active portfolio management and portfolio construction

MASTER THESIS, FALL 2012CAND.MERC. APPLIED ECONOMICS AND FINANCE

COPENHAGEN BUSINESS SCHOOL

AUTHOR: JOHAN CHRISTIAN HILSTEDDATE OF SUBMISSION: DECEMBER 14TH 2012

ACTIVE PORTFOLIO MANAGEMENT AND PORTFOLIO CONSTRUCTION

- IMPLEMENTING AN INVESTMENT STRATEGY

SUPERVISOR: JEPPE SCHOENFELDT

NUMBER OF PAGES: 77

NUMBER OF CHARACTERS: 145.260

SIGNATURE:

Active Portfolio Management and Portfolio Construction – Implementing an Investment Strategy

1

Abstract

This thesis aims at creating an investment strategy for active portfolio management to outperform the

MSCI Denmark from 1992 to 2011. The index development of the Danish stock market has been quite

impressive as it has performed remarkably better than other national indices. It is therefore interesting

to investigate whether active portfolio management constitutes a winning strategy superior to investing

in the MSCI Denmark.

There is no generally accepted approach to conduct active portfolio management. This thesis approaches

the subject by comparing two internationally diversified portfolios to the MSCI Denmark as benchmark -

one portfolio submitted to a 20% maximum asset representation restriction, the other portfolio left

unrestricted.

From investment strategy we conclude that combining strategic and tactical asset allocation constitutes

an appropriate investment strategy for active portfolio management, as it limits the long-term portfolio

investment opportunities and allows for short-term portfolio repositioning. The information ratio

constitutes the performance measure of active portfolio management, as it optimizes portfolio

construction by comparing expected returns of portfolio and benchmark – the residual return. The Capital

Assets Pricing Model (CAPM) was utilized for return estimations for both investment opportunities and

benchmark. Mean-variance portfolio construction was conducted based upon investment opportunities

expected to outperform the benchmark.

The MSCI Denmark provides realized average monthly return of 0,65%, while the actively managed

portfolios produce average realized monthly return of 0,34% and 0,37%, respectively. In that regard,

active portfolio management has not outperformed the benchmark, and statistical findings cannot suggest

portfolio timing skill. However, considering the systematic risk adjusted return, both portfolios yield

significant alpha, or value added, with the unrestricted portfolio being the best performing portfolio.

In conclusion, active portfolio management cannot produce higher return than the MSCI Denmark, but has

proven to benefit the investor, as the market risk exposure justifies both inferior and superior portfolio

return to the benchmark.


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Table of Contents

Abstract .......................................................................................................................................... 1

1. Introduction ................................................................................................................................ 4

1.1 Research Objectives ................................................................................................................................... 6

1.1.1 Superior Research Objective ................................................................................................................... 6

1.1.2 Subordinate Research Objectives ........................................................................................................... 6

1.2 Structure of Thesis...................................................................................................................................... 7

1.3 Methodology .............................................................................................................................................. 8

1.3.1 Financial Assets and Risk ......................................................................................................................... 8

1.3.2 Applied Theoretical Approach ............................................................................................................... 10

1.3.3 Interviews .............................................................................................................................................. 11

1.4 Assumptions and limitations .................................................................................................................... 12

1.4.1 Assumptions .......................................................................................................................................... 12

1.4.2 Limitations ............................................................................................................................................. 13

1.5 Data .......................................................................................................................................................... 14

1.5.1 Equity Sector Return Data ..................................................................................................................... 14

2.Investment Strategy ................................................................................................................... 18

2.1 Investment Strategy as the Source of Portfolio Performance ................................................................. 18

2.2 Strategic Asset Allocation ......................................................................................................................... 19

2.2.1 Discussing Empirical Findings and Brinson et.al. ................................................................................... 21

2.3 Tactical Asset Allocation ........................................................................................................................... 23

2.4 Professional Views upon Asset Allocation ............................................................................................... 24

2.5 Benchmark and Investment Opportunities .............................................................................................. 25

2.5.1 Benchmark............................................................................................................................................. 26

2.5.2 Investment Opportunities ..................................................................................................................... 27

2.6 Crafting the Investment Strategy ............................................................................................................. 30

3.Active Portfolio Management ..................................................................................................... 33

3.1 Defining Active Portfolio Management .................................................................................................... 33

3.2 Performance Measure and Portfolio Added Value .................................................................................. 34

3.2.1 Information Ratio .................................................................................................................................. 34

3.2.2 Portfolio Value Added ........................................................................................................................... 35


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4.Risk and Return in Active Portfolio Management ........................................................................ 38

4.1 Expected Return in Active Portfolio Management .................................................................................. 38

4.1.1 Asset Pricing in an Active Setting .......................................................................................................... 38

4.2 Risk Management ..................................................................................................................................... 46

4.2.1 Investor Utility ....................................................................................................................................... 47

4.2.2 Professional Views upon Risk and Risk Management ........................................................................... 47

4.2.3 Risk Management and Risk Factors ....................................................................................................... 48

4.2.4 Financial Risk ......................................................................................................................................... 49

5.Portfolio Construction ................................................................................................................ 51

5.1 Objective of Portfolio Construction ......................................................................................................... 51

5.2 Choice of Portfolio Model ........................................................................................................................ 51

5.3 Mean-Variance Application in an Active Setting ...................................................................................... 52

5.3.1 The Model ............................................................................................................................................. 53

5.3.2 Model Short-Comings ............................................................................................................................ 55

5.3.3 Portfolio Repositioning and Transaction Costs ..................................................................................... 60

5.4 Model Performance ................................................................................................................................. 63

5.4.1 Sector Distribution ................................................................................................................................ 63

6.Performance Evaluation of the Investment Strategy ................................................................... 67

6.1 Return-Based Performance Analysis ........................................................................................................ 67

6.1.1 Cross-Sectional Comparison .................................................................................................................. 67

6.1.2 Market Timing ....................................................................................................................................... 69

6.2 Analysis of Value Added ........................................................................................................................... 71

7.Conclusion ................................................................................................................................. 75

8.References ................................................................................................................................. 78

9.Appendix Overview .................................................................................................................... 81

Appendix 1: Glossary ...................................................................................................................................... 82

Appendix 2: Sector Market Value and Correlation Matrix of Sector Return ................................................. 86

Appendix 3: Interview Guide .......................................................................................................................... 87

Appendix 4: Active Return and Testing for Return Stationarity..................................................................... 89

Appendix 5: Expected Residual Return .......................................................................................................... 95

Appendix 6: Portfolio Positions of Investment Opportunities ....................................................................... 97


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1. Introduction A common objective of the portfolio investor is to achieve a higher portfolio risk adjusted return as

opposed to investment in a single asset. Combining assets into a portfolio carries the opportunity of risk

reduction and at the same time acquiring a higher return compared to single asset investment.

As financial markets experience different phases, different regimes reside in the markets and many

investment portfolios incur both losses and gains if it is not managed in accordance with the investor’s

expectations to future market developments. For long-term investments such as pension investments,

incurring losses in the short term is of little concern as the investment time frame allows for the

opportunity to reduce such losses by gaining future positive returns. However, for some investors, in

practice, this is not a feasible strategy since they are constrained by consumptions and liabilities.

Accordingly, investors need to liquidate some of their investments in order to fulfill financial needs and

obligations. In other words, the investor buys and sells stocks, and the basis of this decision is the

conviction that abnormal investment returns can be gained. However, the efficient market hypothesis,

which can be traced back to Samuelson (1965) and Farma (1970), states that market prices incorporate all

information rationally and instantaneously, eliminating the possibility for the investor to achieve abnormal

returns and should this hypothesis hold in practice, the only optimal portfolio strategy would be to

conduct portfolio investment and hold the portfolio throughout a predetermined time frame1 2.

However, assuming stock markets are not efficient, in terms of market paradigm we turn to the adaptive

market hypothesis by Lo (2004) who acknowledges the problematic issue of the assumption of market

efficiency3. This paradigm carries some implications that necessitate portfolios to be actively managed.

First, a relationship between asset risk and return exists, but is unlikely to be stable over time. Second,

arbitrage opportunities arise over time. A third implication is that investment strategies might not perform

equally well in different economic environments. A fourth implication is survival, which is enabled by

evolving markets and financial technology. This thesis will not seek to investigate the extent of these

implications but yields an important conclusion: a portfolio has to be actively managed. The most

1 Samuelson (1965): p. 43

2 Farma (1970): p. 383

3 Lo (2004): p. 18


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important reasons are the changing market behavior, and the advances in market research which will lead

to improved tools in portfolio management.

Active portfolio management is a widely used concept where investors compare their investment

performance to the market or a benchmark portfolio in order to determine whether their investment

decision has yielded a higher return than either of these. Commonly applied benchmarks in active

portfolio management are large and highly liquid indices such as the S&P 500 or the Dow Jones Index. In

addition, the investment opportunities are usually limited to the underlying stocks of that benchmark

categorized into sectorial based indices. The advantage of this approach is that the benchmarks underlying

indices are likely to follow a somewhat similar return pattern as the overall market, making it less difficult

to allocate portfolio assets. We will in this thesis deviate from this approach, as we apply the MSCI

Denmark as benchmark and ten globally based sectorial indices as investment opportunities subjected to

active portfolio management.

In order to assemble optimal portfolios, Harry Markowitz (1952)4 introduced the concept of efficient

portfolio, which either optimizes the return of an asset or minimizes the risk of the asset for a given level

of return. The concept is realized by diversifying assets in a portfolio, which is achieved by investing in a

variety of different stocks that change differently in relation to each other – stocks with low covariance.

Therefore, as the results of this thesis are of a theoretical nature, the aim is to apply financial modeling of

Markowitz’ modern portfolio theory, in order to solve the optimal portfolio construction problems. With

regards to portfolio optimization another important topic is considered: Portfolio repositioning – the

process of over- and underweighting portfolio assets on a periodic basis.

4 Markowitz (1952): p. 82


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1.1 Research Objectives

The following research questions will be answered in this thesis with regards to active portfolio

management.

1.1.1 Superior Research Objective

The research objective of this thesis is to devise an investment strategy by assembling a diversified

portfolio with the aim of outperforming the MSCI Denmark by altering positions of portfolio assets on a

short-term basis over a 20 year timeframe. The purpose of this investigation is to determine whether

return generated from such strategy is warranted by its systematic market risk. In that regard, the aim is

to determine whether active portfolio management is more attractive than high performing benchmark

investing on a long-term basis.

1.1.2 Subordinate Research Objectives

In order to accommodate the superior research objectives, a portfolio will be constructed, subjected to

active portfolio management and compared to the portfolio’s benchmark – the MSCI Denmark. In order to

provide reliable results to support the conclusion, the following subordinate research questions must be

answered.

1. How does the mean-variance portfolio model conduct asset allocation in the context of active

portfolio management?

2. How does active portfolio management perform compared to MSCI Denmark between 1992 and

2011?

3. Does active portfolio management performance indicate investment skill on the part of the

investor?

4. With regards to portfolio and benchmark systematic risk, does active portfolio management add

value to the investor?


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1.2 Structure of Thesis

The approach to this thesis is based upon the structure illustrated in figure 1.1.

Figure 1.1: Structure of the Thesis

Figure 1.1 divides the content of the thesis into four sections, each containing underlying chapters.

References made will be with regards to the underlying chapters. This section will continue by explaining

the thesis methodological approach, the limitations imposed and applied data.

Section 2 will start by discussing of the concepts of strategic asset allocation and tactical asset allocation,

in order to frame the investment strategy necessary for the purpose of active portfolio management. It

will continue by providing theoretical considerations of determining and limiting the investment

opportunities available for portfolio construction. Such limitation is deemed necessary in order for the

mean-variance model to construct stable portfolios. Ten globally assembled sector Indices are considered

for active portfolio construction in addition to the MSCI Denmark. The active portfolio management

strategy attempts to outperform the MSCI Denmark by altering portfolio positions of the investment

opportunities. Based on empirical and practical findings with regards to Strategic and Tactical Asset

Allocation, a definition of active portfolio management is given and the importance of the definition of the

benchmark is highlighted. Additionally, appropriate performance measurements will be presented.

• Chapter 1: Introduction Section 1: Introduction

• Chapter 2: Investment Strategy

• Chapter 3: Active Portfolio Management

• Chapter 4: Return and Risk Management

• Chapter 5: Portfolio Construction

Section 2: Areas of Focus and Theoretical Framework

• Chapter 6: Portfolio Performance Evaluation Section 3: Analysis and Evaluation

• Chapter 7: Conclusion Section 4: Conclusion


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The section continues by providing return estimates as input variables for portfolio construction. Based on

theoretical and practical findings, issues regarding the risk active portfolio management are exposed to

will be analyzed and evaluated. The section then concludes by applying the Markowitz mean-variance

portfolio model for portfolio construction. Implementation possibilities with regards to portfolio

repositioning are additionally presented and briefly discussed. The performance of the mean-variance

model in the context of active portfolio management will then be examined. First in terms of asset

allocation, i.e. whether the model has produced stable portfolios during portfolio repositioning. Second,

return estimates will indicate whether outperformance is present on a long-term basis.

Section 3 will present the results of the active portfolio management process. From the portfolio strategy,

the portfolio model presented in section 2 will have assembled portfolios based on the provided risk and

return estimates. This section therefore answers the questions of whether active portfolio management

has added value to the investment and whether these results are due to skill rather than luck.

Section 4 concludes by summarizing the answers to the research questions.

1.3 Methodology

1.3.1 Financial Assets and Risk

An enduring element regarding portfolio performance concerns the relationship between risk and return

on investments. A financial investment, in contrast to a real investment, which involves tangible assets

such as land and production facilities, is an allocation of money whose value is supposed to increase over

time. Therefore a security is a contract to receive prospective benefits under stated conditions like stocks

and bonds.

The two main attributes that distinguish securities are time and risk. Usually the interest rate or rate of

return (depending on whether the security is a bond or stock) is defined as the gain or loss of the

investment relative to the initial value of the investment. An investment always contains some sort of risk,

categorized into two types – systematic and unsystematic risk, and the higher such risks the higher return

is demanded by investors.


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Financial assets are divided into two categories; traditional and alternative investments. Figure 1.2

summarizes the considered assets.

Figure 1.2 Financial Assets

The main traditional assets are cash, fixed income, equities real estate and foreign exchange. Cash is

assumed to be stored in a bank account, yielding an interest rate often referred to as the risk free rate.

Fixed income securities, are government or company issued securities with a year to maturity, issued with

the purpose of managing short-term cash needs. Two important money market interest rates are the

London Interbank Offered Rate (LIBOR), which is the interest rate at which large banks in London lend

money to each other. The other interest rate of importance is the Treasury Bill.

The long-term borrowing needs of corporations are met by issuing bonds. A bond contract provides

periodic coupon payments and the principal value at maturity of the bondholder5.

Stocks are issued by corporations which convey rights to the owners, as they can elect the board of

directors and have a claim of the earnings of the company. The shareholders are compensated with cash

dividends, whose amount is determined by the company’s Management and Board of Directors. When

referring to stocks, publically traded stocks are considered, which are regulated by governments. The

process of arranging the sale of private stocks to the public market is called an IPO (Initial Public Offering).

In contrast, private equity refers to stocks held by private individuals or organizations.

5 http://www.investopedia.com/terms/b/bond.asp#axzz2CCmQC8CG

Traditional Investments Alternative Investments

Cash Hedge Funds

Fixed Income Managed Funds

Equity (stocks) Private Equity Funds

Real Estate Physical Assets (comodities, art etc)

Foreign Exchange Securitized Products (debt obligations etc)

Source: Own Creation

http://www.investopedia.com/terms/b/bond.asp#axzz2CCmQC8CG


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Real estate investments and foreign exchange derivatives are also found in portfolios, the latter for

hedging against currency risks. Alternative investments emphasize the widening spectrum of investment.

These types of investment are beyond the scope of this thesis.

Risk and return obviously depends upon the type of investment. In order to measure investment return on

a frequent basis we turn to equities, or stocks, as return can be realized at any point in time, preferable for

an investor who favors frequent trading. The risk of such investment is presented when positive or

negative return is realized upon trading. Hence, emphasis on risk and return is important to consider,

particularly in the context of active portfolio management, as the investor takes on the risk of frequently

realizing positive and negative returns.

The emphasis of the relationship between risk and return is reflected in the applied theoretical models.

These models are described below. As the research objective is based upon a practical exercise it

important to also include real-life methods and applications with regards to investment strategies.

Therefore, the methods and information provided by selected theoretical concepts applied is

supplemented by the input of two investment professionals. Their contribution to this thesis is described

subsequently to the applied theoretical approach.

1.3.2 Applied Theoretical Approach

Throughout the analysis the following theories will assist in performing active portfolio management.

The framework of the investment strategy will be established by the concepts of strategic and tactical

portfolio management. The investment opportunity set will be limited and the relevance of the

benchmark discussed.

In order to apply the mean-variance portfolio model, expected return estimates and risk measures for

each of the sector Indices suitable for the purpose of active portfolio management will be outlined. The

former will be calculated by use of the Capital Asset Pricing Model (CAPM) model. The advantage of

applying the CAPM model is that we can separate the market risk, beta and expected market return, of

each sector index, and in that manner compare risk and return of sectors and benchmark.


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Portfolio construction will be conducted by Markowitz’ mean-variance portfolio model as it optimizes

asset allocation in Excel based on performance ratios appropriate for the purpose of the investment

strategy6. Thus, optimizing with respect to the information ratio, which indicates relative benchmark

performance with regards to its residual risk, alpha, and residual return, beta, will lead to asset allocations

expected to provide the portfolio with a return superior to the benchmark. The asset allocation will be

conducted as a repetitive process.

1.3.3 Interviews

In order to limit the amount of assumptions made and to provide a practical point of view when

processing empirical data and applying theoretical models, interviews were conducted in order to uncover

relevant areas of study. Also, practical reviews were applied, as some exercised concepts of investment

theory carry universal definitions or conditions for execution.

Empirical and practical data have been obtained through interviews and consultation with two investment

professionals, who provided relevant information, relating to the research objective.

Peter Sjøntoft, Vice President, Global Banking, Citigroup Global Markets Limited, London United

Kingdom

Peter Sjøntoft has provided his personal viewpoints upon issues where elements of investment

theory seem difficult to apply in real-life investment strategies. Furthermore, he has provided

suggestions of where to challenge the application of these theories. He has assisted in adding

practical viewpoints in establishing the framework for active portfolio management, and

discussions regarding the use of investment strategies.

Claus Vorm, Senior Portfolio Manager, Nordea Investment Management, Copenhagen, Denmark

Claus Vorm has been responsible for establishing a team of investment specialists in charge of

managing Nordea’s tactical asset allocation, as well as the banks quantitative products.

Furthermore, he has been responsible for managing various balanced portfolios.

Claus Vorm has contributed with insights into the use of the strategic and tactical asset allocation

processes in Nordea’s investment strategies, which will be included when forming the investment

6 Benninga (2008): p. 338


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strategy for active portfolio management. His contribution also extends to views upon risk

management.

Peter Sjøntoft and Claus Vorm were chosen with the purpose of providing a nuanced representation of

opinions concerning investment decisions, as well as contributing with informational groundwork for the

research objective. Their experiences and information has enabled continuous tightening of the research

objective. The interview with Claus Vorm was recorded and stored on the CD attached. Due to geographic

differences, interviews with Peter Sjøntoft were conducted by phone, so no conversation was recorded,

and therefore no specific citations made. For interview guide, see Appendix 3.

1.4 Assumptions and limitations

In order to maintain a clear focus throughout the thesis it is necessary to define some assumptions and

limitations.

1.4.1 Assumptions

The theoretical discussion and the practical calculations with regards to the portfolio construction, will

take the point view of a Danish investor who has funds available for investments. In that regard

differences between investments by pension funds and private funds, including e.g. tax considerations and

consequences will not be discussed.

All calculations are conducted on the basis of monthly data, stated in US dollars from January 1992 to

December 2011. Data have been extracted from Datastream, MSCI Barra and Statistikbanken. Monthly

observations are opted for as opposed to e.g. daily observations as the former provides clear and

adequate information with regards to the development of the index prices and for sufficient data

management. The time period is considered appropriate as it provides a sufficient amount of data and it

covers significant economic events, affecting the financial markets.

With regards to the issue of transaction costs, we will assume that all transactions have equal expense

over the entire period. In addition, in order to limit the constraints to the mean-variance portfolio model,


13

the transaction costs will be deducted from the return on investment subsequent to portfolio

repositioning.

Finally, I will assume that markets are not completely efficient7. However, I will assume that the investor is

rational suggesting that he prefers more to less. Although market efficiency rests on the assumption that

investors are rational, its validity is not undermined by the investor not being rational, given he does not

trade randomly. In addition, all hedging of currency is completed by future contracts, meaning that only

index movement excluding currency behavior is considered. Moreover, the analysis will not incorporate

any tax effects. This is mainly because of the complexities of the Danish tax system. Furthermore, the

introduction of such a system is in conflict with the conditions of portfolio theory that leads to saying that

the investor should buy the market portfolio.

1.4.2 Limitations

1.4.2.1 Theoretical framework

In portfolio theory there are several models and applications appropriate for portfolio construction. Both

Markowitz (1952) and Black Litterman (1992) propose portfolio models applicable for portfolio

construction. The thesis will apply Markowitz’ mean-variance portfolio model, but argumentation and

justification for the choice of model will be provided. The model will be explained superficially, and

derivations will not be included when explaining the model, as I intend to present the model in the most

comprehensive manner possible.

Short sales will not be introduced throughout this thesis. The reason for this is that the mean-variance

model tends to incorporate extreme values in the asset positions when short sales are included providing

portfolios of poor applicability. Another reason is that major stock exchanges have unique short sales

regulations8. Furthermore, financial gearing is prohibited. Both assumptions contribute to portfolio

robustness, meaning altering investment positions are comparable with changes in return and covariance

estimates.

7 Shleifer (2000): p. 3

8 http://www.sec.gov/spotlight/keyregshoissues.htm

http://www.sec.gov/spotlight/keyregshoissues.htm


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1.4.1.2 Data

In order to construct a globally representative portfolio ten sector indices have been chosen, as they

represent a significant proportion of the world stock market. The indices are presented in chapter 1.5. The

MSCI Denmark and MSCI World Market indices are obtained from MSCI Barra9.

Before selecting the sector Indices I examined their historical returns, variances and covariance along with

the correlation and size of their market capitalization (see Appendix 2). The examination showed a

moderate pattern of a positive risk-return relationship among the sectors. Some of the sectors with the

highest risk-return payoff even had some of the lowest correlations towards other markets. The general

picture, however, showed high correlations among sectors leaving only a few inter-correlations below 0,5

suggesting high integration among sectors (only Technology showed correlation below 0,5). High market

integration is not an attractive property from perspective of investment theory as it constructs portfolios

based upon high return estimations and low covariance, hence low correlations. However, this scenario

highlights whether one major advantage in portfolio management, diversification, can provide the

portfolio with a higher risk adjusted return compared to the benchmark.

1.5 Data

In this chapter the definition and source of the equity sector return applied in the thesis are presented.

1.5.1 Equity Sector Return Data

There is a large industry of providing investors with benchmark data of sectors. They use Global Industry

Classification Standards (GICS) which operates with a ten sector classification (MSCI Barra, 2010): Energy,

Materials, Industrials, Consumer Discretionary, Consumer Staples, Healthcare, Financials, Information

Technology, Telecommunication Services, Utilities. These sector groups can again be classified into 24

industry groups, 68 industries, and 154 sub-industries10.

Equity return data in this thesis is obtained from Datastream and Morgan Stanley Capital International

(MSCI), since they offer data on world sector return covering the needed time periods. With regards to

9 http://www.msci.com/products/indices/country_and_regional/all_country/performance.html

10 MSCI Barra (2010): p. 82

http://www.msci.com/products/indices/country_and_regional/all_country/performance.html


15

Datastream, within each market, stocks are allocated to industrial sectors using the Industry Classification

Benchmark jointly created by FTSE and Dow Jones. The groups are formed from stocks registered on the

largest equity market in 53 countries and all sector Indices consist of 6 sub-indices. The data set divides

the market into 10 sector classifications (somewhat similar to the CICS): Basic Materials (BMATR),

Consumer Goods (CNSMG), Consumer Services (CNSMS), Financials (FINAN), Healthcare (HLTHC),

Industrials (INDUS), Oil & Gas (OILGS), Technology (TECHN), Telecommunications (TELCM) and Utilities

(UTILS)11. The basis for the selection of these sector Indices are based on a preference for global

representation, which is discussed further in chapter 2. Table 1.1 provides summary statistics of the ten

sector Indices along with the MSCI Denmark, based on monthly observations over the time period 1992-

2011.

Table 1.1: Summary Statistics – Monthly Return

Table 1.1 indicates that Oil & Gas and Technology has provided the highest average monthly return over

the period. Technology and Basic Materials have been the most volatile sectors with a standard deviation

11

Datastream (2008): p. 3

Mean Std.dev. Max. Min. Obs

Panel A. Sector Indices

Basic Materials 0,43% 6,22% 18,97% -19,65% 240

Consumer Goods 0,47% 4,63% 12,62% -19,11% 240

Consumer Services 0,35% 4,36% 10,54% -30,06% 240

Finance 0,21% 5,64% 17,85% -12,11% 240

Healthcare 0,48% 3,44% 8,95% -27,41% 240

Industrials 0,47% 5,45% 15,70% -26,09% 240

Oil & Gas 0,67% 5,66% 15,53% -31,10% 240

Technology 0,69% 7,58% 19,98% -17,25% 240

Telecommunications 0,33% 5,31% 16,18% -16,89% 240

Utilities 0,26% 3,84% 8,74% -29,67% 240

Panel B. Benchmark Index

MSCI Denmark 0,65% 5,92% 16,79% -29,67% 240

Panel C. Market Index

MSCI World 0,34% 4,47% 10,35% -21,13% 240

Summary Statistics

Source: Own creation, Datastream, MSCI Barra


16

above 7% and 6%, respectively. Note, that market and benchmark indices are two different indices. When

referring to the benchmark, it is the MSCI Denmark targeted for outperformance, while referring to the

market relates to the MSCI World index. The latter will only be applied for return calculations and

systematic risk estimations. From Appendix 4 all indices are concluded to be stationary indicating that

positive monthly returns are likely to be followed by negative return and vice versa, which in fact

complicates active portfolio management, as it makes the decision of market timing rather difficult. This

problem will be addressed with regards to portfolio construction in chapter 5.

Within the literature of stock returns there is no general convention regarding the use of simple and log-

returns. For example Campbell and Thomson (2008) use the simple mean approach while Benninga (2008)

argues log-returns, which is marginally more precise when modeling assets in Excel1213. Therefore, the

monthly return data is calculated as log-returns, and these returns are applied throughout this thesis. The

simple and log-return methods were tested on a few sector indices and only small differences were found.

Thus, we do not expect the conclusions to be significantly different if simple returns had been used

instead.

Equation 1.1 shows the total return of sector i held from time t-1 to time t. The total return constitutes the

dividends and capital gains. Di,t is the dividend from sector i received by the investor during period t.

Dividends for sector indices were incorporated in the return data upon extraction from Datastream.

)1.1(log1,

,,

,

ti

titi

tiP

DPR

The numerical difference between simple and log-returns are usually small for high frequency data. Both

concepts have their advantages and disadvantages in terms of portfolio and time aggregation. The reader

is referred to Tsay (2001) for more details14.

12

Campbell, Thomson (2008): p. 1517 13

Benninga (2008): p. 503 14

Tsay (2001): p. 3


17

The excess return is defined by the return in excess of the risk free asset.

)2.1(,,, tfti

e

ti RRR

Here, e

tiR , is the monthly excess return of investment i at time t, tiR , is the return of investment i at time t,

and tfR , is the monthly return of the risk free asset at time t.

Active return is defined by the excess return of an asset or portfolio in excess of the benchmark return at

time t.

)3.1(,,, tBtiti RRR

Here, tiR , is the active return and tBR , the benchmark return at time t. Substituting the right hand side of

equation 1.2 into 1.3 and subtracting the risk free rate from the benchmark return yields the following

calculation for active excess return:

tBti

e

t

tftBtfti

e

t

RRR

RRRRR

,,

,,,, )4.1(

From equation 1.4, active return is identical to active excess return.


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1. Investment Strategy

In order to frame the concept of active portfolio management a specified investment strategy is

required. Investors buy and sell stocks based upon individual incentives such as a desire for abnormal

investment returns or because they are constrained by consumption and liabilities. Hence, there is no

single approach defined to actively manage a portfolio as the allocation of assets differs depending

upon the investment objective. Thus, an investment strategy appropriate for answering the research

objective is called for. We will apply the concepts of strategic and tactical asset allocation, two debated

methodologies to portfolio management, in order to establish a framework for such strategy15.

2.1 Investment Strategy as the Source of Portfolio Performance

The accepted advice about spreading investments on several asset classes in order to minimize risk, and

not let emotions or gut feelings control the continuous portfolio allocation process, has become common

knowledge. Nevertheless, the opinions and expectations of the individual investor still dominates the

decision making process when they assemble portfolios16.

According to Peter Sjontoft, identifying an investor who has managed to outperform a benchmark is not

necessarily rare or difficult, when selecting among investors who base their investment decisions on gut

feelings, emotions or even randomly select stocks to invest in. On average, these investors may in fact

outperform a given benchmark, not because they are smart investors with extensive market insights, but

because the stocks they invest in simply happen to perform better than the market over the given

timeframe. Berk (2005) supports this statement, claiming that little evidence of performance persistence

exists – investors that perform well in one year are no more likely to perform as well next year17. One

possible explanation for this is that markets are, as in this case stationary, which opens the possibility for

investor lucky as they happen to buy stocks when markets are down and sell with a positive return. Such

scenario promotes the assumption that investor performance can be due to luck rather than skill and that

active portfolio management could be just as successful as random portfolio management – in an

15

Schneeweis et.al. (2010): p. 91 16

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Berk (2005): p. 30

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individual case, not on average. The investor who chose e.g. Novo Nordisk or Apple five years ago would

likely have outperformed most indices18. The question is really if someone who over-performed was lucky

or skilled, i.e. is his chances of repeating the performance next year higher than average? On that basis the

investor’s management skills is put into context as this constitutes the performance difference between

passive and active portfolio management. In that regard active portfolio return stem from the investment

strategy. The investment strategy constitute the process of asset allocation and security selection, as

these determine what to invest in at which point in time in order to generate positive active return.

2.2 Strategic Asset Allocation

Strategic asset allocation is a static approach to asset allocation where the portfolio assets are allocated

based on a long-term return estimate. Asset positions are retained throughout the period, meaning that

as asset returns change their portfolio weights change correspondingly, and the investor then rebalance

the portfolio by adjusting asset weights back to their initial positions19. Once the assets have been

selected for portfolio construction, no other asset will be introduced at any time.

Markowitz’ extensive work on the modern portfolio theory has yielded a dimension to the asset

management theory, i.e. diversification. This reward emerges when assets, which correlate negatively or

independently with each other, are assembled into a portfolio20. Strategic asset allocation sets forth long-

term allocations for assets possessing such characteristics.

The allocation process relies on the assumption that markets are efficient, which makes it impossible to

obtain abnormal return on investments, and therefore makes market timing irrelevant. On the contrary

active trading will increase transaction costs, which reduces the realized return more than expected. In

order to illustrate the argument against market timing, Ibbotson Associates made the following analysis21:

18

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Schneeweis (2010): p. 99 20

Markowitz (1959): p.102 21

Spar Invest (2007): p. 17

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Figure 2.1 indicates that an investors who invested 1 dollar in the S&P500 in 1926 index and then did

nothing, has achieved a remarkably higher return as opposed to the investor attempting to time the

market and therefore unfortunately has failed to invest during the 35 best months of the period. As a

result, attempting to time the market yielded a return on approximately the same level as T-bills.

Brinson et.al. (1986) conducted an empirical analysis which investigated the extent to which the

investment policy, the market timing and the selection of specific assets, affect the deviations in the total

portfolio return. Based on historic data from US pension funds they investigated which investment

decision had the greatest influence on the observed return and its volatility.

The first studies were conducted based on data from 1974-1983 and they concluded that a better return

could be achieved by solely focusing on a passive strategic asset allocation approach22. By passive is meant

retaining asset position by portfolio rebalancing. Their calculations showed that portfolio managers who

tried to time the market or buy specific stock achieved a lower return compared to the passive investment

strategy. These conclusions emphasize that asset classes with weights comparable to a benchmark

contribute with the largest proportion of the total return of the portfolio. In other words Brinson et.al

(1986) argues for buying a market portfolio, with fixed asset positions which in the long-term will

outperform any other portfolio combination.

22

Brinson et.al (1986): p. 136

2306,45

18,83 26,90

500

1000

1500

2000

2500

S&P500 T-bills S&P500 excl. the best 35 months

Figure 2.1 By how much has 1 dollar increased in value from 1926 to 2006?

Source: Own Creation, Sparinvest (2007)


21

In addition to providing a better return, 93,6% of the deviations of return can be explained by strategic

asset allocation23. Therefore, as regards to long-term investments, literature has proved that in terms of

returns, the best idea is to conduct portfolio investment, and not try to alter investment positions on a

periodic basis. In addition, resources committed to the investment decision should be concentrated

around the strategic decisions – the determination of the investment opportunity set - since the risk of the

investment can be observed here.

In order to substantiate these results, Brinson et.al. (1991) conducted a new analysis on behalf of US

pension funds during the period 1977-1987. They reached the same results as just discussed. For this

period 91,5% of the standard deviation of return could be explained from strategic asset allocation. Only

1,8% of the return deviations was explained by tactical asset allocation - the process of over- and

underweight portfolio sectors24.

Aside from explaining a majority of return deviations, the strategic approach to asset allocation

contributes to a better risk adjusted return in contrast to attempting to time the market. Such approach

offers investors the possibility of achieving a higher return at a lower risk. This is in accordance with

Markowitz (1952) portfolio theory, as he developed the efficient portfolio based on long-term historical

data.

2.2.1 Discussing Empirical Findings and Brinson et.al.

The findings supporting the strategic asset allocation as the prevailing investment strategy assumes

market efficiency, which makes it impossible to obtain abnormal returns, and thus makes market timing

irrelevant. However, to believe investors have the same information available and that the full use of this

information is reflected in asset prices is a naïve assumption. Empirical findings within the area of

behavioral finance have provided evidence that the assumption of a fully informed rational investor is

rather bold. Grossman and Stiglitz (1980) go even as far as stating that if markets were perfectly efficient

there would be no profit from gathering information, in which case there would be no reason to trade,

leading markets to eventually collapse25. In order to adopt a strategy for active portfolio management,

23

Brinson et.al (1986): p. 137 24

Brinson et.al. (1991): p. 45 25

Grossman and Stiglitz (1980): p. 393


22

trading is thus required and although markets are stationary, we can therefore not assume full efficiency

in the market, but refer to the adaptive market hypothesis instead.

Despite their conclusions, Brinson et al. (1986) have, however, received criticism for their analysis. Jahnke

(1997) criticized their use of the variance as risk measurement as opposed to the standard deviation26. If

the variance were to be replaced with the standard deviation, the strategic asset allocation would instead

explain 79% of the return deviations, which is not nearly as seminal as 93,6%.

In addition, the argument that risk of a passive investment strategy can be more easily identified is rather

obsolete. Only if assets expected returns are constant over time, should the asset weights remain

constant. The problem with such assumption is that stocks perform differently over different timeframes

due to their stages in business cycles and changes in macroeconomic developments. Hence, investors

assume changing risk premiums on stocks, leading expectations of asset prices, and as a result, their

portfolio weight to change. On this basis, investors should consider asset allocation as a dynamic process

which allows asset positions to change as their expected premiums change.

Among the critics towards Brinson et.al are also Statman (2000). He concludes that a portfolio manager

who consequently invests in the appropriate asset classes (stocks, bonds and holds cash as well) every

year between 1980 and 1997, achieves a return 8,1% per year in excess of passive strategic approach27. In

addition, 89,4% of the return deviations could be explained by the investment strategy, and the result is

therefore not far from the analysis of Brinson et.al. (1986). His point is that the investor should not only

focus on the strategic approach, but adopt a more active approach as well.

Regardless of whether the investor believes in the conclusions of Brinson et.al or joins the group of critics,

there is no doubt that the opted investment strategy has major influence upon the portfolio return

deviation. Strategic Asset allocation offers an attractive feature in the asset selection. It is fixed, which

means determining a fixed opportunity is supported by literature and carries practical advantage for

portfolio construction as we don’t have to dedicate resources to identifying new opportunities. With

regards to asset allocation we turn to the dynamic approach of tactical asset allocation.

26

Jahnke (1997): p. 2 27

Statman (2000): p. 19


23

2.3 Tactical Asset Allocation

Contrary to strategic asset allocation strategy, another practice within asset allocation assumes a more

active approach to asset management. In order to conduct a thorough investigation of whether active

investment management can outperform a benchmark, a different strategy is considered. The main points

of tactical asset allocation are outlined in the following.

Following a strategic asset allocation approach, changes in the portfolio will exclusively occur ex-post,

meaning that the investor will modify his portfolio as a reaction to events occurred, by rebalancing the

asset weight back to their initial target weights. The initial portfolio composition will therefore be altered

as a result of general market developments. In periods of negative returns for some assets the portfolio

must be rebalanced so the optimal proportion of assets is recreated.

However, asset allocation must be based on expectations of short term future returns in order to

continuously ensure positive active return. In 1971 William Fouse launched the first index fund28. His work

made it possible to control different asset classes simultaneously, and this technique has later been

known as tactical asset allocation. On that basis, compared to strategic asset allocation, tactical asset

allocation is on the other hand an ex-ante investment strategy where the investor proactively adjusts his

portfolio based on market historic developments and expectations29. Thus, the dynamic nature of tactical

asset allocation requires active adjustments to the investment opportunities in response to short-term

changes in the economic environment. Its objective is to adjust the allocation in order to take advantages

of temporary pockets of market inefficiency30.

Contrary to Strategic Asset Allocation the investor has not determined an optimal asset distribution, but

adjusts the portfolio in accordance with his expectations to the market development. Therefore, the

essence of tactical asset allocation is to proactively position portfolio assets based upon changes in

expected returns. Thus, assets with high expected returns are favored, as opposed to the remaining

opportunity set, and assets with low expected returns are less desired. The advantage of the tactical asset

28

Lee (2000): p. 12 29

Picerno (2010): p. 153 30

Schneeweis (2010): p. 101


24

allocation and the main source of its popularity is that it combines Graham and Dodd’s value investment

strategy together with Markowitz modern portfolio theory31.

The concept of value investing by Graham and Dodd has been an active investment strategy. Investors

seek undervalued stocks with low price-to-earnings ratios. On the other hand, Markowitz considers

investments within a determined timeframe, and hence only the market portfolio can be considered a

risky portfolio. Tactical asset allocation made it possible to combine these two strategies into one, which

enables the possibility of active management and thereby a superior return.

2.4 Professional Views upon Asset Allocation

As described above there is no doubt that strategic asset allocation constitutes a relevant investment

strategy and carries the advantage of a predetermined long-term investment universe. However, from the

viewpoint of the active investor, tactical asset allocation also seems a suitable investment strategy as it

proactively repositions the portfolio on a regular basis in accordance with the investor’s expectations. The

extent to which investors follow the strategic or tactical approach or even both when constructing optimal

portfolios remains unknown. The following will therefore include a review of Claus Vorm’s assessment

upon the process of asset allocation and highlight the way Nordea Investment Management applies

portfolio theory.

In relation to balanced portfolios, the initial asset allocation is based on long-term investment decisions

consistent with strategic asset allocation. The asset allocation process begins by considering levels of

equilibrium for interest rate structures, inflation rates etc. From these estimations Nordea attempts to

determine the long-term risk premium on each selected stock. The equilibrium expectations enables

expected return calculations over a strategic default period, which is within a business cycle of

approximately ten years.

Nordea then starts optimizing, by allocating funds into the stocks which are considered below long-term

equilibrium – undervalued stocks. On that basis it is reasonable to form a strategy that considers the state

of the economy compared to long-term equilibrium. Claus Vorm considers this a strategic analysis,

31

Value investment involves investing in stocks with low P/E ratio


25

valuable for creating highly diversified optimal portfolios based on estimated expected return and

covariance among assets. Obviously, as other portfolio models, this method carries pitfalls, but Claus

Vorm believes that the results of these models combined with the investor’s common sense can create

strong diversified portfolios.

On the other hand, Claus Vorm also believes advantages can be utilized in tactical asset allocation. Stocks

may be underpriced as considered in the strategic asset allocation, but they may have to be priced even

lower before returning to equilibrium, hence Nordea will have to purchase the stock e.g. two months

later.

The important conclusion here is that both strategic and tactical asset allocation will not necessarily have

to be present in the same investment strategy. We implement a long-term investment strategy with

changes in short-term portfolio positions, within the boundaries of predetermined risk parameters. This

approach can add value in terms allocating funds on a strategic long-term basis and reposition the

portfolio on a tactical basis. Hence, both the strategic and tactical approach is implemented in a balanced

portfolio, as the portfolio assets are repositioned on a regular basis. Claus Vorm suggests a useful strategy

would be to balance assets within determined boundaries, e.g. portfolio assets can be reweighted ±20% of

their initial portfolio weight each month.

Strategic and tactical asset allocation will both be implemented as part of the investment strategy, in

balanced capacities. Strategic asset allocation offers advantages in terms of limiting the investment

opportunities which combined can be submitted to periodic repositioning in accordance with tactical asset

allocation.

2.5 Benchmark and Investment Opportunities

The choice of benchmark is of significant importance, as its performance obviously plays a key role in

determining the success of the investment strategy. Additionally, the investment opportunities must be

given careful consideration as combining such should constitute a more attractive investment compared

to the benchmark.


26

2.5.1 Benchmark

Rationalizing the choice of benchmark, the Danish index has been considered a “Safe Haven” investment,

which it has proven by retained and even increased returns relative to other major indices in market

turbulences making it a high performing index difficult to outperform32 33. Thus, it remarkable

performance relative to other markets makes successful active portfolio management a challenging task.

Figure 2.2 illustrates its performance against other major national economies.

When applying a small index as benchmark such as the MSCI Denmark, the investor must consider the

case of corporate domestic market dominance in terms of market capitalization. In writing, Novo Nordisk,

constitutes almost half of the basis for the Danish OMXC20 index putting the applicability of MSCI

Denmark as a representative benchmark into question34. On the other hand, the same scenario is likely in

other small or midsize European markets, where few or a single company possesses major influence upon

index development, due to superior market capitalization.

It is evident that MSCI Denmark has performed well relatively to other countries, but for Denmark, high

returns have been followed by high losses, by example of the return development between 2006 and

32

http://borsen.dk/nyheder/investor/artikel/1/229201/udlandet_kaster_sig_over_c20-aktier.html 33

http://borsen.dk/nyheder/investor/artikel/1/221690/udenlandske_investorer_vaelter_ind_over_landets_graenser.html

34 http://borsen.dk/nyheder/investor/artikel/1/240054/novo_nordisks_dominans_mere_end_fordoblet.html

0

100

200

300

400

500

600

700

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

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20

11

Ind

ex

Figure 2.2 Selected Country Indices (92M1=100)

MSCI Denmark MSCI France MSCI GermanyMSCI UK MSCI USA MSCI World

Source: Own Creation, MSCI Barra

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2009. Thus, from its historical performance we can expect the index to carry high market risk – beta. Peter

Sjøntoft suggests that investing in high beta stocks is indeed one way to achieve high return, but as these

returns comes with high risk, investing in low beta stocks with low returns is not an unwise investment

decision. The MSCI Denmark appear as a difficult benchmark to outperform in terms of realized return,

but relatively low return on investments therefore constitute an equally successful investment strategy

with regards to adding portfolio value, given the condition that low returns are warranted by

correspondingly low market risk. From Claus Vorms comments with regards to portfolio construction,

value added stem from selecting stocks with different levels of systematic risk, thus different levels of

return, and based upon these input data construct portfolios carrying systematic risk at a level justified by

the realize a return. The stock selection is determined and limited by the investment opportunities.

2.5.2 Investment Opportunities

Active portfolio management commonly involves altering portfolio asset positions and compares the

portfolio performance to the overall market, such as S&P 500 or Dow Jones, which constitutes many

international corporations. Thus, the stocks included in the portfolio and benchmark are identical and

potential outperformance occurs by altering asset positions in the portfolio. As the Danish market is

relatively small in terms of capitalization, it represents few companies dominating their respective

industries and in some cases the entire market. To illustrate the point consider the correlation between

MSCI Denmark and four of the largest companies residing in the market.

Table 2.1 Correlation between MSCI Denmark and Four Underlying Stocks

The high level of correlation and market capitalization of these companies suggests that if changes in their

respective industries or even the market occur, such change is likely attributable to these stocks. Selecting

the underlying stock indices of the MSCI Denmark makes active portfolio management a difficult task

indeed, as diversification opportunities are narrow, and the investor might be tempted to select only few

stocks as those above, as their development have great influence on the benchmark development.

Broader investment opportunities for active portfolio management are therefore required.

A.P.Moller Maersk B Carlsberg B Danske Bank Novo Nordisk B

MSCI Denmark 0,89 0,83 0,79 0,85

Source: Own Creation, Datastream, MSCI Barra


28

2.5.2.1 Seeking International Opportunities

A variation of different assets will provide the investor with a variability of return in the portfolio and

reduces its risk. In order to achieve portfolio optimization the investor must allocate different asset classes

to the portfolio. According to Litterman (2003), to find independency among assets, and hence reduce the

risk of the portfolio, the investor must consider different markets35. In addition, Markowitz (1959) claims

that in order to achieve optimization at an international level, it is important to consider different types of

sectors and industries36. Hence, the most beneficial way to allocate assets is to invest globally. Portfolio

optimization traditionally requires independency among a diversified selection of assets, thus allocating

assets in different types of sectors and industries seems beneficial to achieve optimization.

When considering an investment in common stock, investors tend to divide the vast universe of stocks

into categories based on general business lines and by industry within these business lines. One way of

dividing this universe of stocks gives classifications for industrial firms, financial institutions and other

industry sectors. An alternative classification scheme separates US and foreign common stocks. I have

avoided the latter division, because the industry breakdown is more useful when constructing the

portfolio of global common stocks. When stocks are sorted by industries rather than geography they

constitute a more comprehensive illustration of company-level performance. It is easier to identify which

stocks are performing better than others as they not only react to global macroeconomic events, but also

individual sectorial events. Therefore, return patterns are assumed to develop somewhat differently,

which enables the identification of diversification opportunities. With a global capital market the focus

should include all the companies in an industry viewed in a global setting. Extensive market integration

advocates for this decision as it has diminished the importance of the geographic location of major

companies, while their sectorial location is better characterized.

2.5.2.2 The Rise of Sector Importance

Obviously, the asset allocation process refers to the decision process of determining the amount of funds

that should be allocated to each financial asset in the existing opportunity set. It is the investor’s objective

to obtain the highest risk adjusted return as possible. Our interpretation from Brinson et. al (1986) showed

that the asset allocation decision is by far the most dominant factor of portfolio performance as it explain

35

Litterman (2003): p. 137 36

Markowitz (1959): p. 89


29

more than 91% of the variation in asset returns. Furthermore, Litterman (2003) suggestions that asset

allocation can be divided into two different types of decisions 1) asset allocation between different asset

classes, e.g. stocks and bonds and 2) asset allocation within one asset class, e.g. countries and sectors.

Hopkins and Miller (2001) analyzed these dimensions of global equity portfolios (countries, sectors,

industries and companies). Their analysis concluded that a significant shift seemed to have occurred in the

importance of global sectors and industries at the expense of geography in global investment strategies37.

Although this emphasis is likely to shift through time the reward for global sector allocation, as well as

organizing stock selection on a sectorial basis, seems to justify allocating resources to sector research.

Their tests further suggested that an industry group orientation, rather than a broader sector-level

orientation can add value to asset allocation research. However, in order to maintain track of an

affordable amount of data in addition to a global representation among the investment opportunities,

further investigation of subgroups below the sectorial level will not be considered in this thesis.

Considering the advice of broad diversification from Claus Vorm, this thesis seeks to allocate assets into a

portfolio, which represents a broad global market portfolio, which is solid and easy to measure. Each asset

represents a sector index which embodies a range of industries. As introduced in chapter 1 the further

analysis considers the Datastream World Indices with ten sub-indices, which have been chosen to

represent ten major industry sectors as introduced in chapter 1.5.

2.5.2.3 Market Integration

Only a few decades ago some national markets were considered difficult to gain access to, limiting

investment opportunities to only domestic markets. As globalization has integrated national economies,

companies, consumers and investors now trade across borders, which results in increasing correlation

between markets. Hence, systematic risk arises as economic development in some countries impact that

of others, which to some extend align their return patterns, as they are affected by the same

developments. However, based on historical performance MSCI Denmark stands out as having performed

remarkably better than other major indices. In terms of benchmark comparison, both advantages and

disadvantages for applying the MSCI Denmark as benchmark exist. Table 2.2 shows the correlation

between each sector index, Denmark and four major national economies.

37

Hopkins and Miller (2001): p. 1


30

Table 2.2: Sector Correlation towards Countries

Although the MSCI Denmark does in fact possess the lowest correlation towards all sector indices (with

the exception of MSCI World), correlations are very high, with no correlation below 0,50. Other countries

are likely to have more companies represented in each sector index leading them to follow a more similar

development as these countries, hence their higher correlation. Thus, the development between Denmark

and the sector indices is somewhat less dependent. The relatively low correlated behavior between the

benchmark and sectors provides better opportunities for portfolio diversification with the purpose of

outperforming the MSCI Denmark (as opposed to other national markets) with reliable estimates of

return. On the other hand, high correlation among sectors may result in sectors being selected for

portfolio investment based upon their return estimations as high market integration leads to high

covariance, and hence high correlations between sectors as indicated in Appendix 2.

2.6 Crafting the Investment Strategy

Considering the advantages of strategic and tactical asset allocation in addition to Claus Vorm’s views

upon active portfolio management, the investment strategy constitutes a combination of both allocation

methods with regards to the investment opportunities. The process of actively managing the portfolio is a

short-term procedure comparable to the tactical asset allocation, but given the extensive empirical

findings of Brinson et.al (1986, 1991) long-term perspectives of strategic asset allocation is included. Thus,

the investment opportunities is limited in the long-term but traded in the short-term, and allocated to the

MSCI Denmark MSCI France MSCI Germany MSCI UK MSCI USA MSCI World

Basic Materials 0,71 0,75 0,73 0,80 0,70 0,13

Consumer Goods 0,66 0,75 0,75 0,76 0,77 0,04

Consumer Services 0,71 0,82 0,81 0,80 0,88 0,12

Finance 0,72 0,81 0,78 0,83 0,83 0,13

Healthcare 0,54 0,64 0,59 0,67 0,72 0,12

Industrials 0,75 0,83 0,82 0,81 0,85 0,14

Oil & Gas 0,67 0,68 0,63 0,77 0,65 0,08

Technology 0,57 0,67 0,69 0,62 0,82 0,12

Telecommunications 0,60 0,72 0,71 0,69 0,76 0,16

Utilities 0,68 0,72 0,67 0,75 0,64 0,15



31

portfolio based upon their expected return and covariance with the other sectors. Figure 2.1 composes

the applied elements of the investment strategy.

By implementing strategic and tactical asset allocation to define different stages of the asset allocation

process, asset allocation is considered an iterative process with a long-term perspective, since a

continuous monitoring of the portfolio characteristics is essential. Figure 2.3 provides an illustration of this

strategy. Note, that the iterative nature of the asset allocation process implies active portfolio

management.

Figure 2.3: Investment Strategy


Figure 2.1 illustrates the four steps of the investment strategy, each introduced in different stages of the

process and thus, is of different lengths. It starts with strategic asset allocation. It is considered the most

Active Portfolio Management Process

Strategic Asset Allocation

Investment Objective: Active Portfolio Management

Investment Opportunities: 10 Global Sector Indices

Benchmark: MSCI Denmark

Tactical Asset Allocation

Modeling Investment Opportunities: Expected Return Estimation

Risk Tolerance and Measure: Tracking Error

Implement Strategy: Portfolio Construction and Repositioning

Strategy Evaluation

Analysis of Realized Return

Benchmark Comparison


32

important part of the success of the investment strategy. It defined the investment objective and the

investment opportunity set. Thus, strategic asset allocation is based on a long-term focus. Therefore, this

part of the strategy has a much lower frequency in terms of asset allocation.

The next step is the modeling of the investment opportunities. For frequent portfolio construction if the

investment opportunities do not comply with the investment objective, i.e. if they are expected to deliver

negative active return, they are excluded from the portfolio at that given time. In that manner, the new

information about the involvement of the prices of the different sectors compared to the benchmark is

incorporated in the optimization problem, i.e. the model parameters are updated and portfolio

repositioning is conducted under the constraints of the investors risk tolerance in addition to the absence

of short sale and financial gearing.

The final step involves the evaluation of the portfolio positions and analysis of its performance in

comparison to the benchmark. No alterations are made from this point as the mean-variance model

ensures no violation of the investment constraints and the portfolio construction is conducted with no

regards to the transaction costs, as they are deducted from the realized portfolio return.


33

2. Active Portfolio Management

In the context of this thesis, active portfolio management involves the dynamic nature of tactical asset

allocation which alters portfolio sector index positions of the investment universe in order to provide a

positive active return compared to benchmark investment. This chapter will provide a formal definition

of the concept and identify performance measurement, which serves the purpose of determining

whether active portfolio management has outperformed the benchmark.

3.1 Defining Active Portfolio Management

Active portfolio management means allocation of funds based on expectations of future market

developments. The strategy is performed against the MSCI Denmark as benchmark. This chapter

introduces the main concept of active portfolio management and its instruments. We begin with the

definition of active portfolio management:

Active portfolio management is the implementation of a dynamic investment strategy that over- and

underweights the predefined investment opportunities over a long-term basis, with the single objective of

outperforming the predefined benchmark at a predefined time in order to add value to the portfolio.

From this definition the importance of the benchmark for active portfolio management is evident. In

terms of risk and performance measures, the use of benchmarks is important in order to obtain clear

measurements in accordance with the investment strategy. In order to evaluate the performance of the

investment strategy we will establish appropriate performance measures which aim at capturing the

systematic risk adjusted return of the portfolio in comparison to that of the benchmark – the residual

return – and measure whether it in fact adds value to the investor.


34

3.2 Performance Measure and Portfolio Added Value

Several performance measures for portfolio evaluation exist, such as the Sharpe Ratio and Jensen’s Alpha,

and they are selected based on the purpose of portfolio management38. As portfolio performance in this

thesis must be considered relative to the benchmark a relative rather than an absolute performance

measure is required. Thus, we will employ a performance measure that captures the expected excess

return of the portfolio in comparison to the benchmark – the active return. The information ratio provides

such estimation39.

3.2.1 Information Ratio

We denote the active return as the difference between the portfolio returns and the benchmark return,

which is illustrated in the nominator of equation 3.1. The mean of the residual returns is usually called

alpha, and standard deviation the tracking error. The quotient of alpha divided by the tracking error is

called the information ratio:

)1.3()(

BP

BP

S

RRrationInformatio

Where RP is the portfolio return, RB is the benchmark return, thus the numerator is the portfolio active

return. SP-B is the tracking error, or the standard deviation of the residual return, measured as the squared

difference between portfolio and benchmark return. Estimates for each three components are provided in

chapter 4. According to Stotz (2005) with regards to the information ratio, the investment strategy

ultimately seeks to either maximize the expected return of the active portfolio or minimizing the tracking

error40. Since the portfolio is compared to the benchmark, active return determines the comparative

capital gains, while the tracking error indicates how well the portfolio tracks the benchmark. In other

words, active return determines whether the portfolio has outperformed the benchmark and the tracking

error determines whether the information ratio is significant.

38

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Stoltz (2005): p. 264

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35

3.2.2 Portfolio Value Added

Obviously, successful execution of the investment strategy involves over- and underweighting of the

investment opportunities expected to perform well and poorly, respectively. The asset selecting approach

only identifies the forthcoming winners and losers. Correspondingly, as shot selling is not allowed, the

investor can allocate a proportion between 0% and 100% to a single asset. Hence, the amount of capital

allocated to each asset need not be sophisticated, as it could just as well be equally weighted. However, if

the mean of the active return of the portfolio is positive, the investor has actually beaten the benchmark,

and whether the outperformance is significant or not is reflected in the information ratio, which will be

investigated in chapter 6. Therefore, the information ratio should rather be seen as an indicator for the

manager’s skill than a performance measure.

I put the above statement in a more mathematical framework. Considering the information ratio in

equation 3.1 We let the return of the actively managed portfolio, tPR , , and the benchmark tBR , be defined

by the following models:

)2.3(10

1

,,,

n

i

tititP RR

)3.3(,,, titBtB RR

The investment universe consists of n=10 investment opportunities for the active portfolio and tiR ,

denotes the excess return of the i-th investment opportunity. ti , denotes the beta of asset i at time t,

and will be applied on a rolling basis rather than an overall average. Maintaining an average beta over the

period is misleading as the environments in which companies operate change, leading the market risk,

which they are exposed to change over time41. As the benchmark is treated as a single stock it only

consists of n=1 investment opportunity, and will therefore not be submitted to reweighting at any time.

Furthermore, I will impose one constraint:

10

1

, 1n

i

tip leaving the investor the opportunity to invest

in the optimal tangent portfolio or hold cash42. Given the relatively small size of the MSCI Denmark in

41

I will explain the basis for this application thoroughly in chapter 5 42

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terms of capitalization, it is neither broad nor representative and hence is not characterized as a market,

as it carries market risk, as well as the sector indices, relative to the global stock market. In addition, the

benchmark does not represent the investment opportunities, meaning they are not indices underlying the

MSCI Denmark, but in fact larger in terms of capitalization, and have developed somewhat

interdependently with regards to the benchmark. Nevertheless, the investor should still have the

opportunity to invest globally within the limits of the investment strategy and opportunity set in order to

provide opportunities for diversification. Hence, the benchmark beta does not represent a weighted

average of the sector’s beta.

We compare active beta and active return as two separate factors in order to measure value added.

Holding high beta investment should only add value to the investor if the return is correspondingly high an

vice versa.

)4.3(*,,

e

ttBtPt Ra

The mechanics of active portfolio management is seen from equation 3.4. It represents a cornerstone for

measuring value added, or residual return, and tracks any value added by active portfolio management.

For the case of a non-negative active return, e

tR ≥0, the exposure of the investor should at least be as big

as the exposure of the portfolio, tBtP ,, in order for active portfolio management to add value on

average. Accordingly, for the case e

tR ≤0, in order to obtain value added tBtP ,, so a positive alpha is

maintained. Thus, the beta adjustments to the excess active return tracks any value added from active

investing. Hence, if a positive alpha is maintained active investing has added value to the investment.

These equations show that security selection and market timing are the same, because in both cases the

investor controls tP, in order to add value to the portfolio.

The beta portfolio is constrained in order to limit the amount of risk the investor can take upon his

investments. Investing in high beta stocks is likely to generate high returns, but its risk deteriorates the

investment value for the investor as well. Pursuing high beta investments, such as the benchmark is a risky

way to generate high returns. Therefore, the crucial point for successful security selection and market


37

timing is the correct prediction of the active return, tR , hence estimates for expected return for the

portfolio and the benchmark.

Note from equation 3.3 that the correct prediction of security return is not the only source of alpha. It was

previously argued that the significance of the outperformance of an investment strategy is reflected by

the information ratio. By now we have shown that the information ratio can be increased by better

predictions of security prices, tR . Obviously, the information ratio may also be increased by variances in

residual return, provided that the mean residual return remains the same. Minimizing the residual risk

hence, becomes important as well for maximizing the information ratio.

Treynor and Black (1973), describes systematic active portfolio management approach, coupling the

identification of alpha, and risk management43. Traditional portfolio theory does not distinguish between

active portfolio management and optimal portfolio construction. This thesis will not attempt to fill this

gap, meaning portfolio construction is conducted with the sole purpose of outperforming the benchmark

on a risk adjusted basis. Whether, a deviation from the investment strategy could in some way have

provided the investor with higher residual return than realized remains hypothetical and will not be

investigated. However, what all active portfolio strategies have in common is that outperformance has to

be gained through altering investment positions, which is emphasized in the definition above.

This chapter provided a review of the framework of active portfolio management. The important

takeaway for the pending analysis is the need for expected return estimations and measures for risk. We

will then have the necessary input to conduct portfolio construction.

43

Treynor, Black (1973): p. 69


38

4. Risk and Return in Active Portfolio Management

In accordance with the information ratio as the performance measurement of active portfolio

management, emphasis is required on active risk and return. This chapter establishes valid estimates for

expected return and risk measures appropriate for portfolio construction. The investment strategy

requires estimates every time the portfolio is to be reweighted. An exposition of the capital Asset

Pricing Model (CAPM) will provide such estimates. Furthermore, we investigate the risk factors the

investment is exposed to in order to determine risk warranting the return.

4.1 Expected Return in Active Portfolio Management

Based on the assumptions of Markowitz portfolio theory Sharpe (1964), have derived the Capital Asset

Pricing Model (CAPM)44. The importance and relevance to this thesis of the CAPM model is derived from

its terminology, i.e. its use of the Greek letters ɑ and β, which is widely used in the context of portfolio

management today.

The CAPM seems to be an attractive approach to the active portfolio management. It has, however,

received extensive criticism, particularly from Farma and French (2004), arguing against its empirical

foundation implying that most implications of the model are invalid45. Nevertheless, I will in this chapter

set up the CAPM model.

4.1.1 Asset Pricing in an Active Setting

The CAPM model plays an important role when selecting portfolios according to mean-variance

optimization. When using the CAPM forecasts of expected return to construct optimal mean-variance

portfolios, those portfolios will consist simply of positions in the market and the risk free asset. In other

words, optimal portfolios constructed under mean-variance optimization will differ from the market

portfolio and cash if the forecasted excess return differ from the CAPM excess return. As we adopt tactical

asset allocation I add components to the asset pricing model. Thus, the expected return, in this thesis is

built on five factors: the risk free interest rate, the sector specific risk adjustment, the market risk

44

Sharpe (1964): p. 436 45

Farma (2004): p. 26


39

premium, a premium for exceptional market return, and an expected residual return. Note, the residual

return is, ai, is a constant.

From these four factors the CAPM in active portfolio management takes the following form:

)1.4(R* ,,

e

tM,,,,,, tititftMtitfti aRRRRE

Here, E(Ri,t) is the expected return of asset i. Rf is the risk free rate, βi,t is the systematic risk of sector i, RM

is the market return. Exceptional market return, ti,

e

tB,R and the expected residual return, ai,t extend

the traditional CAPM model for the investment opportunities only. As the purpose of active portfolio

management is to obtain the highest portfolio residual return possible, the portfolio should not only be

maximized with regards to its own standard deviation, but also with regards to the risk adjusted return of

the benchmark, in order to improve the information ratio. Therefore premiums for selecting the

investment opportunities over the market and benchmark are warranted.

4.1.1.1 The Risk Free Interest Rate

To estimate the risk free rate, Rf, I consider two Danish government default-free bonds. Obviously, no

bonds are default free. However, the selection of the Danish default- free bond is based upon the obvious

reason that the investor is assumed to be Danish and since these bonds are considered safe investments46.

The 10 year government default-free bond rate is commonly used, particularly in valuations as the

maturity of the bond, the market and the forecasting period will be close to each other. Figure 4.1

illustrates the 5 year Danish government bond rate against the 10 year Danish default-free bond rate.

46 http://www.jyskebank.dk/wps/portal/jfo/finansnyt/struktureredeprodukter/danmark2015

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The 10 year default free rate has a lower standard deviation than the 5 year default free rate. Thus, if we

were to use the 5-year default free rate, we would experience marginally larger deviations in the expected

return estimates, than by using the 10-year default free rate.

4.1.1.2 Systematic Risk

According to the CAPM the expected return of an asset is driven by its systematic risk, βi, which indicates

how much on average the stock return change for each additional 1% change in the market return. Beta is

calculated as the covariance between asset and market return divided by the variance of market return as

follows:

)2.4()var(

),cov(

M

Mi

ir

rr

It is important to consider the beta of the benchmark as well. As the Danish index is relatively small on a

global scale it is exposed to systematic risk as well and as beta is a main driver of the expected return

estimation we cannot presume a constant benchmark beta. Therefore, we consider the systematic risk of

both sector indices and benchmark with respect to MSCI World Index.

Estimating beta on a rolling basis is a reasonable approach. Peter Sjøntoft explains that companies change

their strategy in accordance with the altering environment in which they operate. Therefore, the

0

2

4

6

8

10

12

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Pe

rce

nt

Figure 4.1 Danish Default Free Government Bonds - 5 vs. 10 years

Danish default free government bond rate - 5 years

Danish default free government bond rate - 10 yearsSource: Own Creation, Statistikbanken


41

corporate strategy of many international companies is by far not the same as it was ten or twenty years

ago. Thus, markets respond to these changes and their sources. Companies entering new markets conduct

mergers and acquisitions or are subject to sectorial bull or bear markets often takes upon them a varying

amount of risk, and given the long time frame, sectorial risk cannot be submitted to a single average risk

estimate. However, estimating beta on a sectorial basis makes it less sensitive to the market risk of the

underlying companies. Closing this discussion on beta we continue by measuring beta as a rolling

estimation of each investment opportunity. Rolling estimates are obtained by calculating each beta based

on 1 year monthly returns. Figure 4.2 illustrates the rolling beta estimates based on 12 months rolling

average.

Sector betas converged in 2008 and had before that with exceptions such as Technology, trended towards

common beta averages between 0 and 247, which is also illustrated in figure 4.3. The R-square values are,

however quite low, as they indicate beta values fluctuating substantially around average. Initially, such

result seems disappointing, as systematic risk appear to be difficult to control.

47

Koller et. al. (2010): p. 246

-2-10123456789

10

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Be

ta

Figure 4.2 Rolling Beta Estimates

Basic Materials Consumer Goods Consumer Services Finance

Healthcare Industrials Oil & Gas Technology

Telecommunications Utilities MSCI Denmark MSCI World



42

There is a trade-off, however, as volatile beta estimates improves the opportunities of tactical asset

allocation. Portfolio repositioning is conducted frequently based on the expectation that return on

investment opportunities will change between repositioning. This is a reasonable assumption, as sector

returns are stationary, meaning returns fluctuate around their long-term average return. In order to

change return estimations, beta must change correspondingly. Therefore, in order to provide the investor

with incentive to reposition the portfolio, we allow for fluctuating sector beta, hence expected return

changes between months.

4.1.1.3 Market Risk Premium

Two methods are applicable for estimating market risk premium: ex-ante and ex-post. The ex-post

method calculates the historic market return and then subtracts the risk free interest rate. Applying the

ex-post method presents two complications. First, even though this thesis investigates a historical

development, historical data alone is not a reliable indicator of future market expectations. Second, the

market risk premium depends on the periodic time frame which can expose the method to selection bias.

The second method is calculating the risk premium ex-ante.

The country default spread is measured as the relative equity market volatility for the benchmark. We

obtain this measurement by dividing the standard deviation of the benchmark equity market by the

standard deviation of the 10 year Danish default free government bond rate. This ratio is then multiplied

0,35

0,09 0,08 0,08 0,040,30 0,25

0,00 0,00 0,09

0,35

0,00

0,40

0,80

1,20

1,60

2,00

Figure 4.3 Average Beta and R-Square for Each Sector as

Regressed on MSCI World

Beta R-squareSource: Own Creation, Datastream, MSCI Barra


43

by the long term risk premium of the US equity market, in order to obtain an estimate comparable to

other major stable national Indices.

)3.4(*Pr,

premiumriskequityUSemiumRiskEquityMarketf

tB

Here, σM,t is the rolling standard deviation of the market – at time t and σf is the standard deviation of the

risk free rate. The US equity premium is estimated to be 5,5%48.

4.1.1.4 Exceptional Benchmark Premium

I have added the exceptional benchmark return to the CAPM model as a measure that takes into account

the deviation from the market and the benchmark. A premium is presented to the investor when the

market portfolio is expected to deliver higher return than the benchmark, meaning that investing in other

stocks than the benchmark delivers superior return. This premium is measured by the difference between

the excess return on the market and the consensus benchmark return, which is a long-run estimate, as

investors possesses only available market information must rely on historical performance. In other

words, the exceptional benchmark return measures the benchmark timing, and as the issue of timing

refers to the tactical asset allocation, this estimate will be considered on a short term basis, meaning

estimates will change between months. Thus the exceptional benchmark return is estimated as follows:

)4.4()( ,,,, titftMti

e

B RRR

Here, tftM RR ,, is the monthly risk premium calculated above and ti , is the consensus expected excess

return of the benchmark. The latter is a 19 years rolling historical average, as consensus of benchmark

performance among investors represents the current presumption (at time t) of benchmark return.

4.1.1.5 Selection Premium

We conducted stock selection as an ex-ante investment decision as the opportunity set was limited to ten

sector indices with no possibility of substituting indices. Thus a premium for taking such risk is warranted

and determined by the ex-port performance of each sector relative to the benchmark measured by

regression. Thus, it represents the reward for selecting each index into the investment opportunity set. Its

48

Fernández et.al. (2011), p. 3


44

value will therefore be applied as a constant for every time t in the period. The premium will be

determined by a simple one-factor regression model based on the traditional CAPM. The applied

regression model is the following:

)5.4()( tfBiii eRRaRE

iRE and )( fB RR represents the expected return of sector i and the benchmark risk premium,

respectively. A regression of the historical sector return against the benchmark from 1992 to 2011 yields a

constant, ia , which represents the intercept of the regression line. In other words, it represents the

expected return of sector i when the risk adjusted benchmark return is zero, which is the expected long-

term active return. Table 4.1 shows relevant summary statistics of the residual return.

Table 4.1: Summary Statistics for Residual Return Regression

Results are slightly different among sectors. With the exception of Basic Materials, Finance, and Utilities,

all sectors show positive active return. However, no sector shows significant residual return on a 95%

confidence level, as all p-value of all sector indices are above 5%. This means, theoretically the investor

can expect to gain a reward for selecting seven of the ten sector indices, which is however not large

enough for the investor to increase expectations for the return estimations. Expected active returns

indicate that none of the investment opportunities will be able to outperform the benchmark individually.

For more details of active returns, see Appendix 4.

BMATR CNSMG CNSMS FINAN HLTHC INDUS OILGS TECHN TELCM UTILS

Active Return Premium -0,0005 0,0014 0,000 -0,002 0,003 0,000 0,003 0,002 0,000 0,000

t-score -0,18 0,60 0,09 -0,90 1,48 0,12 0,95 0,55 -0,04 -0,14

P-value 0,86 0,55 0,93 0,37 0,14 0,90 0,34 0,58 0,96 0,89

Source: Own Creation, Datastream, MSCI Barra, SAS Enterprise Guide


45

From figure 4.4 exceptional benchmark return has been the least stable of the three. For example, around

the period of the dot.com bubble in late 2000 and the financial crisis in late 2008 and 2009 the investors

experienced increasing returns relative to consensus. The important takeaway here is that the applied

procedure of calculating risk premium includes current expectations about future return, which is very

beneficial from the investor’s point of view, as it enables dynamic asset allocation which is not constrained

by historic performance. This also explains why the association between exceptional benchmark return

and the risk free rate is somewhat clear, but deviates substantially during the periods of the dot.com

bubble and the financial crisis.

Concluding the analysis of estimating expected return we review the relationships estimates for expected

return. Figure 4.4 graphs the historic development of these estimates.

0,00%

0,20%

0,40%

0,60%

0,80%

1,00%

1,20%

1,40%

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Pre

miu

m

Figure 4.4 Estimated Premuims

Government Bond Rate Market Risk Premium

Exceptional Benchmark Premuim

Source: Own Creation, Datastream MSCI Barra, Statistikbanken


46

As a result of rolling beta estimates and risk premiums, from figure 4.5 we see how expected returns are

by no means stable. This is particularly evident by the dot.com-bubble which saw Technology stocks boom

to extraordinary high levels of return. In addition, other investment opportunities are expected to exhibit

correlation within an interval between approximately 1% and 4%. During the financial crisis from late 2008

most sectors plunged increasing their correlation, and from 2009 they converge back to higher return

levels, but maintained a strong pattern of inter-correlation, as a result of market systematic risk levels

becoming more integrated across industries. Expected residual return estimations between each

investment opportunity and the benchmark are illustrated in Appendix 5.

4.2 Risk Management

There are many cases where improper risk management has led investors to accumulate catastrophic

losses. These cases highlight the importance of proper risk management. The purpose of risk management

in this thesis is to identify and limit the type of risk the investor faces and set up risk measures in order to

manage risk in a manner that secures reliable estimates for significant value added. In order to grasp what

the concept of risk involves and how to measure it we will begin by considering investor utility as the first

description of risk followed by Claus Vorm’s views upon risk and risk management. On that basis we frame

-2%

0%

2%

4%

6%

8%

10%

12%1

99

3

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Exp

ect

ed

Re

turn

Figure 4.5 Expected Return Estimates

Basic Materials Consumer Goods Consumer Services Finance

Healthcare Industrials Oil & Gas Technology

Telecommunications Utilities MSCI Denmark



47

a definition of risk in order to limit the types of risk factors the portfolio is exposed to, ultimately leading

to identifying a measurement for the tracking error.

4.2.1 Investor Utility

The first systematic description of risk for financial problems is risk aversion, and I will now give a brief

description of how investor’s utility is treated. A variety of different perspectives upon risk resides among

investors and hence their levels of utility differ.

One of the major subjects of investigation is the relationship between risk and return. In contrast to usual

utility evaluation, where individuals choose between two positive goods, in this case I consider return as a

positive good while treating risk as a negative good as increase in the former increases the information

ratio while increases in the latter decreases it. However, risk and return often comes hand in hand. Theory

generalizes three different types of investors by their risk appetite: risk averse, risk seeking, and risk

loving. The difference between investor types is their demand for compensation for taking on new risk.

This rationale is commonly used in practice and is determined to be the general motive for the difference

in investor’s preference when choosing stocks over e.g. bonds.

On the basis of these considerations that the investor regards risk and return as being a negative and

positive good, respectively, diversification is required as a means for risk management. By spreading the

investment into several investment opportunities the investor should be able to claim a higher risk

adjusted return than any of the assets alone. Accordingly, diversification implies that the compensation

for having risk is increased. Thus, there is a positive relationship between portfolio sectors and their

associated return. Markowitz established the mean-variance approach in portfolio context on the basis of

this relationship. We will ensure diversification with regards to portfolio construction with the objective

for the investor to be compensated for any additional risk taken. We will therefore impose a constraint of

maximum 20% portfolio weight to each sector index upon portfolio reweighting (Portfolio construction

without such constraint will also be conducted). Chapter 5 will discuss the details of this constraint.

4.2.2 Professional Views upon Risk and Risk Management

Claus Vorm explained that a vast variety of risk exists, which the investor is exposed to and which

dependents upon the investment objective. Thus, he acknowledges that risk is based on a point of view, as


48

is it dependent upon investor perception and the investment mandate the manager is given (being the

investor himself or a professional manager). In that sense, proper risk management involves conducting

investments submitted the constraints and risk preference of the investor. Thus, realized risk is obviously

determined ex-ante and must not be higher than the risk permitted by the mandate.

Accordingly, in terms of measuring risk, measurements again depend upon the investor’s presumption of

risk. Claus Vorm explained the variations of investor’s preference. Whether risk is measured as tracking

error, beta or absolute risk is a question of investment objectives. In terms of active portfolio

management the investor chooses an exposure to stocks and allows for a pre-defined tracking error. In

order to control the tracking error, risk can also be controlled in an absolute sense, by setting specific

boundaries in terms of short fall or volatility. However, actively managed portfolios have proven to deliver

better performance with flexible investment mandates49, meaning providing the investor (or portfolio

manager) with no specific investment constraints with regards to choosing risky investments over less

risky investments. The long investment horizon allows for a flexible mandate as the investor has

substantial opportunities for compensate potential losses incurred by potential gains from investments.

4.2.3 Risk Management and Risk Factors

From the discussion above we conclude there is no universal definition of risk and neither is there any one

generally accepted definition of risk in specific environments. However, it is a common presumption

among investors to link risk with uncertainty. In addition the definition of risk must allow for reasonable

measurements. Therefore, for the purpose of active portfolio management we define risk as follows:

Risk is the exposure to some uncertain future events.

Only an event that has a dependency on the portfolio may influence its risk. In many cases of risk

management, probabilities of possible future events are estimated. We do not presume to know these

probabilities as the referred events may not even be known. We will therefore apply an ex-ante measure

for the tracking error with regards to portfolio optimization, and evaluates portfolio performance by

means of an ex-post measure. The focus in this chapter will be on the ex-post measure, and the ex-ante

tracking error will be highlighted with regards to portfolio optimization in chapter 5.

49

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We will refer to ex-post risk management from Claus Vorms statements above. He suggests that risk can

be limited to one or a few measurements, and in that regard we consider risk factors relevant to adding

portfolio value. Based on the fact that the investment universe is limited to stocks, we consider only the

risk within the area of investments. In order to model asset risk, for simplicity, we consider two risk factors

also included in value added:

Systematic risk

Active sector risk to the benchmark.

As a consequence of estimating the tracking error ex-post, the systematic risk is the only risk factor the

investor is able to control. Restricting the portfolio beta to 1, tP provides the option to move from a

portfolio that is fully invested in equities to one that incorporates a proportion of risk equivalent to

holding cash. In a declining market, for example, cash provides a safe haven helping the investor to ride

out a down turn while positioning the portfolio to take advantage of opportunities as they arise. In down

markets high proportions of cash level risk can help the investor to produce milder declines and lower

volatility than the benchmark. In a strong positive market the investor can revert to a more fully invested

portfolio, which will help keep pace and potentially outperform as the benchmark rises.

Estimating the tracking error ex-ante proscribes controlling realized portfolio return deviation from the

benchmark. However, as outlined in chapter 1 the investment opportunities and the benchmark have

shown quite high correlations, and we can therefore expect somewhat similar return development

between the investment opportunities. When returns between investment opportunities and the

benchmark appear to have deviated, the tracking error increases.

4.2.4 Financial Risk

The risk measure with regards to the risk factors and utility seeks to increase risk adjusted return by

diversification. However, we still need a tangible measurement relevant for the investor which

incorporates the risk factors, market risk and idiosyncratic benchmark risk, in order to conduct specific ex-

post estimation of the tracking error. Additionally, it is relevant to adopt a procedure for risk estimation

that reflects the active holding of the investment opportunities. As the portfolio is actively managed, the

investor seeks to acquire residual return and hence also takes active risk upon his investments.


50

One could argue that for the investment opportunity set, active risk is proportional to the capitalization of

each sector. Thus the market weight for e.g. Industrials may be 12% (see Appendix 2). Position limits of 6%

and 18% may be set with the idea that this is a 50% underweighting and 50% overweighting. So the active

exposure of Industrials is limited to ±6%. However, throughout the later investigations we will treat active

risk as being dependent upon active exposure, and not the holdings of each asset. So, while there may be

cost and liquidity reasons for emphasizing large stocks, we do not believe it to be true that an active

position in a large sector is less risky than an active position of the same amount in small sectors.

With respect to the considered risk factors, beta and idiosyncratic risk, we decompose the market risk and

the relative benchmark risk in estimating the tracking error for value added. This possibility is enabled as

the introduction of additional risk premium in our return estimations makes beta and realized returns are

somewhat uncorrelated. The applied estimate for the portfolio to track value added from benchmark

investing is stated in equation 4.6.

)6.4(**1

2

,,

2

,,

2

i

tBti

e

tB

e

tiiP RRw

Here, P is the portfolio tracking error, wi is the asset weight, e

tB

e

ti RR ,, is the residual excess return and

)( ,, tBti is the residual beta. The point of this estimation is to provide an estimate of the additional risk

the exposure of the sector Indices adds to the risk of benchmark investment. E.g. investing in the

benchmark yields zero active exposure (replace e

tiR , bye

tBR , ). Note, that investor risk aversion is not

incorporated into the tracking error, as active portfolio management will not be submitted to specific risk

preference, but rather a general framework of risk reduction, due to the basic consideration of risk being a

negative good.


51

5. Portfolio Construction Implementing the investment strategy involves portfolio construction and repositioning. This chapter

constitutes the final steps of active portfolio management which enables evaluation of portfolio

performance. The primary focus of portfolio construction concerns the process of determining the

amount of funds allocated to each investment opportunity and that process relies on the applied

portfolio model. The process of repositioning simply comprises the timing of when the model conducts

asset allocation as a repetitive exercise.

5.1 Objective of Portfolio Construction

The objective of portfolio construction is to combine the investment opportunities into portfolios which

provide the investor with positive active return compared to investing in one sector index alone. This is

essential in the context of every portfolio management strategy. Therefore, any sector index estimated to

provide such return at any point of portfolio reweighting should be given a correspondingly large portfolio

weight. Markowitz’ mean-variance portfolio model conducts portfolio composition on such basis. As the

model conducts asset distribution based upon maximization processes of performance measures, it fits

the purpose of active portfolio management, since the information ratio constitutes the performance

indicator of active portfolio management.

5.2 Choice of Portfolio Model

Markowitz (1952) derived mean-variance portfolio theory stating that rational investors should either

maximize expected return for a given level of risk or minimize risk for a given level of return. He

additionally emphasized the importance of the investor to observe the movements among the assets – the

covariance. By constructing a portfolio of assets the investor can generate higher expected return at the

same level of risk as the portfolio not considering the covariance of portfolio assets50. This framework

allows for comparing different portfolios on a risk-return basis, and indicates how to choose the fraction

invested in each asset of the portfolio, so each asset best suits the investor’s risk-return expectations.

50

Markowitz (1952): p. 80


52

The mean-variance portfolio model is selected based upon its compatibility with both strategic and tactical

allocation. The classical approach to modern portfolio theory was developed by Harry Markowitz with his

article “Portfolio Selection” in 195251. Subsequent to its development, the model has received criticism,

particularly from Black and Litterman (1992), who introduced the BL-model, with the intention to improve

the deficiencies of Markowitz model52. We apply Markowitz mean-variance model based upon two crucial

criteria.

First, the BL-model presumes to know the investors personal risk preference and conducts asset allocation

in accordance with the market capitalization of the investment opportunities 53. The investor’s risk

preference is considered in this thesis but not specified into a utility function, as the conclusions from

chapter 4 indicated only that diversification is preferred by the investor. In addition, we do not consider

the risk of active holdings dependent on the size of the stocks, but rather the size of the exposure of the

active holdings. Second, the BL-model assumes the investment opportunities of active portfolio

management are underlying indices of the benchmark and that investor utility depends on the active

position and of each portfolio asset54. This is simply not the case in this thesis, as the underlying stocks of

the benchmark and the investment opportunities are two different groups of stocks. The advantage of the

mean-variance model is by treating the benchmark as a single stock, the model conducts tactical asset

allocation based upon optimization of the information ratio by. In other words, based on the return and

covariance estimates, the mean variance model selects stocks from the investment opportunities, on the

basis on the expectation that these opportunities can outperform the benchmark.

5.3 Mean-Variance Application in an Active Setting

In extension to the above, first systematic treatment of the portfolio selection problem is attributed to

Markowitz (1952). It is a popular financial optimization model, although its deficiencies are widely

documented and lacks important properties which are encountered in real-world investment processes.

51

Markowitz (1952): p. 77 52

Litterman (2003): p.76 53

Benninga (2008): p. 357 54

Da Silva et.al. (2009): p. 3-4


53

5.3.1 The Model

With regards to the investors risk preference, chapter 4 yielded an important conclusion. The investor

wants to maximize return and minimize risk, and as a result, the investor prefers portfolio diversification.

The tangent portfolio accommodates this rational. It is derived from the theory of portfolio diversification

with the intention of selecting a set of investment assets that combined possess the highest risk adjusted

return. Having established the idea of the mean-variance portfolio, the model will be explained.

The investment opportunities available are easy to rank by considering the trade-off between residual

return versus residual risk. Thus, the relationship between risk and return again becomes a term relative

to the benchmark, and as the we have limited the risk exposure to βP,t ≤ 1, the tangent portfolio remains

the most preferred investment in active portfolio management. The tangent portfolio assumes that

returns are normally distributed and its association with risk can be defined as the standard deviation of

return and that the return of the portfolio is the weighted combination of assets55:

)1.5(*1

,,,

N

i

tititP RXR

Here, Xi,t represents the weight invested in sector i at time t, and Ri,t represents the return of sector i. The

model applies historical average return estimates given these are normally distributed. However, as there

is a tendency to conduct unreasonable asset allocation based upon such estimates we apply CAPM

estimates from chapter 4 instead. The risk of the portfolio is characterized by its active variance56:

)2.5(2 ,,,

2

,

2

,

2

,

2

,

2

tBijtjtitBjtjtBitiP XXXX

Here, σi-B,t and σj-B,t is the active standard deviation of stock i and j at time t, respectively, and σij-B,t is the

active covariance between stock i and j at t. In that sense the variance of the portfolio depends on the

variance of the investment opportunities and the covariance between each other and the benchmark. The

more negatively correlated the sectors, the more likely it is to find a combination of these sectors with low

risk. The objective of the tangent portfolio, in the active setting, is to maximize the active return and

minimize the tracking error. The information ratio illustrates this:

55

Elton et.al.(2011): p. 52 56

Inspiration from Elton et.al.(2011): p. 54


54

)3.5(errorTracking

returnBenchmarkreturnPortfolioRationnInformatio

In order to maximize residual return, we express the ex-ante information ratio from equation 5.1 and 5.2:

)4.5(2 ,,,

2

,

2

,

2

,

2

,

,,

tBijtjtitBjtjtBiti

tBtP

XXXX

RRRationInformatio

These are subject to the constraints of no short selling, no financial gearing57: 1iX and 0iX

The unknown factor in all three equations above is the portfolio weight, Xi, which each investment

opportunity should possess. Therefore, we find the derivative of this function with respect to all sector

weights in the portfolio. The tangent portfolio for the investment opportunity set is illustrated together

with the residual frontier and in figure 5.1. Recall that in the active setting the objective of active portfolio

management is to outperform the benchmark; hence the portfolio is optimized with regards to its tracking

error. Therefore, in the active setting we will determine the slope of the residual frontier by optimization

of the ex-ante information ratio. In that manner the mean-variance model will conduct tactical asset

allocation that provides the highest residual return possible.

57

Expected portfolio return was additionally constrained by βP≤1

0%

2%

4%

6%

8%

10%

0% 2% 4% 6% 8% 10%

Re

sid

ual

Re

turn

, Alp

ha

Tracking Error, Omega

Figure 5.1 Residual Frontier


B

IR=1


55

The residual frontier plots the expected residual return, alpha, against the residual risk, ωp, and it will

always be a straight line through the origin. Its slope is thus determined by the information ratio and

therefore shows the possible fund allocation which is expected to outperform the benchmark for a

rational investor. The form of a straight line is based upon the assumption that not all investors have equal

market expectations nor the same borrowing and lending rates. Thus, they have different presumptions of

risk and return, but can still hold an optimal portfolio, as the optimal portfolio is situated at any point on

the residual frontier. The investor will, however, hold a portfolio containing no systematic risk above

market level, hence the tangent portfolio, in order to obtain the highest residual return possible. Thus, if

the investor is in the point of the tangency portfolio, on the residual frontier, he has allocated his entire

investment in the portfolio, with βP,t=1. Through portfolio repositioning we maximize the information ratio

in order to keep the portfolio located on the steepest residual frontier possible.

The origin designated B, represents the benchmark portfolio. By definition the benchmark portfolio has no

residual return, in other words both alpha and omega are equal to zero. Obviously, the slope of the

residual frontier represents the performance of the active investor, as a higher information ratio

represents a higher residual return.

5.3.2 Model Short-Comings

Markowitz’ mean-variance model might seem reasonable from a theoretical point of view, as it is easy to

understand and clearly presents the important concepts of risk and return. However, Richard Michaud

(1989) discusses the practical problems in his article The Markowitz Optimization Enigma: Is ‘Optimized’

Optimal?. He claims that that the model often leads to irrelevant optimal portfolios and reviews a number

of disadvantages using the model, which likely appears with the applied data of this thesis, particularly

due to their high correlation. Two of the most important disadvantages are stated and addressed below58.

5.3.2.1 First Disadvantage: Investment Instability

We estimated expected return based on historic data in chapter 4. Regardless of estimation methods,

exact estimates of future returns, variances, or covariance are, however, subject to estimation errors, and

some would even argue they are impossible in the first place. Michaud and Black and Litterman (1992)

58

Michaud (1989): p. 35


56

support this claim, stating that the optimization process inherent in the model maximizes errors59. The

mean-variance model overweight assets with high expected return and negative correlation and

underweight those with low expected return and positive correlation60. These assets are according to

Michaud (1989), those that are most prone to be subject to estimation errors.

This argument appears to be somewhat contradictory. The reason for investors to estimate high return on

assets should be that they believe the asset will return well in the future. It then seems reasonable to

appreciate that the model provides an overweight to these assets in the portfolio. The purpose of

repositioning the portfolio is based on the presumption that returns change over time and are therefore

constituted by the CAPM calculated on a monthly basis. Hence, the return estimate applied in the mean-

variance model for e.g. Technology are higher in mid-2002 before the bursting of the dot.com bubble than

in mid-2008 during the financial crisis. Return estimates during the course of dynamic asset allocation thus

change, but investment opportunities display high covariance suggesting they follow similar return

patterns. The mean-variance model will then have difficulties in selecting investment opportunities that

trend differently. Hence, it is more likely to select to select investment opportunities based on return

estimates. These estimates change between months, and so is their portfolio position likely to as well. One

advantage and disadvantage follows. If one investment opportunity possess substantially higher expected

active return than other, the model is likely to provide substantial portfolio weight to that sector, which it

maintains until portfolio reweighting is initiated again. On the other hand, if that sector is indeed the only

investment opportunity expected to outperform the benchmark upon portfolio repositioning the model

should allocate a correspondingly large amount funds to that sector. The only problem with this scenario

is that if the model allocates all or most funds into a single or a few investment opportunities in the first

period the portfolio is likely to sustain losses in the next period as positive returns are likely to be followed

by negative returns as a result of return stationarity among investment opportunities. This issue however,

refers to market timing and should therefore be addressed accordingly.

5.3.2.2 Second Disadvantage: Concentration

A second disadvantage concerns the use of constraints to the portfolio. In order to place all investment

funds in the portfolio we imposed the constraints of no short sales and no financial gearing meaning

59

Black, Litterman (1992): p. 34 60

Michaud (1989): p. 36


57

investment positions of each sector spans between 0% and 100% of the portfolio. Unfortunately, when

using the mean-variance model to help optimize the critical allocation decision, the unreasonable nature

of the yielded result has proved dissatisfying. When no constraints are imposed, the model tends to ordain

large short and long positions in some sectors, and when constraints are imposed, the model often

prescribed corner solutions with zero weights in many sectors as well as large weights in assets with low

levels of capitalization that have high expected returns and low correlations towards other assets. Such

scenario also applies with the investment opportunities. Figure 5.2 and 5.3 illustrates an example of asset

allocation by the mean-variance model with and without constraints.

Figure 5.2 Short Sale Restricted Sector Allocation

Restricting minimum sector position to zero


When short sale and financial gearing are imposed, minimum sector positions are zero, but dynamic asset

allocation allocates all funds to Technology. The information ratio, 58,20%, on the left hand side of the

figure, is quite attractive, but the model demands high portfolio beta, 4,63, to produce positive residual

return. Restricting the portfolio beta to maximum 1,0 results in the following allocation.

Sector Position Covariance Vector Expected Return Beta Portfolio Expected Return 5,53%

Basic Materials 0,00 -5,16 0,01 0,39 Benchmark Expected Return 1,47%

Consumer Goods 0,00 -21,95 0,01 0,14

Consumer Services 0,00 -16,34 0,01 0,56 Expected Residual Return 4,06%

Finance 0,00 8,43 0,01 0,35 Tracking Error 6,98%

Healthcare 0,00 -18,55 0,01 -0,24 Information Ratio 58,20%

Industrials 0,00 24,87 0,02 1,24

Oil & Gas 0,00 2,89 0,02 0,80

Technology 1,00 13,64 0,06 4,63

Telecommunications 0,00 9,42 0,03 1,71

Utilities 0,00 5,72 0,01 -0,16

Sum 1,00 2,96 4,63

Denmark 1,47% 1,06


58

Figure 5.3 Short Sale and Beta Restricted Sector Allocation

Restricting minimum sector position to zero Restricting portfolio beta to maximum 1,0


Now the asset distribution is more diversified. The model selects sectors with both high and low beta

values, but favors low beta sectors as these are given the larger positions. Restricting beta decreases the

tracking error, and correspondingly the residual return, hence the information ratio, which is now much

lower than without the beta restriction. Although the portfolio undertakes less market risk (beta equals

1,00) than the benchmark (beta equal 1,06) and acquires expected positive residual return, the asset

allocation is not expected to add value to the portfolio as achieving positive active return by a negative

active beta, is considered an act of luck rather than skill.

Even with the restriction of the portfolio beta the portfolios are highly sensitive to errors in their input

data – expected return estimates, beta and covariance estimates. The mean-variance model provides

excessive weight to assets with large expected returns or low beta. A small change in expected return on



Consumer Goods 0,00 -21,95 0,01 0,14




Industrials 0,04 24,87 0,02 1,24

Oil & Gas 0,13 2,89 0,02 0,80

Technology 0,04 13,64 0,06 4,63


Utilities 0,31 5,72 0,01 -0,16

Sum 1,00 2,96 1,00

Denmark 1,47% 1,06


59

one asset might generate a radically different portfolio. According to Michaud this mainly depends on an

ill conditioned covariance matrix, which is exemplified in insufficient historic data61.

An easy but rather primitive approach to avoid portfolio corner solutions and guarantee diversification is

the implementation of the condition of a maximum portfolio sector position. This adjustment carries both

advantages and drawbacks. Assuming that sectors are likely to show realized return fluctuations over

short time periods, and depending on the frequency on portfolio repositioning, the investor may be

unfortunate to conduct reposition during a month where realized returns are low or negative while they

are extraordinary high in both prior and succeeding months. This sector will then accordingly be given zero

or low asset weight during months of high returns and thus bypasses profitable short-term investment

opportunities. This issue concerns market timing and in order to cope with it the investor needs to ensure

that he captures these extraordinary high returns with at least a proportion of his portfolio a limitation of

portfolio proportions is imposed, forcing the mean-variance model to conduct dynamic asset allocation to

a broader number of investment opportunities. However, by ensuring a limited proportion of each

investment opportunity also assumes a high risk as the months between the reweighting months might as

well yield low or negative realized returns. Figure 5.4 extends figure 5.2 and 5.3 by imposing the

restriction maximum 20% portfolio weight. Thus, running the mean-variance model in Excel two different

conditions for the portfolio were tested: a maximum 20% restricted portfolio and an unrestricted

portfolio. The performance of both portfolios is analyzed in the context of active portfolio management in

chapter 6.

61

Michaud (1989): p. 35


60

Figure 5.4 Maximum Asset Position Allocation

Restricting maximum sector position to 20%


The model does not manage to increase expected residual return from figure 5.3 but actually results in a

lower information ratio, given the restriction of beta is imposed. The issue of market timing determines

whether allocating few investment opportunities into the portfolio is a more attractive investment

strategy as opposed to ensuring diversification, as it determines the period of time the investor must hold

each portfolio, and the longer the time frame the more likely the rational investor is to hold the diversified

portfolio.

5.3.3 Portfolio Repositioning and Transaction Costs

In accordance with the investment strategy the investor conducts portfolio repositioning on the basis of

tactical asset allocation. This leads to regular portfolio repositioning in order to maintain a portfolio asset

distribution which provides a positive residual return. As described in chapter 2 the tactical asset

allocation is a proactive exercise, which allocates assets upon the basis future expectations. By a



Consumer Goods 0,00 -21,95 0,01 0,14




Industrials 0,16 24,87 0,02 1,24

Oil & Gas 0,20 2,89 0,02 0,80

Technology 0,06 13,64 0,06 4,63


Utilities 0,20 5,72 0,01 -0,16

Sum 1,00 2,96 1,00

Denmark 1,47% 1,06


61

continuous repositioning process, the investor will sell stocks expected to decrease and acquire stocks

expected to increase in value.

5.3.3.1 Portfolio Repositioning

In order to make the investigation of the research objective more applicable to reality we need to include

an important aspect that is indeed present for the active portfolio investor: transaction costs – the trading

costs associated with both buying and selling stocks during repositioning.

Transaction costs constitute one of the major arguments against active portfolio management, and hence

in order to prove whether if it is in fact possible for active portfolio management to outperform the

benchmark we consider transaction costs with regards to the portfolio repositioning.

In a practical setting there is always a tradeoff between repositioning the portfolio and transaction costs.

If the investor chooses to reposition often, the costs of trading will consume a significant part of the

return. In contrast, too little repositioning may cause the portfolio to deviate from the investor’s goal of

outperforming the benchmark.

We chose to reposition the portfolio every quarter from 1992-2012. The empirical findings of Sun (2006)

suggests high transaction costs for such procedure, and for that reason favors reweighting by dynamic

programming or no repositioning at all62. However, as all investment opportunities display stationary

return patterns, positive returns are likely to be followed by correspondingly high negative returns,

complicating an attempt to identify pockets of market inefficiency where the investor can conduct

portfolio positioning. Thus, the purpose of quarterly repositioning is to acquire a positive average active

return between reweighting. This issue regarding repositioning refers to the timing skill of the investor,

and thus, the next chapter will investigate whether quarterly repositioning does in fact produce superior

active return and whether such return is produced as an act of luck rather than investment skill.

The mean-variance model keeps the asset weights constant in between repositioning. This assumption

under the transaction costs setting is not valid because it causes the transaction costs to be extremely

high. The reason for this is that when one asset moves in one direction the portfolio weight of that asset

moves in the same direction. As a result the goal to keep sector weights constant between all quarters

62

Sun (2006): p. 12


62

means that the investor would most likely need to rebalance the portfolio every trading day. Moreover

assuming that the investor faces transaction costs of 0,15% per trade, the total transaction costs of the

model would amount to sums that would certainly not be in the best interest of the investor.

As a result of the above, we cannot assume that the asset weights are constant between quarters, but will

only be repositioned each quarter. The transaction costs associated with each repositioning is 0,15%. This

cost will be deducted from the portfolio realized return following portfolio repositioning.

In order to comprehend the repositioning approach, the following structure is established:

1) We collect the respective initial asset weights of January 1992 from the mean-variance model.

2) We then multiply these weights with the respective return obtained at the time and find how

much each sector and the portfolio has grown or decreased.

3) For all months except March, June, September and December, each sector weight is calculated by

the following formula:

)5.5()1(

)sec1(*sec1

t

tt

treturnportfolio

returntorweighttorweightSector

To illustrate an example: Suppose the mean-variance model distributed 50% portfolio weight to Financials

and 50% to Utilities in e.g. July. Assume that the realized return for this end-of-quarter-month was 10% for

Financials and 15% for Utilities. The portfolio return is then 12,5%.

The new sector weight for Financials in August is then:

)6.5(%1,51)125,01(

)15,01(*50,0,

weightFinancials

The same calculation for Utilities then yields 48,9%. Moreover, when we reach the three month

benchmark (March, June, September and December), the portfolios are repositioned in the end of the

third month with new portfolio positions including the three new observations. It is important to state

that in order to comply with the framework of tactical asset allocation portfolio repositioning will be

executed with no concern towards the portfolio distribution in the previous repositioning process. The


63

sector distribution may change completely between quarters depending on return and covariance

estimates.

5.4 Model Performance

The calculation of the tangent portfolio on the residual frontier is conducted by collecting the expected

return estimates of the investment opportunities. Realized returns are illustrated below.

Table 5.1 Realized Return and Mean-Variance Approach

The “VarCovar” function in Excel was applied in order to calculate the covariance matrix to obtain the

tangent portfolio by maximizing the information ratio with respect to the portfolio asset positions. This

procedure was conducted for January 1992 and every quarter over the period (81 optimizations were

conducted). The sector positions resulted from this procedure is illustrated in Appendix 6, and summary

statistics of both portfolio weights and returns are analyzed in the following.

5.4.1 Sector Distribution

Table 5.2 illustrates the average sector position in the portfolios.

Table 5.2: Average Sector Positions


0,43% 0,47% 0,35% 0,21% 0,48% 0,47% 0,67% 0,69% 0,33% 0,26%

0,00% 0,04% -0,07% -0,22% 0,05% 0,05% 0,25% 0,26% -0,09% -0,17%

6,22% 4,63% 4,36% 5,64% 3,44% 5,45% 5,66% 7,58% 5,31% 3,84%

0,02% 0,97% -1,66% -3,87% 1,58% 0,87% 4,36% 3,48% -1,74% -4,36%

Source: Own Creation, Datastream, MSCI Barra, Statistikbanken

Return

Excess Return

Standard deviation

Sharpe Ratio


4,73% 2,42% 0,72% 10,40% 15,66% 9,77% 14,53% 15,61% 10,25% 15,92%

16,97% 8,82% 4,64% 17,15% 22,81% 19,72% 18,69% 24,95% 17,29% 21,53%

4,12% 6,54% 8,84% 13,47% 11,37% 12,20% 10,07% 12,89% 10,63% 9,88%

7,71% 8,66% 8,64% 8,17% 9,15% 8,77% 8,89% 7,99% 9,28% 9,48%

Average Portfolio Weight

Std. Dev. Portfolio Weight

Source: Own Creation, MSCI Barra, Datastream, Appendix 6

Panel B. Restricted Portfolio

Average Portfolio Weight

Std.dev. Portfolio Weight

Panel A. Unrestricted Portfolio


64

Healthcare, Technology and Utilities are the most attractive investment opportunities for the unrestricted

portfolio, as the model has allocated most funds into these sectors. Given the average beta estimates in

figure 4.3 the model seems to favor a combination of high and low beta sectors in the unrestricted

portfolio, as Utilities and Technology possess the lowest and highest average beta, respectively.

Furthermore, a positive relationship between beta and realized return is evident from table 5.3, as Utilities

possess the lowest Sharpe Ratio and the Technology the second highest. Thus, imposing the restriction of

a portfolio beta, 1P , the model combines sectors with both high and low beta and realized return.

Such condition is unfortunately likely provide portfolio return inferior to the benchmark, but opportunities

to add significant value remain as the low return is compensated by low beta. The same condition is

evident with regards to Oil & Gas, which constitutes the second largest represented sector with the

second highest beta and the highest Sharpe Ratio. Note that Basic Materials, Consumer Goods, and

Consumer Services provide the lowest average portfolio positions for both portfolios. These sectors

possess only mediocre beta and expected return estimates, and due to high correlation among sectors, we

do not expect their covariance to be small enough to impact the asset distribution process.

High average asset allocation is a result of two possible scenarios. First, the portfolio model allocates

sectors consistently over the period with a high and stable portfolio proportion, resulting in a low asset

allocation spread. Second, the model conducts minimum asset allocation to a portfolio sector, and

occasionally provides solutions with a substantial overweight to the given sector, which results in a high

spread in asset allocation.

Figure 5.5 Average Sector Position

y = 0,831x - 0,0434R² = 0,8243

0%

5%

10%

15%

20%

0% 10% 20% 30%

Ave

rage

Se

cto

r P

osi

tio

n

Standard Deviation

Figure 5.5a Unrestricted Portfolio

Source: Own Creation, Appendix 7

y = 1,0824x + 0,0061R² = 0,046

0%

5%

10%

15%

20%

0,00% 2,00% 4,00% 6,00% 8,00% 10,00%

Ave

rage

Se

cto

r P

osi

tio

n

Standard Deviation

Figure 5.5b Unrestricted Portfolio



65

Figure 5.4 illustrates a positive relationship between average asset allocation and their standard deviation.

The unrestricted portfolio is, however, much more successful in explaining the variation of the

observations. In other words, the regression line for the unrestricted portfolio matches the data points by

83% versus 5% for the restricted portfolio. For the unrestricted portfolio, sectors with high average

weights have constituted portfolio corner solutions, as they carry standard deviations above their average

meaning the position in given periods for these sectors have fluctuated between very high and low values.

Healthcare, Technology and Utilities, possessing the highest average portfolio positions, have either

dominated the portfolio claiming very high portfolio weight (up to more than 90%, respectively) upon

their introduction in some periods or been excluded by the mean-variance model in others.

The distribution pattern is less visible for the restricted portfolio. Imposing a maximum portfolio weight

upon the sectors decreases the standard deviation, resulting in a steeper but much less representable

regression line in figure 5.5. Sector weights therefore fluctuate less in the restricted portfolio, and retains

average values at approximately the same level as the unrestricted portfolio, meaning their distributions

are obviously kept more stable over time as opposed to the unrestricted portfolio.

Note the difference in sector standard deviation. It is not surprisingly higher for the unrestricted portfolio

compared to the restricted portfolio. Any allocation restriction above zero limits the allocation spread,

meaning the lower the restriction of sector distribution the lower the standard deviation is likely to

become. Evidently an equally weighted portfolio would have a zero standard deviation of average

positions63.

Based on the existence of a positive relationship between average portfolio weights and their respective

standard deviation, corner solutions are indeed present in the unrestricted portfolio, which is in fact a

rather disappointing result, given the aim of applying the mean-variance was to secure high risk adjusted

return through diversification. However, tactical asset allocation is based upon expectations of future

return, and estimates showed that benchmark return estimates retained higher levels of return than many

of the investment opportunities. Since the mean-variance model optimizes with regards to which assets

are expected to outperform the benchmark, i.e. the information ratio, only few investment opportunities

might exist, leaving portfolios with only few assets expected to outperform the benchmark.

63

If each sector had a portfolio weight of 10% at all times standard deviations would be zero.


66

5.4.2 Portfolio Returns

The distributions from table 5.2 lead to the following performance of the two portfolios.

Table 5.3: Portfolio Performance

The Benchmark yields higher returns than both portfolios and the market. Both portfolios have yielded

higher return than the market, and since the 20% restriction has led the portfolio to conduct asset

allocation to a larger number of sectors, portfolio standard deviation is slightly lower, which does,

however, result in lower Sharpe Ratio. Thus, in terms of absolute performance, the unrestricted portfolio

has delivered marginally superior performance as opposed to the restricted portfolio. The next chapter

will investigate whether it has done so with regards to its residual return and in that regard evaluate the

portfolio strategy.

Portfolio Return Excess Return Standard Deviation Sharp Ratio

Panel A. Portfolio

Unrestricted Portfolio 0,37% -0,06% 4,94% -1,16%

Restricted Portfolio 0,34% -0,08% 4,66% -1,76%

Panel B. Benchmark and Market

MSCI Denmark 0,65% 0,22% 5,92% 3,69%

MSCI World 0,34% -0,09% 4,47% -1,96%

Source: Own Creation, Datastream, MSCI Barra, Appendix 6


67

6. Performance Evaluation of the Investment Strategy

This chapter analyzes the results of portfolio construction, and seeks to investigate three findings:

comparative absolute return between portfolios and benchmark, presence of investment skill and

finally the extent to which active portfolio management has added value. Chapter 5 concluded that

benchmark investing provided superior active return to the portfolios. However, a timing skill and value

added may still be present as the portfolios did in fact outperform the market index and carried

systematic risk restricted to market level, meaning active return needs be adjusted for systematic risk.

All results are analyzed and explained in terms of theoretical models and parameters.

6.1 Return-Based Performance Analysis

The focus of return based performance analysis rests on portfolio performance in terms of realized return.

Section 6.2 then investigates the presence of portfolio value added, by considering the relationship

between realized return and market risk.

6.1.1 Cross-Sectional Comparison

The simplest type of performance analysis is shown in table 6.1 which ranks the investors active portfolio

management by its total performance over the period. The table illustrates median performance, key

percentiles and the performance of the benchmark. These cross sectional comparisons provides an indication

for the range of performance numbers over the period.

Table 6.1: Monthly Return, 1992-2011

The table exhibits higher benchmark returns for all percentile levels except for the lower quartile and 5th

percentile. Thus, the Benchmark has provided higher positive levels of return but has also incurred greater

Percentile Unrestricted Portfolio Restricted Portfolio MSCI Denmark

95th 7,21% 7,27% 9,11%

Upper Quartile 3,48% 3,31% 4,19%

Median 0,71% 0,69% 1,36%

Lower Quartile -2,14% -2,12% -2,68%

5th -7,77% -8,75% -9,64%

Source: Own Creation, MSCI Barra, Datastream, Appendix 6


68

losses, meaning volatility has been higher providing higher uncertainty with regards to its performance.

The advantage of portfolio diversification comes into view as the spread between the 95th and 5th is higher

for the benchmark than the portfolios. The standard deviations from table 5.5 support this observation

(benchmark standard deviation was 5,9% and unrestricted and restricted portfolio standard deviation

were 4,9% and 4,6%, respectively).

Figure 6.1 considers the investment timeframe, and shows the impact of using cross sectional comparison.

We compare the two portfolios and the benchmark by their cumulative return. Such comparison is

conducted by calculating the percentage difference between portfolio and benchmark cumulative return:

ValueIndexBenchmark

ValueIndexBenchmarkValueIndexPortfolioComparisonturnCumulative

Re

Over the 20 year period the portfolios have accumulated a return of 41% and 42% inferior to the

benchmark, the unrestricted portfolio performing marginally better as previously concluded. The mean-

variance model provides portfolios performing almost equally well over long time frame (20 years). In

addition, had the investor limited the time horizon to 1999, 2001 or 2003 at least on portfolio would have

provided a positive cumulative active return. However, we must keep in mind that the beta restriction on

the portfolios prevents the investor from taking systematic risk above market level, limiting opportunities

-60%

-40%

-20%

0%

20%

40%

60%

Cu

mu

lati

ve R

etu

rn

Figure 6.1 Cumulative Return Comparison 1992-2011

Unrestricted Portfolio vs Benchmark Restricted Portfolio vs Benchmark



69

for realizing a superior return. Systematic risk has been lower, and returns are consequently lower as well

as the investment cannot refrain from selecting low beta investment opportunities. The active investment

evaluation will later investigate whether the superior return of the benchmark to the two portfolios is

warranted by its market risk.

From figure 6.1, similar cumulative return development between portfolios is in fact significant, since the

findings of chapter 5 indicated very different patterns of average sector allocation. As a result, identifying

investment opportunities showing different return patterns at a given time, and conducting asset

allocation accordingly, becomes a fairly redundant process. High covariance resides among investment

opportunities, which makes the ability to identify points in time where some stocks have proven to

perform better than others a difficult task. Such ability refers to skill on the part of the investment

strategy.

6.1.2 Market Timing

Benchmark and portfolio investment both provided positive active return to the world market index. This

subsection seeks to investigate whether such returns are generated as a result of investment skill. With

regards to the portfolios, the influence the quarterly portfolio reweighting, or market timing, have had on

realized portfolio return, meaning how successful the investment strategy has been.

6.1.2.1 Regression Analysis

To examine whether the portfolio return is a result of skill rather than luck we turn to the statistical tool,

Ordinary Least Square (OLS) method. The model below should provide a conclusion to whether

benchmark and portfolio investing can actually be considered a skill, appropriate for the investment

strategy.

)()(,0*)(*)( ttRMaxtRtR PMPMPP

We introduce the variable P to determine whether investment strategy possess any timing skill. The

model includes a down beta, P , and a beta in positive market returns P . If P is significantly positive,

we say there is evidence of a timing skill, meaning market exposure is significantly different in cases of

positive and negative market returns. The variable )(,0 tRMax M assumes the value zero or any positive


70

market return at time t. If P is positive and significant there is evidence that quarterly repositioning is a

timing skill, meaning market exposure is significantly different in up and down cases.

With regards to the error term, )(tP , the model’s quality and value depends heavily on the behavior of

the residuals. Consequently, we need to check whether the residuals behave as the OLS assumptions

required.

The error term at different time stages, must be uncorrelated, in order to maintain an unbiased variance

of the betas, ensuring the reliability of the t-tests, which measures parameter significance. Furthermore,

as the regression model contains more than one explanatory variable and these variables have a good

chance of being highly correlated a problem with multicollinerity arises, as we will not be able to separate

the effects of the individual variables64.

The models test hypothesis is stated below:

H0: 0)(,0 tRMax B : Portfolio performance is a result of investment skill

H1: 0)(,0 tRMax B : Portfolio performance is not a result of investment skill

Before testing the hypothesis, we test for autocorrelation in the regression model. Autocorrelation is a

representation of a degree of similarity between the time series, applied in the regression model, and a

lagged version of themselves over successive time intervals65. Testing the model for autocorrelation using

the Maximum Likelihood test with 4 lags, we find that neither portfolios show significant sign of

autocorrelation in the error term. As a result we can draw reliable conclusions from the t-statistics of

significance. We therefore bring to a close that the models do not contain a problem with regards to

autocorrelation, thus conclude that the OLS assumptions are fulfilled. The models results are described in

table 6.1

64

Multicollinearity is present if there is a linear relationship between the explanatory variables: )(,0, tRMax MP 65

Gujarati et.al (2009): p.413


71

Table 6.2: Regression Results

The timing coefficient does not provide evidence that either portfolio possesses a timing ability. It is

negative and significantly different from zero at a 95% confidence level in both regressions. From the t-

scores, both below ±1,96, we cannot consider the process of quarterly portfolio repositioning to be a

skilled investment strategy. Thus, market exposure of both portfolios is not statistically significant. The

mean-variance model has not utilized the opportunity to construct portfolios with systematic risk at

market level, 1, tP , and at the same time generate a significantly higher return. Thus, in statistical

terms, tactical portfolio investment under the condition of quarterly repositioning has not proven to be a

more skilled investment strategy compared to investing in the world market index.

In defense of quarterly portfolio repositioning, we cannot ignore that investment opportunities have

proven to be stationary. The implication that follows is that identifying points in time of market

inefficiency, at which to reposition the portfolios without superior information becomes a difficult

process. Whether the portfolios had provided different levels of return, had we changed the repositioning

process to e.g. every month, is therefore unknown. However, in such case, transaction costs would

certainly have been higher resulting in diminishing realized portfolio return.

6.2 Analysis of Value Added

The findings from Chapter 6.1 did yield one important conclusion: Active portfolio management by the

mean-variance model is not statistically an investment skill. This conclusion is substantiates this conclusion

and to evaluate the investment strategy, we will investigate whether value has been added to the

portfolio and if such value is significant by means of the information ratio.

t-score P-value

-2,13 0,03

-2,17 0,03


Hypothesis Conclusion

H0: Hypothesis not Rejected

H0: Hypothesis not Rejected

Unrestricted Portfolio

Restricted Portfolio

Parameter Value

-0,4775

-0,4580


72

The portfolios were optimized according to the information ratio in equation 5.4. This portfolio realizes a

return of RP,T in the subsequent quarter while the benchmark index yields a return of RB,T. We referred to

the difference between these two returns as the active return of the portfolios:

)1.6(,, tBtPt RRR

In order to measure whether the investment strategy has added value to the investor, we provided the

information ratio consisting of value added and the ex-ante tracking error for portfolio evaluation. As the

active portfolios were repositioned quarterly over a period of 20 years (240 months) they are evaluated on

an average monthly basis by the ex-post information ratio:

)2.6(

**

*

240

1

1

2

,,

2

,,

2

,,

2011

,,

i

tBti

e

tB

e

tii

e

tB

e

tP

Dect

tBtP

t

RRw

RR

R

If alpha, the numerator of equation 6.2, is significantly greater than zero, the active portfolio strategy has

added portfolio value compared to benchmark investment. Applying optimization from equation 3.3, the

active returns were adjusted for CAPM systematic risk in order to investigate the presence of portfolio

added value.

Figure 6.2 Information Ratio

The development of the information ratio reflects the conclusion that timing skill is not present in active

portfolio management. Evidently, no clear development in information ratios can be detected as spikes

occur occasionally. In addition, 57 and 66 observations for the unrestricted and restricted portfolio,

-0,75

-0,50

-0,25

0,00

0,25

0,50

0,75

1,00

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Info

rmat

ion

Rat

io

Figure 6.2b Unrestricted Portfolio

Source: Own Creation, Appendix 6-3,00

-2,00

-1,00

0,00

1,00

2,00

3,00

4,00

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

Info

rmat

ion

Rat

io

Figure 6.2a Unrestricted Portfolio



73

respectively, carried an information ratio of zero. For these observations, portfolio beta was lower than

benchmark beta but active return was positive. The interpretation is that the investor has overestimated

the market risk and underestimated future active return which is not an act of skill, but neither something

that should be penalized as it still contribute with positive portfolio return.

Table 6.3: Results of Value added and Information Ratio

Panel A of Table 6.3 displays overall value added, between portfolios and the benchmark index66. Panel B

shows the corresponding results for the average information ratio. In general active portfolios achieved

monthly residual return, or value added of 1,56% and 1,16% on average. The observed residual returns are

both economically and statistically significant as all t-values for both portfolios exceed 1,96, and no p-

value exceeds 5%. Grinold and Kahn (1995) suggest that significant information ratio indicates that the

portfolio performance is due to skill rather than luck, as the probability of observing such large alpha by

chance is only 5%67. That basically means that any significantly positive value added is a sign of investment

skill. We previously attributed the source of skill to the timing of portfolio reweighting, however, we could

not determine skill as the source of the performance of the investment strategy. Considering the

information ratios can, however, determine which investment strategy is considered most skilled.

The difference in information ratios is highly significant. Considering the risk factors of the ex-post

tracking error, the unrestricted portfolio tracks the benchmark more appropriately as it recognizes the

benchmark as a single index with changing return and beta estimations. This occurs generally at levels

above the investment opportunities, and conducts asset allocation accordingly. As a result, portfolio

67

Grinold & Kahn (1995): p. 323

t-score P-value

5,78 <0,0001

4,94 <0,0001

6,02 <0,0001

5,95 <0,0001

Source: Own Creation, Datastream, MSCI Barra Appendix 6


Average Value

1,56%

Panel A. Value Added


Panel B. Information Ratio



1,16%

33,14%

6,41%


74

corner solutions then emerges as the mean-variance model tracks benchmark beta and select the

investment opportunity with the beta best matching benchmark beta. In periods where benchmark beta is

higher than any given investment opportunity, the mean-variance model allocates as much funds as

possible into the investment opportunity which best matches the benchmark beta. However, as portfolio

beta is limited to 1 the mean-variance model cannot allocate 100% funds to one sector index with beta

above 1, but instead distributes the remaining funds into low beta sectors. Restricting maximum portfolio

positions presents a tradeoff. The restricted portfolio cannot eliminate active beta as it can only allocate

20% funds into high beta investment opportunities. Thus the restricted portfolio cannot track benchmark

beta as effectively as the other portfolio. However, diversifying investment positions provides better

conditions for eliminating the other risk factor, active risk, as spreading investments would compensate

losses in some investments by gains in others. As the historic performance of the benchmark has proven

superior to both portfolios, tracking active return is a far more difficult task. Thus, the tracking error is

minimized by eliminating active portfolio beta, and the unrestricted portfolio is more successful in doing

so, making it the most preferred portfolio.

In summary, both portfolios yielded inferior cumulative return compared to the benchmark, and analysis could

not detect any form of investment skill. Investigating whether value was added to the portfolio, we found

that the unrestricted portfolio and the restricted portfolio yielded significant residual returns of 1,56% and

1,16%, respectively. These positive returns add value to the investor, resulting in significant information

ratios of 33% and 6%, respectively. The information ratios are quite different indicating the unrestricted

portfolio tracks the benchmark more successfully than the restricted portfolio.


75

7. Conclusion

In this thesis the mechanics of active portfolio management was addressed based upon the motivation

that an investor attempts to outperform a benchmark, the MSCI Denmark. Chapter 1 to 4 established

the investment strategy which involved the determination of a strategic long-term investment

opportunity set and conducting tactical short-term asset allocation by means of Markowitz’ mean-

variance portfolio model. The model was applied each quarter from 1992 to 2011. The asset allocation

was conditional on return and covariance estimations. Two portfolios were constructed: one portfolio

upon which was imposed a restriction of maximum 20% representation of investment opportunities.

The second portfolio was not subject to any constraint with regards to asset allocation.

To answer the superior research objective four sub-questions were identified. Conclusions with respect to

each question and the overall conclusion will be presented in the following based on the findings of

chapter 5 and 6.

How does the mean-variance portfolio model conduct asset allocation in the context of active portfolio

management?

The mean-variance portfolio model was applied for conducting tactical asset allocation in chapter 5. The

model was submitted to three constraints: no short selling, no financial gearing, and a maximum level of

systematic risk constrained to market level, 1, tP . The model conducted asset allocation with regards to

optimization of the information ratio, which measures relative performance of portfolio versus

benchmark. A historical increase in market integration have seen stock markets increase correlation and

hence their covariance towards other markets. Thus, as the investment opportunities display comparable

historical return patterns the mean-variance model primarily selects stocks based upon their expected

return estimates and systematic risk.

Based on the findings in chapter 5, we conclude that optimizing the portfolios against a strong performing

benchmark prescribes concentrated portfolios. In periods of high expected benchmark return, investment

funds need to be allocated to a combination of investment opportunities with both very high and very low

systematic risk, in order to maximize portfolio expected return and retain systematic risk at market level.


76

How does active portfolio management perform compared to MSCI Denmark between 1992 and 2011?

Chapter 6 analyzed the results of portfolio construction. By means of tactical asset allocation and the

mean-variance portfolio model the unrestricted and a restricted portfolio provided average monthly

return of 0,37% and 0,34%, respectively. The MSCI Denmark provided an average return of 0,65% per

month. The market return was 0,34%. Neither portfolio outperformed the benchmark, but both

outperformed the market. High covariance and correlation was detected among investment

opportunities, and given different representation of investment opportunities between portfolios,

restricting portfolio representation has not proven to alter portfolio performance.

The choice of time frame is a contributing factor in determining the success of active portfolio

management. Limiting the timeframe to 1999, 2001 and 2003 would have provided cumulative portfolio

return superior to the benchmark, but from 1992 to 2011 cumulative portfolio return was 41% and 42%

below benchmark, respectively.

Based on the findings in chapter 5 and 6, we conclude that MSCI Denmark has provided the investor with

higher realized return as opposed to active portfolio management. This conclusion is based upon respective

performances from 1992 to 2011. Selection of time frame is, however, important to determine the success

of active portfolio management.

Does active portfolio management performance indicate investment skill on the part of the investor?

In order to determine whether the investment strategy indicates investment skill we considered the

timing of portfolio repositioning and turned to the statistical tool Ordinary Least Square. Market return

was regressed on portfolio return and a second explanatory up-market variable containing only positive

market returns was introduced. The purpose of this variable was to determine whether portfolio market

exposure was significantly different in the event of positive and negative market return. The up-market

variable was statistically significant but negative.

Based on the findings with regards to market timing in chapter 6, we conclude that quarterly portfolio

repositioning cannot be attributed as a timing skill. Even though both portfolios provided return superior to

the market index, market exposure of portfolios is not statistically significant.


77

With regards to the systematic risk of portfolio and benchmark, does active portfolio management add

value to the investor?

Portfolio value added, or alpha, is present under the condition of positive active beta and positive active

return or vice versa. The rationale behind this condition is that the investor is only rewarded for taking

higher systematic risk than the benchmark if active return is positive. On the other hand, negative active

return still adds value to the portfolios, given the portfolio beta is lower than the benchmark beta. The

unrestricted and restricted portfolio added value by providing monthly average residual return of 1,56%

and 1,16%, respectively. As a result of the unrestricted portfolio possessing concentrated sector positions,

this portfolio was more successful in tracking the benchmark performance resulting in a superior

information ratio of 33% against 6%.

Based on the findings of chapter 6, we conclude that active portfolio management has added significant

value to the investor as opposed to benchmark investment. Restricting the portfolio beta to, 1, tP ,

provides the investor with the ability to control market exposure of the portfolio, leading higher portfolio

systematic risk to be warranted by a higher realized return. On the other hand, leading lower realized

return to be justified by lower systematic risk.

The overall conclusion from this thesis is: the investment strategy of active portfolio management

provides inferior return to investing in the MSCI Denmark. However, maintaining a fixed level of

systematic risk upon portfolio repositioning, portfolio return inferior to the benchmark is justified as the

benchmark demands higher systematic risk in order to generate higher return. In addition, given portfolio

systematic risk exceeds benchmark systematic risk portfolio return is in such case positively significant. In

that regard active portfolio management adds value to the investor.


78

8. References

Articles

Berk J. (2005): Five Myths of Active Portfolio Management, The Journal of Portfolio Management,

pp. 27-31

Black F., Litterman R. (1992): Global Portfolio Optimization, Financial Analysis Journal, Vol. 48 No.

5, pp.28-43

Brinson G., Hood L., Beebower G. (1986): Determinants of Portfolio Performance, Financial Analyst

Journal, Vol. 42 No. 4, pp. 133-138

Brinson G., Singer B., Beebower G. (1991): Determinants of Portfolio Performance II: An Update;

Financial Analysts Journal, pp. 40-48

Campbell J., Thomson S. (2008): Predicting Excess Stock Returns Out of Sample: Can Anything Beat

the Historical Average?, The Review of Financial Studies, Vol. 21 No. 4, pp. 1510-1531

Farma E. (1970): Efficient Capital Markets: A Review of Theory and Empirical Work, Vol. 25 No. 2,

The Journal of Finance, pp. 282-417

Farma E., French K. (2004): The Capital Asset Pricing Model: Theory and Evidence, Journal of

Economic Perspectives, Vol. 18, No. 3, pp. 25-46

Grosmann J. and Stiglitz J. (1980): On the Impossibility of Informationally Efficient Markets, Vol. 70,

No. 3, The American Economic Review, pp. 393-408

Jahnke W. (1997): The Asset Allocation Hoax, White Paper, Vol. 1, No. 2, Jahnke & Associates, pp.

1-6

Lo A. (2004): The Adaptive Market Hypothesis: Market Efficiency from an Evolutionary Perspective

Markowitz H. (1952): Portfolio Selection, Journal of Finance, Vol. 7, No. 1, pp. 77-91

Michaud R. (1989): The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?, Financial Analyst

Journal, Vol. 45 No. 1, pp. 31-42

Samuelson P. (1965): Proof that Properly Anticipated Prices Fluctuate Randomly, Industrial

Management Review 6, 41-50

Sharpe W. (1964): Capital Asset Prices: A theory of Market Equilibrium under Conditions of Risk,

Journal of Finance, Vol. 19, pp. 425-442


79

Statman M. (2000): The 93,5% Question of Financial Advisors, The Journal of Investing, pp.16-20

Stoltz (2005): Active Portfolio Management, Implied Expected Returns, and Analyst Optimism,

Swiss Society for Financial Market Research, pp.261-275

Sun W., Fan A., Chen L., Schouwenaars T., Albota M. (2006): Optimal Rebalancing for Institutional

Portfolios, The Journal of Portfolio Management, pp. 33-43

Treynor J., Black F. (1974): How to Use Security Analysis to Improve Portfolio Selection, The Journal

of Business, Vol. 46, No. 1, pp. 66-86

Books

Benninga S. (2008): Financial Modeling, Massachusetts Institute of Technology, Third Edition

Elton E., Gruber M., Brown S., Goetzmann W. (2011): Modern Portfolio Theory and Investment

Analysis, Eighth Edition, John Wiley & Sons Inc.

Grinold R. and Kahn R. (1995): Active Portfolio Management, Irwin Professional Publishing

Gujarati D., Porter D. (2009): Basic Econometrics, Fifth Edition, McGraw Hill

Hopkins P., Miller C. (2001): Country, Sector, and Company Factors in Global Equity Portfolios, The

Research Foundation of AIMR and Blackwell Series in Finance

Koller T., Goedhart M. Wessels D. (2010): Valuation – Measuring the Value of Companies, John

Wiley & Sons Inc.

Litterman R. (2003): Modern Investment Management – An Equilibrium Approach, Goldman Sachs,

John Wiley & Sons Inc.

Markowitz H. (1959): Portfolio Selection – Efficient Diversification of Investments, Second Edition,

Basil Blackwell

Picerno J. (2010): Dynamic Asset Allocation, First Edition, Bloomberg Press, New York

Schleifer A. (2010): Inefficient Markets – An Introduction to Behavioral Finance, Clarendon

Lectures in Economics

Schneeweis T., Crowder G., Kazemi H. (2010): The New Asset Allocation – Risk Management in a

Multi-Asset World, John Wiley & Sons Inc.

Tsay R. (2001): Analysis of Financial Time Series, John Wiley and Sons Inc.


80

Databases

Datastream

MSCI Barra

Statistikbanken

Publications

Da Silva A., Lee W., Pornrojnangkool B. (2009): The Black-Litterman Model for Active portfolio

Management, Forthcomming in Journal of Portfolio Management, Winter 2009

Datastream (2008): Global Equity indices, User Guide, Issue 5

Fernández P., Aguirreamalloa J., Corres L. (2011): US Market Risk Premium used in 2011 by

Professors, Analysts and Companies: A Survey with 5731 Answers, Working Paper, IESE Business

School, University of Navarra

Lee W. (2000): Advanced Theory and Methodology of Tactical Asset Allocation

MSCI Barra (2010): MSCI Global Investable Market Indices Methodology; MSCI Barra Index

Methodology

Sparinvest (2007): Strategisk Asset Allocation - kort fortalt, Second Edition

Websites

www.borsen.dk

www.euroinvestor.dk

www.ft.dk

www.investopedia

www.jyskebank.dk

www.msci.com

www.proinvestor.com

www.sec.gov

http://www.borsen.dk/

http://www.euroinvestor.dk/

http://www.ft.dk/

http://www.investopedia/

http://www.jyskebank.dk/

http://www.msci.com/

http://www.proinvestor.com/

http://www.sec.gov/


81

9. Appendix Overview

Appendix 1: Glossary

Appendix 2: Sector Market Value and Correlation Matrix of Sector Return

Appendix 3: Interview Guide

Appendix 4: Active Return and Testing for Stationarity

Appendix 5: Expected Residual Sector Return

Appendix 6: Portfolio Positions of Investment Opportunities


82

Appendix 1: Glossary

Active Portfolio Management

The pursuit of portfolio investment returns in excess of the benchmark, MSCI Denmark.

Active Return

Return relative to the Benchmark. E.g. if the portfolio return is 5% and the benchmark return is

3%, active return is 2%.

Active Risk

The risk of active return. This is also called the tracking error.

Alpha

The residual return. In the context of this thesis, alpha, also called value added, is the difference

between portfolio and benchmark beta multiplied by active return.

Asset Allocation

The process of allocating funds into the portfolio. In this thesis asset allocation is conducted by

means of Markowitz’ mean-variance portfolio model.

Benchmark

The reference index for active management. In this thesis, the reference index is the MSCI

Denmark. The goal of the investor is to excess the benchmark return.

Information Ratio

The monthly expected residual return divided by the tracking error. Value added is proportional to

the information ratio.


83

Market Index

The portfolio of all assets, MSCI World. The concept of market and benchmark index is separated

in the context of this thesis. The market index is applied for measuring systematic risk of both

benchmark and investment opportunities.

Market Timing

The ability to identify a point in time appropriate for repositioning the portfolios. The concept of

market timing is based upon the belief that markets will provide positive return during periods

between the processes tactical asset allocation.

R-Square

A statistic associated with regression analysis, where it describes the fraction of observed variation

in data captured by the model. It varies between 0 and 1.

Portfolio Repositioning

Also referred to as portfolio reweighting. The process of altering the weight of portfolio assets in

accordance with tactical asset allocation.

Opportunity Set

The investment indices available for active portfolio management. Ten sector indices constitute

the investment opportunity set.

Residual Frontier

A set of portfolios, one for each level of residual return, alpha, with minimum residual risk.

Residual Return

It is the difference between beta adjusted excess return of the portfolio and benchmark.


84

Market Risk Premium

The expected excess return of the market index.

Sharpe Ratio

The ratio of monthly excess return to total risk.

Skill

The ability to accurately forecast returns. Skill is identified through market timing and measured

using the information ratio.

Stationarity

Historical returns of the investment opportunities are said to be stationary as average returns and

standard deviations are constant over time.

Strategic Asset allocation

Involves the fundamental choice of the investment opportunity set and benchmark.

Systematic Risk

It is also called market risk characterized by beta. It measures the sensitivity of a sector, portfolio

or benchmark to the market. For every 1% return to the market we expect a beta times 1% return

to the sector or benchmark. It is calculated as the covariance between a given index and the

market portfolio divided by the variance of the market portfolio.

Tactical Asset Allocation

Tactical asset allocation seeks to obtain positive residual return by periodically changing sector

positions in the portfolio.


85

t-statistic

The t-statistic helps test the hypothesis that a given estimate differs from zero. With some

standard statistical assumptions, the probability that a variable with a true value of zero would

exhibit a t-statistic greater than 1,96 in magnitude is less than 5%.

Tracking Error

See active risk.

Value Added

In the context of this thesis value added is the difference in portfolio and benchmark beta,

multiplied by the active return. Value added depends upon the performance of the investment

strategy.


86

Appendix 2: Sector Market Value and Correlation Matrix of Sector Return


Market Value (mio. USD) 2930674 5207162 3963268 8354357 2841130 4630814 4252271 3416808 2050341 1706757

Relative Proportion 7,45% 13,23% 10,07% 21,23% 7,22% 11,77% 10,81% 8,68% 5,21% 4,34%

Source: Own Creation, Datastream


Basic Materials 1,00 0,81 0,79 0,82 0,60 0,87 0,84 0,58 0,59 0,74

Consumer Goods 1,00 0,88 0,83 0,58 0,90 0,69 0,71 0,67 0,63

Consumer Services 1,00 0,87 0,64 0,92 0,65 0,80 0,79 0,66

Finance 1,00 0,72 0,88 0,71 0,64 0,67 0,76

Healthcare 1,00 0,63 0,54 0,44 0,51 0,69

Industrials 1,00 0,74 0,79 0,74 0,71

Oil & Gas 1,00 0,49 0,51 0,75

Technology 1,00 0,77 0,43

Telecommunications 1,00 0,55

Utilities 1,00

Sector Nominal Return Correlation Matrix

Source: Own creation, Datastream


Basic Materials 1,00 0,68 0,63 0,68 0,47 0,76 0,73 0,36 0,42 0,55

Consumer Goods 1,00 0,88 0,75 0,67 0,84 0,58 0,57 0,64 0,65

Consumer Services 1,00 0,78 0,74 0,86 0,52 0,66 0,76 0,68

Finance 1,00 0,65 0,80 0,55 0,46 0,57 0,64

Healthcare 1,00 0,58 0,51 0,32 0,58 0,81

Industrials 1,00 0,59 0,70 0,66 0,58

Oil & Gas 1,00 0,28 0,38 0,66

Technology 1,00 0,66 0,24

Telecommunications 1,00 0,54

Utilities 1,00


Sector Active Return Correlation Matrix


87

Appendix 3: Interview Guide

First, I would like you to tell me about what you do at Nordea Investment Management. I will afterwards

ask you some questions within the areas of asset allocation and risk management.

Asset Allocation

An area within the literature of finance distinguishes between strategic asset allocation (SAA) and tactical

asset allocation (TAA). SAA accepts that markets are efficient and applies a passive approach to its

investment strategy. On the other hand, TAA is an investment strategy which concerns proactive portfolio

repositioning, based on expectations with regards to the financial markets.

Thus, the difference between TAA and SAA is that TAA does not conduct one long-term based asset

allocation process, but adjusts the portfolio to the market on a periodic basis.

Please provide your assessment upon these two types of asset allocation and you opinion with regards to

the hypothesis of market efficiency?

1) Describe what you consider a good investment strategy with the objective of managing a portfolio

consisting of stocks only.

2) Will you describe this strategy as passive or active portfolio management?

- If passive, is that based on the assumption that it is difficult to produce a return superior to

what the passive market provides, and that opportunities for portfolio diversification are

understated?

- If active, is this based on the conviction that it is in fact possible to outperform the passive

market return?

- Other?

3) Is it your impression that the attempt to time the market by over- and underweighting portfolio

assets based on e.g. sector characteristics, leads to superior return relative to passive investing, or

to transaction costs too high to yield the return your estimations expected?


88

Risk Management

Risk is a universal concept, and numerous definitions exist, as investors has different perceptions of risk.

1) Please provide a definition of risk with regards to financial transactions.

2) Describe risk factors which Nordea’s stock portfolios are exposed to in particular.

3) What requirements do you think necessary for the active investor to conduct effective risk

management?

4) How does Nordea Investment Management evaluate risk?


89

Appendix 4: Active Return and Testing for Return Stationarity

Important knowledge with regards to timing of portfolio repositioning is whether the investment

opportunities are stationary. Non-stationary investment opportunities make market timing relevant as it

enables the investor to utilize pockets of market inefficiency. Should markets be stationary instead,

positive returns are likely to be followed by negative returns making market timing a difficult process. This

Appendix provides a brief analysis of market stationarity. The figures below illustrate the historical return

development of the investment opportunities and active returns.

To test if the indices are stationary the Argumented Dickey Fuller Test is applied which involves running

the following regression model for each index and test the null hypothesis that 01 and 0 in the

following model68:

ttt YY 11

tY is the difference in index return between time t and t-1 and 1tY is then obviously the index return of

time t-1. The parameter )1( and 11 indicates stationarity. Stationarity is present when

is negative. The null-hypothesis cannot be assessed by standard t-statistic because it does not follow a

standard distribution. Instead the test must be performed using critical values from the Dickey-Fuller

distribution.

68

Gujarati, Porter (2009): p. 755


90

The Argumented Dickey Fuller test confirms that the time series follow a stationary process. The return

time series for each sector index is illustrated below (left column) along with active return regressions

(right column).

Basic Materials – Nominal Return Basic Materials against Benchmark

Index Lag 1(δ)

Panel A. Investment Opportunities

Basic Materials -0,73

Consumer Goods -0,87

Consumer Services -0,84

Finance -0,83

Healthcare -0,94

Industrials -0,81

Oil & Gas -0,92

Technology -0,91

Telecommunications -0,87

Utilities -0,80

Panel B. Benchmark and Market

MSCI Denmark -0,90

MSCI World -0,84

Argumented Dickey Fuller Test


y = 0,7426x - 0,0005R² = 0,4995

-40%

-30%

-20%

-10%

0%

10%

20%

30%

-40% -30% -20% -10% 0% 10% 20%

Source: Own Creation, Datastrem, MSCI Barra-40%

-30%

-20%

-10%

0%

10%

20%

30%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5



91

Consumer Goods – Nominal Return Active Return - Consumer Goods vs. Benchmark

Consumer Services – Nominal Return Active Return – Consumer Services vs. Benchmark

Finance – Nominal Return Active Return - Finance vs. Benchmark

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,5198x + 0,0014R² = 0,4421

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

-40% -30% -20% -10% 0% 10% 20%

Source: Own Creation, Datastrem, MSCI Barra

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,5228x + 0,0002R² = 0,5041

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

-40% -30% -20% -10% 0% 10% 20%


-40%

-30%

-20%

-10%

0%

10%

20%

30%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,6812x - 0,0023R² = 0,5127

-40%

-30%

-20%

-10%

0%

10%

20%

30%

-40% -30% -20% -10% 0% 10% 20%



92

Healthcare – Nominal Return Active Return – Healthcare vs. Benchmark

Industrials – Nominal Return Active Return - Industrials vs. Benchmark

Oil & Gas – Nominal Return Active Return - Oil & Gas vs. Benchmark

y = 0,3131x + 0,0028R² = 0,2901

-15%

-10%

-5%

0%

5%

10%

15%

-40% -30% -20% -10% 0% 10% 20%

Source: Own Creation, Datastream, MSCI Barra-15%

-10%

-5%

0%

5%

10%

15%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


-30%

-20%

-10%

0%

10%

20%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,6911x + 0,0003R² = 0,5642

-30%

-20%

-10%

0%

10%

20%

-40% -30% -20% -10% 0% 10% 20%


-30%

-20%

-10%

0%

10%

20%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,6911x + 0,0003R² = 0,5642

-30%

-20%

-10%

0%

10%

20%

-40% -30% -20% -10% 0% 10% 20%



93

Technology – Nominal Return Active Return - Technology vs. Benchmark

Telecommunications – Nominal Return Active Return - Telecommunications vs. Benchmark

Utilities – Nominal Return Active Return - Utilities vs. Benchmark

-40%

-30%

-20%

-10%

0%

10%

20%

30%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,7235x + 0,0022R² = 0,3193

-40%

-30%

-20%

-10%

0%

10%

20%

30%

-40% -20% 0% 20%


-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,5376x - 0,0001R² = 0,3599

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

-40% -20% 0% 20%


-20%

-15%

-10%

-5%

0%

5%

10%

15%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5


y = 0,4429x - 0,0003R² = 0,466

-20%

-15%

-10%

-5%

0%

5%

10%

15%

-40% -20% 0% 20%



94

MSCI Denmark – Nominal Return MSCI World – Nominal Return

-30%

-20%

-10%

0%

10%

20%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5

Source: Own Creation, MSCI Barra-30%

-20%

-10%

0%

10%

20%

1

17

33

49

65

81

97

11

3

12

9

14

5

16

1

17

7

19

3

20

9

22

5

Source: Own Creation, MSCI Barra


95

Appendix 5: Expected Residual Return

Expected Residual Return – Basic Materials Expected Residual Return – Consumer Goods

Expected Residual Return – Consumer Services Expected Residual Return – Finance

Expected Residual Return – Healthcare Expected Residual Return – Industrials

-4,0%

-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%

Source: Own Creation, Datastream, MSCI Barra-4,0%

-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%


-4,0%

-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%


-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%


-4,0%

-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%


-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%



96

Expected Residual Return – Oil & Gas Expected Residual Return – Technology

Expected Residual Return – Telecommunications Expected Residual Return – Utilities

-4,0%

-2,0%

0,0%

2,0%

4,0%

6,0%

8,0%

10,0%


-2,0%

0,0%

2,0%

4,0%

6,0%

8,0%

10,0%


-4,0%

-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%


-3,0%

-2,0%

-1,0%

0,0%

1,0%

2,0%

3,0%

4,0%



97

Appendix 6: Portfolio Positions of Investment Opportunities

Portfolio Weight (mm-yy) 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,94

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,06

Consumer Services 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Finance 0,00 0,00 0,00 0,00 0,00 0,56 0,55 0,55 0,40 0,41 0,41 0,00

Healthcare 0,75 0,75 0,38 0,39 0,38 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,23 0,23 0,22 0,30 0,30 0,29 0,00

Technology 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Telecommunications 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Utilities 0,25 0,25 0,62 0,61 0,62 0,21 0,22 0,22 0,30 0,29 0,30 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Monthly Risk Free Rate of Return 0,7% 0,7% 0,7% 0,7% 0,7% 0,7% 0,7% 0,8% 0,8% 0,7% 0,7% 0,7%

Portfolio 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Return Adj. For Trans. Costs -3,6% -1,8% -3,8% 0,1% 3,5% -3,3% 0,4% 5,0% -2,1% -3,2% 0,5% -0,7%

Beta 0,88 1,37 0,55 0,45 0,58 1,00 1,18 1,26 1,00 0,86 1,02 1,00

Benchmark 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Return -1,4% -6,0% -8,0% 0,0% 11,6% -5,3% -0,5% -7,7% -5,9% -9,7% -0,7% -0,9%

Beta 0,52 0,71 0,71 0,91 1,00 0,76 0,75 0,79 0,96 1,37 1,90 2,78

Portfolio and Benchmark Comparison 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Value Added, Alpha -0,8% 2,8% 0,0% 0,0% 3,4% 0,5% 0,4% 6,0% 0,1% 0,0% 0,0% 0,0%

Tracking Error 0,7% 3,2% 0,5% 0,0% 2,5% 0,6% 0,5% 10,1% 2,1% 2,6% 0,8% 0,5%

Information Ratio -1,22 0,87 0,00 0,00 1,40 0,79 0,75 0,59 0,06 0,00 0,00 0,00

Source: Own creation, Datastream, MSCI Barra, Statistikbanken


Basic Materials 0,94 0,94 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,06 0,06 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,77 0,76 0,77 0,11 0,11 0,11 0,01 0,01 0,01 0,00

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,32 0,31 0,31 0,33 0,32 0,32 0,24

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,37 0,38 0,37 0,42 0,42 0,42 0,48

Technology 0,00 0,00 0,02 0,02 0,02 0,00 0,00 0,00 0,00 0,00 0,00 0,12


Utilities 0,00 0,00 0,00 0,00 0,00 0,20 0,21 0,21 0,24 0,25 0,24 0,16

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93


Portfolio 01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93

Return Adj. For Trans. Costs 0,0% 3,1% 7,0% 5,6% 3,9% -1,6% 2,9% 3,4% -2,1% 2,1% -5,2% 5,4%

Beta 0,77 -0,64 0,93 1,44 1,75 1,00 1,05 1,03 1,00 1,07 1,11 1,00

Benchmark 01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93

Return 12,4% -4,7% 1,2% 4,8% 2,0% 1,2% -3,8% 4,3% 3,4% 4,0% -3,1% 5,8%

Beta 2,35 0,30 -0,28 -0,37 -0,21 0,10 0,35 0,41 0,55 0,73 0,76 0,73


Value Added, Alpha 19,6% 0,0% 7,1% 1,4% 3,7% -2,5% 4,7% -0,6% -2,5% -0,6% -0,7% -0,1%

Tracking Error 18,4% 7,2% 5,3% 2,7% 3,6% 1,6% 2,8% 0,3% 1,7% 0,5% 0,6% 0,3%

Information Ratio 1,07 0,00 1,32 0,51 1,05 -1,53 1,65 -2,12 -1,47 -1,24 -1,28 -0,31



98


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,18 0,18 0,18 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,00 0,00 0,05 0,05 0,05 0,20 0,20 0,20 0,00 0,00 0,00 0,00

Industrials 0,25 0,25 0,34 0,35 0,34 0,64 0,64 0,64 0,58 0,58 0,57 0,33

Oil & Gas 0,48 0,48 0,43 0,43 0,43 0,16 0,16 0,16 0,42 0,42 0,43 0,67

Technology 0,12 0,12 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,15 0,15 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94


Portfolio 01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94

Return Adj. For Trans. Costs 5,7% -1,0% -4,1% 3,6% 0,4% 0,2% 1,9% 3,6% -2,9% 3,3% -6,1% 0,0%

Beta 0,90 0,93 1,00 0,77 0,74 1,00 0,91 0,94 1,00 0,95 0,89 0,11

Benchmark 01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94

Return 8,2% 0,3% -1,5% 1,6% -8,0% 4,3% 4,7% -7,4% 0,2% 1,8% -4,3% 2,5%

Beta 0,69 1,24 1,36 1,37 1,42 1,35 1,24 1,22 0,92 0,65 0,44 -0,21


Value Added, Alpha -0,5% 0,4% 1,0% 0,0% 0,0% 1,4% 0,9% 0,0% -0,2% 0,4% -0,8% -0,8%

Tracking Error 0,3% 0,6% 0,8% 1,2% 3,5% 1,0% 0,4% 2,4% 0,9% 0,2% 0,6% 0,8%

Information Ratio -1,78 0,65 1,15 0,00 0,00 1,47 2,18 0,00 -0,25 2,43 -1,30 -1,01



Basic Materials 0,00 0,00 0,50 0,50 0,50 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,07 0,07 0,07 0,07


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,00 0,00 0,25 0,24 0,24 0,36 0,36 0,35 0,15 0,15 0,16 0,15

Industrials 0,33 0,33 0,12 0,12 0,12 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,67 0,67 0,14 0,14 0,14 0,24 0,23 0,23 0,18 0,18 0,17 0,27

Technology 0,00 0,00 0,00 0,00 0,00 0,27 0,29 0,30 0,30 0,30 0,30 0,25


Utilities 0,00 0,00 0,00 0,00 0,00 0,14 0,13 0,13 0,29 0,30 0,30 0,26

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95


Portfolio 01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95

Return Adj. For Trans. Costs -3,3% 0,6% 4,2% 3,2% -0,5% 1,8% 3,9% -1,5% 2,3% -0,5% 0,6% 2,0%

Beta 0,41 0,48 0,24 0,25 0,43 1,00 1,03 1,22 1,00 1,06 1,16 1,00

Benchmark 01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95

Return 1,3% 2,8% -0,7% 4,6% 4,1% -1,7% 6,7% -5,5% 1,5% 0,1% 0,4% 2,3%

Beta 0,16 0,09 0,59 0,48 0,75 0,94 0,87 1,08 1,00 1,00 0,99 0,82


Value Added, Alpha -1,2% -0,8% 0,0% 0,3% 1,5% 0,2% -0,5% 0,6% 0,0% 0,0% 0,0% -0,1%

Tracking Error 0,9% 0,6% 0,9% 0,3% 2,0% 1,0% 0,9% 1,7% 0,5% 0,4% 0,9% 2,2%

Information Ratio -1,28 -1,50 0,00 0,96 0,74 0,21 -0,50 0,35 0,00 -0,09 0,05 -0,03



99


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,07 0,07 0,14 0,15 0,15 0,14 0,14 0,14 0,14 0,14 0,14 0,06


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,15 0,15 0,28 0,28 0,27 0,24 0,25 0,25 0,26 0,26 0,26 0,25

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,28 0,28 0,23 0,23 0,23 0,32 0,31 0,31 0,31 0,31 0,32 0,46

Technology 0,23 0,23 0,12 0,12 0,13 0,04 0,03 0,03 0,04 0,04 0,04 0,06


Utilities 0,26 0,26 0,22 0,22 0,21 0,27 0,27 0,27 0,25 0,24 0,25 0,17

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96


Portfolio 01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96

Return Adj. For Trans. Costs 1,1% 1,4% 0,6% 3,0% 0,6% 0,8% -4,0% 1,1% 2,5% 1,3% 4,6% -0,3%

Beta 1,01 0,98 1,00 0,91 0,94 1,00 1,00 1,12 1,00 1,17 0,80 1,00

Benchmark 01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96

Return 3,2% 1,3% -2,6% -0,8% 0,2% 2,5% 1,4% 3,5% -0,4% 3,2% 2,3% 4,5%

Beta 0,76 0,78 0,77 0,56 0,44 0,42 0,38 0,58 0,66 0,85 0,89 0,99


Value Added, Alpha -0,5% 0,0% 0,7% 1,3% 0,2% -1,0% -3,4% -1,3% 1,0% -0,6% 0,0% 0,0%

Tracking Error 0,6% 0,8% 1,3% 0,5% 0,9% 0,6% 2,2% 1,1% 1,3% 0,8% 0,4% 1,0%

Information Ratio -0,79 0,04 0,56 2,55 0,23 -1,79 -1,51 -1,20 0,74 -0,74 0,00 -0,04



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,06 0,06 0,60 0,60 0,60 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,06

Healthcare 0,25 0,25 0,00 0,00 0,00 0,25 0,25 0,24 0,24 0,24 0,25 0,33

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,46 0,47 0,00 0,00 0,00 0,70 0,69 0,70 0,63 0,63 0,63 0,45

Technology 0,05 0,06 0,40 0,40 0,40 0,01 0,01 0,01 0,04 0,04 0,04 0,06


Utilities 0,17 0,16 0,00 0,00 0,00 0,05 0,05 0,05 0,09 0,09 0,09 0,11

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97


Portfolio 01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97

Return Adj. For Trans. Costs 2,6% -1,2% -1,9% 5,5% 6,5% 3,9% 3,5% -5,1% 5,8% -5,0% -1,9% 1,1%

Beta 1,03 1,17 1,00 0,85 0,81 1,00 1,02 1,12 1,00 1,01 0,95 1,00

Benchmark 01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97

Return 3,9% -0,7% 3,0% -3,2% 7,2% 2,0% 6,2% -5,2% 10,8% -4,6% 1,0% 8,1%

Beta 1,22 1,57 1,79 1,88 1,38 1,15 0,99 1,09 1,01 1,04 1,00 0,93


Value Added, Alpha 0,3% 0,2% 3,9% 0,0% 0,4% 0,0% -0,1% 0,0% 0,1% 0,0% 0,1% -0,5%

Tracking Error 1,1% 0,5% 4,3% 8,4% 1,9% 0,5% 0,8% 0,6% 1,1% 0,4% 0,7% 1,3%

Information Ratio 0,24 0,40 0,91 0,00 0,19 0,00 -0,10 0,00 0,07 0,02 0,18 -0,34



100


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,06 0,06 0,15 0,15 0,15 0,77 0,77 0,78 0,00 0,00 0,00 0,00

Healthcare 0,33 0,34 0,49 0,49 0,49 0,11 0,11 0,11 0,56 0,54 0,56 0,21

Industrials 0,00 0,00 0,00 0,00 0,00 0,12 0,12 0,12 0,00 0,00 0,00 0,00

Oil & Gas 0,45 0,43 0,15 0,16 0,16 0,00 0,00 0,00 0,31 0,33 0,31 0,00

Technology 0,06 0,06 0,00 0,00 0,00 0,00 0,00 0,00 0,13 0,13 0,13 0,58


Utilities 0,11 0,11 0,21 0,21 0,21 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98


Portfolio 01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98

Return Adj. For Trans. Costs 0,1% 4,8% 3,5% 0,3% -2,0% 0,0% 0,5% -19,2% 6,9% 6,2% 3,8% 9,9%

Beta 0,92 0,75 1,00 1,03 1,03 1,00 1,00 0,96 0,93 0,94 0,89 1,00

Benchmark 01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98

Return 0,3% 2,3% 11,1% -4,4% 2,7% -2,3% 2,9% -12,0% -4,7% 7,2% -5,0% 9,5%

Beta 1,03 1,11 1,13 1,50 1,44 1,43 1,40 1,10 0,96 0,88 0,58 0,03


Value Added, Alpha 0,0% 0,0% 1,0% 0,0% 1,9% 0,0% 0,9% 1,0% 0,0% -0,1% 2,7% 0,4%

Tracking Error 0,7% 0,5% 2,4% 2,1% 2,2% 0,7% 0,9% 0,9% 4,6% 1,1% 2,9% 2,5%

Information Ratio 0,03 0,00 0,41 0,00 0,87 0,00 1,09 1,11 0,00 -0,06 0,92 0,17



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,15 0,15 0,15 0,05 0,05 0,05 0,29 0,29 0,30 0,11

Healthcare 0,20 0,18 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,72 0,72 0,73 0,00 0,00 0,00 0,02

Oil & Gas 0,00 0,00 0,21 0,23 0,24 0,00 0,00 0,00 0,05 0,05 0,05 0,12

Technology 0,60 0,62 0,27 0,28 0,27 0,13 0,14 0,14 0,01 0,01 0,01 0,07


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,37 0,36 0,34 0,34

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99


Portfolio 01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99

Return Adj. For Trans. Costs 10,1% -7,5% 6,1% 6,5% -3,1% 9,1% 1,1% 1,8% -0,3% 4,9% 3,0% 5,3%

Beta 1,29 1,69 1,00 1,11 1,22 1,00 1,15 1,68 1,00 0,79 0,74 1,00

Benchmark 01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99

Return -3,7% -9,1% -1,8% 6,9% -2,9% 1,0% 6,7% 0,2% 2,9% 1,2% 3,3% 5,6%

Beta -0,02 -0,10 -0,29 -0,43 -0,41 -0,39 -0,35 -0,06 -0,02 -0,04 0,39 0,53


Value Added, Alpha 18,0% 2,8% 10,3% -0,6% -0,2% 11,3% -8,4% 2,8% -3,3% 3,0% -0,1% -0,1%

Tracking Error 17,6% 3,3% 7,9% 4,3% 1,3% 8,4% 5,4% 3,4% 2,1% 5,0% 4,7% 4,9%

Information Ratio 1,02 0,86 1,30 -0,13 -0,19 1,34 -1,57 0,81 -1,56 0,61 -0,03 -0,03



101


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,10 0,10 0,09 0,10 0,10 0,13 0,13 0,14 0,07 0,07 0,07 0,01

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,44

Industrials 0,02 0,02 0,07 0,07 0,07 0,03 0,03 0,03 0,00 0,00 0,00 0,00

Oil & Gas 0,12 0,12 0,08 0,08 0,09 0,14 0,14 0,14 0,12 0,12 0,12 0,06

Technology 0,08 0,08 0,00 0,00 0,00 0,02 0,02 0,02 0,05 0,04 0,04 0,29


Utilities 0,32 0,33 0,38 0,38 0,41 0,33 0,32 0,33 0,35 0,37 0,37 0,19

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00


Portfolio 01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00

Return Adj. For Trans. Costs -3,7% 1,2% 4,3% -5,7% -1,5% 0,8% -2,8% 2,4% -2,8% -2,6% -7,2% 0,9%

Beta 1,32 1,52 1,00 0,99 0,95 1,00 1,00 0,85 1,00 0,70 0,71 1,00

Benchmark 01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00

Return -5,6% 3,5% 8,8% -9,6% 6,5% -0,2% 2,0% 5,6% -2,0% -4,7% -5,1% 3,6%

Beta 0,84 1,09 1,00 1,06 1,10 1,06 0,90 0,88 0,22 -0,64 -0,57 -0,18


Value Added, Alpha 0,9% -1,0% 0,0% 0,0% 1,2% 0,0% -0,5% 0,1% -0,6% 2,9% -2,7% -3,1%

Tracking Error 1,9% 5,9% 5,2% 5,9% 9,2% 1,9% 5,4% 4,4% 5,4% 4,4% 9,6% 20,1%

Information Ratio 0,49 -0,17 0,00 0,00 0,13 0,00 -0,09 0,02 -0,12 0,66 -0,28 -0,16



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,01 0,01 0,15 0,15 0,14 0,23 0,24 0,24 0,27 0,26 0,26 0,30

Healthcare 0,45 0,42 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,06 0,06 0,13 0,14 0,14 0,08 0,07 0,07 0,06 0,06 0,06 0,07

Technology 0,27 0,30 0,08 0,07 0,07 0,08 0,08 0,07 0,10 0,09 0,10 0,08


Utilities 0,20 0,19 0,32 0,33 0,32 0,32 0,32 0,32 0,31 0,31 0,31 0,27

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01


Portfolio 01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01

Return Adj. For Trans. Costs -1,5% -9,3% -6,0% 6,8% -3,6% -4,2% -2,7% -4,9% -8,2% 0,7% 2,9% 0,7%

Beta 1,05 1,39 1,00 0,95 0,96 1,00 0,99 1,08 1,00 0,97 0,97 1,00

Benchmark 01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01

Return 11,1% -9,5% -10,6% 1,9% -0,2% -1,7% 3,4% -5,6% -9,2% 2,0% 1,1% 0,1%

Beta -14,3% -36,5% -12,4% 1,2% 20,3% 35,0% 49,5% 61,0% 54,0% 64,8% 71,2% 88,0%


Value Added, Alpha -15,0% 0,3% 5,2% 4,6% -2,6% -1,6% -3,0% 0,3% 0,5% -0,4% 0,5% 0,1%

Tracking Error 13,5% 45,4% 2,7% 7,2% 4,4% 2,0% 5,6% 4,0% 5,8% 4,3% 4,2% 0,3%

Information Ratio -1,11 0,01 1,91 0,64 -0,59 -0,80 -0,53 0,09 0,08 -0,10 0,12 0,24



102


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,05 0,05 0,05 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,31 0,31 0,22 0,22 0,23 0,15 0,15 0,15 0,12 0,12 0,12 0,33

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,19 0,21 0,20 0,08

Industrials 0,00 0,00 0,14 0,14 0,14 0,05 0,05 0,05 0,00 0,00 0,00 0,12

Oil & Gas 0,08 0,08 0,04 0,04 0,04 0,00 0,00 0,00 0,04 0,05 0,04 0,00

Technology 0,08 0,08 0,10 0,10 0,09 0,22 0,21 0,21 0,36 0,33 0,36 0,15


Utilities 0,27 0,28 0,26 0,26 0,27 0,39 0,40 0,40 0,24 0,25 0,23 0,23

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02


Portfolio 01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02

Return Adj. For Trans. Costs -4,8% -2,2% 4,8% -3,6% -0,5% -7,6% -8,8% 0,9% -12,7% 7,4% 6,1% -4,4%

Beta 1,11 0,93 1,00 1,19 1,10 1,00 0,71 0,80 1,00 1,16 1,35 1,00

Benchmark 01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02

Return -5,5% 2,4% 3,0% -4,1% 2,2% 1,2% -13,6% 3,2% -14,5% 2,7% 4,0% 0,4%

Beta 1,13 0,85 0,75 0,86 0,93 0,71 0,21 0,34 0,42 0,65 0,75 0,79


Value Added, Alpha 0,0% -0,4% 0,5% 0,2% -0,4% -2,6% 2,4% -1,0% 1,0% 2,4% 1,3% -1,0%

Tracking Error 1,2% 2,0% 0,7% 1,8% 1,5% 6,2% 1,7% 2,1% 3,1% 8,5% 6,7% 3,9%

Information Ratio 0,00 -0,18 0,68 0,09 -0,30 -0,42 1,42 -0,48 0,32 0,28 0,19 -0,26



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,44 0,44 0,43 0,00


Finance 0,33 0,33 0,14 0,14 0,14 0,43 0,43 0,43 0,55 0,56 0,57 0,00

Healthcare 0,09 0,09 0,09 0,09 0,08 0,24 0,24 0,23 0,00 0,00 0,00 0,00

Industrials 0,12 0,12 0,26 0,26 0,26 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,00 0,00 0,15 0,15 0,14 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Technology 0,14 0,14 0,07 0,07 0,07 0,33 0,33 0,34 0,00 0,00 0,00 0,39


Utilities 0,25 0,26 0,27 0,28 0,28 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03


Portfolio 01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03

Return Adj. For Trans. Costs -2,0% -2,1% -0,8% 7,6% 6,2% 1,5% 3,4% 2,2% 2,1% 6,1% 1,3% 5,0%

Beta 0,94 0,95 1,00 0,97 0,88 0,80 0,85 1,04 1,00 1,00 1,11 1,00

Benchmark 01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03

Return -4,5% -4,6% 7,5% 11,5% 6,7% -0,4% -2,0% 8,5% 3,7% 6,2% -0,5% 6,5%

Beta 0,76 0,84 1,00 0,96 1,16 1,22 1,23 1,25 1,79 1,76 1,85 1,71


Value Added, Alpha 0,4% 0,3% 0,0% 0,0% 0,1% 0,0% 0,0% 1,3% 1,3% 0,0% 0,0% 1,1%

Tracking Error 0,9% 0,8% 1,6% 0,7% 0,1% 0,5% 1,4% 1,3% 1,5% 0,8% 1,2% 0,5%

Information Ratio 0,50 0,33 0,00 -0,05 0,94 0,00 0,00 1,03 0,83 0,05 0,00 2,04



103


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,00 0,00 0,48 0,48 0,49 0,00 0,00 0,00 0,00 0,00 0,00 0,50

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,50

Technology 0,38 0,38 0,00 0,00 0,00 0,43 0,43 0,40 0,71 0,71 0,71 0,00


Utilities 0,00 0,00 0,52 0,52 0,51 0,40 0,39 0,41 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04


Portfolio 01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04

Return Adj. For Trans. Costs 4,0% -0,1% -0,5% -1,0% 0,3% 1,9% -4,4% -0,3% 2,3% 4,6% 5,2% 2,0%

Beta 1,01 1,10 1,00 1,01 1,06 1,00 0,96 0,86 1,00 0,26 -0,04 1,00

Benchmark 01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04

Return 4,5% 5,6% -5,3% -1,7% 0,4% 5,7% -1,9% 1,7% 6,0% -0,9% 7,4% 3,7%

Beta 1,78 1,88 2,07 2,08 2,08 2,16 2,25 2,05 2,21 2,14 1,75 1,82



Tracking Error 0,9% 3,7% 5,1% 1,7% 0,2% 2,8% 3,3% 2,0% 3,2% 8,4% 4,2% 1,5%

Information Ratio 0,35 1,20 0,00 0,00 0,64 1,53 0,97 1,21 1,41 0,00 0,93 0,94



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,90

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,51 0,50 0,00 0,00 0,00 0,00 0,00 0,00 0,04 0,04 0,04 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,49 0,50 0,32 0,32 0,32 0,04 0,04 0,04 0,00 0,00 0,00 0,10

Technology 0,00 0,00 0,68 0,68 0,68 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,96 0,96 0,96 0,96 0,96 0,96 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05


Portfolio 01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05

Return Adj. For Trans. Costs -0,4% 7,7% -3,6% -4,2% 5,3% 3,2% 2,4% 2,1% 3,8% -5,3% 0,9% 4,3%

Beta 1,23 1,27 1,00 1,15 1,11 1,00 1,01 1,06 1,00 1,04 0,75 1,00

Benchmark 01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05

Return -2,7% 7,4% -0,3% -3,5% 2,7% 1,7% 3,1% 4,9% 0,7% -2,2% 2,2% 6,3%

Beta 2,15 2,06 2,37 2,48 2,41 2,30 2,39 2,44 2,55 2,99 2,32 2,17



Tracking Error 0,6% 3,7% 4,0% 0,6% 5,8% 2,0% 1,1% 4,1% 5,1% 6,1% 1,9% 2,4%




104


Basic Materials 0,91 0,90 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20 0,19 0,19 0,29

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,09 0,10 0,00 0,00 0,00 0,14 0,14 0,14 0,00 0,00 0,00 0,00

Technology 0,00 0,00 0,71 0,71 0,71 0,00 0,00 0,00 0,80 0,81 0,81 0,71


Utilities 0,00 0,00 0,00 0,00 0,00 0,86 0,86 0,86 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06


Portfolio 01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06

Return Adj. For Trans. Costs 10,7% -2,5% 2,8% 1,5% -6,7% 0,3% 2,9% 2,9% 3,0% 3,1% 3,5% 0,8%

Beta 1,04 1,39 1,00 1,01 0,99 1,00 0,97 0,98 1,00 0,97 0,76 1,00

Benchmark 01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06

Return 2,4% 0,4% 5,2% 5,8% -4,5% -1,1% -0,4% 6,3% 2,4% 4,3% 6,3% 4,3%

Beta 2,14 2,19 2,20 2,40 2,68 2,85 2,79 2,65 2,78 3,19 3,08 3,20



Tracking Error 9,3% 2,3% 1,9% 4,1% 3,1% 2,6% 5,8% 4,3% 1,8% 2,6% 5,5% 7,7%




Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,21 0,20 0,20 0,00 0,00 0,00 0,00


Finance 0,29 0,29 0,02 0,02 0,02 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Technology 0,71 0,71 0,98 0,98 0,98 0,79 0,80 0,80 0,80 0,80 0,81 0,63


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07


Portfolio 01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07

Return Adj. For Trans. Costs 0,4% -1,9% 0,2% 4,6% 2,8% 1,3% -0,1% 1,2% 3,2% 5,1% -7,2% -1,1%

Beta 1,08 1,26 1,00 0,87 0,99 1,00 1,09 1,00 1,00 0,99 1,13 1,00

Benchmark 01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07

Return 2,7% 0,2% 4,0% 6,6% 2,1% -2,6% 3,7% -0,5% 5,4% 4,0% -4,0% 0,1%

Beta 3,42 3,75 3,75 3,59 3,92 4,28 4,63 4,83 4,91 4,44 4,45 4,19



Tracking Error 4,8% 4,7% 9,9% 5,5% 2,3% 11,6% 10,9% 5,9% 5,8% 4,4% 9,4% 3,8%




105


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,06 0,05 0,04 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,32 0,32 0,32 0,09 0,08 0,09 0,00 0,00 0,00 0,29

Healthcare 0,00 0,00 0,15 0,15 0,14 0,21 0,23 0,24 0,18 0,20 0,23 0,71

Industrials 0,00 0,00 0,40 0,40 0,40 0,66 0,65 0,64 0,66 0,66 0,63 0,00

Oil & Gas 0,00 0,00 0,08 0,08 0,09 0,04 0,04 0,03 0,09 0,09 0,09 0,00

Technology 0,64 0,62 0,03 0,03 0,04 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08


Portfolio 01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08

Return Adj. For Trans. Costs -10,7% -1,3% -2,1% 4,5% 0,7% -9,8% -0,9% -2,5% -16,6% -24,6% -5,9% 5,6%

Beta 0,59 0,73 1,00 1,17 1,26 1,00 1,12 1,19 1,00 1,11 1,31 1,00

Benchmark 01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08

Return -12,2% 8,5% 2,9% -0,9% 6,0% -6,4% -2,8% -4,6% -23,2% -29,7% -7,1% 3,7%

Beta 1,90 1,38 0,51 0,45 0,60 0,06 0,13 0,30 0,72 1,59 2,30 2,80


Value Added, Alpha 0,0% 6,4% -2,5% 3,9% -3,6% -3,2% 1,8% 1,9% 1,9% 0,0% 0,0% 0,0%

Tracking Error 3,3% 4,5% 2,2% 3,8% 4,4% 3,7% 1,6% 1,1% 2,5% 4,1% 0,8% 5,0%

Information Ratio 0,00 1,41 -1,14 1,02 -0,81 -0,87 1,14 1,74 0,76 0,00 0,00 0,00



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,28 0,25 0,22 0,23 0,26 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,72 0,75 0,78 0,77 0,74 0,84 0,85 0,85 0,00 0,00 0,00 0,00

Industrials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,55 0,56 0,57 0,46

Technology 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09


Portfolio 01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09

Return Adj. For Trans. Costs -7,2% -12,8% 6,4% 4,3% 8,8% 1,9% 6,3% 2,2% 5,0% -0,7% 2,7% 0,8%

Beta 0,96 0,94 1,00 1,12 1,27 1,00 1,09 1,09 1,00 1,06 1,13 1,00

Benchmark 01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09

Return -2,3% -10,8% 0,3% 16,8% 12,2% 0,2% 6,9% 7,6% 2,0% -2,9% 3,2% -3,2%

Beta 2,88 2,96 3,09 3,33 3,73 3,68 3,65 3,49 2,47 2,63 2,64 2,61



Tracking Error 5,2% 2,5% 9,5% 31,2% 9,9% 4,8% 1,2% 10,5% 2,6% 2,2% 0,5% 4,8%




106


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,12 0,12 0,12 0,46 0,47 0,48 0,42

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,07 0,07 0,07 0,00

Healthcare 0,00 0,00 0,31 0,31 0,30 0,00 0,00 0,00 0,47 0,46 0,45 0,09

Industrials 0,00 0,00 0,00 0,00 0,00 0,66 0,66 0,66 0,00 0,00 0,00 0,48

Oil & Gas 0,46 0,46 0,00 0,00 0,00 0,02 0,02 0,02 0,00 0,00 0,00 0,00

Technology 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,21 0,21 0,21 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10


Portfolio 01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10

Return Adj. For Trans. Costs -4,9% -0,4% 2,7% -1,7% -7,9% -2,7% 7,9% -3,6% 9,4% 3,4% -2,3% 8,8%

Beta 1,10 1,29 1,00 1,02 0,80 1,00 0,44 0,08 0,68 0,81 1,02 1,00

Benchmark 01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10

Return 3,1% -1,3% 7,0% 5,4% -12,1% 0,9% 9,8% -4,9% 11,4% 3,3% -6,6% 10,0%

Beta 2,70 3,35 3,40 2,96 2,08 1,27 0,24 -0,77 -0,54 0,56 1,23 1,45


Value Added, Alpha 12,8% 0,0% 10,3% 13,9% 0,0% 1,0% -0,4% 1,1% -2,4% 0,0% 0,0% 0,5%

Tracking Error 9,8% 1,4% 8,0% 11,5% 5,6% 0,7% 0,2% 1,0% 2,6% 0,3% 0,6% 0,7%

Information Ratio 1,30 0,00 1,28 1,21 0,00 1,46 -2,12 1,07 -0,93 0,04 0,00 0,79



Basic Materials 0,43 0,42 0,00 0,00 0,00 0,00 0,00 0,00 0,18 0,17 0,17 0,45

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,09 0,09 0,98 0,98 0,98 0,47 0,46 0,46 0,00 0,00 0,00 0,00

Industrials 0,48 0,49 0,00 0,00 0,00 0,00 0,00 0,00 0,53 0,53 0,54 0,00

Oil & Gas 0,00 0,00 0,02 0,02 0,02 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Technology 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,27 0,29 0,28 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11


Portfolio 01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11

Return Adj. For Trans. Costs -0,1% 1,9% 0,6% 6,3% 2,0% -1,5% -0,6% -4,2% -12,6% 9,7% -4,1% -2,7%

Beta 1,40 1,46 1,00 1,04 1,38 1,00 0,95 0,75 1,00 1,15 1,27 1,00

Benchmark 01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11

Return 2,0% 4,9% 1,6% 2,8% -4,9% -4,9% -3,6% -14,6% -9,6% 7,2% 2,9% 0,7%

Beta 1,91 2,14 2,55 2,70 3,17 3,33 3,02 3,47 2,97 3,47 4,03 4,10



Tracking Error 0,3% 1,6% 1,4% 5,9% 12,6% 6,5% 5,2% 20,9% 4,8% 4,7% 11,6% 6,2%




107

Appendix 6 (continued): Restricted Portfolio Positions of Investment Opportunities


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,20

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,20 0,20 0,20 0,19 0,18 0,20 0,20 0,20 0,20 0,20 0,21 0,20

Healthcare 0,20 0,20 0,20 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,17

Industrials 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,19 0,20 0,20 0,20 0,20

Oil & Gas 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,19 0,00

Technology 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Utilities 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92


Portfolio 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Return Adj. For Trans. Costs -2,9% -2,6% -4,8% 0,7% 3,7% -3,2% 0,0% 2,8% -2,1% -4,0% 0,8% 0,2%

Beta 0,19 0,45 0,30 0,39 0,39 0,44 0,52 0,56 0,60 0,54 0,75 1,00

Benchmark 01-92 02-92 03-92 04-92 05-92 06-92 07-92 08-92 09-92 10-92 11-92 12-92

Return -1,4% -6,0% -8,0% 0,0% 11,6% -5,3% -0,5% -7,7% -5,9% -9,7% -0,7% -0,9%

Beta 0,52 0,71 0,71 0,91 1,00 0,76 0,75 0,79 0,96 1,37 1,90 2,78



Tracking Error 7,0% 11,2% 8,0% 9,0% 14,3% 7,1% 8,6% 20,5% 12,1% 15,1% 10,4% 10,5%



Portfolio Weight (mm.yy) 01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93

Basic Materials 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,02 0,02 0,02 0,07 0,07 0,07 0,05 0,05 0,05 0,00


Finance 0,20 0,20 0,20 0,20 0,20 0,14 0,14 0,15 0,11 0,11 0,11 0,10

Healthcare 0,17 0,17 0,00 0,00 0,00 0,06 0,06 0,06 0,08 0,08 0,08 0,10

Industrials 0,20 0,20 0,00 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Oil & Gas 0,00 0,00 0,12 0,12 0,12 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Technology 0,00 0,00 0,20 0,20 0,20 0,13 0,13 0,12 0,17 0,17 0,17 0,20


Utilities 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93


Portfolio 01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93

Return Adj. For Trans. Costs -0,1% 2,1% 7,1% 4,2% 2,7% -1,7% 2,6% 3,6% -1,7% 2,0% -5,3% 5,4%

Beta 0,32 -0,68 0,56 0,87 1,04 1,00 1,03 1,00 1,00 1,05 1,08 1,00

Benchmark 01-93 02-93 03-93 04-93 05-93 06-93 07-93 08-93 09-93 10-92 11-92 12-93

Return 12,4% -4,7% 1,2% 4,8% 2,0% 1,2% -3,8% 4,3% 3,4% 4,0% -3,1% 5,8%

Beta 2,35 0,30 -0,28 -0,37 -0,21 0,10 0,35 0,41 0,55 0,73 0,76 0,73


Value Added, Alpha 25,3% 0,0% 5,0% -0,7% 0,8% -2,6% 4,3% -0,4% -2,3% -0,6% -0,7% -0,1%

Tracking Error 33,5% 19,4% 16,4% 10,1% 11,2% 11,0% 16,8% 4,6% 12,7% 6,5% 11,6% 6,5%

Information Ratio 0,76 0,00 0,31 -0,07 0,07 -0,23 0,26 -0,09 -0,18 -0,09 -0,06 -0,02



108


Basic Materials 0,00 0,00 0,17 0,17 0,17 0,08 0,08 0,08 0,20 0,20 0,20 0,20

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,20 0,00


Finance 0,10 0,10 0,20 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Healthcare 0,10 0,10 0,20 0,20 0,20 0,20 0,20 0,20 0,00 0,00 0,00 0,20

Industrials 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Oil & Gas 0,20 0,20 0,20 0,20 0,20 0,19 0,19 0,19 0,20 0,20 0,20 0,20

Technology 0,20 0,20 0,03 0,03 0,03 0,13 0,13 0,13 0,20 0,20 0,21 0,00


Utilities 0,20 0,19 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94


Portfolio 01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94

Return Adj. For Trans. Costs 5,7% -0,5% -4,3% 3,2% 0,4% 0,2% 1,7% 3,4% -2,4% 3,3% -5,6% 0,1%

Beta 0,93 0,99 1,00 0,79 0,77 0,87 0,79 0,81 1,00 0,98 0,81 0,05

Benchmark 01-94 02-94 03-94 04-94 05-94 06-94 07-94 08-94 09-94 10-94 11-94 12-94

Return 8,2% 0,3% -1,5% 1,6% -8,0% 4,3% 4,7% -7,4% 0,2% 1,8% -4,3% 2,5%

Beta 0,69 1,24 1,36 1,37 1,42 1,35 1,24 1,22 0,92 0,65 0,44 -0,21


Value Added, Alpha -0,6% 0,2% 1,0% 0,0% 0,0% 2,0% 1,4% 0,0% -0,2% 0,5% -0,5% -0,6%

Tracking Error 6,0% 7,4% 7,9% 7,8% 15,5% 10,5% 7,4% 16,1% 6,0% 5,3% 5,6% 5,8%

Information Ratio -0,10 0,03 0,13 0,00 0,00 0,19 0,19 0,00 -0,03 0,09 -0,09 -0,11



Basic Materials 0,20 0,20 0,20 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,12


Finance 0,00 0,00 0,20 0,20 0,20 0,20 0,19 0,20 0,19 0,19 0,19 0,00

Healthcare 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,21 0,21 0,20

Industrials 0,20 0,20 0,20 0,20 0,20 0,00 0,00 0,00 0,20 0,20 0,20 0,08

Oil & Gas 0,20 0,20 0,20 0,20 0,20 0,20 0,19 0,19 0,15 0,15 0,15 0,20

Technology 0,00 0,00 0,00 0,00 0,00 0,20 0,21 0,22 0,20 0,20 0,20 0,20


Utilities 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,19 0,05 0,06 0,06 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95


Portfolio 01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95

Return Adj. For Trans. Costs -2,4% 0,0% 4,2% 3,2% 0,1% 0,5% 4,0% -2,2% 2,4% -1,0% 2,1% 2,2%

Beta 0,35 0,38 0,19 0,22 0,43 0,79 0,80 0,97 1,00 1,08 1,20 1,00

Benchmark 01-95 02-95 03-95 04-95 05-95 06-95 07-95 08-95 09-95 10-95 11-95 12-95

Return 1,3% 2,8% -0,7% 4,6% 4,1% -1,7% 6,7% -5,5% 1,5% 0,1% 0,4% 2,3%

Beta 0,16 0,09 0,59 0,48 0,75 0,94 0,87 1,08 1,00 1,00 0,99 0,82


Value Added, Alpha -0,7% -0,8% 0,0% 0,4% 1,3% 0,0% 0,2% 0,0% 0,0% -0,1% 0,4% 0,0%

Tracking Error 8,3% 8,5% 9,5% 5,1% 10,1% 8,6% 9,0% 11,3% 6,4% 5,9% 8,4% 13,5%

Information Ratio -0,09 -0,10 0,00 0,07 0,13 0,00 0,02 0,00 0,00 -0,01 0,04 0,00



109


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,13 0,13 0,04 0,04 0,05 0,18 0,18 0,18 0,13 0,13 0,13 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,02 0,02 0,02 0,06

Healthcare 0,20 0,20 0,20 0,20 0,19 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Industrials 0,08 0,08 0,20 0,20 0,20 0,05 0,05 0,05 0,14 0,14 0,13 0,18

Oil & Gas 0,21 0,21 0,20 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Technology 0,19 0,19 0,16 0,15 0,16 0,06 0,06 0,06 0,07 0,07 0,07 0,16


Utilities 0,20 0,20 0,20 0,20 0,19 0,20 0,20 0,20 0,20 0,19 0,20 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96


Portfolio 01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96

Return Adj. For Trans. Costs 1,5% 1,3% 0,5% 3,3% 0,3% 0,6% -4,2% 1,0% 2,9% 0,7% 4,8% -1,0%

Beta 1,05 1,06 1,00 0,90 0,95 1,00 1,00 1,12 1,00 1,20 0,80 1,00

Benchmark 01-96 02-96 03-96 04-96 05-96 06-96 07-96 08-96 09-96 10-96 11-96 12-96

Return 3,2% 1,3% -2,6% -0,8% 0,2% 2,5% 1,4% 3,5% -0,4% 3,2% 2,3% 4,5%

Beta 0,76 0,78 0,77 0,56 0,44 0,42 0,38 0,58 0,66 0,85 0,89 0,99


Value Added, Alpha -0,5% 0,0% 0,7% 1,4% 0,1% -1,1% -3,5% -1,4% 1,1% -0,9% 0,0% 0,0%

Tracking Error 7,2% 7,8% 9,8% 7,6% 7,9% 6,5% 13,5% 9,7% 10,4% 8,4% 6,1% 11,7%

Information Ratio -0,07 0,00 0,07 0,18 0,01 -0,17 -0,26 -0,14 0,11 -0,10 0,00 0,00



Basic Materials 0,00 0,00 0,08 0,08 0,08 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,06 0,06 0,20 0,20 0,20 0,04 0,04 0,04 0,10 0,10 0,10 0,20

Healthcare 0,20 0,20 0,12 0,12 0,12 0,20 0,20 0,20 0,20 0,20 0,21 0,20

Industrials 0,18 0,18 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,19 0,00

Oil & Gas 0,20 0,20 0,00 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Technology 0,16 0,16 0,20 0,20 0,21 0,20 0,20 0,22 0,10 0,10 0,10 0,16


Utilities 0,20 0,19 0,00 0,00 0,00 0,16 0,16 0,15 0,20 0,20 0,21 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97


Portfolio 01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97

Return Adj. For Trans. Costs 2,4% -0,8% -2,8% 3,1% 7,4% 4,3% 5,2% -6,0% 4,3% -5,9% 0,5% 1,2%

Beta 1,02 1,15 1,00 0,89 0,80 1,00 1,07 1,23 1,00 1,04 0,96 1,00

Benchmark 01-97 02-97 03-97 04-97 05-97 06-97 07-97 08-97 09-97 10-97 11-97 12-97

Return 3,9% -0,7% 3,0% -3,2% 7,2% 2,0% 6,2% -5,2% 10,8% -4,6% 1,0% 8,1%

Beta 1,22 1,57 1,79 1,88 1,38 1,15 0,99 1,09 1,01 1,04 1,00 0,93


Value Added, Alpha 0,3% 0,1% 4,6% 0,0% 0,0% 0,0% -0,1% -0,1% 0,1% 0,0% 0,0% -0,5%

Tracking Error 11,8% 8,2% 16,5% 15,9% 7,6% 7,4% 11,9% 7,0% 12,4% 7,7% 6,6% 14,0%

Information Ratio 0,03 0,01 0,28 0,00 0,00 0,00 -0,01 -0,02 0,01 0,00 0,00 -0,03



110


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,20 0,21 0,20 0,20 0,20 0,20 0,19 0,19 0,20 0,19 0,20 0,20

Healthcare 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Industrials 0,00 0,00 0,00 0,00 0,00 0,05 0,04 0,04 0,00 0,00 0,00 0,20

Oil & Gas 0,20 0,19 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,02

Technology 0,15 0,16 0,20 0,20 0,21 0,20 0,21 0,21 0,20 0,21 0,21 0,20


Utilities 0,20 0,20 0,10 0,10 0,10 0,00 0,00 0,00 0,00 0,00 0,00 0,04

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98


Portfolio 01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98

Return Adj. For Trans. Costs 1,3% 6,0% 4,1% 0,8% -2,2% 2,7% 1,1% -15,3% 2,0% 8,8% 6,7% 5,6%

Beta 0,92 0,78 1,00 1,03 1,04 1,00 1,06 0,92 0,90 0,90 0,77 0,75

Benchmark 01-98 02-98 03-98 04-98 05-98 06-98 07-98 08-98 09-98 10-98 11-98 12-98

Return 0,3% 2,3% 11,1% -4,4% 2,7% -2,3% 2,9% -12,0% -4,7% 7,2% -5,0% 9,5%

Beta 1,03 1,11 1,13 1,50 1,44 1,43 1,40 1,10 0,96 0,88 0,58 0,03


Value Added, Alpha 0,0% 0,0% 0,9% 0,0% 2,0% 0,0% 0,6% 0,6% 0,0% 0,0% 2,2% -2,8%

Tracking Error 7,9% 7,2% 10,3% 11,5% 10,6% 11,2% 8,9% 6,4% 9,7% 5,2% 13,3% 13,2%

Information Ratio 0,00 0,00 0,09 0,00 0,19 0,00 0,07 0,09 0,00 0,01 0,16 -0,21



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,21 0,02 0,02 0,02 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,12 0,12 0,12 0,00 0,00 0,00 0,00


Finance 0,19 0,18 0,15 0,15 0,15 0,07 0,06 0,06 0,20 0,20 0,21 0,17

Healthcare 0,20 0,19 0,20 0,20 0,19 0,11 0,11 0,11 0,20 0,19 0,19 0,02

Industrials 0,20 0,19 0,00 0,00 0,00 0,06 0,06 0,06 0,04 0,04 0,04 0,18

Oil & Gas 0,01 0,01 0,00 0,00 0,00 0,10 0,10 0,10 0,14 0,14 0,13 0,17

Technology 0,21 0,24 0,20 0,21 0,21 0,02 0,02 0,02 0,00 0,00 0,00 0,06


Utilities 0,04 0,04 0,20 0,19 0,19 0,20 0,19 0,19 0,20 0,20 0,19 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99


Portfolio 01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99

Return Adj. For Trans. Costs 3,8% -4,1% 2,6% 2,7% -1,6% 3,8% 0,7% -0,1% -1,6% 4,6% 2,6% 5,9%

Beta 0,85 1,03 1,00 1,06 1,14 0,47 0,53 0,79 1,00 0,70 0,62 1,00

Benchmark 01-99 02-99 03-99 04-99 05-99 06-99 07-99 08-99 09-99 10-99 11-99 12-99

Return -3,7% -9,1% -1,8% 6,9% -2,9% 1,0% 6,7% 0,2% 2,9% 1,2% 3,3% 5,6%

Beta -0,02 -0,10 -0,29 -0,43 -0,41 -0,39 -0,35 -0,06 -0,02 -0,04 0,39 0,53


Value Added, Alpha 6,5% 5,6% 5,8% -6,2% 2,0% 2,4% -5,2% -0,3% -4,7% 2,5% -0,2% 0,1%

Tracking Error 25,3% 15,5% 24,2% 20,6% 10,9% 11,7% 13,5% 8,7% 14,5% 19,1% 18,5% 20,1%

Information Ratio 0,26 0,36 0,24 -0,30 0,19 0,20 -0,39 -0,03 -0,32 0,13 -0,01 0,01



111


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,16 0,16 0,15 0,15 0,15 0,16 0,16 0,17 0,20 0,21 0,21 0,06

Healthcare 0,02 0,02 0,04 0,04 0,04 0,00 0,00 0,00 0,00 0,00 0,00 0,20

Industrials 0,19 0,19 0,20 0,20 0,20 0,20 0,20 0,20 0,05 0,05 0,05 0,20

Oil & Gas 0,17 0,16 0,14 0,14 0,15 0,13 0,13 0,13 0,19 0,19 0,19 0,10

Technology 0,07 0,07 0,03 0,03 0,03 0,03 0,04 0,03 0,17 0,14 0,13 0,20


Utilities 0,19 0,19 0,20 0,20 0,21 0,20 0,20 0,20 0,20 0,22 0,22 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00


Portfolio 01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00

Return Adj. For Trans. Costs -4,1% 0,3% 5,7% -5,1% -0,9% 1,4% -2,7% 3,7% -4,3% -3,4% -7,5% 1,4%

Beta 1,27 1,40 1,00 1,01 0,99 1,00 0,99 0,84 1,00 0,31 0,46 1,00

Benchmark 01-00 02-00 03-00 04-00 05-00 06-00 07-00 08-00 09-00 10-00 11-00 12-00

Return -5,6% 3,5% 8,8% -9,6% 6,5% -0,2% 2,0% 5,6% -2,0% -4,7% -5,1% 3,6%

Beta 0,84 1,09 1,00 1,06 1,10 1,06 0,90 0,88 0,22 -0,64 -0,57 -0,18


Value Added, Alpha 0,7% -1,0% 0,0% 0,0% 0,8% 0,0% -0,4% 0,1% -1,8% 1,2% -2,4% -2,6%

Tracking Error 10,7% 22,3% 17,5% 18,6% 25,8% 16,0% 19,4% 16,5% 33,1% 16,8% 28,8% 37,1%

Information Ratio 0,06 -0,04 0,00 0,00 0,03 0,00 -0,02 0,00 -0,05 0,07 -0,08 -0,07



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,06 0,06 0,20 0,20 0,19 0,20 0,21 0,21 0,20 0,20 0,19 0,20

Healthcare 0,20 0,19 0,00 0,00 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,00

Industrials 0,20 0,20 0,04 0,03 0,04 0,06 0,06 0,06 0,01 0,01 0,01 0,15

Oil & Gas 0,10 0,10 0,20 0,20 0,21 0,17 0,16 0,17 0,18 0,18 0,18 0,12

Technology 0,18 0,20 0,10 0,09 0,10 0,08 0,08 0,08 0,12 0,10 0,11 0,06


Utilities 0,21 0,20 0,20 0,21 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01


Portfolio 01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01

Return Adj. For Trans. Costs 0,2% -8,8% -6,4% 7,4% -2,4% -4,4% -2,8% -4,8% -9,3% 1,7% 3,3% 1,4%

Beta 1,06 1,21 1,00 0,97 1,00 1,00 0,98 1,07 1,00 0,96 0,97 1,00

Benchmark 01-01 02-01 03-01 04-01 05-01 06-01 07-01 08-01 09-01 10-01 11-01 12-01

Return 11,1% -9,5% -10,6% 1,9% -0,2% -1,7% 3,4% -5,6% -9,2% 2,0% 1,1% 0,1%

Beta -0,14 -0,37 -0,12 0,01 0,20 0,35 0,50 0,61 0,54 0,65 0,71 0,88


Value Added, Alpha -13,1% 1,0% 4,7% 5,3% -1,8% -1,7% -3,0% 0,4% 0,0% -0,1% 0,6% 0,2%

Tracking Error 25,4% 55,1% 17,0% 29,3% 20,4% 13,1% 24,6% 20,3% 25,7% 22,5% 22,0% 6,3%

Information Ratio -0,52 0,02 0,28 0,18 -0,09 -0,13 -0,12 0,02 0,00 0,00 0,03 0,02



112


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00


Finance 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,19 0,19 0,18 0,20

Healthcare 0,00 0,00 0,00 0,00 0,00 0,02 0,02 0,02 0,20 0,22 0,21 0,14

Industrials 0,15 0,15 0,20 0,20 0,20 0,20 0,20 0,21 0,00 0,00 0,00 0,20

Oil & Gas 0,12 0,13 0,11 0,12 0,12 0,00 0,00 0,00 0,00 0,00 0,00 0,01

Technology 0,06 0,07 0,09 0,09 0,08 0,18 0,18 0,17 0,20 0,18 0,20 0,13


Utilities 0,20 0,20 0,20 0,20 0,21 0,20 0,21 0,20 0,18 0,19 0,17 0,20

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02


Portfolio 01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02

Return Adj. For Trans. Costs -4,4% -1,0% 4,9% -3,4% -0,2% -7,7% -8,0% 0,0% -12,6% 8,5% 5,9% -4,4%

Beta 1,13 0,96 1,00 1,20 1,10 1,00 0,66 0,74 0,85 1,00 1,13 1,00

Benchmark 01-02 02-02 03-02 04-02 05-02 06-02 07-02 08-02 09-02 10-02 11-02 12-02

Return -5,5% 2,4% 3,0% -4,1% 2,2% 1,2% -13,6% 3,2% -14,5% 2,7% 4,0% 0,4%

Beta 1,13 0,85 0,75 0,86 0,93 0,71 0,21 0,34 0,42 0,65 0,75 0,79


Value Added, Alpha 0,0% -0,4% 0,5% 0,2% -0,4% -2,6% 2,5% -1,3% 0,8% 2,1% 0,7% -1,0%

Tracking Error 10,1% 12,7% 7,8% 12,6% 11,4% 22,7% 12,7% 13,3% 13,6% 21,8% 19,3% 18,3%

Information Ratio 0,00 -0,03 0,06 0,02 -0,04 -0,12 0,20 -0,10 0,06 0,09 0,04 -0,06



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,20

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,00


Finance 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,21 0,21 0,20

Healthcare 0,15 0,14 0,06 0,06 0,06 0,20 0,20 0,19 0,00 0,00 0,00 0,20

Industrials 0,19 0,19 0,20 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,09

Oil & Gas 0,01 0,01 0,06 0,06 0,06 0,00 0,00 0,00 0,13 0,13 0,13 0,20

Technology 0,12 0,12 0,05 0,05 0,05 0,20 0,20 0,20 0,07 0,07 0,07 0,00


Utilities 0,22 0,22 0,18 0,19 0,19 0,00 0,00 0,00 0,00 0,00 0,00 0,11

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03


Portfolio 01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03

Return Adj. For Trans. Costs -2,2% -2,1% -0,7% 8,6% 5,9% 2,1% 3,4% 3,4% 0,5% 6,5% 1,1% 7,6%

Beta 0,95 0,96 1,00 0,98 0,90 0,70 0,72 0,88 1,00 0,99 1,09 1,00

Benchmark 01-03 02-03 03-03 04-03 05-03 06-03 07-03 08-03 09-03 10-03 11-03 12-03

Return -4,5% -4,6% 7,5% 11,5% 6,7% -0,4% -2,0% 8,5% 3,7% 6,2% -0,5% 6,5%

Beta 0,76 0,84 1,00 0,96 1,16 1,22 1,23 1,25 1,79 1,76 1,85 1,71


Value Added, Alpha 0,4% 0,3% 0,0% -0,1% 0,2% 0,0% 0,0% 1,8% 2,5% 0,0% 0,0% 0,0%

Tracking Error 8,7% 8,5% 11,0% 6,9% 3,1% 8,8% 12,3% 10,0% 11,0% 8,6% 8,4% 10,6%

Information Ratio 0,05 0,04 0,00 -0,01 0,06 0,00 0,00 0,18 0,23 0,00 0,00 0,00



113


Basic Materials 0,20 0,20 0,04 0,04 0,04 0,14 0,14 0,15 0,18 0,18 0,18 0,20

Consumer Goods 0,00 0,00 0,20 0,20 0,21 0,20 0,20 0,21 0,20 0,20 0,19 0,00


Finance 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20

Healthcare 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,09 0,09 0,00 0,00 0,00 0,00 0,00 0,00 0,02 0,02 0,02 0,20

Oil & Gas 0,21 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20

Technology 0,00 0,00 0,16 0,16 0,15 0,20 0,20 0,19 0,20 0,20 0,20 0,17


Utilities 0,11 0,11 0,20 0,20 0,20 0,06 0,06 0,06 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04


Portfolio 01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04

Return Adj. For Trans. Costs 0,6% 2,9% 0,2% -3,4% -0,4% 2,7% -4,0% -0,3% 2,3% 2,8% 5,5% 2,8%

Beta 1,14 1,25 1,00 0,98 0,92 1,00 0,97 0,89 1,00 0,56 0,27 1,00

Benchmark 01-04 02-04 03-04 04-04 05-04 06-04 07-04 08-04 09-04 10-04 11-04 12-04

Return 4,5% 5,6% -5,3% -1,7% 0,4% 5,7% -1,9% 1,7% 6,0% -0,9% 7,4% 3,7%

Beta 1,78 1,88 2,07 2,08 2,08 2,16 2,25 2,05 2,21 2,14 1,75 1,82



Tracking Error 12,2% 8,6% 17,6% 8,7% 10,0% 12,8% 12,6% 11,4% 14,6% 17,7% 14,1% 5,6%




Basic Materials 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,00 0,00 0,00 0,04 0,04 0,04 0,20 0,20 0,20 0,20


Finance 0,20 0,20 0,20 0,20 0,20 0,16 0,16 0,16 0,20 0,20 0,20 0,11

Healthcare 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Industrials 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20

Oil & Gas 0,19 0,20 0,01 0,01 0,01 0,00 0,00 0,00 0,00 0,00 0,00 0,09

Technology 0,17 0,17 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05


Portfolio 01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05

Return Adj. For Trans. Costs -1,3% 5,1% -2,6% -3,4% 2,3% 0,1% 3,9% -0,1% 2,7% -2,4% 4,9% 2,5%

Beta 1,24 1,26 1,00 1,12 1,10 1,00 1,09 1,14 1,00 0,93 0,67 1,00

Benchmark 01-05 02-05 03-05 04-05 05-05 06-05 07-05 08-05 09-05 10-05 11-05 12-05

Return -2,7% 7,4% -0,3% -3,5% 2,7% 1,7% 3,1% 4,9% 0,7% -2,2% 2,2% 6,3%

Beta 2,15 2,06 2,37 2,48 2,41 2,30 2,39 2,44 2,55 2,99 2,32 2,17



Tracking Error 9,0% 14,6% 12,7% 7,0% 14,0% 10,5% 7,8% 17,5% 14,3% 9,6% 14,3% 17,4%




114


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,19 0,00


Finance 0,11 0,12 0,05 0,05 0,05 0,00 0,00 0,00 0,08 0,08 0,08 0,20

Healthcare 0,00 0,00 0,00 0,00 0,00 0,06 0,06 0,07 0,00 0,00 0,00 0,06

Industrials 0,20 0,20 0,20 0,20 0,20 0,14 0,14 0,13 0,20 0,20 0,20 0,20

Oil & Gas 0,09 0,09 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Technology 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,19 0,20 0,20 0,20 0,20


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06


Portfolio 01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06

Return Adj. For Trans. Costs 4,8% -0,3% 2,3% 2,6% -5,0% -0,7% -0,4% 3,4% 2,1% 3,9% 3,1% 2,4%

Beta 1,05 1,23 1,00 1,09 1,18 1,00 0,92 0,84 1,00 0,99 0,81 1,00

Benchmark 01-06 02-06 03-06 04-06 05-06 06-06 07-06 08-06 09-06 10-06 11-06 12-06

Return 2,4% 0,4% 5,2% 5,8% -4,5% -1,1% -0,4% 6,3% 2,4% 4,3% 6,3% 4,3%

Beta 2,14 2,19 2,20 2,40 2,68 2,85 2,79 2,65 2,78 3,19 3,08 3,20



Tracking Error 9,9% 8,9% 13,2% 14,6% 10,3% 8,8% 15,3% 16,8% 9,9% 10,9% 17,8% 15,5%




Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,20


Finance 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,11 0,11 0,11 0,20

Healthcare 0,06 0,06 0,00 0,00 0,00 0,19 0,19 0,18 0,09 0,09 0,09 0,00

Industrials 0,20 0,20 0,20 0,20 0,20 0,01 0,01 0,01 0,00 0,00 0,00 0,12

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Technology 0,19 0,19 0,20 0,20 0,20 0,20 0,20 0,21 0,20 0,20 0,20 0,20


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07


Portfolio 01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07

Return Adj. For Trans. Costs 1,6% -0,7% 1,6% 3,9% 3,1% -0,7% -1,3% 1,1% 3,9% 4,8% -4,5% -1,7%

Beta 1,06 1,22 1,00 0,95 1,07 1,00 1,05 1,02 1,00 0,88 0,93 1,00

Benchmark 01-07 02-07 03-07 04-07 05-07 06-07 07-07 08-07 09-07 10-07 11-07 12-07

Return 2,7% 0,2% 4,0% 6,6% 2,1% -2,6% 3,7% -0,5% 5,4% 4,0% -4,0% 0,1%

Beta 3,42 3,75 3,75 3,59 3,92 4,28 4,63 4,83 4,91 4,44 4,45 4,19



Tracking Error 12,3% 12,0% 17,2% 18,7% 14,4% 19,5% 28,4% 18,3% 19,1% 17,4% 18,7% 18,4%




115


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,19 0,16 0,14 0,00

Consumer Goods 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,03 0,03 0,03 0,00


Finance 0,20 0,20 0,20 0,20 0,20 0,20 0,19 0,19 0,20 0,21 0,20 0,20

Healthcare 0,00 0,00 0,20 0,20 0,19 0,20 0,21 0,22 0,15 0,16 0,19 0,20

Industrials 0,12 0,11 0,20 0,20 0,20 0,20 0,20 0,19 0,20 0,20 0,19 0,00

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,04 0,04 0,04 0,00 0,00 0,00 0,08

Technology 0,20 0,19 0,20 0,20 0,20 0,20 0,20 0,19 0,20 0,20 0,21 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,12

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08


Portfolio 01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08

Return Adj. For Trans. Costs -9,2% -0,6% -1,7% 3,8% 0,9% -9,8% -0,2% -1,4% -16,9% -24,8% -8,7% 4,8%

Beta 0,60 0,72 1,00 1,15 1,23 1,00 1,09 1,13 1,00 1,06 1,19 1,00

Benchmark 01-08 02-08 03-08 04-08 05-08 06-08 07-08 08-08 09-08 10-08 11-08 12-08

Return -12,2% 8,5% 2,9% -0,9% 6,0% -6,4% -2,8% -4,6% -23,2% -29,7% -7,1% 3,7%

Beta 1,90 1,38 0,51 0,45 0,60 0,06 0,13 0,30 0,72 1,59 2,30 2,80


Value Added, Alpha 0,0% 6,0% -2,3% 3,3% -3,2% -3,2% 2,5% 2,7% 1,8% 0,0% 1,9% 0,0%

Tracking Error 15,5% 16,8% 11,5% 15,5% 16,7% 17,9% 14,7% 10,1% 17,0% 19,1% 12,7% 14,8%

Information Ratio 0,00 0,36 -0,20 0,21 -0,19 -0,18 0,17 0,27 0,10 0,00 0,15 0,00



Basic Materials 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,00 0,00 0,08 0,08 0,08 0,20 0,20 0,21 0,11 0,11 0,11 0,12


Finance 0,20 0,18 0,20 0,21 0,23 0,00 0,00 0,00 0,20 0,20 0,20 0,20

Healthcare 0,20 0,22 0,20 0,20 0,18 0,00 0,00 0,00 0,20 0,20 0,20 0,20

Industrials 0,00 0,00 0,12 0,12 0,13 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Oil & Gas 0,08 0,08 0,00 0,00 0,00 0,11 0,11 0,10 0,00 0,00 0,00 0,00

Technology 0,00 0,00 0,00 0,00 0,00 0,09 0,09 0,09 0,20 0,20 0,20 0,08


Utilities 0,12 0,12 0,00 0,00 0,00 0,20 0,20 0,20 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09


Portfolio 01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09

Return Adj. For Trans. Costs -9,1% -9,9% 6,1% 9,1% 8,3% -0,2% 6,6% 2,0% 4,0% -1,8% 3,7% 1,4%

Beta 0,96 0,96 1,00 1,09 1,19 1,00 0,96 0,96 1,00 1,08 1,12 1,00

Benchmark 01-09 02-09 03-09 04-09 05-09 06-09 07-09 08-09 09-09 10-09 11-09 12-09

Return -2,3% -10,8% 0,3% 16,8% 12,2% 0,2% 6,9% 7,6% 2,0% -2,9% 3,2% -3,2%

Beta 2,88 2,96 3,09 3,33 3,73 3,68 3,65 3,49 2,47 2,63 2,64 2,61



Tracking Error 24,8% 18,1% 22,1% 33,9% 24,8% 10,7% 15,3% 26,0% 11,6% 10,1% 10,0% 18,3%




116


Basic Materials 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,20 0,20 0,21 0,20

Consumer Goods 0,13 0,13 0,20 0,20 0,20 0,10 0,10 0,10 0,00 0,00 0,00 0,20


Finance 0,20 0,19 0,07 0,07 0,07 0,10 0,10 0,11 0,20 0,20 0,20 0,00

Healthcare 0,20 0,21 0,20 0,19 0,19 0,00 0,00 0,00 0,20 0,20 0,20 0,20

Industrials 0,00 0,00 0,00 0,00 0,00 0,20 0,20 0,20 0,10 0,10 0,10 0,20

Oil & Gas 0,00 0,00 0,00 0,00 0,00 0,09 0,09 0,09 0,19 0,19 0,19 0,20

Technology 0,08 0,08 0,20 0,20 0,21 0,01 0,01 0,01 0,00 0,00 0,00 0,00


Utilities 0,00 0,00 0,00 0,00 0,00 0,19 0,19 0,19 0,11 0,10 0,10 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10


Portfolio 01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10

Return Adj. For Trans. Costs -3,0% 0,8% 4,8% -0,1% -8,8% -2,8% 7,9% -2,8% 8,8% 3,3% -2,9% 7,7%

Beta 1,13 1,41 1,44 1,45 1,18 1,00 0,53 0,25 0,43 0,58 0,76 0,83

Benchmark 01-10 02-10 03-10 04-10 05-10 06-10 07-10 08-10 09-10 10-10 11-10 12-10

Return 3,1% -1,3% 7,0% 5,4% -12,1% 0,9% 9,8% -4,9% 11,4% 3,3% -6,6% 10,0%

Beta 2,70 3,35 3,40 2,96 2,08 1,27 0,24 -0,77 -0,54 0,56 1,23 1,45


Value Added, Alpha 9,6% 0,0% 4,2% 8,4% 0,0% 1,0% -0,5% 2,1% -2,5% 0,0% 0,0% 1,4%

Tracking Error 21,1% 13,8% 14,3% 18,8% 13,1% 8,1% 4,3% 11,0% 11,8% 3,7% 8,9% 10,2%

Information Ratio 0,46 0,00 0,30 0,45 0,00 0,13 -0,13 0,19 -0,21 0,00 0,00 0,14



Basic Materials 0,21 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

Consumer Goods 0,20 0,19 0,20 0,20 0,20 0,20 0,20 0,20 0,00 0,00 0,00 0,00


Finance 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,20 0,19 0,19 0,20

Healthcare 0,19 0,19 0,20 0,20 0,20 0,20 0,20 0,20 0,20 0,21 0,20 0,20

Industrials 0,20 0,20 0,00 0,00 0,00 0,00 0,00 0,00 0,10 0,10 0,10 0,01

Oil & Gas 0,20 0,21 0,20 0,20 0,20 0,00 0,00 0,00 0,20 0,19 0,20 0,20

Technology 0,00 0,00 0,06 0,05 0,05 0,13 0,13 0,13 0,20 0,21 0,21 0,20


Utilities 0,00 0,00 0,00 0,00 0,00 0,07 0,07 0,07 0,00 0,00 0,00 0,00

Total 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11


Portfolio 01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11

Return Adj. For Trans. Costs 0,4% 2,9% 0,6% 4,2% -1,2% -1,4% -0,8% -5,3% -9,6% 10,0% -3,4% -0,2%

Beta 1,17 1,28 1,00 1,04 1,27 1,00 0,93 0,81 1,00 1,08 1,08 1,00

Benchmark 01-11 02-11 03-11 04-11 05-11 06-11 07-11 08-11 09-11 10-11 11-11 12-11

Return 2,0% 4,9% 1,6% 2,8% -4,9% -4,9% -3,6% -14,6% -9,6% 7,2% 2,9% 0,7%

Beta 1,91 2,14 2,55 2,70 3,17 3,33 3,02 3,47 2,97 3,47 4,03 4,10



Tracking Error 9,8% 10,9% 9,6% 13,3% 20,3% 20,1% 16,7% 33,4% 19,2% 19,3% 28,6% 16,1%




117

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