1
Active mutual fund performance under different levels of
cross-sectional return dispersion:
a global equity market study.
Do active or passive fund perform better during periods of high or low return dispersion?
Abstract
Using a sample of 388 globally investing mutual funds we find that the funds’ risk-adjusted returns and the level of activity of the funds are positively related. However, we cannot relate this relationship to different levels of return dispersion using the equally weighted or the market-cap weighted return dispersion method. Active fund outperformance is concentrated in the lowest and middle return dispersion groups for the market-cap weighted and equally weighted methods respectively. Overall the research suggests that fund managers lack global market timing since they are not able to benefit in times when return dispersion is high. indicating for investors seeking geographical opportunities that global equity funds are not as rewarding as one would expect from a global mutual fund.
Studentnumber: 2597284 Name: Martijn Hubers Supervisor: Dr. A. Plantinga JEL codes: G11,G12,G15,G23
Key words: Return dispersion, cross-sectional volatility, global mutual funds, stock selection, active management, fund activeness.
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1. Introduction
Investors seeking investment opportunities often consider the diversification benefits for lowering the risk of their investments. One of the largest diversification opportunities can be achieved by investing in global equity funds, through these products investors are able to get access to a vast number of stocks around the world. Investing in these different stock markets lowers exposure to regional/country specific risk, thus making it an interesting investment opportunity. According to the Investment Company Institute (ICI) global equity funds are on the rise. In the United States alone the number of global equity funds increased from 1.055 funds in 2000 to 1.487 in 2015 with a growth in net assets of 272% (ICI, 2016). This indicates not only an increase in the number of global equity funds but also in allocated assets to these funds.
Investing in global equity funds requires investors to make decisions on which fund to invest in from a tremendous range of possible funds. Investors can choose between index (tracker) funds and funds which try to beat the benchmark. The funds trying to beat the benchmark do so by allocating different weights to stocks in the portfolio compared to the benchmark (e.g. the MSCI World index, FTSE All World index, STOXX 600 index or the S&P 500 index). An important distinction between these funds is their level of activeness, which shows to what extend a fund differs from its benchmark.
In order to benefit from different asset weights relative to the benchmark there has to be return dispersion. Cross-sectional volatility (henceforth referred to as return dispersion) is the standard deviation of stock or index returns within a market in a given time period. Grant and Satchell (2016) examine return dispersion and find that return dispersion is expected to be high when “variation between stock returns (squared dispersion) is high, when average stock variance is high, and when the correlation between stocks is relatively low” (Grand & Satchell, 2016). During periods of low return dispersion the opportunities for active funds to outperform their benchmark are fewer. As return dispersion increases the potential outperformance of the active funds increases through more opportunities to pick stocks.
risk-3 adjusted returns. All these papers did their research using stock return data within a single country or economic region. However, investors also have the opportunity to invest on a global scale through different international or global equity funds where managers not only look at specific stocks, but also to specific regions of the world or industry sectors.
The presence of return dispersion, particularly high return dispersion, indicates different returns among country indexes. Being able to benefit from these differences in returns indicates the ability to time the market. The effective use of market timing is what distinguishes active funds, since they try to beat the benchmark by investing in the right country at the right time. As the aforementioned papers have shown that the performance of active funds is influenced by return dispersion on a regional/country specific level, we suspect this may also be the case on a global level.
Answering this question gives insight into the relationship between return dispersion and the performance of active global equity funds. It also sheds light on the ability of fund managers to time the market. This helps investors decide when to invest in which fund under different levels of return dispersion. For a fund manager such insights in return dispersion and its relationship with performance of the fund he manages can help him justify decisions he made and help explain returns of the fund.
market-4 capitalization (hereafter referred to as market-cap) weighted constituents returns. Using monthly return data the different portfolios of active mutual funds are linked to the three return dispersion groups through the matching months. Consequently, the alpha (henceforth referred to as risk-adjusted return) of a multifactor regression of the activeness portfolio’s returns over the Fama French Carhart model, from now on referred to as FFC, are estimated and used as the performance indicator of the fund portfolios.
Using a sample of 388 global equity mutual funds we find no evidence of a relationship between return dispersion and fund performance. In addition we find evidence of a relationship between fund performance and its activeness. In the lowest dispersion group the most active funds outperform the more passive funds while still earning a negative risk-adjusted return under market-cap weighted return dispersion. moreover, using equally weighted return dispersion we find positive risk-adjusted returns for the most active funds. We find no evidence of global market timing skills among fund managers. During months of high variation among index returns the managers fail to benefit from this opportunity. One possible explanation for this lack of market timing is their focus on diversifying on the sector level rather than a country level. Diversification on different sectors may provide geographical diversification benefits however, when geographical diversification is not the goal it is reasonable the managers lack the market timing because they do not seek geographical risk-reducing opportunities.
The paper is structured as followed: Section 2 discusses relevant literature, Section 3 describes the methodology used, Section 4 describes the data, Section 5 presents the results, Section 6 contains robustness checks and Section 7 discusses the findings and concludes the paper.
2. Literature review
Earlier papers such as Carhart (1997), Gruber (1996) and Malkiel (1995) observe that mutual funds struggle to meet the performance of the benchmark and even underperform their benchmark after expenses are taken into account. However these findings are not consistent across all the literature, a lot of which is written on the performance of US focused funds and to lesser extent on European or global markets.
5 method, which was introduced by Grinblatt and Titman in 1989. Cumby and Glen (1990) do not find evidence of any outperformance of the funds over the benchmark, which is consistent with the aforementioned papers by Carhart (1997), Gruber (1996) and Malkiel (1995). Gallo and Swanson (1996) also study the performance of 37 US-based international mutual funds. Like Cumby and Glen (1990), they use two methods for calculating the benchmark returns: the international arbitrage pricing theory (IAPT) and an international two-index model. Their paper shows different results. Gallo and Swanson (1996) find superior performances of the international funds but the risk adjusted returns resulting from the IAPT method are more positive and significant than the risk adjusted returns resulting from the index model. Detzler and Wiggins (1997) also find outperformance of the funds in their sample but this outperformance is over an inefficient world index. Using their alternative benchmark, consisting of twelve countries, they do not find superior returns.
International diversification and its opportunities are not limited to international mutual funds. Like mutual funds, pension funds are able to diversify by investing in the international markets as well. Blake and Timmermann (2005) examined the performance of 247 UK-based pension funds. They find underperformance of the pension funds relative to the relevant regional benchmarks. This underperformance is even greater than studies find on pension fund performances relative to the UK market. Their study shows the cause of this underperformance lies with “unsuccessful market timing attempts, i.e. by systematic -and ex post misjudged- changes in the portfolio weight across international regions” (Blake and Timmermann, 2005).
In addition, Kaushik (2013) discusses the performance and persistence of US international active mutual funds. His research is in response to the recent surge in international diversification opportunities sought by investors willing to diversify appropriately. He finds that most of the funds in his sample, which ranges from 1992 to 2011 and consists of 570 funds, do outperform the benchmark. This outperformance indicates the ability of active managers to exploit opportunities in the market. The evidence on persistence of performance is mixed; only a few groups of funds are able to persist their performance.
6 (moving funds between country equity markets). They find no evidence of world market timing. However, they do find evidence of national market timing, though only in Japan. Another relevant study on performance of international and global funds was done by Breloer, Scholz and Wilkens (2014). They analyze the impact of country and sector momentum on the returns of 366 international funds and 124 global funds by adding a country and sector factor to the Fama and French three-factor model. The addition of the country and sector factors affects the performance of the funds negatively, supported by evidence of a strong influence of the added factors on the fund returns. On average Breloer, Scholz and Wilkens (2014) find fund underperformance to their benchmark, which is amplified by the inclusion of index momentum factors.
Furthermore, Tsai and Wu (2015) study the performance of international and global funds using control variables for country and style. The addition of region and style factors decreases abnormal returns of both international and global funds and their ability to select securities. Moreover, the total performance of the mutual funds is negative and significant.
7 that closet indexing has increased in popularity since 2007 and finds that only the most active stock pickers outperform their benchmark. Additionally he finds that active stock selection is most successful during high cross-sectional dispersion of stock returns.
Another method of measuring activeness was introduced by Amihud and Goyenko (2013). They suggest that the performance of a fund can be measured by its 𝑅2 which is obtained from a regression of the fund’s return on a multifactor model. Using this method, they find that more active funds have a higher risk-adjusted return. Smith (2014) researches the performance of equity-oriented hedge funds under different cross-sectional stock market return dispersion environments, using both active share and the 𝑅2 to measure activeness of the fund. Consistent with papers on mutual funds, he finds that performance of the hedge funds is strongly related to the level of return dispersion. According to his paper, the hedge funds earn significantly higher risk-adjusted returns during times of high return dispersion.
Von Reibnitz (2015) finds similar results in her paper on cross-sectional return dispersion and active fund performance. In her study on the US market she finds that during periods of high return dispersion the most actively managed fund earn the highest risk-adjusted returns. In contrast, during periods of low dispersion “the difference in performance between the most and least active funds is not generally significant” (Von Reibnitz, 2015).
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3. Methodology
The objective of this paper is to identify whether passive or active funds perform better during periods of high or low return dispersion. Answering this question requires a combination of three separate calculations. First and second, the data on return dispersion and the level of fund activeness are separately calculated. Finally, the results of these calculations are combined to determine the performance of the fund portfolios under different return dispersion levels.
3.1 Cross-sectional return dispersion
To calculate cross-sectional return dispersion we require data on index returns in the period January 2005 - December 2015 on the FTSEAW, consisting of 45 country indexes (excluding Qatar and United Arab Emirates). The index returns will be collected using Datastream. The return dispersions are calculated following Von Reibnitz (2015) using the following formula:
𝑅𝐷𝑡 = √ 1 𝑛−1∑ (𝑅𝑖𝑡− 𝑅𝑚) 2 𝑛 𝑖=1 (1)
The formula above show the equally weighted return dispersion method. Where 𝑅𝑖𝑡 the return of the country index and 𝑅𝑚 is the return of the FTSEAW. Next to the equally weighted index return dispersions we calculate the return dispersions using market-cap weighted index returns as well. This provides the following formula:
𝑅𝐷𝑡 = √ 1 𝑛−1∑ ((𝑅𝑖𝑡∗ 𝑤𝑖) − 𝑅𝑚) 2 𝑛 𝑖=1 (2)
Where 𝑤𝑖 is the weight of the country index in the FTSEAW based on the market-cap of the FTSEAW and the country index. By using market-cap weighted returns we control for differences in index market-capitalizations, as large return dispersion in the larger indexes can have significant effects on the performance of the index. Therefore the aforementioned weights have to be accounted for in the return dispersion calculation. Measuring return dispersion using both methods allows us to see if the method used influencing the study. Big differences in return dispersion might indicate an over- or underweighting of specific indexes. Using both methods allows us to compare the results.
9 month indicates changes in the return dispersion environment and enables him to react to this change. The same is true for investors who can use the 𝑅𝐷𝑡−1 to decide in which fund to invest. Subsequently, the months are divided into three dispersion environment groups ranging from low (G1) to high (G3) return dispersion. The first group (G1) consists of the 44 months with the lowest return dispersion moving through group two (G2) to group (G3) containing the 44 months with the highest return dispersion.
3.2 Level of activeness
To determine the level of activeness of the mutual funds we use the method of Amihud and Goyenko (2013) called selectivity. The advantage of their method is that is does not require information on the portfolio compositions of the mutual funds or the benchmark. The method regresses the returns of the mutual funds over a multifactor (Fama, French and Carhart) model. The resulting 𝑅2 of the regression represents the amount of fund variation explained by the multifactor model. If the resulting 𝑅2 is low it means the fund diverges from the benchmark and thus is more active. Consequently, selectivity is measured as:
Ω = 1 − 𝑅2 = 𝜎𝑒2
𝜎𝑖2 = 𝜎𝑒2
𝜎𝑏2+𝜎𝑒2 (3)
Where 𝛺 represents the level of selectivity, 𝜎𝑖2 the overall variance of the fund’s returns, 𝜎𝑏2 the total variance resulting from the benchmark factors and 𝜎𝑒2 is the error term variance which denotes the idiosyncratic risk. The more a fund’s volatility is driven by systematic sources, the benchmark, the higher the fund’s 𝑅2. As a fund moves from systematic sources to idiosyncratic sources, the fund’s 𝑅2 decreases since less of its variation is explained by the factors of the benchmark.
The 𝑅2 used for the measurement of activeness among funds comes from a 24-month rolling regression of the fund’s return on the Fama, French and Carhart model (FFC). This model is a combination of the Fama and French three-factor model (1993) and the Carhart model (1997) which adds a fourth momentum factor to the Fama and French model:
10 𝑡, which is represented by the FTSEAW. 𝑆𝑀𝐵𝑡, 𝐻𝑀𝐿𝑡 and 𝑀𝑂𝑀𝑡 are the returns to the size, book-to-market and momentum factors in month 𝑡. The four factors are collected from Kenneth French’s data library.
Next, the funds are ranked each month t based on their selectivity which is based on 𝑅𝑡−12 , where 𝑅𝑡−12 is acquired through regressing the FFC model over 24 months prior to month 𝑡. We use 𝑅𝑡−12 since investors choose the funds ex ante, considering they do not know the 𝑅2 of the present month. Funds are then sorted into three equally weighted selectivity portfolios based on their ranking, ranging from low selectivity (S1) to high selectivity (S3). The three selectivity portfolios contain the equally weighted average returns of the mutual funds per month t. Besides the three portfolios we construct a comparison portfolio (S3-S1) which contains the differences in average fund returns between S3 and S1 in month t.
3.3 Fund performance
After the funds are sorted into the three selectivity portfolios, the performance of the funds in month t can be related to the corresponding return dispersion group. We link the selectivity portfolios and the return dispersion groups based on the months in the sample. For each month we know the level of return dispersion and which returns are generated in the selectivity portfolios in that specific month. This provides three unique selectivity portfolios for each level of return dispersion.
After linking the different portfolios to the dispersion groups, the average returns in excess of the risk free rate are regressed over the FFC model Eq.(4) over the months in the matching dispersion group. The intercept 𝛼𝑖, resulting from the regression, measures the risk adjusted performance of the selectivity portfolios. The method enables us to examine whether the performance of funds with different levels of activeness are affected by different levels of return dispersion.
4. Data
4.1. Mutual fund data
11 database provided by Morningstar. The selection comprises globally active funds focusing on large-capitalization value, growth and mixed stocks as well as mutual funds focusing on small-capitalization stocks.
12 The Morningstar database includes an overview of the top 5 regions in which funds are active:
Table 1. Geographical allocation of funds
Geographical focus % Geographical allocation Number of fund investing in region
US 58% 376
UK 8% 316
West Europe 15% 369
West Europe - non euro 6% 260
Asia developed 3% 136 Asia emerging 3% 101 Japan 8% 267 canada 1% 30 Latin America 0.2% 9 Australasia 0.2% 9 Middle East 0.1% 4 Africa 0.1% 4 Emerging Europe 0.1% 3 Total 100%
The table reports the share of the geographical regions defined by Morningstar. In the total set of funds a total of 378 allocations is given. Percentages shown are the percentage of allocation to a specific region in terms of the total allocation. Note that these percentages are an observation at a given point in time, at times of rebalancing these geographical allocations are prone to change.
As table 1 shows, more than half of the funds allocate their assets to the United States. The remaining assets are allocated to Western Europe which use the euro as currency, the Eurozone, the United Kingdom and Japan. Overall, most of the funds’ assets are allocated to developed countries.
After creating the sample using the Morningstar database, the funds’ monthly returns are collected using Datastream, which provides the monthly returns denoted in euros.
4.2 Fama,French and Carhart model Data
The model used for estimating the 𝑅2 for selectivity is the FFC model. The data on the FFC is collected from Kenneth French’s1 database library with the exception of 𝑅
𝑚𝑡 and 𝑅𝑓𝑡 which are the monthly returns on the FTSEAW and the monthly yield on the German 10-year government bond, which is regarded as the European risk-free rate. The remaining returns 𝑆𝑀𝐵𝑡 , 𝐻𝑀𝐿𝑡 and 𝑀𝑂𝑀𝑡 are the size, book-to-market, and the momentum returns respectively. Where momentum is calculated as prior winners minus prior losers. The FFC model is estimated using Eq.(4).
13 Since the returns of the FFC model collected from Kenneth French’s database library are denoted in US dollars, we have to convert the returns to euros using the following formula:
𝑅𝑒𝑡𝑢𝑟𝑛𝐹𝐹𝐶𝑒𝑢𝑟𝑜𝑠 = [(1 + 𝑅𝑒𝑡𝑢𝑟𝑛𝐹𝐹𝐶𝑈𝑆$)) ∗ (1 + 𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑈𝑆$ (𝐸𝑢𝑟𝑜)] − 1 (5) Nearly all the mutual funds in the sample use the MSCI World index as the benchmark for their returns. Unfortunately, due to access limitations in Datastream we were unable to collect data on the market capitalization of the constituents of the MSCI World index. This required us to search for an alternative benchmark. The FTSE All World index (FTSEAW) is a world index similar to the MSCI World index. Whereas the MSCI World index has 23 constituents, the FTSEAW has 45 (after correcting for missing data on Qatar and the United Arab Emirates). A correlation analysis on the net returns of the indices shows that the FTSEAW and the MSCI World index correlated virtually perfectly with a correlation of 0.996.
Table 3. Correlation matrix benchmark indices.
FTSE All World index MSCI World index
FTSE All World index 1
MSCI World index 0.996 1
Table 3 shows the correlation matrix between the FTSE All World index and the MSCI World index.
As mentioned earlier the rate used for the European Risk-free rate is the monthly yield of the German 10-year government bond. Nonetheless, the use of the German bond as a suitable proxy for the risk-free rate is subject of debate. This is due to quantitative easing by the European Central Bank keeping bond yield artificially low. Still, we believe that the German 10-year government bond is a useful proxy because the research was done with European investors in mind. This bond is available to all investors, unlike other possible risk-free rate proxies such as interbank rates like EURIBOR.
4.3 Selectivity Data
14 Figure 1. Histogram and Descriptive statistics 𝑹𝒕−𝟏𝟐
Mean Median Standard deviation Min Max N
𝑹𝒕−𝟏𝟐 0.59 0.60 0.15 0.012 0.99 38.973
The graph and table above show the composition of the estimated 𝑅𝑡−12 . The fund’s monthly 𝑅𝑡−12 is estimated using a
24-month rolling regression of the funds’ excess return over the FFC model over the period January 2005 to December 2015. The sample consists of 338 actively managed global mutual funds. Frequency represents the number of observed
𝑅𝑡−12 while N is the total number of observations.
The average 𝑅𝑡−12 of the funds is 59% yet the estimated 𝑅𝑡−12 differ significantly among the observed estimates. The minimum value observed is 1.2% and the maximum approaches 100%. We observe a negatively skewed dataset, both observed from the histogram and descriptive statistics in Fig.1. The median shows that for the majority of mutual funds, the variation in returns can be explained for 60% by the benchmark.
It is unclear whether the funds with a high or low 𝑅𝑡−12 are actually passive or active, or if they use schemes which are positive or negatively related to the factors used in the FFC model. Moving on with 𝑅𝑡−12 as the estimator of a fund’s relation to the benchmark, we believe that on average the funds are reasonably active when compared to the estimated 𝑅𝑡−12 (91% on average) of the US-focused funds Von Reibnitz (2015) finds.
15 4.4 Return dispersion data
The benchmark used in this paper is the FTSEAW2 index with its 45 countries. The constituents of the FTSEAW are used for calculating the return dispersion using equations (1) and (2). We use the returns of the FTSEAW and its constituents, collected from Datastream. Nearly all worldwide investments are included in the FTSEAW. Its constituent composition is unlikely to change frequently, as is the case with stock indices in which stocks are added and dropped on a regular basis. For a constituent to be removed from the index, severe country-specific events have to take place such as bankruptcy of the country. Therefore, we can assume that the constituents given at the moment of data collection are a good reflection of the benchmark for the entire range of 11 years. Because we use both the equally weighted and market-cap weighted approach we need to calculate the weights of the different constituents on the FTSEAW, using the market-cap of the full index and the constituents. Because no returns or market capitalizations of Qatar and the United Arab Emirates (UAE) were available, we have to recalculate the market-cap of the FTSEAW without these countries.
Table 4. below displays the 45 countries comprising the FTSEAW with the average percentage weight on the benchmark over the full sample period, based on the market-cap of both the FTSEAW and the constituents. The United States represents the greatest part of the benchmark with 46.5%, Together with the rest of North America (Canada and Mexico) they represent half of the benchmark (50.3%). Europe and Asia have a combined weight of around 40% of which Europe covers the greater share with 25.5%. The rest of the world, including Australia and South American countries, complete the Benchmark.
16 Table 4. Average weight in FTSE ALL-WORLD INDEX
Country index Percentage of full index Country Index Percentage of full index
Canada 3.2% South Korea 1.6%
Australia 2.8% Malaysia 0.4%
Austria 0.1% Netherlands 1.3%
Belgium 0.4% New Zealand 0.1%
Brazil 1.4% Norway 0.3%
Czech Republic 0.0% Peru 0.0%
Chile 0.2% Poland 0.1%
China 1.4% Portugal 0.1%
Columbia 0.1% Russia 0.6%
Denmark 0.4% South Afrika 0.9%
Egypt 0.1% Spain 1.5% Finland 0.4% Sweden 1.1% France 4.1% Switzerland 3.0% Germany 3.2% Turkey 0.1% Greece 0.1% UK 8.7% Hong Kong 1.5% US 46.5% Hungary 0.1% Mexico 0.6% India 0.9% Pakistan 0.0% Indonesia 0.2% Philippines 0.1% ireland 0.2% Singapore 0.5% Isreal 0.2% Taiwan 1.3% Italy 1.3% Thailand 0.2% Japan 8.4%
North America 50.3% Asia 16.6%
Europe(incl. Eurozone) 25.5% Rest of the world 7.6%
Eurozone 12.8%
FTSE all-world Index 100.0%
The table reports the average weights of all constituents in the FTSE all-world index. As the table shows the largest part of the index consists of North America, of which the United States itself is responsible for 46.5%. Europe, including the Eurozone and the United Kingdom, and Asia are the next most prominent regions. The rest of the world comprises countries not directly related to an economic region of notable size.
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Figure 2. Equally- and market-cap weighted return dispersion
Figure 1 outlines the return dispersion of both the equally weighted and the market-cap weighted method using the constituents of the FTSEAW index over the period 1-1-2005 to 1-12-2015. The graph shows that using the equally weighted method, return dispersion is higher compared to the market-cap weighted method.
Figure 2 shows return dispersion normally between 0 and 10%, with spikes during the financial crisis in 2008-2009 and to a lesser extent between 2011 and 2012 during the debt crisis in Europe. The market-cap weighted method displays lower return dispersion than the equally weighted method, especially during the financial crisis. As smaller countries with lower market-cap are weighted more heavily using the equally weighted method, their returns have a bigger impact on the return dispersion. For example, Greece was profoundly affected by the financial crisis, showing large losses on its stock market. Its effect on the return dispersion is larger under the equally weighted method (2%) compared to the market-cap method (0.1%), since the country is weighted more heavily by the first method.
18 Table 5. Descriptive statistics Return dispersion groups.
EQ1 EQ2 EQ3 EQ Full sample
Mean 1.18% 3.60% 8.51% 4.42% Standard Error 0.08% 0.13% 0.58% 0.33% Median 1.22% 3.72% 7.77% 3.72% Standard Deviation 0.56% 0.86% 3.86% 3.82% Kurtosis -0.82 -1.33 8.98 7.44 Skewness -0.28 -0.19 2.50 2.09 Minimum 0.11% 2.14% 4.95% 0.11% Maximum 2.07% 4.93% 26.03% 26.03% Count 44 44 44 132 MW1 MW2 MW3 MW Full sample Mean 0.92% 2.67% 6.91% 3.50% Standard Error 0.08% 0.09% 0.47% 0.27% Median 0.92% 2.54% 6.09% 2.54% Standard Deviation 0.52% 0.61% 3.08% 3.11% Kurtosis -1.39 -1.08 5.02 4.89 Skewness -0.01 0.33 1.75 1.83 Minimum 0.11% 1.80% 3.83% 0.11% Maximum 1.70% 3.75% 19.50% 19.50% Count 44 44 44 132
The table reports the monthly return dispersions per group and the full sample. The groups are created by ranking the months according to the return dispersion at the end of the previous month (𝑅𝐷𝑡−1) each group containing 1/3 of the
months in the sample. The three groups range from low return dispersion (EQ1, MW1) to high return dispersion (EQ3, MW3).
The reported descriptive statistics shown above indicate that the average return dispersion in the highest groups is 8.51% and 6.91% for the equally weighted and market-cap weighted groups, respectively.
5. Results
19 are the different levels of return dispersion, where G1 represents the lowest and G3 the highest return dispersion group for both tables.
Table 6 reports a positive relationship between fund performance and the level of fund activeness. The lowest selectivity portfolio (S1) returns insignificant risk-adjusted returns in all three return dispersion groups as well as the full sample. The portfolio with the medium selectivity funds (S2) returns a positive risk-adjusted return in the medium return dispersion group (G2). The same is true for the most active funds (S3). Portfolios S2 and S3 earn comparable risk-adjusted returns of 10.65% and 11.61% respectively. The comparison portfolio S3-S1 shows no significant values for risk-adjusted returns. Regressing the full sample over the FFC model yields a risk-adjusted return of 10.46% in the second dispersion group (G2). The funds do not show increased risk-adjusted returns resulting from increases in return dispersions, observed by insignificant results in the highest dispersion group (G3).
Table 6. FFC Risk-adjusted returns: equally weighted return dispersion and fund performance.
S1 S2 S3 s3-S1 Full sample G1 -5.47 -4.57 -4.83 0.67 -4.95 (-1.00) (-0.87) (-1.00) (0.45) (-0.97) G2 9.17 10.65* 11.61* 2.25 10.46* (1.53) (1.72) (1.83) (1.37) (1.71) G3 -4.93 -4.84 -4.28 0.68 -4.73 (-1.08) (-1.02) (-0.91) (0.48) (-1.02) Full sample -2.54 -1.82 -1.29 1.28 -1.93 (-0.89) (-0.58) (-0.42) (1.37) (-0.65)
This table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the Fama, French and Carhart model over the period January 2005 - December 2015. The selectivity
portfolios resulted from sorting the funds according to their 𝑅𝑡−12 every month t, which is obtained from a rolling
regression of the fund’s excess returns on the FFC factors over the 24 months prior to month t. The sorting produces three selectivity portfolio portfolios where S1 holds the lowest selectivity funds and S3 holds the funds with the highest selectivity. Subsequently, each month t the average risk-adjusted return is calculated for the selectivity portfolios which in turn is linked to the level of return dispersion for month t. Like the selectivity portfolios, the equally weighted return dispersions are ranked from low (G1) return dispersion to high dispersion (G3) at the end of the month preceding month t (𝑅𝐷𝑡−1). S3-S1 represents the cross-sectional difference in risk-adjusted return between the portfolio with the
20 Table 7 displays that the most active funds outperform less active funds in terms of risk-adjusted returns. The columns S1, S2 and S3 all show negative risk-adjusted returns for the selectivity portfolios in the lowest market-cap weighted return dispersion group (G1). We find significant risk-adjusted returns of -10.39% in the least active portfolio (S1). This is also the case in the other two selectivity portfolios S2 and S3, earning risk-adjusted returns of -9.69% and -9.49% respectively. All risk-adjusted returns are found to be significant on a 10% level. Similarly to the equally weighted regressions there are no risk-adjusted returns found for the comparison portfolio S3-S1. The full sample shows significant results similar to the three portfolios in the lowest dispersion group(G1) where the full sample returns a negative return of -9.86%. Table 7 does not provide evidence of increased benefits of actively managed funds caused by increased return dispersion, observed from insignificant data in higher return dispersion groups G2 and G3.
Table 7. FFC Risk-adjusted returns: market-cap weighted return dispersion and fund performance.
S1 S2 S3 S3-S1 Full sample G1 -10.39* -9.69* -9.49* 0.99 -9.86* (-1.91) (-1.80) (-1.83) (0.62) (-1.86) G2 4.31 6.03 7.34 2.92 5.86 (0.73) (0.90) (1.14) (1.63) (0.93) G3 -1.17 -0.84 -0.62 0.56 -0.94 (-0.29) (-0.20) (-0.15) (0.40) (-0.23) Full sample -2.54 -1.82 -1.29 1.28 -1.93 (-0.90) (-0.59) (-0.42) (1.37) (-0.65)
This table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the Fama, French and Carhart model over the period January 2005 - December 2015. The selectivity
portfolios resulted from sorting the funds according to their 𝑅𝑡−12 every month t, which is obtained from a rolling
regression of the fund’s excess returns on the FFC factors over the 24 months prior to month t. The sorting produces three selectivity portfolio portfolios where S1 holds the lowest selectivity funds and S3 holds the funds with the highest selectivity. Subsequently, each month t the average risk-adjusted return is calculated for the selectivity portfolios which in turn is linked to the level of return dispersion for month t. Like the selectivity portfolios, the market-cap weighted return dispersions are ranked from low (G1) return dispersion to high dispersion (G3) at the end of the month preceding month t (𝑅𝐷𝑡−1). S3-S1 represents the cross-sectional difference in risk-adjusted return between the
21 Table 6 and 7 show differences in risk-adjusted returns and levels of return dispersion at which these returns are earned. The equally weighted setting demonstrates positive risk-adjusted returns in the middle dispersion group (G2), while the market-cap weighted return dispersion test returns negative risk-adjusted returns in the lowest dispersion group (G1). We observe a positive relationship between the performance of funds and the selectivity level of the funds for both return dispersion methods, with significant outperformance of 0.2% and 0.96% using market-cap and equally weighted methods respectively.
The results show no evidence of a relationship between return dispersion and active fund performance, because no increases in risk-adjusted returns are observed in higher levels of return dispersion compared to lower levels of return dispersion.
6. Robustness Checks
To test for validity of the study two additional tests on the performance of the mutual funds are performed. In addition to Carhart’s four factor model Eq.(4) we test the performance of the mutual funds using the Fama and French three-factor model (FF model) and the Capital Asset Pricing (CAPM) single-factor model. Testing the performance with the CAPM and the FF model enables us to detect possible factor loading on momentum, size or value. The two tests are carried out in both the equally and the market-cap weighted return dispersion environments. The results of the tests are found in Appendix A.
6.1 Fama and French three-factor model
The Fama and French three-factor model (Fama and French, 1993) consists of three factors: market risk premium (𝑅𝑚𝑡− 𝑅𝑓𝑡), size expressed as small minus big market capitalization (𝑆𝑀𝐵𝑡) and High minus low book-to-market (𝐻𝑀𝐿𝑡) which represents value.
22 The results show no significant risk-adjusted returns in the equally weighted return dispersion environment. Using market-cap weighted return dispersion we do find significant risk-adjusted returns in contrast to the equally weighted return dispersion. Table A.2. reports significant results only in the lowest dispersion group(G1) for S1 and S2 and in the middle dispersion group for S3. The risk-adjusted return for selectivity portfolio S2 is larger than the one for portfolio S1. Although the results are limited to the two least active selectivity portfolios, a positive relationship between fund performance and the level of activity is observed.
Tests based on the risk-adjusted returns of the fund portfolios under the equally and market-cap weighted return dispersion methods both lack adequate proof of a relationship between active fund performance and return dispersion using the FF model.
6.2 Capital asset pricing model
The capital asset pricing model is a single factor model where risk-adjusted returns are estimated using only the market risk premium. The model evolved from the earlier work of Markowitz on portfolio theory and is independently created by Sharpe (1964), Lintner (1965) and Mossin (1966).
𝑅𝑖𝑡− 𝑅𝑓𝑡= 𝛼𝑖+ 𝛽𝑖𝐸[𝑅𝑚𝑡− 𝑅𝑓𝑡] (6)
Where 𝑅𝑖𝑡 is the return of fund i in month t, 𝑅𝑓𝑡 is the European risk-free rate in month t, which is the German 10-year government bond and 𝑅𝑚𝑡 is the return on the FTSEAW t in month t.
Tables A.3. and A.4. in the appendix show annualized risk-adjusted returns using the CAPM model based on equally weighted and market-cap weighted return dispersion methods.
The risk-adjusted returns we find under all levels of equally weighted return dispersion are insignificant, hence there is no evidence of any risk-adjusted returns of the funds during the different levels of equally weighted return dispersion. The absence of significant risk-adjusted returns rejects not only the relationship between the performance of funds and return dispersion but also one between the level of fund activeness and fund performance.
23 outperform the other two fund portfolios S1 and S2, indicating a relationship between fund activeness and fund performance. Although we perceive a relationship between fund performance and the level of activeness, there is no evidence of a relationship between the performance of active funds and the level return dispersion.
6.3 Validity
Using the Fama and French three-factor model and CAPM model we find robust evidence for the results using the FFC model. Using equally weighted return dispersion, neither the FF nor the CAPM models show significant risk-adjusted returns in all the dispersion groups. This challenges the findings using the FFC model as we find risk-adjusted returns in the medium dispersion group3. The challenging results of the CAPM and FF models may be a result of larger factor loading on the momentum factor by fund managers. The difference between the FFC model and the two robustness models are only observed in the return dispersion group (G2) for S2, S3 and in the full sample. Even though these are the only observed risk-adjusted returns, the differences between the models is small since no differences were observed in the other return dispersion groups. When testing the performance of the selectivity portfolios using the market-cap weighted return dispersion, we find risk-adjusted returns in the lowest return dispersion group (G1) using the CAPM and FF models. This indicates a relationship between the level of activeness and performance of the funds that is even stronger than those found using the FFC model, based on the levels of significance. Because there is no evidence of increasing fund performance when return dispersion increases, we cannot determine a relationship between return dispersion and active fund performance.
The results are in line with the results from the FFC model when return dispersion is based on the market-cap method. Although the returns differ among the models, there is no substantial difference amongst the models. This indicates that the findings using the FFC model are robust to changes in factors. When using the equally weighted return dispersion method, the findings using the FFC model are only partly supported by the results of CAPM and FF models, reducing the strength of the FFC test.
24
7. Conclusion and discussion
Using a sample of 388 globally investing mutual funds we test the relationship between the level of fund activeness and fund performance under different levels of index return dispersion. We find a relationship between funds’ risk-adjusted returns and the level of activity. However, we cannot relate this relationship to different levels of return dispersion using the equally weighted or the market-cap weighted return dispersion method.
The evidence for a positive relationship between fund activeness and fund risk-adjusted returns is obtained in both the equally and market-cap weighted return dispersion methods. Although the observed risk-adjusted returns using the market-cap weighted return dispersion method are negative among all selectivity portfolios the more active funds report the highest risk-adjusted returns. The negative risk-adjusted returns imply underperformance of the funds relative to the FTSEAW benchmark. The negative risk-adjusted returns for all selectivity portfolios in the lowest return dispersion may indicate an overall negative sentiment on the benchmark. This suggests that there are hardly any stock picking opportunities that fund managers can use to increase the performance of the fund.
Additionally, using a method of equally weighted return dispersion we find weak evidence of outperformance of the most active funds over less active fund and the full sample. We detect large positive risk-adjusted returns representing an outperformance of the more active funds over the FTSEAW benchmark. The outperformance is observed in the middle dispersion group which suggests evidence of stock picking abilities with the presence of medium return dispersion.
The research does not provide evidence of a relationship between the level of activeness of funds and return dispersion. The results do not show an increase in returns when higher return dispersion is reached under both return dispersion calculation methods. This is in contrast to the findings of Von Reibnitz (2015). She finds that active funds perform best when return dispersion is high. Additionally, Tsai and Wu’s (2015) findings are partially confirmed. They find negative significant returns of global and international funds, which is also the case in this paper but not to the same extent as Tsai and Wu’s (2015) findings.
25 index returns active managers ought to perform best in these situations. Managers fail to identify countries with higher index returns, causing them to miss profitable index picking opportunities. There are a number of possible reasons for the absence of market timing abilities among active fund managers. Firstly, fund managers might lower their exposure to volatility when return dispersion is high, since this also means that the risks of the equity positions are higher for the funds. During times of lower return dispersion fund managers may be willing to make more active bets since their risk is also lower compared to times of higher return dispersion.
Secondly, fund managers may not base their diversification choices on geographical details but rather on their asset allocation on sector exposure. Increasing integration of economies between countries and aiding policies on globalization decreases possible advantages for country diversification advantages. This gives us reason to suspect fund managers choose to diversify across industries rather than countries. In their study on the importance of country and industry factors, Cavaglia, Brightman and Aked (2000) find evidence of the increasing importance of industry factors. Moreover, they find that diversification across industries proves to be more effective in risk reduction compared to country diversification.
Thirdly, the global market gives funds an enormous range of stocks from which to select. Therefore, the influence of higher return dispersion may be small since fund managers already have the option to choose stocks with different returns. This would explain the significant positive risk-adjusted returns found in the middle dispersion groups under the equally weighted method. This is a plausible explanation since the reason why investors choose global and international funds in the first place is because of their diversification possibilities (Kaushik, 2013).
Research on return dispersion and global funds holds significant potential both in theory and in practice. An increasing number of papers (e.g. Ankrim & Ding (2001), Smith (2014) and Von Reibnitz (2015)) show evidence that return dispersion should be accounted for when making investment decisions. Additionally, the increased popularity of international and global funds indicates its practical relevance, as supported by Tsai and Wu (2015).
26 what parts of the international and global funds are influenced by return dispersion. Amihud and Goyenko (2013) have done so finding positive relations between fund size and their selectivity. It is also preferable as to control for country and sector momentum as Breloer, Scholz and Wilkens (2014) do.
The funds discussed here are all European global and international funds. Including US international and global funds would improve future research by not only increasing the number of observations but also the number of fund characteristics considered. Another limitation of this paper to bear in mind is the considerable survivorship bias inherent to the Morningstar database. Using a dataset free of survivorship bias increases the credibility of the research.
27
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Appendix
Appendix A.Table A.1. FF risk-adjusted returns: equally weighted return dispersion and fund performance
S1 S2 S3 S3-S1 Full sample G1 -4.33 -3.67 -2.89 1.49 -3.64 (-0.85) (-0.72) (-0.60) (0.98) (-0.73) G2 8.61 9.16 9.38 0.71 9.02 (1.45) (1.43) (1.44) (0.46) (1.44) G3 -4.86 -4.79 -4.33 0.55 -4.70 (-1.04) (-0.98) (-0.89) (0.41) (-0.99) Full sample -2.00 -1.47 -0.90 1.13 -1.49 (-0.70) (-0.46) (-0.28) (1.14) (-0.49)
The table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the Fama and French three-factor model over the period 2005-2015. The selectivity portfolios resulted
from sorting every month t the funds according to their 𝑅𝑡−12 , which is obtained from a rolling regression of the fund’s
excess returns on the FFC factor model over the 24 months prior to month t. The sorting produces three selectivity portfolio groups where S1 hold the lowest selectivity funds moving to S3 which hold the funds with the highest selectivity. Each portfolio covers 33% of the full set of Funds. Which correspond to the months in the return dispersion groups. Similarly to the selectivity portfolios, the equally weighted return dispersions are ranked from low (G1) Return dispersion to High dispersion (G3) with 33% of the month in the data set at the end of the month preceding month t (𝑅𝐷𝑡−1). S3-S1 represents the cross-sectional difference in risk-adjusted returns between the portfolio with the lowest
30
Table A.2. FF risk-adjusted returns: market-cap weighted return dispersion and fund performance
S1 S2 S3 S3-S1 Full sample G1 -9.56* -9.34* -8.26 1.43 -9.07 (-1.90) (-1.77) (-1.53) (0.87) (-1.75) G2 7.25 8.74 9.64* 2.24 8.52 (1.44) (1.62) (1.91) (1.32) (1.66) G3 -1.06 -0.71 -0.61 0.45 -0.84 (-0.25) (-0.16) (-0.14) (0.32) (-0.20) Full sample -2.00 -1.47 -0.90 1.13 -1.49 (-0.70) (-0.46) (-0.28) (1.14) (-0.49)
The table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the Fama and French three-factor model over the period 2005-2015. The selectivity portfolios resulted
from sorting every month t the funds according to their 𝑅𝑡−12 , which is obtained from a rolling regression of the fund’s
excess returns on the FFC factor model over the 24 months prior to month t. The sorting produces three selectivity portfolio groups where S1 hold the lowest selectivity funds moving to S3 which hold the funds with the highest selectivity. Each portfolio covers 33% of the full set of Funds. Which correspond to the months in the return dispersion groups. Similarly to the selectivity portfolios, the market-cap weighted return dispersions are ranked from low (G1) Return dispersion to High dispersion (G3) with 33% of the month in the data set at the end of the month preceding month t (𝑅𝐷𝑡−1). S3-S1 represents the cross-sectional difference in risk-adjusted returns between the portfolio with the
lowest selectivity (S3) and the highest selectivity (S1). Standard T-statistics are reported in parentheses with * denoting significance at 10% using the heteroscedasticity and autocorrelation consistent (HAC) standard errors.
Table A.3. CAPM model: Equally weighted return dispersion and fund performance
S1 S2 S3 S3-S1 Full sample G1 -5.20 -5.17 -4.67 0.56 -5.03 (-1.14) (-1.10) (-1.00) (0.46) (-1.10) G2 6.89 7.56 7.68 0.74 7.35 (1.19) (1.19) (1.21) (0.56) (1.20) G3 -5.26 -4.43 -3.94 1.39 -4.58 (-1.16) (-1.01) (-0.88) (0.78) (-1.04) Full sample -2.46 -1.80 -1.32 1.17 -1.89 (-0.87) (-0.60) (-0.43) (1.21) (-0.64)
The table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the CAPM model over the period 2005-2015. The selectivity portfolios resulted from sorting every
month t the funds according to their 𝑅𝑡−12 , which is obtained from a rolling regression of the fund’s excess returns on
31
represents the cross-sectional difference in risk-adjusted returns between the portfolio with the lowest selectivity (S3) and the highest selectivity (S1). Standard T-statistics are reported in parentheses using the heteroscedasticity and autocorrelation consistent (HAC) standard errors.
Table A.4. CAPM model: market-cap weighted return dispersion and fund performance
S1 S2 S3 S3-S1 Full sample G1 -10.18** -10.28** -9.21* 1.08 -9.91 (-2.15) (-2.11) (-1.84) (0.79) (-2.05) G2 2.81 4.55 5.44 2.57 4.24 (0.52) (0.84) (1.09) (1.36) (0.81) G3 0.65 1.36 1.06 0.40 0.98 (0.00) (0.31) (0.23) (0.25) (0.23) Full sample -2.46 -1.80 -1.32 1.17 -1.89 (-0.87) (-0.60) (-0.43) (1.21) (-0.64)
The table reports the annualized selectivity portfolio risk-adjusted returns in percentages, annualized using (1 +
𝛼)12− 1, from the CAPM model over the period 2005-2015. The selectivity portfolios resulted from sorting every
month t the funds according to their 𝑅𝑡−12 , which is obtained from a rolling regression of the fund’s excess returns on
the FFC factor model over the 24 months prior to month t. The sorting produces three selectivity portfolio groups where S1 hold the lowest selectivity funds moving to S3 which hold the funds with the highest selectivity. Each portfolio covers 33% of the full set of Funds. Which correspond to the months in the return dispersion groups. Similarly to the selectivity portfolios, the market-cap weighted return dispersions are ranked from low (G1) Return dispersion to High dispersion (G3) with 33% of the month in the data set at the end of the month preceding month t (𝑅𝐷𝑡−1). S3-S1
