Performance of Dutch mutual equity funds using a time-varying approach

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Performance of Dutch mutual equity funds

using a time-varying approach

Abstract:

Testing a mutual equity fund’s performance, using the traditional CAPM and four-factor model is considered to have one major downside; the stationary beta. In these unconditional models, the risk loadings are assumed to be constant throughout the tested timespan. However, an actively managed fund would adapt its beta throughout time, in order to beat the market. This study uses a free of ‘survivorship bias’ dataset of fifteen domestic and 64 global Dutch mutual equity funds. The unconditional and time-varying variants of the four-factor model by Carhart (1997) are used to estimate the performance of both types of funds over the period 2000-2018. Using different benchmarks for the two fund types and despite using raw returns (excluding managing fees and other costs), the actively managed funds are not able to outperform the market when controlled for the tested risk factors. It also shows that there is little difference in performance between the two fund types when tested against similar benchmarks.

Student: Sander Hakvoort

Student number: S4152034

Supervisor: Dr. Dirk-Jan Janssen

Internship company: KPMG Nederland

Internship supervisor: Erwin Blom

Hand-in date: July 23, 2019

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1. Introduction

At the end of the third quarter of 2018, worldwide mutual funds had €43,274 billion Assets under Management (AuM). The growth rate of the AuM of these open-end funds is equally astonishing. Since the same quarter of 2008, the AuM increased by 252%. The open-end funds of the European mutual fund market and United States (US) mutual fund market accounts for 81% of these AuM (Investment Company Institute, 2018). Most of these funds are led by a number of ‘fund managers’. These fund managers actively pick the stocks and bonds that comprise the mutual fund. Their job is to compile a portfolio that will gain the highest return for the minimum amount of risk and allow ‘ordinary’ investors to invest in a readymade and well-diversified portfolio. However, these fund managers claim a specific fee for the management of these portfolios, which cuts into a fund’s performance (Sharpe 1964; Jensen, 1967; Blake, Caulfield, Ioannidis, & Tonks, 2017).

The above leads to the main question, surrounding the performance of mutual funds. Do investment managers, and therefore actively managed mutual equity funds, generate abnormal risk-adjusted returns (Jensen, 1967; Carhart, 1997; Cuthbertson, Nitzsche & O’Sullivan, 2008)? The excessive returns of a mutual fund have often been established by comparing the returns of a fund with a relevant benchmark factor model, resulting in an alpha (α). Alpha is the risk-adjusted return of a portfolio i.e., the outperformance of the benchmark by the fund. This alpha is one of the main drivers for many investors who seek a mutual fund to invest into. The alpha of a portfolio can be calculated according to several different methods, including multiple different types of risk factors. This has led to an extensive amount of studies on this topic, throughout the past decades.

The results regarding the question posed above have differed per researched type of fund and per model that was used in the study. The first few studies on equity and portfolio performance were based on the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Jensen (1967). The same Sharpe (1964) and Jensen (1967) showed an underperformance of US-based portfolios, by at least the amount that they charged as a fee to the investor. Later research of Ippolito (1989) proved a positive outperformance of US domestic mutual funds in comparison to the Standard and Poor’s 500 Index (S&P 500). However, this study did expose the main shortcoming of the CAPM; it does not control for an extensive amount of stock market anomalies. The CAPM showed skewed effects caused by firm characteristics, such as the size and value of a stock (Da, Guo, & Jagannathan, 2012). Fama & French (1993) and later Carhart (1997) added proxies to adjust for these anomalies. It regarded factors for a stock’s size, value,

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and momentum. The results of Carhart (1997) showed a persistent underperformance of the benchmark, by all but the best performing funds.

Most studies, if not all, discussed above, have been conducted within the primary mutual fund markets of the world; the United States, the United Kingdom (UK) and Europe as a whole. The same can be said for many studies that came after. The studies of Droms & Walker (1996), Otten & Bams (2004), Cuthbertson, et al. (2008) and Bauer, Cosemans & Schotman (2010) are just a few of the studies that examined the performance of domestic mutual equity funds in the US, UK or Europe.

Cumby and Glen (1989) were the first to look into global mutual funds but did not find a difference in alphas, compared to domestic mutual funds. However, Apap and Collins (1994) did find a positive alpha for global mutual funds, when benchmarked against the MSCI Weighted International Index. However, they simply looked at raw returns and did not correct for risk factors, such as the CAPM. Simultaneously, the study of Droms and Walker (1994) used the CAPM to determine the performance and outperformance of funds. They used a domestic benchmark (S&P500), a strictly international benchmark (EAFE index) and a general global benchmark (World index). The result of this study was that the tested US global funds did not significantly outperform these different market benchmarks. Redman, Gullet, and Manakyan (2000) performed a study in which they actually compared global and domestic fund portfolios, using the Vanguard Index 500 mutual fund as the ‘market’ benchmark for both domestic and global funds. The results showed an outperformance by global portfolios of both the US market and the domestic funds between 1985-1989, but an underperformance between 1990-1994. These studies all used different factors to test the performance of these funds, and none of them used the, more accepted and proven, four-factor model by Carhart (1997).

The final addition to the recent literature on the performance of mutual equity funds has been the time-varying beta. The original beta, the coefficient that compares the portfolio’s returns to the market’s returns and adjusts for risk-levels, is kept at a constant over the entire timespan of the study. This is an unrealistic view of an actively managed portfolio whose positions in stocks always differ on a monthly basis. This constant rebalancing would also lead to a change in beta. Therefore, Chen and Knez (1996), Ferson and Schadt (1996), Fama & French (1997) and more recently Otten and Bams (2004) advocate for an approach which allows the betas of a fund to vary over time. This means that the beta of the CAPM and other factors can vary over time and thus create time-varying returns. Most studies showed that the introduction of the time-varying beta increased the model’s explanatory power, but the effects on the alphas of the portfolios differed. Several showed a decrease in alphas, where others

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showed an increase in alpha (Otten & Bams, 2004; Budiono, 2010; Boguth, Carlson, Fisher, & Simutin, 2011; Cederburg, O’Doherty, Savin & Tiwari, 2018).

The discussed literature shows two significant gaps; first, the difference in performance between domestic and global mutual equity funds. As stated, prior studies have focused mostly on mutual equity funds that invested in equities of the same country as the funds were located in, i.e., domestic mutual equity funds (Kool, 2017; Busse, Goyal, & Wahal, 2010). The second gap is the use of the time-varying four-factor model, by Carhart (1997), on a different market than the US, UK, and Europe as a whole. This study intends to close the two stated literature gaps by using the time-varying variant of the four-factor model of Carhart (1997). First, in order to determine the performance of global and domestic Dutch mutual funds in regard to the relevant benchmarks, the returns of domestic funds will be tested against domestic benchmarks, and the global funds will be tested against an international benchmark. The second part of the study focusses on comparing the performance of domestic and global Dutch mutual equity funds, similar to the study of Redman, et al. over the period 2000-2018, based on similar benchmarks, using the time-varying four-factor model.

The results of this study can have a significant impact on the way investors choose a portfolio to invest in. The alpha of a portfolio is one of the main drivers in the choice of a portfolio, and the way this alpha is determined can, therefore, have a significant impact on the massive mutual fund market of the world. A better understanding of the determinants of a portfolio’s performance can also help mutual fund managers in their investment decisions. This study can thus help investors in determining whether Dutch mutual equity funds are a good investment, dependent on their benchmarks. Secondly, by comparing domestic and global mutual equity funds to similar benchmarks, this study can also help investors in making a well-informed decision on whether they want to invest in either one of the two fund types, based on the benchmarks they want to beat.

A time-varying four-factor model of Carhart will thus be used to determine whether Dutch mutual equity funds, in general, outperform the relevant benchmarks and secondly; when choosing a particular benchmark, whether there is a difference in the outperformance of the benchmarks between domestic and global Dutch mutual equity funds. The main question that shall be answered in this study is as follows:

‘Do Dutch mutual equity funds outperform the benchmark, and is there a difference in performance between domestic and global Dutch mutual equity funds?’

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The results of this study show that Dutch mutual equity funds do not outperform the relevant benchmarks. The domestic and global Dutch mutual equity funds either do not perform differently than the benchmarks or perform worse than their benchmarks. This result is the same when a time-varying alpha and time-varying betas are introduced. The comparison of domestic and global Dutch mutual equity funds give no clear winner, since both fund types underperform their benchmarks, however, the global Dutch mutual equity funds underperform the global benchmarks less than the domestic Dutch mutual equity funds.

This study started with a short introduction, in which the research topic and research problem have been introduced, and the practical and scientific relevance of the study were discussed. The remainder of this study will start with an extensive literature review, in which relevant theories and results of previous studies, on the topic of mutual equity fund performance, will be discussed. This will finally lead to a set of hypotheses, which will help answer the research question posed above. The third chapter consists of a methodological chapter, which will contain an elaboration on the chosen methodology, origin of data, the different factor-models, and chosen benchmarks. The fourth chapter will contain the description of the results, an answer to the hypothesis and links to the studies that are addressed in the literature overview. Chapter five will answer the research question and also elaborate on the study’s limitations and possible areas for further research.

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2. Literature overview

This chapter will explain the theories behind the different factor models that were shortly discussed in the introduction. Each paragraph will start with a short introduction of the model and will be followed by an elaboration on the results of previous studies in which the relevant model is used to determine portfolio performance. The factor models themselves will only shortly be discussed where necessary and thoroughly explained in paragraph 3.3 of the methodology chapter.

2.1 Capital Asset Pricing Model Theory

The first model that will be discussed is the Capital Asset Pricing Model developed by Sharpe (1964) and used, for instance, by Jensen (1967). The CAPM is very simplified and assumes that portfolio returns only depend on their correlation with market returns and the portfolio’s level of risk or volatility. The primary assumption, underlying the CAPM, is that all investors are risk averse and are trying to maximize their utility or wealth. This corresponds with the model, which states that a rise in the level of systematic risk, will lead to a higher expected return of a portfolio. This means that an investor wants a higher return on a portfolio when the systematic risk of that portfolio is higher (Jensen, 1967). The CAPM defines the systematic risk as the beta (β) of the portfolio. The beta is the portfolio’s correlation with the benchmark market, so the sensitivity of the portfolio’s return on the benchmark’s return (Rao, Ahsan, Tauni, & Umar, 2017).

The study by Jensen (1967) on mutual fund performance, in the period 1945-1964, showed no outperformance of the benchmark (S&P 500), by almost any mutual fund. The average CAPM beta of a fund was 0.84, and the adjusted R-squared averaged at 86.5%. The average alpha was -0.011, meaning the average fund underperformed the benchmark by 1.1% per month. Jensen stated that even gross of costs and fees, fund managers needed to reevaluate the cost and benefits of their actively traded portfolios. Ippolito (1989) used the CAPM to estimate the performance of a sample of 143 US mutual equity funds over the period 1965-1984 in regard to the S&P 500. 127 out of these 143 US mutual equity funds did not significantly outperform the market, twelve funds outperformed and four underperformed the market benchmark. The mean alpha was 0.81% per month and an average beta of 0.88 (Ippolito, 1989). The beta was thus relatively similar in both studies, but the alphas were very different. Finally, Droms and Walker (1996) tested 151 mutual equity fund’s returns and their performance in regard to the market from 1971 till 1990. The average CAPM beta was 0.98, and the average

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alpha was 0.01%; thus, the funds outperformed the S&P 500 by 0.01% per month. The average CAPM beta seemed to increase in later periods, even though the average alpha varied across the different studies and studied periods.

Many recent studies still use the CAPM, but only as a part of their analysis. Rao et al. (2017) use the CAPM amongst others, to determine the outperformance of 707 Chinese mutual equity funds over the ‘ China A-share stock market composite index’ during the period 2004-2015. The CAPM part of the model did show a significant positive outperformance of the average of the tested funds by 0.37%, an average beta of 0.81 and an R-squared of 69.19%. This means that the CAPM can explain roughly 69% of the portfolio’s performance. Empirical results of the CAPM have differed throughout the past decades. The usefulness of the CAPM has, therefore, been discussed thoroughly. The outperformance of the benchmark by a portfolio (α) has shown to provide skewed effects. One of those effects is that portfolios that focus on either low beta stock, small stock or value stock appear to outperform the benchmark significantly more than the counterparts that do not focus on these type of stocks (Fama & French, 2003; Da et al., 2012). The model has therefore been adapted, to adjust for these factors. This led to the Fama & French model and later the Carhart four-factor model.

2.2 Fama & French Three-Factor and Carhart Four-Factor Model

Although the CAPM would often explain 70% of a portfolio’s returns, Fama & French (1993) added two other factors to this model. The CAPM showed, despite being a good starting point, very little actual empirical results. The two central anomalies were attributed to the size of the stocks in the portfolio and to the value of the stock. Fama & French (1993) added a factor that adjusted for this size anomaly ‘Small market cap Minus Big market cap’ (SMB) and a factor that took the value anomaly ‘book-to-market’ ratio, into account ‘High book value to market ratio Minus Low book value to market ratio’ (HML).

The effect, where stocks with a low market capitalization gain higher average returns than stocks with high market capitalization, was first introduced by Banz (1981). This study also hinted at the presence of a similar effect in regard to a stock’s ‘book-to-market’ ratio. A small market cap stock, or portfolio that contains mostly small-cap stocks, is found to gain higher average returns than their smaller counterparts. Stocks of companies with a high book-to-market ratio (value stocks) are, on average, outperforming the benchmark more often than stocks of companies with a low book-to-market ratio (growth stocks) (Huij & Verbeek, 2009). Carhart (1997) added a fourth factor to the CAPM and Fama French model. He adjusted for one-year momentum, in order to adjust a portfolio’s performance for the influence of them

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having previous ‘winners’ or ‘losers’ in their equity mix (MOM). Carhart showed that portfolio performance was influenced by the previous returns of the stocks that comprised them.

These three different models; the CAPM one factor model, the Fama-French three-factor model, and Carhart’s four-three-factor model have been used extensively in studies, of the past decade, into mutual fund portfolio performance (Carhart, 1997; Otten & Bams, 2002; Busse, et al., 2010; Rao, et al., 2017). Results of these studies have differed in the same way as with the CAPM. Rao et al. (2017) did not only use the CAPM, which was described in paragraph 2.1 but also used the three-and four-factor models. The average outperformance of the 707 Chinese mutual equity funds went down slightly by 0.05% per month, and the average adjusted R-squared rose to 75.32% when using the four-factor model. This outperformance was attributed to the inefficiency of an emerging market, such as the Chinese market. This allows the fund manager to beat the market by picking the stocks with better prospects (Rao et al., 2017).

However, the Dutch market is a developed market, which could alter the results more towards US-based studies. One of the studies that does focus on a more relevant market is the study of Otten and Bams (2004), who tested for the outperformance of 2436 open-ended US mutual equity funds over the ‘Center for Research in Security Prices US total market index’. This time, both the three- and four-factor model showed that mutual equity funds did not outperform the benchmark when correcting for the different risk factors. On average, the funds underperformed the benchmark by 0.51% and 0.54% using the three- and four-factor model. The adjusted R-squared of all the different models is very high, 96%. Otten & Bams (2002) also used the four-factor model to test a sample of 500 European mutual equity funds and found mixed results. Gross of fees, the Dutch portion of the mutual equity funds did outperform the market significantly by 2.64%. However, when subtracting the expenses and fees of the fund managers, this effect was weakened and not significant. The adjusted R-squared of the four-factor models increased to above 95%, a significant improvement over the 70% of the CAPM only model. Busse et al., (2010) examined the performance of 4,617 domestic US mutual equity funds in regard to the S&P 500, over the period of 1991-2008. They used both the three- and four-factor models and concluded that, on average, there was no evidence of superior performance in regard to the benchmark, even before fees. All results yielded a non-significant alpha. Finally, Cuthbertson and Nitzsche (2013) used a sample of 555 German mutual equity funds and performed the three-factor model over the period 1990 – 2009 and found that only a minimal number of funds showed a significant positive alpha (7 out of the 555) and 75 funds that were doing significantly worse than the German index.

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2.3 Time-varying Four-Factor Model

An implicit assumption, underlying the CAPM, Fama-French three-factor and Carhart four-factor models, is the unconditional value of their beta. In other words, the coefficient that describes the correlation between the portfolio returns to the returns of the market or the other factors is kept constant throughout the timespan of a study. However, in the real-world, returns and risks of a fund vary over time, and this would create a time-varying beta. For instance, a mutual fund will try to keep its beta, in comparison to a market’s returns, relatively stable. This would imply that, when the market becomes more volatile, the fund will decrease it’s beta and vice versa when the market is less volatile (Otten & Bams, 2004).

An unconditional performance model, such as the basic four-factor model by Carhart, consists of constant betas between the fund’s returns and tested factors. This implies that the fund’s betas are determined (in regard to the different factors) at a certain point in the overall timespan, often at t=0, and does not change throughout the entire tested period. This is not realistic and there are thus multiple ways in which a time-varying beta can be created. This study has opted for the approach by Fama and French (1997) who created a time-varying beta by using a ‘rolling-window regression’. The statistical implications of a ‘rolling window regression’ shall be explained in subparagraph 3.3.3. This approach allows the beta of the four-factor model to vary over time and produce so-called ‘time-varying risk-adjusted returns’.

The study by Budiono (2010) uses rolling window regressions to estimate the three-factor alphas to test the alpha of 12,348 US mutual equity funds over the S&P 500. The two-year window showed a positive significant annual alpha of 1.83%. Otten and Bams (2004) used, besides the unconditional models that were explained in paragraph 2.2, a conditional model. It showed that the average alpha went up slightly by 0.09% when using the conditional model with a time-varying beta instead of the unconditional model. However, the funds still underperformed the S&P 500 benchmark.

The hypothesis, when based on the literature of all different models, could vary due to the different results of the aforementioned studies. An outperformance of mutual funds was rare and only appeared in studies that used gross of fee returns and/or in emerging markets. This study does not take place in an emerging market. However, it does use gross of fee returns. The addition of the time-varying alpha and betas also seems to increase a fund’s performance and thus alpha. However, this increase is often too small to make-up for the already negative alpha in the unconditional model, for instance in the study by Otten and Bams (2004). The hypotheses is thus as follows:

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H1: Dutch mutual equity funds underperform the relevant benchmark.

The relevant benchmarks are different for the domestic Dutch mutual equity funds and the global Dutch mutual equity funds. For the domestic Dutch mutual equity funds, the AEX Index is the market benchmark and other Dutch or European benchmarks are used for the other factors in the model. The market benchmark for the global Dutch mutual equity funds is the MSCI World Index, the other factors consist of global benchmarks. The exact content of the different benchmarks are described in paragraph 3.4.

2.4 Domestic and global mutual equity funds

Previous studies into the outperformance of mutual equity funds, using different models, have been discussed, and a hypothesis to the first part of the research question has been formulated. However, in order to formulate a hypothesis to the second part of the research question, the difference between domestic and global mutual equity funds needs to be discussed. The second part of this study compares the outperformance of the same benchmark, by domestic and global Dutch mutual equity funds. This will allow investors to choose which type of fund is better suited to outperform the benchmark that they want to beat.

The main advantage of global mutual equity funds, over domestic mutual equity funds, is the ability to diversify their portfolio and holdings even further. Adding international equities to a portfolio is supposed to reduce the risk of the portfolio (Redman, et al., 2000). The underlying assumption of picking stocks outside the domestic market is the ability of these stocks to outperform the chosen benchmark. Otherwise, the extra effort to research these funds is not worthwhile (Redman, et al., 2000). Droms and Walker (1994) tested fifteen international mutual fund’s performance against the domestic US S&P 500 Index. They used the CAPM to calculate the risk-adjusted returns of the international mutual fund (alpha) over the period 1981-1990. They found that out of the fifteen funds, thirteen did not perform significantly better or worse than the S&P 500 and the other two even performed significantly worse. Redman et al. (2000) tested five different types of global funds and one large US equity fund against the Vanguard 500 Index during the period 1985-1994. The Vanguard 500 Index consists almost solely of US-based equity and can thus be named a ‘domestic benchmark’ (Morningstar.com, 2019). Redman et al. (2000) used the different measures to test for the outperformance and showed that the domestic US-equity fund was the only fund type to underperform the Vanguard 500 Index on two out of the three measures. All the global funds outperformed the Vanguard 500 Index on the same two out of three measures. They also noted that the adjusted R-squared

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of the global portfolios were much lower (between 54% and 80%) than the adjusted R-squared of the domestic US equity fund (β=95%). This is due to the fact that almost all of the funds inside the US Equity fund are represented in the Vanguard 500 Index and the returns of both funds will thus be correlated more than between the global funds and the Vanguard 500 Index (Redman et al., 2000).

The idea behind a global fund is that fund managers can pick winners from a wider arrange of equities and also diversify their risk at the same time. It can, therefore, be assumed that global mutual equity funds will have a better chance of beating the domestic benchmark than the domestic mutual equity funds. This also leads to the assumption that domestic funds will be less likely to outperform the global funds in regard to the international benchmark since the number of equities to choose from is less and the domestic funds can be less diversified than global mutual equity funds and also the global benchmark itself. However, as stated in the previous paragraph and hypothesis 1, previous studies often showed an underperformance of the benchmarks by mutual equity funds. This theoretical notion, together with the results of the study by Redman et al. (2000), lead to the following hypothesis to the second part of the research question:

H2: Global Dutch mutual equity funds underperform the benchmarks less than domestic Dutch

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3. Methodology

The methodology chapter contains an introduction to the statistical model, which has been used in this study. It then elaborates on the origins of the data of the study and the fund selection process. The third paragraph provides a detailed explanation of all the factor models and their functional forms. Paragraphs four and five will further explain the formulas and origins of the benchmarks, for both the domestic and global Dutch mutual equity funds. The chapter concludes with a short summary of the robustness checks that have been conducted in order to make the conclusions of this study more valid and reliable.

3.1 Statistical model

A time-series regression is best suited for estimating a fund’s ability to beat the benchmark throughout the past two decades. A non-random sample of Dutch mutual equity funds, both domestic and global, have been selected, and their characteristics and returns will be gathered from the past twenty years. This data will be extracted from several different databases, for instance, Eikon (Thomson Reuters) and Bloomberg. The selection process of the funds that have been used in this study will be further discussed in the next paragraph.

The advantage of time-series analysis is that it can use a non-random database; i.e., a sample of funds which is created by meeting a certain set of criteria and not picked at random, to make estimations of the influence of the independent variables, the factors of the model, on the dependent variable; i.e., the risk-adjusted excess return of the portfolio. It can do so across time and can check for potential lagged effects. The time-varying part of this study will use a rolling-window regression to estimate the factor betas throughout time. This estimation will also use a time-series regression in order to estimate the factor betas.

The statistical model is thus a time-series regression. The second assumption to model the outperformance of mutual equity funds is on the functional form of the time-series regression. This study will use a linear function to estimate a portfolio’s unconditional and time-varying betas. A linear function was introduced by Admati and Ross (1985) and was adopted in many studies that came after, for instance; Ferson & Schadt (1996) and Otten & Bams (2004). Paragraph 3.3 will provide in-depth details on the factor models, their theoretical origin, and statistical power.

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3.2 Data and selection of funds

The data that is required for this study came from different sources with the Eikon (Thomson Reuters) and Bloomberg databases being the most heavily used. The sources of the individual data categories can be found in table 1.

Data-type Source

Returns of Dutch mutual equity funds Eikon (Thomson Reuters)

Returns of the AEX Index Eikon (Thomson Reuters)

Returns of the MSCI World Index Eikon (Thomson Reuters)

Three-month government bond yields Eikon (Thomson Reuters) / Bloomberg Three-month interbank rates Federal Reserve Economic Data Ten-year government bond yield Federal Reserve Economic Data

Dividend yield of the AEX Index Bloomberg

Dividend yield of the MSCI World Index Bloomberg Moody’s corporate bond yields (AAA, Baa) Bloomberg

SMB, HML, MOM factors Kenneth French database

Table 1: The different data-types that are used in this study and their sources.

Most data points are from the period of January-2000 until December-2018, it will be noted throughout this study whenever the data used does not adhere to this fact. The study uses monthly data. Daily data was only available for a number of factors, and the given range still provides a substantial amount of observations, with a maximum of 228 observations per fund. The two types of Dutch mutual equity funds have been selected through a few steps. The selection process of domestic Dutch mutual equity funds will be described first.

The funds were first selected based on their base country, after which only Dutch mutual funds were selected. The second filter was their ‘Lipper asset type’, which indicates the type of assets that the mutual fund invests in. Only the Dutch mutual funds that solely invest in equity were selected, which were 238 funds. The next filter was based on the country or region that the fund invests in, i.e., the target country. The Thomson Reuters database determines the target country by determining in which country a fund invests over 50% of their assets into. This provided 11 domestic Dutch mutual equity funds and 107 global Dutch mutual equity funds. The current selection has one downside; it only contains funds that are ‘alive’. Almost all previous studies used a ‘survivorship-bias free’ database, for instance, Carhart (1997), Otten & Bams (2004), Huij & Verbeek (2009), Busse, et al. (2010) and Rao, et al. (2017). Survivorship bias is the effect where mutual equity funds that have failed, were liquidated or merged, are excluded from the database. This leads to an overrepresentation of mutual equity

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funds that are alive. The dead mutual equity funds are possibly liquidated due to their bad performance and returns. Excluding these dead funds will lead to an overestimation of the performance of a set of mutual equity funds (Chevalier & Ellison, 1997). This study does control for survivorship-bias, by including all Dutch mutual equity funds that have ‘died’ in between the given timespan. After controlling for survivorship-bias, the database contains 21 domestic Dutch mutual equity funds and 128 global Dutch mutual equity funds.

The next step was the elimination of real estate funds that contained no actual equities of stock that can be found on any index1 and of funds with less than 50 observations (so less than approximately four years of data). Studies by Cuthbertson, et al. (2008) and Kool (2017) use a t≥36 benchmark, but to increase the robustness of the results only funds with t≥50 are used. The final step has been the elimination of mutual equity funds that are so-called index funds. These index funds track the benchmark-index and aim to have a beta of one, which means that they are not actively managed portfolios, but follow the weight distribution of the index that is tracked. These funds have been checked based on their rating on ‘Morningstar.com’. This leaves fifteen alive and dead domestic Dutch mutual equity funds which are shown in table 2.

The betas of the individual funds are also included. The functional form of this estimation is similar to the one of the CAPM (equation 1). A detailed description of the model can be found in subparagraph 3.3.1, but the data that has been used will shortly be discussed for clarity. The market returns are the returns of the AEX Index. The domestic risk-free rate is the three-month government bond yield of the Netherlands. This data is only available from March 2010 and onward in both the Eikon and Bloomberg databases. However, the German three-month government bond yields are available from October 2005. The two three-month government bond yields show a correlation of 0.9748 (r=0.9748)2. This means that the German three-month government bond yields of October 2005 until March 2010 can safely be used as a replacement for the absent three-month government bond yield of the Netherlands. This means that the beta of the individual domestic funds is based on the timespan of October 2005 until December 2018. Passive funds allow for a slight variation of returns in regard to the market benchmark, which implies that a beta of exactly 1 is almost impossible to obtain. A beta close to 1 would, therefore, indicate that a fund might be an index fund. A range of the beta of 0.97-1.03 will be used since index funds only allow for a small ‘tracking error’ (the percentage which

1_{For instance real-estate funds. These funds officially contain equities, but not of listed companies. These funds}

can therefore not be benchmarked to a market index and are thus excluded from this study’s database.

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they do not adequately track the index) and this keeps the number of fund that are manually checked manageable. The three funds that come close to a beta of 1 are thus double-checked manually, through ‘Morningstar.com’.

Table 2: List of the selected domestic Dutch mutual equity fund, their status, number of observations, time of entering and leaving the database, and their CAPM-beta.

The selection of domestic Dutch mutual equity funds is now clear. The next part of this study will describe the steps in the selection process of global Dutch mutual equity funds. The first steps are similar to that of the domestic Dutch mutual equity fund selection process. After excluding the index-funds and real-estate funds, the sample consists of 64 dead and alive global Dutch mutual equity funds. The only difference in the process is the determination of the global Dutch mutual equity fund’s beta. In this case, the market returns are the returns of the MSCI World Index, and the risk-free rate is the weighted average of the three-month government bond yields of the ten largest economies. According to the International Monetary Fund’s World Economic Outlook Database (2018), these countries are United States, China, Japan, Germany, United Kingdom, France, India, Italy, Brazil, and Canada. However, the three-month government bond yield of China was unavailable, and the three-month government bond yields of Brazil and India are both outliers, which shift the global risk-free rate significantly. Besides, most mutual equity funds do not contain any equities from these countries. This means that the global risk-free rate consists of the seven countries that are left. The most recent weights per country of the MSCI World Index have been used to calculate the global three-month

Name of the domestic Dutch mutual

equity fund Status

Number of observations Time entering database Time leaving database CAPM-Beta

Achmea NL aandelen fonds 1 Dead 181 September 2000 November 2015 0.864 ADD Value fund NV Alive 141 February 2007 - 0.786 Allianz FUND aandelen fonds cap. Dead 113 November 2004 April 2014 0.976 Avero Achmea Nederland AF Dead 60 August 2010 October 2015 0.815 Bnp Paribas Netherlands Dead 217 March 2000 April 2018 0.942 Delta Lloyd deelnemingen fonds Dead 208 January 2000 April 2017 0.763 FBTO aandelenfonds Nederland Dead 178 January 2000 December 2014 0.859 Holland fund Dead 125 October 2003 April 2012 0.898 Kempen Orange fund NV Alive 227 January 2000 - 0.784 Nederlandse aandelenfonds Alive 150 May 2006 - 0.978

NN Dutch fund Alive 56 March 2014 - 1.245

NN Nederland fonds cap Alive 193 October 2002 - 0.922 Robeco Hollands bezit Alive 227 January 2000 - 0.845 Robeco Hollands bezit EUR g Alive 61 October 2013 - 0.817 Zwitserleven aandelenfonds Dead 216 January 2000 February 2018 0.992

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government bond yield in order to make the ‘global risk-free rate’ more accurate (MSCI, 2019). The global risk-free rate and the returns of the MSCI World Index were then used to determine the CAPM beta of the global Dutch mutual equity funds. The names, status, number of observations, time entering the database, leaving the database, and CAPM betas of the individual global Dutch mutual equity funds can be found in Appendix A.

3.3 The factor models

Both the introduction and the second chapter of this study introduced several different factor models. These factor models can all be used to determine a portfolio’s (out-)performance of the relative benchmark. The methodological and statistical notations of these models will be discussed in this paragraph. All variables that are used in these factor models will also be explained.

3.3.1 Capital Asset Pricing model

The starting model for evaluating the risk-adjusted fund performance is based on the CAPM of Sharpe (1964).

𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖= 𝛼𝛼 + 𝛽𝛽𝑖𝑖(𝑅𝑅𝑅𝑅𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) + 𝜖𝜖𝑖𝑖𝑖𝑖 (1)

Rit is the raw return, so excluding the transaction costs and fees, of mutual fund i at day t. Rft is also called the risk-free rate and resembles the return on a three month T-bill for day t. The combination ‘Rit - Rft’ resembles the excess return of portfolio i at time t. βi is, as stated in the introduction, the coefficient that measures the volatility of portfolio i in regard to the relevant market. A beta coefficient of 1 implies that the portfolio’s returns perfectly mimic the returns of the market, a beta larger than 1 implies that the portfolio’s return are more volatile than the market’s and a beta smaller than 1 would mean that the portfolio’s returns are less volatile than the market. Rmt resembles the return on the equity benchmark that is used for the portfolio, for instance, the AEX-index for domestic Dutch funds, in day t. εit resembles the error term. The intercept alpha describes the performance of the fund, relative to the market and the relevant risk factor of the portfolio. It is thus the performance of a portfolio that cannot be assigned to the tested factors and are thus the result of the active management of a fund’s portfolio (Rao, et al., 2017). The limitations of this single factor model lay in the use of a single market index as a benchmark. This does not account for, for instance, investments in small-cap equities, which are not listed on the used large-cap index.

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3.3.2 Fama & French and Carhart models

Fama and French (1993) introduced two extra factors to improve the explanatory power of the CAPM equation, which resulted in equation 2.

𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖 = 𝛼𝛼 + 𝛽𝛽0𝑖𝑖(𝑅𝑅𝑅𝑅𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) + 𝛽𝛽1𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ 𝛽𝛽2𝑖𝑖𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝜖𝜖𝑖𝑖𝑖𝑖 (2)

The Small –Minus-Big (SMB) factor is a proxy to account for the difference in returns between small-cap portfolios and large-cap portfolios. This effect was thoroughly studied by Fama & French (1992). Small-cap portfolios invest in small companies which often bear more risk but create higher returns than their larger-cap counterparts. The High-Minus-Low (HML) factor serves as a proxy for the value of the companies in which the funds invest. So-called ‘value stocks’ are stocks of large companies i.e., companies with high book-to-market equity (B/M) ratios, high earnings to price (E/P) ratios or a high cash flow to price (CF/P) ratio. They tend to have higher returns than the ‘growth stocks’, which are stocks of companies with low B/M, E/P or CF/P ratios (Fama & French, 1998)3. These additional factors did improve the model. However, Cahart (1997) stated that it did not capture the variation in portfolio returns based on the momentum of a portfolio. He, therefore, added the fourth factor; momentum (MOM).

𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖 = 𝛼𝛼 + 𝛽𝛽0𝑖𝑖(𝑅𝑅𝑅𝑅𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) + 𝛽𝛽1𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ 𝛽𝛽2𝑖𝑖𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝛽𝛽3𝑖𝑖𝑆𝑆𝑀𝑀𝑆𝑆𝑖𝑖+ 𝜖𝜖𝑖𝑖𝑖𝑖 (3)

MOM is the difference in return between a portfolio because of the one-year momentum in the returns of the underlying stocks of the fund. Carhart (1997) showed that buying previous years winning stocks and selling the losing stocks, might be a good investment strategy.

3.3.3 Time-varying beta model

Equations 1 through 3 all have the same shortcoming; the betas are stationary. For the CAPM factor, this would mean that the volatility of a fund’s portfolio, in regard to the market benchmark, is the same throughout time. This assumes that both managers and investors do not use current economic information in adapting their portfolios. However, managers and investors are expected to adapt to current market states and change their portfolio accordingly. The same is true for the SMB, HML, and MOM factors. The composition of the funds changes

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throughout time, which also means that the betas between the portfolio and the three factors change throughout time (Ferson and Schadt, 1996). Thus, using an unconditional beta model to estimate a fund’s alpha would deliver unreliable results. As stated in paragraph 2.3, there are several ways to create a time-varying alpha and beta. This study uses a rolling-window regression. A rolling-window regression uses a window of observations prior to the estimated data point, to estimate the beta for that data point. This study will use a 24 month/observation window, similar to the study of Fung and Hsieh (2005) and Brooks, Clare, and Motson (2007). A window of 24 observations means that, for instance, the CAPM beta at t=25 is determined by the regression of equation 1, using the data of t=1 through t=24. The next data point (t=26) is determined by using the data of t=2 through t=25. The downside of using a rolling-window regression is that the first 24 data points drop out. The regression is only possible for the data points that are preceded by at least 24 observations (so for t>24). The possible effects of the window size are discussed in paragraph 3.5 and tested in paragraph 4.4.1.

Equation 4 shows the adapted equation 3, but now with time-varying betas and alpha.

𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝛽𝛽0𝑖𝑖𝑖𝑖(𝑅𝑅𝑅𝑅𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) + 𝛽𝛽1𝑖𝑖𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ 𝛽𝛽2𝑖𝑖𝑖𝑖𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝛽𝛽3𝑖𝑖𝑖𝑖𝑆𝑆𝑀𝑀𝑆𝑆𝑖𝑖+ 𝜖𝜖𝑖𝑖𝑖𝑖 (4)

The time-varying betas are thus estimated using a rolling-window regression. After the estimation, the different betas are known for each month, as well as the different factors. This allows for a simple subtraction of all the variables from the excessive returns of the fund for that month, resulting in equation 5.

(𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) − (𝛽𝛽0𝑖𝑖𝑖𝑖(𝑅𝑅𝑅𝑅𝑖𝑖− 𝑅𝑅𝑅𝑅𝑖𝑖) + 𝛽𝛽1𝑖𝑖𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖+ 𝛽𝛽2𝑖𝑖𝑖𝑖𝐻𝐻𝑆𝑆𝐻𝐻𝑖𝑖+ 𝛽𝛽3𝑖𝑖𝑖𝑖𝑆𝑆𝑀𝑀𝑆𝑆𝑖𝑖) = 𝛼𝛼𝑖𝑖+ 𝜖𝜖𝑖𝑖𝑖𝑖 (5)

The result of equation 5 is a time-varying alpha, which means that each month has its own alpha. This is in contrast to the unconditional model, where there is only one alpha given for the entire tested period. The overall alpha can thus be determined by its mean. The out- / underperformance of a fund during the studied timespan is thus the mean of all its independent alphas. A t-test can be performed to test whether the alpha is significantly different from zero and thus either significantly out- / underperforms the market benchmark when adjusted for the different risk factors.

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3.4 The benchmarks

The first part of the study will focus on the individual performance of the two types of Dutch mutual equity funds. The first type (domestic) only invests in domestic, Dutch equities and the second type (global) consists of equities from all over the world. This requires two different benchmarks. One for the domestic funds that consist of Dutch parameters and one for the global funds that consist of global benchmarks. Each of the factors, discussed in paragraph 3.3, requires a separate benchmark.

The benchmarks for the CAPM, of equation 1, are the same as the benchmarks that were used in the fund selection process. Domestic Dutch mutual equity funds will use the AEX index as the domestic market benchmark and the Dutch and German three-month government bond yield as the domestic risk-free rate. The reason for the incorporation of the German three-month government bond yield can be found in paragraph 3.2. The global Dutch mutual equity funds will use the MSCI World index as the global market benchmark and the global risk-free rate, determined according to the process described in paragraph 3.2, as its risk-free rate.

The second part of the study tries to compare the performance of the two types of Dutch mutual equity funds. In order to properly compare the two fund types, they will be tested against the same benchmarks. Both the domestic and global Dutch mutual equity funds will first be tested against the domestic benchmarks to see which fund type performs better against the domestic benchmarks. Afterwards both fund types will be tested against the global benchmarks in order to see which fund type is better at beating the global benchmarks. After these comparisons, it will be clear which type of fund is better suited to beat the domestic and the global benchmark. This is a similar method as was used by Redman et al. (2000), which has been explained in paragraph 2.4.

The three other factors, besides the CAPM, can be determined using the chosen benchmarks and ordering them for the relevant factor. As said in paragraph 3.2, this daily data is retrieved from the Kenneth French website. The data is not available for the Netherlands specific, and thus European benchmarks are used for the domestic Dutch funds. This is due to the small amount of Dutch equities, which does not allow for a well-diversified portfolio to create three different factors. The equations to determine each factor (SMB/HML/MOM) are as follows:

𝑆𝑆𝑆𝑆𝑆𝑆 =1₃(𝑆𝑆𝐻𝐻 + 𝑆𝑆𝑆𝑆 + 𝑆𝑆𝐻𝐻) −1₃(𝑆𝑆𝐻𝐻 + 𝑆𝑆𝑆𝑆 + 𝑆𝑆𝐻𝐻) (6)

𝐻𝐻𝑆𝑆𝐻𝐻 =1₂(𝑆𝑆𝐻𝐻 + 𝑆𝑆𝐻𝐻) −1₂(𝑆𝑆𝐻𝐻 + 𝑆𝑆𝐻𝐻) (7)

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The proxies for book-to-market (HML) and size (SMB) are determined by the following process. The size factor of a portfolio is determined by multiplying the underlying stocks stock price by the number of outstanding common shares. The book-to-market(BE/ME) ratio of the portfolio is determined by multiplying the underlying stock’s book value of equity (BE), by the market capitalization of the same stock (M). The B is simply the common shareholder’s equity (total assets-total liabilities). The stocks in the portfolios are then grouped, according to size. The most commonly used cut-off points are the smallest 10% as small stocks and the largest 10% (so 90%+) as large stocks. The stocks that are left are then categorized into three groups, dependent on the BE/Me ratio. The lowest 30% is set as low stocks, the stocks with a ratio within 30% and 70% of the total stocks, are labeled medium stocks. The 30% of stocks with the highest ratio are the high stocks. This provides six combinations and thus, groups of stocks that form a portfolio (SL, SM, SH, BL, BM, BL). After each year, the B/M and size of the stocks are adjusted to the newest information, and the created portfolios are then reshuffled again. This reshuffling often happens in July of year t. The size proxy is determined based on the information that is available in June of year t. However, the B/M ratio is determined based on data from December in year t-1.

Equation 6 calculates the difference between the weighted average return on the small stock portfolio and the weighted average return on the big stock portfolios. Equation 7 does the same for high and low stock portfolios. The momentum proxy (MOM) is determined in a similar way as the HML factor. The stocks are sorted by size, in the same way as with the SMB factor. The stocks that are left are then sorted, based on their performance of the previous 12-months cumulative returns. The cut-off points are 30% marks. The 30% of the best performers are classified as top performers, and the 30% worst performers are classified as worst performers. This, again, leads to six different portfolios whose returns are measured. The MOM factor is then calculated according to equation 8, subtracting the weighted-average of the top performers, from the worst performers.

3.5 Robustness checks

To test whether the results from this study are not affected by the assumptions of this study, several robustness checks will be executed. One of this study’s assumptions is the number of observations that is used for the rolling window regression. Initially, a 24 window is used, a shorter window containing less observations is not relevant, since the 24 observation window is already relatively small for an OLS regression. Thus, a larger window of 48 observations and

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a much larger window of 72 observations will be used to test what the effect of this assumption is on the tested alpha. This is similar to the robustness check by Budiono (2010). These windows are selected to test the entire spectrum, from a small window size of two years, to a large window size of six years.

The second robustness check is to isolate the years of the economic crisis in 2008. The economic crisis of 2008 has sparked many studies into its effects on all kinds of matters, but also on the effects on mutual fund performances and investment styles, for instance, Salganik-Shoshan (2017). Similar to the study by Salganik-Salganik-Shoshan (2017), this study will isolate the period of the economic crisis (December 2007 – June 2009), as described by NBER (National Bureau of Economic Investigation, 2010b). This is officially the date that was set for the economic crisis in the United States but will also be used for the domestic funds.

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4. Results

Now that the relevant literature and methodology of this study has been thoroughly explained, this chapter will show the results of the different factor models. Paragraph 4.1 will elaborate on the different unconditional factor models and the findings for both the domestic and global Dutch mutual equity funds. The second paragraph will focus on the time-varying factor models and its results.

4.1 Unconditional factor model

This paragraph contains the results of the unconditional factor models. The results of the pooled domestic fund and the pooled global fund will be discussed first. The results for the individual performance of the domestic Dutch mutual equity funds will be discussed in subparagraph 4.1.2, and the individual performance of the global Dutch mutual equity funds will be discussed in subparagraph 4.1.3. Paragraph 4.1.4 contains the conclusion in which the results are also compared to the results of similar studies that were mentioned in chapter two of this research.

4.1.1 Pooled domestic fund and pooled global fund

This part of the study uses the average monthly returns of all the domestic Dutch mutual equity funds (pooled domestic fund) and the average monthly returns of all the global Dutch mutual equity funds (pooled global funds), between January 2000 and December 2018. Table 3 shows a summary of the returns of the pooled domestic and pooled global funds.

Type of fund Mean return (% p.m.) Standard deviation Number of funds

Pooled domestic fund 0.443 5,062 15

Pooled global fund 0.291 4.022 64

Table 3: Mean returns, standard deviation, and the number of funds for the pooled domestic, the pooled global.

Table 3 shows that the mean return of the pooled global fund is lower than the mean return of the pooled domestic fund. Table 4 displays the summary statistics of the domestic benchmarks. Table 5 does the same, but for the global benchmarks. Note that the CAPM only shows the raw returns of the market benchmarks. Thus the average of the raw monthly returns of the AEX Index. The global CAPM shows the average of the raw monthly returns of the MSCI World Index. The SMB, HML and MOM factors are determined according to the process described in paragraph 3.4 and are extracted from the Kenneth French Database. This is similar to the study by Otten and Bams (2004). The t-statistic is the result of a one-way t-test to check whether the

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means are significantly different from zero. The cross-correlations are also provided in order to check for possible multicollinearity.

Benchmark Domestic Mean return (% p.m.) Standard deviation t-statistic for a mean of 0 Cross-correlations CAPM(Rm) SMB HML MOM CAPM (Rm) 0.38 5.68 1.01 1.000 SMB 0.168 2.111 1.199 0.357 1.000 HML 0.461 2.637 2.642*** 0.034 -0.118 1.000 MOM 0.778 4.335 2.709*** -0.05 0.193 -0.264 1.000

Table 4: Summary statistics of the domestic benchmarks, including cross-correlations. Significance levels: *(α=10%) **( α=5%) ***( α=1%) Benchmark Global Mean return (% p.m.) Standard deviation t-statistic for a mean of 0 Cross-correlations CAPM (Rm) SMB HML MOM CAPM (Rm) 0,433 4.188 1,56* 1.000 SMB 0.109 2.006 0.819 0.161 1.000 HML 0.438 2.48 2.668*** 0.041 -0.265 1.000 MOM 0.377 4.231 1.344* -0.125 0.282 -0.183 1.000

Table 5: Summary statistics of the global benchmarks, including cross-correlations. Significance levels: *(α=10%) **( α=5%) ***( α=1%)

All the variables in both table 4 and 5 show no signs of multicollinearity. Besides that, it also shows that the mean of the global CAPM benchmark’s returns is slightly higher than the mean of the domestic CAPM benchmark’s returns.

Since this study uses equity returns, which often show signs of autocorrelation, the first step is conducting a test for hetroskedacity and autocorrelation on the residuals of the original unconditional four-factor regression. This is similar to studies by Cuthbertson et al. (2006) and Kool (2017). The histogram of the returns of the pooled Domestic fund’s returns show signs of a leptokurtic distribution. A Breusch Godfrey Lagrange Multiplier test was performed to test for multi-level autocorrelation, including six lags (Thornton, 2016)4. This test showed that the null hypothesis, in which there is no autocorrelation, had to be rejected. The regression will be performed through a Newey-West regression analysis in order to solve this problem of autocorrelation (Newey & West, 1987). Similar to previous researches by for instance Ferson and Schadt (1996), Kool (2017) and Huynh (2017).

The next step is to perform the Newey-West regression analysis with the unconditional four-factor model of Carhart. The regression is based on formula 3 of this study. Note that for the pooled domestic fund, only data between October 2005 and December 2018 is used. Table

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3 shows the results for both the pooled domestic and pooled global Dutch mutual equity funds. The benchmarks are adjusted for the type of Dutch mutual equity fund, as stated in paragraph 3.4.

Pooled domestic fund Pooled global fund

Coeff. NW-std.err. t-value p<|t| Coeff. NW-std.err. t-value p<|t|

α (% p.m.) -0.09 0.11 -0,88 0,379 -0,21 0,05 -3,92 0,000*** CAPM 0.8736 0.0256 34,07 0,000*** _0,9224 _0,0212 _43,43 _0,000*** SMB 0.0878 0.0758 1,16 0,248 0,0463 0,0454 1,02 0,309 HML 0.113 0.0529 2,14 0,034** -0,0036 0,0343 -0,11 0,916 MOM 0.0362 0.028 1,30 0,197 -0,0128 0,0246 -0,52 0,604 Adj. R2 _0.9158 _0.9378

Table 6: Results of the unconditional four-factor model by Carhart, on the pooled excessive returns of both domestic and global Dutch mutual equity funds. Significance levels: *(α=10%) **( α=5%) ***( α=1%)

The results for the pooled domestic fund of table 6 indicate that the four-factor model can explain 91,58% of the change of the pooled domestic fund’s excessive returns. This is even higher, 93,78%, for the pooled global fund. This shows that the returns of both domestic and global Dutch mutual equity funds are mainly determined by the returns of the relevant market index and other benchmarks. This is due to the fact that the funds that are tested against the market benchmark, consist of equities from within that benchmark. This makes it probable for the adjusted R-squared to be as high as it is and this result is similar to that found in prior research by for instance Jensen (1967) and in both studies by Otten & Bams in 2002 and 2004. Table 6 also shows that the pooled domestic fund does not significantly under- or outperform the AEX Index benchmark, when controlled for the other factors (α=-0.09, p<0.38) The pooled global fund does underperform the MSCI World Index benchmark by 0.21% per month (α=-0.21, p<0.01). The market benchmark (CAPM) is highly significant in both the fund types (p<0.01), and both the CAPM-coefficients are lower than one (β=0.87, β=0.92). This indicates that, in general, the pooled domestic fund and pooled global fund consist of relatively ‘safe’ equities with a low CAPM-beta. The HML-factor is significant for the pooled domestic fund (p<0.05). The fact that the HML-coefficient (β=0.113) is positive indicates that the pooled domestic fund is likely to include more equities with a high book-to-market ratio than equities with a low book-to-market ratio. Both the SMB (p<0.25, p<0,31) and MOM (p<0.2, p<0.6) factors are insignificant in both the pooled domestic fund and pooled global fund. The HML factor is also insignificant for the global pooled fund (p<0.92). The insignificant results of the SMB, HML, and MOM factors can be explained by the substantial differences in characteristics

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of the individual funds that comprise the pooled funds. The pooled funds consist of a number of funds that all have different characteristics. For instance, funds that invest in small cap equities or funds that invest in large cap equities. These are all combined in the pooled funds, and these characteristics will then cancel each other out and thus result in insignificant results of the SMB, HML, and MOM factors. To check for this assumption, the next part of this study will perform the same Newey-West regression of the unconditional four-factor model on the individual funds that comprise the pooled funds that were tested in this section.

4.1.2 Individual domestic Dutch mutual equity funds

As explained in the previous subparagraph, this part of the study will focus on the performance of the individual funds that comprise the pooled domestic fund. The next step is thus to perform a Newey-West regression analysis of the unconditional four-factor model by Carhart (equation 3) with the individual domestic Dutch funds mutual equity funds. This allows checking whether the SMB, HML, and MOM factors have a significant effect on the (out)performance of domestic Dutch mutual equity funds.

The results of the domestic funds show that the market benchmark (CAPM) is also highly significant for all individual funds (p<0.01). This was to be expected since it was also highly significant in the ‘pooled domestic fund’ variable. More surprisingly is that three out of the fifteen domestic Dutch mutual equity funds significantly underperform the AEX-benchmark

Table 7: Results of the Newey-West regression of the unconditional four-factor model, on the excessive returns of individual domestic Dutch mutual equity funds. Significance levels: *(α=10%) **( α=5%) ***( α=1%)

Constant CAPM SMB HML MOM _Adj.

R2 α (% p.m.) t-value β-coeff. t-value β-coeff. t-value β-coeff. t-value β-coeff. t-value

Achmea nl aandelen fonds 1 -0.2732** -2.09 0.851*** 21.93 0.086 0.69 0.214** 2.48 0.070 1.2 0.881

Add Value fund NV 0.2357 0.67 0.775*** 13.41 0.081 0.71 0.108 0.66 0.018 0.15 0.602

Allianz FUND aandelen fonds

cap. -0.0912 -0.87 0.972*** 51.37 0.006 0.12 0.049 1.07 -0.019 -0.66 0.979

Avero Achmea Nederland

aandelenfonds 0.1984 1.1 0.787*** 8 0.227 1.2 0.078 1.06 0.039 0.23 0.804

Bnp Paribas Netherlands -0.1974** -2.17 0.934*** 39.55 0.072 1.43 0.051 1.21 0.036 1.39 0.963

Delta Lloyd deelnemingen

fonds -0.2104 -0.74 0.733*** 12.35 0.241 1.19 0.247** 2.1 0.124 1.56 0.616

FBTO aandelenfonds

Nederland -0.2362 -1.22 0.855*** 21.66 0.015 0.12 0.158* 1.85 0.049 0.88 0.872

Holland fund -0.2469 -1.56 0.892*** 20.24 0.012 0.08 0.165* 1.70 0.024 0.45 0.856

Kempen Orange fund NV 0.1925 0.69 0.753*** 13.15 0.258 1.47 0.228* 1.71 0.061 1.04 0.619

Nederlandse aandelenfonds -0.0538 -0.70 0.973*** 79.27 0.039 1.21 0.021 0.50 0.010 0.64 0.961

NN Dutch fund -0.4367 -1.59 1.247*** 6.16 0.010 0.04 -0.348 -1.03 -0.011 -0.11 0.623

NN Nederland fonds cap -0.1257 -1.56 0.918*** 27.44 0.033 0.3 0.147** 2.18 0.076 1.61 0.887

Robeco Hollands bezit -0.1524 -1.29 0.831*** 25.85 0.110 0.88 0.128* 1.67 0.046 1.1 0.846

Robeco Hollands bezit EUR g 0.0361 -0.18 0.798*** 19.51 0.304* 1.83 0.133 1.58 -0.016 -0.17 0.767

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(p<0.05), by somewhere between 0.1% and 0.3% per month (α=-0.27, α =-0.19, α =-0.13). The other twelve funds do not significantly under- or outperform the AEX-benchmark. The HML-factor is significant for seven out of the fifteen funds (p<0.1, p<0.05). These coefficients are all positive (β=0.21, β=0.25, β=0.17, β=0.23, β=0.15, β=0.13) and thus confirm the results of the pooled regression, which indicated that the funds that comprise the pooled domestic fund consist mainly of equities with a high book-to-market ratio and thus have a ‘value bias’. The SMB factor only shows a significant result for the ‘Robeco Hollands Bezit EUR g’ fund (β=0.3, p<0.1). This would imply that this fund consists of mostly small-cap equities and thus has a ‘small cap overweight’. All the other SMB-factor results and MOM-factor results are insignificant. The results that are displayed in table 7 concur with the results of the pooled domestic fund returns of table 6.

4.1.3 Individual global Dutch mutual equity funds

A similar Newey-West regression has been performed on the individual global Dutch mutual equity funds, using the unconditional four-factor model by Carhart (equation 3). The results can be found in Appendix B and will shortly be discussed in this paragraph.

The results are similar to that of the individual domestic Dutch mutual equity funds. Most funds, 42 out of the 64, show no significant over- or underperformance of the benchmark when adjusted for the tested factors. Only two funds significantly outperform the benchmarks by 0.5% and 0.3% per month (α=0,005, p<0.05, α=0,003, p<0.05). the twenty funds that are left significantly underperform the tested benchmarks by anywhere between 0.1% and 0.6% per month. This supports the negative alpha (α=-0.21, p<0.01) that was found in the pooled global fund’s results in table 6. All three other factors: SMB, HML, and MOM, are only significant in seven out of the 64 funds. This also concurs with the results of the pooled global fund in table 6, where these factors are also insignificant.

4.1.4 Conclusion

This part of the study used the formula in equation 3 to estimate the outperformance of the relevant benchmark, by domestic and global Dutch mutual equity funds. Table 6 showed the results of the domestic pooled fund, the returns of all domestic Dutch mutual equity funds pooled together, which did not show a significantly different performance than the AEX benchmark when adjusted for the benchmark factors. It also showed the global pooled funds, the returns of all global Dutch mutual equity funds pooled together, which showed a significant underperformance of the benchmark by 0.21% (α=0.21, p<0.1) per month. Three out of the

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fifteen individual domestic Dutch mutual equity funds showed a significant underperformance of the market benchmark when adjusted for the SMB, HML, and MOM factors (p<0.05). These results can be found in table 7.

The global funds showed a similar image. The pooled global fund attained a significantly negative alpha when adjusted for the four factors (α=-0.21, p<0.01). Of the individual global Dutch mutual equity funds, only two out of the 64 funds showed significant outperformance (p<0.05) of the market benchmark, when adjusted for the other three factors. However, twenty funds significantly underperformed the market benchmark when adjusted for the same factors, and the other 42 did not significantly out- / underperformed the benchmarks.

The results of the test of the individual Dutch mutual equity funds, in which most individual funds did not significantly perform differently, several underperformed and just very few outperformed the benchmark is similar to that of almost all previous studies. As stated in paragraph 2.2 of this study, studies by Droms and Walker of 1994 and 1996, Ippolito (1989) and Jensen (1967) all showed similar results when testing different types of mutual equity funds. More recently, Otten and Bams (2004) also showed that when using a four-factor model the average fund underperformed the market benchmark by 0.54%, similar to the results of the pooled global fund in this study. In a different study, Otten and Bams (2002) showed that funds on average did not significantly perform differently than their benchmark when controlled for different risk factors. This is similar to the results of the pooled domestic fund in this study. It can, therefore, be stated that the results of this study are in line with the results of previous studies.

4.2 Time-varying factor model

This paragraph contains a description of the results of the time-varying four-factor model, as shown in equations 4 and 5 of paragraph 3.3. Subparagraph 4.2.1 contains the results of the time-varying alphas of both fund types. The next subparagraphs contain the explanations of the time-varying betas of both fund types. Finally, subparagraph 4.2.4 offers an answer to the first hypothesis and the first part of the research question of this paper. The results will also be linked to the results of previous studies.

4.2.1 Time-varying alphas of the pooled domestic fund and pooled global fund

In this subparagraph, the excessive returns of the pooled domestic fund and the pooled global fund will be tested for their performance in regard to the market, when controlled for several

Performance of Dutch mutual equity funds using a time-varying approach