Master Thesis
Finance
Active mutual fund performance and
cross-sectional volatility: Evidence from the UK
Luc Tholhuijsen
Abstract
This paper provides new insights into the value of active portfolio management in the UK market. Using a sample of 614 actively managed UK mutual funds over the period January 2000 to August 2016, I find that the level of return dispersion significantly influences the performance of a mutual fund. In addition, in periods of low and medium return dispersion funds do not outperform the benchmark, but in a high return dispersion environment, managers generate significantly negative alphas. In this high return dispersion environment, I find that the most active managers significantly underperform the benchmark and that all managers together underperform the benchmark as well. Furthermore, the most active managers significantly underperform the least active managers during times of high return dispersion and over the full sample period. Overall, if investors forget to take the return dispersion environment into account, active investing in equity mutual funds can result in negative returns.
Student number: s2036940
Program: MSc Finance
Supervisor: Dr. A. (Auke) Plantinga
Date: 12-01-2017
Special Research Project: The value of active portfolio management
Word count: 13,934
Field keywords: Active management, Alpha, Excess performance, Mutual fund,
1 Table of Contents
1. Introduction ... 2
2. Literature review ... 5
2.1 Fund performance ... 5
2.2 Skill and return dispersion ... 6
2.3 Activeness measures ... 7
2.3.1 Tracking error ... 7
2.3.2 Active share ... 8
2.3.3 R-squared ... 8
2.4 Von Reibnitz’s paper ... 9
3. Methodology ... 9 3.1 Return dispersion ... 9 3.2 Fund activeness ... 10 3.3 Performance measurement ... 12 3.4 Factor loadings ... 12 4. Data ... 12
4.1 Mutual fund sample and returns ... 13
4.2 Multifactor benchmark model data ... 14
4.3 Activeness data ... 15
4.4 Return dispersion data ... 16
4.5 Further data inspection ... 17
5. Results ... 18
5.1 General results ... 18
5.2 Factor loadings ... 21
5.3 Investor’s perspective ... 22
5.4 Robustness checks ... 23
5.4.1 Equally weighted return dispersion measure ... 23
5.4.2 Other performance models ... 25
5.4.3 Volatility clustering ... 26
5.5 Timing models ... 27
6. Conclusion, discussion and limitations ... 28
7. References ... 32
8. Appendixes ... 36
A. Time-series plot equally weighted return dispersion ... 36
B. CAPM results ... 36
C. Graphical overview of the Fama-French alphas ... 37
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1. Introduction
For many years there has been an ongoing debate among investors and researchers about passive and active funds. Passive management means that a manager constructs a portfolio that mirrors the market index. Active management, on the other hand, follows a strategy where the manager selects stocks that are expected to outperform the benchmark and do not select stocks that are expected to underperform the benchmark. As a result, active managers give investors the opportunity to receive higher returns than the benchmark. Unfortunately, the chance of higher returns is not a free lunch as active managers charge higher fees than passive managers. Consequently, fees and other expenses must be subtracted to evaluate whether or not active managers add value. Besides the higher costs, there is also the risk that active managers select the underperforming stocks. Therefore, it is important to identify whether a manager has skills to add value and to justify their higher fees.
In recent years, the debate concerningpassive and active investing has received more and more public attention. For example, Het Financieële Dagblad1 reports on the current trend that investors switch from active to passive funds. The article shows that investors spend around 10 times more of their capital in passive funds than a few years ago, and the number of passive funds increased from zero to over 6.000 in 25 years. Despite the increase of inflows to passive investments, approximately two-third of all capital is still invested in active funds. This indicates that the debate whether to follow a passive strategy, active strategy or a combination of both is still unsolved.
One of the most well-known and essential theories related to the investor’s decision regarding passive and active strategies is the efficient market hypotheses (EMH). The theory as developed by Fama (1965) states that all available information is immediately reflected in the price. In other words, according to Fama (1965), an active manager is not able to outperform an efficient market. On the other hand, there is evidence against the EMH, which gives active managers the opportunities to generate returns in excess of the benchmark. In addition, anomalies such as the size effect and the January effect are opportunities to outperform. Therefore, if an investor believes in the EMH, then he or she should follow a passive strategy since it is impossible to beat the market. If an investor does not believe in the EMH, then an active strategy could work.
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3 Should an investor invest in a passive or an active mutual fund? Previous studies show that, on average, investors should not pay for the extra costs of active management since active funds on average underperform passive benchmarks, net of fees and other expenses.2 However, active funds differ in the level of activeness, type of management and skills, which possibly leads to different performance that could justify the fees for successful managers. Cremers and Petajisto (2009) find in a sample of 2,647 funds from the US during the period 1980 to 2003 that the most active funds tend to add value for investors, while the least active funds underperform the benchmark. Cuthbertson, Nitzsche, and O’Sullivan (2008) show with a sample of 900 UK funds over the period April 1975 to December 2002 that a number of top performing funds have stock picking skills. Furthermore, Petajisto (2013) finds that the most active stock pickers outperform their benchmark by 1.26% a year. They also find a positive relationship between return dispersion and performance. Overall, markets seem not to be fully efficient and investing in the most skilled and the most active managers could be a good investment strategy.
In contrast with Petajisto (2013), previous research paid little attention to the fact that active manager’s performance also depends on the alpha opportunity available in the market. The alpha opportunity is measured by cross-sectional volatility (CSV), also known as return dispersion (RD), which is the cross-sectional variety in returns of a universe of stocks. Cross-sectional volatility is of fundamental importance for the potential of skilled managers to outperform a benchmark since it is not possible to add value through active management when CSV is zero. A return dispersion of zero means that all stocks have similar returns and therefore it is impossible for managers to outperform a benchmark. On the other hand, if return dispersion is very high, there is great potential for a high alpha by selecting winners and avoiding losers. This suggests that active managers with skill can perform better in times of high return dispersion. Von Reibnitz (2015) studies this relationship with US data and finds that the most active managers generate significant returns in excess of the benchmark during periods of high return dispersion, indicating that the moment to invest could be as important as selecting the best fund to outperform the benchmark.
To sum up, the performance of active managers depends not only on characteristics such as activeness and skills but also on the state of the investment opportunities environment. The objective of this paper is to investigate the relationship between performance, activeness and
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4 return dispersion in the United Kingdom. In Europe and the United Kingdom, this topic is under-investigated and could possibly lead to different results since culture, markets, funds, and manager’s skills differ from the United States, see for example Blake and Timmermann (1998) as well as Otten and Bams (2002). Furthermore, it provides new insights into the value of active portfolio management. Overall, this paper answers the following research question:
Do active managers perform better during periods of high return dispersion?
To answer this question, the study uses a sample of 614 actively managed mutual funds from the UK in the period from January 2000 to August 2016. First, I construct three portfolios based on the level of a fund’s activeness and define three return dispersion environments. R2 measures activeness, which is obtained by regressing the fund’s excess returns on a multifactor benchmark model. R2 describes how much variability of the returns is explained by the benchmark factors in a regression. Consequently, a lower R2 means that a fund deviates more from its benchmark factors, indicating a higher level of activeness. Next, return dispersion is calculated by using the returns of the FTSE All-Share index constituents. The FTSE All-Share index includes many small, medium and large stocks available for selection in the UK market. Lastly, to measure the ability of a manager to add value, the intercept,
alpha, is obtained from the multi-factor benchmark regression. A positive alpha shows that a
manager is able to add value and a negative one indicates underperformance compared to the benchmark.
This paper contributes to the existing literature by being the first to examine the relationship between cross-sectional volatility, activeness, and performance in the United Kingdom. Interestingly, the results do not confirm the hypothesis that active managers perform better during periods of high return dispersion. As opposed to Von Reibnitz (2015), I find that the medium and the most active managers significantly underperform the benchmark in times of high return dispersion. The underperformance shows that those active managers, on average, should be avoided in times of high return dispersion.
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2. Literature review
2.1 Fund performance
Sharpe (1991) argues that active management is a zero sum game. For each manager with outperformance relative to the stock market index, there must be another one with underperformance. Since active managers charge fees and other costs, active managers as a group must underperform the benchmark. Previous research supports this conclusion. In addition, Blake and Timmermann (1998) as well as Cuthbertson, Nitzsche, and O’Sullivan (2008) report that active mutual funds, on average, underperform the benchmark in the United Kingdom after accounting for fees and other costs. French (2008) conducts research on the aggregate cost of active investing and shows that 0.67% value can be added by switching from an active to a passive strategy. Lastly, Fama and French (2010) find that the aggregate gross returns of active US funds are approximately equal to the market return, but expenses for active managers result in underperformance. Overall, the average active manager should be avoided. However, recent research finds that the successful managers may be found among the most active managers.
Wermers (2003) examines the relationship between performance and the level of activeness. He defines activeness as the number of volatility bets an investor takes. Tracking error measures the number of volatility bets. The paper finds a significant positive relationship between volatility bets and performance. Wermers (2003) suggests by way of possible explanation that active managers with better stock picking skills tend to have larger active management bets. Kacperczyk, Sialm, and Zheng (2005) use another measure, called industry concentration, to test the relationship between performance and activeness. Their research shows that managers, whose portfolio is concentrated in a few industries, outperform diversified market portfolios due to investment skills. Amihud and Goyenko (2013) use the
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2.2 Skill and return dispersion
Jensen (1968) introduces alpha to determine the abnormal performance relative to a benchmark. In addition, Jensen’s alpha is the risk-adjusted return in excess of a benchmark. To evaluate mutual funds and managers, the alpha describes the added value. If the value is positive, then the performance is above the predicted level. If the value is negative, then there is underperformance relative to the predicted level. This under- or outperformance relative to the benchmark shows how skilled a manager or fund is. The fundamental law of active management by Grinold (1989) is another way to evaluate the added value of managers. The added value, called information ratio, depends on the information coefficient, a measure of manager’s skill and market breadth, which is the number of independent investment opportunities a manager has. In other words, the greater the opportunity to make independent bets, the greater the potential to add value for a skilled manager (all else being equal). The active law is described as:
√ (1)
Where, IR is the information ratio, IC is the information coefficient and BR is market breadth. In line with Jensen’s alpha, the active law shows that managers who add value have at least some skills.
7 funds are good stock pickers during booms and have good market-timing abilities in recessions. Overall, the out- or underperformance of an equity mutual fund is an indication of the manager’s skill.
As can be seen from equation 1, performance does not only depend on a manager’s skill but also on market breadth. A common proxy for breadth is cross-sectional volatility (CSV).
Gorman, Sapra, and Weigand (2010a,b) use CSV as a proxy and claim that a higher level of return dispersion results in a greater opportunity to outperform, regardless of the manager’s skills. Bouchey, Fjelstad, and Vadlamudi (2011) show that active manager return dispersion is higher when CSV is higher. This implies that if stock returns do not differ from its benchmark, there is no possibility for active managers to outperform, resulting in a zero alpha. On the other hand, if return dispersion is high there are enough alpha opportunities for skilled managers to outperform the benchmark. Connor and Li (2009) study the impact of CSV on hedge fund’s performance and document a significant positive relation between performance and CSV. Huij and Lansdorp (2012) find a positive relationship between performance persistence and CSV. Lastly, Petajisto (2013) reports that the most active stock pickers perform best during periods of high return dispersion. Overall, there seems to be a positive relation between CSV and performance.
To sum up, skill and return dispersion are two important factors in the debate about active and passive management. A manager is able to add value when skill is present and return dispersion is high. On the other hand, if one of the factors is zero or negative, then a manager cannot add value through active management. Therefore, the successful active managers are skilled and have alpha opportunities to outperform the benchmark.
2.3 Activeness measures
Active management refers to the strategy where a manager attempts to outperform the benchmark. However, there are different ways to deviate from the benchmark and therefore there are several measures for activeness.
2.3.1 Tracking error
Tracking error, which is the times-series standard deviation of the difference in the portfolio and benchmark returns, is a traditional way to measure activeness.3 High tracking error indicates that the returns of a fund vary a lot from its benchmark. This deviation implies
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8 activeness since funds attempt to beat the benchmark by deviating from it. However, recent research claims that tracking error alone is not enough to identify activeness. Cremers and Petajisto (2009) argue that funds with a low tracking error can be very active. According to their paper, active management consists of two parts: stock selection and factor timing, and tracking error is only a suited proxy for factor timing. Amihud and Goyenko (2008) argue that tracking error contains the omitted variable problem. They claim that the systematic volatility of a fund is omitted and that the systematic volatility correlates with tracking error, resulting in a biased estimation of tracking error on performance. Overall, tracking error seems not to be the perfect measurement for activeness.
2.3.2 Active share
Cremers and Petajisto (2009) introduce a new measure, called active share, to overcome the shortcomings of tracking error and to determine the fund’s activeness. Active share is the deviation of the portfolio holdings compared to its benchmark portfolio. The paper provides two arguments in favor of active share. Firstly, active share shows the potential to outperform. Moreover, a positive level of active share means that the portfolio holdings differ from the benchmark, which is a necessary requirement to outperform. Secondly, active share could be used in combination with tracking error to provide a more comprehensive overview of active management. Additionally, active share is a proxy for stock selection and tracking error is a proxy for factor timing. So far, active share might be a good measure for activeness, but the findings of Frazzini, Friedman, and Pomorski (2016) contradicts this view. The authors find no strong economic motivations and empirical support for the correlation between active share and performance. According to the authors, the results of Cremers and Petajisto (2009) are mainly driven by the significant correlation between active share and the benchmark type. After controlling for the benchmark, the predictive power of active share for performance is eliminated.
2.3.3 R-squared
-9 method can be used with respect to multiple benchmarks, which makes the method more accurate to determine activeness. Lastly, the R2 method is also accepted in more recent literature.4
2.4 Von Reibnitz’s paper
Von Reibnitz (2015) is one of the first who combines performance, activeness and return dispersion for mutual funds. She uses a sample of 3,048 US funds over the period 1972 to 2013 and creates a metric with five portfolios based on activeness on one side and five return dispersion quintiles on the other side. Activeness is determined using the R2-method, and return dispersion is calculated by using an equally weighted measure. Next, alpha is calculated for each portfolio for the five return dispersion quintiles and over the full sample to examine whether the fund’s excess performance is sensitive to the different levels of return dispersion. She finds that the most active managers significantly outperform the benchmark during periods of high return dispersion. Additionally, the positive difference between the most active fund and the least fund is only significant in the highest return dispersion quintile. Lastly, a strategy of changing between passive and highly active mutual funds based on the level of return dispersion results in a significant excess return of more than 2.7%, net of fees and expenses.
3. Methodology
This research focuses on the interaction of activeness and return dispersion as the determinant of excess performance. We follow the methodology proposed by Von Reibnitz (2015), which starts by calculating the return dispersion for the UK market in the period from January 2000 to August 2016. After obtaining the return dispersion per month, we construct three return dispersion environments. Next, we carry out the R2-method to determine activeness and make three portfolios based on activeness. Lastly, we calculate the alphas for each portfolio in the various return dispersion environments to compare excess performance.
3.1 Return dispersion
Return dispersion or cross-sectional volatility is the cross-sectional variability of stocks’ returns in a certain market for a specific time period. In this study, return dispersion will serve as the proxy for the independent investment opportunities. In contrast to Von Reibnitz
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10 (2015) and in line with Petajisto (2013), we calculate the return dispersion in month t using a value-weighted standard deviation. A value-weighted measure is used because most indexes are capitalization-weighted.
√∑
(2)
Where, is the monthly return dispersion for the index at time t, is the weight of constituent i at time t, is the monthly return of an index constituent i at time t, and is the monthly value-weighted average return on index constituents at time t.
The next step is determining various return dispersion environments. In contrast to Von Reibnitz (2015), we use low, medium and high return dispersion environments instead of quintiles. Our time period is shorter due to data availability constraints and therefore includes fewer months. These return dispersion environments are more suited since it could prevent the data from being spread too thinly. In addition, by using quintiles our groups could become too small or lose crucial information. Each month, the low environment consists of the bottom 30% return dispersion months, the top 30% return dispersion months are classified as the high environment, and the remaining 40% return dispersion months are classified as the medium environment. Lastly, we use the lagged value of return dispersion, , in order to allow the investor to actually implement a strategy based on return dispersion. This is called the ex-ante perspective or the “investor’s perspective” in this paper.5
3.2 Fund activeness
Fund activeness is measured as the R2 of a mutual fund from a multi-factor regression. R2 is the part of the variation in the returns of a mutual fund that is explained by the variation in systematic factors of the regression. In other words, R2 is a measure of systematic volatility. Consequently, a lower R2 indicates more deviation from the benchmark factors, meaning a higher level of activeness. Amihud and Goyenko (2013) and Von Reibnitz (2015) also use the R2-method to determine a fund’s activeness. Activeness, called “selectivity” by Amihud and Goyenko (2013), is determined as follows:
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(3) Where, is the variance of the residual in the regression, is the total time series variance of the fund’s return, and is the variance related to the risk of the systematic factors in the benchmark model. As equation 3 shows, activeness is the proportion of the total variation that is not explained by the systematic market factors, meaning that an increase in activeness results in a higher exposure to idiosyncratic risk. The increase in idiosyncratic risk indicates that a manager selects stocks that deviate more from the benchmark.
To obtain R2 in month t, we regress the fund’s returns of the previous 36-months on the Four
Factor Carhart Model (FFC). This 36-month window moves exactly with one month to estimate the R2 for the subsequent month. The regression can be described by:
( ) (4)
Where, is the monthly return of active mutual fund i at time t, is the monthly risk-free
rate at time t, is the alpha of mutual fund i at time t, is the monthly return of the market portfolio at time t and and are the factor loadings on, respectively, the market ( ), size , book to market and momentum . The WMLt factor mimicking portfolio is the UK momentum index, obtained from the MSCI website.6 The returns of the SMBt and HMLt factor mimicking portfolios are constructed
using four benchmark portfolios consisting of small/large stocks and value/growth stocks, also obtained from the MSCI website:
(5)
(6)
After obtaining the from the rolling regression on the FFC model, we rank funds in three
groups according to the fund’s level of activeness (1-R2t) each month: low (A1), medium
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12 (A2), and high activeness (A3). The low and high levels consist of the respectively bottom and top 30% active funds. The remaining 40% funds have a medium level of activeness. Lastly, we also use the lagged value, , in order to allow the investor to actually implement a strategy based on activeness. In line with , this is called the ex-ante perspective or the “investor’s perspective” in this paper.
3.3 Performance measurement
After determining the three return dispersion environments and the three activeness portfolios, we can examine whether the excess performance of funds with various rankings of activeness is sensitive to the different return dispersion environments. To do this, alpha is obtained from the FFC model. Alpha shows whether the performance of a fund is below or above the predicted performance by the FFC model. If the value is positive, then a manager outperforms the benchmark.
3.4 Factor loadings
The regression of the fund’s excess returns on the FFC model allows to study the time-varying factor loadings on, respectively, the market ( ), size , book to
market and momentum . First, we look whether the factors have a positive or negative relation with the excess returns. Secondly, we investigate whether funds change their loadings towards factors over time. Stivers and Sun (2010) study the relationship between cross-sectional volatility and the time variation in momentum and value premiums. The authors find that the successive value premium is positively related to cross-sectional volatility and that the successive momentum premium has a negative relationship with cross-sectional volatility. This indicates that skilled managers change their factor loadings based on the return dispersion environment. Additionally, the time-varying factor loadings can give us a better understanding of the manager’s performance.
4. Data
We use data extracted from Datastream, Morningstar, and the MSCI website.7 Our sample ranges from January 2000 to August 2016, resulting in observations over 200 months. All data, if applicable, is in British Pounds and has a frequency of one month.
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4.1 Mutual fund sample and returns
Our sample of mutual funds is obtained from the Morningstar Database. Morningstar provides a list of mutual funds both dead and alive. Therefore, the chance that our data suffer from a survivorship bias is limited.8 We use the “Morningstar category” to include all small, medium and large active mutual funds. Because this study focuses on active funds, two methods are used to eliminate passive funds. Firstly, we follow Huij and Lansdorp (2012) and define an active fund as one that is required to have returns for at least a successive period of 12 months. Secondly, funds are checked and removed on words or abbreviations that indicate passiveness such as “Tracking”, ”Tracker”, “Index”, “Idx” and “FTSE”. Since our access to Morningstar was limited, all the returns are obtained from Datastream. Datastream provides returns that are net of fees, dividends and other costs. The R2-method requires returns for 36-months prior to month t, and therefore the return data covers the period January 1997 to August 2016. Additional information about a mutual fund such as the primary benchmark, currency, and location are obtained from both databases and compared to each other where applicable. We exclude funds that are located outside the UK or have a different currency than the British Pound to eliminate noise due to currency or country specific effects. Furthermore, a few funds are excluded due to missing or extreme values. Finally, Morningstar and Datastream present separate share classes of one mutual fund as a unique entity. In order to avoid double counting of the same fund’s returns, we eliminate these share classes by taking the equally weighted average return of the separate share classes. Our final sample consists of 614 mutual funds.
Table 1. Descriptive statistics of the net mutual fund’s returns
This table presents descriptive statistics of the annualized net returns in British Pounds over the period January 2000 to August 2016, resulting in 200 fund-month observations. The sample comprises 614 active UK equity mutual funds. Returns are calculated using Datastream’s Total Return Index, which incorporates dividends and is net of fees and other expenses. The standard deviation is annualized by using: √ . N shows the number of return observations in the sample. Sources: Datastream and Morningstar
Mean Median Standard Deviation Kurtosis Skewness N
5.62% 8.44% 12.60% 5.02 -0.52 82,710
Table 1 illustrates that the returns are almost normal distributed, with an excess kurtosis of 2.02, indicating a higher likelihood of extreme values. In addition, the returns are negatively skewed, meaning that there is a greater chance of negative outcomes. Overall, the deviations are not substantial to have concerns about non-normality.
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4.2 Multifactor benchmark model data
The multifactor benchmark model as described in equation 4 estimates a fund’s activeness and alpha. To perform the rolling regression, data is obtained from the MSCI website and Datastream. , as described in the previous sector, is the return of an active mutual fund i in month t. The risk-free rate is the yield on the 10-year UK government bond. Because the study is entirely focused on the UK, the 10-year UK government bond is a good proxy for the risk-free rate. Datastream provides an annual risk-free rate, which we convert to a monthly rate to maintain the monthly frequency of our data. The market portfolio is the return on the FTSE All-Share index. According to Morningstar, over 50% percent of the mutual funds has the FTSE Share index as their primary benchmark index. Furthermore, the FTSE All-Share index is the aggregation of the FTSE 100, FTSE 250, and FTSE Small Cap indices, representing 98-99% of the UK market capitalization. Therefore, it seems a good proxy for our sample. As a check, we regress the returns of the FTSE All-Share index on the MSCI UK index, which represents 85% of the UK market capitalization. The regression gives a significant beta of approximately one and a R2 of over 0.99. Lastly, to construct the and factor mimicking portfolios, four benchmark portfolios are downloaded from the MSCI website: a small growth portfolio, large growth portfolio, small value portfolio and a large value portfolio. The portfolio, which is the UK momentum index, is downloaded directly from the MSCI website.
Table 2. Descriptive statistics of the benchmark model factors
This table presents the statistics of the net annualized returns for the factor mimicking portfolios in the FFC model and the correlation between the factors for the period January 2000 to August 2016. RMRF is the excess market return over the 10-year UK government bond yield. SMB, HML and WML are the factor mimicking portfolios for respectively size, book to market and momentum. The standard deviation is annualized by using: √ . Sources: Datastream and MSCI website.
Correlation
Factor Mean Median Standard deviation RMRF SMB HML WML RMRF -2.12% 5.01% 14.69% 1.00 SMB 6.82% 9.57% 12.46% 0.15 1.00
HML 1.03% -0.80% 9.87% 0.05 -0.13 1.00
WML 6.39% 12.23% 14.51% 0.79 0.17 -0.12 1.00
15 correlation in combination with the high variance suggests that these factors could explain a part of the mutual fund’s returns. Lastly, the average excess market return is negative, which could be a result of our time period. The sample includes two events, the dot-com bubble and the financial crisis, with enormous losses.
4.3 Activeness data
We perform a rolling regression on the FFC model to obtain the R2 for each fund in every month. Consistent with Von Reibnitz (2015), we require that a mutual fund has returns in the 36-months prior to month t. This condition leads to a reduction of fund observations compared to the return observations of the mutual funds because not all funds have enough data in the preceding months. Finally, in line with Amihud and Goyenko (2013), we exclude the top and bottom 0.5% of the estimated R2 in every month. By limiting the extreme values, the effects of possible spurious outliers are reduced. Our final sample consists of 614 mutual funds with 69,062 monthly R-squared observations over the period January 2000 to August 2016.
Table 3 and figure 1 present the descriptive statistics for the activeness measure R2. All measures are negatively skewed since the mean is smaller than the median. The effect of trimming is that the mean slightly increases, indicating that the extreme values at the bottom are more extreme (low R2t) than the top 0.5% values (high R2t). Figure 1 shows that over 80%
of the funds have a R2t higher than 0.8 after trimming, demonstrating a higher level of
passiveness. Additionally, the median shows that a combination of passive benchmark factors explains more than 85% of the fund’s return variation. Lastly, the statistics from the investor’s perspective (R2
t-1) do not differ much from the activeness measure at time t (R2t). Figure 1. Frequency distribution of the activeness measure R2
This figure presents the frequency of the number of observations concerning the measure R2t in the period
January 2000 to August 2016. A low R2t means a high level of activeness. The horizontal axis shows the
estimated R2t in groups of 0.025 ranging from low to high and the vertical axis shows the percentage of
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Table 3. Descriptive statistics for the measure R2
This table presents the descriptive statistics for the R2t measureobtained from the Four Factor Carhart model
(FFC) over the period January 2000 to August 2016. The monthly fund’s R2t is obtained by regressing the
mutual fund’s excess returns (in excess of the 10-year UK government bond yield) on the FFC model, using the return data of 36 months prior to month t. The sample comprises 614 active UK equity mutual funds. R2t
Untrimmed is the monthly activeness measure in month t. R2t is the activeness measure where the top and the
bottom 0.5% are trimmed to reduce the estimation error, consistent with Amihud and Goyenko (2013). R2t-1 is
the monthly activeness measure prior to month t, which is used for the analysis from an investor’s perspective.
N is the number of observations.
Measure Mean Median Minimum Maximum N
R2t Untrimmed 0.8547 0.8922 0.0306 0.9999 69,926
R2t 0.8576 0.8922 0.1275 0.9999 69,062
R2t-1 0.8580 0.8924 0.1275 0.9999 68,949
4.4 Return dispersion data
To calculate the monthly cross-sectional volatility, constituent lists of the FTSE All-Share index and the corresponding returns are downloaded from Datastream. Datastream does not provide accurate constituent lists of the FTSE All-Share index before 2000. Therefore, our sample period starts at the beginning of January 2000. Furthermore, Datastream does also not provide a time-series list. Therefore, the constituent list is downloaded for every single year and compared to each other to determine the constituents in a certain year. The FTSE All-Share Index is a good representation of the investment opportunities available in the UK market because it includes over 700 small, medium and large capitalization stocks each year.
Figure 2. Time series plot of the monthly return dispersion based on the constituents of the FTSE All-Share index
This figure shows the value-weighted monthly return dispersion in the UK for the period January 2000 to August 2016, resulting in a time-series plot of 200 months. The cross-sectional volatility is based on the FTSE All-Share index constituents, representing approximately 98% of the UK market capitalization. More than 700 small, medium and large capitalization stocks are included in the index each month.
Figure 2 presents the monthly UK return dispersion for the period January 2000 to August 2016. As can be seen in figure 2 and table 4, return dispersion varies between a minimum of 3.92% in April 2005 and a maximum of 21.56% in March 2000. Furthermore, the figure shows peaks in 2000, 2009 and 2016. The peak in 2000 corresponds to the dot-com bubble.
17 The spike in 2009 represents the financial crisis period and the peak in 2016 corresponds to the Brexit. Based on the figure, there is no single period including all the high return dispersion months, but high return dispersion environments seem to correspond with a crisis situation or at least an unexpected event in the financial markets.
Table 4. Descriptive statistics for return dispersion
This table reports the descriptive statistics for the return dispersion over the period January 2000 to August 2016. Return dispersion is based on the constituents of the FTSE All-Share index, which represents approximately 98% of the UK market capitalization. The table presents the statistics for the various return dispersion environments, where a low environment includes the 30% months with the lowest return dispersion and a high environment comprises the 30% months with the highest return dispersion. The remaining 40% months represent the medium level. All represents the total sample and includes all the months from January 2000 to August 2016. N are the number of observations. The first-order autocorrelation is between month t and month t-1, using a VAR-model for the calculation. *** denotes a significance at the 1% level. Source: Datastream
Return dispersion environment
Measure Low Medium High All
Mean 4.86% 6.35% 10.39% 7.12% Median 4.91% 6.24% 9.83% 6.24% Standard Deviation 1.39% 2.27% 10.26% 9.70% Kurtosis -0.70 -1.10 4.02 6.38 Skewness -0.57 0.41 1.99 2.17 Minimum 3.92% 5.48% 7.76% 3.92% Maximum 5.45% 7.73% 21.56% 21.56% First-order autocorrelation 0.65*** N 60 80 60 200
Table 4 reports the summary statistics for the return dispersion for the full sample and in various return dispersion environments. The median and mean for the high environment are twice as high as the low environment, indicating that environments considerably differ. Especially, the maximum value of 21.56% in the high return dispersion environment differs substantially from the low and medium environment. The maximum value is approximately 4 times higher than the low environment, whereas the minimum value only doubles. The autocorrelation shows that there is a significant first-order autocorrelation between month t and month t-1. This means that managers can predict the return dispersion level for the next month by looking to the previous month. Therefore, we use the lagged value, ,as return dispersion measure for the analysis from an investor’s perspective. Lastly, the first-order autocorrelation is calculated using a vector autoregression (VAR) model, because the VAR model overcomes the unidirectional relationship problem as seen in other models.
4.5 Further data inspection
18 standard errors of the explaining variables. Overestimation of the standard errors could result in a type II error, which is not rejecting a false null hypothesis. In table 2, the correlation diagram displays the correlation between all the explaining variables in the regression. Most variables are not highly correlated, but there might be a problem between the variables excess market return (RMRF) and momentum (WML). Moreover, a correlation of 0.79 indicates that there could be problems with multicollinearity. Besides testing for multicollinearity, it is necessary to check whether a time series is stationary. If a time series is non-stationary, shocks or other events have permanent effects. These permanent effects negatively influence the robustness of our findings. Therefore an Augmented Dicky Fuller (ADF) test is conducted on all variables. For all variables, the null hypothesis of a unit root is rejected, which means that shocks to the system gradually die away. Lastly, we test the efficient market hypothesis (EMH) using an autoregressive (AR) model for the returns. The strict form of the EMH states that all information is reflected in the price and that the returns in month t-1do not have an effect on the returns in month t. The AR model shows that we can reject the null hypothesis at a 5% significance level, indicating that the markets are not fully efficient.
5. Results
5.1 General results
19 Although we do not find significant results on the aggregate level, there are differences between the return dispersion environments. In the low and medium dispersion environment, all alphas are insignificant. The insignificant alphas mean that no significant difference exists between the fund’s performance and the benchmark, after fees and expenses. In addition, investing in the benchmark generates approximately the same returns as investing in active mutual funds in times of low and medium return dispersion. Again, there is no skill to justify the fees for the majority of the funds. Also, the difference between the most active managers (A3) and the least active managers (A1) is insignificant, meaning that selecting managers, based on the level of activeness, has no significant effect on the investor’s returns. In contrast to the low and medium return dispersion environment, the medium (A2) and the most (A3) active managers produce a significant negative alpha in periods of high return dispersion. On a yearly basis, portfolio A2 underperforms the benchmark with 2.84% at a 10% significance level and the most active mutual funds (A3) underperform with 5.09% at a 5% significance level. These findings show that investing in more active managers is not beneficial for investors during periods of high return dispersion. Additionally, the most active managers, compared to the least active managers, generate an alpha that is 3.63% lower. Lastly, the average active manager (column All) significantly underperforms the benchmark by 3.12% during periods of high return dispersion, indicating that investing in the benchmark is a better alternative than following an active strategy.
Table 5. FFC annualized alpha, return dispersion and activeness
This table displays the average annualized alpha for each activeness portfolio for several return dispersion environments in the period from January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R2t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
20
Figure 3. Graphical overview of the FFC alphas
This figure presents the average annualized alpha for each activeness portfolio for several return dispersion environments in the period from January 2000 to August 2016. Activeness portfolios are constructed based on the funds R2t, which is estimated by regressing the fund’s 36-month excess returns (in excess of the 10-year UK
government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. A1 consists of the 30% funds with the lowest activeness and A3 comprises the 30% funds with the highest activeness. The remaining funds (A2) have a medium level of activeness. Three return dispersion (RDt) environments are presented, where
the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months. Finally, the average annualized alpha is calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the FFC model. Within each return dispersion environment, results are reported from the least active portfolio (A1) to the most active portfolio (A3).
As graphically shown in figure 3, the relationship between return dispersion and performance is not constant. Moreover, there is a positive relationship between return dispersion and performance when the environment increases from low to medium. For the increase from the low/medium to high dispersion environment, a negative relationship exists between performance and return dispersion. These results suggest that active management is more beneficial for investors when the environment increases from low to medium or decreases from high to medium/low. On the other hand, when the environment evolves from the low/medium level to a high level, investors lose money. This negative relationship is surprising because the literature suggests a positive relationship between performance and return dispersion.
Overall, in the high dispersion environment, all alphas are negative and there is a negative relationship between activeness and performance. Furthermore, all managers together
-6% -5% -4% -3% -2% -1% 0% 1% 2%
Low Medium High
A n n u al ize d alp h a
Return dispersion environment
21 underperform the benchmark on average during periods of high dispersion. Based on our findings, we conclude that active managers underperform the benchmark in periods of high return dispersion.
5.2 Factor loadings
22
Table 6. Factor loadings of the mutual funds, return dispersion and activeness
This table presents the factor loadings from the FFC model for each portfolio in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R2t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
presented, where the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, factor loadings are calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the FFC model. Panel A, B, C and D display the factor loadings on respectively the market, size, market to book and momentum. The corresponding standard T-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5% and 10% level, respectively.
Panel A: Factor loadings on the RMRF factor Panel B: Factor loadings on the SMB factor
(RDt) Activeness (1- R2 t) (RDt) Activeness (1- R2 t)
A1 A2 A3 A3-A1 All A1 A2 A3 A3-A1 All
Low 0.66*** 0.55*** 0.43*** -0.23*** 0.55*** Low 0.09** 0.17*** 0.29*** 0.20*** 0.18*** (12.96) (10.33) (5.99) (-4.31) (10.17) (2.39) (4.20) (5.38) (4.84) (4.49) Medium 0.57*** 0.50*** 0.41*** -0.16*** 0.49*** Medium 0.04 0.14*** 0.23*** 0.19*** 0.14*** (14.89) (13.00) (8.86) (-5.30) (12.84) (1.47) (4.68) (6.57) (8.02) (4.68) High 0.62*** 0.52*** 0.42*** -0.21*** 0.52*** High 0.09*** 0.20*** 0.32*** 0.23*** 0.20*** (20.12) (14.54) (7.31) (-4.29) (14.06) (4.06) (8.29) (8.18) (7.12) (8.01) All 0.61*** 0.52*** 0.42*** -0.19*** 0.51*** All 0.07*** 0.18*** 0.29*** 0.22*** 0.18*** (29.33) (23.71) (13.42) (-7.90) (23.00) (4.92) (11.72) (13.10) (12.56) (11.40)
Panel C: Factor loadings on the HML factor Panel D: Factor loadings on the WML factor
(RDt) Activeness (1- R2 t) (RDt) Activeness (1- R2 t)
A1 A2 A3 A3-A1 All A1 A2 A3 A3-A1 All
Low -0.03 -0.02 -0.10 -0.07 -0.05 Low 0.15*** 0.18*** 0.18*** 0.02 0.17*** (-0.52) (-0.37) (-1.22) (-1.12) (-0.78) (3.92) (4.34) (3.22) (0.55) (4.12) Medium 0.04 0.05 0.01 -0.03 0.03 Medium 0.18*** 0.19*** 0.16*** -0.02 0.18*** (0.84) (1.12) (0.22) (-0.71) (0.77) (4.35) (4.54) (3.26) (-0.54) (4.29) High 0.08*** 0.04 0.05 -0.02 0.06* High 0.08** 0.13*** 0.16** 0.08 0.12*** (3.01) (1.49) (1.16) (-0.57) (1.86) (2.42) (3.50) (2.61) (1.55) (3.17) All 0.06*** 0.04* 0.03 -0.04* 0.04** All 0.13*** 0.16*** 0.17*** 0.04 0.15*** (3.35) (1.78) (0.90) (-1.71) (2.00) (6.05) (7.24) (5.31) (1.62) (6.72)
5.3 Investor’s perspective
Table 7 displays the average annualized alpha from an investor’s perspective. These results are important because investors want to know whether they can use the R2t-1 and RDt-1 scores
23 outperform the benchmark over the full sample period. Within the return dispersion environments, there are only significant results for the high return dispersion level. The most active managers underperform the benchmark by 3.95% and underperform the least active funds by 2.52% during periods of high return dispersion. Furthermore, the average active fund (column All) underperforms the benchmark during periods of high return dispersion. Lastly, the only difference is that the medium activeness portfolio does not significantly underperform the benchmark when using the lagged values of return dispersion and activeness.
Overall, the results from an investor’s perspective are mainly the same as the ex-post results, showing that investors can use the activeness and return dispersion measure of the previous month to predict the results for the upcoming month. Therefore, these results could help to decide whether to follow a passive or an active strategy.
Table 7. FFC annualized alpha from an investor’s perspective, return dispersion and activeness
This table displays the average annualized alpha for each activeness portfolio in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t-1, where a high R2t-1 means that a fund has
a low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t-1 is
acquired by taking R2t of the previous month, which is obtained by regressing the fund’s 36-month excess
returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Each month, RDt-1 is obtained by taking the RDt of the previous month. Three return dispersion
(RDt-1) environments are presented, where the low environment includes the 30% months with the lowest level
of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, the average annualized alpha is calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the FFC model. These alphas, the intercept of the regressions, are annualized and reported below. The corresponding standard T-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5% and 10% level, respectively.
(RDt-1) Activeness (1-R2t-1) A1 A2 A3 A3-A1 All Low 1.04% -0.01% 0.09% -0.94% 0.33% (0.98) (-0.01) (0.06) (-0.92) (0.31) Medium 0.59% 0.03% 0.34% -0.25% 0.30% (0.53) (0.02) (0.19) (-0.18) (0.24) High -1.45% -2.02% -3.95%** -2.52%* -2.44%* (-1.06) (-1.45) (-2.13) (-1.82) (-1.72) All 0.69% -0.47% -0.95% -1.63%** -0.27% (1.02) (-0.70) (-1.00) (-2.27) (-0.38)
5.4 Robustness checks
5.4.1 Equally weighted return dispersion measure
24 stocks and underweight stocks that are sold at bargain prices. Another argument in favor of an equally weighted approach is that an active investor can choose both small and large capitalization stocks without giving more weight to the large capitalization stocks. Therefore, someone could argue that the equally weighted approach is a better representation of the opportunity set available, which is calculated as follows:
√
∑
(7)
Where, RDt is the monthly return dispersion for the index at time t, n is the number of
constituents in the index at time t, is the monthly return of the index constituent i at time t, and is the monthly equally weighted average return on index constituents at time t.9
Table 8. FFC annualized alpha, equally weighted return dispersion and activeness
This table displays the average annualized alpha for each activeness portfolio in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R2t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
presented, where the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, the average annualized alpha is calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the FFC model. These alphas, the intercept of the regressions, are annualized and reported below. The corresponding standard T-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5% and 10% level, respectively. (RDt) Activeness (1-R2t) A1 A2 A3 A3-A1 All Low 0.95% 0.35% 1.02% 0.06% 0.73% (1.04) (0.35) (0.75) (0.07) (0.73) Medium 0.77% -0.05% 0.06% -0.71% 0.23% (0.72) (-0.04) (0.03) (-0.48) (0.18) High -1.79% -2.69%** -4.01%** -2.26%* -2.82%* (-1.37) (-1.94) (-2.14) (-1.70) (-2.01) All 0.70% -0.52 -0.98% -1.67%** -0.29% (1.07) (-0.76) (-1.01) (-2.21) (-0.42)
Table 8 reports the annualized alphas for all portfolios in several equally weighted return dispersion environments. The alphas in table 8 are similar to the alphas in table 5 with the value-weighted return dispersion measure. On the aggregate level (row All), there are no significant alphas for any activeness portfolio, but the most active funds underperform the least active funds by 1.67%. Within the return dispersion environments, there are only
9
25 significant alphas in the high return dispersion environment. In line with our main results, the most active managers underperform the benchmark by 4.01% at a 5% significance level and all managers together underperform the benchmark by 2.82% during periods of high return dispersion. Furthermore, the most active managers significantly underperform the least active managers in times of high return dispersion. Therefore, we conclude that our results are robust for both return dispersion measures.
5.4.2 Other performance models
Table 2 in the data section reports a high correlation between the RMRF and WML factor. The high correlation could possible influence our results and therefore we regress the excess returns over the Fama-French (FF) and the CAPM model.10 The FF model and the CAPM model do not include the WML factor and are, therefore, good alternatives to overcome the correlation issue. Because the results of the CAPM model overestimate the alphas, the results are not included in the results section but can be found in appendix B. Moreover, an average alpha of 2.23% is reported for the whole sample and without sorting on a specific return dispersion environment. This overestimation is a result of omitting the significant SMB factor, which is positively related to the excess returns and is not highly correlated to the other factors.
Table 9 reports the annualized alphas obtained by regressing the portfolio’s excess returns on the FF model.11 The results are in line with our main results, which show a different interaction between activeness and return dispersion as the determinant of excess performance as Von Reibnitz (2015). The most active managers significantly underperform during periods of high return dispersion. For the full sample period, all funds together do not outperform the benchmark. An important new result is that the least active funds significantly outperform the benchmark by 2.89% during periods of low return dispersion and on the aggregate level by 1.72% (row All). Lastly, all managers together (column All), on average, outperform significantly during periods of low and medium return dispersion by respectively 2.42% and 2.44%.
Overall, omitting the WML factor shows that the underperformance relative to the benchmark by the most active managers during periods of high return dispersion is robust. A
10 Fama-French model:
( )
CAPM model: ( ) 11
26 new insight is that the least active funds significantly outperform the benchmark on the low, medium and aggregate return dispersion level. The outperformance indicates that investing in the least active managers is a good strategy for investors. Furthermore, the excess performance shows that the least active funds have skills that justify fees and expenses.
Table 9. FF annualized alpha, return dispersion and activeness
This table displays the average annualized alpha of the various activeness portfolios in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R
2
t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
presented, where the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, the average annualized alpha is calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the Fama-French three-factor model. These alphas, the intercept of the regressions, are annualized and reported below. The corresponding standard T-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5% and 10% level, respectively.
(RDt) Activeness (1-R2t) A1 A2 A3 A3-A1 All Low 2.89%*** 2.14%* 2.35%* -0.52% 2.42%** (2.78) (1.91) (1.68) (-0.54) (2.19) Medium 2.68%** 2.17%* 2.56%* -0.12% 2.44%** (2.39) (1.94) (1.99) (-0.15) (2.19) High -1.31% -2.52% -4.72%* -3.44%* -2.82%* (-0.96) (-1.52) (-1.89) (-1.70) (-1.68) All 1.72%** 0.74% 0.33% -1.36%* 0.01% (2.48) (0.99) (0.33) (-1.85) (1.20) 5.4.3 Volatility clustering
27
Table 10. GARCH annualized alpha, return dispersion environments and activeness
This table displays the average annualized alpha of the various activeness portfolios in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R2t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
presented, where the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, the average annualized alpha is calculated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the FFC model using a GARCH (1,1) model. These alphas, the intercept of the regressions, are annualized and reported below. The corresponding standard Z-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5% and 10% level, respectively.
(RDt-1) Activeness (1-R2t) A1 A2 A3 A3-A1 All Low 1.00% 0.23% 0.63% 0.37% 0.71% (0.90) (0.22) (0.51) (-0.39) (0.71) Medium 0.96% 1.05% -0.44% 1.06% 1.13% (0.87) (0.90) (-0.34) (1.33) (0.95) High -1.96% -4.56%*** -3.85% -0.35% -4.84%*** (-1.31) (-4.48) (-1.64) (-0.29) (-4.17) All 0.92% -0.04% -0.22% -1.38%*** 0.50% (1.50) (-0.06) (-0.26) (-2.61) (0.74)
5.5 Timing models
As Cremers and Petajisto (2009) argue, active management consists of two parts: stock selection and factor timing. Market timing could, therefore, be an explanation for the alphas in our main analysis. Treynor and Mazuy (1966) and Henriksson and Merton (1981) developed a model to test the influence of market timing on the alphas. Table 11 reports the timing coefficients for both models. Appendix D reports the specifications of both models. As both models are an extension of the CAPM model, alphas are also overestimated and follow a similar pattern as the CAPM alphas.12
For the Treynor and Mazuy model, a manager has timing ability when MT>0 and for the Henriksson and Merton model, c must be larger than zero. Table 11 shows that, in both models, managers have no or negative timing skills since the only significant coefficients are negative. However, the coefficient of the low activeness portfolio (A1) is positive in the low and medium return dispersion environment, suggesting some level of timing ability. Since these coefficients are insignificant, we cannot conclude that managers have positive timing skills. For the full sample period (row All), negative timing skills affect the alphas for the medium and high activeness portfolios. Furthermore, the most active managers have significantly less timing skills than the least active managers. Overall, timing skills provide
12
28 limited new insights for the alphas of fund managers. Lastly, a shortcoming of both models is that it ignores important factors such as SMB, HML and WML, resulting in overestimating the alphas and affecting the market timing coefficients.
Table 11. Market-timing coefficients, return dispersion and activeness
This table displays the timing coefficients of the various activeness portfolios in several return dispersion environments for the period January 2000 to August 2016. In each month, low (A1), medium (A2) and high (A3) activeness portfolios are created based on the mutual fund’s R2t, where a high R2t means that a fund has a
low level of activeness. A3-A1 is the difference between the high and low activeness portfolio. R2t is acquired
by regressing the fund’s 36-month excess returns (in excess of the 10-year UK government bond yield) prior to month t on Carhart’s (1997) Four Factor (FFC) model. Three return dispersion (RDt) environments are
presented, where the low environment includes the 30% months with the lowest level of return dispersion and high includes the 30% months with the highest level of return dispersion. Medium comprises the remaining months and All includes the full sample. Finally, the market-timing coefficient is estimated for each portfolio in the various return dispersion environments, by regressing the excess returns of a portfolio over the Treynor and Mazuy (1966) as well as Henriksson and Merton (1981) model. The corresponding standard T-statistics are shown in parentheses. ***, **, * indicate the significance at the 1%, 5%, 10% level, respectively.
Panel A: Timing coefficients (MT) of the Treynor and Mazuy model
(RDt) Activeness (1-R2t) A1 A2 A3 A3-A1 All Low 0.52 0.29 -0.49 -1.01 0.12 (0.44) (0.21) (-0.26) (-0.80) (0.09) Medium 0.70 0.26 -0.11 -0.80** 0.28 (1.78) (0.57) (-0.18) (-2.18) (0.62) High -0.17 -0.73 -1.03 -0.86 -0.65 (-0.49) (-1.40) (-1.28) (-1.36) (-1.25) All -0.04 -0.49* -0.89** -0.85*** -0.48* (-0.20) (-1.78) (-2.26) (-2.91) (-1.73)
Panel B: Timing coefficients (c) of the Henriksson and Merton model
(RDt) Activeness (1-R2t) A1 A2 A3 A3-A1 All Low 0.03 0.00 -0.05 -0.09 -0.01 (0.27) (-0.00) (-0.26) (-0.64) (-0.04) Medium 0.06 0.00 -0.04 -0.10 0.00 (0.72) (-0.03) (-0.37) (-1.33) (0.04) High -0.01 -0.11 -0.15 -0.14 -0.09 (-0.14) (-0.91) (-0.78) (-0.91) (-0.75) All -0.03 -0.10* -0.16* -0.13** -0.09 (-0.60) (-1.67) (-1.90) (-2.11) (-1.62)
