basis……………………………………………………103
Figure 5.7:
Tendency of Actively Managed Funds to Move between Deciles
on a Three-yearly basis……………………………………………...103
Figure 6.1:
Efficient Frontier of Optimal Combination Strategies……………...109
xv
Figure 6.2:
Distribution of Alphas across Actively Managed Funds over
Rolling 60-month Investment Periods………………………………113
Figure 6.3:
Distribution of Active Risk across Actively Managed Funds over
Rolling 60-month Investment Periods………………………………113
Figure 6.4:
Distribution of Information Ratios across Actively Managed Funds
over Rolling 60-month Investment Periods…………………………114
Figure 6.5:
Example of Optimal Actively Managed and Index Fund Weights
in an Investment Portfolio given various Market Returns………….116
Figure 6.6:
Example of Optimal Actively Managed and Index Fund Weights
in an Investment Portfolio given various Market Returns…. ………117
Figure 6.7:
Example of Optimal Actively Managed and Index Fund Weights
in an Investment Portfolio given various Market Returns………….118
Figure 6.8:
Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 36-month Investment Periods………....123
Figure 6.9:
Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 60-month Investment Periods…………124
Figure 6.10:
Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 120-month Investment Periods………..125
xvi
List of Appendices
Appendix A: Cumulative Return Performance:
Active versus Index Investing………………………………………143
Appendix B: Statistical Tests for the Random Sampling Investment Periods….…151
Appendix C: Statistical Tests for the Rolling Investment Periods………….…….155
Appendix D: Statistical Tests for Risk-adjusted Return Comparisons…................159
Appendix E: Cost Structures of Index Funds……………………………………..163
Appendix F: Tracking Error Analysis for Index Funds………………………...…165
Appendix G: Backtesting Combinations of Active and Passive Investing over
Various Rolling Investment Periods………………………………...169
Appendix H: Memorable Quotes from the Past…...………………………………171
1
CHAPTER 1:
1.1
INTRODUCTION & PROBLEM FORMULATION
Introduction
The advent of exchange traded index funds (ETFs) in South Africa, like the SATRIX
40, over the last couple of years and the attention that it consequently received from
investors and the media have put the concept of index investing in the limelight.
Internationally across the major world markets, ETFs received phenomenal uptake
and success and about $150 billion is invested in 250 ETFs globally. Beside the recent
spate of ETF investing, international investors have over the last decade been steadily
investing in index mutual funds and it is reckoned that between 20-30% of all
invested monies in the United States of America and United Kingdom are invested in
index funds.
In South Africa, to the contrary, index funds attracted no real attention. At the end of
December 2003 a mere 1.5% (about R1 billion) of all invested monies in local equity
unit trusts were allocated to pure index funds. The launch of ETFs by SATRIX and
ABSA have been relatively more successful than the unit trust experience and
accumulated assets to the value of R6 billion at the end of 2003. In general, promotion
of these products concentrates on the convenience and low cost of owning a
substantial share of market returns.
However, these developments do not take place without questions being asked by
sceptics. For example, “Are these low-cost investment vehicles just the latest fad in a
range of investment fads seen in the past?” or “Where does index investing fit in with
many active fund managers out there that supposedly know much more than the
market?”
The study will endeavour to answer these and many other questions in the pursuing
journey of discovering the optimal investment strategy.
2
1.2
Setting the Context of the Study
The investment of capital, whether private or institutional, entails two distinct
processes, namely the formulation of an investment policy and then the investment
strategy to be followed. The former evolves around the question of what asset class
selection (equities, bonds, properties and cash) to use for a chosen set of risk profiles
and time horizons, while the investment strategy refers to the methods used to invest
capital.
Essentially two investment strategies can be identified, namely active investing and
passive investing. The former - whether done by a professional manager on behalf of
investors or by an individual for him/herself - requires active and continuous decisionmaking of which assets to buy and sell, thereby striving for superior returns against
the market average (index). This method necessitates asset selection and market
timing, but comes at a price for investors; both transactional and management fees
will deflate potential returns. Passive investing1 or index investing on the other
accepts the market average (index); it is not concerned with asset selection, but only
to minimise investment costs. Herein lies the basic difference between the two
strategies - superior returns at a cost versus average returns at minimal costs.
The question arises then which strategy is the ultimate or to be more precise with
which strategy an investor will stand the best chance to achieve real growth over time.
Basically it boils down to whether with active investing the extent of achieving aboveaverage returns over time will surpass its cost factors to beat an index investing
strategy.
Passive investing could also refer to a “buy and hold” strategy - basically to make an asset selection
and then backing that decision throughout market cycles. This strategy however is probably more
applicable to individual investors than professional managers. Arguably the most successful investor of
all times – Warren Buffet- is an exponent of this style of investing (Steele, 1999: 200).
1
3
1.3
Defining the Framework of the Study
Active investing done on a professional basis should be appealing at least in theory to
investors by entrusting monies to professional investment managers who supposedly
have the skills and knowledge to beat the market in a very complex environment. For
these professional services fees are charged, upfront and continuous. It represents a
hurdle rate for investors when comparing their returns with the market, in other words
the extra return generated by active investing must first cover these expenses before
the magical out-performance can be attained.
Active investing is a disciplined and scientific approach and success in terms of outperformance should have a high probability, yet reality and past experience indicate
otherwise. Investment performances, especially for portfolios predominantly invested
in equity markets are volatile and fairly unpredictable. No professional money
manager can guarantee that the returns from the investment fund would be better than
the market average (index), or that the out-performance of the market will be
consistent.
The advent of index investment funds internationally over the last two decades has
provided investors with an alternative to active investing at much reduced fees.
Various international studies in the past decade have shown that index investing
outperformed the average actively managed fund and led to the widespread adoption
of this strategy. In most developed capital markets around the world up to 20-30% of
equity investment funds (institutional and private) are invested in index funds and are
growing fast, yet in South Africa index investing is miniscule by comparison and
probably well less than 5% of investment funds are invested in this fashion.
The question arises why the South African investment community has not joined the
worldwide trend in index investing over the past decade. In essence, were the returns
that investors received from active-only investment strategies justifiable and would
there have been scope for index investing?
4
1.4
Aim and Objectives of the Study
The purpose of the study would be to gain insight whether index investing could have
contributed to the overall investment performance of the South African investor in a
historical sense.
The study will be narrowed by focusing on the performances of equity funds in the
South African unit trust industry against its appropriate index benchmark (ALSI) over
the last fifteen years (1988-2003). The overall objective of the study would then be to
answer whether actively managed unit trust funds in the General Equity Sector as a
group outperformed their appropriate benchmark, the ALSI index, over different time
intervals by adjusting for cost and risk measures.
Typical questions to be answered by the study include:
-
Did active fund managers as a group outperform the index over time?
-
Did active fund managers outperform the index after considering upfront
costs?
-
Did active fund managers consistently beat the index?
-
Did active fund managers outperform the index on a risk-adjusted basis?
-
Did the top-performing active fund managers consistently outperform their
peers?
1.5
Methodology
The comparative analysis between active and index investing was performed over
various time spans, which included three, five and ten year periods covering the
period 1988-2003. Comparisons between the strategies were done on a before-cost,
after-cost and risk-adjusted basis to gauge the sensitivities of the results.
Unit price data from the McGregor Raid Station database, available at the University
of Stellenbosch Business School, were used to evaluate the historic performance of
active fund managers. The minimum criterion to include a fund in the analysis was set
at a minimum of three years (36 months) of price data. At the end of 2003 thirty-two
5
active funds in the general equity sector of the South African unit trust industry were
identified. Data on four of these funds dated back to the beginning of 1988 and
formed the starting point of the analysis.
In the general equity sector three index funds were identified, but data dated only back
to 1995. Only one of these funds (Investec Index Fund) represents a true low-cost
index fund, which would fit the definition of a proper index or passive strategy.
Further, the underlying rules that allowed index funds to hold more than 10% of a
specific stock only came into effect in 2003, which is a prerequisite in the South
African milieu with its fairly skewed market capitalisation index.
To overcome the insufficient time span and general deficiencies of the available index
funds it was therefore decided to rather use the underlying benchmark, the FTSE JSE
All Share Index (ALSI) as a proxy for how index investing would have performed
since 1988. Data therefore were obtained from the McGregor Raid Station database.
The use of the ALSI would imply passive investing at zero cost and no tracking
errors, which is unrealistic, but at the same time actively managed funds that were
terminated or merged with other active funds were not available on the database and
thus excluded from the study. These “dead” funds were invariably poor performers
and by excluding them from the analysis it would have enhanced the average
performance of the surviving actively managed funds (survivorship bias). Therefore,
one could argue that these effects would at least cancel each other out.
6
1.6
Outline of the Study
A sensible debate requires a thorough understanding of the principles and theories of
active and passive investing. Therefore much emphasis in the study is initially given
to the basic concepts which will guide one in formulating a knowledgeable argument
either for or against any one of the strategies.
Following the theoretical background a review of past international studies and
comparisons between active and passive investing will be discussed. Different
methodologies and possible caveats in interpreting results and findings are shown.
Thereafter the focus of the study will shift to its primary objective and compare the
performance of active investing with the index benchmark over the last fifteen years
in South Africa. Three different comparisons, namely cumulative performance,
random sampling and rolling investment periods, are used in comparing the results.
The strategies will be evaluated on a pre-cost, after-cost, and risk-adjusted basis.
Further analysis of the results will follow with the specific focus on identifying
performance persistence, which would indicate the reliability of past performance in
predicting future performance.
Consequently a theoretical framework for combining both active and passive
strategies will be developed. A practical application of the model will be tested which
will indicate what strategy or combination thereof would best serve the investment
public. Further, combinations of active and passive strategies for the past fifteen years
will be backtested to identify that strategy that would have added most value.
Last, if value is to be found in passive investing the question remains why does the
use of index funds lag active investing as a popular investment strategy? Possible
reasons are discussed and options for passive investing are given to conclude the
study.
7
CHAPTER 2:
2.1
THE THEORETICAL FRAMEWORK
Arguments for Passive and Active Investing
Three fundamental premises can be identified in evaluating arguments for active and
passive investment strategies.
A)
Active Investing is a Zero-sum Game
Investment performance over time is a positive-sum game - real wealth is created by
exposing capital to markets, which share in the growth of economies. Conversely,
active investing is very much a zero-sum game relative to its index - for every winner
in the market place there must be a loser. The net result of all this active trading in the
marketplace yields the market average or index performance.
Sharpe (1991: 7) developed the theory, which he consequently called The Arithmetic
of Active Management, that before costs the average actively managed investment
would equal the return of the passively managed investment, and that after costs, the
return of the actively managed investment would be less than the return on the
passively managed investment.
Thus purely from a mathematical viewpoint and when properly measured, about 50%
of active investors will under-perform the index. But then by taking into account the
additional costs of active investing, it stands to reason that more than 50% of active
investors will under-perform the index over time (Mintz, Dakin & Willison, 1998:
84).
Further studies by Surz & Stevens (1999) and Ibbotson & Kaplan (2000) confirmed
and strengthened Sharpe’s thesis. Both pairs extended on the work done by Brinson,
Singer & Beebower (1991), which indicated that asset allocation (investment policy)
explained about 90% of the variability in a fund’s performance over time. Ibbotson &
Kaplan (2000: 32) studied both mutual funds and pension plans and found, besides
confirming the result of Brinson, et al. (1991) that asset allocation explained on
average more than 100% of the typical fund’s return level. Active management on
8
average did not add any value above the policy benchmarks and after costs actually
diluted performance. When evaluating the variation in returns among active funds, the
differences in management (style, selection, timing, and fees) did explain 60% of the
variation versus the 40% of the asset allocation decision.
Sharpe (1991: 8) noted that performance evaluations did not always reveal the theory
and identified three main reasons why deviations are possible:
First, when passive managers are not truly passive. Either index funds use only
sample selections of the market and do not track the market properly or charge fees
equal to those of active managers.
Second, active managers do not fully represent the non-passive component of the
market. Individual stock investors are another group of active participants in the
market. Active managers on the aggregate can outperform passive funds, but then
only at the cost of the individual active group.
Last, the equation holds on a capitalisation-weighted average. If the average of active
funds is measured on an equally-weighted basis the thesis might not apply any more.
B)
Efficient Market Hypothesis
A further basis for examining the two investment strategies centres on the efficient
market hypothesis (EMH). When an investor perceives the market to be
informationally efficient he/she believes that the current price of an asset reflects all
the possible information that would have a bearing on that price. No exceptional
performance relative to the market is possible. Thus, by believing that the market will
over time always be correct it would not make sense to follow an active investment
strategy, but rather a low-cost index investing strategy.
9
Conversely, the opposite will hold for inefficient markets, where not all the
information is discounted into the asset price, hence opportunities exists for active
investors to beat the index.
Malkiel (2003: 2) however argued that inefficiencies (anomalies) are generally small
relative to the costs required to exploit them. Further, ex post enough evidence exists
that the market can make large judgement errors in the valuation of certain classes of
securities, but ex ante no clear arbitrage opportunities exist.
Last, but not least, Sharpe’s thesis will stand irrespective whether markets are
perceived to be efficient or not. Inefficient markets would probably lead to a wider
dispersion between the winners and losers, but active investing will remain a zerogame.
C)
Risk
An index replicates a specific market or sector as a whole and would be spread among
various sectors of the economy. By indexing, non-systematic or specific risk is
minimised and only market or systematic risk is assumed. Thus, an index investment
would per se be a well-diversified portfolio.
The active investor will invariably deviate from the market index and beside market
risk will assume specific risk (Kirzner, 2000: 16). Therefore it is conceived that the
active investment portfolio could have a higher risk profile than the index portfolio.
Even if the active investment yields a higher return than the index a comparison
between the two strategies should be done on a risk-adjusted basis.
An index in itself does not imply a low risk investment. Kat (2003: 59) argued that an
equity index is designed to track the overall movement of the stock market and stocks
are merely included on the basis of their market capitalisation. Over time the
composition of indices tends to be unstable with the continuous change in weightings
of individual stocks.
10
Thus, an index investor will face the possibility of changing risk profiles all the time.
For example, it is noted that the technology sector made up 30-35% of the S&P 500
index in 2000 (before the market crash), twice as high it was a mere two years before.
Since 2000 the technology sector returned back to its 15% level. An index investor
without realising the changing risk profile of the S&P500 would have incurred major
losses.
Therefore, Kat (2003: 58) argued that, although by collecting and analysing
information no pay off in efficient markets could be expected, without collecting and
analysing data investors would not gain any insight into the risk-return pay-offs of the
various assets. The process might not directly lead to better returns, but it contributes
to better decision-making and risk management. A passive investment strategy thus
should not imply to be literally passive about investments.
2.2
The Active/Passive Debate: Facts and Fallacies
“Index investing is a much cheaper investment alternative than active management”
Since the sole purpose of index investing is to replicate a specific market, no active
decision-making is required, no active research needs to be done, and no active
management is necessary. Human intervention is therefore minimised. Hence, both
the trading costs and management fees of indexing should be much lower than with
active investing.
Martin (1993) in Kirzner (2000: 27) estimated that active managers face a “hurdle
rate” of 1.25% per annum against passive investing, i.e. the minimum outperformance required to cover the additional cost of active management. Further,
Martin estimated in his study the probabilities of active managers to outperform an
index by taking into account the overall cost impact of active investing. These are
showed in Table 2.1.
11
Table 2.1: The Probabilities of Active Management Outperforming an Index
Number of Years
One Manager
Multi-Manager
Multi-Manager
(Three Managers)
(Five Managers)
1
41%
33%
29%
5
29%
17%
11%
10
22%
9%
4%
20
14%
1%
1%
Source: Martin (1993) in Kirzner, 2000: 28-29
“Active investing would do better than passive investing in inefficient markets”
Sharpe’s thesis will stand irrespective of whether markets are perceived to be efficient
or not. Since performance evaluation is normally measured on an equally-weighted
basis the average of active investing versus passive investing might look better in such
markets, but in reality it cannot be. If active managers on the aggregate outperformed
the index it could only have been at the expense of other non-passive participants.
“Active investing offers better bear market protection than index investing”
Since index funds are obliged to replicate their market benchmarks as closely as
possible cash balances would be kept to a minimum. On the other hand, active funds
would invariably have larger cash positions. Therefore logic determines that active
funds should outperform index funds in bear markets, beside the fact that the
managers could move to defensive stocks to limit their downside risk.2
Evaluation studies confirmed that active funds on average outperformed index funds
in major downtrends. However, the argument in favour of active investing is not very
strong since investors could have re-adjusted their asset allocations themselves.
2
If the argument is valid, the opposite for major bull markets would apply where cash holdings by
active managers would dilute returns.
12
Further, it is not very likely that a manager could predict the exact starting point of a
bear market to take some defensive positions.
“To go passive is to accept mediocrity.”
Multiple studies in the past have shown that passive investing in fact yielded an
above-average performance compared with the average of active management
strategies. Further, the argument denies that in general the market encompasses the
consensus view of a large number of informed participants.
“Indexing would lead to research deterioration”
Many critics note that indexing will decline the level and quality of research, but
Kirzner (2000: 31) argued that if research arbitrage develops with the large-scale use
of index investing it would lead to active managers intensifying their research efforts.
“Indexing creates negative market effects”
Critics argue that indexing causes price distortions, for example small-cap stock not
part of an index would attract less attention and stock included in the index would
attract more money than otherwise.
Woolley & Bird (2003: 307) noted that empirical studies found mixed evidence of a
permanent price effect for index stocks. Studies did indicate that the inclusion of a
stock in an index had at least an initial positive impact on price. On the other, deletion
from an index caused stock prices to fall.
13
“Indexing creates undesired economic effects”
The general theory is that if index investing would become the more preferred
investment method, larger inefficiencies in the market would appear for active
managers to exploit. Since these managers would then outperform index investing a
move back to active investing would result. Eventually a state of equilibrium between
active and passive investing will be found.
However, Woolley & Bird (2003) argued that the theory will not hold since investors
would not be able to recognise when active investing should be the investment
method of choice. The majority of active managers are likely to under-perform the
index, irrespective of whether markets are efficient or not.
Woolley & Bird (2003: 305) further argued that since many active managers are
evaluated against their benchmarks these managers preferred portfolio positions close
to the benchmarks (minimising tracking errors) and acted as quasi-index managers.
Therefore, beside index funds a strong and captive demand for stocks in the index
would exist from active managers. This would lead to situations where these stocks
have easier access to capital and might lead to the improper allocation of resources.
The buying spree of telecommunication, media and technology (TMT) companies in
the late 1990’s serves as a case in point. Additional stock by TMT companies was
issued and willingly accepted by the market, just to turn out to be major wasteful
investments.
“Money flowing into index funds would lead to the price inflation of securities
included in the index and eventually could cause markets to crash.”
Malkiel & Radisich (2001) investigated whether the notion that indexing is selffulfilling and would eventually lead to crashing markets. Their findings were that the
success of indexing is due to the general efficiencies of the market and the
performance gap between active and index investing is fully explained by
management and transaction costs. No empirical evidence was found that indexing
14
was causing the inflation of markets, or that it had a permanent effect on the pricing of
securities.
“Indexing is the ultimate momentum strategy.”
The popular notion is that indexing is similar to the futile strategy of “buying high,
selling low.” Arnott & Darnell (2003) were of the opinion that passive investing puts
the most money into the largest stock, and hence it represents a disproportionate
investment in stocks that have been most successful in the past.
Stein (2001) in Stein (2003: 45) argued that index investing is not a momentum
strategy since the same investment is made in all companies regardless of their price
or recent successes. The investor has to pay more for expensive stocks, but is not
buying more of them.
2.3
Synopsis of the Active/Passive Debate
There are both logical and emotional reasons why investors either prefer active or
passive investing. The emotional issues tend to push investors towards active
investing, while logic and reason will pull investors towards passive.
Three major considerations in the active or passive investing debate can be identified,
namely whether markets are perceived informationally efficient, whether active
managers with persistent skill can be identified and whether the benefits of active
investing will overcome the cost factor thereof (Stein, 2003: 39).
If an investor believes that markets are informationally efficient no scope would exist
for active investing and passive investing would be the only choice. However, past
experience has shown that active managers can outperform the market, albeit not
consistently. Further, irrational behaviour on markets occurs and poses opportunities
for active managers to exploit.
15
Stein (2003) argued that a belief in market efficiency might be sufficient for going
passive, but it is not necessary. Even in less than perfect efficient markets it is not
easy or obvious to add value. Ellis (1992) is quoted by Stein (2003: 41) as saying:
“The market isn’t hard to beat because it is dominated by stupid people. It’s hard to
beat because it’s dominated by very bright people.”
The second consideration requires differentiation between luck and skill, which in
itself is not easy to prove. The track record of an active manager would be a criterion,
but history has shown that little empirical evidence of long-term persistency exists.
Luck could be defined as random and completely unpredictable, whereas skill is
repeatable (Bein & Wander, 2002).
Active managers are hired on the
belief/perception that their past performances were largely attributable to skill. A
manager’s alpha attained over a period is normally used for evaluation purposes and
specifically whether the alpha is uncorrelated with specific styles, sectors or indexes.
Bein & Wander (2002) proposed that a fund manager’s track record should be
evaluated not only by the alpha, volatility and tracking error attained, but by an
analysis of the number of investment decisions made and corresponding success rate.
A strong correlation exists between portfolio turnover and number of active decisions
made. When evaluating two managers with similar track records, the one with the
higher portfolio turnover should have contributed more through skill than his
counterpart.
However it would be impossible to differentiate with absolute certainty between luck
and skill.3 Active managers in all likelihood would struggle to prove their worth to
proponents of passive investing. Rather, it is about what manager could in the most
convincing matter portray their abilities to identify mispriced opportunities. Taleb
(2001) in Stein (2003: 41) pointed out that a manager is considered good because he
made money, he did not make money because he was good.
3
Bodie, Kane & Marcus (1999: 765) showed by an example that more than 30 years of data would be
required to draw any statistically significant conclusion whether the alpha attained by a manager was
due to luck or skill!
16
Last, if the benefits of active investing (out-performance of the market) cannot exceed
the cost of active investing (transaction and trading costs, fees, and stock-specific risk
issues) then passive investing would be the logical choice. When properly accounted
for costs it is known from Sharpe’s thesis that over time well more than 50% of active
managers will under-perform the passive strategy. Hence, even if it was possible to
identify an above-average active manager it might not be good enough. One must be
able to identify a top performer to secure out-performance versus the passive strategy.
From a logical perspective passive investing would undoubtedly make most sense for
most investors. Yet, most investors choose to be active investors. Stein (2003: 42-44)
proposed the following non-quantifiable reasons why investors, despite the odds
stacked against them, choose the active route.
Agency arguments:
Many investors choose to invest through an investment advisor
or consultant who provides personal attention and fulfils the
need for human interaction and relationship.
Psychological arguments:
Active management satisfies the need for control, drama
or thrill and risk-taking. People derive pleasure from
ownership and the selection process of what to buy.
Authority & status arguments:
People like to believe they are independent
thinkers, superior to the mass of average people
and will incur expenses (buy active funds) in the
process to prove their uniqueness. Average is
not good enough, nor is that what people want to
hear, hence the idea of passive investing is
difficult to accept.
Stein (2003: 43) further argued that despite the non-economic sense of some of these
arguments it would play a major role in the decision process. Previous psychological
studies have shown that emotion and reason cannot easily be separated. Since money
to most people are more than its purchasing power and represent a central part of their
17
human being (wealth, security, and status) the value of active investing to investors
goes beyond its economic return.
Opportunities for active managers will always exist and at any point in time there
would be managers outperforming the market. In identifying those managers Stein
(2003: 44) proposed that investors would seek to understand the managers’ source of
skill and not be overly influenced by past performance. When choosing to go active,
investors would be paying for it and therefore it is worth aligning themselves with
those managers that would satisfy their needs, whether economic or psychological.
2.4
Complexities facing Active and Passive Investment Strategies
2.4.1 Tracking the Index
Potential difficulties arise for index managers attempting to exactly replicate the
returns of the target benchmark. Since the index is a mathematical calculation of the
relative weight of each security in the benchmark and re-calculated constantly, it
necessitates the index manager to constantly change the composition of the index.
However the index calculation supposes that re-balancing transactions can occur at
any time without transaction and price pressure (bid-ask spreads) costs, which is not
possible in the real world.
Frino & Gallagher (2001) therefore argued that tracking errors in index funds’
performance are unavoidable. Thus, besides replication, the secondary objective for
index managers would be to minimise divergence from the underlying benchmark, i.e.
minimising the tracking error.
A full replication strategy is costly due to the frequent number of transactions required
to re-balance the portfolio. Alternatively, the index manager could follow nonreplication techniques such as stratified sampling or optimised strategies where
subsets of securities are used which closely resemble the risk and return profile of the
index. These strategies are considerably cheaper to implement, but the potential for
18
tracking error is still high by excluding the securities that are not part of the sample
(Frino & Gallagher, 2002: 205).
In general the tracking error of index funds will be related to transaction costs, cash
flows into the index fund, volatility of the benchmark and changes in the composition
of the benchmark. Frino & Gallagher (2001 and 2002) found in their studies that
index funds in the USA and Australia experienced difficulties with tracking errors due
to the above reasons listed, but the errors were not significant. Therefore they
concluded that the index funds sampled in their study more or less accurately
portrayed the index benchmark.4
2.4.2 Beating the Index
Wander (2003: 54-57) identified two structural characteristics of an index benchmark
which will determine the difficulty level for a fund manager to outperform the index
benchmark and add real value for investors. First, the greater the number of securities
in the index benchmark, the more choices and opportunities the manager will have to
add value. Second, the more evenly weighted the underlying securities of the
benchmark are, the more opportunities the manager will have to outperform. When
benchmarks are concentrated (the index is dominated by a few large securities) the
effective opportunity of the manager is reduced very much and it would become more
difficult to beat the index on a constant basis.
Grinold (1989) in Wander (2003: 54) developed the theory “The Fundamental Law of
Active Management” which illustrates the impact of the number of securities in the
investment universe on the potential for adding value:
IR  IC  N
The added value (alpha) is measured by the information ratio (IR), the manager’s
skill is expressed by the information coefficient (IC) and the manager’s opportunity to
4
A tracking error analysis of three South African index funds in the general equity sector is shown in
Appendix F.
19
add value is expressed by the breadth of the strategy ( N ), which is determined by
the number of securities in the manager’s universe.
If two managers would have the same skill, the manager who has more stock to select
from can expect to add more value. For example, the manager that has 1,000 stocks in
his universe can expect to add twice the value of an equally-skilled manager who has
250 stocks in his benchmark.
Most traditional investment managers face a long-only constraint, thus they are not
allowed to short securities and hence their effective opportunities to add value are
reduced. This constraint is most notable when benchmark weights are highly
concentrated (Wander, 2003: 55).
For example, when one stock dominates the index, the manager can only
meaningfully overweight the other stocks by underweighting the dominant stock.
Such a portfolio’s performance is largely influenced by the manager’s view on the
dominant stock. Therefore, in a highly concentrated benchmark the manager has little
opportunity to exploit his/her skill. On the other hand, when the benchmark is equallyweighted the manager will have an effective opportunity close to the number of stocks
in the index.
Wander (2003) made use of the “Herfindahl Index” methodology (used by economists
to measure the degree of competition amongst firms in a specific industry) to calculate
the effective opportunity some well-known indexes offered to active managers.5
Table 2.2 summarises Wander’s results. The “Efficiency Ratio” refers to the ratio of
“Perceived Opportunity” (actual number of stocks in the index) versus the “Effective
Opportunity” (measured by the Herfindahl methodology).
5
The effective number of stocks (N) in an index is calculated by the inverse of the relative weight of
each stock, squared.
20
Table 2.2: Perceived Opportunity versus Effective Opportunity
Benchmark
Perceived
Effective
Opportunity
Opportunity
(number of
(number of
stocks)
stocks)
Efficiency Ratio
S&P 500
500
102
0.20
Russell 1000
1,000
124
0.12
Russell 2000*
2,000
1,120
0.56
S&P 500/
164
42
0.26
336
70
0.21
500
1.00
Barra Growth
S&P 500/
Barra Value
S&P 500 (equal- 500
weighted)
*
Excluding the largest 1,000 stocks
Source: Wander, 2003: 56
From the above it follows that investors’ expectations for added value from managers
should be aligned with the effective number of securities in a given benchmark.
Managers would prefer an equally-weighted benchmark to show off their skill, but
that would imply including larger portions of smaller securities in the portfolio which
would have additional risk implications for investors and not reflect the true
characteristics of the market.
21
An additional problem posed by a capitalisation-weighted index used as a benchmark
for active portfolio managers is that stocks with large weights in the index contribute
to massive stock-specific risk in the index. Strongin, Petsch & Sharenow (2000)
argued that diversification (adding more stocks to the portfolio to offset stock-specific
risk) only works well in a relative equally-weighted index, but once the weight of a
stock in the capitalisation-weighted index exceeds a certain threshold more stockspecific risk is added than diversified away.6
The concentration of stock-specific risk in a large capitalisation index is normally
more than the stock-specific risk of the portfolio manager. Consequently the
performance of the manager relative to the index is driven more by the index rather
than manager’s skill. Strongin, et al. (2000) argued that the active manager can only
neutralise the risk concentration of the index by owning those large stocks through
passive or derivative positions. No other strategy (better stock selection or evaluation
techniques) would significantly offset these risks. Given that managers possess skill,
their potential level of out-performance might be sacrificed (some funds would be
used to hold a passive position), but consistency of performance would be more likely
than otherwise.7
An extension of the above principles includes the scenario where stock markets are
considered to be skewed, i.e. dominated by certain market sectors, versus diversified
markets (equally-weighted amongst various market sectors).
Table 2.3 illustrates the concept where a manager would be considered in the one
market above-average and in the other below-average, despite delivering the same
nominal returns in both markets.
6
Adding more stock to a portfolio reduces the stock-specific risk of a portfolio by the inverse of the
square root of N, where N represents the effective number of stocks. If the weight of a stock in the
index exceeds a factor of 2/(N+1), then more stock-specific risk is added than diversified (Strongin,
Petsch & Sharenow, 2000: 17).
7
Strongin, et al. (2000) showed by means of simulation studies that when managers implemented this
strategy of neutralising concentrated risks through passive positions Sharpe ratios were doubled as
opposed to managers’ portfolios with no passive holdings.
22
Table 2.3: Relative Performance in Different Markets
Relative Market Weight
Manager Weight
Sector
Return
Allocation
Concentrated
Diversified
Concentrated
Diversified
Market
Market
Market
Market
Market
Manager
Resources
40
20
10
10
15%
17%
Industrials
10
10
15
15
7.5%
9.5%
Consumer
12.5
20
25
25
5%
7%
12.5
20
20
20
7.5%
9.5%
20
25
25
25
7.5%
9.5%
5
5
5
5
-5%
-3%
100
100
100
100
9.56%
7.88%
9.00%
9.00%
Goods
Services
Financial
Information
Tech
Total
Allocation
Total
Return
In Table 2.3 it is shown that even for an above-average skilled manager (outperforms
the different market sectors by 2%) it would be difficult to outperform the overall
market return in a concentrated index when the dominant sector (resources), which the
manager underweighted, performs better than the manager’s expectations. In a more
diversified market, however, it would not have had any real effect and the skilled
manager would still be able to show his worth. However, the opposite is also true in
that if the manager operating in the concentrated market had made his calls correctly,
out-performance relative to the diversified environment would have been made. 8
8
It can be shown that if two equally-skilled managers operating in different market environments
(concentrated and diversified) would have followed similar deviation strategies from their index
benchmark, similar out- or underperformance to the respective benchmarks would have been attained,
although the portfolio returns would differ in nominal terms.
23
These illustrations show that it could well be considered risky business for active
managers operating in skewed markets compared to their counterparts in more
diversified markets.
2.5
Summary
Both strong and poor arguments have been developed over the years in the active
versus passive debate. With basic investment theories and principles in mind, logic
will determine in favour of passive investing. However, the great majority of investors
have adopted an active strategy as the preferred choice, simply because it is more
appealing from an emotional and psychological perspective than a passive stance.
Index investing poses management problems in truly replicating the benchmark with
the cost implications of constantly mirroring the benchmark. Tracking errors are
unavoidable. On the other hand, active managers have to cope with market
constraints, such as skewed or concentrated market segments, which make it difficult
to excel, at least on a consistent basis.
No definite conclusion or winner can be announced from the active versus passive
debate. In a sense it is a futile debate, but for the investor it is necessary to listen to
both sides of the argument to form a balanced view of how investing should be
approached.
24
CHAPTER 3:
3.1
THE INTERNATIONAL EXPERIENCE
Comparative Studies: Active versus Passive
Relevant literature and studies revealed that no single strategy can claim
unambiguously to be superior to the other, although some identifiable patterns
occurred. It depends purely on how the strategies are measured against each other and
what time period is applicable. For example, over one time period index investing
strategies would have yielded a better return than the average of active investing, but
by shifting the review period a couple of years backward or forward just the opposite
result could have been attained.
In the United States of America (USA), which arguably has the most researched
market in the world, one of the earliest studies done by Michael Jensen (Bernstein,
2002: 80) reviewed the performances of mutual funds for the period 1946-1964. The
average of the mutual funds under-performed their index benchmark by 1.1% per
year. Further, the top performers of one year were seldom a top performer the next
year and never over the longer term, a pattern that recurred study after study.
For the period 1971-1997 the average mutual fund under-performed the index
benchmark by 1.5% per annum (Siegel, 1998: 272). By splitting the review period in
two sections, 1975-1983 and 1984-1997, two different results would have been
attained, with active managers on average faring better than the index in the first
period, but index investors performed much better than their active counterparts
during the second period.
Another long term review study done by Fortin and Michelson (2002: 93), which
covered the period 1976-2000 (when the first index mutual fund was launched) found
a similar result, except that small company equity funds and international funds
outperformed the index, which incidentally are probably less efficient markets.
Further, it seemed from the results that in bear markets (1979-82, 1991-93, and 19992000) active funds fared better than index funds.
25
Malkiel (2003: 3) reported in his study that 71% of the actively managed equity funds
over a ten-year review period under-performed the Vanguard S&P500 Index fund (the
largest index mutual fund) and this number varied between 52% and 63% over shorter
terms.
The trend repeated itself in European markets where 69% of the active equity funds
did not beat the relevant index fund (Malkiel, 2003: 9). In the United Kingdom the
Sandler Report into the retail investment management industry showed that the
average active fund underperformed the market by 2.5% per annum due to a
combination of charges and poor management (Reynard, 2002: 20). Further studies
indicated that over 20 years 82% of active funds failed to beat the index before initial
charges. Over shorter periods on average 60% of active funds underperformed the
index.
Index funds in Japanese markets, however, performed poorly over the last decade.
Active managers, by simply avoiding banking stocks or holding cash, would have
outperformed the index (Reynard, 2003: 20).
For Canadian markets Kirzner (2000: 35) reported that index funds generated superior
returns to their active counterparts. Frino & Gallagher (2002: 200) reported that
Australian studies were consistent in their findings with those studies elsewhere.
From the above the case for index investing is overwhelming, yet not every academic
or practitioner is in agreement that index funds outperformed their active counterparts
over time and therefore should be the preferred method of investing.
Proponents of active investing, such as Arnott & Darnell (2003: 31) and Minor (2003:
74-78), gave compelling reasons why the conventional comparative studies between
the two strategies could be misleading. Further in-depth analysis is required and will
be discussed in the following sections.
26
3.2
The Interpretation of Comparative Studies: Caveats
A number of complexities arise when comparing the past performances of actively
managed funds with their passive counterparts.
Survivorship bias is a fairly common occurrence in comparative studies when funds
that became extinct or were merged with others are omitted from databases (Stein,
2003, 41). Since in most cases funds that ceased to exist were underperformers the net
result of omitting them would tend to push up the average of the remaining active
funds.
Most comparative studies have not dealt with the issue of upfront costs (initial
charges) on active funds. Bearing in mind that the initial charges for the individual
investor could be discounted or waived depending on the investment amount it is
understandable why these studies rather omitted the costs. However, it represents a
true cost for investors and will dilute actual returns. Hence, the average of active fund
performance would be overstated compared with the individual investor’s return.
A further problem in performance comparisons arises when comparing active
managers with the broad market index, which does not fully reflect the style or focus
area of active managers. Minor (2003: 75) argued that an appropriate index or
benchmark should be used when comparing how well active managers did against a
passive strategy. An index is normally capital-weighted, whereas active funds are
relatively equally weighted. Return-based styles analysis, where customised index
benchmarks for active funds according to their style orientation are set, would provide
a much clearer comparison than otherwise.
Minor (2003: 77) further noted that since it is true that the index is the capitalisationweighted average of all active investors before expenses, mutual fund active managers
only represent a portion of all participants (about 35% in the USA and 5% in SA),
thus strictly speaking there would be no need for them as a group to equal the market.
Even if the active managers on a capitalisation-weighted basis equalled the market,
there would be no need to do so on an equally-weighted basis.
27
Table 3.1 depicts the above principle in a hypothetical market with only four
participants, three active managers and one passive investor.
Table 3.1: Capitalisation-weighted versus Equally-weighted Performances
Stock
Market Value
(begin)
Return
Resources
Market Value
(end)
-20.00%
200
160
Industrial
15.00%
100
115
Services
25.00%
100
125
Diamonds
25.00%
50
63
Energy
0.00%
100
100
Fashion
-5.00%
50
48
600
610
TOTAL VALUE
Investor
Resources
Industrial
Services
Diamonds
Energy
Fashion
Total
Return
Manager A
100
100
-
-
-
-
200
-2.50%
Manager B
100
-
100
-
-
-
200
2.50%
Manager C
NonManager
-
-
-
50
50
-
100
12.50%
-
-
-
-
50
50
100
-2.50%
200
100
100
50
100
50
600
1.67%
TOTAL
Performance
All Managers Equally
Weighted
Begin
All Managers Cap Weighted
End
Return
4.17%
500
513
All Investors Equally Weighted
All Investors Cap Weighted
Source: Adapted from Minor, 2003: 79
2.44%
2.50%
600
610
1.67%
28
Consequently a number of studies have tried to address the complexities of a fair
comparison between active and passive strategies and are briefly reviewed in the
following sections.
3.3
Alternative Performance Measurement: Return-based Style Analysis
Sharpe (1992) proposed a factor model whereby investment funds can be evaluated on
a comparative basis as differentiation is made between investment style and selection.
Usually comparisons on funds are done without distinguishing between style and
selection attributes.
Passive funds provide an investor with an investor style, whereas an active manager
provides both style and selection. Return-based style analysis focuses on a fund’s
selection return, defined as the difference (tracking error) between the fund’s return
and that of a passive fund with the same style. In statistical terminology, the Rsquared value (coefficient of determination) is attributable to the fund’s style and the
remainder (1-R2) to selection abilities.
The purpose of style analysis is to minimise the variance between the active fund and
its passive benchmark, i.e. to identify the most appropriate benchmark for an active
fund. Once correctly identifying the most appropriate passive benchmark, the tracking
error displays the real efficiency of active investing. That is, whether the manager’s
selection leads to out-performance versus the passive strategy.
Active managers’ portfolios could deviate substantially from the broad market index,
for example it could be tilted more towards value than growth stocks or relatively
more small-cap than large-cap. Therefore, this kind of analysis could be more
appropriate than the conventional methods.
Buetow, Johnson & Runkle (2000) however warned that managers’ styles are not
always easy to define and therefore it could be difficult to accurately ascertain an
appropriate benchmark.
29
Minor (2001) made use of return-based style analysis, where the actual holdings of
the mutual funds were resembled by a customised benchmark (for example 70%
large-cap growth and 30% large-cap value), and not only the broad index (S&P500).
Following this methodology, no significant differences in risk-adjusted returns
between active and passive strategies were found.
Bogle (2002), in response to Minor’s work, used the same methodology, but over a
longer time span and found that in general low-cost funds (index funds) outperformed
high-cost funds (active funds) in nominal and risk-adjusted terms over various style
categories. The study concluded that indexing not only worked well in large
capitalisation markets, but in all style segments. Further, higher returns were directly
associated with lower costs.
Bogle’s notion that high-cost funds in general did not justify themselves and should
be avoided by investors needs further attention. Hence, empirical studies into the cost
aspect are discussed in the following section.
3.4
The Impact of Costs on Performance
Some studies in the past specifically concentrated on the impact that the costs
associated with active management would have had on performance.
Elton, Gruber & Blake (1996) did an analysis of mutual fund performances from 1977
to 1993 and concluded that the poor performance of funds in the lowest decile
(bottom 10%) was largely accounted for by the fact that it contained the majority of
funds with the highest expenses. On the other hand, successful funds did not increase
their fees compared to less successful funds. Carhart (1997) found that expense
ratios, transaction and load fees were significantly and negatively related to fund
performance. Dellva & Olson (1998) concluded that the absence of any fees would
not coincide with superior risk-adjusted performance. It was however found that funds
with front-end loads have had lower risk adjusted performances than funds without
these charges.
30
Wermers (2000) studied mutual funds over the period 1975-1994 and by merging data
from various databases decomposed fund returns and costs into various components.
On average it was found that the stocks held by mutual funds outperformed a broad
market index by 1.3% per year of which 60 basis points (0.6%) could be attributed to
the characteristics of the stock held and the balance (0.7%) due to the skill of fund
managers in selecting stocks to beat the benchmark portfolios.
On a net return level (i.e. what the mutual fund investor received), however, the funds
under-performed the index by one percent per year. In total the mutual fund investor
received 2.3% per year less than what the actual stock holdings delivered. The lower
average return of non-stock holdings (cash and bonds) in the portfolios over the
period explained 0.7% per year of this difference, whereas the transaction costs and
expense ratios of the funds made up the bulk of the difference.
3.5
The Effect of Survivorship Bias
Malkiel (1995) studied the returns from equity mutual funds from 1971 to 1991 and
specifically included all funds in existence each specific year. By comparing these
results with the returns from a database that only contained data from “live” funds at
the end of the review period, the extent of survivorship bias could be established.
On average the “mortality rate” of active funds over a ten year period was more than
15%. Survivorship bias had at least a 1.5% per annum positive effect on the average
active fund performance, i.e. the annual returns from the average active fund was
substantially overstated (Malkiel, 1995: 553). By excluding the effect of survivorship
bias it was shown that active funds on average significantly underperformed index
funds over the review period, even gross of costs.
3.6
The Capitalisation-Weighted Comparison
In one of the most recent studies done on the subject, Reinker & Tower (2004) used a
different concept to those done previously and at the same time eliminated many of
the deficiencies mentioned earlier.
31
First, they only compared funds from one institution (Vanguard) which offered both
strategies to investors since 1977. Hereby constant management styles and
philosophies were ensured.9 Second, the analysis was done relatively free of
survivorship bias, which normally would have benefited the active strategy. Third,
and probably the most important aspect, was that synthetic portfolios were created
according to the relative size of each fund. Hereby a true capitalisation-weighted
range of the active strategies could be determined and compared with the
capitalisation-weighted average of the index funds.
Reinker & Tower (2004: 45) found that over the longest time spans (22-27 years) the
active strategies were superior to the index strategy - both on a risk-adjusted and nonrisk-adjusted return basis. The importance of the time span, however, was evident
when different time spans were considered. For example, if the analysis ended in
1999, the index strategy would have been far superior. Since then the markets fell into
a major downtrend and index funds performed poorly, while active funds offered
some protection against the prevailing bear market.
Reinker & Tower (2004: 48) concluded that no fundamentalist approach can be
followed about either strategy since the answer to which strategy yielded the best
returns depended on the specific time frame used. In general index funds fared better
during bull market years, but gave that advantage away during bear market years.10
Vanguard’s actively managed funds typically have low expense ratios and might as such not be
representative of the industry (Reinker & Tower, 2004: 38).
9
10
All seven directors of Vanguard (one of the largest index fund managers in the world) are invested in
a US managed fund in their personal investment portfolios, six in US index funds, four in an
international index fund, and one in an international managed fund (Reinker & Tower, 2004: 48).
32
3.7
Summary
Most comparative international studies ruled in favour of passive or index investing
and in essence confirmed Sharpe’s thesis that index investing would outperform the
average of active investors.
Nonetheless, interpretation of these results should be handled with caution, because
there normally were some obvious shortcomings for a fair comparison or the period
covered by the study only included bull market phases, and not major downtrends.
Studies that tried to overcome these problems had shown mixed outcomes, again
confirming that no single strategy could be declared as the ultimate winner in the
active versus passive debate.
33
CHAPTER 4:
THE SOUTH AFRICAN EXPERIENCE:
ACTIVE INVESTING VERSUS PASSIVE INVESTING
4.1
Comparison on a Before- and After-Cost Basis
4.1.1 Methodology
The performance of the actively managed funds against its passive benchmark, the
ALSI, was evaluated on three different scales, namely cumulative, random sampling
and on a rolling annualised return basis. A brief description of each follows:
1)
The cumulative performance of the average of actively managed funds
versus the ALSI ranging from the period January 1988 to December
2003 (192 months) to the period January 2001 to December 2003 (36
months) was investigated.
In total 156 investment periods were
identified. Month-end unit prices were used to calculate returns.
2)
The random sampling of investment dates over three, five and ten year
investment periods on a cumulative return basis, and more specifically:

The average cumulative return of 100 investors that could have
invested any day between January 1988 and December 2000 across
all available active funds for an investment period of three years;

The average cumulative return of 100 investors that could have
invested any day between January 1988 and December 1998 across
all available active funds for an investment period of five years;

The average cumulative return of 100 investors that could have
invested any day between January 1988 and December 1993 across
all available active funds for an investment period of ten years.
34
3)
The annualised return of the average of actively managed funds versus
the ALSI over rolling three, five and ten year investment periods over
the period 1988-2003. Month-end unit prices were used to calculate
returns.
The “before-cost” (or sell-to-sell price basis) evaluation excluded the impact of initial
charges on performance, while the “after-cost” (or buy-to-sell price basis) evaluation
included the maximum initial charges applicable. The cost structures of the individual
actively managed funds are given in Table 4.1.
35
Table 4.1: The Cost Structure of Actively Managed Funds
in the General Equity Unit Trust Sector
Fund
ABSA General
ABSA Growth FoF
Allan Gray Equity
Community Growth
CorisCapital General Equity
Coronation Equity
Futuregrowth Albaraka
Futuregrowth Core Equity
Investec Equity
FNB Growth
Mcubed Equity FoF
Metropolitan General Equity
Nedbank Equity
Nedbank Equity FoF
Nedbank Rainmaker
Nedbank Quants Core
Oasis Crescent Equity
Old Mutual Growth
Old Mutual Investors
Old Mutual Top Companies
Prudential Optimiser
RMB Equity
RMB Performance FoF
Sage Fund
Sage MultiFocus FoF
Sanlam General Equity
Sanlam Multi-Manager Equity
Stanlib Capital Growth
Stanlib Prosperity
Stanlib WealthBuilder
Tri-Linear Equity
Woolworths
Average
Source:
Max Initial Fee
5.70%
4.56%
3.42%
5.70%
4.56%
5.70%
5.70%
0.57%
5.70%
5.70%
5.70%
5.70%
5.70%
5.70%
5.70%
3.42%
5.13%
5.70%
5.70%
5.70%
5.70%
3.70%
3.70%
5.70%
5.70%
5.70%
4.56%
5.70%
5.70%
5.70%
2.28%
5.70%
5.04%
Management Fee p.a.
1.71%
1.71%
0-3.42%
0.57%
1.14%
1.14%
1.71%
1.14%
1.71%
1.43%
1.71%
1.43%
1.60%
1.43%
1.60%
0.86%
1.71%
1.14%
1.14%
1.14%
1.43%
1.14%
1.71%
1.71%
1.43%
1.14%
1.71%
1.14%
1.14%
1.14%
1.43%
1.25%
Fund Fact Sheets
The management fees charged by the actively managed funds are deducted on an
ongoing basis and unit price data are given net of all management fees. The initial
charges include distribution fees (payable to intermediaries) and an administration fee,
both of which could be discounted, assuming a sizeable investment is made. For the
sake of uniformity the maximum charges applicable were assumed in the study.
36
The effect of initial charges on the investment return can be fairly accurately
determined and is shown in Figure 4.1.
Impact of Initial Costs on Performance
Average Cost = 5.04%
7%
5%
y = 0.0014e0.4702x
R2 = 0.9828
4%
3%
2%
Cost Impact (per annum)
6%
1%
0%
12
24
36
48
60
120
240
360
Months of Investment
Figure 4.1: Impact of Initial Charges on Investment Performance over Time
Figure 4.1 indicates that if the initial charge is set at about 5% of the investment
amount it would have a 2% per annum adverse effect on the actual performance over
three years, 1% per annum over five years and 0.5% per annum over ten years.
The statistical significance of return differences between the average of actively
managed funds and the ALSI index was measured by the t-test statistic11, where any tvalue larger than two indicated a statistically significant difference between the mean
values of the two variables tested.
11
The t-test statistic value is determined by dividing the observed mean differences of two observations
by the product of the sample standard deviation of the differences and the square root of the number of
observations (Mason & Lind, 1996: 417).
37
4.1.2 Analysis of Results
The results of the different evaluation scales are summarised in tabular and graphical
formats in the following sections.
Cumulative Return Basis
Table 4.2 shows the number of periods expressed as a percentage of the total number
of investment periods under review in which the average return of actively managed
funds outperformed the ALSI index, both on a “before-cost” and “after-cost” basis. In
addition the top 25% and bottom 25% active returns were identified and their outperformance records are shown in similar fashion.
To demonstrate the interpretation of the results the last row of Table 4.2 is used as an
example. The first column refers to the number of investment periods observed over
the last three to five years (2000-1998). The next three columns show the percentage
of periods in which the average, top 25% and bottom 25% respectively outperformed
the index on a “before-cost” basis, while the last three columns illustrate the same, but
on an “after-cost” basis.
Overall the average of actively managed funds outperformed the ALSI index 60% of
the time, but once the initial fees of active investing were taken into account and
subtracted from returns the level of out-performance dropped to a mere 29%. The top
25% of actively managed funds outperformed the index comprehensively before
costs, but dropped to more moderate levels once evaluated on an after-cost basis. Note
that the bottom 25% of actively managed funds never outperformed the index over
any period.
From Table 4.2 it can further be observed that the highest occurrence of outperformance took place over the longest time spans (11-15 years), while the
diminishing effect of initial fees have had the greatest impact over the shorter
investment periods. 12
12
A detailed analysis of the cumulative returns is shown in Appendix A.
38
Table 4.2: The Performance Record of Actively Managed Funds versus the
Index on a Cumulative Return Basis
Investment
Result
Percentage
Periods
Before Cost
After Cost
Active
Top
Bottom
Active
Top
Bottom
Average
25%
25%
Average
25%
25%
Active
Active
Active
Active
156
60%
90%
0%
29%
58%
0%
60
70%
90%
0%
43%
55%
0%
60
68%
97%
0%
30%
77%
0%
36
31%
78%
0%
3%
33%
0%
of Periods
better than
Index
(overall)
Percentage
of Periods
better than
Index
(11-15
years)
Percentage
of Periods
better than
Index
(6-10
years)
Percentage
of Periods
better than
Index
(3-5 years)
39
Cumulative Performance
Active versus Index Investing
(Buy-to-sell price basis)
700%
600%
400%
300%
Return
500%
200%
100%
15
14
13
12
11
10
9
8
7
6
5
4
3
0%
-100%
Years
ALSI Index
ACTIVE Avg
Top 25%
Bottom 25%
Figure 4.2: Cumulative Performance of Active versus Passive Investing
(1988-2003)
Figure 4.2 illustrates the cumulative performance record of the actively managed
funds versus the index on an average, top 25% and bottom 25% performance
categories.
40
Random Sampling
Mixed results were obtained when the investment performances of 100 hypothetical
investors were simulated each for a period of three, five or ten years. The dates of
investment were randomly selected and the investments then kept for a period of
three, five or ten years and compared with the index performance over the same
periods.
The results of the random sampling simulation study are summarised in Table 4.3.
Where the t-statistic value is larger than a value of two, a significant difference
between the observations exists. 13
Before considering upfront charges the average of active investing outperformed the
index statistically significantly at a five percent significance level over five and ten
year investment periods. When costs were taken into account index investing would
have significantly outperformed the average of active investing over three and five
years, but not over a ten year period.
13
A statistical analysis of the random sampling method is shown in Appendix B.
41
Table 4.3: Random Sampling: Comparison between Active and Passive Investing
Period
Category
Observations
Mean
Variance
Return
Pearson
t-Statistic
Correlation
(cumulative)
ALSI Index
Average
3 years
Active
of
100
37.76%
9.60%
100
39.53%
8.08%
87.11%
-1.16
100
32.19%
7.18%
87.20%
3.67
100
76.88%
16.54%
100
80.66%
17.95%
93.85%
-2.58
100
71.00%
16.02%
93.88%
4.16
100
194.05%
42.62%
100
210.35%
58.16%
91.73%
-5.31
100
193.61%
52.06%
91.73%
0.15
Funds
(before cost)
Average
Active
of
Funds
(after cost)
ALSI Index
Average
5 years
Active
of
Funds
(before cost)
Average
Active
of
Funds
(after cost)
ALSI Index
Average
of
10
Active
years
(before cost)
Funds
Average
Active
of
Funds
(after cost)
42
Figures 4.3-4.5 illustrate the performance of the actively managed investments versus
the index performance over the different evaluation periods. Regression lines of the
best, average and worst performing actively managed funds are plotted against the
index performance on the horizontal axis.
For example, when using the regression lines as a performance predictor in Figure
4.4, at an index cumulative return of 100% over five years, the worst active fund
would have delivered less than 50%, the average active fund about 75% and the best
active fund would have returned about 140%.
43
Random Sampling
Three Year Investment Period
Active vs Index Return
(buy-to-sell price basis)
200%
180%
160%
Active Management Return
140%
120%
100%
80%
60%
40%
20%
0%
-20%
-40%
-60%
0%
20%
40%
60%
80%
100%
120%
ACTIVE AVERAGE
Index Return
BEST ACTIVE
WORST ACTIVE
Linear (WORST ACTIVE)
Linear (ACTIVE AVERAGE)
Linear (BEST ACTIVE)
Figure 4.3: Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Three Years
44
Random Sampling
Five Year Investment Period
Active vs Index Return
(buy-to-sell price basis)
200%
180%
160%
Active Management Return
140%
120%
100%
80%
60%
40%
20%
0%
-20%
-40%
-60%
0%
20%
40%
60%
80%
100%
120%
140%
160%
Index Return
ACTIVE AVERAGE
BEST ACTIVE
WORST ACTIVE
Linear (BEST ACTIVE)
Linear (ACTIVE AVERAGE)
Linear (WORST ACTIVE)
Figure 4.4:
Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Five Years
45
Random Sampling
Ten Year Investment Period
Active vs Index Return
(buy-to-sell price basis)
600%
Active Management Return
500%
400%
300%
200%
100%
0%
0%
100%
200%
300%
400%
500%
Index Return
ACTIVE AVERAGE
BEST ACTIVE
WORST ACTIVE
Linear (BEST ACTIVE)
Linear (ACTIVE AVERAGE)
Linear (WORST ACTIVE)
Figure 4.5:
Comparison between Active and Passive Investing on a Random
Sampling Basis for an Investment Period of Ten Years
46
Rolling Investment Periods
Table 4.4 illustrates the rolling average performances of actively managed funds
against the index over three, five and ten year periods. On a “before-cost” basis the
average of active investing statistically outperformed the index only over a ten year
period at a significance level of 5%. When accounting for upfront costs index
investing outperformed the average of actively managed funds significantly over all
three evaluation periods.14
14
A statistical analysis of the rolling period method is shown in Appendix C.
47
Table 4.4: Comparison between Active and Passive Investing over Rolling
Three-, Five-, and Ten-year Periods
Rolling
Category
Observations
Period
Mean
Variance
Return
Pearson
t-Statistic
Correlation
(annualised)
3 years
ALSI Index
156
11.32%
0.66%
Average
156
11.35%
0.54%
85.40%
-0.10
156
9.36%
0.52%
85.49%
5.78
ALSI Index
132
11.05%
0.28%
Average
132
11.12%
0.32%
92.62%
-0.42
132
9.91%
0.31%
92.66%
6.20
ALSI Index
72
10.89%
0.04%
Average
72
11.16%
0.05%
88.37%
-2.19
72
10.55%
0.05%
88.37%
2.77
of
Active
Funds
(before cost)
Average
of
Active
Funds (after
cost)
5 years
of
Active
Funds
(before cost)
Average
of
Active
Funds (after
cost)
10 years
of
Active
Funds
(before cost)
Average
of
Active
Funds (after
cost)
48
Figures 4.6-4.8 depict the variable patterns of how one strategy outperformed the
other in the past as certain economic conditions prevailed.
While the index is dominated by mining and resources counters (and effective
currency hedges) it is clear from Figure 4.6, for example, how bull runs in commodity
cycles coupled with weaknesses in the rand boosted the index performance (early
1990’s and early 2000’s). Active managers have invariably had less exposure to these
counters and as a result underperformed their index benchmarks. On the other hand,
managers have had a tendency to favour financial and industrial stocks relative to the
benchmark weights, which paid off well in the period from 1995-1998 and again in
2003.
Further, it can be seen from Figure 4.6 that the troughs of the average of actively
managed funds during major bear markets (1992 and 1998) were less lower than those
of the index. However, it can be expected, since actively managed funds would
invariably carry larger cash holdings than an index equivalent.
49
Rolling 36-month Investment Period
Active versus Index
(Buy-to-sell price basis)
30.00%
Return(annualised)
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
-5.00%
-10.00%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
Period
ALSI Index
ACTIVE Avg
Figure 4.6: Active versus Passive Investing over Rolling 36-month Investment
Periods
50
Rolling 60-month Investment Period
Active versus Index
(Buy-to-sell price basis)
25.00%
Return(annualised)
20.00%
15.00%
10.00%
5.00%
0.00%
-5.00%
-10.00%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Period
ALSI Index
ACTIVE Avg
Figure 4.7: Active versus Passive Investing over Rolling 60-month Investment
Periods
51
Rolling 120-month Investment Period
Active versus Index
(Buy-to-sell price basis)
Return(annualised)
20.00%
18.00%
16.00%
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Period
ALSI Index
ACTIVE Avg
Figure 4.8: Active versus Passive Investing over Rolling 120-month Investment
Periods
52
Beating the Index
Figures 4.9-4.11 portray the percentage of actively managed funds that over various
investment periods were able to outperform the index after considering the impact of
upfront charges on return.
Over all three evaluation periods (rolling three, five and ten years) roughly 40% of
actively managed funds were able to beat the index, but with large deviations visible.
In bear markets and broadly based bull markets the majority of actively managed
funds outperformed the index, while during periods where mining and resources
counters ran hard, basically no active manager could beat the index.
Percentage of Active Funds outperforming ALSI Index
over a Rolling 36-month period
(Buy-to-sell price basis)
Percentage
100%
80%
60%
40%
20%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
0%
Period
Figure 4.9: Beating the Index over Rolling 36-month Investment Periods
53
Percentage of Active Funds outperforming ALSI Index
over a Rolling 60-month period
(Buy-to-sell price basis)
100%
Percentage
80%
60%
40%
20%
0%
Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03
Period
Figure 4.10: Beating the Index over Rolling 60-month Investment Periods
Percentage of Active Funds outperforming ALSI Index
over a Rolling 120-month period
(Buy-to-sell price basis)
100%
Percentage
80%
60%
40%
20%
0%
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Period
Figure 4.11: Beating the Index over Rolling 120-month Investment Periods
54
4.2
Comparison on a Risk-adjusted Basis
4.2.1 Methodology and Explanation of Terminology
The active manager invariably deviates from the index benchmark and constructs a
portfolio that does not replicate the benchmark. For example, a manager will typically
include larger portions of small-cap stocks in the portfolio than its respective weight
in the index. Normally the manager’s portfolio of stocks would be more equallyweighted than those of the index. Further, investment constraints may prohibit a
manager to accumulate more holdings of a stock than its mandate will allow
(maximum 10% holding of one stock in a portfolio), which is especially relevant in
the South African context.
The rationale for risk-adjusted performance measures rests upon the fact that, if an
active manager pursues a low risk investment strategy, one should not expect the
same returns from that strategy compared with a manager that follows high-risk
strategies. A manager’s worth could then only be judged upon the return that was
delivered versus the risk taken to deliver that return.
A similar argument could be put forward in comparing the two investment strategies.
If, for example, index investing outperformed active investing over time it could have
been achieved with a relatively higher risk profile than active investing and
consequently on a risk-adjusted basis would show equal or lesser qualities. Therefore,
a meaningful comparison between the two strategies is not possible without adjusting
for risk.
Two risk-adjusted measures, Sharpe and Treynor, were used in the study to evaluate
whether any significant return differences between active and index investing
occurred over time.15 In analysing the individual active funds an additional measure,
the information ratio, was used to identify those funds that delivered exceptional
value.
15
A statistical analysis for the risk measures is shown in Appendix D.
55
An explanation of the terminology used in the ensuing sections of the study is
presented as follows:
Explanation of Terminology
Fund return:
Monthly return over rolling three year, five year and ten year
periods.
Risk-free return: Average treasury bill rate on a monthly basis over three, five
and ten years respectively.
Excess return:
Fund return less risk-free return.
Volatility:
Standard deviation of monthly excess returns over rolling three,
five and ten year periods.
Beta:
Indicative of the systematic component of total risk and is the
percentage change expected in fund excess return per unit
change in market excess return, given by:
Covariance between fund return and market return
Variance of market return
Alpha:
The out-performance of fund excess return over market excess
return, given by the regression function:
rp  rf  p  p (rm  rf )] ,
p  rp  [rf  p (rm  rf )]
and therefore,
(4.1)
56
Where:
αp =
average of the abnormal fund excess return over
market excess return;
rp-rf =
average fund excess return over period;
rf =
risk-free return over period;
βp =
beta of fund return with market return;
(rm-rf) =
average of market excess return over period.
Non-systematic (Active) risk:
Part of the total volatility of fund return that
cannot be explained by market or systematic
risk, where systematic risk is explained by the
coefficient of determination (r2), hence nonsystematic risk is explained by:
 (e ) 
(1 r 2 )( 2P )
P
Sharpe ratio:
(4.2)
(Fund return – risk-free return)
Standard deviation of fund
( RP  RF ) P
Treynor ratio:
(4.3)
(Fund return – risk-free return)
Beta of active fund
( RP  RF ) P
Information ratio:
(4.4)
Alpha of fund
Active risk of fund
 /  (e )
P
P
(4.5)
57
4.2.2 Analysis of Results
Data
Tables 4.5-4.7 present the data gathered from the monthly unit price data. Returns
were calculated on a monthly basis and excluded the effect that upfront fees would
have had on actual performances.
From these tables it is noted that the volatilities, beta and correlation statistics are
more or less similar (few exceptions), but average gross returns and excess returns
deviate substantially among the active funds.
Further, the ALSI and active funds’ monthly excess returns are in most cases
negative, amplifying the general impression that bonds and cash (ignoring tax)
outperformed equity investments over the last decade and more. Alternatively stated,
the returns delivered by equity investments did not compensate for the risk in
pursuing the returns.
58
Table 4.5: Risk Data of Actively Managed Funds over Rolling 36-month
Investment Periods
Active Fund
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
CorisCap_GE
Coronation_Equity
Futuregro_Albaraka
Futuregro_Core
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank Equity FoF
Nedbank_Rain
Nedbank_Quants
Oasis_Cresc
OM_Growth
OM_Invest
OM_TopCo
Prudential_Opt
RMB_Equity
RMB_Perform
Sage_Fund
Sage_MultiF
Sanlam_GE
Sanlam_MM_Equity
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Tri-Linear_Equity
Woolworths
Periods
117
30
27
103
12
57
102
24
156
27
37
111
38
20
27
14
13
93
156
110
17
71
30
148
4
156
23
62
77
156
13
15
Monthly
Return
0.64%
0.57%
2.08%
0.88%
0.08%
0.78%
1.13%
0.51%
1.25%
0.96%
0.43%
1.06%
-0.15%
0.44%
1.32%
0.33%
1.81%
0.69%
1.08%
0.92%
0.69%
0.69%
0.56%
0.99%
0.85%
0.88%
0.32%
0.03%
0.69%
1.00%
-0.08%
0.36%
INDEX
ALSI Index
Periods
156
Monthly
Return
1.06%
Monthly
Excess
Return
-0.43%
-0.31%
1.21%
-0.19%
-0.80%
-0.25%
0.05%
-0.36%
0.11%
0.09%
-0.49%
-0.01%
-1.08%
-0.43%
0.44%
-0.55%
0.93%
-0.40%
-0.06%
-0.15%
-0.18%
-0.38%
-0.33%
-0.13%
-0.03%
-0.26%
-0.55%
-1.02%
-0.40%
-0.14%
-0.96%
-0.52%
Monthly
Excess
Return
-0.08%
Volatility
5.72%
4.33%
4.81%
5.79%
6.23%
5.20%
5.42%
5.12%
5.19%
5.26%
5.99%
5.56%
6.57%
4.21%
5.60%
3.98%
3.82%
6.33%
5.58%
5.59%
5.85%
6.26%
4.82%
4.53%
4.19%
5.12%
4.18%
6.50%
6.13%
5.02%
5.34%
5.00%
Volatility
5.84%
Beta
80%
56%
56%
74%
73%
60%
69%
70%
78%
69%
78%
76%
80%
37%
73%
36%
48%
83%
88%
79%
72%
80%
62%
69%
53%
78%
35%
41%
82%
76%
67%
64%
Correlation
87%
83%
73%
80%
75%
82%
78%
86%
88%
82%
88%
85%
82%
55%
82%
58%
80%
84%
92%
88%
78%
89%
82%
89%
82%
89%
53%
47%
90%
88%
79%
82%
59
Table 4.6: Risk Data of Actively Managed Funds over Rolling 60-month
Investment Periods
Active Fund
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
Coronation_Equity
Futuregro_Albaraka
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank_Rain
OM_Growth
OM_Invest
OM_TopCo
RMB_Equity
RMB_Perform
Sage_Fund
Sanlam_GE
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Periods
93
6
3
79
33
78
132
3
13
87
14
3
69
132
86
47
6
124
132
38
53
132
Monthly
Return
0.59%
0.75%
2.64%
0.86%
0.77%
0.94%
1.28%
1.46%
0.27%
1.15%
0.14%
1.22%
0.67%
1.07%
0.87%
0.70%
0.66%
0.96%
0.86%
0.03%
0.73%
0.96%
INDEX
Periods
132
Monthly
Return
1.05%
ALSI
Monthly
Excess
Return
-0.51%
-0.19%
1.73%
-0.25%
-0.26%
-0.17%
0.15%
0.55%
-0.70%
0.04%
-0.83%
0.31%
-0.44%
-0.07%
-0.24%
-0.37%
-0.28%
-0.16%
-0.27%
-1.01%
-0.37%
-0.17%
Monthly
Excess
Return
-0.09%
Volatility
6.12%
4.32%
5.60%
6.36%
5.20%
5.87%
5.31%
5.24%
6.50%
5.96%
6.61%
5.64%
7.08%
5.75%
5.99%
6.47%
4.98%
4.65%
5.18%
6.67%
6.47%
5.12%
Volatility
5.93%
Beta
83%
53%
68%
79%
58%
74%
78%
66%
79%
78%
78%
71%
88%
89%
83%
82%
59%
70%
78%
42%
84%
76%
Correlation
86%
79%
75%
81%
81%
82%
88%
79%
86%
85%
83%
78%
85%
93%
90%
90%
76%
90%
90%
45%
91%
89%
60
Table 4.7: Risk Data of Actively Managed Funds over Rolling 120-month
Investment Periods
Active Fund
ABSA_General
Community_Growth
Futuregro_Albaraka
Investec_ Equity
Metropolitan_GE
OM_Growth
OM_Invest
OM_TopCo
Sage_Fund
Sanlam_GE
Stanlib_Wealth
Periods
33
19
18
72
27
9
72
26
64
72
72
Monthly
Return
0.65%
0.90%
1.23%
1.31%
1.02%
0.85%
1.08%
0.95%
0.95%
0.87%
0.95%
INDEX
Periods
72
Monthly
Return
1.05%
Alsi
Monthly
Excess
Return
-0.42%
-0.16%
0.18%
0.18%
-0.03%
-0.21%
-0.06%
-0.11%
-0.17%
-0.27%
-0.19%
Monthly
Excess
Return
-0.09%
Volatility
6.01%
5.86%
5.45%
5.37%
5.78%
6.22%
5.82%
5.78%
4.73%
5.23%
5.21%
Volatility
5.96%
Beta
82%
76%
68%
80%
79%
81%
91%
82%
70%
79%
78%
Correlation
85%
81%
79%
89%
85%
83%
93%
89%
90%
90%
89%
61
Return/Risk Profile
The average monthly returns by the individual actively managed funds and index
against the respective average volatilities over the various evaluation periods are
shown in Figures 4.12-4.14.
Over all three periods the ALSI index had an above-average risk/return profile
compared with the average of the actively managed funds. Notable is the presence of
outliers within the active funds’ range of return versus risk, a few funds that
performed exceptionally well and then those active funds that did exceptionally badly.
Further, a declining trend, albeit not very strong, is noted between return and risk.
Those funds that experienced higher volatilities on average performed worse than the
funds that followed moderate or market risk strategies.
62
Return/Risk Profile
Rolling 36-month Periods
2.50%
1- Absa General
2- Absa Growth
3- Allan Gray Equity
4-Community Growth
5- Coris Capital GE
6- Coronation Equity
7- Futuregro Albaraka
8- Futuregro Core
9- Investec Equity
10- FNB Growth
11- MCubed Equity
12- Metropolitan GE
13- Nedbank Equity
14- Nedbank Equity FoF
15- Nedbank Rain
16- Nedbank Quants
17- Oasis Crescent
18- OM Growth
19- OM Investors
20- OM TopCo
21- Prudential Opt
22- RMB Equity
23- RMB Perform
24- Sage Fund
25- Sage MultiFocus
26- Sanlam GE
27- Sanlam MM Equity
28- Stanlib CapGro
29- Stanlib Prosp
30- Stanlib Wealth
31- Tri-Linear Equity
3
2.00%
17
1.50%
Return pm
15
9
7
1.00%
30
24
10
26
6
25
2
0.50%
23
14
16 27
12
19
20
4
21
29 22
18
1
8
11
32
5
0.00%
28
31
13
2
R = 0.0936
32- Woolw Equity
-0.50%
0%
1%
2%
3%
4%
5%
6%
7%
Volatility
Active Avg
Alsi
Linear (Active Avg)
Figure 4.12: Return/Risk Profile of Actively Managed Funds and Index over
Rolling 36-month Investment Periods
63
Return/Risk Profile
Rolling 60-month Periods
3.00%
3
2.50%
1- Absa General
2- Absa Growth
3- Allan Gray Equity
4- Community Growth
5- Coronation Equity
6- Futuregro Albaraka
7- Investec Equity
8- FNB Growth
9- Mcubed Equity
10- Metropolitan GE
11- Nedbank Equity
12- Nedbank Rain
13- OM Growth
14- OM Investor
15- OM TopCo
16- RMB Equity
17- RMB Perform
18- Sage Fund
19- Sanlam GE
20- Stanlib CapGro
21- Stanlib Prosp
22- Stanlib Wealth
Return pm
2.00%
1.50%
8
7
12
10
14
1.00%
18
22
19
6
15
5
2
4
21 16
17
13
1
0.50%
9
2
11
R = 0.1384
20
0.00%
0%
2%
4%
6%
8%
Volatility
Active Avg
Alsi
Linear (Active Avg)
Figure 4.13: Return/Risk Profile of Actively Managed Funds and Index over
Rolling 60-month Investment Periods
64
Return/Risk Profile
Rolling 120-month Periods
1.40%
4
3
1.20%
7
5
1.00%
9
11
Return pm
10
8
2
1- Absa General
2- Community Growth
3- Futuregro Albaraka
4- Investec Equity
5- Metropolitan GE
6- OM Growth
7- OM Investor
8- OM TopCo
9- Sage Fund
10- Sanlam GE
11- Stanlib Wealth
6
0.80%
1
0.60%
0.40%
0.20%
R2 = 0.1055
0.00%
0%
1%
3%
2%
4%
5%
6%
7%
Volatility
Active Avg
Alsi
Linear (Active Avg)
Figure 4.14: Return/Risk Profile of Actively Managed Funds and Index over
Rolling 120-month Investment Periods
65
Risk Measure: Sharpe Ratio
The Sharpe ratio or “reward-to-risk” ratio is probably the most commonly used
measure to express performance on a risk-adjusted basis. The ratios over various
evaluation periods were measured by dividing the monthly excess return of the index
and actively managed funds by its monthly volatility (standard deviation). The
average results are shown in Table 4.8.
No statistically significant difference, except over the longest rolling period, was
observed between the risk-adjusted performances of the index and the average of
actively managed funds.
Table 4.8: Statistical Significance of Sharpe Ratios
Rolling
Category
Observations
Period
Mean
Variance
Reward-to-
Pearson
t-Statistic
Correlation
Risk Ratio
ALSI Index
156
-0.96%
1.20%
156
-0.73%
0.85%
132
-0.74%
0.32%
132
-0.92%
0.38%
72
-1.48%
0.06%
72
-1.89%
0.06%
36
months
Average
of
85.52%
-0.52
88.33%
0.71
83.05%
2.52
Active Funds
ALSI Index
60
Average
months
Active Funds
of
ALSI Index
120
Average
months
Active Funds
of
Figures 4.15-4.17 show the rolling Sharpe ratio averages of the index and active funds
over three, five and ten year periods.
66
Rolling 36-Month Period
Sharpe Ratio
Ratio
(Monthly Return)
0.25
0.20
0.15
0.10
0.05
-0.05
-0.10
-0.15
-0.20
-0.25
-0.30
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
Period
Active Average
ALSI Index
Figure 4.15: Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 36-month Investment Periods
67
Rolling 60-Month Period
Sharpe Ratio
(Monthly Return)
0.20
0.15
0.10
Ratio
0.05
-0.05
-0.10
-0.15
-0.20
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Period
Active Average
ALSI Index
Figure 4.16: Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 60-month Investment Periods
68
Rolling 120-Month Period
Sharpe Ratio
(Monthly Return)
0.08
0.06
Ratio
0.04
0.02
-0.02
-0.04
-0.06
Sep-03
May-03
Jan-03
Sep-02
May-02
Jan-02
Sep-01
May-01
Jan-01
Sep-00
May-00
Jan-00
Sep-99
May-99
Jan-99
Sep-98
May-98
Jan-98
Period
Active Average
ALSI Index
Figure 4.17: Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing
over Rolling 120-month Investment Periods
69
Risk Measure: Treynor Ratio
The Treynor measure, similar to Sharpe, gives a reward-to-risk unit, but uses the
systematic risk (represented by beta) instead of total risk. The index has a beta of 1
since it is representative of market risk.
Table 4.9 shows that the index outperformed the average of active funds over rolling
five and ten year periods at a significance level of 5%. Figures 4.18-4.20 illustrate the
relative performances of the Treynor ratios of both the index and active funds over
rolling three, five and ten year periods.
Table 4.9: Statistical Significance of Treynor Ratios
Rolling
Category
Observations
Period
Mean
Variance
Excess
Pearson
t-Statistic
Correlation
Return
(monthly)
ALSI Index
156
-0.08%
0.0039%
156
-0.11%
0.0019%
132
-0.09%
0.0011%
132
-0.14%
0.0021%
72
-0.09%
0.0002%
72
-0.13%
0.0002%
36 months
Average
of
58.61%
0.65
84.60%
2.52
80.88%
3.89
Active Funds
ALSI Index
60 months
Average
of
Active Funds
ALSI Index
120
Average
months
Active Funds
of
70
Rolling 36-Month Period
Treynor Ratio
Risk-adjusted Return (p.m.)
1.50%
1.00%
0.50%
0.00%
-0.50%
-1.00%
-1.50%
-2.00%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
Period
Alsi Index
Active Average
Figure 4.18: Treynor Ratio of Active versus Passive Investing over Rolling
36-month Investment Periods
71
Risk-adjusted Return (p.m.)
Rolling 60-Month Period
Treynor Ratio
1.00%
0.50%
0.00%
-0.50%
-1.00%
-1.50%
-2.00%
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Period
Alsi Index
Active Average
Figure 4.19: Treynor Ratio of Active versus Index Investing over Rolling
60-month Investment Periods
72
Rolling 120-Month Period
Treynor Ratio
Risk-adjusted Return (p.m.)
0.50%
0.40%
0.30%
0.20%
0.10%
0.00%
-0.10%
-0.20%
-0.30%
-0.40%
Jul-03
Jan-03
Jul-02
Jan-02
Jul-01
Jan-01
Jul-00
Jan-00
Jul-99
Jan-99
Jul-98
Jan-98
Period
Alsi Index
Active Average
Figure 4.20: Treynor Ratio of Active versus Index Investing over Rolling
60-month Investment Periods
73
Risk Measure: Information Ratio
The previous risk measurements (Sharpe and Treynor) focused on total return versus
risk, either total risk (systematic and non-systematic) or systematic risk only. These
measurements are certainly helpful, but do not specifically display whether an
individual fund’s performance was due to luck (market performance) or manager’s
skill (in-depth knowledge).
The information ratio (appraisal ratio) is an appropriate tool to identify those active
funds that delivered the highest out-performance (alpha) with the least non-systematic
or active risk. In other words, similar to the Sharpe ratio, but it focuses on the active
return (above the expected market return) versus the active risk taken, which could
have been diversified away by holding a portfolio similar to the market.
By regressing a manager’s performance on the market index the alpha estimate (outperformance) can be determined. Further, calculating the standard error of the alpha
estimate, the significance of the t-statistic of the alpha estimate can be used to
differentiate whether a manager’s performance was due to luck or skill.16
Tables 4.10-4.12 show the individual active funds’ value-added information over the
various time periods.
The standard error of the alpha estimate (σα) is determined by dividing the active risk (σ e) by the
square root of the number of observations. The t-statistic is then calculated by dividing the average
alpha (α) by the standard error of the alpha estimate (σα) (Bodie, Kane & Marcus, 1999: 764).
16
74
Table 4.10: Value Added by Actively Managed Funds over Rolling 36-month
Investment Periods
Fund
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
CorisCap_GE
Coronation_Equity
Futuregro_Albaraka
Futuregro_Core
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank Equity FoF
Nedbank_Rain
Nedbank_Quants
Oasis_Cresc
OM_Growth
OM_Invest
OM_TopCo
Prudential_Opt
RMB_Equity
RMB_Perform
Sage_Fund
Sage_MultiF
Sanlam_GE
Sanlam_MM_Equity
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Tri-Linear_Equity
Woolworths
Average
Alpha
-0.34%
-0.38%
1.13%
-0.03%
-0.50%
-0.17%
0.21%
-0.38%
0.21%
0.02%
-0.56%
0.13%
-1.15%
-0.38%
0.36%
-0.41%
1.12%
-0.17%
0.04%
-0.02%
0.01%
-0.12%
-0.41%
-0.04%
0.07%
-0.17%
-0.54%
-0.91%
-0.10%
-0.04%
-0.68%
-0.29%
Std
Error of
Alpha
0.26%
0.44%
0.63%
0.32%
1.16%
0.40%
0.31%
0.51%
0.19%
0.57%
0.45%
0.26%
0.59%
0.78%
0.62%
0.86%
0.63%
0.35%
0.17%
0.23%
0.87%
0.32%
0.51%
0.17%
1.19%
0.18%
0.74%
0.73%
0.29%
0.18%
0.90%
0.72%
t-statistic
-1.28
-0.86
1.80
-0.10
-0.43
-0.43
0.68
-0.74
1.10
0.03
-1.24
0.51
-1.94
-0.48
0.58
-0.47
1.78
-0.50
0.22
-0.10
0.02
-0.37
-0.80
-0.25
0.06
-0.96
-0.73
-1.24
-0.34
-0.24
-0.76
-0.41
Active Risk
2.86%
2.43%
3.28%
3.23%
4.01%
2.99%
3.09%
2.51%
2.37%
2.98%
2.74%
2.74%
3.66%
3.49%
3.23%
3.23%
2.28%
3.36%
2.08%
2.46%
3.57%
2.69%
2.77%
2.02%
2.39%
2.24%
3.54%
5.77%
2.51%
2.27%
3.24%
2.78%
Info Ratio
-0.10
-0.16
0.34
-0.00
-0.15
-0.07
0.07
-0.17
0.10
0.01
-0.21
0.04
-0.32
-0.11
0.15
-0.13
0.50
-0.00
0.02
0.02
-0.00
-0.04
-0.15
-0.00
0.03
-0.07
-0.16
-0.18
-0.04
-0.01
-0.22
-0.12
75
Table 4.11:
Value Added by Actively Managed Funds over Rolling 60-month
Investment Periods
Fund
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
Coronation_Equity
Futuregro_Albaraka
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank_Rain
OM_Growth
OM_Invest
OM_TopCo
RMB_Equity
RMB_Perform
Sage_Fund
Sanlam_GE
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Table 4.12:
Average
Alpha
-0.34%
-0.26%
1.57%
-0.02%
-0.14%
0.04%
0.23%
0.40%
-0.55%
0.24%
-0.70%
0.15%
-0.15%
0.02%
-0.03%
-0.15%
-0.36%
-0.09%
-0.20%
-0.91%
-0.11%
-0.09%
Std Error
of Alpha
0.32%
1.07%
2.13%
0.40%
0.53%
0.36%
0.21%
1.87%
0.87%
0.32%
0.96%
2.05%
0.45%
0.18%
0.27%
0.40%
1.31%
0.18%
0.19%
0.96%
0.35%
0.20%
t-statistic
-1.05
-0.25
0.74
-0.05
-0.27
0.11
1.09
0.21
-0.63
0.76
-0.73
0.07
-0.33
0.11
-0.13
-0.38
-0.27
-0.48
-1.01
-0.94
-0.32
-0.45
Active
Risk
3.13%
2.63%
3.69%
3.52%
3.06%
3.19%
2.44%
3.24%
3.14%
2.97%
3.58%
3.55%
3.71%
2.10%
2.53%
2.77%
3.22%
2.05%
2.23%
5.95%
2.55%
2.31%
Info Ratio
-0.09
-0.10
0.43
0.00
-0.05
0.01
0.10
0.12
-0.18
0.08
-0.19
0.04
-0.02
0.01
0.00
-0.05
-0.11
-0.04
-0.09
-0.15
-0.05
-0.03
Value Added by Active Managed Funds over Rolling 120-month
Investment Periods
Fund
ABSA_General
Community_Growth
Futuregro_Albaraka
Investec_ Equity
Metropolitan_GE
OM_Growth
OM_Invest
OM_TopCo
Sage_Fund
Sanlam_GE
Stanlib_Wealth
Average
Alpha
-0.37%
-0.09%
0.25%
0.25%
0.01%
-0.06%
0.02%
-0.06%
-0.09%
-0.19%
-0.12%
Std Error
of Alpha
0.55%
0.78%
0.78%
0.29%
0.58%
1.16%
0.25%
0.51%
0.26%
0.26%
0.28%
t-statistic
-0.67
-0.11
0.31
0.86
0.02
-0.05
0.09
-0.12
-0.35
-0.73
-0.42
Active Risk
3.15%
3.41%
3.33%
2.47%
3.03%
3.48%
2.14%
2.61%
2.09%
2.24%
2.37%
Info Ratio
-0.12
-0.03
0.07
0.10
0.00
-0.02
0.01
-0.02
-0.04
-0.08
-0.05
76
From Tables 4.10-4.12 it can be seen that the minority of active funds displays
positive alphas and no fund has a significant t-statistic value of more than two. Thus,
from a statistical viewpoint no fund manager exhibited sufficient skill to outperform
the market over time, yet as for reasons noted earlier in the study (amount of data
required to prove skill) it would be unfair to argue that no active manager possessed
skill to outsmart the market.
Attention and credit should be given to those funds that comprehensively beat the
market, but maybe even more importantly those that consistently beat the market over
various time periods.
Funds like Investec Equity, Futuregrowth Albaraka, and
Metropolitan General Equity performed well over all the periods, while Allan Gray
Equity, Oasis Crescent Equity and Nedbank Rainmaker gave excellent value for
money over the shorter evaluation periods.
The individual funds’ information ratios are graphically displayed in Figures 4.214.23. Again, only a few active funds display positive information ratios across all the
rolling periods. The wide dispersion between the best and worst performers is notable.
77
Alpha/Risk Tade-Off
Rolling 36-Month Period
1.50%
1- Absa General
2- Absa Growth
3- Allan Gray Equity
4-Community Growth
5- Coris Capital GE
6- Coronation Equity
7- Futuregro Albaraka
8- Futuregro Core
9- Investec Equity
10- FNB Growth
11- MCubed Equity
12- Metropolitan GE
13- Nedbank Equity
14- Nedbank Equity FoF
15- Nedbank Rain
16- Nedbank Quants
17- Oasis Crescent
18- OM Growth
19- OM Investors
20- OM TopCo
21- Prudential Opt
22- RMB Equity
23- RMB Perform
24- Sage Fund
25- Sage MultiFocus
26- Sanlam GE
27- Sanlam MM Equity
28- Stanlib CapGro
29- Stanlib Prosp
30- Stanlib Wealth
31- Tri-Linear Equity
3
17
Alpha (Return pm)
1.00%
0.50%
15
7
9
12
25
19
21
10
4
24 30 20
29 22
6
26
18
0.00%
32
2
-0.50%
8
1
23
16 14
5
27
11
31
28
-1.00%
13
R2 = 0.1741
32- Woolw Equity
-1.50%
0%
1%
2%
3%
4%
5%
6%
7%
Non-systematic Risk
Figure 4.21: Alpha/Active Risk Profile of Actively Managed Funds over Rolling
36-month Investment Periods
78
Alpha/Active Risk Tade-Off
Rolling 60-month Period
2.00%
3
1.50%
1- Absa General
2- Absa Growth
3- Allan Gray Equity
4- Community Growth
5- Coronation Equity
6- Futuregro Albaraka
7- Investec Equity
8- FNB Growth
9- Mcubed Equity
10- Metropolitan GE
11- Nedbank Equity
12- Nedbank Rain
13- OM Growth
14- OM Investor
15- OM TopCo
16- RMB Equity
17- RMB Perform
18- Sage Fund
19- Sanlam GE
20- Stanlib CapGro
21- Stanlib Prosp
22- Stanlib Wealth
Alpha (Return pm)
1.00%
0.50%
8
10
7
12
6
14
0.00%
15
18 22 21
16
19
2
5
13
1
-0.50%
4
17
9
11
20
-1.00%
R2 = 0.0431
-1.50%
0%
1%
2%
3%
4%
5%
6%
7%
Non-systematic Risk
Figure 4.22: Alpha/Active Risk Profile of Actively Managed Funds over Rolling
60-month Investment Periods
79
Alpha/Risk Tade-Off
Rolling 120-Month Period
0.30%
4
3
0.20%
Alpha (Return pm)
0.10%
7
0.00%
6
8
2
9
-0.10%
1- Absa General
2- Community Growth
3- Futuregro Albaraka
4- Investec Equity
5- Metropolitan GE
6- OM Growth
7- OM Investor
8- OM TopCo
9- Sage Fund
10- Sanlam GE
11- Stanlib Wealth
5
11
10
-0.20%
-0.30%
1
-0.40%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
R2 = 0.0008
3.50%
4.00%
Non-systematic Risk
Figure 4.23: Alpha/Active Risk Profile of Actively Managed Funds over Rolling
120-month Investment Periods
80
The rolling average information ratios of the actively managed funds are portrayed in
Figures 4.24-4.26. From these it can be seen that the average information ratio is
never constant and moves in cycles tied closely with bull and bear markets in general
and specifically whether the mining and resources sector had a bull run or not. In
these cases the active funds, which are normally underweight this sector, on average
could not match the market or index return.
81
Rolling 36-month Period
Average Information Ratio
0.25
0.20
0.15
0.05
-0.05
-0.10
-0.15
-0.20
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
-0.25
Jan-91
Ratio
0.10
Period
Information Ratio
12 per. Mov. Avg. (Information Ratio)
Figure 4.24: Average Information Ratio over Rolling 36-month
Investment Periods
82
Rolling 60-month Period
Average Information Ratio
0.20
0.15
0.05
-0.05
-0.10
-0.15
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
-0.20
Jan-93
Ratio
0.10
Period
Information Ratio
12 per. Mov. Avg. (Information Ratio)
Figure 4.25: Average Information Ratio over Rolling 60-month
Investment Periods
83
Rolling 120-month Period
Average Information Ratio
0.06
0.04
-0.02
-0.04
-0.06
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
-0.08
Jan-98
Ratio
0.02
Period
Information Ratio
12 per. Mov. Avg. (Information Ratio)
Figure 4.26: Average Information Ratio over Rolling 120-month
Investment Periods
84
4.3
Summary
By making use of different methodologies different approaches could be followed in
analysing active management performance against its index benchmark. By excluding
the upfront costs associated with active investing, it was found that in general the
average of active management performance was superior to that of index investing.
Once these costs were considered, a different outcome was established in favour of
index investing.
On a risk-adjusted performance basis it was determined that index investing, on
balance, outperformed the average performance of active investing over the various
investment periods.
Further analysis of the individual actively managed funds revealed that the minority
of funds exhibited positive alphas and consequently positive information ratios over
the various rolling periods considered. The average information ratio of actively
managed funds moved in a cyclical manner above and below the nil level, confirming
that index investing and active investing alternate one another as the dominant
investment strategy over time.
85
CHAPTER 5:
THE PERSISTENCE OF ACTIVE MANAGEMENT
PERFORMANCE
5.1
Review of International Studies
The active manager’s best proof of ability to outperform the market is found in his or
her performance track record and serves as the criteria on which the manager is
judged and selected. Professional investment advisors and the media devote much
time and energy to study and document the past performance of mutual funds on the
premise that an analysis thereof would indicate future winners. However, question
marks are raised around the consistency of performance and whether past
performance is a reliable indicator of future performance.
The efficient market hypothesis implies among other that past performance is no
guarantee for future performance, the average manager will not be able to beat a
passive strategy, and top managers will not be expected to outperform in future.
Excess performance is the result of luck, not skill. Further, track records are useful for
evaluating the riskiness of managers’ strategies, but not to ascertain the skill of
managers (Goetzmann & Ibbotson, 1994).
Michael Jensen studied mutual fund performance over the period 1945-1964 and
concluded that not only the average fund performance, but also individual
performance was no better than that predicted from mere random chance. Later
studies confirmed Jensen’s view, but some such as those done by Hendricks, Patel and
Zeckhauser (1993) came to contrary conclusions where some consistency in winning
and losing funds was found.
Goetzmann & Ibbotson (1994) established in their studies done on raw returns, riskadjusted alpha returns and style-categorised groups that past return and relative
rankings were useful in predicting the returns and rankings of mutual funds. The topquartile performers were most likely to be in the same quartile in successive periods,
and the lower the initial ranking the worse the subsequent performance.
86
Studies by Kahn & Rudd (1995) focused on whether past performance carried any
information regarding future performance. It differed from the majority of previous
studies by making use of a style analysis method. Mutual funds were categorised into
growth versus value and large cap versus small cap orientated styles. Hereby style
returns were separated from selection returns. For example, if value managers
outperformed the broad market index (S&P 500) over two review periods an alpha
analysis might have indicated persistence, but not when done on the style analysis
method. With the latter method a value manager would be evaluated with a value
index over both periods and then whether persistence existed.
Kahn & Rudd (1995) did not find evidence of performance persistence among equity
mutual funds, before and after accounting for expenses. Their conclusion was that
with no persistence of selection returns investors would be better off to make use of
index investing, which due to its low cost would yield better returns than the median
of active funds.
Kahn & Rudd (1995) further noted that survivorship bias would make it appear that
winners repeat. Through Monte Carlo simulation studies it was proved that the tstatistic of surviving funds’ persistency was enhanced by increasing the cut-off
percentage of funds at the bottom of performance rankings.
Elton, Gruber & Blake (1996) studied the predictability of stock mutual funds using
risk-adjusted returns and concluded that funds that did well in the past continued to do
well in the future on a risk-adjusted basis. They found that both one- and three-year
alphas conveyed information about future performance, but one-year performance
periods conveyed much more information about future performance than three-year
periods.
When optimal portfolios based on past information were formulated it led to a
positive and statistically significant return compared to a portfolio where funds were
equally weighted. Elton, et al. (1996) concluded that the differences between the top
and bottom performance deciles were attributed to differences in selection skill and
expenses.
87
Carhart (1997) suggested that persistence in mutual fund performance did not reflect
superior stock-picking skill, but was rather explained by common factors in stock
returns and differences in fund expenses and transaction costs. It was found that
performance persistence among funds was short-lived and mostly eliminated after one
year. Except for the persistent underperformance of the worst-performing funds the
mean returns across deciles did not differ statistically significantly after one year.
For example, when following a strategy of buying last year’s top-decile funds and
selling last year’s bottom-decile funds a significant difference in return between the
deciles was noted after one year. Most of the spread between the deciles could be
explained by differences in the momentum of stock return and investment costs
between funds. Over the longer term these differences narrowed and except for the
bottom decile could be explained mostly by common stock factors and investment
costs.
Zheng (1999) investigated whether investors’ purchasing and selling decisions were
able to predict funds’ future performances, thus whether investors in general were
smart in selecting funds. Evidence was found that funds that received more inflows
subsequently perform significantly better than those that have had a net outflow.
Zheng (1999) noted that previous studies reported that money flows into past good
performers and flows out of past poor performers. The studies by Goetzmann &
Ibbotson (1994) and Carhart (1997) suggested that past performance persisted at least
over the short term. These two phenomena indicated that active fund investors might
have had selection ability. The study supported the “smart money” effect. Investors
were able to select funds by divesting from poor performers and investing in good
performers as the latter group outperformed the former over the short term (on
average 30 months).
However, Zheng (1999) reported that when constructing a portfolio of funds with net
inflows, no abnormal positive returns over the market returns were evident. Investors’
cash flow could not be used to predict or earn abnormal returns, thus the “smart
money” effect carried no information value.
88
Chavalier & Ellison (1999) examined whether mutual fund performance was related
to the characteristics of fund managers. Most of the raw differences in fund returns
could be explained by differences in risk, expenses and investment styles. However,
some differences remained. By isolating the style, risk and expense differences the
inherent characteristics of the fund manager were an important dividing line between
good and bad performance.
For example, managers that attended more selective tertiary institutions had on
average higher returns than those managers who attended less selective institutions.
Superior stock-picking ability existed for a subgroup of managers and could be
explained by differences in inherent abilities, benefits from better education, value of
social networks or difference in the characteristics of fund management companies
that hire managers from the different schools.
In summary, many studies were done on the persistence of mutual fund returns, but
with different conclusions reached. Some found no persistence; others experienced
persistence at least over the short term. The difference in conclusions, as noted by
Kahn & Rudd (1995), could be attributed to the different evaluation methods used, the
effect of survivorship bias, whether accounted for fees or not, and the integrity of
databases used.
On balance it seems that short-term persistence, whether good or bad, was found, but
vanished over longer review periods. The difference between the top performing
funds and the worst performing funds could be ascribed to a combination of
differences in managers’ skill, expense ratios and the momentum effect of stock
return.
89
5.2
The South African Experience: Persistence in Fund Performance
Some studies have been done in South Africa over the last number of years to
evaluate performance persistence. The findings from a few of these research studies
are subsequently highlighted.
Bradfield & Swartz (2001) analysed the persistence of general equity unit trusts over
the period 1995 to 2001. They found that some top performing funds consistently
delivered superior returns and concluded that those managers possessed significant
skill to outperform their peers.
Gopi, Bradfield & Maritz (2004) elaborated on the work done by Bradfield & Swartz
(2001). They found a high degree of persistence among the top quartile funds when
evaluated on a quarterly forward-looking basis, while the worst-performing funds
showed persistence in poor performance. However, when the forward-looking basis
was extended to two quarters (6 months) the persistence declined. The top quartile
funds still exhibited significant persistence, but the inter-quartile movements in the
other quartile groups became more random in nature.
When evaluating two possible fund allocation (fund-of-funds) strategies, based on a
quarterly and annual “look-back” period respectively, it was found that a strategy of
allocating funds to top quartile funds would have yielded in both cases the highest
return. Further, the quarterly “look-back” strategy yielded a better return than the
annual “look-back” strategy. This could be explained by short-term trending or
momentum effects, but the quarterly “look-back” strategy would only be feasible if
substantial discounted fees could be negotiated.
Oosthuizen & Smit (2002) applied the evaluation techniques used by Zheng (1999) to
establish whether South African unit trust investors displayed ex ante selection ability
of investing in funds that would perform better. The results from the analysis
indicated that investors on aggregate displayed a weak, but statistically significant,
skill in identifying winners. Nonetheless, no evidence was found that investors could
beat the market by investing in funds with positive money flows. Thus, similar to the
findings of Zheng (1999), the “smart money” effect carried no information value.
90
5.3
Persistence Analysis
5.3.1
Methodology
By ranking the performance of the actively managed funds in each period, the
persistence of funds following their rankings in subsequent periods could be
established. Further, the tendency of relative performance to be repeated over
different forward-looking or successive periods could be determined in order to gauge
whether persistence in general existed or not.
Performance rankings, in terms of percentiles, deciles and quartiles, were done
following the statistical convention where, for example the 25th percentile (first or
bottom quartile) performance would have been that value corresponding to the point
below which 25% of the observations lie (75% of the observations are above this
value). Similarly, a 75th percentile performance (third or top quartile) will be that
value corresponding to the point above which 25% of the observations lie (75% of the
observations are below this value). Deciles were ranked from 1 to 10, with 1 the
lowest and 10 the highest ranking.
Performance data were used from the “after-cost” analysis over rolling three, five and
ten year investment periods and the results from the analysis are subsequently
discussed.
91
5.3.2
Results
Quartile Ranking
The quartile ranking of active funds and their relative persistence of performance over
the three rolling periods are exhibited in Figures 5.1-5.3. Notable is the consistent
performance of a few funds, either in the top or bottom quartile.
Active funds such as Allan Gray Equity and Oasis Crescent Equity performed
consistently in the top quartile over rolling 36-month periods, while FNB Growth and
Investec Equity together with Allan Gray Equity did exceptionally well over 60month periods. Over the rolling ten year investment period Investec Equity and
Futuregrowth Albaraka had an excellent track record.
On the other side of the performance scale some active funds, like Coris Capital
General Equity, Nedbank Equity, Tri-Linear Equity, MCubed Equity, Stanlib Capital
Growth, ABSA General Equity and Sanlam General Equity fared poorly consistently.
92
Relative Fund Performance over Rolling 36-month Periods
Buy-to-sell price basis
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Allan Gray_Equity
Oasis_Cresc
Investec_ Equity
Nedbank_Rain
Futuregro_Albaraka
Coronation_Equity
Metropolitan_GE
Stanlib_Prosp
OM_TopCo
Stanlib_Wealth
FNB_Growth
Sage_Fund
RMB_Equity
OM_Growth
OM_Invest
Community_Growth
Prudential_Opt
Sanlam_GE
ABSA_Growth
ABSA_General
Stanlib_CapitalGrowth
Futuregro_Core
Nedbank_Quants
RMB_Perform
Sage_MultiF
Woolworths
Nedbank Equity FoF
Mcubed_Equity
Sanlam_MM_Equity
CorisCap_GE
Nedbank_Equity
Tri-Linear_Equity
Bottom 25%
Figure 5.1:
Middle
Top 25%
Quartile Ranking of Actively Managed Funds over Rolling
36-month Investment Periods
93
Relative Fund Performance over Rolling 60-month Periods
Buy-to-sell price basis
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Allan Gray_Equity
FNB_Growth
Investec_ Equity
Coronation_Equity
Metropolitan_GE
Futuregro_Albaraka
OM_Growth
Stanlib_Wealth
Stanlib_Prosp
RMB_Equity
OM_TopCo
Community_Growth
Sage_Fund
OM_Invest
Sanlam_GE
ABSA_Growth
Nedbank_Rain
RMB_Perform
ABSA_General
Nedbank_Equity
Mcubed_Equity
Stanlib_CapitalGrowth
Bottom 25%
Figure 5.2:
Middle
Top 25%
Quartile Ranking of Actively Managed Funds over Rolling
60-month Investment Periods
94
Relative Fund Performance over Rolling 120-month Periods
Buy-to-sell price basis
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Futuregro_Albaraka
Investec_ Equity
Metropolitan_GE
OM_Invest
Sage_Fund
OM_TopCo
OM_Growth
Community_Growth
Stanlib_Wealth
ABSA_General
Sanlam_GE
Bottom 25%
Figure 5.3:
Middle
Top 25%
Quartile Ranking of Actively Managed Funds over Rolling
120-month Investment Periods
95
Percentile Ranking
Percentile rankings of the actively managed funds are shown in Tables 5.1-5.3. Some
funds, like Allan Gray Equity, Oasis Crescent, FNB Growth, Investec Equity and
Futuregrowth Albaraka had shown exceptional persistence in achieving top
performance rankings over the different rolling periods. By the same token some
funds, like Nedbank Equity, Absa General Equity, Sanlam General Equity and Stanlib
Capital Growth had a similar persistence, but only to underperform.
Otherwise there was a relatively wide dispersion in the persistence of performance
over the rolling investment periods. If the index performance is ranked relative to the
active fund performance, it can be seen that the index performance ranked at about the
60th percentile over the periods, but with large deviations in between.
96
Table 5.1:
Percentile Ranking of Actively Managed Funds over Rolling
36-month Investment Periods
Fund
Allan Gray_Equity
Min Decile
Ranking
Max Decile
Ranking
Periods
27
Average Percentile
96
Std Dev
5
9
10
Oasis_Cresc
Nedbank_Rain
13
27
94
71
5
27
9
2
10
9
Sage_MultiF
FNB_Growth
4
27
70
68
0
11
7
5
7
9
Investec_ Equity
Coronation_Equity
156
57
68
65
33
31
1
1
10
10
Prudential_Opt
Futuregro_Albaraka
17
102
64
57
6
37
6
1
8
10
RMB_Equity
Metropolitan_GE
71
111
54
53
19
41
2
1
8
10
OM_TopCo
Stanlib_Wealth
110
156
50
50
28
35
1
1
10
10
Sage_Fund
Futuregro_Core
148
24
49
49
24
6
1
4
10
6
OM_Invest
Stanlib_Prosp
156
77
49
48
24
35
1
1
10
9
Community_Growth
Nedbank_Quants
103
14
46
45
22
13
1
2
9
6
OM_Growth
ABSA_Growth
93
30
44
41
33
12
1
2
9
7
RMB_Perform
Nedbank Equity FoF
30
20
39
34
10
20
2
1
6
6
Sanlam_GE
Woolworths
156
15
32
31
24
9
1
2
10
5
ABSA_General
Mcubed_Equity
117
37
25
23
22
10
1
1
8
5
Sanlam_MM_Equity
Stanlib_CapitalGrowth
23
62
19
16
9
25
1
1
4
9
CorisCap_GE
Nedbank_Equity
12
38
9
5
11
9
1
1
4
4
Tri-Linear_Equity
ALSI Index
13
156
5
59
5
32
1
1
1
10
97
Table 5.2:
Percentile Ranking of Actively Managed Funds over Rolling
60-month Investment Periods
Fund
Min Decile
Ranking
Max Decile
Ranking
Periods
Average Percentile
Std Dev
Allan Gray_Equity
FNB_Growth
3
3
100
90
0
0
10
9
10
9
Investec_ Equity
Coronation_Equity
132
33
84
78
24
20
1
3
10
10
Metropolitan_GE
Nedbank_Rain
87
3
76
70
27
0
1
7
10
7
RMB_Equity
Futuregro_Albaraka
47
78
55
53
16
36
3
1
9
10
ABSA_Growth
Community_Growth
6
79
52
51
8
20
4
2
6
8
OM_TopCo
OM_Invest
86
132
49
49
23
18
2
1
8
8
Stanlib_Prosp
Sage_Fund
53
124
48
48
23
21
1
1
9
9
Stanlib_Wealth
RMB_Perform
132
6
45
37
32
8
1
3
10
5
OM_Growth
Sanlam_GE
69
132
36
19
34
21
1
1
9
8
Mcubed_Equity
ABSA_General
13
93
17
13
5
19
1
1
2
6
Nedbank_Equity
Stanlib_CapitalGrowth
14
38
11
1
9
4
1
1
3
2
132
65
26
1
10
ALSI Index
Table 5.3:
Percentile Ranking of Actively Managed Funds over Rolling
120-month Investment Periods
Fund
Investec_ Equity
Futuregro_Albaraka
Metropolitan_GE
OM_Invest
Sage_Fund
OM_TopCo
Community_Growth
OM_Growth
Stanlib_Wealth
Sanlam_GE
ABSA_General
ALSI Index
Periods
72
18
27
72
64
26
19
9
72
72
33
72
Average
Percentile
99
88
66
64
59
39
36
29
24
8
0
57
Std Dev
3
9
14
11
11
13
13
3
15
8
0
21
Min Decile Ranking
9
8
5
3
4
2
2
2
1
1
1
1
Max Decile
Ranking
10
10
8
8
8
7
6
3
7
2
1
9
98
Beating the Index
Besides the persistence of performance it is also relevant to what extent active funds
were repeatedly able to beat the index. The percentage success rate of each active
fund in outperforming the index is shown in Table 5.4.
Table 5.4:
Consistency of Actively Managed Funds in Beating the ALSI Index
Funds
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
CorisCap_GE
Coronation_Equity
Futuregro_Albaraka
Futuregro_Core
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank Equity FoF
Nedbank_Rain
Nedbank_Quants
Oasis_Cresc
OM_Growth
OM_Invest
OM_TopCo
Prudential_Opt
RMB_Equity
RMB_Perform
Sage_Fund
Sage_MultiF
Sanlam_GE
Sanlam_MM_Equity
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Tri-Linear_Equity
Woolworths
Rolling
Rolling
Rolling
Three Year Period
Five Year Period
Ten Year Period
Percentage
Percentage
Percentage
Periods Outperforming Periods Outperforming Periods Outperforming
117
16%
93
15%
33
0%
30
0%
6
0%
27
100%
3
100%
103
37%
79
37%
19
26%
12
8%
57
40%
33
48%
102
48%
78
47%
18
100%
24
8%
156
62%
132
74%
72
100%
27
41%
3
100%
37
3%
13
0%
111
44%
87
57%
27
48%
38
0%
14
0%
20
0%
27
59%
3
67%
14
7%
13
100%
93
46%
69
33%
9
0%
156
31%
132
17%
72
51%
110
39%
86
45%
26
31%
17
29%
71
42%
47
17%
30
3%
6
0%
148
42%
124
22%
64
44%
4
100%
156
26%
132
9%
72
1%
23
0%
62
13%
38
0%
77
17%
53
15%
156
21%
132
19%
72
4%
13
0%
15
7%
99
When considering the number of periods under review the Investec Equity fund had a
high success rate in beating the index. To a lesser extent funds like Futuregrowth
Albaraka Equity and Metropolitan General Equity funds had good successes. The
Allan Gray Equity and Oasis Crescent Equity had a 100% success rate, but with
considerably less review periods than the earlier-mentioned equity funds.
Predictability of Performance
In the analysis thus far it has been established that some funds exhibited exceptional
persistence in keeping their relative performance rankings. Other funds again showed
large deviations from their average ranking. Beside this knowledge one would like to
ascertain to what extent the persistence information could be used as a tool to predict
performance. For example, if a fund is delivering a good performance now, what are
the probabilities that it will still be a good performer in twelve months’ time?
The performance data of the rolling three year period was selected to test the
information value of performance persistence, because it had more periods (156) to
analyse and, secondly, it had more funds than those in the other rolling periods to
establish any trends.
By studying the past track records of the active funds it was possible to derive
probabilities that a similar performance in successive periods would be repeated.
Different successive periods were selected, namely monthly, quarterly, yearly and
three-yearly. Further, to identify whether top performing funds had a greater chance to
repeat performance the funds were split into three groups according to their average
percentile ranking, specifically the top third, middle third and bottom third funds.
Table 5.5 illustrates the tendency of fund performance to be repeated over the
different successive periods - either in the same decile, or alternatively to change to
another decile; thus either improving or weakening the performance profile. If no or
little persistence existed, one would expect that the movement between successive
periods would assume a random character, thus roughly a 30% movement to any of
the three decile positions.
100
Table 5.5:
Relative Movement of Actively Managed Funds between Deciles
over Different Forward-looking Periods
Relative
Movement
Same
Decile
Improved
Decile
Worse
Decile
Active Fund
Ranking
Monthly
Forward
Quarterly
Forward
Yearly
Forward
Threeyearly
Forward
Overall
64%
55%
25%
8%
Bottom Third
64%
57%
21%
5%
Middle Third
61%
52%
23%
9%
Top Third
75%
68%
37%
6%
Overall
18%
22%
37%
41%
Bottom Third
17%
20%
38%
37%
Middle Third
19%
24%
36%
41%
Top Third
13%
16%
32%
30%
Overall
18%
22%
38%
51%
Bottom Third
19%
23%
41%
58%
Middle Third
20%
24%
41%
50%
Top Third
12%
17%
31%
64%
101
From Table 5.5 it is observed that fund performance tends to persist over the shortterm successive periods, especially top performing funds tend to repeat their
performance. The top funds also exhibited lower tendencies to weaken their decile
rankings than the bottom third or middle third groups.
When the successive period was extended to one year forward the movements to the
different decile positions became more random in nature. The top performing group
showed a slightly higher tendency to repeat performance than the other two groups,
but in essence persistence disappeared.
Over a three-year successive period it was found that the likelihood that a fund would
have remained in the same performance decile was very slim, but rather tended to
move into lower performance deciles than higher rankings. Notable is that the top
performing funds had a higher tendency to drop performance than the other two
groups over the three-year forward-looking period.
The findings from the analysis are graphically displayed in Figures 5.4-5.7.
102
Ranking of Active Funds (All)
Average Movement between Deciles
Month-on-Month Forward
18%
18%
64%
Same Decile
Figure 5.4:
Improved Decile
Worse Decile
Tendency of Actively Managed Funds to Move between Deciles
on a Month-to-Month basis
Ranking of Active Funds (All)
Average Movement between Deciles
Quarter-on-Quarter Forward
22%
56%
22%
Same Decile
Figure 5.5:
Improved Decile
Worse Decile
Tendency of Actively Managed Funds to Move between Deciles
on a Quarterly basis
103
Ranking of Active Funds (All)
Average Movement between Deciles
Year-on-Year Forward
25%
38%
37%
Same Decile
Figure 5.6:
Improved Decile
Worse Decile
Tendency of Actively Managed Funds to Move between Deciles
on a Yearly basis
Ranking of Active Funds (All)
Average Movement between Deciles
Three Year-on-Three Year Forward
8%
51%
41%
Same Decile
Figure 5.7:
Improved Decile
Worse Decile
Tendency of Actively Managed Funds to Move between Deciles
on a Three-yearly basis
104
5.4
Summary
Results from the study have shown similar trends than those established in
international and local studies. Short-term persistence in performance return was
found, but in general it did not exhibit any long-term predictability value.
A few funds showed remarkable persistence in keeping their performance in the top
quartiles or alternatively to beat the index on a regular basis. However, in similar style
some funds showed persistence in underperforming. The rest delivered a wide
dispersion of relative performance.
Index investing ranked at about the 60th percentile of active fund performance over
the various investment periods, but showed large deviations in performance ranking
over time. Nonetheless, its average ranking of the 60th percentile confirms that index
investing indeed yields better-than-average results over time.
105
CHAPTER 6:
6.1
TOWARDS AN OPTIMAL COMBINATION SOLUTION
The Question
From the analysis of performance comparisons between active and passive investing,
does it mean one only has to select those active funds that were consistently able to
deliver top-notch returns and outperformed the index benchmark?
Supposedly, randomness of results does not apply to these funds. Yet, the odds and
probabilities of long-term consistent performance are against these funds. Numerous
studies in the past have indicated that an investing strategy of buying past winners
does not deliver the desired results over the long run. Further, in the results thus far it
has been shown that there were periods that basically no active fund was able to beat
the index and that it could last for a considerable period.
However, index investing has not been a consistent performer either. An index
investor would have experienced volatile returns over the various investment periods.
Thus, an index strategy on its own does not necessarily provide an optimal solution in
the South African context with its concentrated market characteristics.
Probably one of the most important trends identified in the study was that index
investing and active investing significantly outperformed one another over time in a
cyclical manner.
Thus, as a logical step forward, what if these strategies could be combined to deliver
an overall consistent return for investors? Further, is there an optimal combination
level to be found? These aspects will be investigated and discussed in the following
sections.
106
6.2
Theoretical Framework
Treynor and Black (Bodie, Kane & Marcus, 1999: 877) developed an optimal
portfolio construction model based on modern portfolio theory principles whereby the
optimal active fund exposure relative to the market portfolio (index) could be
constructed.
The optimal combination of active portfolio A with the passive portfolio M is given
by the following determinants:

[  A 2 2 M   2 (eA) ]
σA =
where σA =

(6.1)
standard deviation of active portfolio A;
βA=
beta of active portfolio with market portfolio M;
σ2 M =
variance of market portfolio M;
σ2(eA) =
variance of non-systematic risk of active portfolio A.
  r   [ E (r )  r ]
E(rA) =
A
where E(rA) =
f
A
M
f
(6.2)
expected return of portfolio A;
αA =
abnormal return expected from active portfolio A;
rf =
risk-free rate of return;
E(rM)-rf =
expected excess market return above the risk-free rate
And,

 /  2 (e )
A
Wopt =
A
[ E ( rM )  rf ] /  2 M
where Wopt = weight of active portfolio A in optimal portfolio, if βA = 1
(6.3)
107

Wopt /[1  (1  A)Wopt]
Wadj =
(6.4)
where Wadj = adjusted weight of portfolio A to actual βA
In essence the Treynor-Black model uses Sharpe’s measure of reward-to-risk in
determining the weight of the active portfolio in the optimal solution, where the
abnormal return (αA) is divided by the non-systematic risk of the active portfolio,
σ(eA), otherwise known as the appraisal or information ratio. Hence, the reward-torisk components of the optimal portfolio could be separated as:
2
 E (rM )  rf 
 A 

 + 

 (eA)
M

2
Sharpe =
2
(6.5)
The components (underlying active funds) of the active portion that will be included
in the optimal solution will be selected according to those with the highest
information ratio and is given by:
 /  2 (ek )
k
Wk =
  /
A
where Wk =
2
(eA)
(6.6)
weight of active fund k relative to active portfolio A
Waring & Siegel (2003) supported the above approach and argued that active
managers should be used and paid only for generating pure active return (alpha).
Their arguments are based on the premise that total risk could be broken into policy
risk (strategic asset allocation), which is duly rewarded by the equity risk premium
over time, and non-systematic or active risk, which is a zero-sum game on the
aggregate and not rewarded on average.
However manager skills differ and capital markets are not completely efficient,
therefore there is scope for skilled active managers to outperform the market.
While
the pay-off to market-related risk is linearly related to the amount of policy risk taken,
108
it is not true for active risk. Without any skill there is no reward, but in the presence of
skill it will be rewarded and decline in proportion to the amount of active risk taken.
Therefore preference should be given to active managers that can generate high
alphas, but not with the corresponding active risk.
In assessing active managers with potential high information ratios Waring & Siegel
(2003) proposed not to place too much emphasis on analysing past performances,
since in itself it is a poor predictor of the future and it does not differentiate between
luck and skill.
Statistical tests (t-statistic) are used to indicate whether past
performances of managers were due to luck or skill, but even a high t-statistic (greater
than two) does not prove skill without any doubt, rather a low t-statistic should be
interpreted as having no evidence of skill. The same applies in using style boxes or
maps to indicate managers’ past performances relative to risk. Rather, more time and
effort should be going towards predicting or forecasting alphas together with correctly
benchmarking the managers’ performances. Although a daunting task by all measures,
it is very much on par with what the active manager is trying to achieve: constructing
a portfolio of securities which will outperform the market.
Waring, Whitney, Pirone & Castille (2000) developed a manager structure
optimisation (MSO) model, similar to the Markowitz mean-variance method, which
basically requires the expected alphas and active risks of managers, and a description
of the manager’s customised benchmark. Hereby an efficient frontier of optimal
combinations of index funds, risk-controlled funds (enhanced index funds) and active
funds can be formed for certain levels of active risk required. Figure 6.1 illustrates the
MSO model where the horizontal axis is represented by the expected active risk and
the vertical axis by the expected alpha.
109
Active Return versus Active Risk
3.00%
Expected Alpha
2.50%
44% Index
33% Enhanced Index
23% Active
2.00%
17% Enhanced Index
83% Active
1.50%
1.00%
0.50%
0.00%
0.00%
0.50%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
Active Risk
100% Index
Figure 6.1:
1.00%
Efficient Frontier of Optimal Combination Strategies
Source: Adapted from Waring & Siegel, 2003: 42
From Figure 6.1 it can be seen that at zero active risk only index funds will be held,
but as risk tolerance increases the proportions of enhanced index funds and active
funds will increase.
The holding weight of an active manager will be directly proportional to the expected
information ratio of the manager and inversely proportional to the volatility of the
manager’s alpha around a properly established benchmark. Kahn (2000) in Waring &
Siegel (2003: 43) proposed the following utility function for active management:
 Infomgr
hmgr ~ 

 (emgr) 
(6.7)
Where, hmgr is equal to the percentage allocation of a manager,
Infomgr is the expected information ratio of the manager, and
σ(emgr) is the expected volatility of the manager’s α around its benchmark.
110
Since risk is used as a denominator in the information ratio and used on its own in the
above function, risk is squared. Therefore risk is the most important determinant in
allocating managers’ proportions. The information ratio, all else being equal, will be
reduced with an increased level of active risk. Therefore in a normal long-only
portfolio (constrained portfolio) the information ratio will decline with an increase in
active risk. However, in an unconstrained portfolio (long-short portfolios) where the
manager besides having a zero exposure can short a specific security the efficient
frontier will assume a straight line.
To illustrate the principle of declining information ratios in constrained portfolios
Kahn (2000) in Waring & Siegel (2003: 44) found that at a given skill level enhanced
index funds and market-neutral long-short funds had twice as high information ratios
than their long-only, traditional active counterparts.
Since active risk is uncorrelated with policy risk, the total risk of an active portfolio is
less than the sum of policy and active risk, and typically slightly more than policy risk
alone. For example, if policy risk is 9% and active risk is 3%, the total risk of the
portfolio will be 9.5% (given by 92  32 ). Hence, the argument could be put forward
that a more aggressive stance on the active risk component of a portfolio could be
afforded.
Waring & Siegel (2003: 44) proposed that the appropriate level of active risk in a
portfolio should be in line with studies done by Brinson, Singer & Beebower (1991)
where it was found that 90% of the variance of a typical portfolio’s return was
attributed to strategic asset allocation decisions (market risk) and only 10% attributed
to active decisions (selection and timing).
Therefore in a portfolio with a policy risk of 9% (0.81% variance) and active risk of
3% (0.09% variance) the level of active risk is appropriate since the ratio between
policy variance and active variance is 90 to 10.
111
Waring & Siegel (2003: 45) reasoned further that market risks are rewarded
unconditionally and proportional to market risk taken, while active risks are only
rewarded conditional and in declining proportion to active risks taken. Therefore it
would be rational in any portfolio to place a much larger bet on market risk than
active risk.
Table 6.1 summarises possible allocation weights for each active risk level. Most
investors would be comfortable with active risk levels of 1.5% to 2%, while the
largest investors (pension funds) would even prefer less active risk (Waring & Siegel,
2003: 46).
Table 6.1: Example of Optimal Manager Allocations
Type
0%
0.5%
1.0%
1.5%
2.0%
2.5%
3%
Of
Active
Active
Active
Active
Active
Active
Active
Fund
Risk
Risk
Risk
Risk
Risk
Risk
Risk
Index Fund
100
72
44
16
0
0
0
Enhanced Index
0
16
33
50
52
39
17
Active Growth
0
5
10
15
21
26
35
Active Value
0
5
10
15
21
26
35
Active Concentrated
0
2
3
4
6
9
13
Source: Waring & Siegel, 2003: 47
The process described above integrates both active and passive strategies, therefore
the debate should not be whichever strategy yields the highest return, but rather how
these strategies could be combined to yield the highest return at the most appropriate
risk levels for investors.
112
6.3
Developing an Optimal Allocation Model
Table 6.2 exhibits risk data from the rolling 60-month investment periods and which
are graphically depicted in Figures 6.2-6.4. The rolling 60-month data is used as an
example, but data over the other rolling periods exhibit the same trends.
Table 6.2: Risk Data and Ranking of Actively Managed Funds over Rolling
60-month Investment Periods
Funds
ABSA_General
ABSA_Growth
Allan Gray_Equity
Community_Growth
Coronation_Equity
Futuregro_Albaraka
Investec_ Equity
FNB_Growth
Mcubed_Equity
Metropolitan_GE
Nedbank_Equity
Nedbank_Rain
OM_Growth
OM_Invest
OM_TopCo
RMB_Equity
RMB_Perform
Sage_Fund
Sanlam_GE
Stanlib_CapitalGrowth
Stanlib_Prosp
Stanlib_Wealth
Alpha
-0.340%
-0.265%
1.572%
-0.022%
-0.143%
0.038%
0.231%
0.395%
-0.548%
0.241%
-0.697%
0.148%
-0.146%
0.021%
-0.035%
-0.152%
-0.361%
-0.089%
-0.196%
-0.911%
-0.112%
-0.091%
Active Risk
3.13%
2.63%
3.69%
3.52%
3.06%
3.19%
2.44%
3.24%
3.14%
2.97%
3.58%
3.55%
3.71%
2.10%
2.53%
2.77%
3.22%
2.05%
2.23%
5.95%
2.55%
2.31%
Info Ratio
-0.1086
-0.1007
0.4264
-0.0061
-0.0469
0.0120
0.0948
0.1221
-0.1745
0.0813
-0.1944
0.0419
-0.0394
0.0099
-0.0136
-0.0548
-0.1120
-0.0432
-0.0882
-0.1532
-0.0440
-0.0395
Percentile
(Info)
19%
24%
100%
67%
38%
76%
90%
95%
5%
86%
0%
81%
57%
71%
62%
33%
14%
48%
29%
10%
43%
52%
113
Alpha Added Range
Rolling 60-month Data
2.000%
1.500%
Alpha (p.m.)
1.000%
0.500%
0.000%
-0.500%
-1.000%
100%
95%
90%
86%
81%
76%
71%
67%
62%
57%
52%
48%
43%
38%
33%
29%
24%
19%
14%
10%
5%
0%
-1.500%
Percentile Ranking (Info Ratio)
Figure 6.2:
Distribution of Alphas across Actively Managed Funds over
Rolling 60-month Investment Periods
Active Risk Range
Rolling 60-month Data
7.00%
6.00%
Active Risk
5.00%
4.00%
3.00%
2.00%
1.00%
100%
95%
90%
86%
81%
76%
71%
67%
62%
57%
52%
48%
43%
38%
33%
29%
24%
19%
14%
10%
5%
0%
0.00%
Percentile Ranking (Info Ratio)
Figure 6.3:
Distribution of Active Risk across Actively Managed Funds over
Rolling 60-month Investment Periods
114
Value Added Range
Rolling 60-month Data
0.5000
0.4000
Information Ratio
0.3000
0.2000
0.1000
-0.1000
-0.2000
100%
95%
90%
86%
81%
76%
71%
67%
62%
57%
52%
48%
43%
38%
33%
29%
24%
19%
14%
10%
5%
0%
-0.3000
Percentile Ranking (Info Ratio)
Figure 6.4: Distribution of Information Ratios across Actively Managed Funds
over Rolling 60-month Investment Periods
From the above information some findings can be made:

Information ratios are only positive from around the 70th percentile and would
thus serve as the logical starting point where actively managed funds would be
used in an optimal combination portfolio.

A strong correlation (0.98) exists between the alpha attained and information
ratio of an actively managed fund. A very weak inverse correlation between
risk and the information ratio was identified.

Exceptionally good or bad alphas (and information ratios) are visible at the
outer ends of the percentile rankings. A typical leptokurtic distribution is
found. These outliers would increase the error term in predicting results.
115

The “normal zone” for evaluating both strategies would be considered as
between the 70-80th percentile ranking, or otherwise top quartile performance.
Expected performance less than that would make index investing the only
choice, and performance above this range would necessitate only active
investing.
6.4
Results from the Optimal Allocation Model
In developing an optimising model, based on the theories put forward by Treynor and
Black, three different alpha levels with corresponding active risks were selected to
give the expected information ratios at the 70th, 75th, and 80th percentile of active
management. These were based on the findings from the rolling 60-month periods
(Table 6.2).
The following risk information, shown in Table 6.3, was entered into the TreynorBlack optimising model. The average volatility and beta measures used in the
optimising model were gathered from the rolling 60-month risk data (Table 4.6). The
results from the model are exhibited in Tables 6.4-6.6 and graphically depicted in
Figures 6.5-6.7.
Table 6.3: Data input of the Optimal Allocation Model
Fund Ranking
70th Percentile
75th Percentile
80th Percentile
Index Fund
Average
Beta
75%
75%
75%
100%
Average
Alpha
(pm)
0.035%
0.050%
0.120%
0%
Average
Volatility
6.00%
6.00%
6.00%
6.00%
Average
Active
Risk
3.25%
3.20%
3.00%
0%
Average
Information
Ratio
0.0108
0.0156
0.0400
116
Table 6.4: Optimising Results with 70th Percentile Active
Investment Performance
Expected Excess
Active Fund
Index Fund
Market Return
Allocation
Allocation
0.25%
37%
63%
0.50%
19%
81%
0.75%
13%
87%
1.00%
10%
90%
1.25%
8%
92%
1.50%
7%
93%
Active Fund Weight in Portfolio
Active Fund Performance in 70th Percentile
100%
90%
Percentage Allocation
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.25%
0.50%
0.75%
1.00%
1.25%
1.50%
Expected Excess Market Return (p.m.)
Figure 6.5:
Example of Optimal Actively Managed and Index Fund Weights in
an Investment Portfolio given various Market Returns
117
Table 6.5:
Optimising Results with 75th Percentile Active
Investment Performance
Expected Excess
Active Fund
Index Fund
Market Return
Allocation
Allocation
0.25%
49%
51%
0.50%
26%
74%
0.75%
18%
82%
1.00%
14%
86%
1.25%
11%
89%
1.50%
9%
91%
Active Fund Weight in Portfolio
Active Fund Performance in 75th Percentile
100%
90%
Percentage Allocation
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.25%
0.50%
0.75%
1.00%
1.25%
1.50%
Expected Excess Market Return (p.m.)
Figure 6.6:
Example of Optimal Actively Managed and Index Fund Weights in
an Investment Portfolio given various Market Returns
118
Table 6.6:
Optimising Results with 80th Percentile Active
Investment Performance
Expected Excess
Active Fund
Index Fund
Market Return
Allocation
Allocation
0.25%
100%
0%
0.50%
77%
23%
0.75%
55%
45%
1.00%
43%
57%
1.25%
35%
65%
1.50%
30%
70%
Active Fund Weight in Portfolio
Active Fund Performance in 80th Percentile
100%
90%
Percentage Allocation
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.25%
0.50%
0.75%
1.00%
1.25%
1.50%
Expected Excess Market Return (p.m.)
Figure 6.7:
Example of Optimal Actively Managed and Index Fund Weights in
an Investment Portfolio given various Market Returns
119
From the results it can be seen that the optimal active fund weight in the portfolio will
increase with an increase in the percentile ranking of active fund performance. For
example, when active fund performance is to be expected in the 75th percentile range,
26% exposure would be given to active investing when excess market return of 0.50%
per month is expected. Similarly, an allocation of 77% would be given to active
investing if active fund performance is expected to be in the 80th percentile range.
Within the same percentile ranking the passive fund allocation will increase with
increasing excess market performance expectations. In other words, the better the
expected excess return from the market, the lower the allocation towards active
investing should be.
120
6.5
The Quest for an Optimal Solution
Where do the results from the optimal allocation model leave one in deciding how
much exposure to give to any one of the strategies? Performance from active
managers needs to be in the top echelons of returns to justify an active management
strategy, otherwise only index investing will do. On the other hand, if the active
manager is successful in achieving top performance then index investing is obsolete.
Basically the answer to the question boils down to personal beliefs and perceptions. If
one does not believe that active managers will on average over time beat the market,
then index investing is the logical choice. Convincing evidence exists that the market
cannot be beaten over the long term by active management. Yet, there are managers
who have beaten the market comprehensively over time and this elite group attracts
the attention and monies of investors. No guarantees can be given that future
performance will be repeated, but nevertheless investors buy their story in utmost
belief and confidence, but have no backup strategy if things go horribly wrong.
A more logical approach needs to be formulated. The concept of index investing is
appealing and logical, but does not attract emotional intelligence. If one wants to
believe in the story of active management one must believe that the average
performance is going to be at least in the 70-80th percentiles; if that belief is not
convincing enough, then index investing should be the choice. Any performance
better than the target range would be an absolute bonus and anything less would be a
calculated misjudgement.
Further to this argument, if one perceives the equity premium in general to be around
7% per annum (0.6% pm) one could use the results from the optimising model to
formulate an allocation strategy between active and index investing, depending on
one’s perceptions of the performance level that will be achieved with active investing.
Table 6.7 highlights possible allocation ratios between active and index investing for
different performance expectations.
121
Table 6.7: Optimal Allocation between Active and Passive Strategies at an
expected 0.6% per month Excess Return
Percentile
Active Allocation
Index Allocation
70th
16%
84%
75th
22%
78%
80th
67%
33%
From the above it seems that, even if one is a devoted active management supporter, a
prudent strategy would be to allocate at least 30% of the total portfolio weight
towards index investing strategies. Hereby the maximum reward for risk is ensured.
To verify the above argument the historic performance of active investment combined
with index investing was backtested. Active fund performance in the top quartile (top
25%) was considered over the three rolling periods (three, five and ten years). The
return from top quartile active performance was then mixed with index investing in a
range from 0-100%, by an increment of 10% per combination.
122
The input data for backtesting are shown in Table 6.8.
Table 6.8: Return and Risk Measures for Active and Index Investing
Rolling
Number
Period
Measure
Top Quartile
ALSI Index
of
Active Management
Return
Periods
Performance
(per
(per annum)
annum)
Before Cost
Average
36 months
60 months
120 months
156
132
72
After Cost
13.69%
11.63%
11.32%
Std Deviation
7.26%
7.12%
8.14%
Average
12.49%
11.25%
11.05%
Std Deviation
5.23%
5.17%
5.27%
Average
11.52%
10.90%
10.89%
2.29%
2.27%
2.11%
Return
Return
Return
Std Deviation
A “reward-to-risk” (adjusted Sharpe) ratio was calculated for each combination over
the various rolling periods. The maximum “reward-to-risk” ratio found was then used
to identify the optimal mix between the active and passive strategy. Figures 6.8-6.10
illustrate the reward/risk results for the respective rolling investment periods.17
17
The detailed results of the different combinations are shown in Appendix G.
123
Reward-to-Risk
Rolling 36-month Period
Top Quartile Active Performance
2.00
1.80
1.60
1.40
Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Indexing
Before Cost
After Cost
Figure 6.8: Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 36-month Investment Periods
124
Reward-to-Risk
Rolling 60-month Period
Top Quartile Active Performance
2.45
2.40
2.35
2.30
Ratio
2.25
2.20
2.15
2.10
2.05
2.00
1.95
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Indexing
Before Cost
After Cost
Figure 6.9: Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 60-month Investment Periods
125
Reward-to-Risk
Rolling 120-month Period
Top Quartile Active Performance
5.30
5.20
5.10
Ratio
5.00
4.90
4.80
4.70
4.60
4.50
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Indexing
Before Cost
After Cost
Figure 6.10: Reward-to-Risk Ratio for Various Active/Index Investing
Combinations over Rolling 120-month Investment Periods
126
From the rolling three year period (Figure 6.8) no convincing evidence is found that
indexing would have contributed to investment performance, but then again how
much emphasis should be put on relative short term data? Over the rolling five year
investment period (Figure 6.9) indexing would not have added any value when
upfront costs were ignored. However, when these costs were considered, an optimal
reward-to-risk would have been attained with a 30% index investing level. Over the
rolling ten year period (Figure 6.10) the story for index investing is very convincing
where the optimal reward-to-risk level necessitated a 60-90% index strategy.
The message is clear: over the long term active management is going to struggle to
beat index investing. If one is investing for the long term, which invariably should be
the case for equity investing, then index investing should form part and parcel of the
investment strategy. The actual level required would vary with personal preferences
and beliefs, but to exclude it would be irresponsible.
Alternatively viewed, a strong case can be made for enhanced index investing, which
combines some benefits of active investing (alpha with a limited tracking error) with
the cost benefits of index investing. The same effect is more or less achieved by
mixing the strategies in one’s overall investment portfolio.
Hereby the debate between active and passive investing is put to rest. Any debate
without realising that both strategies should be used in conjunction with each other,
has failed, yet very often these debates are held to serve the interests of one particular
group. The rational approach advocated, however, ultimately benefits the investor,
who in the first place should have been the focus of any active/passive debate.
127
CHAPTER 7:
THE ROAD AHEAD:
APPLYING PASSIVE STRATEGIES
Despite the impressive performance of index investing versus active management in
general and the potential value in combining the two strategies, relatively little interest
is shown by individual investors towards index funds. The phenomenon is universal,
but probably more apparent in South Africa than most of the developed economies of
the world.
In the USA and UK between 25% and 30% of institutional monies are invested in
passive funds, but individual investors on average only invest 5-10% of their assets in
this fashion. Elsewhere around the world these numbers would even be lower.
Internationally, companies like Vanguard, Dimensional Fund Advisors and Barclays
Global Investors are the leading index fund providers, but lately ETF investing has
become popular with about $150 billion under management in more or less 250
different funds (Wood, 2004a). Barclays Global Investors is the dominant player in
this market with a wide range of ETF products developed for specific needs.
In South Africa, especially, modest attention is given to index investing. In the unit
trust business only 1.5% of the total equity assets are invested in index funds
(enhanced index funds excluded). Within the different sectors, there are three index
funds in the general equity sector with total assets of R150 million out of R34 billion,
and three index funds in the large capitalisation sector with assets of R900 million out
of R3.6 billion (Association of Collective Investments, 2004).
The recent introduction and acceptance of ETFs by South African investors
(predominantly institutional) seem promising, but will still have to go a long way
before it will be broadly accepted by the investment public. Four different ETFs were
launched over the last couple of years, namely SATRIX 40, SATRIX FINI, SATRIX
INDI and ABSA’s New Rand, which focuses specifically on the top ten rand hedge
stocks. The SATRIX 40 is the dominant ETF with R3,2 billion invested out of a total
of R6 billion invested in all the ETFs (Wood, 2004a). However, compared with the
128
international market the range of ETFs is still very limited and more sector-specific or
style-specific funds will probably be developed in the future.
The underlying reasons why investors do not make use of index investing on a larger
scale seem universal. Kirzner (2000: 11), for example, noted that the slow growth and
acceptance of index funds by individuals can be contributed to a general lack of
understanding of passive investing, fear that investors will miss out on the outperformance by “star” fund managers, and poor promotion of index products by
investment advisors. The latter reason could be coupled to the lack of monetary
incentives paid to these advisors.
Similar reasons should be valid for South African investors. No formal numbers are
available, but one would guess that the majority of individual equity investments is
done through financial advisors who could place investments either directly with the
fund management company or through administration platforms, which on its own
make up about 30% of the unit trust market (Turpin, 2004). Whether advisors do not
understand or believe in the concept of index investing or whether it is a lack of
monetary incentives is not clear.
Most of the South African index funds, including the ETFs, make provisions for
upfront commissions to be paid to intermediaries.18 The channelling of investments
through an administration platform in any event makes remuneration possible for the
advisor, irrespective of whether the underlying investment funds pay fees or not.
One could thus argue that the incentive aspect for advisors could not be the only
reason why index funds are not popular. Most certainly it also has to do with
problems around perceptions and lack of emotional attractiveness attached to index
funds.
Investors should, however, realise when investing in high-cost index funds, it is less
likely that the index fund return will match the index benchmark, and to a certain
effect negate the whole purpose of index investing. Low-cost index funds (like
18
The cost structures of the various index unit trust funds and ETFs are shown in Appendix E.
129
Investec Index and Kagiso Top 40) have the best chance to closely track the market
index, all else being equal.
Enhanced index funds, given that the tracking error is minimised to say 1-2% and that
the ongoing management fee is say within 0.50% of that of the low-cost index funds,
could be a prudent option instead of a regular index fund. With these products certain
limited deviations from the benchmark are made towards those segments where the
most potential gains are seen. Since out-performance (alpha) is possible with low
active risk involved the resultant information ratio might be very attractive.
Quantitative fund managers, like Futuregrowth, Prescient and Kagiso, have developed
enhanced index products over the last couple of years and more developments should
be forthcoming (Wood, 2004b).
One cannot foresee that the market perception of index funds will change to the
extreme that the majority of investors will adopt passive strategies. It is, as mentioned
before, against human nature to accept averaging or mediocrity. Yet, this study, as
many before, has shown that indexing gives the investor better-than-average returns
over time. Maybe even more importantly, combining active and passive strategies
could lead to more consistent returns and less volatility. The astute advisor and
investor have an alternative at hand to secure better and consistent value for money.
130
CHAPTER 8:
ANSWERING THE SCEPTICS
In closing, the two questions posed at the beginning of the paper can now be answered
with confidence:
“No, index investing is not a fad, it’s not a specific investment style or strategy which
often comes to the fore in the investment game as the “new solution” just to be
replaced by another a few years later, it’s the average result of all active trading in the
marketplace and that can’t change.”
“No, the great majority of active managers do not know specifically where the equity
market is heading, they can more or less predict it in general terms, sometimes they
will be spot on, other times they will get it wrong, on average they will give you the
market return, but then you still would have had to pay them.” 19
19
A summary of some memorable quotes made by well-known investment gurus is shown in
Appendix H.
131
CHAPTER 9:
9.1
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
In general, the findings of the study corresponded with the theories and principles of
active versus passive investing. Similar results were obtained than those studies done
elsewhere in the world in which passive or index investing performed better than the
average of active investing over time.
However, caution should be exercised in concluding that passive investing is the only
viable investment strategy to follow. Many of the underlying assumptions in building
such a theory could be wrong; there are comparative issues such as equally-weighted
versus capitalisation-weighted measurements or lack of appropriate benchmarks that
could skew performance comparisons. Further, the net outcome of such an analysis
depends on the time frame used. Different conclusions can be reached by shifting the
review period forward or backward.
Rather, an investor needs a balanced approach on the active versus passive investing
debate. A fundamentalist approach regarding any one of the strategies is prone to be
proven wrong. In developing such a balanced viewpoint it is necessary to reflect on
the findings of the study. The conclusions that can be made from the study support
such a stance in the active versus passive debate.
The study revealed that when upfront costs attached to active investing were ignored,
active fund managers have beaten the index benchmark over the various measurement
periods and methods used in the study. The average performance of active fund
managers more than compensates for the ongoing fees applicable to manage active
funds and delivered out-performance versus the index.
For example, if a cumulative performance measurement approach is used, the average
of active funds beat the index in 60% of the 156 periods under review. In the random
132
sampling study the average of active funds statistically outperformed the index over a
five and ten year investment period at a 5% significance level, while a similar result
manifested over a rolling ten year period.
However, when the upfront cost of active investing was included in the performance
analysis a different conclusion to the above was made. Upfront costs have had a
significant impact on the performance of actively managed funds, especially over the
shorter investment periods.
Hence with the random sampling method index investing statistically outperformed
the average of active funds (at a 5% significance level) over three and five year
investment periods. Index investing also fared significantly better than the average of
active funds over the rolling investment periods and active funds out-performed the
index in only 30% of the cumulative performance periods.
An analysis of the risk-adjusted returns (Sharpe and Treynor) showed that the index
significantly outperformed the average of active funds over rolling five and ten year
periods, with no statistical significant difference (at a 5% level) over the three year
periods.
In general it was found that the hypothesis that more than 50% of active funds will
under-perform the index, holds and on average only 40% of active funds fared better
than the index over rolling three, five and ten year periods respectively. Further, one
can conclude that on average the active fund manager did not add significant value to
fund performance by being different to the market risk profile. However, notable
exceptions to the rule were identified.
Similar exceptions were identified when the consistency of fund performance was
analysed. A few funds exhibited extraordinary persistence - either in out-performing
or under-performing. In general it was found that over the short term (month-to-month
and quarter-to-quarter basis) there was a tendency that the current performance of a
fund would be repeated, with especially a greater tendency among the top performing
funds to remain a top performer.
133
However, when the consistency of fund performance was measured on a year-to-year
basis, less consistency among funds was identified. The decile ranking movement of a
fund - upwards, downwards or sideways - became more random in nature. When the
forward-looking period was extended to three years, however, the chances that the
fund would have stayed in the same decile became very slim.
Herein lies the danger of placing your trust with one active manager only; over the
long run the performance ranking of managers can assume a random nature if
manager skill is not persistent.
When comparing the index performance with the percentile rankings of the active
funds one could place the index at about the 60th percentile over the three different
rolling periods, which in itself is an “above-average” performance. When viewed on a
return/risk level only the minority of active funds contributed any alpha or positive
information ratios. By ranking active funds according to their information ratios,
value was found only from the 70th percentile onwards, highlighting the thin edge
active management treads on to beat the market over time.
Consequently index investing could arguably be considered as a sound investment
strategy where a perceived average return is turned into above-average when
compared with that of active investing.
Index investing normally implies a diversified investment approach; however, in a
South African context it is not necessarily valid due to market concentration where the
mining and resources sector on its own make up 45% of the market. Active unit trust
funds on the other, normally assume a much more diversified and equally-weighted
profile than the market on its own.
The study revealed that index investing indeed yielded volatile returns to investors,
but, more importantly, over time index investing and active management alternated
one another as the dominant investment strategy. Therefore, index investing at least in
the South African context might not be a solution as a standalone strategy, but should
rather be combined with active investing strategies. Hereby the overall volatility of
134
portfolio return is reduced over time, which ultimately leads to higher reward per unit
risk ratios.
Nonetheless, concluding that active and passive investing strategies should be
combined in investment portfolios to yield higher reward-to-risk ratios is a relatively
straight forward conclusion, but to know what level of index investing to use or which
active managers to select is a different challenge altogether.
9.2
Recommendations for Implementing Investment Strategies
Combining Strategies
The extent to which index investing (including enhanced index funds) should be used
in an investment portfolio depends on one’s perceptions or expectations of active
management’s performance. For example, from the study it was shown that when the
performance contribution of active management was expected to be in the top quartile
of investment returns that at least a 30% exposure to passive investing would be a
prudent strategy.
Further, when different combinations of index investing with top quartile active fund
performance were backtested over various rolling periods the results indicated that the
allocation of index investing in the combined portfolio should increase the longer the
investment horizon, in general confirming the belief that over the long run it is
difficult for active managers to beat the market.
Selecting Active Managers
No infallible method exists to identify those active managers in advance that will
substantially outperform the index. One possible alternative would have been to
evaluate the past performances of active managers over time whereby the consistency
of a fund manager or company can be evaluated against complete randomness that
would have prevailed if no manager skills were present.
135
Probably more important is to gather information from active managers in terms of
their investment philosophies, processes and styles to form an opinion about the
capabilities of the manager to deliver out-performance over time.
Furthermore, selection of active managers should focus on those managers that do not
necessarily replicate the market closely and whose portfolios could deviate
substantially from the index. Hereby a costly duplication of the index strategy is
prevented and fees are rather paid for managers’ skills to identify stocks that offer
exceptional value going forward. For example, investment styles such as value
investing or small capitalisation styles could be combined with index investing.
9.3
Recommendations for Future Research

The development of an optimising (manager allocation) model and a
corresponding database whereby portfolio weights between index strategies
(including enhanced index strategies) and active funds could be allocated. The
model will serve as a valuable tool for the professional investment advisor in
formulating and advising investors on multi-manager strategies and portfolios,
whereby strategies will be evaluated on a reward-to-risk scale and formulated
according desired risk exposures.
The manager allocation model can be used in the “third dimension” of
advising investors on their investment portfolios, whereas identifying
appropriate risk profiles and suitable asset allocation strategies (investment
policy) would form the former two dimensions. For example, once the specific
risk profile of an investor through a rigorous process has been identified, a
suitable asset allocation policy would be formulated. The manager allocation
model would then be used to implement various investment strategies to give
effect to the overall objectives and risk control of the investment plan.
136
In support of building a comprehensive database the following specific
research should be done:

Extending the existing study to other asset classes and investment categories,

A return-based style analysis of active management performance against an
appropriate benchmark, which will describe more accurately which managers
delivered value according to their specific style,

Developing a matrix of expected alphas versus the expected active risk for
various investment styles and categories.
137
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APPENDICES
143
Appendix A
Cumulative Return Performance: Active versus Index Investing
144
Cumulative Performance: Active vs. Index Investing
Years
15
14
Date
Jan-88
Feb-88
Mar-88
Apr-88
May-88
Jun-88
Jul-88
Aug-88
Sep-88
Oct-88
Nov-88
Dec-88
Jan-89
Feb-89
Mar-89
Apr-89
May-89
Jun-89
Jul-89
Aug-89
Sep-89
Oct-89
Nov-89
Dec-89
JSE-ALSI
471%
562%
584%
518%
547%
520%
492%
473%
502%
462%
428%
430%
424%
381%
355%
310%
300%
333%
295%
288%
273%
276%
285%
263%
Active Avg
542%
580%
592%
548%
567%
545%
520%
500%
520%
485%
468%
468%
451%
420%
396%
369%
362%
384%
343%
337%
319%
321%
350%
328%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
607%
451%
646%
497%
661%
508%
621%
456%
640%
469%
614%
447%
584%
420%
556%
406%
578%
426%
493%
404%
463%
384%
467%
385%
450%
366%
431%
341%
405%
317%
380%
297%
365%
286%
389%
307%
350%
271%
346%
270%
328%
251%
329%
254%
355%
275%
333%
256%
After-Cost Performance
Active Avg
507%
544%
555%
513%
531%
510%
487%
468%
486%
454%
438%
438%
421%
392%
369%
343%
337%
358%
319%
313%
297%
298%
325%
305%
Top 25% Active
569%
606%
620%
582%
600%
575%
547%
520%
541%
461%
433%
436%
420%
402%
378%
354%
340%
362%
326%
322%
305%
306%
331%
309%
Bottom 25% Active
422%
464%
475%
426%
439%
417%
392%
379%
398%
377%
358%
359%
341%
317%
294%
276%
265%
285%
251%
250%
233%
235%
255%
237%
145
Cumulative Performance: Active vs. Index Investing
Years
13
12
Date
Jan-90
Feb-90
Mar-90
Apr-90
May-90
Jun-90
Jul-90
Aug-90
Sep-90
Oct-90
Nov-90
Dec-90
Jan-91
Feb-91
Mar-91
Apr-91
May-91
Jun-91
Jul-91
Aug-91
Sep-91
Oct-91
Nov-91
Dec-91
JSE-ALSI
249%
225%
237%
219%
243%
226%
238%
230%
247%
279%
289%
299%
282%
306%
271%
261%
242%
233%
214%
198%
210%
215%
195%
193%
Active Avg
303%
282%
289%
267%
294%
272%
279%
270%
289%
308%
325%
323%
302%
323%
286%
269%
236%
229%
214%
200%
199%
203%
192%
193%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
308%
233%
296%
221%
300%
224%
277%
205%
297%
221%
278%
202%
277%
208%
275%
204%
294%
219%
310%
233%
317%
238%
313%
234%
291%
219%
311%
247%
275%
214%
263%
199%
247%
160%
239%
154%
226%
143%
209%
135%
207%
135%
213%
139%
205%
136%
205%
144%
After-Cost Performance
Active Avg
281%
261%
268%
247%
273%
252%
259%
250%
268%
286%
302%
300%
281%
300%
266%
249%
218%
211%
197%
184%
183%
187%
176%
177%
Top 25% Active
286%
274%
278%
256%
275%
257%
257%
255%
273%
288%
294%
291%
270%
289%
255%
244%
229%
221%
208%
193%
190%
196%
189%
189%
Bottom 25% Active
215%
204%
206%
189%
204%
186%
192%
188%
202%
215%
220%
216%
202%
228%
197%
183%
146%
141%
130%
122%
122%
126%
124%
131%
146
Cumulative Performance: Active vs. Index Investing
Years
11
10
Date
Jan-92
Feb-92
Mar-92
Apr-92
May-92
Jun-92
Jul-92
Aug-92
Sep-92
Oct-92
Nov-92
Dec-92
Jan-93
Feb-93
Mar-93
Apr-93
May-93
Jun-93
Jul-93
Aug-93
Sep-93
Oct-93
Nov-93
Dec-93
JSE-ALSI
202%
188%
189%
193%
201%
178%
184%
203%
230%
223%
244%
225%
Active Avg
197%
183%
183%
183%
194%
172%
178%
209%
224%
216%
228%
220%
219%
203%
204%
192%
178%
160%
155%
149%
157%
176%
165%
149%
206%
197%
196%
191%
188%
177%
169%
174%
176%
184%
180%
162%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
208%
148%
191%
142%
190%
143%
190%
143%
201%
148%
180%
128%
184%
142%
205%
162%
232%
168%
221%
160%
240%
165%
229%
158%
215%
205%
212%
200%
194%
183%
176%
176%
179%
189%
186%
168%
148%
149%
147%
141%
142%
129%
123%
128%
130%
134%
133%
119%
After-Cost Performance
Active Avg
181%
167%
168%
168%
179%
158%
163%
193%
206%
199%
210%
203%
Top 25% Active
192%
176%
175%
174%
185%
165%
169%
189%
214%
204%
222%
211%
Bottom 25% Active
135%
129%
130%
130%
135%
116%
129%
148%
154%
146%
151%
144%
189%
181%
180%
176%
173%
162%
154%
159%
161%
169%
164%
147%
198%
188%
195%
183%
178%
168%
161%
162%
164%
173%
170%
153%
134%
135%
134%
128%
129%
116%
111%
116%
118%
121%
121%
107%
147
Cumulative Performance: Active vs. Index Investing
Years
9
8
Date
Jan-94
Feb-94
Mar-94
Apr-94
May-94
Jun-94
Jul-94
Aug-94
Sep-94
Oct-94
Nov-94
Dec-94
Jan-95
Feb-95
Mar-95
Apr-95
May-95
Jun-95
Jul-95
Aug-95
Sep-95
Oct-95
Nov-95
Dec-95
JSE-ALSI
Active Avg
112%
118%
114%
110%
94%
92%
92%
84%
78%
83%
81%
80%
77%
106%
102%
97%
90%
90%
92%
91%
87%
84%
79%
74%
136%
141%
136%
131%
120%
108%
107%
102%
94%
100%
97%
92%
88%
107%
110%
106%
100%
96%
97%
99%
94%
89%
83%
73%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
144%
147%
143%
146%
137%
131%
130%
124%
111%
118%
117%
112%
107%
129%
138%
130%
118%
117%
118%
120%
114%
108%
99%
91%
97%
103%
98%
96%
84%
77%
76%
72%
67%
70%
67%
65%
61%
81%
81%
76%
69%
69%
69%
68%
64%
62%
60%
50%
After-Cost Performance
Active Avg
123%
128%
123%
119%
108%
97%
96%
91%
84%
89%
86%
82%
78%
96%
99%
95%
89%
86%
87%
89%
84%
80%
73%
64%
Top 25% Active
131%
134%
130%
132%
124%
119%
118%
112%
99%
106%
105%
100%
96%
117%
130%
122%
111%
109%
110%
112%
106%
100%
92%
84%
Bottom 25% Active
86%
92%
88%
86%
74%
67%
67%
62%
58%
61%
58%
57%
52%
71%
72%
67%
60%
60%
60%
59%
56%
54%
51%
42%
148
Cumulative Performance: Active vs. Index Investing
Years
7
6
Date
Jan-96
Feb-96
Mar-96
Apr-96
May-96
Jun-96
Jul-96
Aug-96
Sep-96
Oct-96
Nov-96
Dec-96
Jan-97
Feb-97
Mar-97
Apr-97
May-97
Jun-97
Jul-97
Aug-97
Sep-97
Oct-97
Nov-97
Dec-97
JSE-ALSI
Active Avg
67%
51%
55%
54%
49%
52%
51%
57%
55%
51%
49%
55%
57%
56%
45%
46%
46%
48%
40%
39%
42%
46%
58%
64%
66%
54%
58%
59%
59%
62%
56%
60%
59%
52%
52%
53%
54%
52%
43%
44%
42%
41%
35%
33%
34%
38%
51%
47%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
82%
72%
76%
75%
76%
79%
71%
76%
73%
67%
65%
63%
67%
64%
53%
54%
51%
51%
45%
45%
46%
50%
64%
60%
44%
35%
38%
36%
34%
37%
30%
37%
35%
29%
32%
34%
36%
36%
27%
29%
27%
27%
19%
19%
20%
24%
36%
29%
After-Cost Performance
Active Avg
Top 25% Active
57%
46%
49%
50%
51%
54%
47%
51%
50%
44%
44%
44%
46%
44%
35%
37%
35%
34%
28%
26%
27%
31%
43%
39%
74%
63%
67%
68%
68%
71%
63%
68%
65%
60%
57%
56%
59%
56%
46%
47%
45%
44%
38%
38%
40%
43%
57%
53%
Bottom 25% Active
36%
27%
30%
29%
27%
30%
23%
30%
28%
22%
25%
27%
29%
29%
20%
22%
20%
20%
12%
13%
14%
17%
29%
22%
149
Cumulative Performance: Active vs. Index Investing
Years
5
4
Date
Jan-98
Feb-98
Mar-98
Apr-98
May-98
Jun-98
Jul-98
Aug-98
Sep-98
Oct-98
Nov-98
Dec-98
Jan-99
Feb-99
Mar-99
Apr-99
May-99
Jun-99
Jul-99
Aug-99
Sep-99
Oct-99
Nov-99
Dec-99
JSE-ALSI
Active Avg
67%
59%
46%
37%
26%
36%
53%
48%
111%
104%
78%
85%
91%
79%
76%
63%
47%
60%
47%
46%
50%
52%
45%
38%
49%
42%
29%
20%
11%
16%
24%
21%
68%
71%
76%
77%
79%
69%
62%
49%
44%
51%
43%
43%
47%
54%
47%
37%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
64%
57%
45%
36%
30%
37%
47%
44%
100%
95%
91%
92%
96%
87%
80%
63%
60%
66%
54%
53%
55%
64%
54%
44%
25%
18%
3%
-4%
-12%
-8%
-5%
-4%
43%
43%
32%
38%
40%
36%
32%
25%
24%
30%
24%
25%
28%
36%
30%
22%
After-Cost Performance
Active Avg
Top 25% Active
41%
34%
22%
13%
5%
10%
18%
15%
59%
62%
67%
68%
70%
61%
54%
42%
37%
44%
36%
36%
40%
47%
40%
31%
57%
49%
39%
29%
25%
29%
39%
36%
89%
85%
80%
82%
86%
77%
70%
54%
51%
57%
46%
45%
47%
55%
46%
36%
Bottom 25% Active
18%
11%
-2%
-9%
-17%
-13%
-10%
-9%
35%
35%
25%
30%
32%
28%
26%
18%
17%
23%
17%
19%
21%
28%
23%
16%
150
Cumulative Performance: Active vs. Index Investing
Years
Date
JSE-ALSI
Active Avg
Jan-00
22%
Feb-00
23%
Mar-00
30%
Apr-00
31%
May-00
40%
Jun-00
41%
3
Jul-00
35%
Aug-00
34%
Sep-00
22%
Oct-00
26%
Nov-00
28%
Dec-00
33%
Percentage better than Index (overall)
Percentage better than Index (years 11-15)
Percentage better than Index (years 6-10)
Percentage better than Index (years 3-5)
# Periods
# Periods
# Periods
# Periods
Overall
11-15
6-10
3-5
156
60
60
36
27%
22%
28%
30%
43%
43%
38%
37%
28%
30%
38%
37%
60%
70%
68%
31%
Pre-Cost Performance
Top 25%
Active
Bottom 25% Active
34%
28%
41%
40%
51%
49%
43%
45%
34%
33%
43%
41%
90%
90%
97%
78%
10%
6%
10%
10%
24%
25%
21%
20%
15%
14%
21%
21%
0%
0%
0%
0%
After-Cost Performance
Active Avg
Top 25% Active
21%
16%
21%
24%
37%
36%
32%
30%
22%
23%
31%
30%
29%
43%
30%
3%
27%
21%
33%
32%
43%
41%
37%
37%
26%
25%
35%
33%
58%
55%
77%
33%
Bottom 25% Active
4%
0%
4%
5%
18%
18%
15%
14%
9%
8%
16%
15%
0%
0%
0%
0%
151
Appendix B
Statistical Tests for the Random Sampling Investment Periods
152
Random Sampling
Three Year Investment Period (cumulative return)
Sell-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
37.76%
9.60%
100
87.11%
0
99
-1.160591682
0.124299502
1.660391717
0.248599003
1.984217306
ACTIVE AVERAGE
39.53%
8.08%
100
Random Sampling
Three Year Investment Period (cumulative return)
Buy-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
37.76%
9.60%
100
87.20%
0
99
3.671049107
0.000195791
1.660391717
0.000391582
1.984217306
ACTIVE AVERAGE
32.19%
7.18%
100
153
Random Sampling
Five Year Investment Period (cumulative return)
Sell-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
76.88%
16.54%
100
93.85%
0
99
-2.582442442
0.005636861
1.660391717
0.011273722
1.984217306
ACTIVE AVERAGE
80.66%
17.95%
100
Random Sampling
Five Year Investment Period (cumulative return)
Buy-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
76.88%
16.54%
100
93.88%
0
99
4.163455354
3.34931E-05
1.660391717
6.69862E-05
1.984217306
ACTIVE AVERAGE
71.00%
16.02%
100
154
Random Sampling
Ten Year Investment Period (cumulative return)
Sell-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
194.05%
42.62%
100
91.73%
0
99
-5.306985954
3.4137E-07
1.660391717
6.8274E-07
1.984217306
ACTIVE AVERAGE
210.35%
58.16%
100
Random Sampling
Ten Year Investment Period (cumulative return)
Buy-to-sell price basis
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
INDEX
194.05%
42.62%
100
91.73%
0
99
0.15082248
0.440211319
1.660391717
0.880422638
1.984217306
ACTIVE AVERAGE
193.61%
52.06%
100
155
Appendix C
Statistical Tests for the Rolling Investment Periods
156
Statistical Significance:
Three Year Rolling Investment Period
Annualised Performance
Active vs. Index on Pre-Cost Basis (sell-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
11.32%
0.66%
156
85.40%
0
155
-0.0984
0.460869
1.654744
0.921738
1.975386
Active Avg
11.35%
0.54%
156
Active vs. Index on After-Cost Basis (buy-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
11.32%
0.66%
156
85.49%
0
155
5.779383
2E-08
1.654744
3.99E-08
1.975386
Active Average
9.36%
0.52%
156
157
Statistical Significance:
Five Year Rolling Investment Period
Annualised Performance
Active vs. Index on Pre-Cost Basis (sell-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
11.05%
0.28%
132
92.62%
0
131
-0.42104
0.33721
1.656567
0.674419
1.978237
Active Average
11.12%
0.32%
132
Active vs. Index on After-Cost Basis (buy-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
11.05%
0.28%
132
92.66%
0
131
6.195521
3.49E-09
1.656567
6.99E-09
1.978237
Active Average
9.91%
0.31%
132
158
Statistical Significance:
Ten Year Rolling Investment Period
Annualised Performance
Active vs. Index on Pre-Cost Basis (sell-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
10.89%
0.04%
72
88.37%
0
71
-2.18485
0.016101
1.666599
0.032202
1.993944
Active Average
11.16%
0.05%
72
Active vs. Index on After-Cost Basis (buy-to-sell price)
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
10.89%
0.04%
72
88.37%
0
71
2.766867
0.003605
1.666599
0.007211
1.993944
Active Average
10.55%
0.05%
72
159
Appendix D
Statistical Tests for Risk-adjusted Return Comparisons
160
Risk-adjusted Returns:
Sharpe Ratio
Active Management versus Index over 36-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-0.9639%
1.1991%
156
85.52%
0
155
-0.52406286
0.300491698
1.654743755
0.600983397
1.975386112
Active Average
-0.7257%
0.8446%
156
Risk-adjusted Returns:
Treynor Ratio
Active Management versus Index over 36-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-0.0817%
0.0039%
156
58.61%
0
155
0.648920947
0.2586749
1.654743755
0.517349801
1.975386112
Active Average
-0.1082%
0.0019%
156
161
Risk-adjusted Returns:
Sharpe Ratio
Active Management versus Index over 60-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-0.7372%
0.3179%
132
88.33%
0
131
0.713769317
0.238319796
1.656567292
0.476639592
1.978237378
Active Average
-0.9174%
0.3809%
132
Risk-adjusted Returns:
Treynor Ratio
Active Management versus Index over 60-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-0.0856%
0.0011%
132
84.60%
0
131
2.519491637
0.006477247
1.656567292
0.012954493
1.978237378
Active Average
-0.1408%
0.0021%
132
162
Risk-adjusted Returns:
Sharpe Ratio
Active Management versus Index over 120-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-1.4820%
0.0561%
72
83.05%
0
71
2.523829986
0.006923645
1.666599019
0.013847291
1.993944352
Active Average
-1.8914%
0.0556%
72
Risk-adjusted Returns:
Treynor Ratio
Active Management versus Index over 120-month rolling periods
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Index
-0.0919%
0.0002%
72
80.88%
0
71
3.890046738
0.000111718
1.666599019
0.000223437
1.993944352
Active Average
-0.1321%
0.0002%
72
163
Appendix E
Cost Structures of Index Funds
164
Cost Structures of Index Funds in the General Equity Sector
Fund
Upfront Charges
Management Fee
(max)
Gryphon All Share Tracker Fund
4%
1.00%
Investec Index
0%
0.39%
Stanlib Index Fund
5.70%
0.57%
Cost Structures of Index Funds in the Large Capitalisation Sector
Fund
Upfront Charges
Management Fee
(max)
Kagiso Top 40 Index Fund
0%
0.57%
RMB Top 40 Index
3.70%
0.86%
Sanlam Index Fund
5.70%
0.57%
Cost Structures of Exchange Traded Funds
Fund
Upfront Charges
Management Fee
(max)
SATRIX (direct)
0.65%
0.80%
SATRIX (distribution channel)
4.91%
0.80%
ABSA New Rand (direct)
0.74%
0.91%
ABSA New Rand (distribution channel)
5.21%
0.91%
165
Appendix F
Tracking Error Analysis for Index Funds
166
Tracking Error Analysis for Investec Index Fund
Rolling Three-year period
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Alsi
6.54%
0.51%
70
94.32%
0
69
-2.63054
0.005253
1.667239
0.010505
1.994945
Investec
7.31%
0.53%
70
Regression Statistics
Multiple R
94.32%
R Square
88.96%
Adjusted R
Square
88.79%
Standard Error
2.44%
Observations
70
ANOVA
df
SS
Regression
MS
1
0.3257
0.3257
Residual
68
0.0404
0.0006
Total
69
0.3661
Coefficients
Standard
Error
t Stat
F
547.7346
P-value
Significance
F
0.0000
Lower 95%
Upper
95%
Intercept
0.0102
0.0040
2.5816
0.0120
0.0023
0.0181
X Variable 1
0.9607
0.0411
23.4037
0.0000
0.8788
1.0426
167
Tracking Error Analysis for Gryphon All Share Tracker Fund
Rolling Three-year period
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Alsi
8.56%
0.47%
47
85.67%
0
46
7.207033
2.23E-09
1.67866
4.46E-09
2.012896
Gryphon
4.76%
0.44%
47
Regression Statistics
Multiple R
85.67%
R Square
73.39%
Adjusted R Square
72.80%
Standard Error
3.46%
Observations
47
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
1
45
46
SS
0.1485
0.0538
0.2023
MS
0.1485
0.0012
F
124.1359
Significance F
0.0000
Coefficients
-0.0234
Standard Error
0.0081
t Stat
-2.8817
P-value
0.0060
Lower 95%
-0.0398
Upper
95%
-0.0071
0.8297
0.0745
11.1416
0.0000
0.6797
0.9797
168
Tracking Error Analysis for Stanlib Index Fund
Rolling Three-year period
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Alsi
6.61%
0.51%
71
95%
0
70
0.901716
0.18515
1.666914
0.3703
1.994437
Stanlib
6.36%
0.51%
71
Regression Statistics
Multiple R
94.79%
R Square
Adjusted R Square
Standard Error
89.85%
89.70%
2.30%
Observations
71
ANOVA
Regression
Residual
df
1
69
SS
0.3229
0.0365
Total
70
0.3594
Coefficients
0.0006
0.9536
Standard Error
0.0037
0.0386
Intercept
X Variable 1
MS
0.3229
0.0005
F
610.8814
Significance F
0.0000
t Stat
0.1608
24.7160
P-value
0.8727
0.0000
Lower 95%
-0.0068
0.8766
Upper
95%
0.0080
1.0305
169
Appendix G
Backtesting Combinations of Active and Passive Investing
over Various Rolling Investment Periods
170
Backtesting Combinations of Active and Passive Investing over Various Rolling Investment Periods
Rolling Period
Pre-cost
Indexing
Average
Std Deviation
Sharpe (adj)
3
After-cost
Pre-cost
5
After-cost
10
After-cost
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
13.69%
13.45%
13.21%
12.98%
12.74%
12.50%
12.27%
12.03%
11.79%
11.56%
11.32%
7.26%
7.26%
7.27%
7.31%
7.37%
7.46%
7.56%
7.68%
7.81%
7.97%
8.14%
1.886
1.854
1.817
1.774
1.728
1.677
1.623
1.567
1.509
1.450
1.391
11.63%
11.60%
11.57%
11.53%
11.50%
11.47%
11.44%
11.41%
11.38%
11.35%
11.32%
Std Deviation
7.12%
7.13%
7.16%
7.22%
7.29%
7.39%
7.50%
7.64%
7.79%
7.96%
8.14%
Sharpe (adj)
1.634
1.627
1.615
1.598
1.577
1.553
1.525
1.494
1.461
1.426
1.391
Average
Average
12.49%
12.34%
12.20%
12.05%
11.91%
11.77%
11.62%
11.48%
11.33%
11.19%
11.05%
Std Deviation
5.23%
5.19%
5.16%
5.13%
5.12%
5.12%
5.13%
5.15%
5.18%
5.22%
5.27%
Sharpe (adj)
2.386
2.379
2.366
2.349
2.326
2.299
2.267
2.230
2.190
2.145
2.097
11.25%
11.23%
11.21%
11.19%
11.17%
11.15%
11.13%
11.11%
11.09%
11.07%
11.05%
5.17%
5.13%
5.10%
5.09%
5.08%
5.09%
5.10%
5.13%
5.16%
5.21%
5.27%
Average
Std Deviation
Sharpe (adj)
Pre-cost
0.00%
2.178
2.189
2.197
2.200
2.198
2.192
2.181
2.166
2.147
2.124
2.097
11.52%
11.46%
11.40%
11.33%
11.27%
11.21%
11.14%
11.08%
11.02%
10.95%
10.89%
Std Deviation
2.29%
2.25%
2.22%
2.19%
2.17%
2.15%
2.13%
2.12%
2.11%
2.11%
2.11%
Sharpe (adj)
5.039
5.092
5.138
5.176
5.205
5.224
5.233
5.231
5.218
5.194
5.158
Average
Average
10.90%
10.90%
10.90%
10.90%
10.90%
10.90%
10.90%
10.90%
10.89%
10.89%
10.89%
Std Deviation
2.27%
2.24%
2.21%
2.18%
2.16%
2.14%
2.12%
2.11%
2.11%
2.11%
2.11%
Sharpe (adj)
4.796
4.870
4.938
4.999
5.052
5.095
5.129
5.153
5.166
5.167
5.158
171
Appendix H
Memorable Quotes from the Past
172
“I have little confidence even in the ability of analysts, let alone untrained investors,
to select common stocks that will give better than average results. I feel that the
standard portfolio should be to duplicate, more or less the DJIA.”
-
Benjamin Graham
“How can institutional investors hope to outperform the market…when, in effect, they
are the market?”
-
Charles D. Ellis
-
Warren Buffet
“My favourite holding period is forever.”
“It is not easy to get rich in Las Vegas, at Churchill Downs, or at the local Merrill
Lynch office.”
-
Paul A Samuelson
“If I have noticed anything over these 60 years on Wall Street, it is that people do not
succeed in forecasting what’s going to happen to the stock market.”
-
Benjamin Graham
“There are two kinds of investors…those who don’t know where the market is headed
and those who don’t know that they don’t know. Then again, there is a third type of
investor- the investment professional, who indeed knows that he or she doesn’t know,
but whose livelihood depends upon appearing to know.”
-
William Bernstein
“By day we write about ‘Six Funds to buy NOW!’….By night, we invest in sensible,
index funds. Unfortunately, pro-index fund stories don’t sell magazines.”
- Anonymous Fortune Magazine Writer
173
“Most institutional and individual investors will find the best way to own common
stock is through an index fund that charges minimal fees. Those following this path
are sure to beat the net result delivered by the great majority of investment
professionals.”
-
Warren Buffet
“So who still believes markets don’t work? Apparently it is only the North Koreans,
the Cubans and the active managers.”
- Rex A. Sinquefield