• No results found

The Presence of the Low-Volatility Anomaly in Fund Management - Empirical evidence from the European fund market

N/A
N/A
Protected

Academic year: 2021

Share "The Presence of the Low-Volatility Anomaly in Fund Management - Empirical evidence from the European fund market"

Copied!
38
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

*University of Groningen, faculty of economics and business. E-mail: j.m.cavas@hotmail.com, studentnumber: 1530739.

The Presence of the Low-Volatility Anomaly in Fund Management

-

Empirical evidence from the European fund market

Michel Cavas* 2013

Master’s thesis Finance University of Groningen Supervisor: dr. Auke Plantinga

Abstract

Abstract

(2)

1

I. Introduction

The Capital Asset Pricing Model (CAPM) had been independently developed in the 1960’s by Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966), Black, Jensen, and Scholes (1972), and Miller and Scholes (1972). Shortly after that Black, Jensen, and Scholes (1972), and Miller and Scholes (1972) observe that low-beta stocks in the United States of America performed better than their high-beta counterparts. This low-volatility anomaly, as it came to be known, troubles the financial world as it is counter-intuitive. How can it be that investors are being rewarded for holding low volatility stocks, and ‘punished’ for holding high volatility stocks.

For example, the U.S. stock market clearly outperformed the U.S. bond market as an asset class, however the higher the risk within an asset class the lower the realized return (Baker, and Haugen 2012). Baker, Bradley, and Wurgler (2011) found that for the period 1968-2008, the spread of low volatility portfolio over high volatility portfolio amounted to 5.22% annually. More research has been conducted on markets outside of the U.S. to see if this effect transcends the borders. Dutt and Humphery-Jenner (2013) and other researchers have found that this indeed the case. They found that this anomaly not only exists in the U.S. market, but in emerging markets and developed markets outside of the U.S. as well. The fact that this anomaly invalidates the basic prediction of modern portfolio theory, greater risk bears greater rewards, will afflict many theories based on this prediction.

Baker, Bradley, and Wurgler (2011) discuss the possibility that the low volatility effect exists due to institutional investors tracking a benchmark. This limits the institutional investor’s ability to entirely exploit arisen arbitrage opportunities, although it could enable them to earn systematically higher returns while facing lower risk. Supporting this theory, Chan, Chen, and Lakonishok (2002) find that institutional investors tend to stick towards a broad market benchmark, allowing the low volatility anomaly to persist as these large investors cannot or will not ‘arbitrage’ it out of the market.

Using the prediction of modern portfolio theory that higher risk generates higher rewards, professional investors allocate vast amounts of capital based on the idea. The question here is, do these professionals indeed use these “misguided theories” as Haugen (2012) calls them, or are these professionals aware of the allegedly inverse relationship between risk and return?

(3)

2 This paper is structured as follows; the following section will discuss the theoretical background of the low-volatility anomaly, in section 3 the methodology will be described and explained. Following the methodology section, in section 4 the data will be discussed. Section 5 contains the results, lastly section 6 will provide a conclusion.

II. Literature review

An important prediction forwarded by modern portfolio theory is that high risk yields high rewards and vice versa. It is intuitive and probably therefore widely accepted. However, there is substantial empirical evidence which challenge this prediction. This section explores the theoretical background and empirical evidence related to the subject.

In 1952 Markowitz laid the foundation for modern portfolio theory basis, in the 1960’s Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966) independently developed the capital asset pricing model (CAPM) based on earlier work of Markowitz. The CAPM model relates risk to return, more specifically non-diversifiable risk to expected returns (beta). According to the model, low beta stocks earn lower expected returns compared to high beta stocks, revealing a reward for taking on non-systematic risk. In 1992 Fama and French find that the high-beta portfolios have expected returns which are close to or less than the expected returns of the low-beta portfolios. Black, Jensen, and Scholes (1972), and Miller and Scholes (1972) find that low-beta stocks in the United States of America for the period 1931 through 1965 perform better than the CAPM model predicts, and that high-beta stocks performed worse than expected by the CAPM model.

(4)

3 According to Black (1972) borrowing restrictions, like margin requirements, could be the cause for low-beta stocks performing relatively well. Baker et al. (2011) look for explanations in the field of behavioral finance, hypothesizing that at the basis are two drivers: investors are less than fully rational and underappreciate limits on arbitrage. The preference for high-volatility stocks derives from the preferences (biases) of the individual investor. Noticeable biases are: preference for lotteries (Barberis, and Huang 2008), representativeness fallacy (Tversky and Kahneman 1974), and overconfidence (Alpert and Raiffa 1982, Cornell 2009). Preference for lotteries derives from the Investors preference for a high chance to lose a small amount and low chance to win a large amount over a coin flip where both gambles present an equal expected pay off. Barberis and Huang (2008) provide evidence that investors tend to depart from predictions of expected utility, when they have to make decisions facing risk with lottery aspects.

Representativeness refers to judgments based on stereotypes; a common stereotype is that a renowned well performing firm is a good investment. An investment is considered good when the returns, which can be generated through dividends or an increase in stock value, are better than the market or another relevant benchmark. These two definitions are not identical, however often they are perceived as such. Lakonishok, Shleifer, and Vishny (1994) research this investor preference for glamour stocks (which is how Lakonishok et al. identify stocks which have performed well in the past and are currently overpriced due to hyping) and find that these stocks underperform value stocks (stocks which have performed poorly in the past, and suffer from an overreaction from the market). The representativeness bias also relates to individual investors behavior to look at investments in hindsight. In hindsight the investors identify single stocks which paid out big, often being small and risky firms. These individual investors then neglect the population of small and risky firms as a whole and ignore the fact that the success chance of these firms paying off big is rather low.

(5)

4 therefore marginalizing risk associated with these uncertain outcomes. This results in overestimating the returns on high volatility stocks.

Baker et al. (2011) explain that the persistence of the low-volatility anomaly lies in the fact that exploiting it proves to be difficult. Institutional investor’s performance is measured by relating the performance to a benchmark. By creating a tracking portfolio the performance is more or less guaranteed. In order for these institutional investors to engage in arbitrage of this anomaly, one would need to hold stocks with approximately similar long-term returns while having different risks. This only leads to an increase in tracking error (assuming institutional investors with fixed benchmarks). Although these low volatility funds would enable them to earn systematically higher returns, having to measure up against a fixed benchmark restrains these investors from actually doing so. Supporting this theory, Chan, Chen, and Lakonishok (2002) find that institutional investors tend to stick towards a broad market benchmark. This allows the low volatility anomaly to persist, as these large investors cannot or will not ‘arbitrage’ it out of the market.

Dutt and Humphery-Jenner (2013), Blitz and van Vliet (2007), Ang, Hodrick, Xing, and Zhang (2006), Baker and Haugen (2012) show that the low-volatility anomaly exists in emerging markets and developed markets outside of North America. Furthermore Dutt and Humphery-Jenner (2013) show that low-volatility stocks generate higher operating income (gross income less operating expenses, depreciation, and amortization), hypothesizing that this could be one of the drivers for the low-volatility anomaly. Finally, they observe that controlling for operating performance significantly influences the relationship between stock returns and volatility. This further invalidates the assumption that risk is the sole driver of return.

(6)

5

III. Methodology

In this section the methodology of this study will be discussed, and the regressions described. The model will be explained, while checks for validation will be supplied.

A. Research objective

The goal is to test whether the low volatility anomaly applies to European mutual funds. The universe of mutual funds exists of active stock funds, bonds funds, and mix funds offered by financial institutions in Europe. In this paper the MSCI Europe Index (Index) will be used as the benchmark. For the period 2003-2013 tests will be performed to assess the performance of European funds, to check for the presence of the low volatility anomaly. The central question is: ‘Does the low-volatility anomaly apply to funds in the European market?’. Of interest is how the funds perform amongst each other, how the funds perform against the index. Furthermore the performance relative to the risk the funds bear is of importance. These results will be checked accordingly by means of a robustness test.

A.1 Research model

Three different models and four performance metrics will be used to determine the performance of the European funds in this paper. The three models are:

 Capital Asset Pricing Model

 Fama and French three-factor model  Carhart four-factor model

The four performance metrics are:  Sharpe ratio

 Risk-adjusted performance alpha  Information ratio

(7)

6 A.1.1 Capital Asset Pricing Model

The first model is the CAPM, where the performance measure is Jensen’s alpha (Jensen, 1967). Jensen’s alpha is a risk-adjusted performance measure of a portfolio’s return. It is calculated as the difference between the return obtained by the fund and the return predicted by the CAPM model. The latter is driven by the risk-free rate and the beta of the portfolio. The CAPM model is given by:

( ) (1)

By rearranging equation 1, we calculate Jensen’s alpha as:

[ ( )] (2)

In equation 1 and 2, αp represents Jensen’s alpha for the portfolio, is the return on the portfolio, rf

is the risk-free rate, is the beta of the portfolio, and rm is the return on the market index. The beta of

the portfolio in this model is calculated as the covariance of the returns of the portfolio and the market index divided by the variance of the portfolio.

A.1.2 Fama and French three-factor model

(8)

7 The Fama and French three-factor model uses as the exposure to the market. The factor SMB is the ‘small minus big’ factor. This measures the historic excess returns which investments in small market capitalization firms have generated over investments in firms with large market capitalizations. These higher historic returns are accompanied by higher volatility for these small funds. This size premium is captured in the SMB factor and differs per region. For this paper the SMB factors for the European region, provided by the Fama and French online database1, are utilized. HML is the ‘high minus low’ factor, which measures the premium derived from holding investments with high relative to low book-to-market values (Fama and French, 1993). The firms with high book-to-book-to-market ratio are considered to carry higher expected risk related to the relative earnings performance, and are expected to generate high future returns. This value premium is captured by the HML factor, which, like the SMB factor, differs per region. For this paper the HML factors for the European region, provided by the Fama and French online database, are utilized. The model is calculated as:

( ) (3)

In equation 3, represents the Fama and French 3-factor model market beta which may differ from the beta used in Jensen’s model when there is correlation between the , , and the factor. SMB

corresponds to the historic excess return of small capitalization funds over large capitalization funds, HML corresponds to the historic excess returns of high market ratio funds over low book-to-market ratio funds. is the exposure of the portfolio to the SMB-factor, is the exposure of the portfolio to the HML-factor. The factor represents the Fama and French 3-factor model alpha of the portfolio.

A.1.3 Carhart four-factor model

Finally, the third model is the Carhart four-factor model (1997), it expands the CAPM model by adding momentum (MOM) as a fourth factor. This factor captures the tendency of assets to exhibit positive serial autocorrelation, e.g. positive returns are more likely to be followed by positive returns. Jegadeesh and Titman (1993, 2001) provide evidence for this empirically observed effect. By including this factor,

1

(9)

8 the model controls for the effects of momentum on the performance of funds. The model is calculated as:

( )

(4)

represents the Carhart model market beta, represents the exposure to the MOM factor, and is the Carhart model’s alpha. For this paper the MOM factor for the entire time period in the European region, provided by the Fama and French online database, are utilized.

A.1.4 Risk-adjusted performance metrics

In addition to the CAPM, Fama and French, and the Carhart models, four alternative risk-adjusted performance metrics will be utilized for robustness purposes. They have been selected based on their widespread usage in the financial world and simplicity in calculation and understanding. The following risk-adjusted performance metrics will be utilized as well:

 Sharpe ratio

 Risk-adjusted performance alpha  Information ratio

 Treynor ratio

These metrics allow for the ranking of the portfolios based on their risk-adjusted performance, and serve as a robustness check for the three models.

The Sharpe ratio (Sharpe, 1966) measures the performance of a portfolio adjusted for risk. And is calculated as:

(10)

9 Where rf has the same meaning as in the previous models, and E(rp) represents the expected return of the portfolio. The term represents the standard deviation of the excess returns (rp-rf). This model

reveals whether the return is generated through above average investor skills or through taking on excess risk (both systemic and idiosyncratic risk are included). To compare the Sharpe ratios, we use the Jobson and Korkie test (1981) with Memmel (2003) adjustment:

( ) ( [ ])

(6)

SI,j is the Sharpe ratio of the respective portfolios, N is the number of observations, and ρi,j is the correlation between portfolios i and j.

The Modigliani risk-adjusted performance (RAP), developed by Modigliani and Modigliani in 1997, measures the returns of a portfolio, which are adjusted for the risk of the portfolio, in proportion to a designated benchmark. This risk adjusted excess return is derived from the Sharpe ratio, but has the advantage that resulting unit of measurement of the RAP is in percentage returns. This allows for more intuitive interpretations, in contrast to the Sharpe ratio which only provides a metric for ranking but which holds no intrinsic value. The risk-adjusted performance alpha (RAPA) however does have the same ranking as the Sharpe ratio. In this paper the related statistic RAPA will be used, which is obtained by subtracting the risk-free rate from the RAP. This provides us with a risk-adjusted excess return statistic. The RAP is calculated as:

̅̅̅̅ ̅̅̅ ̅̅̅ (7)

In Equation 7, ̅̅̅̅ is the average portfolio return, ̅̅̅ is the average risk-free rate, is the standard deviation of the excess returns of the benchmark, and is the standard deviation of the excess returns of the portfolio. The RAPA is calculated as:

̅̅̅̅ ̅̅̅ (8)

(11)

10 The information ratio measures the excess returns of the portfolio over the benchmark to the volatility of these returns. If the benchmark is chosen to be the risk-free rate, it will yield the same ratio as the Sharpe ratio. However for this paper the benchmark will be the index. The information ratio is calculated as:

(9)

Here rp as before represents the return on the portfolio, rb represents the return on the benchmark.

The factor is the standard deviation of the excess returns of the portfolio over the benchmark. The

key of this metric, is to relate excess returns to the deviation from the benchmark. This metric thus only includes idiosyncratic risk. A higher information ratio signals better performance of the portfolio, therefore being a useful measure to compare multiple portfolios if they use the same benchmark.

The Treynor ratio (1965) measures the excess returns of the portfolio over the risk-free rate to the beta of this portfolio. Similar to the Sharpe ratio, the Treynor ratio provides a risk-adjusted performance measure, however it utilizes the beta of the portfolio ( over the standard deviation of the portfolio. The Treynor ratio is calculated as:

(10)

(12)

11 ( ̅ ̂ √ ̅ ̂ ̂ ̂ ] ̂ ̂ ) (11)

Here γ represents the significance level, Tp is the Treynor ratio of the portfolio, and ̅ is the average

excess return of the portfolio. ̂ is the estimator of the beta of the portfolio, t is is the confidence level with n-1 degrees of freedom from the t-distribution. Finally is the variance of the excess returns of the portfolio, and ̂ is the variance of the estimated beta of the portfolio.

The Sharpe ratio and the risk-adjusted performance alpha cover both idiosyncratic and systematic risk. The Information ratio only covers idiosyncratic risk and the Treynor ratio only covers systematic risk.

A.2 Hypothesis

The hypotheses are tested using a longitudinal data analysis. In order to test for the presence of the low volatility anomaly in the European funds market, the funds are grouped into five portfolios, and 36 regression models are estimated using ordinary least squares (OLS). There are two main hypotheses, where the first one focusses on the beta of the returns being the metric for risk. The second hypothesis uses the volatility of the returns, the standard deviation of the returns is used as the risk metric. The two main hypotheses are subsequently divided into four sub-hypotheses each. Hypotheses 1.a and 2.a will use the CAPM model as a framework to provide evidence to resolve the hypotheses. Hypotheses 1.b and 2.b will use the Fama and French three-factor model as a framework to resolve the hypotheses. Next hypotheses 1.c and 2.c will use the Carhart four-factor model framework to resolve the hypotheses. Concluding with hypotheses 1.d and 2.d, which will use the Sharpe ratio, the Risk-adjusted performance alpha, the Treynor ratio, and the Information ratio to compare the risk-adjusted performance of the high and low risk portfolios.

During the research these hypotheses will be tested:

(13)

12 a. Do low beta mutual funds perform better than high beta mutual funds, within the CAPM

model framework.

b. Do low beta mutual funds perform better than high beta mutual funds, within the Fama and French three-factor model framework.

c. Do low beta mutual funds perform better than high beta mutual funds, within the Carhart four-factor model framework.

d. Do low beta mutual funds perform better than high beta mutual funds, according to widely employed performance metrics.

H2 Do low volatility mutual funds perform better than high volatility mutual funds.

a. Do low volatility mutual funds perform better than high volatility mutual funds within the CAPM model framework.

b. Do low volatility mutual funds perform better than high volatility mutual funds, within the Fama and French three-factor model framework.

c. Do low volatility mutual funds perform better than high volatility mutual funds, within the Carhart four-factor model framework.

d. Do low volatility mutual funds perform better than high volatility mutual funds, according to widely employed performance metrics.

The goal of hypotheses H1.a through H1.d, and H2.a through H2.d is to provide information and outcomes on which a balanced and an as objective as possible answer is formulated for hypotheses 1 and 2. Out of these sub-hypotheses 1.c and 2.c will carry the most weight, whereas 1.a, 1.b, 2.a, and 2.b will act as a sensitivity analysis for 1.c and 2.c. Sub-hypotheses 1.d and 2.d are slightly different from the other sub-hypotheses as such that they look specifically at empirically applied methods to assess the risk-adjusted performance. These hypotheses (1.d and 2.d) will function as a robustness check for the results of the other hypotheses.

Hypotheses 1.a and 2.a will directly compare the high risk (measured in beta and volatility) to the low risk fund, equation 1 in a slightly adjusted form will be used for these hypotheses. The adjusted form is:

(12)

In this equation 12, represents the return on the low risk portfolio, and represents the

(14)

13 based portfolios) portfolio, and is the beta of the high risk portfolio. The factors and as before

represent the market index return and the risk-free rate. Finally captures the performance of the low risk portfolio in comparison to the high risk portfolio. The value for alpha will signal outperformance of the low risk portfolio over the high risk portfolio if positive and vice versa if the value for this factor is negative.

Hypotheses 1.b and 2.b again will directly compare the high risk (measured in beta and volatility) to the low risk fund, however instead of using the CAPM model the Fama and French 3-factor model will be used. Equation 3 in a slightly adjusted form will be used for these hypotheses. The adjusted form is:

( ) (13)

The symbols in equation 13 retain the same definition as used for equations 3 and 12. The value for will signal outperformance of the low risk portfolio over the high risk portfolio if positive and vice versa if the value for this factor is negative.

For hypotheses 1.c and 2.c the Carhart model is used to directly compare the high risk to the low risk fund. Equation 3 in a slightly adjusted form will be used for these hypotheses, the adjusted form is:

( ) (14)

The symbols in equation 14 which have been used before, retain the same definition as in equation 4, 12, and 13.

(15)

14 A.3 Research method

To test these hypotheses, a time-series data analysis will be performed. The European funds will be drawn from the FN Universe, which is a universe constructed by Fondsnieuws to contain the most brokered (active) European funds. Fondsnieuws selects these European funds (equity, mix, and bond funds) from the advice lists (both retail and private banking) of the three largest banks in the Netherlands (ABN Amro, ING, and Rabobank)

The performance of the funds is determined based on the total returns over the period 2003-2013. The geometric returns are then used to calculate the quarterly returns for these funds. Next the volatility of these quarterly returns and the quarterly beta’s will be calculated. The volatility of the returns in this paper is synonymous to the standard deviation of the returns, the betas are calculated by taking the covariance of the returns of the portfolio and the returns of the market index divided by the variance of the portfolio. Using these betas and volatilities, the funds are ranked in ascending order. The 238 funds will be allocated evenly to portfolio 1 through 5, where portfolio 1 is the lowest risk portfolio and 5 the highest risk, based on their risk ranking in the previous quarter. Ultimately the data ends up being formed into two different sets of five portfolios, where one set of portfolios is based on the ranking of their betas and the other set of portfolios on the ranking of their volatilities. This results in five quarterly time-series for the five portfolios, which will be analyzed based on their quarterly returns and risk.

When using OLS regressions, the lowest beta portfolio will be compared with the highest beta portfolio. This procedure will be repeated for the lowest volatility and highest volatility portfolios. The Newey-West standard errors will be used in the regression analysis, to have heteroscedastic and autocorrelation consistent standard errors.

B. Robustness tests

(16)

15

IV. Data

In this section the data used in this paper will be discussed, and the limitations of the data elaborated upon. In addition summary statistics for the dataset will be provided and discussed.

A. Data requirements and availability

Data will be gathered on funds which are:  European funds;

 Offered to retail and/or private investors;  In the period 2003-2013;

 The fund must have been actively traded during this period.

Furthermore, a proxy for the risk-free rate is required, as this paper focusses on European funds, the ten year German Government bonds will be used as a proxy. In addition, the regional factors for the ‘High minus low’, ‘Small minus Big’, and ‘Momentum’ are needed.

A hurdle for this research is the availability of data, finding sufficient funds which satisfy the set of conditions mentioned under Data requirements might present itself as difficult task. The databases used are Bloomberg2 and Thomson Reuters Datastream3. During preliminary searches for funds, which have already been filtered for time-period, being publically listed on an exchange in Europe and having fund data available, 700 funds have been found. The non-active funds are recognizable in the fact that they will display identical returns for prolonged periods of time, these non-active funds are filtered out.

From the FN universe 238 European funds have been identified as suiting the requirements. The list of European funds included is presented in Appendix A. The daily returns of the included funds, the daily returns of the MSCI Europe Index, and the quarterly 10 year German Government bond rates have been extracted from the Datastream database. Finally, the Fama and French 3-factor model factors have been extracted from the Fama and French website.4

(17)

16 An initial goal set out in the research proposal, was to use the market capitalization of these European funds for robustness testing. However after having looked extensively with help and consultation of the Bloomberg database service desk, the market capitalization of these funds could not be found.

C. Summary statistics

The dataset consists of 238 European funds with 41 quarters of data, which have been arranged into five portfolios over 40 quarters. In table I the descriptive statistics on the quarterly geometric returns regarding the portfolios ranked by beta and volatility are presented. The MSCI Europe Index is provided for reference.

Table I: Descriptive statistics of the quarterly geometric returns (beta and volatility portfolios)

This table represents the descriptive statistics on the time-series of geometric returns per quarter for the beta ranked portfolios. The portfolios are formed based on the ascending beta or volatility ranking of the funds in the previous quarter. This results in four portfolios of 48 funds and one portfolio of 47 funds. The data in this table represent the summary statistics of the specific portfolios over the 40 quarters included in this paper. The funds included for this paper are drawn from the FN universe. The data of these funds for these statistics are from the time period 2003Q1 to 2013Q2. The average risk-free rate over this period is

0.53%.

Portfolios

Beta Statistics low 2 3 4 high MSCI Europe Index

(18)

17 Volatility

Statistics

low 2 3 4 high MSCI Europe Index

Mean 1.25% 1.48% 1.46% 1.44% 1.40% 1.07% Median 2.83% 3.05% 3.66% 3.88% 3.58% 2.26% St. deviation 5.35% 7.38% 7.15% 7.24% 8.77% 11.27% Range 26.32% 40.34% 38.84% 38.89% 49.14% 57.23% Minimum -16.74% -26.28% -24.93% -24.26% -33.46% -36.23% Maximum 9.58% 14.06% 13.91% 14.64% 15.69% 21.00% Observations 40 40 40 40 40 40

Table I shows that the mean return increases with beta of the portfolio. Furthermore, the range of returns is also increasing with beta. Portfolio 1 has the lowest mean quarterly geometric returns of the 5 portfolios and the market index. Portfolio 5 features the second highest standard deviation and the highest range of the returns.

Table I shows that neither the mean return nor the median return is monotonously increasing with return volatility. Portfolio 1, which based on volatility is the least risky portfolio, displays the characteristics of a low risk portfolio. By having the lowest values for the standard deviation, and range it is less risky than its counterpart portfolios. Compared to the beta portfolios, the difference in standard deviation between the different portfolios is smaller, having a range of 3.42 percent points compared to the 8.5 percent points range for the volatility portfolios. The returns of the portfolios are quite close to each other, having a maximum range of 0.23 percent point.

In table II we can see that the average beta for portfolio 1 is 0.00, whereas the beta of portfolio 5 is 0.71. The table reveals that portfolio 1, which by design should have the lowest beta, indeed has the lowest risk according to the beta metric. The increase in beta of the portfolios going from 1 through 5 appears to be gradual, there appears to be nothing out of the ordinary.

(19)

18 Table II: Descriptive statistics of the portfolio betas (beta and volatility portfolios)

This table represents the descriptive statistics of the betas of the quarterly geometric returns per quarter of the beta and volatility ranked portfolios. The portfolios are formed based on the ascending beta/volatility ranking of the funds in the previous

quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The data in this table represent the summary statistics of the specific portfolios over the 40 quarters included in this paper. The funds included for this paper are drawn from the FN universe. The data of these funds for these statistics are from the time period 2003Q1 to 2013Q2. The average risk-free

rate over this period is 0.53%.

Portfolios

Beta Statistics low 2 3 4 high

Mean 0.00 0.16 0.35 0.50 0.71 Median -0.00 0.15 0.34 0.49 0.69 Standard Deviation 0.05 0.08 0.11 0.11 0.14 Range 0.23 0.44 0.79 1.02 1.44 Minimum -0.07 0.06 0.18 0.31 0.44 Maximum 0.15 0.38 0.61 0.71 1.00 Volatility Statistics Mean 0.21 0.36 0.36 0.40 0.38 Median 0.20 0.36 0.36 0.38 0.37 Standard Deviation 0.06 0.09 0.08 0.10 0.12 Range 0.47 0.79 0.75 0.86 0.77 Minimum 0.12 0.21 0.22 0.23 0.17 Maximum 0.34 0.58 0.53 0.63 0.60 Observations 40 40 40 40 40

(20)

19 Table III: Normality test on beta and volatility portfolios

This table represents the normality test on the time-series of geometric returns per quarter of portfolios 1 and 5 for both the beta and the volatility portfolios. The Jarque-Bera statistic is calculated as JB= n/6[S^2+1/4 (K-3)^2], where n is the amount of observations, S is the skewness, and K is the kurtosis of the portfolio. The Jarque-Bera statistic is asymptotically distributed,

following a chi-squared distribution with two degrees of freedom. The alpha level is set at α=0.05, the portfolios which are significant at this level are not normally distributed.

Beta Volatility

Portfolios Portfolios

Statistics 1(low) 5(high) 1(low) 5(high)

Skewness 0.18 -1.67 -1.18 -1.79 Kurtosis 2.54 7.47 4.82 7.72 Jarque-Bera 0.57 51.82 14.80 58.41 Probability 0.75 0.00 0.00 0.00 D. Omissions

Commonly in the analysis of an OLS regression the R2, as a measure of the goodness of fit of a model, and the significance of the model are evaluated to determine the usefulness of a model. However the goal with this paper is not to prove the significance or the validity of the models used, but only to look at the performance measures generated by these models. Furthermore, these models have been extensively tested in the field of finance and their use is widespread. Therefore the R2 and the significance of these models (CAPM, Fama and French 3-factor, and Carhart four-factor model) are omitted.

(21)

20

V. Results

The results are presented in three parts in this section. First the results in general will be discussed, next the hypothesis and the corresponding results will be discussed. Lastly the results of the robustness tests will be discussed.

A. General observations and discussion on results

In Table IV several returns metrics are provided for the five beta portfolios and the market index, including the returns in excess of the risk-free rate, and the market index. In addition three risk measures are provided: the standard deviation, the tracking error, and beta.

According to the low-volatility anomaly, the low risk portfolio should outperform the high risk portfolio. However, looking at table IV, we notice that in absolute terms the returns of portfolio 1 are lower than portfolio 5, while having a lower beta than portfolio 5. The portfolios in between increase gradually, in both returns and beta, from low to high. This result is in contrast with Baker, Bradley, and Wurgler (2011), Baker, and Haugen (2012), and Miller and Scholes (1972), whom found that the low risk portfolio outperforms the high risk portfolio in absolute terms.

Table IV: Beta portfolio series returns

This table represents the time-series of geometric and arithmetic returns per quarter of the beta ranked portfolios, furthermore the market excess returns are included. The two standard deviation metrics are from the geometric returns series. The tracking error refers to the standard deviation of the portfolio geometric returns in excess of the market index.The portfolios are formed based on the ascending volatility ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds are from the time

period 2003Q1 to 2013Q2. The geometric average risk-free rate over this period is 0.53%.

I. Beta series

low 2 3 4 high Index

Geometric average return 0.87% 1.18% 1.56% 1.71% 1.94% 1.07%

Average Rp 0.87% 1.19% 1.57% 1.73% 1.96% 1.07%

Standard deviation 2.50% 6.32% 8.03% 9.50% 11.00% 11.27%

Average Rp-Rm -0.20% 0.12% 0.49% 0.65% 0.88%

Tracking error 10.03% 7.26% 6.17% 4.88% 4.87%

(22)

21 Graph 1 plots the value for each of the five portfolios over time. The graph allows us to observe the subprime mortgage crisis, which manifests itself in this graph starting 2008Q1. From the first quarter in 2008 until the first quarter in 2009, the portfolios seem to be locked into a free fall. During this period portfolio 5 lost 52.84% of its value, for reference, the market index lost 56% over this period. Due to their reduced risk characteristics portfolios 4 through 1 lost less, with portfolio 1 losing 8.74% over this period. Starting in the second quarter of 2009, the portfolios start to recover. This recovery seems to be of the same intensity as the fall before it. However this recovery meets its end in the second development, being the European credit crisis. The European crisis starts manifesting itself in this graph in the first quarter of 2010, this coincides with the timeline of the credit crisis provided by the European Central Bank5. At first the European credit crisis only dampens the recovery after the Subprime mortgage crisis, however starting 2011 the recovery is stopped entirely and followed by another sharp fall. In the last quarter of 2011, recovery starts to set in again. Looking at the value development from the first quarter of 2008 until the second quarter of 2013, we observe that portfolio 1 has generated a gain of 15.03%. Portfolio 5 has generated a loss of 6.09% over this same period, for reference the market index has generated a loss of 31.83% over this period.

5

(23)

22 Graph I: Beta portfolio series returns

This graph presents the value development of €1 invested in each of the five beta ranked portfolios. The portfolios are formed based on the ascending beta ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for this

graph are from the time period 2003Q1 to 2013Q2.

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2002Q2 2004Q2 2005Q2 2006Q2 2007Q2 2008Q2 2009Q2 2010Q2 2011Q2 2012Q2 2013Q2 Val u e o f 1 in ve ste d in 2002Q2

Returns of beta portfolios

(24)

23 Table V: Volatility portfolio series returns

This table represents the time-series of geometric and arithmetic returns per quarter of the volatility ranked portfolios, furthermore the market excess returns are included. The two standard deviation metrics are from the geometric returns series.

The tracking error refers to the standard deviation of the portfolio geometric returns in excess of the market index.The portfolios are formed based on the ascending volatility ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for these statistics are from the time period 2003Q1 to 2013Q2. The geometric average risk-free rate over this period is

0.53%.

In Table V several returns metrics are provided for the five volatility portfolios, including the returns in excess of the risk-free rate, and the market index. In addition three risk measures are provided: the standard deviation, the tracking error, and beta. Aside from the five volatility portfolios, an additional portfolio ‘B&H’ is constructed and added to this table. The B&H portfolio is a Buy and Hold portfolio, constructed to see if it can match the results of volatility portfolio 1. It is constructed by taking a long position in the funds selected for portfolio 1 in the first quarter (2003Q2) and holding that position for the remainder of the time window. If the volatility characteristics are relatively stable, then the ranking of the funds should be stable. If the ranking is indeed relatively stable, then a Buy and Hold portfolio should be able to track portfolio 1.

According to the low-volatility anomaly, the low risk portfolio should outperform the high risk portfolio. However looking at table V, we notice that in absolute terms the returns of portfolio 1 are lower than portfolio 5, while having a lower volatility than portfolio 5. Erratic behavior is displayed by the portfolios in between. Out of the five portfolios, portfolio 2 generates the highest returns, and portfolio 1 has the lowest volatility. Portfolio 5 ranks only second to last in returns, while having the highest volatility. The low volatility portfolio, in contrary to the low beta portfolio, generates higher returns than the market index.

II. Volatility series

low 2 3 4 high B&H

(25)

24 This result is contrary to the results of Ang, Hodrick, Xing, and Zhang (2006), Blitz and van Vliet (2007), Baker, Bradley, and Wurgler (2011), Baker, and Haugen (2012), and Dutt and Humphery-Jenner (2013) whom found that the low-volatility portfolio outperforms the high-volatility portfolio in absolute terms.

Comparing the returns of the B&H portfolio to volatility portfolio 1, we can observe that it generates a slightly higher return, while featuring slightly higher standard deviation and beta. The beta of the B&H portfolio with regard to volatility portfolio 1 is 0.994. It appears that the Buy and Hold portfolio is an excellent tracker of the low volatility portfolio.

In graph 2 the value development of €1 invested in each of the five volatility portfolios is presented. Identical to graph 1, the start of the subprime crisis can be observed starting in the first quarter of 2008. During this crisis the five portfolios lost a majority of their value. Portfolio 5 lost up to 28.43% (2008Q4) of its value in a single quarter, losing a total of 46.67% of its value in five quarters. Although portfolio 1 lost considerably less, it still lost up to 15.41% in a single quarter, and a total loss of 30.87% of its value in the same period. Although the portfolios recover as fast as they fell, the start of European credit crisis (2010Q1) means that this recovery is abruptly halted. Looking at the value development from the first quarter of 2008 until the second quarter of 2013, we observe that portfolio 1 has generated a gain of 1.13%. Portfolio 5 has generated a loss of 8.33% over this same period.

(26)

25 Graph II: Volatility portfolio series returns

This graph presents the value development of €1 invested in each of the five volatility ranked portfolios. The portfolios are formed based on the ascending volatility ranking of the funds in the previous quarter, 4 portfolios of 48 funds and 1 portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for this

graph are from the time period 2003Q1 to 2013Q2.

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2002Q2 2004Q2 2005Q2 2006Q2 2007Q2 2008Q2 2009Q2 2010Q2 2011Q2 2012Q2 2013Q2 Val u e o f 1 in ve ste d in 2002Q2

Returns of volatility portfolios

(27)

26 B. Hypothesis and results

In Table VI the results for the ordinary least squares regression of the Carhart four-factor model for both the volatility and the beta portfolios are presented. All of the portfolios generate a positive alpha, to check for the performance of the low-risk portfolio over the high-risk portfolio, two new portfolios are created. For both volatility and beta the portfolio’s 1-5 are created based on equation 14.

The results for the 1-5 volatility portfolio reveal that the alpha is 0.000, but is not significant, therefore we can state that the low volatility portfolio does not outperform the high volatility portfolio. Looking at the coefficients of volatility portfolio 1-5, the market risk premium coefficient is significant and negative at -0.287. This was expectable due to the beta of portfolio 1 being lower than portfolio 5, as observed in table II. Next we observe a significant and negative coefficient of -0.005 for size premium, meaning that portfolio 5 has higher loadings on small cap assets. The positive and significant value coefficient of 0.005 indicates that portfolio 1 has higher allocations to value stocks. Finally, the momentum factor for this portfolio is 0.000 and not significant.

Table VI: Results Carhart model

This table presents the ols regression results of the Carhart four-factor model for both the top and bottom volatility and beta portfolios. The Newey-West standard errors have been employed to assure heteroscedasticity and autocorrelation robust standard errors. Additionally an extra portfolio is created to measure the difference between the top and bottom portfolio, named 1-5. The market, size, value, and the momentum coefficients measure the respective exposure to these factors. The portfolios are formed based on the ascending volatility/beta ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for this graph are from the time period 2003Q1 to 2013Q2. Coefficients significant at the 10% level are marked with

*, significance at the 5% level is marked with **, and significance at the 1% level is marked with ***.

Coefficients Volatility portfolios Beta portfolios

1(low) 5(high) 1-5 1(low) 5(high) 1-5

(28)

27 The results for the 1-5 beta portfolio reveal that the alpha is -0.006, but is not significant, therefore we can state that the low beta portfolio does not outperform the high beta portfolio. Looking at the coefficients of beta portfolio 15, the market risk premium coefficient is significant and negative at -0.755. This was expectable due to the beta of portfolio 1 being lower than portfolio 5, as observed in table II. Next we observe an insignificant and positive coefficient of 0.005 for size premium. The negative and significant value coefficient of -0.007 indicates that portfolio 5 has higher allocations to value stocks. Finally, the momentum factor for this portfolio is 0.001 and not significant.

C. Sensitivity analysis

In Table VII the results for the ordinary least squares regression of the CAPM and Fama and French three-factor model, for both the volatility and the beta portfolios, are presented. All of the portfolios generate a positive alpha, to check for the performance of the low-risk portfolio over the high-risk portfolio, four new portfolios are created. Portfolios 1-5 are created for both beta and volatility series, based on equation 12 for the CAPM model and equation 13 for the Fama and French three-factor model.

C.1 Fama and French three-factor model, and the CAPM model

The results for the 1-5 volatility portfolio reveal that the alpha is 0.000, but is not significant. Looking at the coefficients of volatility portfolio 1-5, the market risk premium coefficient is significant and negative at -0.287. This result is according to expectations as the beta of portfolio 1 is lower than portfolio 5, as observed in table II. Next we observe a significant and negative coefficient of -0.005 for size premium, meaning that portfolio 5 has higher loadings on small cap assets. Finally, the positive and significant value coefficient of 0.005 indicates that portfolio 1 has higher allocations to value stocks.

(29)

28 Finally, the negative and significant value coefficient of -0.007 indicates that portfolio 5 has higher allocations to value stocks.

Table VII: Results CAPM and Fama and French models

This table presents the OLS regression results of the Fama and French three-factor model and the CAPM model, for both the top and bottom volatility and beta portfolios. The Newey-West standard errors have been employed to assure heteroscedasticity and autocorrelation robust standard errors. Additionally an extra portfolio is created to measure the difference between the top and bottom portfolio, named 1-5. The market, size, and value coefficients measure the respective exposure to these factors. The portfolios are formed based on the ascending volatility/beta ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for this graph are from the time period 2003Q1 to 2013Q2. Coefficients significant at the 10% level are marked with

*, significance at the 5% level is marked with **, and significance at the 1% level is marked with ***.

Jensen’s alpha for the 1-5 volatility portfolio is 0.000, this appears to be in line with the results of the Fama and French three-factor, and Carhart four-factor model. For the 1-5 beta portfolio, Jensen’s alpha is -0.007, this value is in line with the results of the Fama and French three-factor, and Carhart four-factor model.

Coefficients Volatility portfolios Beta portfolios

1(low) 5(high) 1-5 1(low) 5(high) 1-5

Fama and French

market 0.432*** 0.719*** -0.287*** 0.141*** 0.900*** -0.759***

size 0.011*** 0.016*** -0.005* -0.003 -0.007 0.004

value -0.006* -0.011** 0.005* -0.003 0.004 -0.007**

Fama and French's alpha 0.005 0.005 0.000 0.003 0.009 -0.006

R2 0.818 0.826 0.707 0.316 0.827 0.809

adjusted R2 0.803 0.811 0.683 0.259 0.813 0.793

Jensen

(30)

29 C.2 Alternative performance metrics

In table VIII the results of the four alternative performance metrics are presented for both the high and low risk portfolios of the volatility and beta series. The Sharpe Ratio, Risk Adjusted Performance Alpha, and the Treynor Ratio are higher for the low risk portfolio in the volatility series. However these values are not significant. The Information Ratio indicates that the high risk portfolio perform better, this can be explained by the fact that low volatility portfolios take on more idiosyncratic risk than the high volatility portfolios. Although it is understandable that portfolios which take on more risk than the market index should earn more, it is however not intuitive when the portfolio takes on less risk than the market index. Portfolios which take on less risk are penalized in the same way as portfolios which take on more risk. This hints at a convex relationship, opposed to the positive linear relationship, between risk and return.

The performance of the beta portfolios in table VIII are straight forward, the high risk portfolio outperforms the low risk portfolio in every metric. However the results are not significant. The exception here is the Treynor ratio, where the low beta portfolio scores extremely high. This outlier can be attributed to the fact that beta portfolio 1 has an average beta of 0.001, as the beta of the portfolio is the denominator in the calculation, this causes an extreme outcome. As such this outlier should be disregarded as a performance measure for beta portfolio 1.

Table VIII: Results of alternative performance metrics

This table presents the results of the 4 alternative performance metrics employed. For all these measures, the higher the value, the better the performance. The portfolios are formed based on the ascending volatility/beta ranking of the funds in the previous quarter, four portfolios of 48 funds and one portfolio of 47 funds are created. The funds included for this paper are drawn from the FN universe. The data of these funds for this graph are from the time period 2003Q1 to 2013Q2. Significance at the 10% level is marked with *, significance at the 5% level is marked with **, and significance at the 1% level is marked with

***.

Metrics Volatility portfolios Beta portfolios

1(low) 5(high) 1(low) 5(high)

Sharpe Ratio 0.131 0.098 0.126 0.127

Risk Adjusted Performance Alpha (M2)

1.485% 1.110% 1.432% 1.440%

Information Ratio 0.026 0.060 -0.020 0.180

(31)

30

VI. Summary and conclusions

This paper investigates whether the low risk anomaly applies to the fund market in Europe. To test this, two sets of hypothesis have been set up. One set uses beta, while the other uses volatility as the risk measurement. The Carhart four-factor model is employed to test for performance differences between the low and high risk portfolios. For the sensitivity analysis, the CAPM model, Fama and French three-factor model, Sharpe ratio, Risk adjusted performance alpha, Information ratio, and the Treynor ratio are employed.

The results split two-way, for the volatility portfolios no evidence can be found for difference in performance in the three models. Looking at the alternative performance metrics, we can see that the results for the Sharpe ratio, the Risk adjusted performance alpha, and the Treynor ratio are not significant, and the Information ratio is in favor of the high volatility portfolio. Therefor we conclude that there is no evidence in support of the low volatility anomaly with regard to the volatility based portfolios in the European fund market. This means that there does not appear to be a negative correlation between the volatility and the return of a fund in the European fund market.

For the beta portfolio all three models indicate that the high risk beta portfolio outperforms the low risk beta portfolio, although these results are not significant. This indicates that there is no evidence supporting the hypothesis that there is a negative risk-return relationship. We look at the alternative performance metrics to see if they underline this conclusion. The high risk beta portfolio outperforms the low risk beta portfolio in every metric, assuming we remove the outliers as mentioned in the results section. Although these outperformances are not significant, we conclude that there is no evidence supporting the low volatility anomaly with regard to the beta based portfolios in the European fund market. This means that there appears to be a positive correlation between the volatility and the return of a fund in the European fund market.

(32)
(33)

32

VII. References

Alpert, Marc, and Howard Raiffa, 1982, “A Progress Report on the Training of Probability Assessors”, Judgment under uncertainty: Heuristics and biases, Cambridge University Press, 294-305.

Ang, Andrew, Robert Hodrick, Yuhang Xing, and Xiaoyan Zhang, 2006, “The Cross-Section of Volatility and Expected Returns”, The Journal of Finance 61, 259-299.

Baker, Malcolm, Brendan Bradley, and Jeffrey Wurgler, 2011, “Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly”, Financial Analysts Journal 67, 40-54.

Baker, Nardin, and Robert Haugen, 2012, “Low Risk Stocks Outperform within All Observable Markets of the World”, Unpublished paper.

Barberis, Nicholas, and Ming Huang, 2008, “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices”, American Economic Review 98, 2066-2100.

Black, Fischer, 1972, “Capital Market Equilibrium with Restricted Borrowing.”, Journal of Business 45:3, 444-455.

Black, Fischer, Michael Jensen, and Myron Scholes, 1972, “The Capital Asset Pricing Model: Some Empirical Tests”, Studies in the Theory of Capital Markets, New York: Praeger Publishers, 79-121.

Blitz, David, and Pim van Vliet, 2007, “The Volatility Effect: Lower Risk Without Lower Return”, Journal of Portfolio Management 34, 102-113.

Carhart, Mark M., 1997, “On Persistence in Mutual Fund Performance”, The Journal of Finance 52:1, 57-82.

Chan, Louis, Hsiu-Lang Chen, and Josef Lakonishok, 2002, “On Mutual Fund Investment Styles”, Review of Financial Studies 15:5, 1407-1438.

Cornell, Bradford, 2009, “The Pricing of Volatility and Skewness: A New Interpretation”, Journal of Investing 18, 27-30.

(34)

33 Fama, Eugene, and Kenneth French, 1992, “The Cross-Section of Expected Stock Returns”, Journal of Finance 47:2, 427-465.

Fama, Eugene F., and Kenneth R. French, 1993, "Common Risk Factors in the Returns on Stocks and Bonds", Journal of Financial Economics 33:1, 3–56.

Griffin, John M., 2002, “Are the Fama and French Factors Global or Country Specific?”, Review of Financial Studies 15:3, 783-803.

Jegadeesh, Narasimhan, and Sheridan Titman, 1993, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency”, Journal of Finance 48:1, 65-91.

Jegadeesh, Narasimhan, and Sheridan Titman, 2001, “Profitability of Momentum Strategies: An Evaluation of Alternative Explanations”, The Journal of Finance 56:2, 699-720.

Jensen, Michael C., 1967, “The Performance of Mutual Funds in the Period 1945-1964”, Journal of Finance 23:2, 389-416.

Jobson, J. D., and R. Korkie, 1981, “Performance Hypothesis Testing with the Sharpe and Treynor Measures”, Journal of Finance 36, 889–908.

Kahneman, Daniel, and Amos Tversky, 1983, “Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment”, Psychological Review 90:4, 293-315.

Karceski, Jason, 2002, “Returns-Chasing Behavior, Mutual Funds, and Beta’s Death”, Journal of Financial & Quantitative Analysis 37:4, 559-594.

Lakonischok, Josef, Andrei Shleifer, and Robert W. Vishny, 1994, “Contrarian Investment, Extrapolation, and Risk”, The Journal of Finance 49:5, 1541-1578.

Lintner, John, 1965, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets”, The Review of Economics and Statistics 47, 13-37.

Markowitz, Harry, 1952, “Portfolio Selection”, The Journal of Finance 7:1, 77-91.

(35)

34 Miller, Merton, and Myron Scholes, 1972, “Rate of Return in Relation to Risk: A Reexamination of Some Recent Findings”, Studies in the Theory of Capital Markets, New York: Praeger Publishers, 47-78.

Modigliani, Franco, and Leah Modigliani, 1997, "Risk-Adjusted Performance", Journal of Portfolio Management 23:2, 45–54.

Montier, James, 2006, “Behaving Badly”, Dresdner Kleinwort Wasserstein – Global Equity Strategy. Morey, Matthew R., and Richard C. Morey, 2003, “An Analytical Confidence Interval for the Treynor Index: Formula, Conditions and Properties”, Journal of Business Finance & Accounting 27:1-2, 127-154.

Mossin, Jan, 1966, “Equilibrium in a Capital Asset Market”, Quarterly Journal of Economics 80, 376-399.

Newey, Whitney K., and Kenneth D. West, 1987, “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix”, Econometrica 55:3, 703-708.

Sharpe, William F., 1966, "Mutual Fund Performance", Journal of Business 39:1, 119–138.

Sharpe, William F., 1964, "Capital Asset Prices – A Theory of Market Equilibrium Under Conditions of Risk", Journal of Finance 19, 425–442.

Treynor, Jack, 1962, “Towards a Theory of Market Value of Risky Assets”, Unpublished manuscript. Treynor, Jack, 1965, “How to Rate Management of Investment Funds”, Harvard Business Review 43, 63-75.

(36)

35

Appendix A: List of European funds included in this paper.

1 ABERDEEN INV.SERVICES GLB.ASIA PACIFIC EQ.A2 41 BNP PARIBAS L1 BOND ER. LONG TERM CLASSIC CSN. 2 ABERDEEN INV.SERVICES GLB.EMRG.MARKETS A2 42 BNP PARIBAS L1 BOND USD CLASSIC CSN.

3 ABERDEEN GLOBAL WORLD EQUITY A2 CAP V 43 BNP PARIBAS L1 BOND WLD. CLASSIC CSN. 4 ABN AMRO MLTMGR.FUND. DEFV.PROFILE CAP. 44 BNP PARI.L1 EQ.BST.SEL. EURO CLASSIC CSN. 5 ABN AMRO MLTMGR.FUND. DIVR.PROFILE CAP. 45 BNP PARIBAS INV.PARTNER L1 EQ.CHI CLS CAP USD 6 ABN AMRO MLTMGR.FUND. DYM.PROFILE A CAP. 46 BNP PARIBAS INV.PARTNER L1 EQ.EUR EMG C CAP EUR

7 AMUNDI ETF CAC 40 47 BNP PARIBAS L1 EQUITY GERMANY CLC.CSN.

8 CREDIT AGRICOLE FUNDS ER.INFL.BD.FD.CAP.CLC. 48 BNP PARI.L1 EQ.HI.DIV. USA CLC.CSN. 9 AMUNDI FUNDS LATIN AM. EQUITIES CLC.C DS.USD 49 BNP PARIBAS L1 EQUITY USA CLC.DS.

10 AMUNDI INTERTIOL CLASS AU 50 BNP PARIBAS L1 EQUITY USA SMALL CAPS CLC.DS. 11 BLACKR.ML INV.MGRS.IIF EMRG.EU.A2 EUR 51 BNP PARIBAS L1 EQ.WLD. CSM.DURABLES CLC.CSN. 12 MRLY.INTL.INV.FUND.EMRG. MARKETS FD.A 2 EUR 52 BNP PARIBAS L1 EQ.WLD. CSM.DURABLES CLC.DS. 13 BLACKR.ML INV.MGRS.IIF EURO BD.A2 EUR 53 BNP PARIBAS L1 EQ.WLD. CSM.GOODS CLC.CSN. 14 BLACKR.ML INV.MGRS.IIF EUR.OPPS A2 EUR 54 BNP PARIBAS L1 EQ.WLD. CSM.GOODS CLC.DS.

15 BLACKROCK LX.BGF EUR.FD. A2 55

BNP PARIBAS INV.PARTNER L1 EQ.WLD.EMG C CAP USD

16 BLACKR.ML INV.MGRS.LX. IIF EUR.GW.A2 EUR 56 BNP PARI.INV.PARTNER L1 EQ.ENEGY WD C DS.EUR 17 BLACKR.ML INV.MGRS.IIF EUR.VAL.A2 EUR 57 BNP PARIBAS L1 EQ.WLD. FINCE CLC.DS.

18 BLACKROCK GLB.FUNDS LUX ALLOCATION C EUR 58 BNP PARIBAS L1 EQ.WLD. MERGED SEE 88716U 19 BLACKR.GLB.FUNDS LUX NEW ENERGY A2 USD 59 BNP PARIBAS L1 EQ.WLD. HEALTH CARE CLC.DS. 20 BLACKR.ML INV.MGRS.IIF US BASIC VAL.A2 USD 60 BNP PARIBAS L1 EQ.WLD. TECHNOLOGY CLC.CSN. 21 BLACKR.ML INV.MGRS.LX. IIF US FLEX.EQ.A2 USD 61 BNP PARIBAS L1 EQ.WLD. TECHNOLOGY CLC.DS. 22 BLACKROCK GLOBAL FUNDS LX.WORLD ENERGY A2 USD 62 BNP PARIBAS L1 EQ.WLD. TELECOM CLC.CSN. 23 BLACKR.ML INV.MGRS.IIF WLD.GOLD A2 USD 63 BNP PARIBAS L1 EQ.WLD. TELECOM CLC.DS. 24 BLACKR.ML INV.MGRS.LX. IIF JAPAN OPPS.A2 EUR 64 BNP PARIBAS L1 EQ.WLD. UTILITIES CLC.DS. 25 BLACKROCK LATIN AMERICA A2 EUR 65 BNP PARI.INV.PARTNER L1 MODEL 1 C EUR 26 BLACKR.ML INV.MGRS.LX. IIF NEW EN.A2 EUR 66 BNP PARI.INV.PARTNER L1 MODEL 2 C EUR 27 BLACKR.ML INV.MGRS.LX. IIF US FLEX.EQ.A2 EUR 67 BNP PARI.INV.PARTNER L1 MODEL 3 EUR 28 BLACKR.GLB.FUND.US S&M. CAP.OPPS.FD.CL.A2 CSN. 68 BNP PARI.INV.PARTNER L1 MODEL 4 C EUR 29 MRLY.INTL.INV.FUND.WLD. EN.FUND A 2 EUR 69 BNP PARI.INV.PARTNER L1 MODEL 5 C EUR 30 BLACKR.ML INV.MGRS.LX. IIF WLD.FINLS.A2 EUR 70 BNP PARI.INV.PARTNER L1 MODEL 6 C EUR 31 BLACKROCK GLOBAL FUNDS LX.WORLD GOLD A2 EUR 71 BNP PARIBAS L1 OPPS.WLD. CLC.CSN. 32 BLACKR.ML INV.MGRS.LX. IIF WLD.HLTH.SCI.A2 EUR 72 BNP PARI.L1 RLST.SECS. EUROPE CLC.DS. 33 BLACKROCK GLB.FUND.WORLD MINING FUND CLASS A EUR 73 BNP PARIBAS NETHERLANDS FUND 34 BLACKROCK GLOBAL FUNDS LX.WLD.TECHNOLOGY A2 EUR 74 BNP PARIBAS PLAN INTL. DERIVATIVES CSN. 35 BNP PARIBAS AEX INDEX FUND 75 BNP PARIBAS PROPERTY SECURITIES FUND EUROPE 36 BNP PARIBAS GLOBAL PR. SECURITIES FUND 76 BNP PARIBAS PROPERTY SECURITIES FUND FAR EAST 37 BNP PARI.L1 EQ.BST.SEL. ASIA EX JAP.CLC.CSN. 77 CARMIGC GESTION INVESTISSEMENT FCP 2 D C 38 BNP PARI.L1 EQ.BST.SEL. ASIA EX JAP.CLC.DS. 78 COMGEST ASTMGMT.GROWTH EUROPE 39 BNP PARIBAS L1 BOND EU. EMERGING CLASSIC CSN. 79 COMGEST MAGELLAN

(37)

36

81 DEXIA BONDS EURO CLC.C CAP. 121 HENDERSON HRZ.FD.PAN EUR.EQ.FD.A2 AC. 82 DEXIA SUSTAIBLE PAC. C CSN. 122 HSBC INVS.LUX GIF CHINESE EQUITY AD $

83 DWS INVESTMENT AKN. STRATEGIE DTL. 123 HSBC INVS.LUX GIF PAN EUROPEAN EQUITY P DS.EUR 84 DWS INVESTMENT SLT.RENT 124 HSBC INV.FD.LX.GIF INDIAN EQ.A DIS

85 DWS GLOBAL VALUE 125 ING INV.MAN.LX.BKG.&. INSURANCE P HGD.CAP.EUR

86 DWS VERMOGENBILDUNGS FUNDS I 126 ING LX.INVEST EMRG.EU. EQ.P CAP.

87 EURO CAPIT HLDG. 127 ING LX.INVEST EURO HIGH DIV.DS.

88 FIDELITY INTL.LUX AMERICA A USD 128 ING LX.INVEST EUROPEAN EQ.P CAP. 89 FIDELITY FUNDS AMER.GW. FD.A GLB.CERT. 129 ING LX.INVEST EUR.REAL EST.P CSN. 90 FIDELITY FUNDS AN.SPSIT. FUND A GLB.CERT. 130 ING LX.INVEST GREATER CHI P CAP. 91 FIDELITY INTL.LUX EMRG. MARKETS A USD 131 ING L HEALTH SHS P HGD. CAPITALISATION 92 FIDELITY FUNDS ER.BLCHP. FUND A GLB.CERT. 132 ING INV.MAN.LX.MATERIALS P HEDGE CAP.EUR 93 FIDELITY FUNDS ER.BD. FD.A GLB.CERT. 133 ING LX.INVEST SUST.GW.P CAP.

94 FIDELITY FUNDS EUR. AGRSIV.FD.A GLB.CERT. 134 ING INV.MAN.LX.TELECOM P CAP.HGD.EUR 95 FIDELITY FUNDS EUR.GW. FD.A GLB.CERT. 135 ING INV.MAN.LX.RENTA FD. EMM.DB.LC P CAP.USD 96 FIDELITY FUNDS EUR.HIY. FD.A GLB.CERT. 136 ING INV.MAN.LX.RENTA FD. EURO P CAP.EUR 97 FIDELITY FUNDS EUR. LARGER COS.FD.A GLB. 137 ING INV.MAN.LX.RENTA FD. GLB.HIY.P CAP.EUR HGD. 98 FIDELITY FUNDS EUR.SML. COS.FD.A GLB.CER 138 ING GLOBAL REAL ESTATE FUND

99 FIDELITY FUNDS CSM.INDS. FUND A GLB.CERT. 139 ING INV.MAN.L INVEST GREATER CHI P DS.

100 FIDELITY FUNDS GLOBAL FINCIAL SVS. 140 ING INV.MAN.LX.RENTA FD. EMM.DB.HC P C EUR HGD. 101 FIDELITY FUNDS GLOBAL FOCUS FD.A EUR GLB.CERT 141 ING INV.MAN.LX.RENTA FD. EMM.DB.HC P DS.EUR HGD. 102 FIDELITY HLTHCR.FUND EURO 142 INVESCO GLOBAL SMALL CAP EQUITY FUND DUB A 103 FIDELITY INDUSTRIALS FD. 143 JPMF.ASTMGMT.EU.EMRG. MARKETS DEBT FD.A DS.ER. 104 FIDELITY FUNDS TECH.FUND A GLB.CERT. 144 JPMF.ASTMGMT.EU.MIDDLE EAST EQ.A DS.DL

105 FIDELITY FUNDS TELECOM. FD.A GLB.CERT. 145 JPMF FDS EUROLAND EQ.FD. 106 FIDELITY FUNDS INTL.FD. A GLB.CERT. 146 JPM FUND.JPM EUROPE EQ. A DS. 107 FIDELITY FUNDS LATIN AM. FUND A GLB.CERT. 147 JPMF.ASTMGMT.EU.STGC.GW. A DS.EO 108 FIDELITY FUNDS PACIFIC FD.A GLB.CERT. 148 JPMF.ASTMGMT.EU.STGC. VAL.A DS.V EUR 109 FIDELITY FUNDS SING.FD. A GLB.CERT. 149 JP MORGAN BK.LX.FLEM. INV.EUR GLB.BAL.FD. 110 FIDELITY FUNDS WLD.FD.A GLB.CERT. 150 JPMF GLB.CV.BD.FD.A

111 FRANK.TMPLTN.INV.FUNDS EUR.GW.A AC. 151 JPMF.ASTMGMT.EU.GLOBAL DYM.A DS.DL 112 FRANK.TMPLTN.INV.FUNDS MUT.EUR.A AC.EO 152 JPMORGAN ASTMGMT.I GLB. HIY.BD.FD.A AC.EO 113 FRANK.TMPLTN.INV.FUNDS F U S OPPOR FD.A SC. 153 JPMF.ASTMGMT.EU.INDIA FD.JF A

114 OEKOVISION LUX. 154 JPMF.ASTMGMT.EU.LATIN AM.EQ.A DS.DL

115 GAM STAR FUND JAP.EQ. AC.EO 155 JPMF.ASTMGMT.EU.US STGC. VALUE A DS.DL 116 GAM STAR FUND JAP.EQ. AC.YN 156 KBC EQ.FD.UTILITIES CAP

(38)

37

161 M&G GLOBAL BASICS A EUR 201 SARASIN INVESTMENT FONDS EQUISAR GLOBAL 162 MORGAN STANLEY EURO CPRT.BD.FD.A CAP 202 SARASIN SUSTAIBLE BOND EUR

163 MORGAN STANLEY EUR.VAL. EQ.FD.A 203 SCHRODER INV.MAN.LX.ISF EMERGING EU.A AC. 164 NEUFLIZE AMBITION A ER. NEUFLIZE OBC ASST.MAN. 204 SCHRODER INV.MAN.LX.ISF EURO CPRT.BD.A AC.

165 ODIN FORVALTNING AS NORGE NOK 205 SCHDR.INV.MAN.USD BD.

166 OYSTER EUROPEAN OPPORTUNITIES EUR 206 SCHRODER INV.MAN.LX.ISF JAPANESE EQ.A AC.

167 PARVEST EURO BD.D 207 SCHRODER INV.MAN.LX.ISF EUROPEAN BD.C DS.

168 PARVEST EURO BOND CAP. 208 SKAGEN GLOBAL FUND

169 PARVEST EURO CORPORATE BOND CAP. 209 SKAGEN KON-TIKI

170 PARVEST EURO CPRT.BD.DS. 210 SPARINVEST SICAV GLB. VALUE

171 PARVEST EURO ADVG.BD.DS. 211 SPDR AEX ETF

172 PARVEST EUROPEAN BOND CAP.CLASSIC 212 SPDR MSCI FINC ETF

173 PARVEST EUR.CONV BD. 213 FRANK.TMPLTN.INV.FUNDS TMPLTN.CHI FD.A AC.

174 PARVEST BALANCED EURO CAP. 214 FRANK.TMPLTN.INV.FUNDS TMPLTN.EMRG.MKTS.FD.A DS

175 PARVEST JAPAN D 215 FRANK.TMPLTN.INV.FUNDS TMPLTN.GLB.BD.FD.A DS.

176 PARVEST JAPAN C JPY 216 FRANK.TMPLTN.INV.FUNDS TMPLTN.GLB.BD.FD.A AC.EO

177 PARVEST LATIN AMERICA CAP. 217 FRANK.TMPLTN.INV.FUNDS TMPLTN.GLB.FD.A DS.

178 PARVEST USA CAP. 218 THREADNEEDLE INV.FUND. ICVC ASIA FD.

179 PARVEST US DOLLAR D 219 THREADNEEDLE EUR.HIY.BD. RET.GR.AC.EUR

180 PETERCAM B FUND BONDS EUR DS. 220 THD.NEEDLE INV.EUR. SMCOS.GW.C1 OFF

181 PETERCAM B FUND BONDS EUR CSN. 221 THREADNEEDLE UK 1

182 PETERCAM B FUND EQUITIES EUROPE DIVIDEND CSN. 222 UBS BD.FD.MAN.CO.LUX BF CONVERT EU.B 183 PETERCAM B FD.SECS.REAL ESTATE EUROPE DS. 223 UBS BD.FD.MAN.CO.LUX BF EUR B 184 PICTET FXD.INC.FD.EUR CPRT.BDS.P DS. 224 UBS EMRG.ECS.FD.MAN.CO. LUX GLB.BDS. 185 PICTET FXD.INC.FD.GLB. EMRG.DEBT P DS. 225 UBS EQ.FD.MAN.CO.L ASIAN TECHNOLOGY

186 PICTET FXD.INC.FD.WT.P 226 UBS EQ.FD.MAN.CO.L BIOT.

187 PIMCO FUNDS TR BOND INV INC 227 UBS EQ.FD.MAN.CO.LUX EUR.GROWTH 188 PIONEER FUNDS GLOBAL ECOLOGY 228 UBS EQ.FD.MAN.CO.LUX FINL.SERVICES 189 ROBECO CAP.GW.FUND. MLTMGR.AI.PAC.EQTIES.CAP 229 UBS EQ.FD.MAN.CO.LUX GLB.INNOVATORS B 190 ROBECO CAP.GW.FUND. CHINESE EQTIES.EUR D 230 UBS EQ.FD.MAN.CO.LUX HEALTH CARE 191 ROBECO CAP.GW.FUND. EMRG.MKTS.EQTIES.EUR D 231 UBS EQ.FD.MAN.CO.LUX MID CAPS EU. 192 ROBECO GROUP CONSUMER TRENDS EQ.D 232 UBS EQ.FD.MAN.CO.LUX TAIWAN 193 ROBECO GROUP HIGH YIELD BONDS B EUR 233 UBS L EQ.FD.MAN.CO.LUX MID CAPS USA 194 ROBECO CAP.GW.FUND. HIY.BDS.EUR D 234 UBS STGY.FD.MAN.LUX EQ. EUR B 195 ROBECO LUX O RENTE D SHARES CAP. 235 VANGD.EURO GVT.BD.IDX. INSTL.CAP 196 ROBECO CAP.GW.FUND. NTRL.RES.EQUITIES D 236 VANGD.ER.INVT.GDE.BD. IDX.INSTL.CAP 197 ROBECO CAP.GW.NEW WLD. FUND.FINLS.EQ.EUR D CSN. 237 VANGUARD INV.EUR.STK. IDX.FD.INSTL.SHS. 198 ROBECO CAP.GW.FUND. PROPERTY EQTIES.EUR D 238 VANGUARD US 500 STK.IDX. INSTL.SHS.CAP 199 ROBECO CAP.GW.FUND. EUR.EQTIES.EUR D CSN.

Referenties

GERELATEERDE DOCUMENTEN

Er is gekozen voor deze kenmerken omdat in deze scriptie de vraag centraal staat op welke manier Bureau Wibaut georganiseerd is en of dit collectief kenmerken vertoont van een van

In dit theoretisch kader is uiteengezet dat de criteria waaraan moet worden getoetst bij een beroep op de derde bewijsuitsluitingsregel zijn: (1) Het belang van het

Once an object is developed for a specific ADIDA-card it can be used with any application that uses the virtual AD/DA-card object.. The AD/DA-card object uses all the functionality

The aim of this study is to investigate the purification (recovery of limonene and reduction of benzothiazole) of TDO using a novel green separation technology,

De steekproeven komen uit de dubbelexponenti~le verdeling: Ook nu verscbillen de adaptieve-, Van der Waerden- en Kruskal Wallis toets weinig in power.. Ook de

Specifieke aandacht gaat in deze studie uit naar het belang van draagvlak voor het beleid dat de overheid voert ten aanzien van gezondheidszorg met winstoogmerk.. Als

Therefore, in this paper, our starting point is that performance defined as (a) the level of scientific and technological achievements, (b) the degree to which

In particular, the Black-Scholes model leads to a more attractive Delta-hedging strategy than the standard VG model in 25 and 18.75 percents of the scenarios for both the Sharpe