Smart Beta
Alternative Concepts in Passive Portfolio Management
©2014
Master's Thesis
75 Pages
Summary
In economics, each and every rational decision made is supposed to maximize individual utility. This approach especially applies to the investor in financial goods. In accordance with neoclassical utility optimization, the individual investors are supposed to be willing to exchange investment good in order to maximize their expected future return. This approach anticipates every individual investor to try and estimate the future cash flows of the investment in order to evaluate its current value. Hence, trades at every stock exchange are to be executed at all times where you have two investors differing in their estimation of the intrinsic value of an investment product. As a consequence, every investor is supposed to create a portfolio with assets that in turn maximize his/her expected return. Every investor is supposed to make an individual and rational attempt to maximize his/her utility and to behave in a risk-averse manner. However, according to the neoclassical theory, it is not possible to gain more from an investment than the market does, as long as markets are efficient. Financial markets can be seen as the most efficient markets, if not the only efficient markets in real economy, as, in the market context, information is transferred the fastest and prices are thus adopted nearly instantly. Nevertheless, all investors at the stock exchanges try to make money by using their individual knowledge in order to gain something from investing in some assets. They have of course, at the same time, the possibility to follow the market themselves or to try to bet against the market. Every investor hence always faces the question of whether to trade on the market with his/her own individual knowledge in order to gain some additional utility, or to simply attempt to do the same as the whole market and follow the belief of the market at a whole. The question thus arises of what exactly efficient fund management looks like. This paper will discuss several possibilities which arise in literature and in the real economy when thinking about fund management, and will discuss the rather new concept of “Smart Beta” investments, in particular. The focus of this paper thus lies in the question of whether smart beta concepts serve as potential superior alternatives to the classical passive investment products.
Excerpt
Table Of Contents
Troberg, Romedius: Smart Beta: Alternative Concepts in Passive Portfolio
Management, Hamburg, Anchor Academic Publishing 2015
PDF-eBook-ISBN: 978-3-95489-908-1
Druck/Herstellung: Anchor Academic Publishing, Hamburg, 2015
Additionally: Leopold-Franzens-Universität Innsbruck, Innsbruck, Deutschland, Master
Thesis, 2014
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- 4 -
Table of Contents
List of Figures ... 1
List of Tables ... 2
List of Abbreviations ... 3
Introduction Why new concepts like Smart Beta? ... 4
1. Traditional Concepts ... 6
1.1. Active Fund Management and the Alpha ... 8
1.2. Passive Fund Management and the Beta ... 10
2. Market Capitalization Weights (CW) ... 13
3. Smart Beta Concepts ... 16
3.1. Fundamental Weights (FW) ... 18
3.2. Style Indices ... 21
3.2.1. Max. Deconcentration (MD)/Equal Weighting (EW) ... 21
3.2.2. Diversity Weights (DW) ... 23
3.3.3. Most Diversified Portfolio (MDP) ... 25
3.3.4. Global Minimum Variance (GMV) ... 26
3.3.5. Risk Parity (RP) also known as Equal Risk Contribution (ERC) ... 28
3.3.6. Maximum Sharpe Ratio (MSR) ... 30
4. Existing Indices ... 33
5. Practical Part Development of new indices ... 36
5.1. Idea ... 36
5.2. Stock selection ... 36
5.3. Fundamental Data ... 37
5.3.1. Return ... 37
5.3.2. Volatility ... 39
5.3.3. Sharpe Ratio ... 40
5.3.4. ADTV ... 40
5.3.8 Effective number of stocks ... 41
5.4. Backtest ... 41
5.4.1. Equally Weighted Portfolio ... 42
5.4.2. Equal Risk Weighted Portfolio ... 44
5.4.3. Most Diversified Portfolio ... 46
5.4.4. Out of Sample Minimum Variance Portfolio ... 48
5.4.5. Out of Sample constrained Minimum Variance Portfolio ... 50
5.4.6. Out of Sample Maximum Sharpe Ratio Portfolio ... 52
5.4.7. Out of Sample constrained Maximum Sharpe Ratio Portfolio ... 54
Conclusion ... 56
List of References ... 58
Appendix ... 67
1
List of Figures
Figure 1: Markowitz efficient frontier ...7
Figure 2: Minimum Variance Portfolio vs. Maximum Sharpe Ratio Portfolio
according to Markowitz (1952)...31
Figure 3: Performance MSCI World Equal Weighted vs. MSCI World ...33
Figure 4: Weights for the 30 DAX constituents, according to Deutsche Börse (2013a) ...36
Figure 5: Equally Weighted Portfolio ...41
Figure 6: Equal Risk Portfolio ... 43
Figure 7: Maximum Diversified Portfolio ...45
Figure 8: Minimum Variance Portfolio ... 47
Figure 9: Minimum Variance Portfolio constrained ...49
Figure 10: Maximum Sharpe Ratio ...51
Figure 12: Maximum Sharpe Ratio constrained ...53
2
List of Tables
Table 1: Illustration of the meaning of beta... 12
Table 2: Return Characteristics of Alternative Indexing Metrics... 19
Table 3: Liquidity Characteristics of Alternative Indexing Metrics ... 20
Table 4: Example for different percentages of the diversification weights ... 24
Table 5: An overview of stock selection and weighting decisions of some alternative equity
indices ... 32
Table 6: Risk and Return Characteristics of the MSCI World Index and the MSCI World
Equal Weighted Index ... 34
Table 7 Financial Ratios Equally Weighted Portfolio vs. DAX ... 42
Table 8 Financial Ratios Equal Risk Weighted Portfolio vs. DAX ... 44
Table 9 Financial Ratios Most Diversified Portfolio vs. DAX ... 46
Table 10 Financial Ratios Out of Sample Minimum Variance Portfolio vs. DAX ... 48
Table 11 Financial Ratios Out of Sample constrained Minimum Variance Portfolio vs.
DAX ... 50
Table 12 Financial Ratios Out of Sample Maximum Sharpe Ratio vs. DAX ...52
Table 13 Financial Ratios Out of Sample constrained Maximum Sharpe Ratio vs. DAX 54
3
List of Abbreviations
ALLORDS = All Ordinary Index
BLUE
= Best Linear Unbiased Estimator
CAP
=
Capitalization
CAPM
= Capital Asset Pricing Model
CR
= Concentration Ratio
DAX
= Deutscher Aktien Index
DR
= Diversification Ratio
DW
=
Diversity
Weights
ERC
= Equal Risk Contribution
ETF
= Exchange Traded Fund
EW
= Equal Weighting
FTA
= Financial Times Actuaries
FTSE
= Financial Times Stock Exchange
FW
= Fundamental Weights
GMV
= Global Minimum Variance
MCW
= Market Capitalization Weights
MD
= Maximum Deconcentration
MDP
= Most Diversified Portfolio
MPT
= Modern Portfolio Theory
MSCI
= Morgan Stanley Capital International
MSR
= Maximum Sharpe Ratio
OLS
= Ordinary Least Squares
p.a.
= per annum/per year
RAFI
= Research Affiliates Fundamental Index
RP
= Risk Parity
SD
=
Standard
Deviation
SP
= Standard and Poor's
s.t.
= subject to
TE
=
Tracking
Error
TOPIX
= Tokyo Stock Price Index
VAR
=
Variance
4
Introduction Why new concepts like Smart Beta?
In economics, each and every rational decision made is supposed to maximize individual
utility. This approach especially applies to the investor in financial goods. In accordance
with neoclassical utility optimization, the individual investors are supposed to be willing to
exchange investment good in order to maximize their expected future return. This
approach anticipates every individual investor to try and estimate the future cash flows of
the investment in order to evaluate its current value. Hence, trades at every stock exchange
are to be executed at all times where you have two investors differing in their estimation
of the intrinsic value of an investment product. As soon as one investor holds some asset
that has a higher market price than he/she estimated the value of the asset to be, he/she is
then supposed to want to sell this asset instantly. On the other hand, in the case of an
investor expecting an asset to be undervalued, he/she should try to invest in that asset. As a
consequence, every investor is supposed to create a portfolio with assets that in turn
maximize his/her expected return. Every investor is supposed to make an individual and
rational attempt to maximize his/her utility and to behave in a risk-averse manner. That
means that every investor is supposed to choose the respective investment asset that shows
a lower risk with the same expected return or show a higher expected return with the same
risk. All information that may have an influence on the valuation of the asset is to be
observed at the same time by every individual investor and taken into consideration at the
same time. As every shred of information is evaluated in its own individual way, the
individual estimate of the current value of an asset should differ for each and every
investor. However, according to the neoclassical theory, it is not possible to gain more
from an investment than the market does, as long as markets are efficient. Financial
markets can be seen as the most efficient markets, if not the only efficient markets in real
economy, as, in the market context, information is transferred the fastest and prices are
thus adopted nearly instantly. Nevertheless, all investors at the stock exchanges try to make
money by using their individual knowledge in order to gain something from investing in
some assets. They have of course, at the same time, the possibility to follow the market
themselves or to try to bet against the market. Every investor hence always faces the
question of whether to trade on the market with his/her own individual knowledge in order
to gain some additional utility, or to simply attempt to do the same as the whole market
and follow the belief of the market at a whole. The question thus arises of what exactly
efficient fund management looks like. This paper will discuss several possibilities which
arise in literature and in the real economy when thinking about fund management, and will
5
discuss the rather new concept of "Smart Beta" investments, in particular. The focus of this
paper thus lies in the question of whether smart beta concepts serve as potential superior
alternatives to the classical passive investment products.
6
1. Traditional Concepts
In 1952 one man stepped onto the stage of (financial) economic research: The 25 year old
Harry Markowitz published in this year a paper called "Portfolio Selection". This work can
be seen as the foundation of modern portfolio theory and indeed it revolutionized the
thinking about portfolio selection theories at the time. In 1959 Harry Markowitz
additionally published a book called "Portfolio Selection Efficient Diversification of
Investments" that then goes into greater depth about his theory in round about 300 pages.
In these works Harry Markowitz laid down his understanding of modern portfolio theory.
The Modern Portfolio Theory is based on the assumption of rational investors seeking to
maximize their wealth. As Markowitz (1952) states "there is a rule which implies that an
that the investor should diversify and that he should maximize expected return."
(Markowitz, 1952:79) In accordance with this assumption, he introduced the concept of
mean-variance analysis and the efficient frontier.
This efficient frontier, shown in Figure 1, reflects all efficient portfolios, where the
expected return (E(R
p
)) is the highest according to the risk level (SD(R
p
)) chosen by the
investor, or - vice versa - where the risk level is minimized given a specifically chosen
level of return. Fabozzi and Markowitz (2011) illuminate as much: "an efficient portfolio
Figure 1 Markowitz efficient frontier, Fabozzi et al., 2011: 45
7
is one that provides the greatest expected return for a given level of risk, or equivalently,
the lowest risk for a given expected return." (Fabozzi/Markowitz, 2011:6) The concept is
rather simple and intuitive. Yet the concept does not answer the basic question which
arises from the work of Markowitz (1952) on how to create an efficient portfolio.
The Modern Portfolio Theory relies on the expected return, as, the investor cannot be sure
about the "real" return involved in a risky investment. As "expected" implies, this is not
yet known, and so it has to be somehow arrived at through estimation. James Tobin (1958)
realized this problem and wrote a paper to that end called "Estimation of relationships for
limited dependent variables".
According to Tobin (1958) this expected return has to be estimated from the return of a
portfolio
1
, that he defines as partly calculated from the current and observable rate of
return r and partly from some expected and unobservable rate g. Thus, "since g is a
random variable with expected value zero, the expected return on the portfolio is: E(R) =
R
=A
2
r" (Tobin, 1958: 9). However, as some amount
2
of the portfolio is invested in a
risky asset, the return has a standard deviation
3
. Therefore, the amount held by the investor
in risky assets influences both the expected return and the standard deviation. As a result,
the investor can only expect a higher return by accepting a higher level of risk in his
portfolio, because the expected return is directly dependent on the standard deviation
4
.
This finding complies with the Modern Portfolio Theory of Markowitz (1952).
The construction of a portfolio can either be done actively by choosing a portfolio manager
or passively, for example, by following an index as a benchmark. While active portfolio
management does not follow a strict rule of portfolio creation, the classical concept of
index development or passive portfolio management is the weighting scheme of the
constituents according to market capitalization. While the active portfolio management
tries to beat the "market" by outperforming some benchmark return, the passive investment
tries to track some underlying, which means to represent the development of the
underlying by investing passively in the constituents included
(Bruns/Meyer-Bullerdiek,
2008).
The challenge thus for the passive portfolio management is to replicate the
underlying as exactly as possible.
1
R=A
2
(r+g)
2
A
2
3
R
= A
2
g
4
=
8
There has been a hot debate in academic literature for quite a long time on whether active
or passive portfolio management is superior in terms of the investments' performance. This
question cannot be answered easily. Therefore I would like to briefly establish some
aspects of both the active and of the passive portfolio management to explain their
differences and highlight some pros and cons for both approaches.
1.1. Active Fund Management and the Alpha
The basic goal of active portfolio management is to create a portfolio which outperforms
some benchmark portfolio. (Bruns/Meyer-Bullerdiek, 2008: 101) The effort of
outperforming a benchmark's return can be divided into two main strategies for beating the
market: "stock picking" and "market timing".
The first strategy aims to create a portfolio by picking the "right" stocks for the portfolio
("stock picking") that will create an overall portfolio return that is higher than the
respective market return. Hence, the selected stocks should show a better performance than
other stocks in the market and therefore build a portfolio which performs superior to that of
the market.
Following the other strategy, the portfolio manager tries to buy and sell the portfolio's
assets at the "right" time in the market ("market timing"). A portfolio manager who
follows this approach tries to find the "right" point in time, when assets are undervalued
and will consequently outperform other assets of the market in the future.
According to the efficient market hypothesis, all available information on the market is
already reflected in the prices, when markets are efficient. The only departure from this
theory that might exist, generally creates only such small possible gains that the
transactions costs which arise from trading in these anomalies would be higher than the
potential profit.
Malkiel (2003) clearly shows that the active management has not only the ability to
outperform the market, but after adjusting for the costs of the transactions, passive
management has the ability even to surpass active fund management. As he calculated with
data from 1970 to 2001, the median return of active fund management underperformed the
benchmark by 3 % on average, not only in the period of 10 years but also 15 and 20 years.
To conclude, the author stresses the finding that no investment strategy is able to predict
any possibility to outperform the benchmark. The same findings are reported in Malkiel
(2005), where the author states emphatically that "active equity management were, in the
words of Ellis (1998), a loser's game." (Malkiel, 2005)
9
This approach, however, does not leave any room for acknowledging that there are some
portfolio managers who could outperform the benchmark, even consistently over time. By
ignoring the potential of active portfolio management, one ignores any insights on the part
of an active manager. As Davidow (2013), among others, writes, the only challenge is to
pinpoint these managers. Furthermore the market environment is not equal all the time:
"There is a rotation from growth to value and a rotation among the types of value and
growth managers that perform well in a given market environment. Active manager
selection requires advisors to understand the types of managers that perform well in a
given market environment." (Davidow, 2013:7) This additionally raises the question of
whether any search costs would be covered by the surplus of selecting the "appropriate"
active portfolio manager.
To evaluate the ability of active portfolio managers one refers to a so-called "alpha". In
general, alpha can be seen as the rate of return created by the active management of the
portfolio. (Rose, 2013: 1) Hence, alpha is calculated against some specific benchmark
which the portfolio manager tries to beat. The ability to beat this benchmark's return
generates either a positive or negative alpha in retrospection. Alpha refers to the excess
return, meaning the return above the benchmark's return. Yet actively managed portfolios
have often been strongly correlated with the overall market situation. This means that most
portfolios rose in value during positive market movements, also known as Bull Markets.
The same is true vice versa, as, during the time of market downturns, known as Bear
Markets, these portfolios also lost in value. (Rose, 2013:2) In so doing, it becomes much
more difficult for active portfolio managers to outperform the benchmarks, particularly
after one evaluates the return adjusted for the costs of active portfolio management.
Within active portfolio management, however, it is the excess return and risk of a portfolio
which the investor should be mindful about. The risk of a portfolio is reflected by the
tracking error. The tracking error shows how close the portfolio's return follows the
benchmark's return.
One very demonstrative study on the "ability" of mutual fund managers is Jensen's (1967)
study of "The Performance Of Mutual Funds In The Period 1945-1964". In this study he
measures the ability of 115 mutual fund managers to outperform the market. According to
this study, the average mutual fund manager was not even able to outperform a simple
buy-and-hold strategy. Furthermore, he finds evidence that in the case of a single fund
manager who managed to outperform, the buy-and-hold strategy nevertheless yields very
low results. In summary, this study shows that the average portfolio manager does not have
10
the ability to gain any more than the market return. That is to say that no one can have an
insight in the long run that helps him in gaining from active portfolio management.
Yet, on average, we can confidently conclude that active portfolio management does not
bring in any appreciable surplus for the investor. According to the literature, no active
strategy in portfolio management is superior to the passive buy-and-hold strategy in the
long run, despite the fact that active fund managers try to convince customers of exactly
the opposite.
To settle this a bit more conclusively, the following chapter will focus on the passive
portfolio management itself and establish some illustrative pros and cons.
1.2. Passive Fund Management and the Beta
In contrast to active portfolio management, passive portfolio management involves the
investor trying, for example, to track an index by investing only once in the titles contained
in this index, whilst leaving the portfolio otherwise unchanged. In that sense, tracking
means to replicate a given target portfolio with your investment portfolio as closely as
possible.
This can either be done by fully replicating or by sampling. The sampling itself can further
be subdivided into heuristic methods, or so-called stratifying sampling or optimizing
sampling. Finally the way in which this optimization is done can be subdivided into a
linear optimization, a quadratic optimization, or according to specific models. (Poddig et
al., 2009:250/251)
The approach of passive portfolio management directly follows the work of Markowitz
(1952) and is based on the efficient market hypothesis, which states that it is not possible
to persistently outperform the market. Various studies like Malkiel's (2003) and Malkiel's
(2005) support this philosophy. According to his approach, all available information on the
market is reflected at all times by the prices. No investor can, thus, have more information
than there is available on the market. (Hebner, 2005: 69 ff.)
The individual investor, furthermore, need only invest in one product. Having invested in
this product, the investor does not have to bother with any adaption of his portfolio. Hence,
the investor has only low costs compared to the steep buying and selling actions involved
in active portfolio management. (Bellet, 2013: 1) What's more, with this single
investment, the investor can well diversify his portfolio. These investment goods are
known as exchange traded funds (ETFs) or exchange traded products (ETPs). The
underlying motivation for investment in such products are often broadly diversified
11
indices. Hence, the performance, for example, of an ETF which follows the performance of
a broad diversified index does so without relying so heavily on a single stock development
like an active portfolio which is less diversified. An ETF, for instance, with the Euro Stoxx
50
5
as the underlying index, reflects the performance of the stocks of the 50 largest
European listed companies.
Furthermore, in contrast to active portfolio management, tracking an index, by definition,
does not create any alpha and tries to limit instances of tracking error as much as possible.
(Smith, 2012) The tracking error indicates the difference between the portfolio and the
benchmark. In so doing, the tracking error can be defined as the variance between the
benchmark's return and the portfolio's return.
Yet the literature does not provide one uniform definition of tracking error. While some
authors define the tracking error as the variance between the benchmark's return and the
portfolio's return
6
, others define it as the standard deviation between these two returns
7
(Poddig et al., 2009:258).
The difference in the performance of a passive portfolio and a benchmark is called the beta
(
p
) of a portfolio. Beta simply measures the ability of the passive portfolio to track the
benchmark. The portfolio which is then created should track the target portfolio as
precisely as possible. The following table shows some interpretation of the coefficient.
Value of Beta
Interpretation of Beta
0
The portfolio and the benchmark move in opposite
directions
= 0
There is no correlation between the portfolio's movement
and the benchmark's movement
0 1
The portfolio moves generally less in the same direction as
the benchmark
= 1
The portfolio moves in the same way as the benchmark
0
The portfolio moves in the same direction as the benchmark
but further
Table 1 Illustration of the meaning of beta
In recent years numerous indices have been created which can be seen as underlyings for
the passive portfolio management.
Yet the ability to invest passively in a broad stock
5
For more information on the Euro Stoxx 50 see STOXX Ltd. (2014)
6
=
( ) =
( - )
7
=
( ) =
( - )
12
market index is rather new. In the time before indices were created, investors were only
able to invest in the market via an active fund manager. The first index fund which opened
for individual investors was the Vanguard 500 Index Fund
8
. This fund was created in 1976
with the aim of tracking the Standard Poor's 500 Index.
Passive portfolio investment differs in the way in which the underlying for an ETF, for
example, is created and calculated. Nowadays there exists a broad range of possible
weighting schemes, which allow the investor in passive products huge selection. Every
investor can follow his specific investment preferences, such as weighing stocks according
to market capitalization, weighing them equally, or following more advanced concepts like
minimum variance or maximum Sharpe Ratio approaches, which involve investing in
passive products. Yet one has to say that with the development of new passive products, it
is not only the supply for these products which is growing, but also the complexity with
which those products are being calculated. A product with an equally weighted portfolio as
underlying might be easily understandable, but concepts like the minimum variance
weighting or the maximum Sharpe Ratio weighting require a deep mathematical
understanding in order to appreciate the underlying concept. Investing in such complex
instruments is rather like / finding a needle in a haystack.
The following chapters will be dedicated to some of these concepts in order to give the
reader a better understanding of the complex weighting schemes of the passive investment
products. In the beginning, the classical market capitalization weights will be described, as,
they are still the most common weighting method for most underlying, followed by the
most popular alternative weighting schemes, commonly known as smart beta concepts.
8
For further information see Vuangard (2014)
13
2. Market Capitalization Weights (CW)
The traditional weighing scheme for passive investment funds is the concept of assessing
the weights according to the market capitalization of the constituents. All information for
this concept is generally transparent and readily observable. The market capitalization is
the product of all tradable stocks multiplied by the price of the stock.
This is illustrated, for example, by company A allotting one million stocks and holding
100.000 stocks in its own portfolio. In this case the free float factor would be 0.9. If we
assume that the current price for one stock at the stock exchange is 100 EUR, then the
overall market capitalization of company A would be 90.000.000 EUR. If we further
assume that an index I is built out of company A plus two additional companies, B and C,
whose market capitalization is 180.000.000 EUR and 45.000.000 EUR, respectively, then
we would expect that company A has a weight of round about 28.6 % in the index
(company B 57.14 %, company C 14.3 %). That means that more than half of the
performance of index I depends on the performance of the stock of company B. If the stock
price of company A, for example, rises from 100 EUR to 200 EUR, then the index I would
rise by round about 28.57 %.
The basic work for this concept is Sharpe's 1964 published paper A Theory of Market
Equilibrium under Conditions of Risk.
According to this concept each individual weight (w
it
) is calculated using free-float market
capitalization, defined as
=
Where,
p
it
= Price of a company (i) at time (t),
n
it
= Number of shares of a company (i) at time (t),
ff
it
= Free-float factor of company (i) at time (t), and
n = Number of shares.
This formula uses the concept of Laspeyres' price index:
=
The index (I) is calculated by the quotient of the sum of all individual prices at time t = n
times their quantity at time t = 0, divided by the sum of the individual prices at time t = 0
times the quantities at time t = 0. (Armknecht, Silver, 2012: 5)
The biggest advantage of this concept is the tangibility which it yields. Furthermore,
14
portfolios or indices which are weighted by market capitalization are said to be the best
reference for representing overall market movements. (Amenc, 2012:1) It follows thus that
if an investor wants to follow the market, which, theoretically is the best opportunity he
has, then, this concept should be his primary choice. This statement has to be supported in
such a way that the main countries' indices represent a big part of the market capitalization
at the respective stock exchanges. The main German index, the DAX 30, for example,
represents 80 % of the market capitalization of the German stock market. (Deutsche Börse
(2009))
While this concept is a rather simple and obvious method, however, it also entails some
shortcomings. As market capitalization weighted indices weigh their constituents
according to their market capitalization, the development of the index is strongly
influenced by the price movements of its largest components. Hence these kinds of indices
have a very strong cap bias. (
Davidow, 2013:7)
One could furthermore argue that this kind of indexation gives the stocks which have
already yielded fast growth in the past, and which have perhaps already come out of this
strong growing stage, a very strong influence on the future return of the index. (Bellet,
2013: 2) Subsequently, investors willing to participate in a strong growing market in the
future might better be better poised to choose another kind of weighting scheme.
Concomitant with this argument, another possible disadvantage of the market
capitalization weighted indices stems from the fact that these kinds of indices invest very
little in the current small companies and subsidiaries. Yet those very companies and
subsidiaries may show significant growth potential. A different weighting scheme from
that of market capitalization could give those subsidiaries a higher weight in a portfolio.
Nevertheless, market capitalization weighted indices present some very important
advantages. Investing in the biggest stocks also means investing in very liquid stocks. The
weights of the components furthermore adjust themselves, which means that the portfolio's
turnover is very small, and hence, only entails very low trading costs. (Roncalli, 2012:16)
At the same time, market capitalization weighted indices pose some big disadvantages
compared to other weighting schemes. This kind of portfolio shows a rather poor
performance compared to the risk being faced, due to the fact that they do not take
correlations between the constituents of the portfolio into account. To support this
statement Haugen and Baker (1991), among others, show that market capitalization
weighted portfolios are solely efficient under very unrealistic assumptions that, in reality,
are never fulfilled: The first two assumptions, namely that investors are risk averse and act
