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**Methodology**

This section covers the research methods which are used in the study and the selection of funds which consists of time period, data and impact on survivorship bias. Moreover, the data sources are defined and the compo-sition of returns and risk-free rate are presented in this section. After all, the variables used in the regression analysis are explained in more detail and the empirical method is presented in this chapter.

** Research methods**

According to Kothari (2004), research is an academic activity and consists of defining and redefining problems, formulating research questions or proposed solutions; collecting, ar-ranging and evaluating the data and bringing up implications. Finally, testing if the research questions are being answered by the achieved implications. The aim of the research is to determine answers to questions by applying scientific procedures.

In order to conduct the research it is necessary to determine what philosophies, approaches and choices of data to adopt to it that the research would be consistent and sufficient and presented implications would be reliable. According to Saunders, Lewis and Thornhill (2012), there are four types of research philosophies in business management: positivism, realism, interpretivism and pragmatism. The positivistic view believes in the possibility to observe and describe reality from an objective point of view. For instance, the philosophy can determine ―general‖ relationships and ―general‖ laws or test the theories (Saunders et al., 2012). The authors of this thesis believe to reflect the positivism in this study where the data, based on empirical observations, is collected to describe the objective reality of fund’s performance.

To be able to answer the research question, the deductive research approach was chosen. Based by Saunders et al. (2012), the deductive research approach is used to test the theory and moves from theory to data. In addition, the approach is mainly used for collecting quantitative data, applying controls for validity of data, selecting the samples of a sufficient size. This was also the case in this thesis, where the research question has tested the effi-cient market hypothesis in the Swedish market, based on quantitative fund-data. Moreover, a deductive approach is related to the development of a hypothesis and is based on existing theory and includes the composition of the research strategy to test the hypothesis (Saun-ders et al., 2012). Although, this thesis has not based the research on hypothesis testing ex-plicitly by using H 0 and H1 from statistics, the research questions arisen from the theory were considered as the hypothesis which was needed to be answered.

Following the deductive approach, quantitative data was used in this thesis. The decision to use quantitative data instead of qualitative data (interviews) is due to that if the perform-ance evaluation of mutual funds would have been tested by using qualitative data, it could have resulted in a study concentrated only on strategies the managers use or valuation techniques of the stocks they apply. As far as the authors of this thesis know, the majority of this type of information is confidential in the mutual funds industry. Moreover, the best way to test the efficient market hypothesis was considered by the authors of this thesis to be the quantitative approach. Moreover, the use of quantitative data when measuring per-formance of mutual funds is justified in previous research (Fama & French, 2009; Elton et al., 2011).

** Selection of funds**

In order to avoid biases in the sample, only equity based mutual funds which should be de-fined as the actively managed funds were included. The reason for the sample chosen was that passively managed funds did not line up with the purpose of the thesis since they are tracking specific indexes. Actively managed equity mutual fund managers are seeking to over perform the market by selecting the exact securities which seem to be perspective in their analysis (Elton et al., 2011). As the model in this thesis was applied for the Swedish market, the sample was extended with another boundary, namely the Swedish based equity mutual funds, which invests the major part of their capital in Sweden. The other boundary that was set for the sample was that the funds chosen should be surviving for the estimated time period. This means that that the funds should be active during the time period that was studied.

** Time period**

A time period of ten years for the period 2003-2013 was chosen. The period was chosen due to the exact availability of the data. In addition, the choice of the time span was based by the fact that the longer the time period, the higher the probability to avoid the biased es-timation errors (Bartholdy & Peare, 2005). The importance of this time span was also based by the rapid increase of funds’ asset values in recent time. According to the Swedish In-vestment Fund Association (2014), the Swedish fund market has more than twice as much assets as in year 2003. The authors of this thesis considered that the period of ten years contained sufficient amount of information to present insights and implications and to per-form an in-depth analysis in this study.

**Data**

The data was collected using Morningstar of Sweden and Thomson Reuters Datastream databases, as well as data provided by the Swedish Investment Fund Association, which supplies the data of the operating funds in Sweden. First of all, 108 Swedish based equity mutual funds investing in Sweden were found. The funds were sorted out in line with our timeline (2003-2013) and the funds which were out of the time period were eliminated since only ten years data was needed. The names and the ISIN codes of a total of 42 equity mutual funds investing in Sweden were extracted from Morningstar of Sweden. After-wards, Datastream was used in order to get the monthly Net Asset Values (NAVs) of the funds with the adjustment for dividends. The data of only 21 out of 42 equity mutual fund was provided using this database. Subsequently, the authors of this thesis turned to the Swedish Investment Fund Association to get the data of the remaining funds. The adjusted daily data of 21 equity mutual fund was presented and the monthly NAVs were obtained from this data by taking the adjusted closing NAV value of every month in order to be in line with the remaining fund data obtained from the Datastream database. Hence, the total number of funds in the sample was 42.

The data collected from Datastream was considered to be secondary data, since this type of data include raw data or was used previously for some other purposes (Saunders et al., 2012). Even though the data is secondary data, the authors of this thesis assume that Thomson Reuters Datastream is a reliable resource since previous academics have used it for their empirical studies (Dalquist, Martinez & Söderlind, 2014) and it is widespread be-tween the practitioners in finance. Moreover, the Swedish Investment Fund Association provides their data to Datastream for onward transmission to the media.

** Return**

Mutual funds are traded using the Net Asset Values (NAV). In other words, it is the term of the underlying securities of the fund per share. The NAV is calculated one time per day at the end of the trading day and reflects the mutual fund’s share price for the next trading day (Farlex Financial Dictionary, 2009). The NAV comprises of the market value of the different assets that the fund holds and dividing it by the number of shares in the fund. The NAV includes reinvestments of income and capital gains. The monthly return of the mutual fund was calculated using the following formula:

= +1− ,+1 where +1 denotes the return in month t+1, +1 is the net asset value of the fund on the last trading day of the month t+1, is the net asset value for the fund the last trading day at month t (Simons, 1998).

The analysis was performed by focusing on the equally weighted portfolio. This was done by taking the average of the monthly returns of every fund in order to get the equally weighted portfolio. Monthly excess returns were calculated from February year t to De-cember year t+1. The returns were calculated from January year t, except for 2003, when returns were calculated from February 2003 due to the starting data point of monthly NAV as January 2003.

** Risk free rate of return and the market return**

As the risk free rate, the monthly 90-days treasury bills of Sweden was obtained from the Swedish Central Bank. The monthly rates were chosen in order to be in line with the same time span as the funds’ returns (Fama & French, 2009). The OMX Stockholm 30 Index was used as the market return in this thesis based on previous research.

** Management fees**

The yearly management fees were obtained from the Swedish Morningstar database for most of the funds and other fees were taken from the funds’ prospectus. Subsequently, the yearly fees were adjusted for the monthly data by dividing each fund’s early fee by twelve and as a result obtaining the monthly number. The yearly management fees of the actively managed equity mutual funds varied between 0.3 % and 2.5 % in our sample. The idea to include fees into the analysis of this thesis was due to the claim that if the efficient market hypothesis holds, equity mutual funds managers should not be able to outperform the market. Additionally, to test if underperformance of the funds was due to the expenses they charge.

**Sorting into deciles**

In order to perform the broader analysis, the data was sorted out into deciles (Flam & Vestman, 2014). First of all, the 42 regressions were run against each of the 42 funds net and gross of management fees and 42 alphas were obtained. The alphas were sorted out from the largest to the smallest by value in line with the funds. The funds were sorted out into deciles by the best performing funds to the least performing funds according to the obtained alphas. Each decile was composed by averaging the alphas of the funds in the de-cile. The funds were sorted out into ten deciles that all of the deciles would have an integer number of the funds.

**Alpha transformation**

The observed alphas were denoted as monthly alphas since monthly data was used in this thesis. For comparison purposes, the alphas were annualized and reported as both monthly and annualized alphas in the result section of this thesis. The monthly alpha was annualized by employing the following formula (Betker & Sheehan, 2013):

= 1+ ℎ 12− 1

**Impact on survivorship bias**

Some of the previous studies have presented that survivorship biases might have a substan-tial impact in estimating funds performance since it can cause an over-estimation of funds returns (Malkiel, 1995; Elton, Gruber & Blake, 1996b). By only using a survivorship bias free screened sample of funds, it was possible to analyze the effect of using only surviving funds in this thesis. For the ten year time period, only funds which survived during this pe-riod were included in the sample in order to avoid the survivorship bias effect in this thesis. Even though it was not tested if the mean returns of surviving funds were statistically dif-ferent from the mean returns when including all funds, and therefore if the alpha was over-estimated in the model, the authors of this thesis relied on the previous studies which stated the importance of survivorship bias and the need to eliminate the dead funds from the sample (Leite et al., 2009).

** Presentation of the model**

The model that was used in this thesis was the Fama-French three factor model. As men-tioned before, the lack of Swedish papers using this model and the fact that it is a base for all multi-factor models, was the reason for the choice of the model. Furthermore, Hou, Xue and Zhang (2015) argue that including too many factors, in this case using different modifications of the Fama-French model, does not necessarily mean that the factors can explain the performance better. This also justified why the FF3FM was used in the thesis.

Regarding the regression model, two different regressions were performed in this study to be able to answer the research questions and the purpose related to the net- and gross excess returns of management fees. Both regressions were performed by means of ordinary least squares (OLS) regression analysis. The regression equation below was used to run the regression net of the management fees and one more time run the regression gross of the management fees. In the regression equation, country specific factors were used in order to see the power of the test in Sweden.

The model and regression equation can be presented as follows:

− = + − Rft SWE + SMBSWE + HMLSWE + ,

where the detailed explanation of the dependent and explanatory variables are covered in the following subsections.

To ensure the validity of the results, first of all, the variables were tested for stationarity. Moreover, both regressions were checked for residual diagnostics: autocorrelation, hetero-scedasticity, normality and miss-specification. The results of the previously mentioned tests had no issues, except for autocorrelation. The regressions were adjusted for autocorrelation problems by applying autoregressive and moving-average processes or the combination of both. The Eviews outputs of residual diagnostics are available upon request.

**Explanatory variables**

In this section, the explanatory variables which were used in the regression model are ex-plained. To be more detailed, this section covers MRP, SMB and HML factors. The reader should be aware that only the MRP factor was constructed by the authors of this thesis. However, the construction of all factors will be explained in the following subsections in order to provide the reader with a comprehensive view on their foundations.

** MRP**

MRP is defined as the historical differential return on the market portfolio over the risk-free rate. It can be defined as the excess market return and calculated as follows:= − ,

where denotes the OMX Stockholm 30 Index returns and denotes 90-day treas-ury bills of Sweden. Since the MRP is used to predict expected returns, the use of this proxy is based by the idea that security’s returns are dependent on a market beta.

** SMB and HML**

As stated previously, the SMB and HML factors were not constructed by the authors of this thesis but were instead provided by the Italian professors Stefano Marmi and Flavia Poma (2012) from their website. This was the only source providing Fama-French factors for the Swedish market. The reliability of the factors were checked by comparing the distri-bution of the European factors and the US factors taken from Marmi and Poma’s website with the distribution of the same factors taken from Fama-and French’s original website. The results were plotted and the authors of this thesis did not observe a significant differ-ence between the factors. Hence, the factors provided by the Italian academics were consi-dered as reliable, since they are based on the Fama-French methodology. The authors of the thesis believed that it was necessary to explain the factors more explicitly. Hence, the computation of the factors are presented below.

The factors are constructed by using the 6 value-weight portfolios formed on size and book-to-market (Fama & French, 1993). According to Fama and French (1993), the port-folios for July of year t to June of year t+1 comprise all stocks market equity data for the last fiscal year end before March and June of year t and book equity data for the last fiscal year’s end before March of year t.

According to the Italian professors, the portfolios were constructed at the end of each June following the methodology provided by Fama and French (1993). The methodology indi-cates that the portfolios are the crossroads of the two portfolios formed on size (market equity, ME) and three portfolios formed on the proportion of book equity to market equity (BE/ME). The size for year t is the medium market equity for the last fiscal year end be-fore March t divided by ME for March of t. The dividing line for BE/ME are the 30th and 70th percentiles.

The stocks are separated by the median into two size groups which is small and big (S and B).

Source: Authors’ illustration (based on Fama and French, 1993)

The stocks are also separated into three book-to-market groups denoted as low, medium and high (L, M and H). The smallest 30 % is the low group, the middle 40 % is the medium group and the maximum 30 % is the high group (Fama & French, 1993).

Figure 3-4-2b Sorting by book-to-market ratio (X is a stock in the high group)

Source: Authors’ illustration (based on Fama and French, 1993)

In total, there are three BE/ME groups and two size groups. Every stock is presented in one of the size groups and one of the BE/ME groups.

**1 Introduction **

1.1 Background

1.2 The Swedish mutual fund industry

1.3 Problem statement

1.4 Purpose

1.5 Limitations

1.6 Organization of the thesis

**2 Frame of References **

2.1 Equity mutual funds

2.2 Active management

2.3 Modern portfolio theory

2.4 Capital asset pricing model

2.4.1 Jensen’s alpha

2.5 Efficient market hypothesis

2.6 Modified efficient market hypothesis

2.7 Multi-Factor models

2.8 Fama-French three factor model

2.8.1 Market risk premium

2.8.2 The Size factor and the Value factor

2.9 Previous research

**3 Methodology **

3.1 Research methods

3.2 Selection of funds

3.2.1 Time period

3.2.2 Data

3.2.3 Impact on survivorship bias

3.3 Presentation of the model

3.4 Explanatory variables

3.4.1 MRP

3.4.2 SMB and HML

3.5 Dependent variable

**4 Empirical results **

4.1 Descriptive statistics

4.2 Output of the regression model

**5 Analysis **

**6 Conclusion and discussion **

**List of references**

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