Albin Tyllgren
Applying Treynor-Black Model with
AP7 Såfa in the Swedish Premium
Pension System
To choose between active and passive portfolio
management
Tillämpandet av Treynor-Black Model med AP7 Såfa
i det Svenska Premiepensionssystemet
Att välja mellan aktiv och passiv portföljförvaltning
Nationalekonomi
Examensarbete – Civilekonomprogrammet
Term:
VT 2021
Supervisor:
Karl-Markus Modén
Karlstad Business School
Karlstad University SE-651 88 Karlstad
Phone: +46 54 700 10 00
E-mail: handels@kau.se kau.se/en/hhk
Acknowledgements
Firstly, I would like to express my gratitude to my supervisor, Karl-Markus Modén, for support,
dedication and guidance throughout the working process writing this thesis.
I would also like to thank my associated students for the encouragement and inputs from several
seminars during the period.
Albin Tyllgren
ii
Abstract
Background: Since 1998 Sweden has individual accounts as a part of both public and
occupational schemes (Sundén 2006). Yearly, 2,5% of the pensionable income is set aside to
the premium pension (The Swedish Pension Agency 2021) Individuals are able to choose how
the premiums should be paid in the system and in what way the money should be invested,
either by choosing from the fund market or by refraining from making an active choice and
instead let the Swedish pension agency management their money in the passive alternative
called AP7 Såfa. The passive alternative AP7 Såfa is a portfolio which adapts to the age of the
investor and is built to fit a long-term pension investment.
Purpose: This study will focus on evaluating if the passive alternative AP7 Såfa has an excess
risk-adjusted return compared to given portfolios in the premium pension selection system, or
if the investor would benefit from managing the portfolio more actively. The study will also
search for benefits using the Treynor-Black model to check the optimal allocation between this
actively managed portfolio versus the passive alternative AP7 Såfa.
Conclusion: This thesis has shown that there might be superior strategies rather than the index
fund to find risk-adjusted excess return in the premium pension system. However, those
strategies require professional analysts in order to forecast securities. For households choosing
between active management themselves or the passive index fund AP7 Såfa, the most beneficial
investment is to be passive and to not actively manage the portfolio. The optimum strategy is
found to be the Treynor-Black model with a combined portfolio of the index fund and the active
portfolio.
Keywords:
Index Funds, Mutual Funds, Premium Pension System, Treynor-Black Model
iii
Sammanfattning
Bakgrund: Sedan 1998 har Sverige enskilda konton som en del av både offentliga och
yrkesmässiga pensionsystemet (Sundén 2006). Årligen avsätts 2,5% av den pensionsgrundande
inkomsten till premiepensionen (Pensionsmyndigheten 2021). Individer kan välja hur
premierna ska betalas ut i systemet och på vilket sätt pengarna ska investeras, antingen genom
att välja från fondmarknaden eller genom att avstå från att göra ett aktivt val och istället låta
det svenska pensionsföretaget förvalta sina pengar i det passiva alternativet AP7 Såfa. Det
passiva alternativet AP7 Såfa är en portfölj som anpassar sig till investerarens ålder och är
byggd för att passa en långsiktig pensionsinvestering.
Syfte: Denna studie fokuserar på att utvärdera om det passiva alternativet AP7 Såfa har en
riskjusterad överavkastning jämfört med givna portföljer i premiepensionsvalssystemet, eller
om investeraren skulle ha nytta av att förvalta portföljen mer aktivt. Studien kommer också att
söka efter fördelar med Treynor-Black-modellen för att kontrollera den optimala fördelningen
mellan den aktivt förvaltade portfölj kontra det passiva alternativet AP7 Såfa.
Slutsats: Denna avhandling har visat att det kan finnas bättre strategier än indexfonden för att
hitta riskjusterad överavkastning i premiepensionssystemet. Dessa strategier kräver dock
professionella analytiker för att kunna prognostisera värdepapper och fonder. För hushåll som
väljer mellan aktiv förvaltning själva eller den passiva indexfonden AP7 Såfa är den mest
fördelaktiga investeringen att vara passiv och att inte förvalta portföljen aktivt. Den optimala
strategin visar sig vara Treynor-Black-modellen med en kombinerad portfölj av indexfonden
och den aktiva portföljen.
Nyckelord:
Indexfonder, Fonder, Premiepensionsystemet, Treynor-Black-modellen
iv
Table of Contents
1.
2.
3.
Introduction ...................................................................................................................... 1
1.1
Problem description ................................................................................................... 2
1.2
Purpose ....................................................................................................................... 3
1.3
Delimitations .............................................................................................................. 3
1.4
Outline........................................................................................................................ 4
The Swedish Premium Pension System ......................................................................... 5
2.1
AP7 Såfa .................................................................................................................... 6
2.2
Morningstar ................................................................................................................ 7
Theoretical framework .................................................................................................... 8
3.1
Risk-Return Trade-Off ............................................................................................... 8
3.2
Efficient Market Hypothesis (EMH) ......................................................................... 9
3.3
Modern Portfolio Theory (MPT) ............................................................................. 10
3.4
The Single-Index Model .......................................................................................... 10
3.5
The Efficient Frontier .............................................................................................. 11
3.6
Capital Asset Pricing Model (CAPM) ..................................................................... 11
3.7
Capital Market Line (CML) ..................................................................................... 12
3.8
Capital Allocation Line (CAL) ................................................................................ 12
3.9
Performance Measures ............................................................................................. 13
3.10
Treynor-Black Model............................................................................................... 15
3.10.1
4.
Portfolio construction ...................................................................................... 15
Previous Research .......................................................................................................... 19
4.1
Active versus passive portfolio management .......................................................... 19
4.2
Households’ performance ........................................................................................ 21
4.3
Performance in the premium pension system (PPM) .............................................. 21
v
4.4
5.
6.
Treynor-Black Model............................................................................................... 22
Method ............................................................................................................................ 23
5.1
Choice of method ..................................................................................................... 23
5.2
Collection of Data .................................................................................................... 23
5.3
Research Design....................................................................................................... 24
5.3.1
Sampling .......................................................................................................... 24
5.3.2
Calculations, Assumptions and Benchmark indexes ........................................ 25
5.4
Hypothesis Testing................................................................................................... 25
5.5
Critical assessment ................................................................................................... 26
Empirical Results and Analysis .................................................................................... 28
6.1
Risk-Adjusted Performance ..................................................................................... 28
6.2
Risk Exposure .......................................................................................................... 28
6.3
Portfolio Performance Evaluation............................................................................ 30
6.3.1
Active versus passive managed portfolio ......................................................... 30
6.3.2
Treynor-Black Model and the combined Portfolio P ....................................... 32
7.
Conclusion ...................................................................................................................... 34
8.
Further research ............................................................................................................ 36
9.
References ....................................................................................................................... 37
vi
1. Introduction
Retirement is for all individuals in Sweden where the working life ends and continues with free
time. To finance that free time, countries got different set-ups to create the highest possible
utility for its citizens. In Sweden, this is made by the Swedish Pension Agency whose mission
is to administrate and pay out the common pension to savers and pensioners with the vision to
make pensions easier for everyone (The Swedish Pension Agency 2021).
To enable that, the Swedish government in 2000 announced the premium pension system. The
purpose of this system is to find easy ways for individuals to get access to a portfolio and the
possible returns that comes out of the investments. In the system, individuals can choose up to
five options of funds taken from the fund market, or they can attain passive and stay with the
default option called AP7 Såfa. The default fund can be mixed with others or chosen just by
itself (The Swedish Pension Agency 2021a).
Statistics show that individuals who followed the passive investment alternative, i.e. AP7 Såfa,
have performed better than those savers who have retained services from financial advisors or
made an active choice themselves (AP7 2020). Although, the level of risk in the AP7 Såfa for
savers up to 55 years of age, is 1,24 times higher than an ordinary global equity fund. This can
be explained by the change in strategy that was done in 2010 where the AP7 enabled to leverage
its investment by loans (AP7 2021).
Thus, the premium pension system is built on the purpose that investments in securities create
value for the investor and increases over long-time horizons. Although, the question is which
strategy is the best to create high returns for the lowest risk possible. Researchers and investors
still disagree on what strategy is the most profitable with the aim to create excess return over
time. William Sharpe (1991) defined these strategies by stating that the returns for average
active investments would equal the average passive investments, before costs. This is why the
return for the active investments over time would be lower than the passive investments after
costs. Sharpe defined active investors as those who are not passive, and passive investors as
those who hold all securities in the market.
1
1.1 Problem description
With the premium pension system, the responsibility for the pension payment is shifted partially
towards the households and the individuals having the retirement.1 In one way this is creating
opportunities to improve the overall wealth for each individual, but it is also pressuring them
to take active interest in what strategy is the best to invest their money (Engström and
Westerberg 2003).
When the system was created, it was created with a broad opportunity to select funds, why all
fund companies that had a license got the chance to operate in the system (Sundén 2006). Still,
the number of funds is over 800 when selecting funds to the active investment (The Swedish
Pension Agency, 2019). Since a large part of the total pension payment is placed in the premium
pension system, the choice of being active and which securities to pick have to be related to the
overall risk preference of each individual (Palme, Sundén, and Söderlind 2007).
Due to the potential lack of knowledge and interest to make these kinds of decisions, by some
individuals, the government created an alternative investment strategy called AP7 Såfa
(Engström and Westerberg 2003). The fund has a generational approach where the risk is
adjusting according to the age of the investor. Until the age of 55, the distribution is 100%
equity while it sequentially decreases to lower risk investments in order to solve the issue of
investors who retire in the middle of a stock-market drop (Cobley 2009).
The number of active investors was decreasing rapidly in the beginning of the system. Initially,
in 2000, 68% of the investors were active which dropped dramatically to 20% in 2001. Already
in 2004, the number had decreased to 10% (Sundén 2006). However, that number has
sequentially increased to 43% in 2019 (The Swedish Pension Agency 2020).
The choice of passive investments, such as the AP7 Såfa, is a result of lack of knowledge and
needs of security. Madrian and Shea (2001) argue that choosing a passive alternative can be
equated with not making a choice at all, since the benefits from an active choice are hidden by
the cost of collection and assessing needed information in order to make a good investment
decision.
1
2,5% of the annual income is invested in the Premium Pension System.
2
1.2 Purpose
The purpose of this paper is to investigate if the default fund option, AP7 Såfa, has created
excess return to its investors relative given active portfolios in the premium pension system,
PPM, during 2000-2015. The paper will use risk-adjusted measurements to interpret the data
and to draw conclusions beneficial for the investors.
Furthermore, the study will use the Treynor-Black Model in order to create opportunities for
investors to use sophisticated models when making investment decisions. The model will
propose an optimal allocation between the active management and the passive index fund
alternative AP7 Såfa.
The questions which are stated in this paper is:
•
Has the AP7 Såfa had an excess risk-adjusted return compared to given portfolios in the
premium pension selection?
•
How to improve the risk-adjusted return in the premium pension system using the
Treynor-Black model with a constructed portfolio P?
1.3 Delimitations
To be able to focus on the stated questions, limitations have been made. First, this paper has a
limited scope to the Swedish pension system and pension systems in other countries than
Sweden will not be taken into account or consideration in this paper. The same is for the pension
system as a whole, where no statements will be taken for the occupational system or for the
private pension savings made by households. The only subject searched for in this paper is the
premium pension system.
Although changes were made in the AP7 system in 2010, this study will be studying the period
2000-2015. This means that the study will consider separate systems, earlier mentioned as
“Sparfonden” and “Valfonden”, which had other arrangements than the current AP7 Såfa.
The study has not taken into account any fees or transaction costs. However, all returns are
presented as net returns although transaction costs have not been evaluated for the individual
investor.
3
Furthermore, no limitations regarding ages have been made. The investigated fund, AP7 Såfa,
contains allocations adjusted for ages and to find fairly results when comparing to given
actively managed portfolios the ages included extends from 0-75 years old.
Since the scope of this study tries to find excess return compared to benchmark indexes, the
study will not be limited to just equity funds.
1.4 Outline
The outline of this paper will be as follows: The thesis starts by describing the Swedish
premium pension system and how it is created to bring benefits to households. In section three,
theoretical framework is presented to bring knowledge and calculations used to answer the
research questions. In section four previous empirical findings are presented to the field of this
research. Section five describes the method used in this study, the collection of data and some
critical assessment. In section six, results and analysis are presented followed by section seven
with conclusions of this study. Lastly, section eight contains of suggestions for future research
topics.
4
2. The Swedish Premium Pension System
Funds are collections of securities that are held by investors. Instead of having individual stocks
from the stock market, funds give the opportunity for households to diversify their savings and
by that lower the risk. In Sweden, a large part of every household’s savings is placed in what is
called Premium Pension Funds, which is 2,5% of the yearly earned labor income for every
individual. The system is self-directed, and all individuals can invest in a broad fund market of
domestic and international funds. For those individuals who wish to not make an active
allocation, the government has established a default alternative fund called AP7 Såfa, which in
this text is characterized as a index fund.
The system was introduced in 1998 and took place in the fall of 2000 with all Swedes born after
1938. At this time, about 500 mutual funds were available to choose (Sundén 2006). All funds
are held by professional managers and analysts who receives payment through fees calculated
from the total investment in each fund. This has been subject for some fraud cases where fund
companies have been taking advantage of the large amount invested in the market. Although,
these frauds won’t be taken into account in this study. Nowadays, all funds accessible in the
premium pension selection have been approved by the Swedish authorities where all managers
have to be certified in order to manage a fund (The Swedish Pension Agency 2021a).
In the Premium Pension System, there exist four types of funds: equity funds, interest-bearing
funds, mixed funds and generational funds. The reason why it’s divided into four groups is to
make it easier for investors to separate them and by that be able to make comparisons to
benchmark indexes. What type the fund belongs to depend on what combination of securities
that are used. Generational funds diverse from the other categories by successively decreasing
the share of stocks and by increasing the share of interests closer to pension-age.
The fund categories are divided into specific areas depending on, how and where, the fund
invest. For an example geographical position, sector, or if the fund invests in specifically
products or services. Funds placed in the same specific area can be separated by placement,
fees, management, currency or returns.
5
Figure 1 The Swedish Pension System
In a questionnaire made by AMF in a sample of people in ages 25-50 years, about 50% of the
group said that they had no idea of how much that was placed in the pension system, as many
did think about the pension rarely or never (The Swedish Pension Agency 2021b).2
2.1 AP7 Såfa
The AP7 Såfa fund is the default alternative for individuals in the premium pension system,
which is chosen by those individuals who do not make an active portfolio choice, this
alternative is characterized by 43% of the total PPM market (The Swedish Pension Agency
2020). The fund is specialized for those individuals who not got active portfolio management
as an everyday hobby and are comfortable with letting the government manage their money.
The default option consists of two funds, the AP7 Equity Fund and the AP7 Bond Fund. The
distribution of the two funds adjusts to the age of the investor. Until the age of 55 the AP7 Såfa
contains of 100% equity, while after that age the share of equity is decreasing until the investor
gets 75 years old. According to the annual report of AP7, the return goal is to give its investors
a long-term return in comparison to the occupational income by 2-3% per year.3
2
AMF is an insurance company that offer pension insurances.
3
Occupational pension is another part of the national retirement pension which originates from working and its
agreements with the employer.
6
2.2 Morningstar
Morningstar Inc. is a leading supplier of independent research all over the world. The company
supply a broad portfolio of products and services aimed to facilitate the everyday investments
for households and investors (Morningstar 2021). In total, they have more than 500 global
analysts who focus on collecting data, making analysis and to do quality control of funds.
7
3. Theoretical framework
3.1 Risk-Return Trade-Off
Since financial markets are efficient and highly competitive, investors invest their money to
find future returns (Bodie, Kane, & Marcus 2010). A lot of rational investors all over the world
aim to find the greatest investments to yield the highest expected return to the lowest possible
risk.4 To improve the expected return, the investor has to accept a higher degree of investment
risk. If higher expected returns can be achieved without higher level of risk, the price will adjust
immediately. This is what is called the trade-off between risk and return.
To compare financial securities, it has to be measured by a couple of tools based on
mathematical models. These measurements are well-known and central in the financial
community when looking for risk and return (Higgins 2015). These tools enables and analyst
to measure the risk-return relationship and to value the effect of diversification on portfolio
risk, the mix of assets and the expected return.
Portfolios consisting of two risky assets are relatively easy to analyze and evaluate. The
expected rate of return for a stock, at any time, can be written as:
𝐸(𝑟! ) =
𝐷! + (𝐸(𝑃! ) − 𝑃!"# )
𝑃!"#
where 𝐷! is the dividends, and 𝐸(𝑃! ) − 𝑃!"# the expected capital gains. Putting this in a
portfolio context, we get:
𝐸(𝑟$ ) = 𝜔% ∗ 𝐸(𝑟% ) + 𝜔& ∗ 𝐸(𝑟& ) + ⋯ + 𝜔' ∗ 𝐸(𝑟' ) + ⋯ + 𝜔( ∗ 𝐸(𝑟( )
Where 𝜔' is the weight in asset i. This can be simplified as:
(
𝐸(𝑟$ ) = - 𝜔' ∗ 𝐸(𝑟' )
')#
4
The “expected” return is not the “actual” return given by the investment, it is the result of averaging all possible
outcomes.
8
3.2 Efficient Market Hypothesis (EMH)
Eugene Fama (1965) introduced what is called the Efficient Market Hypothesis (EMH). The
theory says that only investors with important information are able to consistently beat the
market and create a positive excess return. Fama found strong support for the model called
random walk, which implies that chart reading of pastime is of no real value for an investor.
This means that forecasting alphas or abnormal returns have no value when investing in
securities, since the returns follow a random walk and therefore is completely randomized. The
efficiency can be divided into three parts: Weak form efficiency, Semi-strong form efficiency
and Strong form efficiency.
Weak Form Efficiency
Share prices reflects all historical information already used in historical prices, which implies
that it is not possible to forecast future prices or price development. Using technical trading
strategies cannot provide any consistent excess return. The prices will increase, although, over
time equal to the drift term, 𝑒 *+,! (Bodie, Kane, & Marcus 2010).
Semi-strong Form
Prices at the market reflect all public information available. This implies that rational investors
make predictions about future prices based on the long run value on each security. To make
such predictions the investor has to take into account all relevant information about the
individual security. Good information which can be interpreted as news that improves the
underlying value, will increase the price immediately after that the information got available.
In order to beat this market, the information has to be handled before other investors to be able
to take advantage and act before the prices adjust (Bodie, Kane, & Marcus 2010).
Strong Form Efficiency
Market prices reflect all information available, including that information which is not yet
published to the market. With this assumption taken into account, not even insiders with nonpublic information are able to make abnormal returns, since prices reflect all information
available (Bodie, Kane, & Marcus 2010).
9
3.3 Modern Portfolio Theory (MPT)
In 1952 the professor Harry Markowitz wrote an article named “Portfolio Selection”.
Markowitz, who started his career as a mathematician, and moved mathematical and statistical
concept into the financial world. He argued in his article that it is not enough to just focus on
the return, investors also have to consider the risk they are taking. One of the tools doing that
is to diversify and bring other securities into the portfolio. Markowitz showed that an expected
return of let say 8% could be accomplished not only with 100% stocks, but also with a given
share of bonds and gold still with an expected return of 8%, now with a lower degree of risk.
This has become the modern portfolio theory, MPT, which says that low risk is better than high
when comparing two portfolios with the same expected return.
Markowitz (1952) theory is basically built around two assumptions: that all investors are
rational in their decision-making process and that all investors want to achieve the highest
possible return to the lowest degree of risk. By this statement one could say that investors are
risk-averse, meaning that investors choose to avoid risk. The Modern Portfolio Theory contains
of several risk-measurements which helps the investor to calculate for systematic risk and future
prices.
3.4 The Single-Index Model
The Single-Index Model was introduced by William Sharpe (1963). The model says that the
systematic risk that affects the return of the securities is caused only by macroeconomics factors
such as the world index MSCI or the S&P 500. The regression equation is:
𝑟' (𝑡) = 𝛼' + 𝛽' 𝑟- (𝑡) + 𝑒' (𝑡)
The equation contains of historical samples, 𝑅' (𝑡) and 𝑅- (𝑡), where t denotes the date of each
pair of observations. The intercept, 𝛼' , is the expected excess return of the security when the
market excess return is equal to zero. The slope coefficient, 𝛽' , is the denoted beta, which is a
measure of the sensitivity to the market.
10
3.5 The Efficient Frontier
Markowitz (1952) introduced the efficient frontier where portfolios got different returns and
risks which can be calculated. The frontier tells what gives the highest return for the lowest
degree of risk, which also is the most optimal portfolio to select.
The portfolios that fulfill the requirements of the efficient portfolio lies on what is called the
efficient frontier. According to the theory by Markowitz, the portfolios that are not held on the
efficient frontier are insufficient since they do not offer the level of return required for the given
level of risk, or they yield a higher level of risk given the level of return.
3.6 Capital Asset Pricing Model (CAPM)
One fundamental question looking into finance is how risk affect the expected return of
securities. Capital Asset Pricing Model, CAPM, is a set of predictions started by Harry
Markowitz (1952) continued by William Sharpe (1964), John Lintner (1965a and 1965b) and
Jan Mossin (1966). Roughly, the theory says that a risk which is diversified away in an overall
portfolio with other securities is not a risk at all.
The theory is based on four main assumptions:
•
All investors are risk-averse where financial assets consist of both diversifiable and nondiversifiable risk.
•
All investors will make assumptions on individual assets proportional to the risk
premium on the market portfolio where the risk of the security is measured in
relationship to the risk of the market, noted as the beta coefficient.
•
All investors are rational and have the same opportunity to make transactions and do
investments.
•
The equation of CAPM is measured by the security market line, which is the formula
that relates the expected return and beta coefficient of the security.
The assumptions state a simple world where expectations are homogenous which make the riskfree asset available for all investors, why they all will hold the market portfolio as the optimal
portfolio. However, these are the assumptions needed for CAPM to hold (Bodie, Kane, &
Marcus 2010).
11
3.7 Capital Market Line (CML)
When the index portfolio, i.e. the tangent portfolio, is the same for all investors the efficient
frontier become the same for all. This is called the Capital Market Line, CML, where a portfolio
P that lies on the CML is noted to be efficient. The equation for CML can be written as:
𝑟̅- − 𝑟.
𝑟̅$ = 𝑟. + 4
6 ∗ 𝜎$
𝜎where the intercept 𝑟. is characterized as the reward for time, i.e. the reward that the investor
receives for abstaining its money from consumption during the period of time. The slope,
7
/̅" "/#
1"
8, is characterized as the reward for risk, i.e. the expected return the investor is given for
the increasing amount of risk taken from the efficient portfolio (Bodie, Kane, & Marcus 2010).
3.8 Capital Allocation Line (CAL)
The capital allocation line represents what we earlier called Sharpe ratio. The slope coefficient
is used to check for how well the return of a security compensate the investor for the risk taken.
This means, the higher the Sharpe ratio gets, the steeper is CAL which represents a higher riskadjusted return to the investor (Bodie, Kane, & Marcus 2010). The slope is dependent on which
securities that is hold in the risky portfolio A, where the most beneficial choice is to maximize
the slope. In Figure 2, the most efficient portfolio is T, since it lies on the steepest line with the
highest Sharpe ratio. When 𝑟. is given, the investor should then choose the portfolio that
maximize the 𝐸(𝑟), i.e. where the CAL tangents the efficient frontier line.
12
Figure 2 Capital Allocation Line and the optimal risky portfolio P.
When combining the risk-free asset 𝑟. with a portfolio on the efficient frontier, the possibility
to create portfolios which risk-return are superior to those portfolios that lie on the efficient
frontier appear.
3.9 Performance Measures
Variance
One commonly used measure for price risk is variance of the rate of return on an asset (Bodie,
Kane, & Marcus, 2010). Variance, which is the expected value of squared deviations, can be
written as:
(
𝜎
2 (𝑟)
= - 𝑝(𝑖)[𝑟(𝑖) − 𝐸(𝑟)]2
')#
Using historical data with n number of observations, the estimated variance is:
(
𝜎>
2 (𝑟)
1
= -[𝑟(𝑖) − 𝑟̅ ]2
𝑛
')#
where 𝜎> illustrates that it is an estimate, rather than 𝜎. In practice, it is difficult to obtain the
realized rate of return why the estimation of the expected return is needed.
Standard Deviation
The standard deviation is often referred to as the volatility and is calculated as the square root
of the variance value. A low value of the standard deviation, SD, tells us that the points lie close
to the overall mean of the data set. A higher deviation means that the points lie further from the
mean. The SD can be written as (Bodie, Kane, & Marcus 2010):
𝜎(𝑟) = A𝜎 2 (𝑟)
Sharpe Ratio
Investors are interested in the expected excess return that can be made over a given period of
time. When the investor is taking risks, she wants to be rewarded with return by the risk she is
taking in terms of standard deviation. The trade-off between reward (the excess return and risk
premium) and the risk (measured as standard deviation) can be measured by the ratio of its risk
13
premium to the standard deviation of its excess return. This ratio was introduced by William
Sharpe (1966) and it is called the Sharpe ratio, written as:
𝑆ℎ𝑎𝑟𝑝𝑒′𝑠 𝑅𝑎𝑡𝑖𝑜 =
𝑟̅3 − 𝑟.
𝜎(𝑟3 )
The ratio is a widely used tool to evaluate performance of risk-adjusted excess return made by
households and investment managers.
Beta Coefficients
The beta coefficient is a tool to measure in what degree the individual asset and the market
move together and is defined as:
𝛽' =
𝐶𝑜𝑣(𝑟' , 𝑟- )
𝜎-2
where the risk premium on individual assets is:
𝛽' = [𝐸((𝑟4 ) − 𝑟. ]
Since 𝛽- = 1, a value of 𝛽' lower than 1 indicates that the asset is less volatile than the market.
If the value of 𝛽' is greater than 1, the volatile is greater than the market, whereas 𝛽' = 1
indicates that the price of the asset is the same as the market. For every 1% change in the index,
the security will follow by the measure of 𝛽' (Bodie, Kane, & Marcus 2010).
Jensen’s Alpha
The value of Alpha was introduced by Michael Jensen (1968) and is known as the Jensen’s
Performance Index, also known as Jensen’s Alpha. It is used to determine the excess return
given by individual assets, portfolios or securities, in relation to the returns from the Capital
Asset Pricing Model (CAPM). The asset, which can be stocks, bonds etc, is fairly priced when
the actual return and the value of alpha is zero, which indicates that the return follows the theory
of CAPM. A positive alpha indicates that the security receives a higher risk-adjusted return
than the theory of CAPM, why a positive alpha is positive grade for the investment manager
indicating that the manager has delivered an excess return and brought value to its customers.
The formula can be written as (Bodie, Kane, & Marcus 2010):
𝛼' = 𝑟̅ − [𝑟̅. + 𝛽(𝑟̅- − 𝑟̅. )]
14
3.10 Treynor-Black Model
Suppose that the market does not hold for the EMH, i.e. it is not perfect, it will then be possible
for investors to make alpha forecasts by making individual analysis to find securities that are
mispriced. Even if it is possible for investor to do find mispriced securities to invest in, the
diversification is still important to keep (Bodie, Kane, & Marcus 2010). Jack Treynor and Fisher
Black (1973) introduced a portfolio with respect to those assumptions, this portfolio was named
the Treynor-Black Model (TB). The TB model challenges investors to find and identify
mispriced securities that could be combined with a passive index. To do so, forecasted alpha
from macroeconomics developments securities are added to a diversified portfolio which
provide a greater return than the index itself. The portfolio, which becomes the optimal active
portfolio A, will contain of a mix of picked securities and the index (market) portfolio, M, that
result in a tangency portfolio on the Capital Allocation Line, CML, (Bodie, Kane, & Marcus
2010).
3.10.1 Portfolio construction
The Treynor-Black model starts from the Single-Index Model to determining the rate of return
for securities that are not mispriced (Bodie, Kane, & Marcus 2010):
𝑟' = 𝑟. + 𝛽' (𝑟- − 𝑟. ) + 𝑒'
where 𝑒' is a firm specific error term with an expected return equal to zero. To perform market
timing, the model assumes that the macro-forecast of 𝑟- and 𝑟. has been done in a proper way.
In the next step constructing the model, a new variable is added to the equation in order to find
mispriced shares. The extra term, 𝛼5 , is called the shift factor and implies that, if 𝛼5 > 0, the
residual, i.e error term, in the equation is no longer zero and therefor shows the excess of return
for share 𝑗. The equation becomes:
𝑟5 = 𝑟. + 𝛽5 N𝑟- − 𝑟. O + 𝑒5 + 𝛼5
The optimal active portfolio, A, consists of different weights on the analyzed securities which
enable to find 𝛼% , 𝛽% and 𝜎 2 (𝑒% ). The variance of the portfolio is the sum of the systematic
and the residual variance which can be written as:
𝜎%2 = 𝛽%2 𝜎-2 + 𝜎 2 (𝑒% )
15
If the index portfolio, M, had been efficient, there would have been no need for any forecasted
alpha securities nor any actively managed portfolio. With the assumption that it is possible to
forecast alpha securities and find mispriced assets, as well as that the index portfolio, M, is not
an efficient investment, it will be possible to increase the Sharpe ratio by creating a new
tangency portfolio, P, which becomes a mix of the actively managed portfolio, A, and the index
portfolio, M.
Figure 3 Illustration made by the author of the efficient frontier with portfolio P at the optimal tangency lying
above the CML line and at the CAL line, combined with the portfolio A and M.
In this case, with two risky assets, the expected return of the portfolio P becomes:
𝐸(𝑟$ ) = 𝜔% ∗ 𝐸(𝑟% ) + 𝜔- ∗ 𝐸(𝑟- )
where the variance of the portfolio P becomes:
2
𝜎$2 = 𝜔%2 ∗ 𝜎%2 + 𝜔∗ 𝜎-2 + 2 ∗ 𝜔% ∗ (1 − 𝜔% ) ∗ 𝐶𝑜𝑣(𝑅% , 𝑅- )
Defining 𝜔- = 1 − 𝜔% , the maximization of the Sharpe ratio in portfolio A becomes:
𝜔% ∗ 𝐸 (𝑟% ) + (1 − 𝜔% ) ∗ 𝐸 (𝑟- ) − 𝑟.
max
𝑆
=
$
𝜔%
A𝜔%2 ∗ 𝜎%2 + (1 − 𝜔% )2 ∗ 𝜎-2 + 2 ∗ 𝜔% ∗ (1 − 𝜔% ) ∗ 𝐶𝑜𝑣(𝑅% , 𝑅- )
where the solution to find the weight of portfolio A is to:
𝜔% =
T𝐸(𝑟% ) − 𝑟. U ∗ 𝜎-2 − T𝐸(𝑟- ) − 𝑟. U ∗ (1 − 𝜔% ) ∗ 𝐶𝑜𝑣(𝑅% , 𝑅- )
T𝐸(𝑟% ) − 𝑟. U ∗ 𝜎-2 − T𝐸(𝑟- ) − 𝑟. U ∗ 𝜎%2 − T𝐸(𝑟% ) − 𝑟. + 𝐸(𝑟- ) − 𝑟. U ∗ 𝐶𝑜𝑣(𝑅% , 𝑅- )
16
By simplifying these expressions and combine them into the equation of the single-index model
the optimal weight in portfolio A becomes:
𝛼%
𝜔∗ =
𝛼% (1 − 𝛽% ) + 𝑅-
𝜎 2 (𝑒% )
𝜎-2
If the beta coefficient, i.e. the systematic risk, is 𝛽 = 1, the formula can be written as:
𝛼%
𝛼%
𝑅𝜔7 =
=
𝜎 2 (𝑒% ) 𝜎 2 (𝑒% )
𝑅𝜎-2
𝜎-2
The higher alpha is compared to the excess return on the index and the lower unsystematic risk
is compared to the index risk. The higher it gets, the higher gets the weight in portfolio A.
If the beta coefficient is not the same as index, i.e. 𝛽 ≠ 1, the formula has to be rewritten:
𝜔∗ =
𝜔7
1 + (1 − 𝛽% ) ∗ 𝜔7
This formula shows that when 𝛽% increases, the value of 𝜔∗ increases as well. The reason is
that when the systematic risk increases, the advantages of having the mispricing security in
portfolio A increases as well. Sharpe ratio then become higher for P than for M, which can be
expressed as:
2
𝑆$2 = 𝑆+
𝜎-2
𝑅𝛼%
=4 6+4
6
2
𝜎 (𝑒% )
𝜎𝜎(𝑒% )
2
Where 𝑆$2 is the square of Sharpe ratio of the overall portfolio (𝑆is the square of the Sharpe
ratio for the passive index).
8
This formula shows that the highest Sharpe ratio is created by maximizing the value of 1(:$ ),
$
which can be done by choosing the weight for security 𝑗 in the active portfolio A, expressed as:
𝜔5 =
𝛼5
2
𝜎 (𝑒5 )
∑(')#
𝛼'
2
𝜎 (𝑒' )
17
The weight in each individual security increases when alpha increases relative to the residual
variance, compared to the sum of all security ratios in portfolio A (Bodie, Kane, & Marcus
2010).
18
4. Previous Research
4.1 Active versus passive portfolio management
A study made by Cremers et al. (2019) shows that other studies during the last ten years still
confirm earlier made studies and that no one has been able to rebut them. One of the most
famous studies was made 1997 by Mark Carhart, who made the conclusion that an advisor
didn’t create any excess value, it was just a waste of money. Although, later it has been shown
that some advisors actually are able to create excess value, but still the best alternative for
households is said to be cheap index funds with low fees such as the AP7 Såfa in the Swedish
premium pension system.
The academic research and investors have for a long time searched for evidence that mutual
funds outperform its benchmarks indexes. Barras et al. (2010) show in their study that 75% of
actively managed funds present a zero alpha. The study, which was made between 1975 and
2006, looked at more than 2000 funds, dead or alive. They concluded that when an advisor
succeeds to outperform its index it depends on two things: skill or luck, and that only 0,6% of
all professional investors consistently beat the index.
Berk and Green (2004) confirm that advisors who perform active management do not create an
excess return compared to its passive benchmarks because of the competitive market. They
argue that forecasting alphas of past performance cannot be used to predict future returns. Other
studies, made by Jensen (1968), Elton et al. (1993), and Carhart (1997), do find similar results
with negative average alphas. However, some later studies have found that a few managers do
have enough skills to select stocks that outperform its benchmark.
Flam and Vestman (2014) made a similar study but on Swedish equity mutual funds during the
period 1993-2013. The conclusion was that there is basically no evidence of skills to select
stocks by Swedish fund managers, not even by those who did outperform its benchmark index.
They also argue that excess return or loss cannot be concluded either by skilled or unskilled
advisors, it’s more about lucky or unlucky advisors. In this study the authors also come with a
recommendation which says that investors wanting exposure to the Swedish stock market
should be aware of the lack of persistence in fund return and instead of choosing actively
managed funds, choose cheap passively managed index funds with low fees.
19
Another study that concludes the uncertainty of investing in actively managed fund was written
by Fama and French (2010) where they studied more than 3000 actively managed funds during
1984-2006. In the results they argue that the net excess return is no better than what would be
expected by flipping a coin, i.e. by random chance. Still, they conclude that there are some
managers that have enough skills to outperform benchmark index, but that these managers are
hidden by those who cannot, similar to the conclusion made by Barras et al. (2010).
However, some researchers mean that these arguments are not complete. Pedersen (2019)
doesn’t say that researchers such as Fama and French (2010) are wrong, he says that the
dynamic market has to be taken into account before making conclusions. Pedersen argues that
because of the dynamic market of share repurchases, issues and IPOs, there have to be
anomalies. But still, even with this taken into consideration, the trades between fund managers
are still a zero-sum game where someone who sell and make a gain must be mirrored by
someone who buy and make a loss. The conclusion from this study is that even those who
critique other researchers in the area, still conclude that passive index funds with low fees are
the best alternative for households to invest in.
Although a lot of studies argue that the best alternative for households is to choose passive
index funds rather than actively managed ones, critique have been made against it. Michael
Burry (2019) explains his critique in an article made by Bloomberg about savings made in index
funds. In the article he argues that index funds don’t take into account the value of companies
and stocks, why index funds got the wrong prices making it profitable trading because of
anomalies. He continues and says that when the market falls the households won’t be able to
sell the stocks, and that many investors don’t understand that index funds don’t own the
underlying stocks, but just the index. At last, he argues that it’s better to invest in Japanese
undervalued small-cap companies in order to create excess return.
Other arguments against passive index funds such as the AP7 Såfa are the difficulty of market
timing. Bhattacharya et al. (2016) conclude in their paper that users of ETFs do not improve
their actual portfolio performance because the lack of ETF timing as well as the lack of ETF
selection.5 Although, they conclude that ETFs are important financial innovation instruments
with huge potential to act as a low-cost opportunity for diversification.
5
An ETF, Exchange Traded Fund, is a fund that is traded at the market just as usual stocks.
20
4.2 Households’ performance
Some studies have been made to search for the performance of households versus the
professional managers. Morningstar (2019) found in their study that households do
underperform the market nine of eleven years, which confirms the earlier studies where a
passive managed fund is a better alternative than actively managed funds finding the greatest
return over time.
Meyer et al. (2012) find evidence that is consistent with earlier research. In their study made in
Germany 2005-2010 they looked into 9000 households and concluded that 91% of these
households did underperform the market.
4.3 Performance in the premium pension system (PPM)
Applying active versus passive portfolio management in the Swedish premium pension system
has been made in a lot of studies. Researchers do not really agree with the performance of the
AP7 Såfa and therefore have varying conclusions of the allocation alternatives, where some
promote the actively choice from the fund market and some the passive alternative AP7 Såfa.
Michelsson and Klarin (2018) conclude that activity in the PPM is negatively correlated with
returns, why the best performing group were the one with 100% allocated in the passive
alternative AP7 Såfa. Johansson (2019) shows that households that have not invested in the
AP7 Såfa have received lower returns for all alternatives and conclude that the passive
alternative cannot be said to underperform the actively managed funds at the market in PPM.
Although, none of the results are statistically significant why any conclusions cannot be made.
Svensson and Khouchaba (2018) investigate the performance of 51 equity funds available in
the Swedish premium pension and conclude that there are funds to select in order to reach
excess return. At the same time, they conclude the importance for investors to remain active
and to alter their selections continuously over the years.
Jacobson and Lundgren (2009) searched for evidence to find which alternative was the most
beneficial, when investing in the premium pension system: to actively manage the portfolio or
to choose the passively managed default fund AP7 Såfa.6 Their findings were that the mutual
6
Before 2010, when the premium schemes were updated, the AP7 Såfa was called Premiesparfonden.
21
funds did reveal a higher utility than the default funds. Although, due to the costs to find these
top performing funds the investor couldn’t benefit from the excessive utility coming from the
mutual funds. However, the performance of the passive alternative PPM and the overall fund
market in PPM seems to have varied conclusions depending on the research method.
4.4 Treynor-Black Model
Few studies have really been made to search for the optimal tangency portfolio P using TreynorBlack model. Brown (2015) found that creating accurate forecasting alphas using historical
prices were dependent of using a professional analyst team. Using historical prices himself
didn’t result in any definite pattern.
Kane et al. (2003) used data of forecasted alpha from a real analyst firm and concluded that the
profitable forecast of abnormal returns was extremely low. They also concluded that the
profitability of low-precision forecast needs the use of sophisticated econometric models, such
as Ordinarye Least Squares (OLS), and is not available for households due to the problem of
forecasting alpha and abnormal returns.
22
5. Method
5.1 Choice of method
The researcher has not been able to control the data, why any manipulation or editing in the
data has been feasible. The researcher has faith in that the data which is collected and analyzed
are accurate in its results and are giving the best objective sight on the relevant information
(Cooper and Schindler, 2011).
The study is made with a positivistic approach where research findings have been observed and
quantified. The approach will allow the researcher of this paper to analyze findings and draw
conclusions in an objective manner, making the researcher independent with results based on
facts.
The paper will apply a formal study in order to investigate whether the default option in the
premium pension scheme, AP7 Såfa, has delivered excess return compared to given actively
managed portfolios. This type of quantitative approach is commonly used when searching for
information about behavior, choice and attitudes (Cooper and Schindler 2011). The research
will be performed by collecting numerical data which are analyzed by mathematical
measurements taken from early studies and research in order to find answers for the stated
research questions (Watson 2015).
5.2 Collection of Data
All data in this paper is to be considered as secondary data, where all information presented
will be evaluated and analyzed in order to find answers to the research questions. The data is
mainly collected from the Swedish pension agency, but also from articles and books which
have been considered as relevant for this study.7 The use of secondary data has made it possible
to gather a remarkable large amount of data for long time horizons (Bryman and Bell 2011).
Because of the secondary data, biases and research errors can have been made. However, the
researcher has good faith in the collected data which sources have been carefully considered.
7
The Swedish Pension Agency is the Swedish authority, appointed by the Swedish government, that has the
responsibility for pension payouts and to administrate the fund market.
23
The data of the AP7 Såfa has been collected from the Swedish pension agency, so have the
compositions of the benchmark index called “Fund 2”. This fund contains of the top five
selected funds each year in the premium pension system.
The annual top five selected funds are the active choice made by the investors in the system,
presented yearly by the agency. Fund 2 is supposed to reflect the actual choice for those
individuals in the premium pension system composing their own portfolio of funds. The fund
composition in Fund 2, which has been yearly updated, is presented in appendix Table 8.
The Swedish pension agency is one of the most reliable sources since it is under surveillance
by the Swedish government. The data do also follow the requirements needed to fulfil the dataquality requirements presented by Jesilevska (2017). Those are the data objectiveness, data
representativeness, data completeness and data accuracy.
The data for professional advisors, i.e. “Fund 1”, has been taken from Morningstar, which has
presented advisory investments alternatives since the beginning of 2000 when PPM was
introduced. Because of the closure of these advises in 2015, the study will focus on the years
available with the data coming from Morningstar. Inc.
Fund 1 contains of the annual fund recommendation made by professional advisors at
Morningstar. Inc, presented in appendix Table 5. Fund 1 is supposed to reflect the alternative
of buying the service and letting a professional advisor compose the portfolio in the premium
pension system. The composition contains of an average from six annual recommended funds
composed in order to offer different level of risks to the individual buying the investment
service.
5.3 Research Design
5.3.1
Sampling
The population of this study has been taken from the Swedish premium pension system. Some
of the funds are selected by professional advisors, such as those from Morningstar. Inc, and
some of them have been selected based on the most selected funds by investors in the system.
The sample has no criteria for lifetime or size but are selected from the funds with the highest
rank in the investor portfolio. The researcher believe that this sample will be a good reflection
of the overall active management in the premium pension system made by investors. See
appendix for the funds included in this paper.
24
The sample contains annual data over the period 2000-2015, why a total of 15 points are taken
into account in the regression analysis. The reason of 15 years data is the closure of
Morningstar. Inc public advice which in this study are considered to reflect the portfolios by
investment advisors. The period of time actually included two financial crises, which gives the
opportunity to analyze and conclude for results even in periods of distress and panic.
5.3.2
Calculations, Assumptions and Benchmark indexes
The fundamental of this study is built upon the theories described in the theoretical framework,
which include the risk-adjusted performance measurements and the underlying theory coming
from the Efficient Market Hypothesis, the Single-Index Model, Modern Portfolio Theory,
Capital Asset Pricing Model and the Treynor-Black Model. These theories with the associated
models have been central in the research design, method and evaluation of the results. The
measurement tools like the Standard Deviation, Sharpe Ratio, Beta, Alpha and Variance have
been necessary calculations in order to compare the results with the benchmark indexes.
The data has been annual updated with the latest ranks of securities in the premium pension
system and the latest advises taken from Morningstar. Inc.
As the benchmark to AP7 Såfa and the related portfolios, the MSCI World Index has been used.
This is the benchmark that is used to evaluate the performance of AP7 and its default fund AP7
Såfa (AP7 2020). The index is a worldwide equity benchmark which includes large- and midcap equity across 23 countries (MSCI 2018). Since this is the benchmark index for the premium
pension system, the researcher considers this benchmark as suitable for the purpose of this
study.
The risk-free rate, RF, used for equations in the regressions is the Riksbank’s reference rate,
which is an interest rate that is set by the Swedish Riksbank twice a year (Riksbanken, 2021).
The reference rate is steered by the repo rate rounded up to the closet half percentage point, if
necessary. The reference rate used in this paper is available in appendix.
5.4 Hypothesis Testing
To be able to draw conclusions of the data and the AP7 Såfa, the statistical inference method
of hypothesis will be used. By creating constant decision-making principles gives the
opportunity to find whether probabilities of given assumptions, hypothesis or statements are
true or false. The phases include (Pereira and Leslie 2009):
25
1. Formulation of null hypothesis
2. Select test statistics and significance level
3. Compare computed value to the designated significance level
This paper will consider and test whether the yearly alpha for the given active managed
portfolios, during the period 2000-2015, is significant with a two-tailed hypothesis test. Since
the one-tailed test only allows for the alternative hypothesis to be either higher or lower than
the null hypothesis, the two-tailed test used in this study allows for the value to be both higher
or lower than the null hypothesis. The two-tailed hypothesis test can be written as (Anderson et
al. 2010):
𝑡=
𝑥̅ − 𝜇7
𝑠
√𝑛
where 𝑥̅ is the sample mean, 𝜇7 the mean of the population and
<
√(
the standard error.
The hypothesis in this study will use the significance level of 1.96 with alpha equal to 5%
(0.05). The hypothesis can be formulated as:
𝐻7 = −1.96 > 𝛼 > 1.96
𝐻# = −1.96 < 𝛼 < 1.96
5.5 Critical assessment
Sortino and Satchell (2001) criticized the Sharpe ratio due to the standard deviation which was
considered to not be good enough measuring risk. In their paper they argue that the standard
deviation may be misrepresentative due to non-normally distributed returns and variation in the
level of risk from the investor. However, the Sharpe ratio is one of the most popular ratios
measuring risk.
An issue that is taken up by Admati (1985), Dybvig and Ross (1985) and Kane and Marks
(1990) is that Treynor-Black point out that the quality of forecasts when optimizing the
portfolio has to be explicitly accounted. Since a large part of the TB is to find securities in order
to optimize the portfolio, alpha forecasting is an important step when constructing the portfolio.
Although, alpha forecasting based on historical information using prior years data, as in this
26
paper, the outcome will probably not be as good as professional’s analysis. Accurate forecasting
is not an easy task even for professional analysts (D.Brown, 2015).
27
6. Empirical Results and Analysis
6.1 Risk-Adjusted Performance
Risk-adjusted performance has been calculated for each portfolio composition in order to give
answers for the research questions in this paper. The measurements used to find the riskadjusted performance is the Sharpe ratio which is calculated as a mean value for the entire timeperiod.
6.2 Risk Exposure
The measurements used to find the risk-exposure of AP7 Såfa to clarify if the AP7 Såfa has had
an excess risk-adjusted return compared to the benchmark MSCI World Index is beta, standard
deviation and alpha. The outcome of the calculations is shown in Table 1 where each fund,
including the index fund AP7 Såfa, is presented.
Table 1. Average risk premiums, standard deviations, alpha, beta and significance of Fund 1, Fund 2 and, the
index fund AP7 Såfa and the MSCI World Index risk. RF is the average reference rate taken from the
Swedish Riksbank during the period.
Fund 1
Fund 2
AP7 Såfa
MSCI
World
Index-RF
Average
0,0579111
0,0618667
0,0602667
0,0284000
Std. Dev
0,1651277
0,2387419
0,2210438
0,1935266
Alpha
0,0354127
0,0290694
0,0292091
0,0000000
Sig.
0,6921674
0,5429120
0,5583467
Beta
0,7921991
1,1548325
1,0935771
Sharpe Ratio 0,3507049
0,2591362
0,2726458
RF
0,0200000
1,0000000
0,1467499
Source: MSCI (2018).
The beta has been calculated to show which of the composed funds that has experienced the
most response to market fluctuations, i.e. which one of the funds that has been most affected
by movements in the MSCI World Index, the benchmark index to AP7 Såfa.
The highest beta is found for Fund 2, the household portfolio, which indicates higher systematic
risk than the market (𝛽 > 1) and therefore more fluctuations than MSCI World Index.
28
Furthermore, looking at the fund compositions, the lowest value of beta is found in Fund 1 the
advisor portfolio, indicating that the composition is less volatile relative to the market index.
The index fund got a value that is less volatile than Fund 2 but more volatile than the MSCI
World Index, but also Fund 1.
An alternative measurement of risk is the standard deviation. Even in this case, Fund 2 got the
highest level of risk calculated as the mean standard deviations for the measured period. This
is to be compared with Fund 1, which standard deviation is higher during the period. These
results are a good reflection of the betas where the funds, including the index fund, got the same
rank as with the measurement of beta.
Alpha has been calculated for each fund, including the index fund. The superior value relative
to the benchmark index is pretty much the same for each fund, where Fund 1 has a small
superiority to the others. Although, all three alternatives show a positive alpha, meaning that
investing in the index fund as well as in the active management compositions, is better than
investing in the benchmark MSCI World Index.
To check if the annual alpha is significant or not, a hypothesis testing using a t-test was
conducted in addition to the calculated alpha. From these testing, the author can conclude that
the alpha was not significant for either of the funds, including the index fund. Thus, the
calculations can prove that none of the funds have an alpha lower or higher than the significance
level of -1,96 or 1,96, why the conclusion is that neither fund performed significantly worse or
better than the MSCI World Index.
The preferred level of risk differs among each individual investor. Since there exists risk-averse,
risk-neutral and risk-seeking investors, investments are due to be various attractive depending
on each individual. Having this in mind, it may be difficult to find a solution that fits all due to
the differences in risk-preferences among different investors. However, the purpose of this
thesis has been to investigate the performance of the AP7 Såfa and to find benefits using the
Treynor-Black model.
Observing the calculated risk-exposure measurements, the index fund is not the best alternative
but still not the worst. The index fund is more volatile than its benchmark MSCI World Index,
but so is the household portfolio Fund 2.
Fund 1 on the other hand has a lower beta and standard deviation. Digging into the composition
of Fund 1, there is a clear pattern where the lower risk portfolios have a low degree in beta but
29
also in the standard deviation. However, the highest level of Sharpe ratio is found in the active
management portfolios, where all the ratios are higher than Fund 2 and the index fund.
Table 2. Risk performance measures of Fund 1.
Fund 1
Average
0,0579111
Std. Dev
0,1651277
Alpha
0,0354127
Sig.
0,6921674
Beta
0,7921991
Sharpe Ratio 0,3507049
6.3 Portfolio Performance Evaluation
6.3.1
Active versus passive managed portfolio
For each of the composed fund the risk-adjusted performance has been calculated in order to
analyze whether the investors are compensated for active managed portfolios or if they should
be satisfied with the passive index fund alternative AP7 Såfa.
Table 2 shows that only one of the two actively managed funds, Fund 1, have outperformed the
index fund. Although, it is also shown that the risk for Fund 1, considered to beta and standard
deviation, is remarkably lower than the index fund. Fund 2 has, as shown before, has the highest
level of both beta but also the standard deviation, meanwhile the average return is the same as
the index fund. Observing the risk-adjusted performance measurement, Sharpe ratio, the highest
value is found for Fund 1 followed by the index fund and Fund 2.
Table 3. Average risk premiums, standard deviations, alpha, beta and significance of the Fund 1, Fund 2 and the
index fund.
Average
Std. Dev
Alpha
Sig.
Index
Fund 1
Fund 2
Fund
RF
0,0579111 0,0618667 0,0602667 0,0200000
0,1651277 0,2387419 0,2210438
0,0155174 -0,0009590 0,0000000
-0,0552483 0,0259560 0,0000000
30
Beta
0,7034363
Sharpe Ratio 0,2901457
1,0424615
0,2172500
1,0000000
0,2274059
Observing alpha, the same results are shown, where Fund 1 has a positive alpha relative to the
index fund, and Fund 2 conversely has a negative alpha. Although, neither results are
statistically significant why no conclusion of positive compensations for the actively managed
portfolios can be made. However, these findings seem to be similar with Barras et al. (2010)
who showed in their study that 75% of actively managed funds present a zero alpha, and that
only 0,6% of all professional investors consistently beat the index.
The Sharpe ratios are evident for that the actively managed funds do not have a superior Sharpe
ratio in comparison to the index fund. Analyzing the results of the risk-adjusted performance
measurements there is no given answer for which strategy is the best when investing the money.
Although Fund 1 has a superior average return and a lower level of risk regarding to beta,
standard deviation and alpha, there exist no statistical significance to prove that the active
alternative is the most beneficial. Observing the household portfolio, Fund 2, the results are
even more scattered since the risk is higher but with an expected return with the highest rank
of them all.
Investors often argue that they have to be appropriately compensated for the additional risk they
are taken on for having risky assets in their portfolio. The same argumentation could be done
for the actively managed portfolio where investors have to be compensated both for the
additional risk they are taking on, but also to the amount of time that is needed to find the
outperforming securities. Since the performance for Fund 1 seems to be higher than for Fund
2, the investor might consider buying the service to invest the money rather than do it itself.
Although, as Berk and Green (2004) confirmed, advisors who perform active management do
not create an excess return compared to its passive benchmarks because of the competitive
market. However, since no evidence could be found for the abnormal returns in Fund 1 and
Fund 2, the investor might buy the index fund after all. Given these results and the
argumentation above, the investors could not be said to be compensated for the additional risk
they take on using the active alternatives.
31
Figure 4. Illustration of the results for each fund.
6.3.2
Treynor-Black Model and the combined Portfolio P
Referring to Table 3, it shows how an investor that is aggressive in its investments could benefit
from using the Treynor-Black Model when investing in the premium pension system. The
values described at the left in the table are results of calculations made from the Treynor-Black
model portfolio construction.
Table 4. The optimate portfolio P calculated by calculations from the portfolio construction theory of TreynorBlack Model described in Theoretical Framework.
32
The Sharpe ratio for the index fund during the measured period is increasing when using the
active portfolio A as a combination in the portfolio P. With the combined portfolio P, the Sharpe
ratio increases. Furthermore, the standard deviation of the combined portfolio P is decreasing
and so does the beta, indicating that the overall risk is decreasing when using the index fund
and the actively portfolio A as a combination portfolio P. Since Fund 2 has a negative alpha
relative to the index fund it has a negative weight, 𝑊' , in the portfolio P. For an investor active
at stock markets who is able to forecast that companies in Fund 2 would underperform the
market in given years, the fund could be sold short in order to increase the overall return.
However, since short selling is not available in the premium pension system this is not
considered as an alternative arbitrage opportunity.
The combination of the index fund and the active portfolio A allows the investor to potentially
create abnormal returns. This tells the investor that it is efficient to not only invest in the index
fund alternative, but to combine it with an actively managed portfolio A to reach highest level
of Sharpe ratio. However, as mentioned earlier, an important process of the Treynor-Black
model is to forecast the actively managed securities, i.e. the securities in the active portfolio A
that will be combined with the index fund creating the combined portfolio P. As Brown (2015)
argued, creating accurate forecasting alphas using historical prices is in fact dependent on the
use of a professional analyst team. Using historical prices itself do not result in any definite
pattern.
33
7. Conclusion
The purpose of this study was to evaluate if the passive alternative in the premium pension
system AP7 Såfa has had an excess risk-adjusted return compared to given portfolios in the
premium pension selection system, and how the investor would benefit from managing the
portfolio more actively. The study has also searched for how to improve the risk-adjusted return
using the Treynor-Black model in order to check the optimal allocation between the active
managed portfolio versus the index fund AP7 Såfa.
The thesis has shown evident for how investors could improve the risk-adjusted return by using
sophisticated strategies in the premium pension system. Although the return doesn’t increase,
the overall risk is decreasing substantially. The thesis has also shown that returns coming from
portfolios made by advisors seem to have higher risk-adjusted returns than those portfolios
made by households.
The index fund AP7 Såfa has an overall risk level that is lower than the average risk coming
from households’ investments. At average, the households would take advantage from using
the index fund and not manage the portfolio themselves. However, using a financial advisor
may be another profitable way forward. Although, the average return from the household
portfolio may be the highest of the three compared alternatives, but this is undeniably a
consequence of the risk that is taken, where the risk is remarkably high in all performance
measurement made.
The thesis found abnormal returns opportunity using the Treynor-Black model, where the
expected return ended up at average, but with the benefit of a considerably lower risk. However,
for households to use a sophisticated strategy such as the Treynor-Black model, it requires
knowledge of market fluctuations and how to find securities that will be winners for the coming
up periods. Although, even if strategies like Treynor-Black model may be difficult for
households to use, the paper has shown that is possibly for investors in the premium pension
system to improve their risk-adjusted return by combining active and passive management,
such as the portfolio construction in the TB model.
The calculations made in this study can prove that none of the funds have an alpha lower or
higher than the significance level made in the t-test, why the conclusion is that neither fund
performed significantly worse or better than the MSCI World Index. The question asked in this
34
thesis, whether the AP7 has had an excess risk-adjusted return compared to given portfolios in
the premium pension selection, can therefore not be said to be the case.
To conclude, this thesis has shown that there might be superior strategies rather than the index
fund to find risk-adjusted excess return in the premium pension system. However, those
strategies require professional analysts in order to forecast securities. For household choosing
between active management themselves or the index fund AP7 Såfa, the most beneficial
investment is to choose the index fund and not active manage the portfolio. The optimum
strategy is found to be the Treynor-Black model with a combined portfolio of the index fund
and the active portfolio.
35
8. Further research
The efficient market hypothesis, EMH, suggest that expected returns are a consequence of
available information. Thus, the investors with the most information should be those having the
best returns. Finding information is a matter of time invested but also a consequence of skills
and contacts. In PPM, the investors consist of households who are amateurs in the financial
market. Since strategies such as the Treynor-Black model requires knowledge and good
forecasting skills, time and information, further research is suggested to find what strategies are
realistic for amateurs with lack of knowledge, time and information to take on.
Since the premium pension system contains 2,5% of the annual income, the author believes that
a study with regard to the complete fund selection in the occupational pension system should
be interesting. All Swedish employees with an agreement for occupational pension have the
right to invest 50% of their pension into insurances with funds in order to obtain higher returns
than in traditional insurances. By using PPM and the occupational system as a whole, the reader
should have a broader picture of the risks that are taken on for the households when investing
for their pension.
In this thesis no delimitations have been made for costs, why another proposal for further
research is to include costs in order to analyze and compare for which strategy is the most
beneficial for the investor. Since the results in this thesis show a strong advantage for Fund 1,
the advisor portfolio, this should be delaminated for it costs of buying the service. Further
research should then take into account the costs of advisors and actively managed funds in terms
of fees and absent returns. This will perhaps also find evidence enough to answer the question
if the households lose money due to the financial turmoil.
36
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40
Appendix
Table 5. Risk premiums of the advisor Portfolio=Fund 1 (average taken from portfolio 1-6)
Passive
Low Risk
Passive
Medium
Risk
Passive
Active
High Risk Low Risk
Active
Medium
Risk
Active
High Risk
Fund 1
2001
0,0050000 -0,0760000 -0,0570000 -0,0290000 -0,0310000 -0,0090000 -0,0328333
2002
-0,2660000 -0,3880000 -0,3630000 -0,1930000 -0,2510000 -0,1950000 -0,2760000
2003
0,1040000 0,1270000 0,1380000 0,1770000 0,2640000 0,3930000 0,2005000
2004
0,0790000 0,0550000 0,0490000 0,0470000 0,0610000 0,0550000 0,0576667
2005
0,1810000 0,3390000 0,3280000 0,1500000 0,2050000 0,2950000 0,2496667
2006
0,0510000 0,0350000 0,0380000 0,0000000 0,0040000 0,0020000 0,0216667
2007
0,0190000 0,0100000 0,0110000 -0,0080000 -0,0050000 -0,0100000 0,0028333
2008
-0,1990000 -0,3240000 -0,3410000 -0,1070000 -0,1290000 -0,1530000 -0,2088333
2009
0,1980000 0,2570000 0,2870000 0,3670000 0,4490000 0,4870000 0,3408333
2010
0,0530000 0,0660000 0,0830000 0,0340000 0,0580000 0,0720000 0,0610000
2011
-0,0380000 -0,0700000 -0,0920000 -0,0190000 -0,0790000 -0,0900000 -0,0646667
2012
0,0920000 0,0860000 0,1080000 0,0950000 0,1240000 0,1250000 0,1050000
2013
0,2150000 0,2270000 0,2330000 0,1300000 0,2130000 0,1930000 0,2018333
2014
0,1160000 0,2090000 0,2210000 0,1090000 0,1490000 0,1800000 0,1640000
2015
0,0380000 0,0620000 0,0560000 0,0380000 0,0440000 0,0380000 0,0460000
Average
0,0432000 0,0410000 0,0466000 0,0527333 0,0717333 0,0922000 0,0579111
Std. Dev
0,1331525 0,1987885 0,2008858 0,1307629 0,1721687 0,1919405 0,1651277
Alpha
0,0244740 0,0122197 0,0176570 0,0370935 0,0508569 0,0701749 0,0354127
Sig.
0,4304849 0,2454850 0,3508874 0,7207138 0,9747954 1,2873588 0,6921674
Beta
0,6593674 1,0133891 1,0191210 0,5507000 0,7350857 0,7755315 0,7921991
Sharpe Ratio 0,3244399 0,2062494 0,2319726 0,4032746 0,4166456 0,4803571 0,3507049
41
Table 6. Risk premium of the household portfolio=Fund 2 (annual top-5 funds from PPM)
Fund 2
2001
-0,1020000
2002
-0,3970000
2003
0,1700000
2004
0,0580000
2005
0,2940000
2006
0,0870000
2007
-0,0140000
2008
-0,3980000
2009
0,4880000
2010
0,1590000
2011
-0,0890000
2012
0,1220000
2013
0,2380000
2014
0,2300000
2015
0,0820000
Average
0,0618667
Std. Dev
0,2387419
Alpha
0,0290694
Sig.
0,5429120
Beta
1,1548325
Sharpe Ratio 0,2591362
42
Table 7. The average reference rate.
RF
2001
0,0200000
2002
0,0450000
2003
0,0400000
2004
0,0300000
2005
0,0200000
2006
0,0150000
2007
0,0300000
2008
0,0400000
2009
0,0200000
2010
0,0050000
2011
0,0150000
2012
0,0200000
2013
0,0100000
2014
0,0100000
2015
0,0000000
Average
0,0200000
Table 8. Constructed portfolios named as the household portfolio=Fund 2 (annual top-5 funds
from PPM)
Return
Date
001231
Name of Fund
2001
Roburs Aktiefond Contura
-32
AMF Pensions Aktiefond - Världen
-8
Roburs Aktiefond Medica
-3
Didner & Gerge Aktiefond
6
AMF Pensions Aktiefond Sverige
-4
-8
Return
Date
011231
Name of Fund
2002
Roburs Aktiefond Contura
-49
AMF Pensions Aktiefond - Världen
-32
Roburs Aktiefond Medica
-35
43
Didner & Gerge Aktiefond
-34
AMF Pensions Aktiefond Sverige
-26
-35
Return
Date
021231
Name of Fund
2003
Roburs Aktiefond Contura
18
AMF Pensions Aktiefond - Världen
22
Roburs Aktiefond Medica
1
Didner & Gerge Aktiefond
33
AMF Pensions Aktiefond Sverige
31
21
Return
Date
031231
Name of Fund
2004
Roburs Aktiefond Contura
-10
AMF Pensions Aktiefond - Världen
14
Roburs Aktiefond Medica
-1
Didner & Gerge Aktiefond
21
AMF Pensions Aktiefond Sverige
20
9
Return
Date
041231
Name of Fund
2005
Roburs Aktiefond Contura
23
AMF Pensions Aktiefond - Världen
32
Didner & Gerge Aktiefond
34
AMF Pensions Aktiefond - Sverige
37
Roburs Aktiefond Medica
31
31
Return
Date
051231
Name of Fund
2006
Robur Contura
-7
AMF Pensions Aktiefond - Sverige
31
AMF Pensions Aktiefond - Världen
19
Didner & Gerge Aktiefond
17
Robur Medica
-9
44
10
Return
Date
061231
Name of Fund
2007
AMF Pensions Aktiefond - Sverige
-4
Swedbank Robur Contura
8
AMF Pensions Aktiefond - Världen
2
Didner & Gerge Aktiefond
0
Swedbank Robur Aktiefond Pension
2
2
Return
Date
071231
Name of Fund
2008
AMF Pensions Aktiefond - Sverige
-38
Swedbank Robur Contura
-30
AMF Pensions Aktiefond - Världen
-35
Didner & Gerge Aktiefond
-42
Swedbank Robur Aktiefond Pension
-34
-36
Return
Date
081231
Name of Fund
2009
AMF Pensions Aktiefond - Sverige
55
Swedbank Robur Contura
39
AMF Pensions Aktiefond - Världen
41
Didner & Gerge Aktiefond
82
Swedbank Robur Aktiefond Pension
37
51
Return
Date
091231
Name of Fund
2010
AMF Aktiefond Sverige
26
SKAGEN Global
9
Swedbank Robur Contura
2
AMF Aktiefond Världen
16
Didner & Gerge Aktiefond
29
16
Return
45
Date
Name of Fund
AMF Aktiefond Sverige
Swedbank Robur Sverigefond MEGA
101231
2011
-15
9
Didner & Gerge Aktiefond
-18
SKAGEN Kon-Tiki
-15
Swedbank Robur Contura
2
-7
Return
Date
111231
Name of Fund
2012
AMF Aktiefond Sverige
18
Didner & Gerge Aktiefond
26
Swedbank Robur Contura
5
AMF Aktiefond Världen
14
SKAGEN Kon-Tiki
8
14
Return
Date
121231
Name of Fund
2013
Swedbank Robur Technology
23
AMF Aktiefond Sverige
27
AMF Aktiefond Världen
25
Didner & Gerge Aktiefond
28
Swedbank Robur Aktiefond Pension
21
25
Return
Date
131231
Name of Fund
2014
Swedbank Robur Technology
43
AMF Aktiefond Sverige
16
Didner & Gerge Aktiefond
19
AMF Aktiefond Världen
20
Swedbank Robur Aktiefond Pension
22
24
Return
Date
141231
Name of Fund
Swedbank Robur Technology
2015
11
46
AMF Aktiefond Sverige
8
Didner & Gerge Aktiefond
9
AMF Aktiefond Världen
9
Swedbank Robur Aktiefond Pension
4
8
Table 9. Yearly risk premiums of Fund 1, Fund 2, the index fund AP7 Såfa and the MSCI
World Index risk.
Fund 1
Fund 2
AP7 Såfa
MSCI
World
Index-RF
RF
2001
-0,0328333 -0,1020000 -0,1250000
-0,0950000 0,0200000
2002
-0,2760000 -0,3970000 -0,3150000
-0,3800000 0,0450000
2003
0,2005000
0,1700000
0,1470000
0,0590000
0,0400000
2004
0,0576667
0,0580000
0,0710000
0,0300000
0,0300000
2005
0,2496667
0,2940000
0,2310000
0,2910000
0,0200000
2006
0,0216667
0,0870000
0,0900000
0,0170000
0,0150000
2007
0,0028333 -0,0140000 0,0170000
-0,0020000 0,0300000
2008
-0,2088333 -0,3980000 -0,4020000
-0,3320000 0,0400000
2009
0,3408333
0,4880000
0,3310000
0,1930000
0,0200000
2010
0,0610000
0,1590000
0,1270000
0,0430000
0,0050000
2011
-0,0646667 -0,0890000 -0,1300000
-0,0550000 0,0150000
2012
0,1050000
0,1220000
0,1650000
0,0790000
0,0200000
2013
0,2018333
0,2380000
0,3300000
0,2410000
0,0100000
2014
0,1640000
0,2300000
0,3010000
0,2690000
0,0100000
2015
0,0460000
0,0820000
0,0660000
0,0680000
0,0000000
47