What drives the distribution of mutual funds ? An analysis based on the investment style

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What drives the distribution of mutual funds ? An analysis based on the investment style

Auteur : Ohnmacht, Simon

Promoteur(s) : Hambuckers, Julien

Faculté : HEC-Ecole de gestion de l'Université de Liège

Diplôme : Master en sciences de gestion, à finalité spécialisée en Banking and Asset Management Année académique : 2019-2020

URI/URL : http://hdl.handle.net/2268.2/8700

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What drives the distribution of mutual funds?

An analysis based on the investment style.

Master en Management Sciences Master Thesis

submitted by Simon Ohnmacht simon@ohnmachts.de

# S184767

Academic Supervisor: Prof. Julien Hambuckers

Stuttgart, December 17, 2019

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List of Figures

1 Equity Morningstar style box . . . 3

2 Fixed income Morningstar style box . . . 3

List of Tables

1 Descriptive statistics of investment styles . . . 25

2 Descriptive statistics of covariates . . . 28

3 Risk comparison across investment styles . . . 31

4 Covariate impact comparison with 99,9% VaR of the GPD with the V aR₉₉ as threshold . . . 40

5 Covariate impact comparison with 99,9% VaR of the GPD with the V aR95 as threshold . . . 47

6 ⇠ Lowest 1% of data . . . ii

7 Lowest 1% of data . . . iii

8 ⇠ Lowest 5% of data . . . iv

9 Lowest 5% of data . . . v

10 Average risk measurements according to the dimensions of the investment styles . . . vi

11 1% Growth rate of the Gross Domestic Product USA . . . vii

12 1% Growth rate of the Unemployment-Rate of the USA . . . vii

13 1% Growth rate of the Gross Domestic Product of Germany . . . viii

14 1% Growth rate of the WTI Oil Price . . . viii

15 1% Growth rate of the covariate M1 . . . ix

16 1% Growth rate of the VIX . . . ix

17 1% Growth rate of the federal funds rate of the United States . . . . x

18 1% Growth rate of the S&P 500 . . . x

19 1% Growth rate of the Personal-Savings-Rate of the United States . . xi

20 1% Growth rate of the Consumer Price Index of the USA . . . xi

21 Covariate impact comparison with the 99,9% VaR, based of the GPD with the V aR95 as threshold . . . xii

22 Covariate impact comparison with the 99,9% VaR, based of the GPD with the V aR99 as threshold . . . xiii

23 Covariate impact comparison with the 99% quantile of the GPD with the V aR95 as threshold . . . xv

24 Covariate impact comparison with the 99% quantile of the GPD with the V aR99 as threshold . . . xvi

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25 Covariate impact comparison with the 99% quantile of the GPD with the V aR95 as threshold . . . xvii 26 Covariate impact comparison with the 99% quantile of the GPD with

the V aR₉₉ as threshold . . . xviii

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List of Abbreviations

(99) 99% confidence interval

(95) 95% confidence interval

Cap Market capitalization

CPI Consumer Price Index discrete growth rate

E.g. For example

ES Expected Shortfall

ESG Enviromental Social Governance

ESGHigh Investment style that focus on companies with a high ESG score

ESGLow Investment style that focus on companies with a low ESG score

Ext Extensive interest rate sensitivity

ExtHigh Extensive interest rate sensitivity + High credit quality investment style

ExtLow Extensive interest rate sensitivity + Low credit quality investment style

ExtMid Extensive interest rate sensitivity + Medium credit quality investment style

FundRate Federal fund rate USA discrete growth rate

GDPDE Gross domestic product of Germany discrete growth rate

GDPUS Gross domestic product of the USA discrete growth rate

GPD General pareto distribution

GrowthLarge Growth + high market capitalization investment style

GrowthLow Growth + low market capitalization investment style

GrowthMid Growth + mid market capitalization investment style

Growth Growth investment style

Iid Independent and identically distributed

Ltd Limited interest rate sensitivity

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LtdHigh Limited interest rate sensitivity + high default probability investment style

LtdLow Limited interest rate sensitivity + low default probability investment style

LtdMid Limited interest rate sensitivity + medium default probability investment style

M1 Money supply of the USA discrete growth rate

Mio. Million

Oil WTI oil price discrete growth rate

PSR Personal savings rate of the USA discrete growth rate

S.P Standard & Poor’s 500 index discrete growth rate

S.t Saint

U.S. United States

UnempUS Unemployment rate of the USA discrete growth rate

USA United States of America

Value Value investment style

ValueLarge Value + large market capitalization investment style

ValueMid Value + mid market capitalization investment style

ValueSmall Value + small market capitalization investment style

VaR Value at Risk

VIX Volatility index for S.P discrete growth rate

WTI West Texas Intermediate

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Preamble

Completing this master thesis has probably been one of the biggest challenge in my life so far. For me it was the first time I did a complex empirical analysis on my own. This master thesis gave me the chance to learn the statistical programming language R. Furthermore, it was the first time I used LaTeX in my life. I enjoyed working with both R and LaTeX and I will keep these skills for the rest of my life.

It is my proud privilege to express my gratitude for having the opportunity to study at the University of Hohenheim and the University of Liège, both institutes added knowledge and understanding to my character and thus prepared me for this master thesis. I am extremely thankful to Prof. Monika Gehde-Trapp and the well- structured courses in quantitative risk management. I acknowledge the DALAHO Hohenheim and the HEC Liège trading room for extant access to their databases.

My special thanks goes to my supervisor Prof. Julien Hambuckers for giving me the opportunity to get involved in his current research, for his support and encour- agement to familiarize myself with these statistical sophisticated topics. Through his ideas, guidance and clarifications, he has contributed significantly to the success of this master thesis. Lastly, I want to thank my family and girlfriend for their constant support.

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Summary

This master thesis examines the loss distribution of fourteen mutual fund investment styles, based on the Morningstar style boxes and the Environmental Social Governance score. A large dataset of 276056 to 1122872 monthly return observations were utilized for every investment style, from the observation period October 1999 to September 2019. We first use the concept of the standardized momentums to compare the investment style returns. After that we apply risk measurement techniques such as value at risk, expected shortfall and the parameters of the generalized pareto distribution to compare the probability of high negative returns across the investment styles. Finally we investigate the eﬀect of macroeconomic changes on extreme negative mutual fund returns, by using the parameters of the generalized pareto distribution to calculate and compare the value at risk with a confidence level of 99.9%. To this end, we use U.S. and German data series for variables of money growth, economic growth, inflation, interest rates, VIX, equity and commodity markets as a fair representation of the macroeconomic fundamentals that can possibly influence mutual fund returns.

Most results from our empirical study agree with the existing literature about the diﬀerent risks and returns in regard to the mutual fund style dimensions and the impact of covariates on extreme negative returns of these investment styles. However, some of our findings are not in line with our expectations and the existing literature.

Our key findings are, growth investment styles have on average a higher return than value investment styles. Furthermore, when the inflation is low growth investment styles have a lower probability of extreme negative returns than value investment styles. Moreover mutual funds that focus on companies with high market capitalization have on average higher returns by a similar risk, than mutual funds that focus on companies with low market capitalization. Lastly, the style dimensions, credit quality and interest sensitivity are not relevant for mutual funds, since they have similar returns and risk across the investment styles.

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1 Introduction

In theory, a mutual fund is an investment product where the money of many indi- viduals and institutional investors is pooled into a single investment product. The mutual fund then focuses on the use of this money to invest in a group of assets to reach the mutual fund’s investment goals. A mutual fund is mutual because all of the returns (from dividends, interest, and capital gains) and all of its expenses are shared by the fund’s investors. Mutual funds can provide investors several advantages over investing securities directly. Obviously, investors like these advantages, since investors hold a total of over $30 trillion in fund assets at the end of 2013.

(Pozen and Hamacher; 2015) Till now private U.S. investors invest more of their money in mutual funds than in any other asset, this makes mutual funds the most important investment product for many people. (Pozen and Hamacher; 2015; Bricker et al.; 2012) For private and especially institutional investors there are many diﬀer- ent types of mutual funds available. Though, this vast amount of choices, can be overwhelming for some investors.

This master thesis analysis the risk of different mutual fund investment styles, by using the Morningstar style boxes. Specifically, the style categories are based on five dimensions: debt-equity, market capitalization, value-growth orientation, interest rate sensitivity and credit quality. Furthermore we add a sixth dimension for comparing social responsible investments. Although the issue of mutual fund performance is not our main concern, our empirical analysis let’s investigate whether differences in style are associated with differences in performance. This thesis focuses on the comparison of high and extreme negative returns for mutual fund investment styles. Finally, we try to explain the difference in risk between the investment styles with the help of macroeconomic variables. For this we investigate which impact an increase in a macroeconomic variable has on the extreme negative returns of the investment styles.

Previous research show that mutual fund investment styles have an impact on the the fund performance and risk. (Brown and Goetzmann; 1997; Carhart; 1997) How- ever no direct comparisons of the investment styles in relation to macroeconomic variables for extreme negative returns have been undertaken.

According to our knowledge, this empirical study contributes to the existing literature in several respects.¹ On the methodological front, this is the first paper

1Please be aware, that I am a master student that worked eﬀectively three months on this thesis and can’t be certain that I found all the relevant literature.

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that uses a vector of covariates to predict the scale and shape parameter for the generalized pareto distribution (GPD) to estimate the value at risk (VaR) for extreme negative mutual fund returns. Furthermore this is the first paper that uses the predicated VaR to investigate the impact of a covariate increase on mutual fund returns.

In this thesis we first present the diﬀerent investment styles in chapter 2. Here we link the investment styles to the literature and try to give expectations related to the loss distribution of the investment styles. In chapter 3 we argue how this thesis is related to ethical and sustainable issues. For this we present an investment style that focuses on companies that follow ethical and sustainable values and an other investment style that doesn’t focus on companies with ethical and sustainable values. In chapter 4 we present the diﬀerent covariates that we use in this thesis.

Here we investigate the literature about the influence of changes in macroeconomic conditions on capital markets. Chapter 5 is about the methodology of risk measurement, which we use in this thesis. In chapter 5.1 we first introduce the concept of the standardized momentums. In chapter 5.2 and in chapter 5.3 we present the VaR and expected shortfall (ES) and in chapter 5.4 we introduce the generalized pareto distribution. The focus will be on chapter 5.4, here we also explain how we estimate the scale and shape parameter of the generalized pareto distribution based on a vector of covariates. In addition we introduce the VaR concept based on the parameters of the generalized pareto distribution, to see which influence an increase in a covariate has on the loss distribution of the investment style returns. Chapter 6 is about the data we use in this thesis. In chapter 6.1 we present the mutual fund returns and use the concept of the standardized momentums from chapter 5.1 to compare the investment style returns. In chapter 6.2 we do the same for the covariates. After that we apply the methodology from chapter 5 to the diﬀerent investment style returns in chapter 7. Here we first describe the results in detail and later compare the investment style in relation to their VaR, ES and the parameters of the generalized pareto distribution. In chapter 8 we apply the methodology from chapter 5.4. Here we calculate the VaR 0.999 based on the parameters of the generalized pareto distribution for every investment style and every covariate increase.

We then compare these results to see which covariate has an influence on the loss distribution of the investment styles. In chapter 8.1 we describe the observations in detail. In chapter 8.2 we introduce robustness tests and in chapter 8.3 we compare the investment styles based on the covariates, to see which covariate has a special influence on which investment style. Finally in chapter 9 we summarize the results from chapter 6 to 8.

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2 Mutual fund investment styles

Mutual funds represent a heterogeneous asset class that is diﬃcult to generalize and hard to cluster. However with the Morningstar style box we have an accepted agreement about the way in which mutual funds can be classified. (Bogle; 1998) The Morningstar style boxes consist of a nine-square framework that represents a graphical overview of mutual fund investment styles.

Figure 1: Equity Morningstar style box

Figure 2: Fixed income Morningstar style box

There are two kinds of Morningstar style boxes, one represents mutual funds which consists of stocks and the other represents mutual funds which consists of bonds. For stocks the vertical axis arranges the mutual funds according to the market capitalization of their securities into the three categories: small, mid and large market capitalization. On the other side, the horizontal axis arranges the mutual funds according to the growth rate of their securities into the three categories: value, blend and growth. For bond mutual funds, also known as fixed income funds, the vertical axis arranges the funds according to the credit quality of their securities into the categories: high, medium and low credit quality. On the other side the horizontal axis arranges the mutual funds according to their sensitivity to changes

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in interest rates into the groups: limited, moderate and extensive interest rate sensitivity.

2.1 Equity vs Debt

Investors have the choice of whether to buy debt or equity securities. Debt investments also known as fixed income payments, are for example mortgages and bonds, including interest payments. On the other side with equity investments, for example stocks, the investor receives a certain right on the earnings and/or assets of the corporation. The choice often depends upon the following factors: which risk the investor is willing to take, the companies cash flow and control rights over the company. To separate between debt and equity investments, Morningstar has two diﬀerent style boxes: one is the equity style box and the other is the debt style box.

(Mor; 2019)

Equity investments are usually riskier than debt investments but normally oﬀer a higher but less consistent return. (Mehra and Prescott; 1985) Debt investments are less volatile than equity investments, with fewer ups and downs than the equity market and in case of a default bondholders are paid first. On the other side the fix income market historically has fewer price changes. (Mehra and Prescott; 1985) One of the main reason for the diﬀerence in risk is that debt holders have priority rights if a company is liquidated. Additionally interest payments for debt must be paid, on the other side dividends for stocks do not have to be paid and can be suspended if the company has financial problems. Moreover equity holders have voting rights, which debt holders don’t have. In general debt holder have a lower return with by a lower risk.

2.2 Market capitalization

Market capitalization is defined as the value of all outstanding shares of a company.

According to Morningstar companies that belong to the large-market capitalization group are corporations with a market capitalization of over US$10 billion. Com- panies which belong to the mid-market capitalization group are corporations with a market capitalization between $2 and $10 billion and companies which belong to the small-market capitalization group have a market capitalization between $300 million and $2 billion. (Mor; 2019)

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The market capitalization of a firm is an important characteristic for an investor since it can give a suggestion of the size of the firm and can also be used to compare the size of one firm to another. The characteristic can also give a suggestion of what the other investors think about the future outlook of that firm, since the market capitalization measures how much other investors are willing to pay for the company.

The brand names of companies with a large market capability are often known by consumers and are historically known to produce high-quality goods and high- quality services. (Resnick et al.; 2000; Willmott; 2010) These high-quality goods and high-quality services are often proven on both a national and international scale. Firms with large market capability tend to have steady dividend payments and a consistent growth. That is way, large market capitalization stocks tend to be treated as rather conservative investments compared to companies with a small market capitalization and have a smaller probability of high negative returns. (Minier;

2003) On the other side, large market capitalization stocks are so big and so established that they have problems to increase their market share. That’s why big companies have a lower growth potential than companies with a small market capitalization. Therefore small companies have a higher probability to become large very quickly, because there are many new fields for the companies to expand into.

A large company, on the other hand, has very little possibilities to expand into new fields because it has already done so in the past. (Beckers and Vaughan; 2001) Furthermore, one of the assumptions of the eﬃcient market hypothesis is that stock returns reflect expected cash flows of companies. (Malkiel; 1989) However one of the anomalies of this hypothesis is that on average small-cap stocks outperform large cap stocks. (Banz; 1981) On the other hand there is an advantage for large caps in terms of information density and liquidity. (Dimson and Marsh; 1999) This is because large companies trade at higher volumes than small companies. Further- more many people know the big companies, therefore they are often mentioned in the news or in magazines. (Shapiro; 2002) Also as an analyst, it is easier to get information from companies with a large market capitalization than from companies with a small market capitalization. (Zhou; 2011)

Therefore, investors want to have a risk premium when investing in small companies.

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2.3 Growth vs. Value

The goal of a growth investment style is to invest in firms that are growing at a faster than average rate. These firms often prioritize accelerating cash flows, revenues and earnings. On the other hand they normally have a rather high price-to-earnings ratio. These firms typically have no or low dividend payouts, because these earnings are used to keep growing and expand the business.

The goal of a value investment style is to invest in firms whose stock prices don’t reflect their fundamental or intrinsic value. Value investments have typically a rather constant and easy to forecast profit and sales growth rate. They are often ma- ture companies that have suﬀered from temporary liquidity, earnings, political or economical diﬃculties. These companies have usually a low price-to-earnings, or price-to-book ratio. Furthermore they have often high dividend payouts.

According to Morningstar if an investment belongs to the growth or value style depends on the Morningstar value and growth scores. These scores are based on five value and five growth metrics. The diﬀerence between the growth score and the value score of a stock is the net style score. If the net style score is strongly negative, the investment corresponds to a value orientation. If the result is very positive, the investment is classified as a growth style. (Mor; 2019)

Historically mutual funds that focus on value stocks modestly outperformed, on average, their growth-focus peers. (Chan and Lakonishok; 2004) However there are several studies that come up with diﬀerent results, depending on which period and which region we are looking. Historical analysis showcases that growth stocks tend to outperform value stocks during bull markets. In contrast value stocks outperform growth stocks during downturns e.g. the financial crises in 2008/ 2009. It can be suggested that value stocks have a lower risk because they perform better than growth stocks in recessions.

There are many different reasons that try to explain the difference in return between value and growth investment style. According to Fama and French (1992) value strategies have a higher risk than growth strategies. This would be in line with the efficient market hypothesis. If an investment has higher average returns, it should have a higher risk. On the other hand, Lakonishok et al. (1994) propose that the behavior and wrong assessments of investors and especially professional investment managers could be the reason for the better performance of value stocks.

And Kothari et al. (1995) suggests that inaccuracies in the data selection and dif-

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ferentiation between value and growth investment styles could be the reason for the diﬀerent returns.

2.4 Credit quality

Credit quality is a measure that stands for the creditworthiness of the investment.

The goal of this measure is to inform investors what risk the fixed income investment has, this means what risk of default it has.

To determine the credit rating of a mutual fund Morningstar uses the average credit rating of a bond portfolio by taking a weighted average of ratings. Here, Morningstar uses the industry-established Standard & Poor’s credit rating. Fixed income investments with low credit quality have an average credit rating of less than "BBB-".

Fixed income investments with medium credit quality have an average credit rating of less than "AA-" but at least “BBB-”. And fixed income investments with high credit quality have an average credit rating of at least "AA-". (Mor; 2019)

The credit rating is strongly related to the companies financial flexibility. That’s the ability to invest in new investment opportunities or respond to shocks. (Graham and Harvey; 2001) Companies with high credit quality normally have a higher financial flexibility than companies with a low credit quality. On the other side companies with a high credit quality are more concerned about their credit rating, because changes in the credit rating could have a bigger impact on several benefits. (Gilson and Warner; 1997) For example, access to some instruments in the capital market usually requires a certain level of credit quality. Furthermore, many bond contracts have a clause to maintain a specific minimum credit rating, otherwise a downgrade in the credit rating can release a higher cost of debt, financial distress and additional disclosure burden. Moreover this problem in the credit rating downgrade can cause high-quality firms to maintain a lower leverage than implied by the traditional trade oﬀ and pecking order theories. (Kisgen; 2006)

The main advantage of low credit quality mutual funds compared to high credit quality mutual funds is the income. As a result of the increased interest rates of low credit quality bonds, low credit quality investments have generally produced better returns than high credit quality bonds. (Avramov et al.; 2007) On the other side the main disadvantage of low credit quality mutual funds compared to high credit quality mutual funds is the risk. Because low credit quality mutual funds have a

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much higher default probability, and are a lot more sensitive to crises.

2.5 Interest rate sensitivity

The interest rate risk can be measured with the interest rate sensitivity of a bond.

This measure displays how strong the market price of a bond shifts when the interest rate environment changes. Bonds that are more sensitive to the interest rate have greater price fluctuations than bonds that are less sensitive to the interest rate. In- terest rates and bonds are inversely correlated. Because of that, when interest rates climb, prices of bonds normally drop. The duration is a typical way to determine how interest rates aﬀect a bond’s portfolio. As larger the bond’s duration as larger the bond sensitivity to changes in interest rates. (Cooper; 1977)

Morningstar measures the interest-rate sensitivity by the eﬀective duration of the bond’s portfolio. For non US and US funds prior to 2009, funds that have limited sensitivity to interest changes are short-term mutual funds, those funds have a duration of 3.5 years or less. Funds that have extensive sensitivity to interest changes are called long-term mutual funds, these funds have a duration of at least 6 years. For US funds Morningstar changed the duration breakpoints from a static to a dynamic separation in October 2009. (Mor; 2019)

According to the literature the interest rate sensitivity is a systemic risk which is non-diversifiable. It is important to market participants because it is priced. But it is also important to regulators, lawmakers and other stakeholders because it could potentially threaten financial stability. (Flannery; 1981; Flannery and James; 1984;

Saunders and Yourougou; 1990)

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3 Sustainable investments

Companies have two objectives: profit maximization and social performance. (Husted and de Jesus Salazar; 2006) Therefore, topics such as sustainability, philanthropy and equality take on increasing importance. (Silvestre et al.; 2018) And also in the last years the public attention to social, ethical and environmental aspects of society increased significantly. (Dees et al.; 1998; Tracey et al.; 2011; Gramlich and Finster;

2013) As a result, more and more investors want to invest their money meaning- fully. In the center of their investment decision are not only the financial indicators such as sales and profits, they are looking especially at non-financial indicators for example the corporate social performance. (Mair and Marti; 2006; Zahra et al.; 2009) The definition of social investment varies in literature as well as amongst investors.

Typically, social investors have specific criteria, according to their own beliefs and values, but with a constant aim: to perform as good as they can. This is further based on the determination of positive and negative investment criteria for creating a socially responsible portfolio, which includes supporting sustainability, environmental protection, fair working conditions, gender equality and society friendly ac- tivities. (Hamilton et al.; 1993) This social responsibility performance of a portfolio can be evaluated with the environmental, social, and governance score (ESG score).

(Bassen and Senkl; 2011; Sassen et al.; 2016)

According to Morningstar the ESG rating measures how well the diﬀerent positions in a portfolio are performing on environmental, social and governance issues relative to a portfolio’s peer group. (Mor; 2018) The Morningstar ESG score is calculated with a three-step process. First, Morningstar calculates the Morningstar portfolio sustainability score for every portfolio reported within the trailing 12 months.

Afterwards they use these numbers to calculate the portfolio’s Morningstar historical portfolio sustainability score. And the last step is to assign the Morningstar sustainability rating for a portfolio based on its Morningstar historical portfolio sustainability score relative to its Morningstar global category. (Mor; 2018)

For this thesis we compare the 5000 mutual fund shares with the highest ESG score with the 5000 mutual fund shares with the lowest ESG score. Since we are only looking at extreme negative returns we are especially interested in the literature about social responsible investment and firm risk. For simplification we assume social responsible investment has the same meaning as investing in a high ESG score.

In the literature there are many arguments which justify that companies with high

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ESG score have less risk. For example McGuire et al. (1988) find out that companies with a low corporate social performance have a higher probability of legal fines and law suits than companies with a high corporate social performance. He argues that a reason for this could be that companies with a higher corporate social performance have better relationships with their stakeholders. Moreover, Cheng et al. (2014) dis- covered that shareholders are more likely to invest money in companies with a high ESG score, rather than in companies with a low ESG score. As a result, companies with a high ESG score have less capital constraints. Furthermore, a better corporate social performance can increase the company‘s reputation and brand value.

(Cornell and Shapiro; 1987) This can improve the sales of the companies products and also increase the companies attractiveness as an employer. (Brown and Dacin;

1997; Greening and Turban; 2000) In summary, a higher ESG score leads to lower financial risks and a lower probability of company crises. (Oikonomou et al.; 2012) In addition, in the case of a company crisis, Godfrey (2005) suggests that companies with a high ESG score have a higher probability to collect capital from several stakeholders. Furthermore the employees have a better attitude towards the company and are willing to sacrifice more to survive the crises. (Luo and Bhattacharya;

2009) Moreover, stakeholders do not necessarily insist on their rights and deadlines, are more willing to forgive mistakes and accept financial troubles of the company, as they have a good relationship and attitude towards the company. (Chang et al.;

2014) Also investors who focus on social responsibility are more willing to let their money in the company during times of negative financial performance. (Chang et al.;

2014; Bollen; 2007) This is in line with Godfrey et al. (2009) and Sassen et al. (2016) empirical studies, in times of crises companies with a high ESG score have lower negative returns than companies with low ESG scores.

On the other side there is also a theory that suggests that the ESG score can increase the firm risk. The managerial opportunism theory suggests that managers have an incentive to look at short term returns rather than for long term returns. (Bouslah et al.; 2013) Cespa and Cestone (2007) found evidence that managers who invest in a high ESG score do this regularly for their own private interest. When managers invest in such projects they can gain support from their stakeholders, which can reduce the probability of replacement or hostile takeovers. Furthermore, the manager often invest too much in the ESG score to improve the manager’s reputation, but on the other side increases the companies risk. (Barnea and Rubin; 2010) In addition managers are incentivized by short-term profit objectives. In times of high profits, they will underinvest in the ESG score to cash in, thereby condoning risks that occur in the long run. By contrast, they tend to overinvest in ESG when profits

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are low to have a better reputation as good citizen. (Preston and O’bannon; 1997;

Sassen et al.; 2016)

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4 Covariates

A number of articles have tried to identify economic factors that influence the capital markets. (Chen et al.; 1986; Ratanapakorn and Sharma; 2007; Gjerde and Saettem;

1999) There is also a lot of literature that tries to determine the right sets of covariates that explain capital market returns.² However so far there is no general consensus as to what is the correct set of factors. The same is true for the set of covariates determining mutual fund returns. Furthermore, there is already some literature that studies the impact of firm-specific and macroeconomic variables on the loss distribution. E.g. Chernobai et al. (2011); Chavez-Demoulin et al. (2016);

Hambuckers et al. (2018) Although firm specific variables have a higher impact on loss distribution than macroeconomic variables, we only consider macroeconomic variables in this thesis. We chose the following set of macroeconomic and financial variables as a fair representation of the macroeconomic and financial fundamentals that can influence mutual fund prices: For the economic growth rate we can look at the covariates gross domestic product of the USA (GDPUS), unemployment rate of the USA (UnempUS), personal savings rate of the USA (PSR) and gross domestic product of Germany (GDPDE). For commodity and equity price we have the WTI oil price (Oil) and Standard Poor’s 500 index (S.P). We can approximate inflation with the consumer price index of the US (CPI). The money growth rate will be approximated with the money supply (M1) and the interest rates can be approximated with the federal fund rate (FundRate).³

This chapter briefly describes the theoretical link between market returns and changes in our covariates, with special focus on high negative returns.

4.1 Economic growth rate

Several models suggest that an increase in the gross domestic product raises the pressure on the capital markets. This would lead to an average increase in the real rate of return on capital, which pushes capital expenditures. (Jorgenson; 1971;

Fama; 1981) On the one side an increase in the GDP could increase the market’s expectations of future economic growth, this would make capital markets more attractive and raise prices (returns), on the other side this could lead to a higher amount of extreme losses, due to heightened pressure from investors. Furthermore, when we have a strong increase in the economic growth rate, the market prices will

2E.g LASSO based methods can help to determine the right set of covariates.

3See chapter ??for detailed description of the covariates.

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increase. When the prices increase there is more money that can be lost in a default event. In addition, in times of high economic growth Cope et al. (2012) suggest that the amounts of fines and compensation claims in lawsuits increase. Moreover, (Povel et al.; 2007) suggest that in times of good economic conditions the amount of fraud increases. Furthermore, if an increase in the GDP is linked with an increase in inflation or money growth, investors could predict an increase in interest rates which would have a negative impact on the capital markets.

4.2 Interest rates

An increase in the interest rates leads to a higher discount rate. In theory this decreases the value of equity investments, since the present value of the expected future cash flows from these investments decreases. In addition, an increase in the interest rate could decrease future investments and consumption, since the returns from fixed income securities become more attractive. (Spahn; 2013) On the one hand an increase in the interest rates could increase the number of extreme negative returns, because we expect lower returns. But, on the other hand it could decrease extreme negative returns, since investors are more willing to invest in fixed income securities. There is also literature which suggest a decrease in the interest rate, increases extreme negative returns due to the fact that investors are ready to accept more risks. (Boubaker et al.; 2017; Delis and Kouretas; 2011)

4.3 Money growth rate

There are two effects on how the monetary growth rate could affect the capital markets, the interest rate and the credit effect. The interest rate effect suggests that an increase in the money supply leads to a decrease in the interest rates.

Whereas the credit effect suggests than an increase in the money supply decreases the difference between the cost of funds raised externally and internally. (Bernanke and Gertler; 1995) This can improve the companies balance sheet positions due to an increase in the net cash flows. Due to these two effects, the literature suggests that there is a positive relationship between changes in the money supply and capital markets. On the other hand, there is a theory that suggests that an increase in the money supply increases the inflation, which has a negative impact on the capital markets. (Spahn; 2013)

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4.4 Inflation

In practice many people believe that stocks are a good way to hedge against an increase in inflation. However several empirical findings suggest that stock prices are negatively related to inflation. There are a lot of diﬀerent explanations for this negative relationship in the literature. For example investors expect higher returns, due to an increase in inflation and are more reluctant to invest. To decrease inflation, central banks could increase interest rates. (Spahn; 2013)

Overall for the macroeconomic variables: interest rates, money supply and inflation there is no consensus in the literature, whether or not it has an impact on extreme negative returns. However there is a lot of literature about the subject of unexpected changes, so-called shocks. But, this is not part of this thesis.

4.5 VIX

The VIX is the volatility index of the S.P and represents the uncertainty of the capital markets. It includes information on the expected stock market volatility as well as on risk aversion through a variance premium component. (Bekaert et al.;

2013) In general a high VIX signals a high probability of future financial instability.

Bekaert and Hoerova (2014) This increases the risk aversion of investors. (Bekaert et al.; 2013) suggest that an increase in the VIX and the associated increase in risk aversion of investors could lead to a looser monetary policy which would lead to a decrease in interest rates.

4.6 WTI oil price

The WTI oil price stands for a very important price of a commodity. Oil is the most important source of energy and we need this resource for many products. Several empirical studies have shown that the oil price aﬀects the economy. (Jones and Kaul; 1996; Sadorsky; 1999; Papapetrou; 2001) A lot of empirical studies found a negative relationship between oil prices and stock market or global stock indices.

(Jones and Kaul; 1996; Sadorsky; 1999; Papapetrou; 2001; Nandha and Faﬀ; 2008) Because of that we can suggest that an increase in the oil price could increase the probability of extreme negative returns.

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5 Methodology

This chapter is concerned with formal financial theory. We provide a general summary of some of the basic concepts in risk management and explain our methodology which is used in the thesis. With this foundation, the discussion of VaR, ES and generalized pareto distribution analyzing mutual fund investment styles becomes more meaningful and clear.

5.1 Risk measurement

Defining risk is a especially hard task because no generally agreed definition exists.

In academic and business financial literature, risk is usually viewed as exposure to uncertainty or the danger posed to future outcomes by a decision made today. Risk is generally considered as exposure to uncertainty. This also includes the future dan- gers that are consciously and unconsciously taken with a decision today. To measure this uncertainty, we can assign the potential results to the specific probabilities. In practice it is often very diﬃcult to assign all the potential results to the specific probabilities. Because of that a lot of statistical methods are developed to quantify the risk. The standard deviation or variance is one of the most used methods to quantify this risk. The standard deviation describes the variation or dispersion of a set of values. (Bland and Altman; 1996) A high standard deviation signals that there is a high risk, while a low standard deviation signals a low risk.

The concept of the standard deviation and variance becomes popular due to Markowitz (1952). His paper deals with the question of how to construct eﬃcient portfolios, reduce the risk of a portfolio and thus get better returns. In his framework, the risk of an investment is equal to the uncertainty. For this he introduced the mean-variance concept, which had huge influences on today’s financial theory and practice. In the following we present the consideration of distributional assumptions in measuring risk, which is one of these influences of Markowitz (1952) developments.

Let us assume X is a random variable, that stands for a quantity whose return is uncertain and the distribution of X is defined by the probabilities of all events which depend on X. We can define this with the probability distribution function.⁴

F(x) =P(X x), 1< x <1 (1)

4See (Bruning and Kintz; 1987) for the properties and derivation of F(x)

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We can transform this function into:

F(x) = Z x

1

x(t)dt (2)

The equation (2) implies that F(x) is a continuous function of x. Furthermore the first derivative of X must exist and is continuous. Here f(x) is called the probability density function of the random variable X and t is used as the variable of integration.

The central aspects of a distribution function F(x) are usually expressed by moments that represent its central aspects. Hence, the s^th standardized moment of X can be defined as

E[X^s] = Z ₁

1

x^sf(x)dx (3)

The expected value or mean is the first standardized moment it is usually denoted by µ and defines the centre of the distribution. The central moment of order s is defined as

µs=E[(X µ)^s] = Z ₁

1

(x µ)^sf(x)dx (4)

Thus,pµ2 is the standard deviation which measures the variation around the mean of X and µ₂ is the variance of X.

The third standardized moment µ3 is the skewness that measures the asymmetry of the probability distribution of X about its mean. And the fourth standardized momentµ4 is the kurtosis which measures the "tailedness" or the shape of the probability distribution of X.

For example, in probability theory, a useful distribution is the normal (or Gaus- sian or Gauss or Laplace–Gauss) distribution. Normal distributions are important in statistics and are often used in finance to represent real-valued random variables whose distributions are not known. (Casella and Berger; 2001) The normal distribution is a bell-shaped curve. It is symmetric around its mean and we only need the first and the second moment to describe the distribution. In this example the second moment is the risk measure, however, the second moment as risk measure is only useful when the returns are normal distributed. (Markowitz; 1952)

One of the milestones for the mean-variance theory is the measurement of the diver- sification benefits. Here Markowitz (1952) finds out that investors shouldn’t invest in securities that have high covariances. The covariance is a measure of the joint variability of two random variables X and Y. (Rice; 2006; Park; 2018)

cov(X, Y) =E[(X E[X])(Y E[Y]) (5)

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Therefore, investors should not only consider the mean and the variance to reduce the risk. They should also consider the covariance and build a well diversified portfolio.

The last component which is required for Markowitz’s model of the modern portfolio theory is the correlation. Correlation is a technique that can show whether and how strongly pairs of variables are related.

corr(X, Y) = cov(X, Y)

µ_2X ⇤µ_2Y (6)

One big critic of the mean-variance approach is that returns are not symmetric around the mean. The volatility of returns is time varying and high negative and positive returns are much more common than expected by the normal distribution.

(Mandelbrot; 1997) Therefore, the variance, covariance and correlation of returns are not enough to predict acceptable forecasts about the risk. Another critic of the mean-variance approach is that the returns have equal likelihood in downside and upside movements, however investors like upside movements but dislike down-side movements.

To face these two critics, risk measures that focus on negative returns have been proposed. One of the most used risk measures are the VaR and the ES. (Jorion;

1997) These risk measures are especially important to specify the capital require- ments of a financial institution.

In the last years empirical studies found out that in periods of many high negative returns correlation between investments change dramatically. As a result diversi- fication is less valuable than expected. (Longin and Solnik; 2001; Drobetz et al.;

2002) This has led to a development of approaches that focus on tail correlation by applying the extreme value theory. (Longin and Solnik; 2001; Poon et al.; 2003) One of the most known extreme value distribution is the generalized pareto distribution which we will focus on in chapter 5.4.

5.2 Value at Risk

The concept of VaR became popular when the US investment bank J.P. Morgan published their risk measurement system, they named it RiskMetrics. (Longerstaey and Spencer; 1996) The aim of VaR is to make a statement of the form “We are P percent certain that we will not lose more than V monetary units in the next

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N days.” The variable V is the VaR, P is the confidence level, and N is the time horizon. (Jorion; 1997)

The big advantage of the VaR compared to other risk measurement techniques is the simplicity in calculation and reporting. For example, a one-month VaR with 99% confidence of value $1 mio. means that, the probability of losing more than $1 mio. is 1% if we hold this position for only 1 month. In the next chapters we will mainly work with the 95% confidence and the 99% confidence which we will write asV aR95 and V aR99.

The calculation of VaR can be done either on a historical basis which involves historical data or with a model-building approach which uses volatilities and corre- lations. The second approach was used for example for the J.P Morgan Risk Metrics.

(Longerstaey and Spencer; 1996) One of the big critics of this approach is that it has the assumption that returns are normally distributed. On the other hand with this approach we can express the VaR as a function of the standard deviation of the returns.

V aRp =µ1 +p

µ2⇤ ¹(p) (7)

Here ¹(p) is the inverse of the normal distribution function.

The first approach is the one we will use in the empirical part of this thesis. By using historical data we only rely on the assumption that the returns are kind of independent and identically distributed (iid).⁵ (El-Jahel et al.; 1999) Here we can calculate the VaR by using the quantile with the desired confidence level from the histogram. Since we totally rely on past data, the number of observations construct- ing our data set is very important for this approach. If we want a high confidence interval for our VaR we first need to make sure that we have enough observations.

(Ridder; 1998) Therefore, diﬀerent observation periods can cause big diﬀerences in the VaR estimation for the same security. As a result by using the historical data approach we have the problem to decide between short and long observation periods.

(Hendricks; 1996) Short observation periods have fewer observations which lead to a decrease in the statistical accuracy. On the other hand long observation periods have the problem that some observations are not relevant anymore, due to the changes in the market conditions, regime or other events that could violate the (iid) assumption. Nonetheless, the VaR can fluctuate significantly from month-to-month.

(Allen; 1994)

5We are aware that the idd assumption is partially violated. E.g. the mutual fund returns are actually mutual fund share returns, so the individual mutual fund correlates with each other.

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5.3 Expected Shortfall

The main disadvantage of the VaR is that it only gives a statement of a certain confidence level. (Danıelsson; 2002; Embrechts et al.; 2002) The VaR gives no statement about the magnitude of the loss, if the loss is above the VaR confidence level.

Therefore, the VaR has no information about the tail of the loss distribution. As an example, let us assume the confidence level of the VaR is 99% and the VaR is $1 mio., in this case we don’t know what is the loss if we are above $1 mio., it can be

$2 mio. or even $5 mio., this depends on the tail of the loss distribution.

We only receive the information from the VaR that the likelihood of receiving a loss greater than $1 mio. is 1%. As a result we shouldn’t use the VaR to forecast the maximum expected loss, the VaR answers the question of what is the minimum expected loss given we are in the worst 1% quantile. (Acerbi et al.; 2001) In order to avoid the problems with VaR Artzner et al. (1999) introduced the ES, which can be used additionally to the VaR. The ES is defined as

ESp =E[X|X > V aRp]. (8) Consequently, by using the historical VaR approach we can simply estimate the ES by taking the average losses above our VaR significance level. (Moix; 2012) For example when we look at the 1% worst returns, the ES gives us the expected loss when we are actually beyond theV aR99.

5.4 Generalized Pareto Distribution

The generalized pareto distribution (GPD) is part of the extreme value theory. In case the loss distribution is not normally distributed, we can use the GPD to fit the tail of the return distribution to estimate its risk parameters. The GPD is a continuous probability distribution. In risk management it is used to model the left tails of a loss distribution. (Dargahi-Noubary; 1989) Since the GPD is only for extreme returns we first have to decide at which return level we consider the return to be extreme. To do this we first have to set a certain threshold. Then we only consider observations which are larger than the threshold. There are a lot of techniques to automatically select the threshold. (Wadsworth and Tawn; 2012) Due to the comparability of our investment styles and the GPD condition that only positive values can be used, we choose our threshold to be theV aR₉₅ and V aR₉₉, across the whole

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data set and across all investment styles. ⁶

Let us define the observations that exceed the threshold as: (Hambuckers et al.;

2018)

Y_t,i,p =X_t,i V aR_p (9)

given that Xt,i V aRp, p = the significance level and i = 1, ... , nt. Thus the index i refers to the index of the ith excesses of the investment styles andnt is the total number of excesses. For p 95, V aRp is always a positive value across all investment styles, since we are working with the loss distribution.

We are now interested in the conditional excess distribution function: (Jondeau and Rockinger; 1999; McNeil and Saladin; 1997)

FV aRp(Yt,i,p)=P(Xt,i V aRp Yt,i,p|X > V aRp) (10)

For0Yt,i,p. This can be also written as

FV aRp(Yt,i,p) = F(V aRp +Yt,i,p) F(V aRp)

1 F(V aRp) = F(Xt,i) F(V aRp)

1 F(V aRp) (11) The excesses Yt,i,p over V aRp can be now modeled by a GPD with the distribution function (Pickands III et al.; 1975)⁷

GP D(Yt,i,p;⇠, ) = 8>

>>

><

>>

:

1 (1 + ⇠Yt,i,p

) ^1/⇠ ⇠ 6= 0

1 exp( Yt,i,p

) ⇠= 0

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with y 0, ⇠ 2R and > 0.

In the following chapters we denote as the scale parameter and ⇠ as the shape parameter of our GPD. We only consider the case where ⇠ > 0, that is the heavy tail case. This consideration is in line with most operational loss data and with the Gnedenko and Pickands–Balkema–De Haan theorems. (Chavez-Demoulin et al.;

2016; Balkema and De Haan; 1974; Gnedenko; 1943; Pickands III et al.; 1975) Let’s now extend the GPD to more dynamic one, where the model parameters

6Other approach like the Mean Residual Plot and monthly VaR to calculate the threshold, do not work for our study because we need a comparability between the investment styles and we have some months that have not enough negative observations.

7For proofs and derivation of the GPD see Leadbetter (1991); Chavez-Demoulin et al. (2016).

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and ⇠ depend on covariates.

Yt,i,p ⇠GP D(Yt,i,p;⇠(x^⇠_t,i,p), (x^⇠_t,i,p)) (13)

with Yt,i,p 0, ⇠t,i,p 0, t,i,p 0, and where the parameters ⇠t,i,p and t,i,p can be

calculated as⁸

(x_t,i,p) = e ^(x^t,i,p⁾

1 +⇠(x^⇠_t,i,p) (14)

⇠(x^⇠_t,i,p) = ↵^⇠₀+

n⇠

X

l=1

↵^⇠_lx^⇠_t,i,p(l), (15)

(x_t,i,p) =↵₀ + Xn

l=1

↵_lx_t,i,p(l), (16)

wherex^✓_t,i,p(l)denotes the lth component of the vector of covariates x^✓_t,i,p associated

with Yt,i,p for ✓ 2 ⇠, , , and n (resp. n⇠) denoting the number of covariates for ⇠

(resp. ). The parameters (x_t,i,p) and ⇠(x^⇠_t,i,p) can be estimated with a likelihood maximization procedure. ⁹

L(Yt,i,p;✓, x) = YT t=1

nt

Y

i=1

gdp(Yt,i,p;⇠(x^⇠_t,i,p), (x^⇠_t,i,p)) (17) where gpd denotes the probability density function of the GPD. An estimator ✓ is obtained by maximizing the likelihood function with respect to ✓:

✓b=argmax✓(L(Yt,i,p;✓, x)) (18) The goal of this thesis is to compare the changes in risk depended on covariates for extreme negative returns across investment styles. For this we need to bring the change of the scale and shape parameter into a single risk measure. One way to do this is to use the inverse of the GPD, the quantile function:

qGP D= (x_t,i,p)

⇠(x^⇠_t,i,p)((1 p) ^⇠(x^⇠^t,i,p⁾ 1) (19)

An other way is by redefining the GPD as a function ofXt,i withXt,i =Yt,i,p+V aRp, and using equation 11, we can derive the model to build a tail estimate of F(Xt,i)

8The following equations and explanations are close to Hambuckers et al. (2018) and Chavez- Demoulin et al. (2016).

9We provide an idea how to estimate the scale and the shape parameter of the GPD. See Chavez-Demoulin et al. (2016) for a derivation and proof.

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(McNeil and Saladin; 1997):

F(Xˆt,i) = (1 F(V aRp))GP D _(x

t,i,p),⇠(x^⇠_t,i,p),V aRp(Xt,i) +F(V aRp) (20) F(V aRp) now is replaced by GP D _(x

t,i,p),⇠(x^⇠_t,i,p),V aRp and the F(V aRp) can be estimated by (n NV aRp)/n, where n is the total number of observations and NV aRp

the number of observations exceeding the threshold V aRp. This turns to F(Xˆt,i) = NV aRp

n (1 (1 +⇠(xˆ^⇠_t,i,p)xt,i V aRp

(xˆ_t,i,p) ) ^1/^⇠(x^⇠^t,i,p^ˆ ⁾+ (1 n NV aRp

) (21) and by inverting for a given probability p >F(V aRp)one obtains theV aR _(x ˆ

t,i,p),⇠(x^⇠_t,i,p),V aRp

estimation:

V aR _(x ˆ

t,i,p),⇠(x^⇠_t,i,p),V aRp =V aR_p+

(xˆ_t,i,p)

⇠(xˆ^⇠_t,i,p) (( n

NV aRp

(1 p)) ^⇠(x^⇠^t,i,p^ˆ ⁾ 1). (22)

Which will be our main measurement for chapter 8 to compare the changes in risk of a covariate increase.

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6 Data

In this chapter, we first present data of the investment styles that will be used throughout the master thesis. The data for investment style returns are from the Morningstar database at the University of Liège. Furthermore we explain the covariates that we use to estimate the scale and shape parameter of our generalized pareto distribution. The covariates are from the Thomason Reuter CapitalIQ database and the federal reserve bank of St. Louise.¹⁰

6.1 Investment style returns

The data set employed in this study consists of mutual fund share returns over the period of October 1999 to September 2019.¹¹ To decrease distortions between the investment styles in terms of the amount of data, we limited the maximum amount of mutual funds to 5000 per investment style. For the investment style ESGHigh we filtered the data according to the ESG score and included the 5000 mutual funds with the highest ESG score into the ESGHigh investment style. For the investment style ESGLow we also filtered the data according to the ESG score and included the 5000 mutual funds with the lowest ESG score into the ESGLow investment style.

For the other 12 investment styles we used the Morningstar style boxes to filter the mutual funds. To reduce the data concentration on the current months we filtered the data. Furthermore, we filtered the data according to the first month of October 1999 and second to the month of October 2007.

The investment styles GrowthLarge, GrowthMid and GrowthSmall consist of stocks which follow a growth investment style. Whereas the investment style GrowthLarge consists mostly out of companies with high market capitalization, the investment style GrowthMid consists of stocks that contain mostly companies with medium market capitalization and the investment style GrowthSmall consists of stocks that consist mostly out of companies with small market capitalization.

Moreover, the investment styles ValueLarge, ValueMid and ValueSmall consist of stocks which follow a value investment style. Whereas the investment style Value-

10To get access to Thomason Reuter CapitalIQ, we used the DALAHO provided by the University of Hohenheim.

11Mutual fund companies can have several diﬀerent shares for the same mutual fund. Each of these shares has various benefits and drawbacks. For this thesis we define each mutual fund share as being an independent mutual fund. However, we are aware of the violations of the idd assumptions.

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Large consists mostly out of companies with high market capitalization, the investment style ValueMid consists of stocks that contain mostly companies with medium market capitalization and the investment style ValueSmall consists of stocks that consists mostly out of companies with small market capitalization.

Furthermore, the investment styles ExtHigh, ExtMid and ExtSmall consist of fixed income investments which have an extensive interest rate sensitivity. Whereas the investment style ExtHigh consists mostly out of bonds with high credit quality, the investment style ExtMid consists mostly out of bonds with medium credit quality and the investment style ExtSmall consists mostly out of bonds with low credit quality.

In addition, the investment styles LtdHigh, LtdMid and LtdSmall consist of fixed income investments which have a limited interest rate sensitivity. Whereas the investment style LtdHigh consists mostly out of bonds with high credit quality, the investment style LtdMid consists mostly out of bonds with medium credit quality and the investment style LtdSmall consists mostly out of bonds with low credit quality.

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Table 1: Descriptive statistics of investment styles

Style Observ. Mean Std.Dev Skew Kurt Min Max K-S

ESGHigh 476223 0.39 5.46 -0.40 5.59 -52.31 72.06 0

ESGLow 460463 0.68 5.98 -0.14 10.23 -95.07 193.8 0

GrowthLarge 1122872 0.65 5.77 -0.15 10.56 -90.23 214.32 0

GrowthMid 791096 0.64 6.26 -0.23 7.24 -86.75 133.61 0

GrowthSmall 489688 0.62 6.09 -0.21 7.05 -99.51 84.65 0 ValueLarge 928226 0.52 5.43 -0.22 8.42 -90.67 122.91 0

ValueMid 582979 0.51 5.41 -0.43 9.69 -98.33 152.9 0

ValueSmall 517976 0.44 5.11 1.28 98.97 -99.88 310.21 0

ExtHigh 276045 0.31 3.15 -0.14 12.85 -34.22 108.59 0

ExtMid 586082 0.36 2.91 -0.42 10.84 -31.22 103.57 0

ExtLow 365202 0.31 3.27 -0.75 10.47 -41.66 45.05 0

LtdHigh 637443 0.32 3.64 -0.18 15.01 -94.84 131.3 0

LtdMid 638870 0.27 2.71 -0.66 15.81 -98.27 44.24 0

LtdLow 668414 0.39 3.31 -0.88 18.82 -98.44 125.68 0

Observ. = amount of observations per investment style; Mean = the arithmetic mean; Std.Dev = standard deviation; Skew = skewness; Kurt = kurtosis; Min and

Max represent the lowest and highest monthly return, respectively; K-S test = Kolmogorow-Smirnow-normality test. Sample window (monthly data): Oct. 1999

to Sep. 2019.

The investment style ESGHigh consists of 476223 observations with an average return of 0.39 and a standard deviation of 5.46. The skewness is -0.4 and the kurtosis is 5.59. The lowest return is -52.31 and the highest return is 72.06. The investment style ESGLow consists of 460463 observations with an average return of 0.68 and a standard deviation of 5.98. The skewness is -0.14 and the kurtosis is 10.23. The lowest return is -95.07 and the highest return is 193.8. The investment style Growth- Large consists of 1122872 observations with an average return of 0.65 and a standard deviation of 5.77. The skewness is -0.15 and the kurtosis is 10.56. The lowest return is -90.23 and the highest return is 214.32. The investment style GrowthMid consists of 791096 observations with an average return of 0.64 and a standard deviation of 6.26. The skewness is -0.23 and the kurtosis is 7.24. The lowest return is -86.75 and the highest return is 133.61. The investment style GrowthSmall consists of 517976 observations with an average return of 0.62 and a standard deviation of 6.09. The skewness is -0.21 and the kurtosis is 7.05. The lowest return is -99.51 and the highest return is 84.65. The investment style ValueLarge consists of 928226 observations with an average return of 0.52 and a standard deviation of 5.43. The skewness is