Performance Measurement: - The SA Index Investor - … · Web viewHierdeur kan aangevoer word dat aktiewe bestuur oor die langer termyn moeilik die mark gaan uitpresteer. Indien ‘n

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

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

ii

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.

iii

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.

iv

Opsomming

Die twee verskillende beleggingsbenaderings, naamlik aktiewe en passiewe (indeks)

beleggingsbestuur, is beoordeel deur die gemiddelde opbrengste van die aktief-

bestuurde 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.

v

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.

vi

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

vii

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

viii

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




Rolling 120-month Investment Periods………………………………60

Table 4.8: Statistical Significance of Sharpe Ratios……………………………..65

ix

Table 4.9: Statistical Significance of Treynor Ratios……………………………69

Table 4.10: Value Added by Actively Managed Funds over






Table 5.1: Percentile Ranking of Actively Managed Funds over

Rolling 36-month Investment Periods……………………………......96





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


Table 6.3: Data input of the Optimal Allocation Model………………….…….115

x

Table 6.4: Optimising Results with 70th Percentile

Active Investment Performance…………………………………….116





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

xi

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


Sampling Basis for an Investment Period of Five Years……………..44


Sampling Basis for an Investment Period of Ten Years……………..45

Figure 4.6: Active versus Passive Investing over



Rolling 60-month Investment Periods……………………………….50



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

xii

Figure 4.12: Return/Risk Profile of Actively Managed Funds and Index over






Figure 4.15: Reward-to-Risk Ratio (Sharpe) of Active versus Passive Investing

over Rolling 36-month Investment Periods………………………......66


over Rolling 60-month Investment Periods………………………......67


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 4.21: Alpha/Active Risk Profile of Actively Managed Funds over




xiii



Figure 4.24: Average Information Ratio over Rolling 36-month

Investment Periods…………………………………………………...81





Figure 5.1: Quartile Ranking of Actively Managed Funds over






Figure 5.4: Tendency of Actively Managed Funds to Move between Deciles

on a Month-to-Month basis…………………………………………102


on a Quarterly basis…………………………………………………102


on a Yearly basis……………………………………………………103


on a Three-yearly basis……………………………………………...103

Figure 6.1: Efficient Frontier of Optimal Combination Strategies……………...109

xiv

Figure 6.2: Distribution of Alphas across Actively Managed Funds over


Figure 6.3: Distribution of Active Risk across Actively Managed Funds over


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


in an Investment Portfolio given various Market Returns…. ………117


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


Combinations over Rolling 60-month Investment Periods…………124


Combinations over Rolling 120-month Investment Periods………..125

xv

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

xvi

CHAPTER 1: INTRODUCTION & PROBLEM FORMULATION

1.1 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.

1

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 decision-

making 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 above-

average returns over time will surpass its cost factors to beat an index investing

strategy.

1 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).

2

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 out-

performance 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?

3

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

4

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.

5

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.

6

CHAPTER 2: THE THEORETICAL FRAMEWORK

2.1 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

7

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.

8

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 zero-

game.

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.

9

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 out-

performance 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.

10

Table 2.1: The Probabilities of Active Management Outperforming an Index

Number of Years One Manager Multi-Manager(Three Managers)

Multi-Manager(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.

Further, it is not very likely that a manager could predict the exact starting point of a

bear market to take some defensive positions.

2 If the argument is valid, the opposite for major bull markets would apply where cash holdings by active managers would dilute returns.

11

“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.

12

“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 self-

fulfilling 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

13

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.

14

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!

15

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

16

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 non-

replication 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

17

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:

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.

18

add value is expressed by the breadth of the strategy ( ), 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 equally-

weighted 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.

19

Table 2.2: Perceived Opportunity versus Effective Opportunity

Benchmark Perceived Opportunity(number of

stocks)

Effective Opportunity(number of

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/Barra Growth

164 42 0.26

S&P 500/Barra Value

336 70 0.21

S&P 500 (equal-weighted)

500 500 1.00

* 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.

20

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 stock-

specific 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.

21

Table 2.3: Relative Performance in Different Markets

SectorRelative Market Weight Manager Weight

AllocationReturn

Concentrated Market

Diversified Market

Concentrated Market

Diversified Market

Market Manager

Resources 40 20 10 10 15% 17%

Industrials 10 10 15 15 7.5% 9.5%

Consumer Goods

12.5 20 25 25 5% 7%

Services 12.5 20 20 20 7.5% 9.5%

Financial 20 25 25 25 7.5% 9.5%

Information Tech

5 5 5 5 -5% -3%

Total Allocation

100 100 100 100

Total Return

9.56% 7.88% 9.00% 9.00%

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

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.

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.

22

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.

23

CHAPTER 3: THE INTERNATIONAL EXPERIENCE

3.1 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 1999-

2000) active funds fared better than index funds.

24

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.

25

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 capitalisation-

weighted 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.

26

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 ReturnMarket Value

(begin)Market Value

(end)

Resources -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

TOTAL VALUE 600

610

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 -

-

-

50

50 - 100 12.50%

Non-Manager

- - -

-

50

50 100 -2.50%

TOTAL 200 100 100 50 100 50 600 1.67%

Performance Begin End ReturnAll Managers Equally Weighted 4.17%

All Managers Cap Weighted 500

513 2.44%

All Investors Equally Weighted 2.50%

All Investors Cap Weighted 600

610 1.67%

Source: Adapted from Minor, 2003: 79

27

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 R-

squared 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.

28

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.

29

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.

30

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 non-

risk-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

9 Vanguard’s actively managed funds typically have low expense ratios and might as such not be representative of the industry (Reinker & Tower, 2004: 38).

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).

31

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.

32

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;



all available active funds for an investment period of five years;



all available active funds for an investment period of ten years.

33

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.

34

Table 4.1: The Cost Structure of Actively Managed Funds

in the General Equity Unit Trust Sector

Fund Max Initial Fee Management Fee p.a.ABSA General 5.70% 1.71%ABSA Growth FoF 4.56% 1.71%Allan Gray Equity 3.42% 0-3.42%Community Growth 5.70% 0.57%CorisCapital General Equity 4.56% 1.14%Coronation Equity 5.70% 1.14%Futuregrowth Albaraka 5.70% 1.71%Futuregrowth Core Equity 0.57% 1.14%Investec Equity 5.70% 1.71%FNB Growth 5.70% 1.43%Mcubed Equity FoF 5.70% 1.71%Metropolitan General Equity 5.70% 1.43%Nedbank Equity 5.70% 1.60%Nedbank Equity FoF 5.70% 1.43%Nedbank Rainmaker 5.70% 1.60%Nedbank Quants Core 3.42% 0.86%Oasis Crescent Equity 5.13% 1.71%Old Mutual Growth 5.70% 1.14%Old Mutual Investors 5.70% 1.14%Old Mutual Top Companies 5.70% 1.14%Prudential Optimiser 5.70% 1.43%RMB Equity 3.70% 1.14%RMB Performance FoF 3.70% 1.71%Sage Fund 5.70% 1.71%Sage MultiFocus FoF 5.70% 1.43%Sanlam General Equity 5.70% 1.14%Sanlam Multi-Manager Equity 4.56% 1.71%Stanlib Capital Growth 5.70% 1.14%Stanlib Prosperity 5.70% 1.14%Stanlib WealthBuilder 5.70% 1.14%Tri-Linear Equity 2.28% 1.43%Woolworths 5.70% 1.25%Average 5.04%

Source: 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.

35

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 PerformanceAverage Cost = 5.04%

y = 0.0014e0.4702x

R2 = 0.9828

0%

1%

2%

3%

4%

5%

6%

7%

3602401206048362412

Months of Investment

Cos

t Im

pact

(per

ann

um)

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 t-

value 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).

36

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 out-

performance 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 out-

performance 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.

37

Table 4.2: The Performance Record of Actively Managed Funds versus the

Index on a Cumulative Return Basis

ResultInvestment

PeriodsBefore Cost After Cost

Active Average

Top 25%

Active

Bottom 25%

Active

Active Average

Top 25%

Active

Bottom 25%

ActivePercentage of Periods better than Index (overall)

156 60% 90% 0% 29% 58% 0%

Percentage of Periods better than Index (11-15 years)

60 70% 90% 0% 43% 55% 0%


60 68% 97% 0% 30% 77% 0%


36 31% 78% 0% 3% 33% 0%

38

Cumulative PerformanceActive versus Index Investing

(Buy-to-sell price basis)

-100%

0%

100%

200%

300%

400%

500%

600%

700%

1514131211109876543

Years

Ret

urn

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.

39

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.

40

Table 4.3: Random Sampling: Comparison between Active and Passive Investing

Period Category Observations Mean Return

(cumulative)

Variance Pearson Correlation

t-Statistic

3 years

ALSI Index 100 37.76% 9.60%

Average of Active Funds (before cost)

100 39.53% 8.08% 87.11% -1.16

Average of Active Funds (after cost)

100 32.19% 7.18% 87.20% 3.67

5 years

ALSI Index 100 76.88% 16.54%


100 80.66% 17.95% 93.85% -2.58


100 71.00% 16.02% 93.88% 4.16

10 years

ALSI Index 100 194.05% 42.62%


100 210.35% 58.16% 91.73% -5.31


100 193.61% 52.06% 91.73% 0.15

41

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%.

42

Random SamplingThree Year Investment Period

Active vs Index Return(buy-to-sell price basis)

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0% 20% 40% 60% 80% 100% 120%

Index Return

Activ

e M

anag

emen

t Ret

urn

ACTIVE AVERAGE BEST ACTIVE WORST ACTIVE

Linear (WORST ACTIVE) Linear (ACTIVE AVERAGE) Linear (BEST ACTIVE)


Sampling Basis for an Investment Period of Three Years

43

Random SamplingFive Year Investment Period


-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0% 20% 40% 60% 80% 100% 120% 140% 160%

Index Return

Activ

e M

anag

emen

t Ret

urn


Linear (BEST ACTIVE) Linear (ACTIVE AVERAGE) Linear (WORST ACTIVE)


Sampling Basis for an Investment Period of Five Years

44

Random SamplingTen Year Investment Period


0%

100%

200%

300%

400%

500%

600%

0% 100% 200% 300% 400% 500%

Index Return

Activ

e M

anag

emen

t Ret

urn


Linear (BEST ACTIVE) Linear (ACTIVE AVERAGE) Linear (WORST ACTIVE)


Sampling Basis for an Investment Period of Ten Years

45

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.

46

Table 4.4: Comparison between Active and Passive Investing over Rolling

Three-, Five-, and Ten-year PeriodsRolling Period

Category Observations Mean Return

(annualised)


t-Statistic

3 years

ALSI Index 156 11.32% 0.66%


156 11.35% 0.54% 85.40% -0.10


156 9.36% 0.52% 85.49% 5.78

5 years

ALSI Index 132 11.05% 0.28%


132 11.12% 0.32% 92.62% -0.42


132 9.91% 0.31% 92.66% 6.20

10 years

ALSI Index 72 10.89% 0.04%


72 11.16% 0.05% 88.37% -2.19


72 10.55% 0.05% 88.37% 2.77

47

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.

48

Rolling 36-month Investment PeriodActive versus Index


-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

Jan-91

Jan-92

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Ret

urn(

annu

alis

ed)

ALSI Index ACTIVE Avg

Figure 4.6: Active versus Passive Investing over Rolling 36-month Investment

Periods

49



-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Ret

urn(

annu

alis

ed)



Periods

50



0.00%2.00%4.00%6.00%8.00%

10.00%12.00%14.00%16.00%18.00%20.00%

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Ret

urn(

annu

alis

ed)



Periods

51

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 Indexover a Rolling 36-month period


0%

20%

40%

60%

80%

100%

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Period

Perc

enta

ge

Figure 4.9: Beating the Index over Rolling 36-month Investment Periods

52



0%

20%

40%

60%

80%

100%

Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03

Period

Perc

enta

ge




0%

20%

40%

60%

80%

100%

Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03

Period

Perc

enta

ge


53

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 equally-

weighted 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.

54

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:

, and therefore,

(4.1)

55

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 non-

systematic risk is explained by:

(4.2)

Sharpe ratio: (Fund return – risk-free return)

Standard deviation of fund

(4.3)

Treynor ratio: (Fund return – risk-free return)

Beta of active fund

(4.4)

Information ratio: Alpha of fund

Active risk of fund

56

(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 PeriodsMonthly Return

Monthly ExcessReturn Volatility Beta Correlation

ABSA_General 117 0.64% -0.43% 5.72% 80% 87%ABSA_Growth 30 0.57% -0.31% 4.33% 56% 83%Allan Gray_Equity 27 2.08% 1.21% 4.81% 56% 73%Community_Growth 103 0.88% -0.19% 5.79% 74% 80%CorisCap_GE 12 0.08% -0.80% 6.23% 73% 75%Coronation_Equity 57 0.78% -0.25% 5.20% 60% 82%Futuregro_Albaraka 102 1.13% 0.05% 5.42% 69% 78%Futuregro_Core 24 0.51% -0.36% 5.12% 70% 86%Investec_ Equity 156 1.25% 0.11% 5.19% 78% 88%FNB_Growth 27 0.96% 0.09% 5.26% 69% 82%Mcubed_Equity 37 0.43% -0.49% 5.99% 78% 88%Metropolitan_GE 111 1.06% -0.01% 5.56% 76% 85%Nedbank_Equity 38 -0.15% -1.08% 6.57% 80% 82%Nedbank Equity FoF 20 0.44% -0.43% 4.21% 37% 55%Nedbank_Rain 27 1.32% 0.44% 5.60% 73% 82%Nedbank_Quants 14 0.33% -0.55% 3.98% 36% 58%Oasis_Cresc 13 1.81% 0.93% 3.82% 48% 80%OM_Growth 93 0.69% -0.40% 6.33% 83% 84%OM_Invest 156 1.08% -0.06% 5.58% 88% 92%OM_TopCo 110 0.92% -0.15% 5.59% 79% 88%Prudential_Opt 17 0.69% -0.18% 5.85% 72% 78%RMB_Equity 71 0.69% -0.38% 6.26% 80% 89%RMB_Perform 30 0.56% -0.33% 4.82% 62% 82%Sage_Fund 148 0.99% -0.13% 4.53% 69% 89%Sage_MultiF 4 0.85% -0.03% 4.19% 53% 82%Sanlam_GE 156 0.88% -0.26% 5.12% 78% 89%Sanlam_MM_Equity 23 0.32% -0.55% 4.18% 35% 53%Stanlib_CapitalGrowth 62 0.03% -1.02% 6.50% 41% 47%Stanlib_Prosp 77 0.69% -0.40% 6.13% 82% 90%Stanlib_Wealth 156 1.00% -0.14% 5.02% 76% 88%Tri-Linear_Equity 13 -0.08% -0.96% 5.34% 67% 79%Woolworths 15 0.36% -0.52% 5.00% 64% 82%

INDEX PeriodsMonthlyReturn

Monthly ExcessReturn Volatility

ALSI Index 156 1.06% -0.08% 5.84%

59

Table 4.6: Risk Data of Actively Managed Funds over Rolling 60-month

Investment Periods

Active Fund PeriodsMonthlyReturn


ABSA_General 93 0.59% -0.51% 6.12% 83% 86%ABSA_Growth 6 0.75% -0.19% 4.32% 53% 79%Allan Gray_Equity 3 2.64% 1.73% 5.60% 68% 75%Community_Growth 79 0.86% -0.25% 6.36% 79% 81%Coronation_Equity 33 0.77% -0.26% 5.20% 58% 81%Futuregro_Albaraka 78 0.94% -0.17% 5.87% 74% 82%Investec_ Equity 132 1.28% 0.15% 5.31% 78% 88%FNB_Growth 3 1.46% 0.55% 5.24% 66% 79%Mcubed_Equity 13 0.27% -0.70% 6.50% 79% 86%Metropolitan_GE 87 1.15% 0.04% 5.96% 78% 85%Nedbank_Equity 14 0.14% -0.83% 6.61% 78% 83%Nedbank_Rain 3 1.22% 0.31% 5.64% 71% 78%OM_Growth 69 0.67% -0.44% 7.08% 88% 85%OM_Invest 132 1.07% -0.07% 5.75% 89% 93%OM_TopCo 86 0.87% -0.24% 5.99% 83% 90%RMB_Equity 47 0.70% -0.37% 6.47% 82% 90%RMB_Perform 6 0.66% -0.28% 4.98% 59% 76%Sage_Fund 124 0.96% -0.16% 4.65% 70% 90%Sanlam_GE 132 0.86% -0.27% 5.18% 78% 90%Stanlib_CapitalGrowth 38 0.03% -1.01% 6.67% 42% 45%Stanlib_Prosp 53 0.73% -0.37% 6.47% 84% 91%Stanlib_Wealth 132 0.96% -0.17% 5.12% 76% 89%



ALSI 132 1.05% -0.09% 5.93%

60

Table 4.7: Risk Data of Actively Managed Funds over Rolling 120-month

Investment Periods

Active Fund PeriodsMonthlyReturn


ABSA_General 33 0.65% -0.42% 6.01% 82% 85%Community_Growth 19 0.90% -0.16% 5.86% 76% 81%Futuregro_Albaraka 18 1.23% 0.18% 5.45% 68% 79%Investec_ Equity 72 1.31% 0.18% 5.37% 80% 89%Metropolitan_GE 27 1.02% -0.03% 5.78% 79% 85%OM_Growth 9 0.85% -0.21% 6.22% 81% 83%OM_Invest 72 1.08% -0.06% 5.82% 91% 93%OM_TopCo 26 0.95% -0.11% 5.78% 82% 89%Sage_Fund 64 0.95% -0.17% 4.73% 70% 90%Sanlam_GE 72 0.87% -0.27% 5.23% 79% 90%Stanlib_Wealth 72 0.95% -0.19% 5.21% 78% 89%



Alsi 72 1.05% -0.09% 5.96%

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 ProfileRolling 36-month Periods

17

3

15

1331

27

5

9

19

25

2426

28

11

23

141

32

1230

20

29

10

7

21

422618

16

28

R2 = 0.0936

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0% 1% 2% 3% 4% 5% 6% 7%Volatility

Ret

urn

pm

Active Avg Alsi Linear (Active Avg)

1- Absa General2- Absa Growth3- Allan Gray Equity4-Community Growth5- Coris Capital GE6- Coronation Equity7- Futuregro Albaraka8- Futuregro Core9- Investec Equity10- FNB Growth11- MCubed Equity12- Metropolitan GE13- Nedbank Equity14- Nedbank Equity FoF15- Nedbank Rain16- Nedbank Quants17- Oasis Crescent18- OM Growth19- OM Investors20- OM TopCo21- Prudential Opt22- RMB Equity23- RMB Perform24- Sage Fund25- Sage MultiFocus26- Sanlam GE27- Sanlam MM Equity28- Stanlib CapGro29- Stanlib Prosp30- Stanlib Wealth31- Tri-Linear Equity32- Woolw Equity


Rolling 36-month Investment Periods

63


3

8

7

1012

11

20

13

9

14

18

19

2215

21 162 5

6

117

4

R2 = 0.1384

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

0% 2% 4% 6% 8%

Volatility

Ret

urn

pm


1- Absa General2- Absa Growth3- Allan Gray Equity4- Community Growth5- Coronation Equity6- Futuregro Albaraka7- Investec Equity8- FNB Growth9- Mcubed Equity10- Metropolitan GE11- Nedbank Equity12- Nedbank Rain13- OM Growth14- OM Investor15- OM TopCo16- RMB Equity17- RMB Perform18- Sage Fund19- Sanlam GE20- Stanlib CapGro21- Stanlib Prosp22- Stanlib Wealth



64


4

3

7

5

89 11

106

2

1

R2 = 0.1055

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

0% 1% 2% 3% 4% 5% 6% 7%

Volatility

Ret

urn

pm


1- Absa General2- Community Growth3- Futuregro Albaraka4- Investec Equity5- Metropolitan GE6- OM Growth7- OM Investor8- OM TopCo9- Sage Fund10- Sanlam GE11- Stanlib Wealth



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 Period

Category Observations Mean Reward-to-Risk Ratio


t-Statistic

36 months

ALSI Index 156 -0.96% 1.20%

Average of Active Funds

156 -0.73% 0.85% 85.52% -0.52

60 months

ALSI Index 132 -0.74% 0.32%


132 -0.92% 0.38% 88.33% 0.71

120 months

ALSI Index 72 -1.48% 0.06%


72 -1.89% 0.06% 83.05% 2.52

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 PeriodSharpe Ratio

(Monthly Return)

-0.30-0.25-0.20-0.15-0.10-0.05

-0.050.100.150.200.25

Jan-91

Jan-92

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Rat

io

Active Average ALSI Index


over Rolling 36-month Investment Periods

67

Rolling 60-Month PeriodSharpe Ratio(Monthly Return)

-0.20

-0.15

-0.10

-0.05

-

0.05

0.10

0.15

0.20

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Rat

io




68

Rolling 120-Month PeriodSharpe Ratio(Monthly Return)

-0.06

-0.04

-0.02

-

0.02

0.04

0.06

0.08

Jan-98

May-98

Sep-98

Jan-99

May-99

Sep-99

Jan-00

May-00

Sep-00

Jan-01

May-01

Sep-01

Jan-02

May-02

Sep-02

Jan-03

May-03

Sep-03

Period

Rat

io




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 Period

Category Observations Mean ExcessReturn

(monthly)


t-Statistic

36 months

ALSI Index 156 -0.08% 0.0039%


156 -0.11% 0.0019% 58.61% 0.65

60 months

ALSI Index 132 -0.09% 0.0011%


132 -0.14% 0.0021% 84.60% 2.52

120 months

ALSI Index 72 -0.09% 0.0002%


72 -0.13% 0.0002% 80.88% 3.89

70

Rolling 36-Month PeriodTreynor Ratio

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

Jan-91

Jan-92

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Ris

k-ad

just

ed R

etur

n (p

.m.)

Alsi Index Active Average

Figure 4.18: Treynor Ratio of Active versus Passive Investing over Rolling

36-month Investment Periods

71


-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Jan-03

Period

Ris

k-ad

just

ed R

etur

n (p

.m.)


Figure 4.19: Treynor Ratio of Active versus Index Investing over Rolling


72


-0.40%

-0.30%

-0.20%

-0.10%

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

Jan-98

Jul-98

Jan-99

Jul-99

Jan-00

Jul-00

Jan-01

Jul-01

Jan-02

Jul-02

Jan-03

Jul-03

Period

Ris

k-ad

just

ed R

etur

n (p

.m.)


Figure 4.20: Treynor Ratio of Active versus Index Investing over Rolling


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 (out-

performance) 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.

16 The standard error of the alpha estimate (σα) is determined by dividing the active risk (σe) 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).

74

Table 4.10: Value Added by Actively Managed Funds over Rolling 36-month

Investment Periods

FundAverage

Alpha

Std Error of Alpha t-statistic Active Risk Info Ratio

ABSA_General -0.34% 0.26% -1.28 2.86% -0.10 ABSA_Growth -0.38% 0.44% -0.86 2.43% -0.16 Allan Gray_Equity 1.13% 0.63% 1.80 3.28% 0.34 Community_Growth -0.03% 0.32% -0.10 3.23% -0.00 CorisCap_GE -0.50% 1.16% -0.43 4.01% -0.15 Coronation_Equity -0.17% 0.40% -0.43 2.99% -0.07 Futuregro_Albaraka 0.21% 0.31% 0.68 3.09% 0.07 Futuregro_Core -0.38% 0.51% -0.74 2.51% -0.17 Investec_ Equity 0.21% 0.19% 1.10 2.37% 0.10 FNB_Growth 0.02% 0.57% 0.03 2.98% 0.01 Mcubed_Equity -0.56% 0.45% -1.24 2.74% -0.21 Metropolitan_GE 0.13% 0.26% 0.51 2.74% 0.04 Nedbank_Equity -1.15% 0.59% -1.94 3.66% -0.32 Nedbank Equity FoF -0.38% 0.78% -0.48 3.49% -0.11 Nedbank_Rain 0.36% 0.62% 0.58 3.23% 0.15 Nedbank_Quants -0.41% 0.86% -0.47 3.23% -0.13 Oasis_Cresc 1.12% 0.63% 1.78 2.28% 0.50 OM_Growth -0.17% 0.35% -0.50 3.36% -0.00 OM_Invest 0.04% 0.17% 0.22 2.08% 0.02 OM_TopCo -0.02% 0.23% -0.10 2.46% 0.02 Prudential_Opt 0.01% 0.87% 0.02 3.57% -0.00 RMB_Equity -0.12% 0.32% -0.37 2.69% -0.04 RMB_Perform -0.41% 0.51% -0.80 2.77% -0.15 Sage_Fund -0.04% 0.17% -0.25 2.02% -0.00 Sage_MultiF 0.07% 1.19% 0.06 2.39% 0.03 Sanlam_GE -0.17% 0.18% -0.96 2.24% -0.07 Sanlam_MM_Equity -0.54% 0.74% -0.73 3.54% -0.16 Stanlib_CapitalGrowth -0.91% 0.73% -1.24 5.77% -0.18 Stanlib_Prosp -0.10% 0.29% -0.34 2.51% -0.04 Stanlib_Wealth -0.04% 0.18% -0.24 2.27% -0.01 Tri-Linear_Equity -0.68% 0.90% -0.76 3.24% -0.22 Woolworths -0.29% 0.72% -0.41 2.78% -0.12

75

Table 4.11: Value Added by Actively Managed Funds over Rolling 60-month

Investment Periods

FundAverage

AlphaStd Error of Alpha t-statistic

Active Risk Info Ratio

ABSA_General -0.34% 0.32% -1.05 3.13% -0.09 ABSA_Growth -0.26% 1.07% -0.25 2.63% -0.10 Allan Gray_Equity 1.57% 2.13% 0.74 3.69% 0.43 Community_Growth -0.02% 0.40% -0.05 3.52% 0.00 Coronation_Equity -0.14% 0.53% -0.27 3.06% -0.05 Futuregro_Albaraka 0.04% 0.36% 0.11 3.19% 0.01 Investec_ Equity 0.23% 0.21% 1.09 2.44% 0.10 FNB_Growth 0.40% 1.87% 0.21 3.24% 0.12 Mcubed_Equity -0.55% 0.87% -0.63 3.14% -0.18 Metropolitan_GE 0.24% 0.32% 0.76 2.97% 0.08 Nedbank_Equity -0.70% 0.96% -0.73 3.58% -0.19 Nedbank_Rain 0.15% 2.05% 0.07 3.55% 0.04 OM_Growth -0.15% 0.45% -0.33 3.71% -0.02 OM_Invest 0.02% 0.18% 0.11 2.10% 0.01 OM_TopCo -0.03% 0.27% -0.13 2.53% 0.00 RMB_Equity -0.15% 0.40% -0.38 2.77% -0.05 RMB_Perform -0.36% 1.31% -0.27 3.22% -0.11 Sage_Fund -0.09% 0.18% -0.48 2.05% -0.04 Sanlam_GE -0.20% 0.19% -1.01 2.23% -0.09 Stanlib_CapitalGrowth -0.91% 0.96% -0.94 5.95% -0.15 Stanlib_Prosp -0.11% 0.35% -0.32 2.55% -0.05 Stanlib_Wealth -0.09% 0.20% -0.45 2.31% -0.03

Table 4.12: Value Added by Active Managed Funds over Rolling 120-month

Investment Periods

FundAverage

AlphaStd Error of Alpha t-statistic Active Risk Info Ratio

ABSA_General -0.37% 0.55% -0.67 3.15% -0.12 Community_Growth -0.09% 0.78% -0.11 3.41% -0.03 Futuregro_Albaraka 0.25% 0.78% 0.31 3.33% 0.07 Investec_ Equity 0.25% 0.29% 0.86 2.47% 0.10 Metropolitan_GE 0.01% 0.58% 0.02 3.03% 0.00 OM_Growth -0.06% 1.16% -0.05 3.48% -0.02 OM_Invest 0.02% 0.25% 0.09 2.14% 0.01 OM_TopCo -0.06% 0.51% -0.12 2.61% -0.02 Sage_Fund -0.09% 0.26% -0.35 2.09% -0.04 Sanlam_GE -0.19% 0.26% -0.73 2.24% -0.08 Stanlib_Wealth -0.12% 0.28% -0.42 2.37% -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 4.21-

4.23. 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-OffRolling 36-Month Period

17 3

15

13

31

27 5

9

19 25

24

26

2 8

11

23 14132

12

30 2029

10

7

214

226 18

16

28

R2 = 0.1741

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

0% 1% 2% 3% 4% 5% 6% 7%

Non-systematic Risk

Alp

ha (R

etur

n pm

)

1- Absa General2- Absa Growth3- Allan Gray Equity4-Community Growth5- Coris Capital GE6- Coronation Equity7- Futuregro Albaraka8- Futuregro Core9- Investec Equity10- FNB Growth11- MCubed Equity12- Metropolitan GE13- Nedbank Equity14- Nedbank Equity FoF15- Nedbank Rain16- Nedbank Quants17- Oasis Crescent18- OM Growth19- OM Investors20- OM TopCo21- Prudential Opt22- RMB Equity23- RMB Perform24- Sage Fund25- Sage MultiFocus26- Sanlam GE27- Sanlam MM Equity28- Stanlib CapGro29- Stanlib Prosp30- Stanlib Wealth31- Tri-Linear Equity32- Woolw Equity

Figure 4.21: Alpha/Active Risk Profile of Actively Managed Funds over Rolling


78

Alpha/Active Risk Tade-OffRolling 60-month Period

4

171

6

5

2

162115

2219

18

14

9

13

20

11

12107

8

3

R2 = 0.0431

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

0% 1% 2% 3% 4% 5% 6% 7%

Non-systematic Risk

Alp

ha (R

etur

n pm

)

1- Absa General2- Absa Growth3- Allan Gray Equity4- Community Growth5- Coronation Equity6- Futuregro Albaraka7- Investec Equity8- FNB Growth9- Mcubed Equity10- Metropolitan GE11- Nedbank Equity12- Nedbank Rain13- OM Growth14- OM Investor15- OM TopCo16- RMB Equity17- RMB Perform18- Sage Fund19- Sanlam GE20- Stanlib CapGro21- Stanlib Prosp22- Stanlib Wealth



79

Alpha/Risk Tade-OffRolling 120-Month Period

1

26

10

119

8

57

34

R2 = 0.0008

-0.40%

-0.30%

-0.20%

-0.10%

0.00%

0.10%

0.20%

0.30%

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00%

Non-systematic Risk

Alph

a (R

etur

n pm

) 1- Absa General2- Community Growth3- Futuregro Albaraka4- Investec Equity5- Metropolitan GE6- OM Growth7- OM Investor8- OM TopCo9- Sage Fund10- Sanlam GE11- Stanlib Wealth



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 PeriodAverage Information Ratio

-0.25

-0.20-0.15

-0.10

-0.05-

0.05

0.10

0.150.20

0.25Ja

n-91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Period

Rat

io

Information Ratio 12 per. Mov. Avg. (Information Ratio)


Investment Periods

82


-0.20

-0.15

-0.10

-0.05

-

0.05

0.10

0.15

0.20Ja

n-93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Period

Ratio



Investment Periods

83


-0.08

-0.06

-0.04

-0.02

-

0.02

0.04

0.06

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Period

Rat

io



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, risk-

adjusted alpha returns and style-categorised groups that past return and relative

rankings were useful in predicting the returns and rankings of mutual funds. The top-

quartile 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 t-

statistic 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 25 th 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 60-

month 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 PeriodsBuy-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% Middle Top 25%

Figure 5.1: Quartile Ranking of Actively Managed Funds over Rolling


93


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




94


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




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


Fund PeriodsAverage

Percentile Std DevMin DecileRanking

Max DecileRanking

Allan Gray_Equity 27 96 5 9 10 Oasis_Cresc 13 94 5 9 10 Nedbank_Rain 27 71 27 2 9 Sage_MultiF 4 70 0 7 7 FNB_Growth 27 68 11 5 9 Investec_ Equity 156 68 33 1 10 Coronation_Equity 57 65 31 1 10 Prudential_Opt 17 64 6 6 8 Futuregro_Albaraka 102 57 37 1 10 RMB_Equity 71 54 19 2 8 Metropolitan_GE 111 53 41 1 10 OM_TopCo 110 50 28 1 10 Stanlib_Wealth 156 50 35 1 10 Sage_Fund 148 49 24 1 10 Futuregro_Core 24 49 6 4 6 OM_Invest 156 49 24 1 10 Stanlib_Prosp 77 48 35 1 9 Community_Growth 103 46 22 1 9 Nedbank_Quants 14 45 13 2 6 OM_Growth 93 44 33 1 9 ABSA_Growth 30 41 12 2 7 RMB_Perform 30 39 10 2 6 Nedbank Equity FoF 20 34 20 1 6 Sanlam_GE 156 32 24 1 10 Woolworths 15 31 9 2 5 ABSA_General 117 25 22 1 8 Mcubed_Equity 37 23 10 1 5 Sanlam_MM_Equity 23 19 9 1 4 Stanlib_CapitalGrowth 62 16 25 1 9 CorisCap_GE 12 9 11 1 4 Nedbank_Equity 38 5 9 1 4 Tri-Linear_Equity 13 5 5 1 1 ALSI Index 156 59 32 1 10

97



Fund PeriodsAverage

Percentile Std DevMin DecileRanking

Max DecileRanking

Allan Gray_Equity 3 100 0 10 10 FNB_Growth 3 90 0 9 9 Investec_ Equity 132 84 24 1 10 Coronation_Equity 33 78 20 3 10 Metropolitan_GE 87 76 27 1 10 Nedbank_Rain 3 70 0 7 7 RMB_Equity 47 55 16 3 9 Futuregro_Albaraka 78 53 36 1 10 ABSA_Growth 6 52 8 4 6 Community_Growth 79 51 20 2 8 OM_TopCo 86 49 23 2 8 OM_Invest 132 49 18 1 8 Stanlib_Prosp 53 48 23 1 9 Sage_Fund 124 48 21 1 9 Stanlib_Wealth 132 45 32 1 10 RMB_Perform 6 37 8 3 5 OM_Growth 69 36 34 1 9 Sanlam_GE 132 19 21 1 8 Mcubed_Equity 13 17 5 1 2 ABSA_General 93 13 19 1 6 Nedbank_Equity 14 11 9 1 3 Stanlib_CapitalGrowth 38 1 4 1 2 ALSI Index 132 65 26 1 10



Fund PeriodsAverage

Percentile Std Dev Min Decile RankingMax Decile

RankingInvestec_ Equity 72 99 3 9 10 Futuregro_Albaraka 18 88 9 8 10 Metropolitan_GE 27 66 14 5 8 OM_Invest 72 64 11 3 8 Sage_Fund 64 59 11 4 8 OM_TopCo 26 39 13 2 7 Community_Growth 19 36 13 2 6 OM_Growth 9 29 3 2 3 Stanlib_Wealth 72 24 15 1 7 Sanlam_GE 72 8 8 1 2 ABSA_General 33 0 0 1 1 ALSI Index 72 57 21 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

Rolling Three Year Period

Rolling Five Year Period

Rolling Ten Year Period

PeriodsPercentage

Outperforming PeriodsPercentage

Outperforming PeriodsPercentage

OutperformingABSA_General 117 16% 93 15% 33 0%ABSA_Growth 30 0% 6 0%Allan Gray_Equity 27 100% 3 100%Community_Growth 103 37% 79 37% 19 26%CorisCap_GE 12 8%Coronation_Equity 57 40% 33 48%Futuregro_Albaraka 102 48% 78 47% 18 100%Futuregro_Core 24 8%Investec_ Equity 156 62% 132 74% 72 100%FNB_Growth 27 41% 3 100%Mcubed_Equity 37 3% 13 0%Metropolitan_GE 111 44% 87 57% 27 48%Nedbank_Equity 38 0% 14 0%Nedbank Equity FoF 20 0%Nedbank_Rain 27 59% 3 67%Nedbank_Quants 14 7%Oasis_Cresc 13 100%OM_Growth 93 46% 69 33% 9 0%OM_Invest 156 31% 132 17% 72 51%OM_TopCo 110 39% 86 45% 26 31%Prudential_Opt 17 29%RMB_Equity 71 42% 47 17%RMB_Perform 30 3% 6 0%Sage_Fund 148 42% 124 22% 64 44%Sage_MultiF 4 100%Sanlam_GE 156 26% 132 9% 72 1%Sanlam_MM_Equity 23 0%Stanlib_CapitalGrowth 62 13% 38 0%Stanlib_Prosp 77 17% 53 15%Stanlib_Wealth 156 21% 132 19% 72 4%Tri-Linear_Equity 13 0%Woolworths 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

Active FundRanking

MonthlyForward

QuarterlyForward

YearlyForward

Three-yearly

Forward

Same Decile

Overall 64% 55% 25% 8%

Bottom Third 64% 57% 21% 5%

Middle Third 61% 52% 23% 9%

Top Third 75% 68% 37% 6%

Improved Decile

Overall 18% 22% 37% 41%

Bottom Third 17% 20% 38% 37%

Middle Third 19% 24% 36% 41%

Top Third 13% 16% 32% 30%

Worse Decile

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 short-

term 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

64%

18%

18%

Same Decile Improved Decile Worse Decile


on a Month-to-Month basis


Quarter-on-Quarter Forward

56%

22%

22%



on a Quarterly basis

103


Year-on-Year Forward

25%

37%

38%



on a Yearly basis

Ranking of Active Funds (All)Average Movement between Deciles Three Year-on-Three Year Forward

8%

41%51%



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: TOWARDS AN OPTIMAL COMBINATION SOLUTION

6.1 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:

σA = (6.1)

where σA = standard deviation of active portfolio A;

βA= beta of active portfolio with market portfolio M;

σ2M = variance of market portfolio M;

σ2(eA) = variance of non-systematic risk of active portfolio A.

E(rA) =

(6.2)

where E(rA) = 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,

Wopt = (6.3)

where Wopt = weight of active portfolio A in optimal portfolio, if βA = 1

107

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-to-

risk components of the optimal portfolio could be separated as:

Sharpe2 = +

(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:

Wk = (6.6)

where Wk = 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

108

the pay-off to market-related risk is linearly related to the amount of policy risk taken,

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

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00%

Active Risk

Expe

cted

Alp

ha

Figure 6.1: 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:

hmgr ~ (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.

44% Index33% Enhanced Index23% Active

17% Enhanced Index83% Active

100% Index

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 ). 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.

Waring & Siegel (2003: 45) reasoned further that market risks are rewarded

unconditionally and proportional to market risk taken, while active risks are only

111

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 Of

Fund

0% Active Risk

0.5% Active Risk

1.0% Active Risk

1.5% Active Risk

2.0% Active Risk

2.5% Active Risk

3% Active Risk

Index Fund 100 72 44 16 0 0 0Enhanced Index 0 16 33 50 52 39 17Active Growth 0 5 10 15 21 26 35Active Value 0 5 10 15 21 26 35Active 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


Funds Alpha Active Risk Info RatioPercentile

(Info)ABSA_General -0.340% 3.13% -0.1086 19%ABSA_Growth -0.265% 2.63% -0.1007 24%Allan Gray_Equity 1.572% 3.69% 0.4264 100%Community_Growth -0.022% 3.52% -0.0061 67%Coronation_Equity -0.143% 3.06% -0.0469 38%Futuregro_Albaraka 0.038% 3.19% 0.0120 76%Investec_ Equity 0.231% 2.44% 0.0948 90%FNB_Growth 0.395% 3.24% 0.1221 95%Mcubed_Equity -0.548% 3.14% -0.1745 5%Metropolitan_GE 0.241% 2.97% 0.0813 86%Nedbank_Equity -0.697% 3.58% -0.1944 0%Nedbank_Rain 0.148% 3.55% 0.0419 81%OM_Growth -0.146% 3.71% -0.0394 57%OM_Invest 0.021% 2.10% 0.0099 71%OM_TopCo -0.035% 2.53% -0.0136 62%RMB_Equity -0.152% 2.77% -0.0548 33%RMB_Perform -0.361% 3.22% -0.1120 14%Sage_Fund -0.089% 2.05% -0.0432 48%Sanlam_GE -0.196% 2.23% -0.0882 29%Stanlib_CapitalGrowth -0.911% 5.95% -0.1532 10%Stanlib_Prosp -0.112% 2.55% -0.0440 43%Stanlib_Wealth -0.091% 2.31% -0.0395 52%

113

Alpha Added RangeRolling 60-month Data

-1.500%

-1.000%

-0.500%

0.000%

0.500%

1.000%

1.500%

2.000%

100%95%

90%

86%

81%

76%

71%

67%

62%

57%

52%

48%

43%

38%

33%

29%

24%

19%

14%

10%5%0%

Percentile Ranking (Info Ratio)

Alph

a (p

.m.)

Figure 6.2: Distribution of Alphas across Actively Managed Funds over


Active Risk RangeRolling 60-month Data

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%10

0%95%

90%

86%

81%

76%

71%

67%

62%

57%

52%

48%

43%

38%

33%

29%

24%

19%

14%

10%5%0%


Act

ive

Ris

k

Figure 6.3: Distribution of Active Risk across Actively Managed Funds over


114

Value Added RangeRolling 60-month Data

-0.3000

-0.2000

-0.1000

-

0.1000

0.2000

0.3000

0.4000

0.5000

100%95%

90%

86%

81%

76%

71%

67%

62%

57%

52%

48%

43%

38%

33%

29%

24%

19%

14%

10%5%0%


Info

rmat

ion

Ratio

Figure 6.4: Distribution of Information Ratios across Actively Managed Funds


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 Treynor-

Black 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

Average Beta

AverageAlpha (pm)

AverageVolatility

Average Active Risk

AverageInformation

Ratio

70th Percentile 75% 0.035% 6.00% 3.25% 0.0108 75th Percentile 75% 0.050% 6.00% 3.20% 0.0156 80th Percentile 75% 0.120% 6.00% 3.00% 0.0400 Index Fund 100% 0% 6.00% 0%

116

Table 6.4: Optimising Results with 70th Percentile Active

Investment Performance

Expected Excess Market Return

Active Fund Allocation

Index Fund 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 PortfolioActive Fund Performance in 70th Percentile

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.25% 0.50% 0.75% 1.00% 1.25% 1.50%

Expected Excess Market Return (p.m.)

Perc

enta

ge A

lloca

tion

Figure 6.5: Example of Optimal Actively Managed and Index Fund Weights in

an Investment Portfolio given various Market Returns

117




Active FundAllocation

Index FundAllocation

0.25% 49% 51%0.50% 26% 74%0.75% 18% 82%1.00% 14% 86%1.25% 11% 89%1.50% 9% 91%


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.25% 0.50% 0.75% 1.00% 1.25% 1.50%


Perc

enta

ge A

lloca

tion



118




Active FundAllocation

Index Fund 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%


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.25% 0.50% 0.75% 1.00% 1.25% 1.50%


Perc

enta

ge A

lloca

tion



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 Allocation70th 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 Period

Number of

Periods

Measure Top QuartileActive Management

Performance(per annum)

ALSI Index Return

(per annum)

Before Cost After Cost

36 months 156Average Return

13.69% 11.63% 11.32%

Std Deviation 7.26% 7.12% 8.14%


12.49% 11.25% 11.05%

Std Deviation 5.23% 5.17% 5.27%


11.52% 10.90% 10.89%

Std Deviation 2.29% 2.27% 2.11%

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-RiskRolling 36-month Period

Top Quartile Active Performance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Indexing

Ratio



Combinations over Rolling 36-month Investment Periods

124



1.95

2.00

2.05

2.10

2.15

2.20

2.25

2.30

2.35

2.40

2.45

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Indexing

Ratio




125



4.50

4.60

4.70

4.80

4.90

5.00

5.10

5.20

5.30

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Indexing

Ratio




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.

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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 out-

performance 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: CONCLUSIONS AND RECOMMENDATIONS

9.1 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

Pre-Cost Performance After-Cost Performance

Years Date JSE-ALSI Active AvgTop 25% Active Bottom 25% Active Active Avg Top 25% Active Bottom 25% Active

15

Jan-88 471% 542% 607% 451% 507% 569% 422%Feb-88 562% 580% 646% 497% 544% 606% 464%Mar-88 584% 592% 661% 508% 555% 620% 475%Apr-88 518% 548% 621% 456% 513% 582% 426%

May-88 547% 567% 640% 469% 531% 600% 439%Jun-88 520% 545% 614% 447% 510% 575% 417%Jul-88 492% 520% 584% 420% 487% 547% 392%

Aug-88 473% 500% 556% 406% 468% 520% 379%Sep-88 502% 520% 578% 426% 486% 541% 398%Oct-88 462% 485% 493% 404% 454% 461% 377%Nov-88 428% 468% 463% 384% 438% 433% 358%Dec-88 430% 468% 467% 385% 438% 436% 359%

14

Jan-89 424% 451% 450% 366% 421% 420% 341%Feb-89 381% 420% 431% 341% 392% 402% 317%Mar-89 355% 396% 405% 317% 369% 378% 294%Apr-89 310% 369% 380% 297% 343% 354% 276%

May-89 300% 362% 365% 286% 337% 340% 265%Jun-89 333% 384% 389% 307% 358% 362% 285%Jul-89 295% 343% 350% 271% 319% 326% 251%


145




13

Jan-90 249% 303% 308% 233% 281% 286% 215%Feb-90 225% 282% 296% 221% 261% 274% 204%Mar-90 237% 289% 300% 224% 268% 278% 206%Apr-90 219% 267% 277% 205% 247% 256% 189%

May-90 243% 294% 297% 221% 273% 275% 204%Jun-90 226% 272% 278% 202% 252% 257% 186%Jul-90 238% 279% 277% 208% 259% 257% 192%


12

Jan-91 282% 302% 291% 219% 281% 270% 202%Feb-91 306% 323% 311% 247% 300% 289% 228%Mar-91 271% 286% 275% 214% 266% 255% 197%Apr-91 261% 269% 263% 199% 249% 244% 183%

May-91 242% 236% 247% 160% 218% 229% 146%Jun-91 233% 229% 239% 154% 211% 221% 141%Jul-91 214% 214% 226% 143% 197% 208% 130%


146




11

Jan-92 202% 197% 208% 148% 181% 192% 135%Feb-92 188% 183% 191% 142% 167% 176% 129%Mar-92 189% 183% 190% 143% 168% 175% 130%Apr-92 193% 183% 190% 143% 168% 174% 130%

May-92 201% 194% 201% 148% 179% 185% 135%Jun-92 178% 172% 180% 128% 158% 165% 116%Jul-92 184% 178% 184% 142% 163% 169% 129%


10

Jan-93 219% 206% 215% 148% 189% 198% 134%Feb-93 203% 197% 205% 149% 181% 188% 135%Mar-93 204% 196% 212% 147% 180% 195% 134%Apr-93 192% 191% 200% 141% 176% 183% 128%

May-93 178% 188% 194% 142% 173% 178% 129%Jun-93 160% 177% 183% 129% 162% 168% 116%Jul-93 155% 169% 176% 123% 154% 161% 111%


147




9

Jan-94 112% 136% 144% 97% 123% 131% 86%Feb-94 118% 141% 147% 103% 128% 134% 92%Mar-94 114% 136% 143% 98% 123% 130% 88%Apr-94 110% 131% 146% 96% 119% 132% 86%

May-94 94% 120% 137% 84% 108% 124% 74%Jun-94 92% 108% 131% 77% 97% 119% 67%Jul-94 92% 107% 130% 76% 96% 118% 67%


8

Jan-95 77% 88% 107% 61% 78% 96% 52%Feb-95 106% 107% 129% 81% 96% 117% 71%Mar-95 102% 110% 138% 81% 99% 130% 72%Apr-95 97% 106% 130% 76% 95% 122% 67%

May-95 90% 100% 118% 69% 89% 111% 60%Jun-95 90% 96% 117% 69% 86% 109% 60%Jul-95 92% 97% 118% 69% 87% 110% 60%


148




7

Jan-96 67% 66% 82% 44% 57% 74% 36%Feb-96 51% 54% 72% 35% 46% 63% 27%Mar-96 55% 58% 76% 38% 49% 67% 30%Apr-96 54% 59% 75% 36% 50% 68% 29%

May-96 49% 59% 76% 34% 51% 68% 27%Jun-96 52% 62% 79% 37% 54% 71% 30%Jul-96 51% 56% 71% 30% 47% 63% 23%


6

Jan-97 57% 54% 67% 36% 46% 59% 29%Feb-97 56% 52% 64% 36% 44% 56% 29%Mar-97 45% 43% 53% 27% 35% 46% 20%Apr-97 46% 44% 54% 29% 37% 47% 22%

May-97 46% 42% 51% 27% 35% 45% 20%Jun-97 48% 41% 51% 27% 34% 44% 20%Jul-97 40% 35% 45% 19% 28% 38% 12%


149




5

Jan-98 67% 49% 64% 25% 41% 57% 18%Feb-98 59% 42% 57% 18% 34% 49% 11%Mar-98 46% 29% 45% 3% 22% 39% -2%Apr-98 37% 20% 36% -4% 13% 29% -9%

May-98 26% 11% 30% -12% 5% 25% -17%Jun-98 36% 16% 37% -8% 10% 29% -13%Jul-98 53% 24% 47% -5% 18% 39% -10%

Aug-98 48% 21% 44% -4% 15% 36% -9%Sep-98 111% 68% 100% 43% 59% 89% 35%Oct-98 104% 71% 95% 43% 62% 85% 35%Nov-98 78% 76% 91% 32% 67% 80% 25%Dec-98 85% 77% 92% 38% 68% 82% 30%

4

Jan-99 91% 79% 96% 40% 70% 86% 32%Feb-99 79% 69% 87% 36% 61% 77% 28%Mar-99 76% 62% 80% 32% 54% 70% 26%Apr-99 63% 49% 63% 25% 42% 54% 18%

May-99 47% 44% 60% 24% 37% 51% 17%Jun-99 60% 51% 66% 30% 44% 57% 23%Jul-99 47% 43% 54% 24% 36% 46% 17%


150




3

Jan-00 22% 27% 34% 10% 21% 27% 4%Feb-00 23% 22% 28% 6% 16% 21% 0%Mar-00 30% 28% 41% 10% 21% 33% 4%Apr-00 31% 30% 40% 10% 24% 32% 5%

May-00 40% 43% 51% 24% 37% 43% 18%Jun-00 41% 43% 49% 25% 36% 41% 18%Jul-00 35% 38% 43% 21% 32% 37% 15%


Percentage better than Index (overall) 60% 90% 0% 29% 58% 0%Percentage better than Index (years 11-15) 70% 90% 0% 43% 55% 0%Percentage better than Index (years 6-10) 68% 97% 0% 30% 77% 0%Percentage better than Index (years 3-5) 31% 78% 0% 3% 33% 0%

# Periods Overall 156 # Periods 11-15 60 # Periods 6-10 60 # Periods 3-5 36

151

Appendix B

Statistical Tests for the Random Sampling Investment Periods

152

Random SamplingThree Year Investment Period (cumulative return)Sell-to-sell price basis

t-Test: Paired Two Sample for Means

INDEX ACTIVE AVERAGEMean 37.76% 39.53%Variance 9.60% 8.08%Observations 100 100Pearson Correlation 87.11%Hypothesized Mean Difference 0df 99t Stat -1.160591682P(T<=t) one-tail 0.124299502t Critical one-tail 1.660391717P(T<=t) two-tail 0.248599003t Critical two-tail 1.984217306

Random SamplingThree Year Investment Period (cumulative return)Buy-to-sell price basis


INDEX ACTIVE AVERAGEMean 37.76% 32.19%Variance 9.60% 7.18%Observations 100 100Pearson Correlation 87.20%Hypothesized Mean Difference 0df 99t Stat 3.671049107P(T<=t) one-tail 0.000195791t Critical one-tail 1.660391717P(T<=t) two-tail 0.000391582t Critical two-tail 1.984217306

153

Random SamplingFive Year Investment Period (cumulative return)Sell-to-sell price basis


INDEX ACTIVE AVERAGEMean 76.88% 80.66%Variance 16.54% 17.95%Observations 100 100Pearson Correlation 93.85%Hypothesized Mean Difference 0df 99t Stat -2.582442442P(T<=t) one-tail 0.005636861t Critical one-tail 1.660391717P(T<=t) two-tail 0.011273722t Critical two-tail 1.984217306

Random SamplingFive Year Investment Period (cumulative return)Buy-to-sell price basis


INDEX ACTIVE AVERAGEMean 76.88% 71.00%Variance 16.54% 16.02%Observations 100 100Pearson Correlation 93.88%Hypothesized Mean Difference 0df 99t Stat 4.163455354P(T<=t) one-tail 3.34931E-05t Critical one-tail 1.660391717P(T<=t) two-tail 6.69862E-05t Critical two-tail 1.984217306

154

Random SamplingTen Year Investment Period (cumulative return)Sell-to-sell price basis


INDEX ACTIVE AVERAGEMean 194.05% 210.35%Variance 42.62% 58.16%Observations 100 100Pearson Correlation 91.73%Hypothesized Mean Difference 0df 99t Stat -5.306985954P(T<=t) one-tail 3.4137E-07t Critical one-tail 1.660391717P(T<=t) two-tail 6.8274E-07t Critical two-tail 1.984217306

Random SamplingTen Year Investment Period (cumulative return)Buy-to-sell price basis


INDEX ACTIVE AVERAGEMean 194.05% 193.61%Variance 42.62% 52.06%Observations 100 100Pearson Correlation 91.73%Hypothesized Mean Difference 0df 99t Stat 0.15082248P(T<=t) one-tail 0.440211319t Critical one-tail 1.660391717P(T<=t) two-tail 0.880422638t Critical two-tail 1.984217306

155

Appendix C

Statistical Tests for the Rolling Investment Periods

156

Statistical Significance: Three Year Rolling Investment PeriodAnnualised Performance

Active vs. Index on Pre-Cost Basis (sell-to-sell price)


Index Active AvgMean 11.32% 11.35%Variance 0.66% 0.54%Observations 156 156Pearson Correlation 85.40%Hypothesized Mean Difference 0df 155t Stat -0.0984P(T<=t) one-tail 0.460869t Critical one-tail 1.654744P(T<=t) two-tail 0.921738t Critical two-tail 1.975386

Active vs. Index on After-Cost Basis (buy-to-sell price)


Index Active AverageMean 11.32% 9.36%Variance 0.66% 0.52%Observations 156 156Pearson Correlation 85.49%Hypothesized Mean Difference 0df 155t Stat 5.779383P(T<=t) one-tail 2E-08t Critical one-tail 1.654744P(T<=t) two-tail 3.99E-08t Critical two-tail 1.975386

157

Statistical Significance: Five Year Rolling Investment PeriodAnnualised Performance



Index Active AverageMean 11.05% 11.12%Variance 0.28% 0.32%Observations 132 132Pearson Correlation 92.62%Hypothesized Mean Difference 0df 131t Stat -0.42104P(T<=t) one-tail 0.33721t Critical one-tail 1.656567P(T<=t) two-tail 0.674419t Critical two-tail 1.978237



Index Active AverageMean 11.05% 9.91%Variance 0.28% 0.31%Observations 132 132Pearson Correlation 92.66%Hypothesized Mean Difference 0df 131t Stat 6.195521P(T<=t) one-tail 3.49E-09t Critical one-tail 1.656567P(T<=t) two-tail 6.99E-09t Critical two-tail 1.978237

158

Statistical Significance: Ten Year Rolling Investment PeriodAnnualised Performance



Index Active AverageMean 10.89% 11.16%Variance 0.04% 0.05%Observations 72 72Pearson Correlation 88.37%Hypothesized Mean Difference 0df 71t Stat -2.18485P(T<=t) one-tail 0.016101t Critical one-tail 1.666599P(T<=t) two-tail 0.032202t Critical two-tail 1.993944



Index Active AverageMean 10.89% 10.55%Variance 0.04% 0.05%Observations 72 72Pearson Correlation 88.37%Hypothesized Mean Difference 0df 71t Stat 2.766867P(T<=t) one-tail 0.003605t Critical one-tail 1.666599P(T<=t) two-tail 0.007211t Critical two-tail 1.993944

159

Appendix D

Statistical Tests for Risk-adjusted Return Comparisons

160

Risk-adjusted Returns: Sharpe RatioActive Management versus Index over 36-month rolling periods


Index Active AverageMean -0.9639% -0.7257%Variance 1.1991% 0.8446%Observations 156 156Pearson Correlation 85.52%Hypothesized Mean Difference 0df 155t Stat -0.52406286P(T<=t) one-tail 0.300491698t Critical one-tail 1.654743755P(T<=t) two-tail 0.600983397t Critical two-tail 1.975386112

Risk-adjusted Returns: Treynor RatioActive Management versus Index over 36-month rolling periods


Index Active AverageMean -0.0817% -0.1082%Variance 0.0039% 0.0019%Observations 156 156Pearson Correlation 58.61%Hypothesized Mean Difference 0df 155t Stat 0.648920947P(T<=t) one-tail 0.2586749t Critical one-tail 1.654743755P(T<=t) two-tail 0.517349801t Critical two-tail 1.975386112

161







162







163

Appendix E

Cost Structures of Index Funds

164

Cost Structures of Index Funds in the General Equity SectorFund Upfront Charges

(max)Management Fee

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 SectorFund Upfront Charges

(max)Management Fee

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 FundsFund Upfront Charges

(max)Management Fee

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


Alsi InvestecMean 6.54% 7.31%Variance 0.51% 0.53%Observations 70 70Pearson Correlation 94.32%Hypothesized Mean Difference 0df 69t Stat -2.63054P(T<=t) one-tail 0.005253t Critical one-tail 1.667239P(T<=t) two-tail 0.010505t Critical two-tail 1.994945

Regression StatisticsMultiple R 94.32%R Square 88.96%Adjusted R Square 88.79%Standard Error 2.44%Observations 70

ANOVA

df SS MS FSignificance

F

Regression 1 0.3257

0.3257

547.7346

0.0000

Residual 68 0.0404

0.0006

Total 69 0.3661

CoefficientsStandard

Error t Stat P-value 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



Alsi GryphonMean 8.56% 4.76%Variance 0.47% 0.44%Observations 47 47Pearson Correlation 85.67%Hypothesized Mean Difference 0df 46t Stat 7.207033P(T<=t) one-tail 2.23E-09t Critical one-tail 1.67866P(T<=t) two-tail 4.46E-09t Critical two-tail 2.012896


ANOVA df SS MS F Significance F

Regression 1 0.1485 0.1485 124.1359 0.0000 Residual 45 0.0538 0.0012 Total 46 0.2023

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%

Intercept -0.0234 0.0081 -2.8817 0.0060 -0.0398 -0.0071 X Variable 1 0.8297 0.0745 11.1416 0.0000 0.6797 0.9797

168

Tracking Error Analysis for Stanlib Index Fund



Alsi StanlibMean 6.61% 6.36%Variance 0.51% 0.51%Observations 71 71Pearson Correlation 95%Hypothesized Mean Difference 0df 70t Stat 0.901716P(T<=t) one-tail 0.18515t Critical one-tail 1.666914P(T<=t) two-tail 0.3703t Critical two-tail 1.994437


ANOVA df SS MS F Significance F

Regression 1 0.3229 0.3229 610.8814 0.0000 Residual 69 0.0365 0.0005 Total 70 0.3594

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%

Intercept 0.0006 0.0037 0.1608 0.8727 -0.0068 0.0080 X Variable 1 0.9536 0.0386 24.7160 0.0000 0.8766 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 Indexing 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%

3

Pre-cost Average 13.69% 13.45% 13.21% 12.98% 12.74% 12.50% 12.27% 12.03% 11.79% 11.56% 11.32%Std Deviation 7.26% 7.26% 7.27% 7.31% 7.37% 7.46% 7.56% 7.68% 7.81% 7.97% 8.14%Sharpe (adj) 1.886 1.854 1.817 1.774 1.728 1.677 1.623 1.567 1.509 1.450 1.391

After-cost Average 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

5


After-cost Average 11.25% 11.23% 11.21% 11.19% 11.17% 11.15% 11.13% 11.11% 11.09% 11.07% 11.05%Std Deviation 5.17% 5.13% 5.10% 5.09% 5.08% 5.09% 5.10% 5.13% 5.16% 5.21% 5.27%Sharpe (adj) 2.178 2.189 2.197 2.200 2.198 2.192 2.181 2.166 2.147 2.124 2.097

10


After-costAverage 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

“My favourite holding period is forever.”

- Warren Buffet

“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

174

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