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The impact of the rise in popularity of passive investing on
active funds’ performance
1Master Thesis MSc Finance
Faculty of Economics and Business Rijksuniversiteit Groningen
Abstract
This study analyzes the effects of the increasing popularity of passive funds on active funds’ performance using data on European mutual funds from 2008 to 2020. A Carhart 4-factor model showed significant negative alphas for active funds in both bull and bear markets. The
results showed evidence of active fund underperformance as allocation towards passive funds increase. The panel-level regression indicated that increases in passive investment flow led to lower alphas for active managers and consequently to lower excess returns. Multiple GARCH (1,1) models on major worldwide stock indices showed no significant signs of volatility spill over effects. This paper showed prevailing negative return effects for active
funds as passive funds’ allocation increases.
Name: Bas Bleumer
Supervisor: dr. Ioannis Souropanis Date: 11-01-2021
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1. Introduction
In the last years, passive investing has grown in popularity. In the US, the allocation between passive and active funds is near equal nowadays, while equity funds in 2000 were for 85% actively managed (source Morningstar). A graphical representation of how passive funds have risen over the years can be seen in graph 1. Note that this paper views passive funds as exchange traded funds (ETF’s) and other index trackers, whereas active funds are funds which are actively managed similar to the distinction made by Morningstar in graph 1. In Europe, the difference in allocation between active and passive funds remains larger than in the US. Nevertheless, this difference has been decreasing over the last years (source
Thomson Reuters).
Graph 1: Development of US mutual funds
The consequences of this shift and specifically its effect on financial markets are still ambiguous. The efficient market hypothesis states that all information is already incorporated in stock prices and that any supplementary analysis does not result in an advantage over other investors (Fama 1970). Consequently, economic agents should invest in index tracker funds which simply track a given index. On the other hand, it can be argued that active investors are a vital part of the stock markets and that they improve its efficiency by continuing to trade and influence prices (Wermers (2020)). The approach to evaluate the performance of active fund managers is to measure the active performance against an appropriate benchmark and then determine the existence and significance of abnormal returns (Carhart 1997).
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Conversely, there are also famous economists who are advocates of active investing. Nobel prize winner Robert Shiller has stated that passive investing is a pseudoscience and that those investors are free riding on other people’s work. This debate has become more active again as investors notice that passive investing is growing in popularity and growing quickly. A consequence of the increase in passive funds is that stocks which are part of the index experience higher demand. This leads to price premiums for index-linked stocks whereas non-index-linked stocks do not enjoy the increased demand (Wurgler 2011). The index premium increases, as the demand for index trackers increases (Yang and Morck 2001). Subsequently, it becomes increasingly complicated for active managers to outperform the benchmark by investing in stocks which are not incorporated in the index. However, it can also be suggested that this demand increase is encouraging for active managers since price anomalies are bound to occur more often. Active managers can capitalize on their analytical skills by identifying winners and losers more accurately if more investors follow the same index as well as take advantage of passive managers’ predictable trading patterns (Sushko 2018).
The main question of this paper is to investigate what the effect of the increase in popularity of passive funds is on active funds, particularly, the effect on manager’s ability, alpha.
Furthermore, this topic will be researched in the European market where ETF’s and Index Trackers are not as dominant as in the US.
Moreover, this paper will test the effect of the shift to passive investment funds on market volatility. The world is becoming more globalized every year and this accompanies an effect on stock indices. The correlation between major stock indices has grown, partially due to globalization (Bekaert, Harvey, Kiguel and Wang (2016)). As indices become more correlated, it becomes more difficult to properly diversify one’s portfolio. This could lead to an increase in volatility for active investors as they primarily invest in individual stocks.
It is also interesting to study how active and passive funds behaved during the covid-19 crisis of March 2020. Active funds tend to outperform the passive funds in times of crises and downturns. However, after the crisis of 2008, US active funds have suffered from outflows, whereas passive funds gained. The aim of this paper is to add to the existing literature about passive and active investment strategies. With recent data starting from January 2008 until august 2020, this paper aspires to add new inference by analysing the investment strategies in a global pandemic of such scale and compare it with previous bear markets and bull markets. Furthermore, this paper aims to elaborate on the existing literature regarding the increasing allocation towards passive funds and its consequences by investigating both returns and volatility effects in European mutual funds and stock indices. Data from 2008 to 2020 was used which makes the inferences relevant, since allocation towards passive funds is at an all time high.
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2. Literature review
There is already considerable existing literature regarding passive vs active fund
performance. The literature predominantly states that passive funds outperform active funds when the costs are included. However, it does divide the debate up into essentially four parts: performance in bull markets, performance in bear markets, performance
indicators, and effects on market volatility. The majority of research in this field of finance is either based on cross-sectional data or time-series data. This paper aims to contribute to existing literature by adding inference based on panel data. Inferences based on panel data with sufficient data points are more robust than cross-sectional or time-series inferences and could prove to be an improvement of previous studies (Kremnitzer and Malmendier 2012). Furthermore, the existing literature predominantly investigates US mutual funds. Anadu et al (2018) indicated that passive investment strategy amplified market volatility in the US market This study aims to add new inferences regarding active and passive funds by researching this relation in European mutual funds. Moreover, the Carhart 4-factor (Carhart, 1997) model is broadly used to investigate abnormal returns. Usually following a time-series regression, existing papers found no evidence of active fund outperformance (Fama and French (2010), Berk and van Binsbergen (2014). However, there are cases in which evidence of active outperformance was found (Wermers (2000). These results were all based on gross returns. Alpha was found to be significantly negative when net returns were used.
In 1993, Hendricks, Patel, and Zeckhauser investigated the persistence of mutual funds and concluded that the top performing fund in one year yielded above average returns in the following year. This “hot hands” performance persistence resulted in returns above the benchmark if active managers rolled over the top performing fund. Later, Carhart (1997) discovered that this momentum effect generally only lasts for one year after the top performance. There are multiple studies that compare passive and active funds in the long run (10~15 years). Nanigian (2018) describes how the difference in performance of active and passive funds disappears when passive funds are compared to an active fund which is competitively priced. This is in line with findings from Philips, Kinniry and Walker (2014) who analyzed 10-year mutual fund performance and explained that actively managed funds can extract more value than passive funds in the period of a business cycle. The period from 2009 to 2019 was one of the longest bull markets in history. This implies that longer bull markets could prove to be advantageous for active funds.
2.1 Fund fees
Carhart (1997) states that investment costs such as transaction costs and load fees have a negative impact on performance. Jensen’s study (1968) corroborates these findings and states that active funds underperform gross of fees as well. This shows that active funds have difficulty earning back their investment expenses. Fama and French (2010) employed bootstrap simulations to investigate mutual fund performance and found that only few active funds earn superior returns. This shows that some active fund managers exhibit good enough stock picking skills to cover their investment costs. From an equilibrium point of view, Sharpe (1991) argued that if passive fund returns receive an alpha of 0 against a passive benchmark, then active fund returns should also receive an alpha of 0 before costs. He argued that active fund returns net of costs should be negative. This “arithmetic of active management” is widely accepted by investors, among Warren Buffett. However, Pedersen (2018) showed that active funds’ alphas can be positive in a world where shares are
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fund performance, which is why the expense ratio is included as a control variable. Furthermore, net returns will be added as a dependent variable next to gross returns to signify a potential difference in fund performance.
2.2 Fund size
Another predictor of fund performance is fund size. Chen et al (2004) found a negative relation between lagged fund size and fund performance. This effect is most prevalent in small cap stocks where liquidity issues diminish performance. An alternative explanation is that hierarchy costs and diseconomies of scale are negatively related to performance. This is in line with Indro et al (1999) who claim mutual funds should adhere to their optimal fund size and found evidence of negative returns if the optimal fund size is exceeded. Ciccotello and Grant (1996) corroborate these findings and argue that large equity funds do not outperform other equity funds once they have considerably increased in size. 2.3 Fund flow
Multiple studies have considered fund flow as a possible determinant of fund performance. Berk and Green (2002) have found a positive relation between fund flow and lagged
performance measures. This implies that investors follow performance measures thinking the excess returns will continue to exist. Rakowski and Beardsley (2009) found that a momentum strategy seems to yield positive results for investors, as he found evidence of a positive relation between lagged fund flows and future fund returns. However, a fund inflow can also affect a fund manager’s ability to select securities and potentially result in holding too much cash. Managers will then not be able to allocate fund inflows effectively which will result in a negative relation between fund flow and performance (Chou and Hardin (2014)). 2.4 Fund age
Fund age also seems to be a relevant measure of mutual fund performance. Otten and Bams (2002) found a negative relation between age and risk-adjusted returns. This implies that younger funds tend to detect better investment opportunities and therefore perform better. However, there is also evidence that younger funds tend to have an investment learning period wherein performance is negatively affected (Gregory, Matatko and Luther (1997)). This could also result from a relatively small fund size in the startup period in which a fund cannot exploit its optimal fund size benefits. The literature is less developed for European funds compared to US funds. Otten and Schweitzer (2002) concluded that European funds are smaller in asset size and average fund size. This could potentially explain an age effect although the existing literature is somewhat ambiguous.
2.5 Passive flow
Passive investment flow can be considered a relatively new factor for measuring
performance. A study by Sushko and Turner (2018) showed that a potential shift to passive investing could affect security markets by causing higher correlation of returns and thereby decreasing asset-specific information2.Moreover, the share of passive funds drastically
increased in all geographical locations mentioned in the second graph in the appendix. This paper will elaborate on the passive fund flow debate by testing the impact of this passive investment flow on active fund manager’s ability to generate returns.
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2.6 Bear markets
Furthermore, the literature on active performance during crises is still somewhat ambiguous on performance.Sun, Wang, and Zheng (2009) found that active funds outperform the least active funds as well as passive counterparts. They conclude that this outperformance in bear markets convinces investors to invest in active funds, even though active funds do not perform as well in bull markets as passive funds. However, Pástor, and Vorsatz (2020) have used recent data of the Covid-19 crisis and found that active funds underperform with respect to passive benchmarks. Moreover, their findings state that there is a positive
relation between sustainable funds and performance. These contradicting results prove that the 2008 and the 2020 crises have different impacts on performance. The general
agreement regarding bear market performance is that active funds underperform. Philips (2010) follows this view and failed to find evidence of active fund outperformance. Pfeiffer and Evensky (2012) are somewhat more centered and have found evidence of a small group of active managers adding alpha in bear markets, however the persistence is negligible. 2.7 Volatility effects
The latest literature focuses on the consequences of the shift from active funds to passive funds. Anadu et al (2018) researches these potential risks and found that this shift could lead to an increase in market volatility as risky passive investment approaches such as inversed or leveraged ETF’s gain in popularity. These findings are supported by Bessler and Hockmann (2016) who state that the shift in fund allocation causes negative effects on systematic risk. On the other hand, the shift could lead to less liquidity transformation risks, since passive funds generally do not invest in illiquid assets. Deslisle, French, and Schutte (2017) stated that the rise in passive funds results in an increase in stock correlations. Moreover, they applied a proxy for firm-specific information and tested this against passive ownership. They concluded that there is a negative effect between passive ownership and firm-specific components. The impact of firm-specific news might even decrease further as passive ownership grows. Considerable studies were conducted on correlation between stock indices. Chandra (2005) indicated that correlation between Asian markets is higher since the Asian financial crisis of 1997. Chandra (2003) supports these findings and finds that
correlation between Australia, Hong Kong, Japan and Singapore has increased during this time too. There are also studies which focuses on correlation in European stock indices. Dajcman, Festic, and Kavkler (2012) found that co-movement between index returns are time varying and the financial crisis of 2008 slightly increased index correlations. The introduction of the Euro in 2002 also caused for higher correlations in European stock indices as well as volatility spill overs to New York (Savva, Osborn, Gill (2009)). These papers predominantly show an increase in correlation between stock indices during crises and that those increases lasts for multiple years.
3. Hypotheses
The main research question of the paper is: “What is the effect of the increasing popularity of passive funds on active funds?” The question mainly relates to fund parameters such as risk and return and investigates possible changes throughout the years. The primary hypothesis is
H1: “The increasing popularity of passive funds negatively affects active manager’s ability to
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This implies that outperformance of active funds is hardly possible anymore. Investors have noticed this trend and therefore are shifting towards a passive investment strategy. The hypothesis will be tested using a passive investment parameter which measures passive investment flows over the years. It will then be shown if there exists a relation between passive investment flow and active manager’s ability measured by alpha. This hypothesis will be tested in different markets, such as bull markets and bear markets. The null hypothesis and alternative hypothesis are formulated below where PF resembles passive investment flow.
H0: PF < 0 and Ha: PF ≥ 0
This main research question will be answered through multiple sub-questions, such as “Do active funds outperform passive funds in bull markets?” Data from 2009 until 2020 will be used since it is one of the longest bull markets in history with enough data to properly analyze and compare.
Hypothesis 2 is based on the results of Jensen (1968) who found that active funds were not able to beat the passive index benchmark. This hypothesis is also in line with the increasing trend in passive funds, which suggests that investors are aware that active funds do not necessarily outperform. Hypothesis 2 is formulated as follows:
H2: “Active funds do not outperform passive funds in bull markets.”
The null hypothesis and alternative hypothesis are formulated below: H0: αt ≤ 0 and Ha: αt > 0
The research method sub-section will provide a more detailed approach of the regression analysis.
Another sub-question is “Do active funds outperform passive funds in times of crises and if so, how?” Recent data from the crisis in 2020 will be used to answer this question as well as data from the 2008 economic crisis. The hypothesis is:
H3: “Active funds outperform passive funds during crises”.
The reason behind this is that it is generally believed active funds perform better than passive funds in bear markets, due to its ability to hold cash. The null hypothesis and alternative hypothesis are formulated below:
H0: αt > 0 and Ha: αt ≤ 0
The last sub-question focuses on volatility effects and is formulated as: “what is the effect of passive funds on active funds’ volatility?” The hypothesis for this question is the following:
H4: The gain in popularity of passive funds increases stock correlations and therefore
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This hypothesis is based on results of Deslisle, French, and Schutte (2017) which showed that a gain in passive funds reduces firm-specific components. Active funds primarily invest in individual stocks in order to construct a portfolio. If stock correlations increase, then portfolios will increase in volatility, since diversification benefits are weakened. This
hypothesis will be tested by focusing on major stock indices and testing if index correlations have increased over time. The null hypothesis and alternative hypothesis are formulated as:
H0: 𝛾𝑖𝑗 > 0 Ha: 𝛾𝑖𝑗 ≤ 0
𝛾11 is the coefficient for volatility spill over effects. A detailed description of the employed GARCH model is given later.
4. Dataset
In this section the dataset used to test the hypotheses from the section above will be described. The mutual fund data concerning active fund characteristics and passive investment flow was extracted from Morningstar Direct and it covers the period from January 2008 to August 2020. The initial sample of active funds consisted of 5000 active EU funds. Morningstar Direct offers the option to include funds that are closed nowadays, leading to a sample free of survivorship bias as well as a sample free of funds with missing data points. Furthermore, only funds that are categorized as Equity Funds are included in the sample as well as funds which have data available regarding their tracking error and
benchmark. Only funds with a minimum size of €15 million are included in the sample, since relatively smaller funds have a tendency to be upward biased (Chen et al (2004). The dataset does not take direct investments into account and only supplies fund-specific data. The fund data required a minimum of 30 months of return data similar to Carhart (1997).
This resulted in a final active sample of 3101 active funds. The dataset consists of fund characteristics such as gross monthly return, tracking error, fund size, net fund flow, age, management fee and the corresponding date. Descriptive statistics of those fund
characteristics can be found in table 1. It can be seen that the average passive flow is 0.0124 or 1.24% each month. Graph 2 shows how passive fund flows develop during the sample period. Net monthly return is inferred from the gross monthly return and the fund’s expense ratio. The median of the expense ratio will be used to infer net returns for funds which lack information regarding their expense ratios. There are funds in the sample that are quoted in dollars, pounds, and other currencies. Following Fama and French (2012), purchasing power parity is assumed such that exchange rate risk is ignored. The sample of passive funds consisting of ETF’s and index trackers consists of 3072 funds. The same characteristics as with the active sample are collected. The Fama-French monthly variables HML, SMB, the market risk premium, and the risk-free rate are collected from the Kenneth French database as well as the momentum factor. An overview of those statistics can be found in table 2. It can be seen that the average monthly market return equals around 0.84%. The alphas which are estimated using regression (2) are stored in Stata. An overview of descriptive statistics of alpha can be found in table 3 and it is clear that all average alphas are positive. The
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again around 2019. It is noteworthy to state that alpha expresses more volatile behavior around bear markets as opposed to bull markets.
The data for hypothesis four consists of weekly data of five major stock indices. The stock indices are the FTSE 100, the DAX, the CAC, the S&P500 and the ASX. They each represent the United Kingdom, Germany, France, the United States and Australia respectively. The UK, Germany and France were chosen based on the European focus of the paper, whereas Australia and the US can be considered large trading partners with the European Union. The weekly price data were collected from Yahoo Finance. Table 4 shows descriptive statistics of the five stock indices. The relatively high standard deviation for the DAX and CAC shows that these indices can be considered more volatile than the others in this sample period. The Jarque-Bera (Jarque and Bera, 1980) test statistic is significant at the 1% level for all indices which implies a rejection of normality for the data. The Portmanteau Ljung-Box test (Ljung and Box, 1978) cannot be rejected for normal residuals, but it can be rejected for the squared residuals of the FTSE, CAC and the S&P500. This shows there is no evidence of autocorrelation up to lag 16. However, for those three indices, there is evidence of autocorrelation in the squares which suggests evidence of autoregressive conditional heteroskedasticity. The LM-test shows evidence of ARCH effects and volatility clustering for all indices except the FTSE.
Table 5 presents the correlation between the stock indices. Correlation seems to be high between most indices, except for the FTSE. The FTSE does not seem to have a significant correlation with any of the other indices
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Table 1: Descriptive statistics of fund characteristics
Variable Obs Mean Std. dev. Median
Passive flow 471.352 0.0124 0.0582 0.0195
Age 274.759 95.0031 82.3934 74
Fund size 350.334 935.4044 1530.718 453.562
Fund flow 347.919 0.0121 0.2435 0.0089
Expense ratio 144.540 0.0145 0.0081 0.0132
The table reports descriptive statistics of mutual fund characteristics in the period 2008-2020. The mean, standard deviation, and median of passive flow, fund flow and expense ratio are expressed as percentages. Age is in months and fund size is in € mln.
Table 2: Descriptive statistics Risk-adjusted performance measurements
Variable Obs Mean Std. dev. Median
Gross return 276.078 0.3456 4.8707 0.4903 Net return 276.078 0.2296 4.8705 0.3774 Market return 471.352 0.8399 4.7103 1.395 SMB 471.352 0.0585 2.3498 0.235 HML 471.352 -0.4007 2.9706 -0.455 MOM 471.352 0.0413 4.8265 0.28
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Graph 3: Scatter graph of mean gross alphas (monthly) Table 3: Descriptive statistics alpha
Alpha whole Alpha bull markets Alpha bear markets
Gross Net Gross Net Gross Net
Mean 0.7609 0.7493 0.7664 0.7535 0.3773 0.3431
Median 1.1774 1.1831 0.9591 0.9585 1.6886 1.6316
Std. Dev. 3.5994 3.5775 2.8469 2.8189 6.9365 6.9339
Obs 276.078 276.078 241.549 241.549 34.529 34.529
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Table 4: Descriptive statistics stock indices returns
DAX FTSE CAC S&P500 ASX
Mean 0.1258 0.0206 0.0347 0.1763 0.0316 Median 0.2738 0.1191 0.2866 0.2991 0.1653 Maximum 15.9690 18.1617 15.0169 17.3974 13.8012 Minimum -17.7201 -11.2823 -17.5545 -13.8502 -13.1252 Std. Dev. 3.1762 2.4814 3.1276 2.7825 2.4970 Skewness -0.5447 0.0252 -0.4666 -0.1059 -0.4801 Kurtosis 7.0920 9.1268 6.6858 9.6656 7.7337 Jarque-Bera 1415.94 (0.0000) 1229.32 (0.0000) 2314.76 (0.0000) 2570,39 (0.0000) 1670,25 (0.0000) Sum 84.1579 13.6039 22.9050 116.3760 20.8374
Results of residuals tests
LB-Q 13.8115 (0.6128) 19.1328 (0.2618) 20.4188 (0.2019) 22.3883 (0.1311) 14.7709 (0.5415) LB-Q2 18.0865 (0.3189) 159.2469*** (0.0000) 132.5065*** (0.0000) 271.7970*** (0.0000) 14.3453 (0.5730) LM test 40.145*** (0.0000) 2.281 (0.8921) 72.271*** (0.0000) 26.783*** (0.0002) 207.266*** (0.0000)
This table shows descriptive statistics of returns of the chosen stock indices. LB-Q and LB-Q2 are the Portmanteau Ljung-Box Q test statistics for testing autocorrelation of residuals and squared residuals respectively. 16 lags were used for this statistic. LM test shows the results for ARCH effects up to and including 6 lags. The numbers in parentheses depict the corresponding P-value. Note that the mean, median, minimum, maximum, standard deviation and sum are all written in percentages.
Table 5: Correlation matrix
DAX FTSE CAC S&P500 ASX
DAX 1 0.1700 0.9398 0.8178 0.6751
FTSE 0.1700 1 0.1724 0.1391 0.2596
CAC 0.9398 0.1724 1 0.8305 0.7028
S&P500 0.8178 0.1391 0.8305 1 0.7206
ASX 0.6751 0.2596 0.7028 0.7206 1
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5. Research method
The research method is a panel data regression of European active funds. Pooled OLS is not recommended in this case, since it assumes that the average value of the parameters is constant over time and cross-sectionally (Brooks (2002)). This assumption is too restrictive as there is likely either a fund specific or time specific effect. A Hausman test (Hausman (1978)) will be conducted to test if fixed effects or random effects are preferred. Then, the fund data will be analysed using the Carhart 4-factor model to check for significant alphas (Carhart 1997). This way, the regression is able to capture the effects of value, size and persistence. This is in line with prior research of Blake, Caulfield and Ioannidis (2014) who researched panel data on UK active funds using the same method. Equation (1) shows how alpha is obtained in order to test hypothesis 2 and 3, however data from bull markets will be used to test hypothesis 2 and data from bear markets will be used to test hypothesis 3. From this point on, this paper defines bear markets as markets in times of economic contraction in the business cycle as determined by the US national bureau of economic research. An overview of post-war periods of economic contraction and economic expansion can be found in table A in the appendix.
𝑅𝑖𝑡− 𝑅𝑓𝑡 = 𝛼𝑖𝑡 + 𝛽1∗ (𝑅𝑀𝑡− 𝑅𝑓𝑡) + 𝛽2∗ 𝑆𝑀𝐵𝑡+ 𝛽3∗ 𝐻𝑀𝐿𝑡+ β4∗ 𝑀𝑂𝑀𝑡+ 𝜖𝑖𝑡 (1) Where 𝑅𝑖𝑡 − 𝑅𝑓𝑡 is the risk-adjusted return of fund i at time t. 𝛽1∗ (𝑅𝑀𝑡− 𝑅𝑓𝑡) describes
the excess market return. 𝑆𝑀𝐵𝑡 explains the size effect and 𝐻𝑀𝐿𝑡 controls for value stocks.
𝑀𝑂𝑀 controls for persistence in returns.
𝑅𝑖𝑡− 𝑅𝑓𝑡 = 𝛽1∗ (𝑅𝑀𝑡− 𝑅𝑓𝑡) + 𝛽2∗ 𝑆𝑀𝐵𝑡+ 𝛽3∗ 𝐻𝑀𝐿𝑡+ β4∗ 𝑀𝑂𝑀 + 𝜖𝑖𝑡 (2) 𝛼𝑖𝑡 = 𝛼 + 𝛽1∗ 𝑃𝐹𝑡−12+ 𝛽2∗ 𝑎𝑔𝑒𝑖𝑡−12+ 𝛽3∗ 𝑠𝑖𝑧𝑒𝑖𝑡−12+ 𝛽4∗ 𝑓𝑙𝑜𝑤𝑖𝑡−12+ 𝛽5∗ 𝐸𝑅𝑖𝑡−12+ 𝜖𝑖𝑡 (3)
5.1 Estimating and storing alphas
Equation (2) will be used to obtain the values for alpha which will be used in equation (3). Note that the Carhart 4-factor model is modified by excluding the constant in this regression. In the original model, the expected value of the error term equals zero. In other words, 𝐸(𝜀𝑖𝑡) = 0. By excluding the constant in this alternative specification, the expected value of
the error term becomes alpha, 𝐸(𝜀𝑖𝑡) = 𝛼. The expected value of 𝑅𝑖𝑡− 𝑅𝑓𝑡 in this
specification is equal to the expected value of 𝑅𝑖𝑡 − 𝑅𝑓𝑡 in the original specification since the
error term absorbs the effect of the constant. This offers the opportunity to predict the residuals from the regression and thereby obtain a value of alpha for each fund return in time. A drawback of this specification is that the coefficients are biased. However, this paper primarily focuses on the obtained values of alpha since those are used to test the first hypothesis.
Equation 3 will then be used to test the relation between passive investment flow and managers’ alpha. In the equation, 𝑃𝐹𝑡−1 is the fund flow of passive funds in percentages
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parameters are all lagged by one year, because it has a greater impact on the return at time t than the actual values for time t. The paper’s main focus is on PF, since it gauges the effect of passive investment flow. Specifically, PF measures the effect of a change in passive fund flows on the ability of active fund managers.The determination of the control variables is in line with existing literature (Guercio, Reuter (2013)).
To compare passive and active funds in times of crises, data from the financial crisis of 2008 as well as the recent crisis of 2020 will be used. Similarly to the main question, the data will be analysed using the Carhart 4-factor model to check for significant alphas. This method will help to analyse if active funds have superior performance in bear markets, because only data from dates in bear markets are used and alpha is widely accepted as a good indicator of superior performance. Comparable to the first hypothesis, the alphas will be inferred from the Carhart 4-factor model and then used as a dependent variable in the equation (3). The main difference is that data points in times of crises are used3. Another difference is that
the variables in the equation (3) will be lagged by one month instead of one year. This is in line with Remolona, Kleiman, and Gruenstein (1997) who argued that it is more applicable to use one-month lags in times where asset prices are downward spiralling.
5.2 volatility spill over effects
To examine the effect of passive funds on active funds’ volatility, this paper will test the correlation between major stock markets and see if it has increased over time. A GARCH (1,1) model will be used to test correlation and volatility spill over effects in major European stock markets. This paper chose for a GARCH (1,1) model following the paper of Sakthivel, Bodkhe and Kamaiah (2012). This method is similar to Tsui and Yu’s (1999) method to test correlation in Chinese stock markets. This method will help to determine if the correlation between stock markets has increased over time, which could be explained by the rise of passive investment funds as described above. First, closing prices of major European stock markets such as the FTSE 100, CAC 40, and the DAX 30 will be obtained as well as closing prices from two non-European stock markets: the S&P 500 and the ASX.
The closing price will be converted to log-values and the daily percentual change will be computed as well. For a given stock index i, this looks like:
𝑙𝑆𝑖𝑡 = ln(𝑆𝑖𝑡)
𝑅𝑖𝑡 =
𝑆𝑖𝑡− 𝑆𝑖𝑡−1 𝑆𝑖𝑡−1
Where R stands for return at time t and S denotes the closing price at time t.
Then, a Dickey-Fuller test4 (Dickey, Fuller (1979will be implemented to determine if the
behaviours of the stock indices are stationary. Stationarity is important, since the employed method for this study relies on the data being stationary. The next step is to test for
cointegration. The Johansen test5 (Johansen 1991) will check if the stock indices are 3 Note that this paper defines bear markets as times of economic contraction defined by the US
national bureau of economic research.
4 The results of the Dickey-Fuller test can be seen in table E in the appendix.
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cointegrated. It implies that both indices are impacted by the same shocks, but in different magnitudes in the long run. The cointegration test sheds light on that degree. Then, error correction terms are estimated accordingly with respect to the test. Error correction terms are necessary to draw inferences on a sample with cointegrated variables. The first GARCH model measures return spill over effects. For a bivariate case between indices, the
GARCH(1,1) model is defined as follows:
𝑅1𝑡 = 𝛼 + 𝛽11∗ 𝑅1𝑡−1+ 𝜃12∗ 𝜀2𝑡−1+ 𝜐1𝑡 𝑅2𝑡 = 𝛼 + 𝛽21∗ 𝑅2𝑡−1+ 𝜃22∗ 𝜀1𝑡−1+ 𝜐2𝑡
Where 𝑅1𝑡 is the return of index 1 at time t and 𝑅2𝑡 is the return of index 2 at time t.
𝛽11 and 𝛽21 are the parameters for the lagged values of index 1 and 2 respectively. 𝜀1𝑡−1 and
𝜀2𝑡−1 are the lagged values of the error terms of index 1 and 2 respectively and are derived from the error correction model. Finally, 𝜐1𝑡 and 𝜐2𝑡 denote the error terms. To capture
volatility spill over effects, error correction terms will be used in the conditional variance equations which leads to the following expansion of the conditional variance equation:
ℎ11𝑡 = 𝑐11+ 𝛿11∗ 𝜀1 𝑡−12 + 𝜑11∗ ℎ11 𝑡−1+ 𝛾11∗ 𝜺1 𝑡−12 ℎ22𝑡 = 𝑐22+ 𝛿22∗ 𝜀2 𝑡−12 + 𝜑22∗ ℎ22 𝑡−1+ 𝛾22∗ 𝜺2 𝑡−12
Where ℎ11 is the conditional variance of index 1 at time t and ℎ22𝑡 is the conditional variance
of index 2 at time t. Both equations consist of functions regarding their past conditional variance, ℎ11 𝑡−1 and ℎ22 𝑡−1 for index 1 and 2 respectively. This term is known as the GARCH
term. Furthermore, they have a function of its own lagged squared residuals, which is 𝛿11∗
𝜀1 𝑡−12 for index 1 and 𝛿22∗ 𝜀2 𝑡−12 for index 2. This term is known as the ARCH term. The last term is a function of lagged squared residuals from the error correction model. 𝛾11 and 𝛾22
measure the volatility spill over effects from index 1 to 2 and from index 2 to 1 respectively. The results from the GARCH model will prove if there exists volatility spill over effects between the two markets. The model will be extended to cover more stock indices. 5.3 Panel data estimator
In this section, the appropriate panel data estimator will be estimated and discussed. The dataset including both cross-sectional properties as well as time-series properties is a strongly balanced dataset. This means that each individual fund contains the same time entries.
The model was first estimated using entity fixed effects. That would imply that the average value of alpha changes cross-sectionally but not over time. The resulting F-statistic was highly insignificant, indicating a pooled OLS is preferred over an entity fixed effects model. The model was then estimated using time fixed effects which would mean that the average value of alpha would change over time and not cross-sectionally. Using dummy variables to indicate a given month, the F statistic following the fixed effects regression was highly significant. Therefore, a time fixed effects model is preferred over pooled OLS. A Hausman test6 was conducted in order to determine whether fixed effects or random effects are more 6 The results of the F-tests for fixed effects as well as the Hausman test statistics are shown in table D
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applicable for the estimation. The test resulted in a significant chi-squared value. Therefore, fixed effects are preferred over random effects since the difference in coefficients is
systematic. That means a demeaned value is desired as the error term is correlated with explanatory variables. This justifies the choice of time fixed effects in equation (3) for all samples.
5.4 OLS assumptions
It is critical for the OLS estimators to be BLUE in order to draw reliable inferences from equation (3). An estimator is assumed to be BLUE if it satisfies the Gauss-Markov
assumptions. The Durbin-Watson test for autocorrelation cannot be applied to panel-level data. Therefore, the Wooldridge (Wooldridge, 2002) test for autocorrelation in panel data is applied to equations (1) and (3). The results are shown in table B in the appendix. The results show evidence of autocorrelation in all samples. The White test for heteroskedasticity cannot be used at panel-level. Therefore, an iterated GLS estimator will be applied to equations (1) and (3) to fit the model with heteroskedasticity. Then, the heteroskedastic model and the normal model will be compared using a ratio test. The likelihood-ratio test indicated evidence of heteroskedasticity in all samples except for the bull market sample in equation (3). The results of the likelihood-ratio test are shown in table C in the appendix. The samples will be corrected accordingly following Hoechle (2007)7.
7 This implies all samples will be corrected for autocorrelation and heteroskedasticity by using the
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6. Results
In this section, the results of the research method described in section 4 will be addressed and linked to the hypotheses described in section 3. Each subsection will elaborate on the results for the corresponding hypothesis starting with hypothesis 1 obviously. Note that subsections 1,2 and 3 correspond to return effects of passive investing on active investing whereas subsection 4 focuses on volatility effects.
Hypothesis 1 is tested in multiple samples. The sample as a whole and the bull market sample contain lagged values of fund characteristics of 12 months. The bear market sample contains lagged values of 1 month. The alphas are obtained following the first regression based on Carhart (1997) and used in the second regression. The results of equation (1) for all samples including the constant are shown in table 6. All coefficients are statistically
significant at the 1 percent level.
The market risk premium coefficient is positive for all sample sizes and smaller than 1. This shows that active funds, on average, move in the same direction as the market, albeit with a smaller magnitude. The coefficient for smb is negative for all three sample sizes. The
coefficient for HML is negative for the sample as a whole and the bull market sample. For the bear market sample, the HML coefficient is positive. The coefficient for MOM is negative for all samples. This implies there is no persistence in returns and that top performing funds quickly stop generating excess return. The coefficients are all statistically significantly lower than zero, hence it can also be argued that there is evidence of reversal effects. The results for hypothesis 2 and 3 will elaborate more on the coefficients and the constants from the Carhart 4-factor model.
6.1 Hypothesis 1
Regression (3) is similar to the Carhart 4-factor model of regression (1) except the constant is omitted. As explained above, the error term will then contain the expected value of the constant which can then be estimated and used for regression (2). In order to test
hypothesis 1, the alphas are stored and used in the regression (3) as dependent variable. Regression (3) has been conducted according to the results of the heteroskedasticity and autocorrelation tests shown in table 12 and 13 in the appendix. This means that all samples are corrected for autocorrelation and heteroskedasticity.8. The results of regression (3) with
corresponding samples are given in table 7.
The coefficient for passive flow is significant for the sample as a whole and the bull market sample. The difference between using gross returns or net returns is negligible. It seems that passive fund flow negatively affects manager’s ability to select stocks as the coefficient for the whole sample is -0.8295 for gross returns. This implies that if passive fund flows
increased with 1% the year before, then it generally leads to a decrease in manager’s ability of 0.8295. However, when observing only months in bull markets, then an increase in
passive fund flows of 1% last year leads to a decrease in manager’s ability of 0.1443. It shows that it is difficult for active managers to generate excess returns in upward-trending markets where the allocation towards passive funds increases. This is in line with Sushko and Turner (2018) who states this as a possible result of the increase in passive fund flow. The
8 Note that the samples use cluster standard errors to counter the effects of heteroskedasticity and
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coefficient is not significant in bear markets. This shows there is no clear relation between passive investment flow and manager’s ability to generate excess returns when markets are downward trending. The absence of a significant coefficient could potentially be caused by the fact that monthly lags were used in the bear market sample instead of yearly lags. Passive flow lagged by 1 month perhaps has not had the chance to affect the market in this shorter time period.
These contradicting results make it difficult to relate them to hypothesis 1. It can be said that passive fund flow is negatively related to alpha in bull markets and over the course of a business cycle while it is not significantly related to alpha in bear markets. Therefore, the hypothesis is accepted for the sample as a whole and for bull markets but is rejected for bear markets.
The coefficient for age is positive and significantly different from zero in the whole sample. This implies older funds, in general, are positively related to manager’s performance during the course of a business cycle. Paradoxically, age is negatively related to alpha in bull and bear markets although the coefficient is not significantly different from zero in bear markets. This means that older active funds experience lower returns in bull markets than younger active funds. The change of sign could also indicate a learning effect or the disability to use size effects as stated in Gregory, Matatko and Luther (1997).
Similar to age, the coefficient for fund size is positive and significantly different from zero in the whole sample, but negative in the bear and bull market samples. For bear markets, this implies than an increase in fund size of approximately €1 billion 12 months prior is related with a decrease in manager’s ability of 0.02. The change of sign shows support for the theory of Ciccotello and Grant (1996) stating funds should adhere to their optimal fund size.
The coefficients for fund flow are negative and statistically different from zero for all samples. This means that an increase in fund flow of 1% 12 months prior is related with a decrease in active manager’s ability of approximately 0.006 in bull markets and 0.008 in bear markets. It shows that those extra transactions corresponding to fund flow do not
necessarily add value for active funds which is in line with Chou and Hardin (2014).
The coefficients for the expense ratio are positive and statistically different from zero for the whole sample and for bear markets. This positive relation implies that an increase in expense ratio of 1 percent 12 months prior is associated with an increase in managers’ ability of approximately 0.17 in bear markets. This shows evidence that more expensive funds are positively related with performance which is in line with Fama and French (2010).
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Table 6: Carhart 4-factor model regression output
Whole sample Bull markets Bear markets
Gross return Net return Gross return Net return Gross return Net return
-0.5255*** (0.0068) -0.6415*** (0.0061) -0.4665*** (0.0049) -0.5820*** (0.0052) -0.7489*** (0.0346) -0.8671*** (0.0349) 𝑅𝑀𝑡− 𝑅𝑓𝑡 0.8097*** (0.0063) 0.8098*** (0.0063) 0.7866*** (0.0065) 0.7865*** (0.0065) 0.8352*** (0.0066) 0.8358*** (0.0067) 𝑆𝑀𝐵𝑡 -0.2148*** (0.0019) -0.2151*** (0.0019) -0.2222*** (0.0020) -0.2223*** (0.0020) -0.0566*** (0.0068) -0.0566*** (0.0068) 𝐻𝑀𝐿𝑡 -0.0900*** (0.0027) -0.0903*** (0.0027) -0.1459*** (0.0023) -0.1463*** (0.0023) 0.0569*** (0.0072) 0.0574*** (0.0072) 𝑀𝑂𝑀𝑡 -0.1197*** (0.0018) -0.11196*** (0.0018) -0.1733*** (0.0015) -0.1734*** (0.0015) -0.0481*** (0.0039) -0.0478*** (0.0039) R2 0.5749 0.5750 0.5202 0.5203 0.6709 0.6709
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Table 7: Regression with alpha as dependent variable
Whole sample Bull markets Bear markets
Gross return Net return Gross return Net return Gross return Net return
𝑃𝐹𝑡−12 -0.8295*** (0.0247) -0.8222*** (0.0246) -0.1443*** (0.0045) -0.1474*** (0.0045) 0.0246 (0.1469) 0.0187 (0.1434) 𝑎𝑔𝑒𝑖𝑡−12 0.0779*** (0.0009) 0.0775*** (0.0009) -0.0586** (0.0254) -0.0577** (0.0072) -1.3855 (1.711) -1.3352 (1.6691) 𝑠𝑖𝑧𝑒𝑖𝑡−12 3.41e-06*** (7.98e-07) 3.39e-06 *** (7.93e-07) -3.28e-06*** (1.19e-06) -3.23e-06*** (1.17e-06) -0.00002*** (5.11e-06) -0.00002*** (4.98e-06) 𝑓𝑙𝑜𝑤𝑖𝑡−12 -0.0001** (0.0001) -0.0001** (0.0001) -0.0006*** (0.0001) -0.0006*** (0.0001) -0.0008*** (0.0002) -0.0008*** (0.0002) 𝐸𝑅𝑖𝑡−12 0.0034** (0.0017) 0.0034** (0.0017) -0.0016 (0.004) -0.0016 (0.004) 0.1773*** (0.0607) 0.1729*** (0.0592) Within R2 0.9995 0.9995 0.9699 0.9702 0.9902 0.9906
This table presents estimates of regression coefficients following regression (3) for the entire sample, bull markets and bear markets. The results are obtained using time fixed effects. The regression analysis covers both gross returns and net returns for all three samples. The alphas are estimated using the Carhart 4-factor model and serve as dependent variable. All variables are lagged by 12 months except for bear markets. PF, flow and ER are depicted in percentages. Age is interpreted as the number of months an active fund is active. Size is characterized in €1 million. The numbers between brackets represent the robust standard errors for the corresponding coefficient. *** depicts statistical significance at 1% alpha level.
6.2 Hypothesis 2
The Carhart 4-factor model is used to test if active funds outperform passive funds in bull markets. Note that this paper distinguishes the period from June 2009 until February 2020 as a bull market.
As stated above, the market risk premium is positive and statistically significant for bull markets. It shows that if the market return increases with 1%, then active fund returns generally increase with 0.79%. The fact that it is positive and smaller than 1 shows that active funds move in the same direction as the market, but with a smaller magnitude. The difference between gross returns and net returns is negligible.
The coefficient for SMB is negative for bull markets. This negative relation towards the size factor generally implies that the mutual funds in the sample negatively react to
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The coefficient for HML is negative for bull markets. The negative relation towards the value factor means active funds’ returns negatively react to outperformance of value stocks over growth stocks. Potentially, this is an indicator that the sample funds generally contain more growth stocks than value stocks.
The coefficient for MOM is negative for bull markets. This implies there is no persistence in returns and that top performing funds quickly stop generating excess return. The coefficients for gross returns and net returns are statistically significantly lower than zero, hence it can also be argued that there is evidence of reversal effects during bull markets.
The constant is negative and significantly different from zero, although the magnitude differs between gross returns and net returns. The fact that the average alpha in bull markets is significantly negative implies that active funds do not earn excess returns over the market during bull markets. Furthermore, managers seem to experience more problems generating excess returns when the net returns of an active fund are considered rather than the gross returns. This supports the theory of the zero-sum game by Sharpe (1991) which states that returns of actively managed funds are lower after costs and this difference is reflected in the gap between gross and net returns. The negative alpha also means that hypothesis 2 cannot be rejected and therefore the null hypothesis is accepted.
6.3 Hypothesis 3
The Carhart 4-factor model is used to test if active funds outperform passive funds in bear markets. Note that this paper distinguishes the period from January 2008 until May 2009 as a bear market as well as the period from February 2020 until August 2020.
The coefficient for the market risk premium is, similar to bull markets, positive and
statistically significant. It shows that if the market decreases by 1%, active funds generally decrease by 0.84%. This is favorable during times of economic downturn, since the market decreases with a higher magnitude than active funds, keeping all other variables constant. Note that the coefficient for market risk premium is higher compared to bull markets. This shows that active funds possess a higher systematic risk compared to the market in bear markets than in bull markets.
The coefficient for SMB is negative and statistically significant. As mentioned above, this shows a negative relation towards the size factor and small-cap outperformance. In general, a 1% excess return of small-cap stocks compared to large-cap stocks leads to decrease in active funds return of 0.06%. The coefficient is significantly lower in bear markets than in bull markets. This implies that active funds are generally less prone to small-cap
outperformance in bear markets.
The coefficient for HML is positive for bear markets. A positive relation towards the value factor implies that outperformance of value stocks compared to growth stocks generally lead to higher returns of the active fund. In this case, an outperformance of 1% in the value factor leads to an increase of 0.06% in active funds’ returns, in general. The sign changed compared to bull markets. This potentially means that active funds switch to value stocks in bear markets, since they are considered safer assets compared to growth stocks.
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The constant is negative and statistically significant in bear markets. This shows that active funds do not outperform passive funds in bear markets. There is a considerable difference between the constant when gross returns are used and the constant when net returns are used. This difference shows that active funds have more difficulty generating excess returns compared to the market, since their costs are driving the return down. Furthermore, the constant in bear markets is substantially lower than in bull markets. It shows that active fund managers have greater difficulty generating excess returns compared to the market in bear markets than in bull markets. The difference for gross returns is 0.2824. This means that active funds generate, on average, a 0.28% lower return in bear markets when compared to bull markets, ceteris parabus. All in all, a negative alpha also means that hypothesis 3 is rejected since active funds do not earn excess returns in bear markets. This paper shows higher negative values of alpha than Carhart (1997) which can be explained by the shift towards passive investing. This shift makes it harder for active managers to generate excess returns which is in line with Anadu et al (2018).
6.4 Hypothesis 4
This section reports the results for hypothesis four concerning mean and volatility spill over effects. Note that this hypothesis focuses on volatility spill over effects between major European stock indices as well as European towards non-European. As mentioned before in the data section, table 4 shows evidence of volatility clustering for all indices except the FTSE9.
Table E in the appendix shows test results from the augmented Dickey-Fuller test and the Phillips-Perron (Phillips and Perron, 1988) test. Both tests measure stationarity. The augmented Dickey-Fuller test shows that stock index levels expressed in natural logs are non-stationary. However, index returns are considered stationary as the null hypothesis is rejected. The Phillips-Perron test corroborates these results.
Table F in the appendix reports the results of the Johansen cointegration test. The optimal lag length for this test was chosen by the Akaike information criteria and the final prediction error and equals 3. The trace statistic exceeds the critical value at 5% only at rank 1 which means that there exists 1 cointegrating relation among the five stock indices.
Table 8 below this paragraph shows the results from the vector error correction model. The coefficients for the lagged error correction term are significant for the FTSE and the ASX. This can be interpreted as an adjustment term. For the FTSE and the ASX, previous week’s
deviations from the long-run equilibrium will be corrected for in the present week at a convergence speed of 1.72% and 8.02% respectively. Furthermore, it can also be stated that German, French and US markets are first affected by external shocks and transmit these shocks to UK and Australian markets.
9 This paper follows the method of Sakthivel, Bodkhe & Kamaiah (2012) to measure volatility spill
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Table 8: Vector Error Correction Model Results
Error correction DAX FTSE CAC S&P500 ASX
LECT 0.0116 (0.64) -0.0172* (-1.93) -0.0377 (-1.42) -0.0107 (-0.94) -0.0802** (-2.35) DAX (-1) 0.1211 (1.04) 0.0758 (1.34) 0.1304 (1.14) 0.1371 (1.35) 0.1144 (1.26) DAX (-2) 0.0668 (0.57) 0.0219 (0.39) 0.0895 (0.79) 0.0135 (0.13) 0.0078 (0.09) FTSE (-1) -0.0336 (-0.40) -0.3568*** (-8.83) -0.0186 (-0.23) -0.0092 (-0.13) -0.1418** (-2.19) FTSE (-2) 0.0341 (0.63) -0.0665** (-2.54) 0.0372 (0.70) -0.0202 (-0.43) -0.0610* (-1.45) CAC (-1) -0.0632 (-0.50) 0.2755*** (4.53) -0.0753 (-0.61) 0.0434 (0.40) 0.0788 (0.81) CAC (-2) -0.2208* (-1.76) 0.0632 (1.04) -0.2496** (-2.03) -0.1468 (-1.35) -0.0897 (-0.92) S&P500 (-1) -0.1519* (-1.70) 0.3214*** (7.44) -0.1858** (-2.13) -0.3096*** (-3.99) -0.0405 (-0.58) S&P500 (-2) 0.0760 (0.81) 0.0569 (1.26) 0.0466 (0.51) 0.0804 (0.99) 0.1491** (2.05) ASX (-1) 0.1204 (1.46) 0.0472 (1.19) 0.1175 (1.46) 0.0995 (1.39) -0.0636 (-1.00) ASX (-2) 0.0609 (0.76) 0.0778** (2.01) 0.0493 (0.63) 0.0700 (1.01) 0.0737) (1.19)
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Table 9: Bivariate GARCH model between DAX and FTSE
Coefficient Z-value P-value
𝛽11 -0.0340 -0.82 0.411 𝛽21 -0.0169 -0.46 0.648 𝜃12 -0.0175 -1.27 0.203 𝜃22 0.0433 3.48*** 0.000 𝛿11 0.1891 7.08*** 0.000 𝛿22 0.1465 6.37*** 0.000 𝜑11 0.7547 23.70*** 0.000 𝜑22 0.7828 20.37*** 0.000 𝛾11 0.0338 0.45 0.653 𝛾22 0.0778 1.17 0.241
This table reports the results of the GARCH(1,1) model between the DAX and the FTSE. Results were obtained in Stata. *, ** and *** indicate significance at 10%, 5% and 1% respectively.
Table 9 above shows the results of a bivariate GARCH(1,1) case between the DAX and the FTSE. The return spill over coefficient (𝜃𝑖𝑗) is significant in one case. 𝜃22 is statistically
significant at the 1% level. This means there is evidence of mean spill over effects from the FTSE to the DAX of 0.0433. This positive relation means that the return of the DAX is positively impacted by the lagged return of the FTSE. The volatility spill over coefficients 𝛾11 and 𝛾22 are not statistically significant, hence there are no signs of volatility spill over
effects between the FTSE and the DAX. The ARCH and GARCH parameters 𝛿𝑖𝑗 and 𝜑𝑖𝑗 are
statistically significant which shows that the conditional variances of both indices depend on their own past values as well as their past errors.
Tables G until N in the appendix show the results of the remaining bivariate GARCH models. The return spill over coefficient (𝜃𝑖𝑗) is significant in some cases. For example, there is a
positive mean spill over effect from the CAC to the DAX of 0.0259. On the other hand, there exists negative mean spill over effects from the CAC to the FTSE and vice versa of -0.0264 and -0.0650 respectively. This implies that the return of the CAC is negatively impacted by the lagged return of the FTSE and the other way around.
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The volatility spill over coefficient (𝛾𝑖𝑗) is not significant in any of the bivariate GARCH
models. The sign of the coefficients is positive in all cases, which suggests a positive volatility spill over effects between indices. However, the coefficients Z-value is not high enough to reject the null hypothesis of 𝛾11 = 0. Therefore, a positive volatility spill over effect cannot be
inferred from the data at the 10% level or lower. Using an alpha of 0.25, there are significant positive volatility spill over effects from the FTSE towards the DAX and the CAC of 0.0778 and 0.1841 respectively. There is no evidence of reverse volatility spill over effects. Furthermore, there is a significant volatility spill over effect between the FTSE and ASX using an alpha of 0.20 of 0.529. It can be concluded that the FTSE is responsible for the highest volatility spill over effects when an alpha of 0.25 and 0.20 is employed. Other volatility spill over
coefficients are considerably closer to zero and therefore less significant. The fact that the FTSE contains the highest coefficient may potentially be attributable to the uncertainty concerning the Brexit and the corresponding volatility effects it causes. When relating the results to hypothesis 4, it can be concluded that there is no evidence of an increase in index correlations and thus hypothesis 4 is rejected. The findings are not in line with Sakthivel, Bodkhe and Kamaiah (2012) which implies that the European stock markets are not as integrated as other non-European stock markets such as the Indian and Japanese markets. The ARCH and GARCH parameters, 𝛿𝑖𝑗 and 𝜑𝑖𝑗, are statistically significant in all cases. This
implies that the conditional variances of the indices depend on its own past values as well as its past errors. For example, the lagged conditional variance of the FTSE explains the
volatility of the FTSE for 78%. Moreover, the volatility of the FTSE depends for approximately 15% on past errors. The conditional variance is stable since the sum of the ARCH term and the GARCH term does not exceed 1. This applies for all conditional variance of the five indices.
7. Robustness checks
Certain robustness checks are necessary to ascertain the robustness of the results. An
argument can be made that active funds used in the sample are not truly active, but basically track a given index similar to passive funds. Another robustness check addresses the
question if effects on active funds’ alpha have increased with time. Subsection 7.1 focuses on the most active funds in the sample and subsection 7.2 splits the sample based on years. 7.1 Most active funds
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To test hypothesis 1, the alphas are estimated using only funds with a higher tracking error than the median. Those alphas are then used as dependent variable and the results can be seen in table 8. Unlike the results from equation (1), this regression does not yield many significantly different results when compared to table 7. Passive investment flow is now significantly negative for bear markets when net returns are used. The magnitude of the coefficients for passive flow has decreased. Table 11 therefore shows a more nuanced view of the effect of passive flow on managers’ alpha when only the most active funds are considered. Although the magnitude has decreased, the sign remains the same, showing evidence of robustness.
Table 10: Carhart 4-factor model regression output using most active funds
Whole sample Bull markets Bear markets
Gross return Net return Gross return Net return Gross return Net return
-0.3811*** (0.0069) -0.4894*** (0.0074) -0.3565*** (0.0063) -0.4645*** (0.0065) -0.0579 (0.0479) -0.1682*** (0.0483) 𝑅𝑀𝑡− 𝑅𝑓𝑡 0.6329*** (0.0077) 0.6329*** (0.0077) 0.5505*** (0.0080) 0.5505*** (0.0080) 0.7089*** (0.0091) 0.7089*** (0.0091) 𝑆𝑀𝐵𝑡 -0.1777*** (0.0031) -0.1776*** (0.0030) -0.1979*** (0.0029) -0.1978*** (0.0029) 0.0835*** (0.0129) 0.0839*** (0.0129) 𝐻𝑀𝐿𝑡 -0.0442*** (0.0044) -0.0441*** (0.0044) -0.1318*** (0.0031) -0.1317*** (0.0031) 0.0526*** (0.0109) 0.0524*** (0.0110) 𝑀𝑂𝑀𝑡 -0.0578*** (0.0039) -0.0577*** (0.0039) -0.1579*** (0.0021) -0.1579*** (0.0021) 0.0943*** (0.0089) 0.0944*** (0.0089) R2 0.4458 0.4458 0.3705 0.3706 0.5721 0.5719
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Table 11: Regression with alpha as dependent variable using most active funds
Whole sample Bull markets Bear markets
Gross return Net return Gross return Net return Gross return Net return
𝑃𝐹𝑡−12 -0.4871*** (0.0013) -0.4799*** (0.0012) -0.078*** (0.0041) -0.0818*** (0.004) -0.0229 (0.1188) -0.0277** (0.1159) 𝑎𝑔𝑒𝑖𝑡−12 0.0658*** (0.0001) 0.0653*** (0.0001) -0.1005*** (0.0102) -0.0985*** (0.0099) -0.8356 (1.3824) -0.7988 (1.3486) 𝑠𝑖𝑧𝑒𝑖𝑡−12 3.88e-06*** (1.19e-06) 3.86e-06*** (1.18e-06) -3.34e-06 (1.89e-06) -3.28e-06 (1.86e-06) -0.00003*** (7.47e-06) -0.00003*** (7.29-06) 𝑓𝑙𝑜𝑤𝑖𝑡−12 -0.0002*** (0.00004) -0.0002*** (0.00004) 0.0002 (0.0056) 0.00002 (0.0001) -0.0001** (0.00001) -0.0001** (0.00001) 𝐸𝑅𝑖𝑡−12 0.0046 (0.0024) 0.0046 (0.0024) 0.0023 (0.0056) 0.0023 (0.0055) 0.1394** (0.0667) 0.1359** (0.0651) Within R2 0.9997 0.9997 0.9603 0.9609 0.9898 0.9903
This table presents estimates of regression coefficients following regression (3) for the entire sample, bull markets and bear markets. The sample only consists of active funds with a tracking error greater than the median. The results are obtained using time fixed effects. The regression analysis covers both gross returns and net returns for all three samples. The alphas are estimated using the Carhart 4-factor model and serve as dependent variable. All variables are lagged by 12 months except for bear markets. PF, flow and ER are depicted in percentages. Age is interpreted as the number of months an active fund is active. Size is characterized in €1 million. The numbers between brackets represent the robust standard errors for the corresponding coefficient. *** depicts statistical significance at 1% alpha level.
7.2 Differences in time
It would also be interesting to see if the coefficients change significantly when the sample is split into two based on years. Inferences can then be drawn from any significant changes and linked to developments on active fund performance. When the sample is split into two parts, the Carhart 4-factor model yields the results shown in table 12. For simplicity, only gross returns are used in the regression. The results show a clear change in the constant. Alpha has significantly decreased from -0.3909 to -0.5093. This shows that active funds have greater difficulty generating excess returns in the last few years compared to the period from 2008 to 2013. Furthermore, the coefficient for the market return decreased
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Table 12: Carhart 4-factor model regression output split by years.
First 6 years Last 7 years
-0.3909*** (0.0104) -0.5093*** (0.0047) 𝑅𝑀𝑡− 𝑅𝑓𝑡 1.0851*** (0.0084) 0.6578*** (0.0053) 𝑆𝑀𝐵𝑡 -0.3247*** (0.0037) -0.1818*** (0.0018) 𝐻𝑀𝐿𝑡 -0.3206*** (0.0049) -0.0452*** (0.0029) 𝑀𝑂𝑀𝑡 -0.1166*** (0.0026) -0.1079*** (0.0018) R2 0.6801 0.5152
This table presents estimates of regression coefficients following regression (1) for the sample split in two based on years. The first 6 years represent 2008-2013, whereas the last 7 years represent 2014-2020. The regression analysis covers gross returns. The numbers between brackets represent the robust standard errors for the corresponding coefficient. *** depicts statistical significance at 1% alpha level
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Table 13: Carhart 4-factor model regression output split by years.
First 6 years Last 7 years
𝑃𝐹𝑡−12 -0.0278*** (0.0007) -0.2834 *** (0.0004) 𝑎𝑔𝑒𝑖𝑡−12 0.2086*** (0.0006) 0.0613*** (0.0001) 𝑠𝑖𝑧𝑒𝑖𝑡−12 9.08e-06 (6.53e-06) 5.08e-06 *** (8.65e-07) 𝑓𝑙𝑜𝑤𝑖𝑡−12 0.00003 (0.0005) -0.0017*** (0.0002) 𝐸𝑅𝑡−12 0.0074 (0.0075) 0.0051** (0.0015) Within R2 0.9348 0.9847
This table presents estimates of regression coefficients following regression (3) for the sample split in two based on years. The results are obtained using time fixed effects. The regression analysis covers gross. The alphas are estimated using the Carhart 4-factor model and serve as dependent variable. All variables are lagged by 12 months. PF, flow and ER are depicted in percentages. Age is interpreted as the number of months an active fund is active. Size is characterized in €1 million. The numbers between brackets represent the robust standard errors for the corresponding coefficient.*, ** and *** depict statistical significance at 10%, 5% and 1% alpha level.
8. Conclusion
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The empirical analysis concerning the Carhart 4-factor model exhibited significant results for the four factors as well as the constant. The constant was found to be significantly negative for all samples. The results showed therefore evidence of underperformance of active funds in bull markets and bear markets. The fact that active funds show underperformance during bull markets is in line with hypothesis 2. These results are supported by Jensen (1968) and Ikenberry, Shockley and Womack (1998) whose empirical studies also showed signs of active fund underperformance. Underperformance was initially present for bear market samples. However, when the sample was split into funds based on their active share, the alpha for bear markets was not statistically significant for gross returns. This is not in line with hypothesis 3 which expected a positive alpha for bear markets. However, the existing
literature acknowledges an alpha of zero for gross returns as evidence of the zero-sum game of Sharpe (1991). Similar to Sharpe, the alpha of net returns is negative, indicating that active funds’ costs generate negative excess returns in bear markets. It can also be
concluded that the constant is significantly lower in bear markets for net returns. Moreover, alpha is lower in the last seven years of the sample compared to the first six years, showing a decreasing trend in alpha. This trend is in line with the findings of Anadu et al (2018).
The Carhart 4-factor model was then modified by omitting the constant in the regression. This led to the error term taking on the value of alpha which could then be estimated following the regression. The panel-level regression with alpha as dependent variable yielded significant coefficients for the control variables as well as the passive flow variable. The results showed that passive investment flow is negatively related to manager’s ability to select stocks over the course of a business cycle and in bull markets. The coefficient for passive flow is not significant for the bear market sample. The first robustness check confirmed the initial results, only lowering the magnitude of the effect in bull markets and for the sample as a whole. Moreover, the coefficient for bear markets is now also significant when net returns are considered. Hypothesis 1 is therefore accepted in the case of the whole sample and for bull markets. It cannot be accepted in the case of bear markets. The second robustness check also showed significant negative coefficients for passive
investment flow. It was shown that the magnitude of the negative effect of passive investment flow on alpha increased considerably over the years. The results depict the growing threat of passive funds for active managers to generate excess returns profoundly. The fact that the coefficients remain negative showed robust support for the results. Multiple bivariate GARCH(1,1) models measured the effects of mean spill over and volatility spill over between major stock indices. Error correction terms were implemented in the GARCH model and in the conditional variance equation to account for mean spill over and volatility spill over effects. The Johansen cointegration test showed 1 cointegrating relation between stock indices from the sample. The bivariate GARCH(1,1) models showed signs of mean spill over effects between several indices. However, the volatility spill over coefficient was insignificant in all models which resulted in a rejection of the null hypothesis of
hypothesis 4. This result is not in line with previous literature since most studies have found support of volatility spill over effects. However, this paper only focuses on major stock indices from developed countries, whereas the existing literature mainly focuses on volatility spill over effects from developed countries towards developing countries.
