Measuring True Active Management Author

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Measuring True Active Management

Author

Maurits van Driem Student number: 1474553

University of Groningen

Faculty of Economics and Business Master’s Thesis, MSc Business Administration

Specialization: Finance

Supervisor

Dr. A. Plantinga

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ABSTRACT

Active share is a new measure to calculate the degree of active portfolio management. This study investigates the practical applicability of active share as a tool for the selection of asset managers. Furthermore, I study the determinants of active share. The sample consists of four U.S. asset managers for the period January 2000 to December 2009. Results show that active share significantly predicts fund performance. In addition, I find that the variables tracking error, number of stocks in the portfolio, lagged benchmark adjusted return and cross sectional market volatility explain around 80% in the variance of active share. Finally, I find that cross sectional market volatility is a new, significant predictor of active share.

JEL classification: G11, G23

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Introduction

Since the creation of the first index fund in 1973, passive management has increased dramatically. Passive management of a portfolio can be defined as “replicating the return on an index with a strategy of buying and holding all (or almost all) stocks in the same proportions as the index” (Cremers and Petajisto (2009)). While passive management is a relatively new investment strategy, active investing however, is as old as money management itself. Active management can be defined as any deviation from passive management (Cremers and Petajisto (2009)). Active mangers mostly rely on two strategies to produce outperformance, stock picking and market timing (Fama (1972)). Stock picking is about the ability of the fund manager to include (exclude) undervalued (overvalued) stocks in (from) the portfolio. Market timing involves manager’s skill in anticipating market movements and adjusting the risk level of the portfolio accordingly (Matallin (2006)). Active managers usually charge higher fees than passive managers (Cuthbertson, Nitzsche and O’Sullivan (2010)). The rationale behind those higher fees is that outperformance of the index is only possible by deviating from it. The portfolio manager is thus expected to have skill in either timing or stock picking (or both) to realize outperformance. This outperformance should cover, at a bare minimum, the management fees and other expenses. Otherwise an investor is better of by investing his capital in an index fund1_.

Academics have conducted numerous studies to test if active management outperforms passive management and so far the results are mixed. For example, studies by Jensen (1968), Gruber (1996) and Carhart (1997) find that the average mutual fund fails to outperform a passive benchmark. However, there are also several studies that document significant stock picking ability among active managers (Daniel et al. (1997), Wermers (2000), and Kosowski (2006)). These studies do a good job in determining the return difference between active and passive managers. However, from an investor point of view, these previously mentioned studies fail to cover an important aspect. With literally thousands of managers to choose from, varying from passive to very active and from low to high fees, the question that remains is: how can one verify if the manager is truly active? And what should be the fee for the varying degrees of active management? For

1_{Strictly speaking this is not always the case. Investors could settle for lower returns for various reasons. For}

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example, a study by Wermers (2000) compares mutual fund returns before and after expenses against a passive benchmark. However, he does so without differentiating between the varying management styles of the mutual funds. This distinction is crucial because the past twenty years showed a steady increase in the amount of closet indexers; these are funds which claim to be active, while in fact, they are not (Miller (2005)). An investor is thus paying fees for active management, while the manager is merely mimicking the index. This problem, measuring the degree of active management and the associated costs, has received relative little attention so far (Miller (2005) Cremers and Petajisto (2009)).

Miller (2005) is one of the first to provide a solution to the problem of measuring the true cost of active management. The author develops a measure to allocate fund expenses between an active and passive part of the portfolio. The results of this breakdown show that the average fund charges fees too high for the degree of active management delivered. Although this measure by Miller (2005) provides a way to gauge the cost of active management, it still fails to provide the investor with a measure that shows exactly how active the manager is. Recognizing the need for such a tool, Cremers and Petajisto (2009) take a different approach. Instead of focussing on returns they focus on fund holdings. Their measure is called “active share” and it represents the percentage of fund holdings that are different from the (benchmark) index. By construction, active share ranges between 0% and 100%. For example, an active share of 0% means that the fund holdings are identical to those of the index. An active share of 100%, however, indicates that the fund has zero overlap with the index. Active share solves the problem of finding true active managers by introducing transparency among funds. With active share, investors can easily identify and avoid closet indexers. Furthermore, Cremers and Petajisto (2009) find that active share is a significant predictor of fund return. Funds with the highest active share outperform their benchmark, both before and after expenses, and show strong persistence (Cremers and Petajisto (2009)).

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under management. TKPI makes use of a multi manager investment approach, meaning that they select and employ asset managers around the world. Since TKPI employs external managers to control their funds, it is imperative to have a good framework for the selection of their asset managers. The aim of this research is therefore to investigate the usefulness of active share as a selection tool for asset managers of TKPI. The research will be based on the methodology used by Cremers and Petajisto (2009) and the research questions are:

1. Is active share a predictor of fund return?

2. Can active share easily be explained by other variables?

Answering these questions should provide TKPI with a clear answer whether it can use active share as a tool in the selection process for their external managers. In addition, this research contributes to the literature in the following ways:

 First of all, this study adopts active share in a practical setting. So far, no tests have been done to check the applicability of active share as a selection tool for asset managers.

 Secondly, I add the variable “cross-sectional market volatility” as a new determinant of active share. To my knowledge, no study has yet tested whether cross-sectional market volatility explains active share.

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I Literature review

Traditionally, research about passive versus active investing focuses on the question whether active management generates outperformance or not2_{. The first one to} thoroughly investigate this question is Jensen (1968). In this seminal article he estimates a single factor model where fund return is corrected for market risk. The intercept of the regression equation represents the measure of security selection, also known as Jensen’s alpha. Jensen (1968) documents that, on average, mutual funds are unable to outperform a simple buy-hold strategy. Most of the studies hereafter use the single factor model of Jensen (1968) to investigate the benefits/detriments of active management. However, as the number of academic studies on mutual fund performance increases, researchers start to find evidence of flaws in the single factor model of Jensen (1968). The main criticism is that results from a single factor model are sensitive to the type of benchmark used (Grinblatt and Titman (1989)). Furthermore, in the 1980’s researchers find return anomalies and a certain degree of predictability in fund returns on the basis of fundamental values like dividend yield and size (Malkiel (1995)). Grinblatt and Titman (1989) recognize these flaws and the authors take a new approach to evaluating fund performance. Instead of using the traditional CAPM benchmark, they employ a benchmark which is based on 8 factor portfolios selected on the basis of size, dividend-yield and past returns. In addition, Grinblatt and Titman (1989) evaluate mutual funds on the basis of gross returns. Since almost all studies are based on net returns, the authors argue that a manager with alpha generating capabilities is more likely to charge higher fees. These fees will erode any alpha created by the manager and therefore an analysis based on net returns will fail to uncover this alpha (Grinblatt and Titman (1989)). In order to calculate gross returns for each fund, they look at quarterly portfolio holdings and construct the fund return based on those holdings. The results are interesting; first of all, they compare the hypothetical gross returns with the observed net returns and find that transaction costs and fees are quite large, around 2.5%. Secondly, abnormal performance, based on gross returns, is inversely related to fund size. Finally, they find that only aggressive-growth and growth funds exhibit outperformance. However, these positive, abnormal returns disappear when transaction

2_{Following Drew, Veeraraghavan and Wilson (2005), a manager has realized outperformance when the investment}

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costs and fees are taken into account (Grinblatt and Titman (1989)). More recent studies find similar results to those of Grinblatt and Titman (1989), i.e. successful active managers generate outperformance just enough to cover expenses. For example, Carhart (1997) does a comprehensive study among mutual funds and he finds that only the top mutual funds earn back their expenses due to higher gross returns. Furthermore, he finds that expense ratios and portfolio turnover are significantly, negatively related to performance.

In the 1990’s most studies continue to focus on the performance of mutual funds but they never make the distinction between the varying degrees of active management. Wermers (2003), however, is one of the first to make such a distinction. He uses tracking error as a measure for active management. Tracking error measures the standard deviation of the difference between fund return and benchmark return. In this case, the benchmark index is the S&P 500. Wermers (2003) reasons that although mutual funds in general underperform the index, there could be a small fraction of funds that outperform the index. Since outperformance can only be achieved by deviating from the index, a manager with “great” information will deviate more from the index than a manager with “good” information. Based on this line of reasoning, Wermers (2003) therefore states that it is useful to research whether funds with high tracking error outperform funds with low-to-zero tracking error. The results from his study are based on a sample of almost 2000 mutual funds and show that a substantial minority of mutual funds outperform. These funds can be characterized by a high degree of active management, i.e. tracking error. Wermers (2003) thus concludes that active management adds value, but that this added value is only reflected in a small number of funds that take large bets away from the S&P 500.

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better off investing in an index fund3_{. Miller (2005) therefore develops a measure to} allocate the expenses of a mutual fund to an active and a passive part. In order to measure how active a mutual fund is, Miller (2005) determines the R-squared of the fund. The R-squared is obtained by regressing excess fund returns on excess index returns. An R-squared of 100%, for example, would mean that all of the return variance of the fund could be explained by the index. In order to measure the true cost of active management, Miller (2005) develops a formula based on R-squared which gives the weights for the active part and the passive part of the fund. These weights form the basis of his “active expense ratio”, which are the fund expenses adjusted for the degree of active management. When this active expense ratio is applied to a sample of 152 large cap mutual funds, compromising both institutional and individual funds, Miller (2005) documents several noteworthy results. First of all, the mean R-squared of the sample is 96%. This is larger than the 95% threshold, which is generally viewed as a signal of closet indexing (Bogle (1999)). Secondly, the average fund has a mean published expense ratio of 1.15%, compared to an expense ratio of 0.18% for individual index funds and 0.05% for institutional index funds (Miller 2005)). This high R-squared (96%) combined with the relatively high expense ratio (1.15%) indicates that the average fund is probably overcharging investors for the degree of active management delivered. The results from Miller (2005) show that this is indeed the case. The average, active expense ratio is six times higher at 6.99% than the published expense ratio of 1.15%. Miller (2005) goes even further by reasoning that the outperformance, or alpha, of the fund should also be allocated to a passive and an active component which he calls “active alpha”. The results show that the average alpha was -1.5% while the resulting active alpha was -9.01%. Miller (2005) conducted the same tests on a larger sample of 4752 mutual funds and the results remain similar; measuring the degree of active management provides useful information for investors. Unfortunately, Miller (2005) implements no tests to investigate if the active expense ratio is a predictor of performance.

In a related paper, Kacperczyk, Sialm and Zheng (2005) also acknowledge the usefulness of distinguishing between the varying degrees of active management. They recognize that, on average, mutual funds underperform a passive benchmark. However, it could be

3_{An example often used is that of the Magellan fund. In 2004, 99% of the variance in Magellan’s returns could be}

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the case that mutual fund managers differ substantially in their investment abilities. For that matter, they reason that investment managers will hold more concentrated portfolios if they believe that certain industries will outperform the overall market, or if the manager has superior information regarding the selection of some stocks in particular industries. Consequently, Kacperczyk, Sialm and Zheng (2005) expect funds with skilled managers to hold more concentrated portfolios. Thus, a positive relation is expected between fund performance and industry concentration. In order to measure the industry concentration of a portfolio, the authors develop a measure called “Industry Concentration Index” (ICI). This measure closely resembles active share but instead of focussing on individual shares, the ICI focuses on industry holdings. More formally, the ICI quantifies the extent of portfolio concentration in 10 broadly defined industries. The index is equal to zero when the fund has exactly the same industry composition as the market index. An increase in the ICI indicates that the portfolio is more concentrated in a few industries. Their sample compromises 1771 actively managed equity mutual funds. The ICI for their sample ranges between 0.01% and 83.42% with a mean of 5.98%. In order to measure the relationship between fund performance and industry concentration, they first estimate outperformance for all of the individual funds according to a variety of performance attribution models. Next, all of the mutual funds are sorted into 10 portfolios based on their ICI. For each decile portfolio the average return is calculated. Their results show that the most concentrated portfolios significantly outperform more diversified portfolios. Similar results are obtained when they take expenses into account; concentrated funds outperform diversified funds even in the case of net returns (Kacperczyk, Sialm and Zheng (2005)). Besides this portfolio approach, the authors also examine the relationship between ICI and individual fund performance in a multivariate regression. They regress fund return on ICI and several other variables in order to control for risk and style exposures. Again, ICI is significantly positively related to performance. A 5% increase in ICI leads to 0.52% increase in yearly abnormal performance. As a result, the authors conclude that investment ability is more evident among managers who hold concentrated portfolios (Kacperczyk, Sialm and Zheng (2005)).

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and portfolio holdings (ICI). Cremers and Petajisto (2009) are the first to combine both methods in a framework which identifies active managers based on portfolio returns as well as portfolio holdings. First of all, they argue that the use of tracking error alone, as a measure for active management, is not sufficient. As mentioned earlier, active management consists of market timing and stock picking. However, these two styles contribute differently to tracking error. In order to illustrate this point, I will use the example provided in the paper from Cremers and Petajisto (2009). Consider two mutual funds; the first one is a pure stock picker and hopes to realize outperformance by picking stocks within industries, while at the same time aiming for high diversification across industries. The other fund is a market timer, and relies on picking entire sectors/industries which outperform the market as a whole while holding mostly diversified, i.e. passive, positions within those sectors. Clearly, both funds are engaged in active management but solely looking at their tracking error would provide a distorted picture. The tracking error of the diversified stock picker is considerably lower than the tracking error of the sector timer. This would lead to the incorrect conclusion that the former is less active while in fact its tracking error is simply lower because the individual stock picks allow for greater diversification (Cremers and Petajisto (2009)). Consequently, the authors propose the use of a new measure to fully capture both dimensions of active management. Their measure is called active share and, as noted earlier, closely resembles the ICI from Kacperczyk, Sialm and Zheng (2005). Active share is a measure which compares the portfolio holdings to the benchmark index. More specifically, it measures the fraction of the portfolio that is different from the index. Active share is zero if the portfolio has the exact same holdings as the index. If the manager starts to deviate from the index holdings, i.e. over/underweighting index stocks, his active share rises. An active share of 30% means that 70% of the portfolio holdings are identical to the index and the remaining 30% represent the manager’s active bets. Because active management consists of market timing and stock picking, Cremers and Petajisto (2009) propose to combine tracking error with active share. They argue that tracking error can be used as a proxy for market timing and active share as a proxy for stock picking4_.

4_{To understand why tracking error can be used as a proxy for market timing, remember that tracking error is the}

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Figure 1 illustrates the different types of active management according to this concept. First of all, a closet indexer has low tracking error and low active share, but still claims to be an active manager. The diversified stock picker, however, is despite its low tracking error an active manager because stock selection within industries can still lead to large deviations from the benchmark portfolio. On the other hand, factor bets can lead to high tracking error even without large deviations from the benchmark holdings. Finally, the most active managers have both high tracking error as well as high active share.

Figure 1: Different types of active and passive management

The y-axis represents active share, which is the fraction of the portfolio holdings that is different from the index. The x-axis represents tracking error, which measures the volatility of the fund return in excess of the benchmark return.

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High Diversified Concentrated stock

picks stock picks

Low Closet Factor bets

indexing 0 Pure indexing 0 Low High Tracking error

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II Methodology

II.1 Active share

Active share is a simple concept which provides an intuitive way of measuring active management. I use the measure proposed by Cremers and Petajisto (2009):

,

2

1

1 , ,









N i i index i fund

W

share

Active

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where Wfund,i and Windex,i are the portfolio weights of asset i in the fund and in the index.

Basically, a portfolio can be decomposed into a 100% position in the benchmark index plus a zero-net-investment long-short portfolio. This zero-net-investment long-short portfolio represents the active bets of the manager. Because the sum of the portfolio weight differences is divided by two, active share will always range between 0% and 100%5_{. For example, a fund that is for 10% invested in the index will have an active} share of 90%. Active share can thus be interpreted as “the fraction of the portfolio that is different from the benchmark index” (Cremers and Petajisto (2009)).

II.2 Model specification

In order to estimate the relationship between fund return and active share, a pooled OLS regression is performed. It is expected that an increase in active share will lead to a higher fund return while controlling for market exposure, size, value and momentum. This leads to the following expression:

,

, 5 4 3 2 , 1 ,t f it it i

R

AS

RMRF

HML

SMB

MOM

R































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where Ri,t is gross fund return at the end of month t; Rf is the risk free rate; α is a

constant; ASi,t is active share at the end of month t. Based on the findings by Cremers

and Petajisto (2009) it is expected that the coefficient of active share will be positive and significant and thus providing evidence that active share is a useful tool for the selection of asset managers. Finally, RMRF, HML, SMB and MOM are zero investment, factor mimicking portfolios for market exposure, size, book-to-market equity and momentum. These four factors are commonly used for the evaluation of fund performance and are an extension of the three factor model developed by Fama and French (1993). Fama and French (1993) showed that most of the variability in fund returns could be explained by

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three factors: market exposure, value and size. Carhart (1997) complemented the three factor model of Fama and French (1993) by adding a fourth factor, momentum, to explain the tendency of past winners to continue strong performance for several periods. This four factor model can explain most of the variance in returns and is therefore commonly used to evaluate portfolio performance.

If active share is indeed positive and significant then the next step is to test what explains active share. If active share is not easily explained by other variables then it is indeed a new dimension to measure active management. In order to explain active share a pooled OLS regression is performed where active share is regressed on tracking error, stock holdings, lagged benchmark-adjusted returns and cross-sectional market volatility:

_, ₁ _, ₂ _, ₃

(

_, ₁ _, ₁

)

₄ _, _i_,_t

,

t cs t m t i t i t i t i

TE

Stocks

R

AS

















_



_











(3)

where TEi,t is the annualized tracking error at the end of month t. Tracking error is

constructed by regressing excess fund returns on excess benchmark returns and taking the standard deviation of the residuals. This eliminates the effect on tracking error caused by any persistent allocation to cash or high-beta, low-beta stocks (Cremers and Petajisto (2009)).

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(5) where Ri,t is the fund return and Rm,t is the benchmark index return. Beforehand the

sign of tracking error is not known since, as shown in figure one, high tracking error does not necessarily mean a high level of active share. Continuing with the variables in equation 3, Stocksi,t is the number of different stocks held in the portfolio at the end of

month t. A high number of different stocks in the portfolio is likely to lead to more overlap with the index compared to a fund with less diversity. Consequently, I expect a negative relationship between active share and the number of different stocks in the portfolio. Ri,t-1 is the benchmark adjusted return at the end of month t-1. Findings from

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tend to increase their active share. Therefore, I expect that good prior performance will lead to an increase in active share. σcs,t is the cross-sectional standard deviation of the

market return at the end of month t. The cross sectional standard deviation of the market return is calculated in the following way:

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where σcs,t is the cross-sectional market volatility at the end of month t; Ri,t is the return

of security i in the market index at the end of month t; Rm,t is the equally weighted

market index return at the end of month t. The S&P 500 is used to represent the market index. Until now, no studies have tested the influence of market volatility on the degree of active management. As a result, prior research provides no indication about the expected sign. However, I expect that higher cross-sectional market volatility will lead to an increase in active share. A volatile market provides more opportunity for generating excess return. Consequently, this provides an incentive for skilled managers to increase their active bets. Table I provides an overview of all the variables and their expected sign.

Table I: Overview of the independent variables including their expected sign

Independent Variable Definition Expected sign

Active Share The fraction of the portfolio holdings that are

different from the benchmark index +

Tracking Error

The standard deviation of the residuals obtained by regressing excess fund returns on excess benchmark returns

+/-

Stocks Number of different stocks in the portfolio -

Lagged benchmark

adjusted return Fund return (t-1) minus benchmark return (t-1) +

σcs

Cross-sectional standard deviation of the market

(S&P 500) +

Control Variables

RMRF Excess market return HML High Minus Low book-to-price ratio SMB Small Minus Big capitalization

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III Data

III.1 Sample

TKPI employs 22 asset managers around the world to manage its equity portfolio. Together these managers have a total of €3.4 billion in assets under management for TKPI (July 2010). Since an active share study involving all the asset managers is unmanageable because of the large amount of holdings, a sample was chosen from the 22 managers. In order to select the sample, three criteria were used. The first criterion is the availability of data. There is considerable variation in the length of service for the asset managers and thus the availability of historical data. The second criterion is that the manager must have an all-equity, long only portfolio. Although active share can still be calculated for portfolios with bonds and derivatives, it greatly complicates calculations. Finally, heterogeneity in the investment style among funds is preferred. A sample compromising only quantitative managers would probably result in a sample with low active share since quantitative managers mainly optimize their portfolio against the benchmark. Therefore, a diverse sample consisting of both fundamental and quantitative managers is preferred.

When the previously mentioned criteria are applied, the resulting sample compromises all the asset managers in the U.S. for the period of January 2000 to December 2009. These managers are: Asset Manager A, Asset Manager B, Asset Manager C and Asset Manager D. Of the aforementioned managers, only Manager C is no longer employed by TKPI.

III.2 Data collection

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and returns. As already mentioned, Manager C was fired in 09/2009, which results in unavailable data for the final three months of the research period. Finally, data on fund returns received from the managers are returns net of transaction costs. Table II shows an overview of the four managers, their investment style, monthly holdings, employment period, the final sample period and the number of months of available data.

Table II: Overview of investment manager style, monthly holdings, employment period, final sample period and total # of observations.

Asset Investment Average Employment Final # of Manager style monthly holdings Min Max period sample period months

A Fundamental 49 46 51 2006-now 01/2000 - 12/2009 120 B Fundamental 57 49 74 2006-now 01/2000 - 12/2009 120 C Quantitative 171 122 261 1998-2009 01/2000 - 09/2009 117 D Quantitative 238 150 401 2001-now 12/2001 - 12/2009 97

Total 454

The U.S. managers are all evaluated against the MSCI USA index. Consequently, this index is used as the main benchmark index for the active share study. In addition, data on the S&P 500 is also acquired. This in order to evaluate which index produces the lowest active share. The benchmark which produces the lowest active share has the most overlap with the portfolio and is therefore assigned as the “correct” benchmark for that period. Data on the benchmarks holdings and returns was retrieved from multiple sources. The holdings of the MSCI USA index were retrieved from MSCI and the holdings for the S&P 500 were obtained via Asset Manager D. All the returns for the benchmark indices were downloaded via Thompson DataStream and include dividends. Finally, it must be noted that the portfolio of Manager D was benchmarked to the FTSE US for the period 12/2001 to 12/2005. Unfortunately, no data was available for this index and therefore no changes were made in the benchmark.

III.3 Active share

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After these modifications for Manager C, the next step was to create a unique ID code for each security. The ID code is based on a combination of the date and its SEDOL6 code. In some cases a fund only had CUSIP7_{codes so in that case an ID code was created} based on date and CUSIP. For Manager C neither SEDOL nor CUSIP was available for the period 2008-2009. In this case an ID code was made based on date and ticker symbol (downloaded via Bloomberg). For the benchmark indices the same process of creating a unique ID based on SEDOL, CUSIP and ticker was used. This procedure results in one file with both the fund holdings and the benchmark holdings for the entire sample period. Next, a lookup function in Excel matches the securities in the fund to the appropriate securities in the index. If the function could not find the security, i.e. the fund is investing outside the index, it would show a zero (i.e. a weight of zero % in the index). Finally, the sum of the absolute differences between the fund and the index were taken for each month to obtain active share. However, only the over weighted positions in the portfolio were summed because this saves the trouble of finding all the implicit under weightings. Since only the over weightings were summed, the final active share value was not divided by two. Graph 1 shows the development of active share over time for the four funds. As expected, the graph shows a clear distinction in active share between the quantitative managers and the fundamental managers. The former has an active share ranging between 40% and 70% while the latter shows a higher and less volatile active share of 70% to 80%. Finally it must be noted that the sharp drop in active share for Manager D in 2007 is due to significant rebalancing of the portfolio.

III.4 Tracking Error

Tracking error is computed in two ways. The first method is by simply taking the time series standard deviation of the difference between the fund return and the benchmark return. The second method is by regressing excess fund returns on excess index returns and using the standard deviation of the residuals as tracking error. Both methods make use of monthly returns and the resulting tracking error is on a yearly basis. Returns prior to 2000 were available for Manager A, B and C. Since the fund of Manager D started in December 2001, tracking error is available starting from December 2002. Table III shows summary statistics for the key variables of the four managers and the corresponding correlation matrix can be found in appendix A.

6_{SEDOL: Stock Exchange Daily Official List. A SEDOL is a security identifier used in the U.K. and Ireland.} 7_{CUSIP: Committee on Uniform Securities Identification Procedures. A CUSIP is a security identifier used in the}

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Graph I: Development of active share for the U.S. managers from 2000-2010 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Development of active share from 2000-2010

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Table III: Summary statistics key variables

Ri-Rf is the monthly fund return net of transaction costs minus the risk free rate; AS is active share;

TE* is yearly tracking error calculated as the standard deviation of the difference between the fund return and the index return; TE is yearly tracking error calculated by regressing excess monthly returns on excess index returns and taking the standard deviation of the residuals as tracking error; Stocks is the number of different stocks in the portfolio; Rm-Rf is the benchmark return minus the

risk-free rate and Ri-Rm (t-1) is the one month lagged benchmark-adjusted return.

Manager A Ri-Rf AS TE* TE Stocks Rm-Rf Ri-Rm (t-1)

Mean 0.20 72.31 4.71 4.72 49 -0.23 0.42 Median 0.31 72.36 4.09 4.09 50 0.44 0.34 Maximum 12.02 76.08 10.02 9.96 51 9.56 4.82 Minimum -17.29 66.81 2.09 2.10 46 -16.88 -3.65 Std.Dev. 4.89 1.97 2.15 2.15 1.12 4.69 1.43 Skewness -0.45 -0.40 0.94 0.91 -0.77 -0.51 0.64 Kurtosis 3.88 2.78 2.68 2.62 3.14 3.73 3.94 N 120 120 120 120 120 120 120

Manager B Ri-Rf AS TE* TE Stocks Rm-Rf Ri-Rm (t-1)

Mean 0.20 74.12 5.11 5.08 57 -0.24 0.42 Median 0.08 74.42 5.01 4.94 55 0.44 0.41 Maximum 10.48 78.83 8.89 8.92 74 9.56 4.76 Minimum -17.72 67.07 2.81 2.84 49 -16.88 -3.02 Std.Dev. 5.04 2.21 1.57 1.58 6.77 4.69 1.56 Skewness -0.43 -0.44 0.36 0.38 1.10 -0.51 0.56 Kurtosis 3.75 3.10 1.96 1.98 3.13 3.73 3.42 N 120 120 120 120 120 120 120

Manager C Ri-Rf AS TE* TE Stocks Rm-Rf Ri-Rm (t-1)

Mean -0.24 52.63 2.40 2.37 171 -0.25 -0.19 Median 0.61 55.75 2.32 2.29 159 0.40 0.62 Maximum 8.78 63.70 4.38 4.04 261 9.56 8.78 Minimum -16.55 34.83 1.33 1.28 122 -17.18 -16.55 Std.Dev. 4.63 9.06 0.76 0.70 38.24 4.70 4.64 Skewness -0.55 -0.44 0.72 0.45 0.62 -0.53 -0.55 Kurtosis 3.50 1.68 2.98 2.39 2.09 3.80 3.47 N 117 117 117 117 117 117 118

Manager D Ri-Rf AS TE* TE Stocks Rm-Rf Ri-Rm (t-1)

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IV Results

The results of the first regression, as described in equation (2), can be found in table IV. First of all, the three control variables HML, SMB and MOM have a positive sign but the results are not significant. Therefore, none of the funds had considerable exposure to value, size or momentum factors. However, the variable RMRF is highly significant. With a coefficient of almost 1 there is substantial market exposure. Furthermore, table IV shows that the active share coefficient is positive and highly significant. A 1% increase in active share leads to a 0.016% increase of the monthly excess return. These findings are in line with the rese arch of Cremers and Petajisto (2009) where they find that active share significantly predicts fund performance, although their coefficient is much lower with a value of 0.0048_{. This lower coefficient is likely to be the result of a} small difference in the specification of the dependent variable. The study by Cremers and Petajisto (2009) makes use of benchmark adjusted returns, whereas I make use of fund return in excess of the risk free rate.

Table IV: Effects of active share on excess fund return

The following equation is estimated in a pooled regression for the period 2000-20109:

t i t i f t i R AS RMRF HML SMB MOM R,  1 , 2 3 4 5 ,

where Ri,t is gross fund return at the end of month t; Rf is the risk free rate; α is a constant; ASi,t is active share; RMRF,

HML, SMB and MOM are zero investment, factor mimicking portfolios for market exposure, size, book-to-market equity

and momentum. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

Variable Coefficient t-Statistic

Constant -0.809 -2.520* AS 0.016 2.864** RMRF 0.988 42.317** HML 0.027 1.024 SMB 0.044 1.811 MOM 0.005 0.231 R-squared 0.934 Adjusted R-squared 0.933 N 454

In addition, the study by Kacperczyk, Sialm and Zheng (2005) documents similar results based on their Industry Concentration Index, a measure strongly related to active share. They find that more concentrated portfolios perform better than funds with a more diversified portfolio; a 5% increase in portfolio concentration leads to a 0.5% increase in

8_{The results from the study of Cremers and Petajisto (2009) are on a yearly basis. For comparative purposes I have}

transformed the coefficient from a yearly basis to a monthly basis.

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yearly return. Continuing with table IV, the R-squared and adjusted R-squared are very high with values of 0.934 and 0.933 respectively. Next, I also estimated a pooled regression where active share is a cross-sectional varying coefficient. This leads to a breakdown of active share into four coefficients which represent the four managers. Table V shows the results of this pooled regression with a cross-sectional varying active share coefficient. The coefficients of active share are positive for all of the managers. In addition, the active share coefficients of Asset Manager A and B are significant at the 5% level. These coefficients are slightly lower (0.011 and 0.011) compared to the results from the first regression (0.016). Again, the regression has a very high R-squared (0.934) and adjusted R-squared (0.933), indicating a good fit of the model. As mentioned earlier, Cremers and Petajisto (2009) make use of benchmark adjusted returns for their research. As a robustness check, I have estimated two additional pooled regressions where benchmark adjusted returns and fund returns are used as a dependent variable10_. The results remain the same for both specifications. However, if the dependent variable is benchmark adjusted returns, the R-squared and adjusted R-squared drop significantly with values of 0.041 and 0.030 respectively.

Table V: Effects of active share on excess fund return with a cross-sectional varying coefficient

t i t i f t i R AS RMRF HML SMB MOM R_,  ₁ _, ₂ ₃ ₄ ₅  _,

where Ri,t is gross fund return at the end of month t; Rf is the risk free rate; α is a constant; ASi,t is active share with a cross sectional varying coefficient for the four managers; RMRF, HML, SMB and MOM are zero investment, factor mimicking portfolios for market exposure, size, book-to-market equity and momentum. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

C -0.405 -1.213 AS Manager A 0.011 2.094* AS Manager B 0.011 2.021* AS Manager C 0.007 1.146 AS Manager D 0.009 1.460 RMRF 0.989 42.220** HML 0.027 1.022 SMB 0.043 1.783 MOM 0.006 0.258 R-squared 0.934 Adjusted R-squared 0.933 N 454

10_{These results can be found in appendix B.}

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The previous results show that active share is indeed a significant predictor of fund return. In order to find out what explains active share, I estimated a pooled regression where active share is regressed on a variety of explanatory variables as described in equation (3). The results of this pooled regression can be found in table VI. It must be noted that for this regression a fixed effects model was used. A fixed effects model is used to account for latent firm-specific effects. In the case of a simple pooled regression it is assumed that the intercept is the same across funds and through time. A fixed effects model, however, allows the intercept to vary across the different funds (but not trough time) instead of keeping it constant12_{(Brooks (2008)). The results in table VI show that} all the variables, except for the lagged benchmark adjusted return, are significant at the 1% level.

Table VI: Explaining active share

The following equation is estimated in a pooled, fixed effects regression for the period 2000-201013:

t i t cs t m t i t i t i t i TE Stocks R R AS, 1 , 2 , 3( ,1 ,1)4 , , ,

where TEi,t is the annualized tracking error at the end of month t; Stocksi,t is the number of different stocks held in the portfolio at the end of month t; Ri,t-1-Rm,t-1 is the one month lagged benchmark adjusted return and σcs,t is the cross-sectional standard deviation of the S&P 500 at the end of month t. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

Constant 75.383 50.189**

TE 0.757 4.622**

Stocks -0.096 -7.899**

Ri-Rm (t-1) 0.099 0.705

σcs -1.743 -3.141**

Fixed effects (cross-sectional) Constant Manager A 0.173 Constant Manager B 2.444 Constant Manager C -5.986 Constant Manager D 4.546 R-squared 0.824 Adjusted R-squared 0.821 N 442

Tracking error has a positive sign and is highly significant14_{. The relationship indicates} that for every 5% increase in tracking error, active share will rise with almost 4%. Cremers and Petajisto (2009) find similar results; they find a highly significant

12_{The regressions from equation (2) were also estimated as a fixed effects model. However, a redundant fixed effects}

test revealed that it is not valid to allow for a cross-sectional varying intercept and therefore the results of this regression are not shown.

13_{The residual plot for these results can be found in appendix C3.}

14_{The same regression was also performed where tracking error is simply the standard deviation of the difference}

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coefficient of 1.811. Next, stocks are negatively related to active share, although the effect is quite small (-0.096). This result was expected since a portfolio with a high number of different stocks is more likely to have a large overlap with the index resulting in a lower active share. Cremers and Petajisto (2009) also document a (negligible) negative relationship between stocks and active share. The variable lagged benchmark adjusted return is positive but not significant. Apparently good prior performance tends to result in more active bets by the manager, but not in a significant way. Interestingly, there is a negative relationship between cross-sectional market volatility and active share. A positive relationship was expected since a volatile market provides more opportunities for stock picking. However, results show that an increase of 1% in market volatility is associated with a decrease in active share of 1.74%. An explanation for this negative relationship could be that asset managers want to reduce the chances of underperformance during volatile markets. Although a volatile market provides ample opportunities for outperformance, an (unskilled) manager also has a higher chance of underperforming. Therefore, a manager unsure of his stock picking ability is more likely to reduce his active share, instead of increasing it. Overall, the four variables in equation (3) explain about 82% of the variability in active share. This is higher compared to the results from the study by Cremers and Petajisto (2009) where their broadest specification has an R-squared of only 32%. These results indicate that the four variables from equation (3) do a reasonably good job in explaining most of the variance in active share.

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more stocks are included in the portfolio. Continuing with tracking error, only Manager A shows results similar to the previous regression. Manager B has an insignificant positive coefficient while Manager C has a significant negative coefficient (-1.354). Manager D has an extremely high coefficient of 2.470 which is significant at the 1% level. Finally, the results for the lagged benchmark adjusted return are similar to the previous regression with no significant coefficients. Strangely, all the variables for Manager C are negatively related to active share. Except for the variable “stocks”, I can find no plausible explanation why this is the case.

Table VII: Explaining active share with a cross-sectional varying coefficient

The following equation is estimated in a pooled, fixed effects regression for the period 2000-201015_:

t i t cs t m t i t i t i t i TE Stocks R R AS, 1 , 2 , 3( ,1 ,1)4 , , ,

where TEi,t is the annualized tracking error at the end of month t; Stocksi,t is the number of different stocks held in the portfolio at the end of month t; Ri,t-1-Rm,t-1 is the one month lagged benchmark adjusted return and σcs,t is the cross-sectional standard deviation of the S&P 500 at the end of month t. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

C 71.001 23.080** TE Manager A 0.789 5.384** TE Manager B 0.108 0.549 TE Manager C -1.354 -2.523* TE Manager D 2.470 5.383** Stocks Manager A 0.034 0.175 Stocks Manager B 0.166 4.018** Stocks Manager C -0.154 -8.319** Stocks Manager D -0.049 -4.924** Ri-Rm (t-1) Manager A 0.112 0.979 Ri-Rm (t-1) Manager B 0.051 0.348 Ri-Rm (t-1) Manager C -0.610 -0.817 Ri-Rm (t-1) Manager D 0.668 1.256 σcs -1.594 -2.738**

Fixed Effects (Cross)

Constant Manager A -2.175 Constant Manager B -5.000 Constant Manager C 13.069 Constant Manager D -7.860 R-squared 0.851 Adjusted R-squared 0.846 N 442

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V Conclusion

V.1 Summary of key findings

With the development of the active share measure by Cremers and Petajisto (2009), investors have a new tool at their disposal for the selection of asset managers. Active share can be interpreted as “the fraction of the portfolio that is different from the benchmark index” (Cremers and Petajisto (2009)). Recent research about the performance of active management finds that differentiating between the degree of active management is valuable; more active funds tend to outperform less active/passive funds (Wermers (2003), Kacperczyk, Sialm and Zheng (2005) and Cremers and Petajisto (2009)). TKPI, a company specializing in fiduciary management, selects external managers to invest their assets. Consequently, the purpose of this study was to test whether active share can be used as a tool for the selection of external managers. The resulting research questions were: is active share a predictor of fund performance and what explains active share? The sample used in this study consists of four investment managers employed by TKPI. The portfolio holdings and return data were supplied by the managers and covers the period January 2000 trough December 2009. In order to test if active share is a predictor of fund return, active share was regressed on excess gross return while controlling for market exposure, value, size and momentum. To test what explains active share, a pooled regression was performed with cross sectional market volatility, tracking error, number of stocks in the portfolio and lagged benchmark adjusted return as independent variables.

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variables cross sectional market volatility, tracking error, number of stocks and lagged benchmark adjusted return explain 83% of the variance in active share. This number is higher compared to the results of Cremers and Petajisto (2009) where they find that their broadest specification results in an R-squared of only 32%. Finally, I found that all the variables, except for lagged benchmark adjusted return, are significantly related to active share. Prior research has not yet investigated the relationship between active management and market volatility. My findings show that there is a significant negative relationship between active share and market volatility. A possible explanation for this phenomenon could be that mangers want to minimize the risk of underperformance during volatile markets. To conclude, I find that active share significantly predicts performance and other variables can, at most, explain around 80% in the variance of active share. Consequently, TKPI can use active share as an additional measure for the selection of asset managers.

V.2 Limitations

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References

Bogle, John C., 1999, Common sense on mutual funds (New York, John Wiley & Sons). Brooks, Chris, 2008, Introductory econometrics for finance (Cambridge University Press, Cambridge).

Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 57-82.

Cremers, Martijn K.J., and Antti Petajisto, 2009, How active is your fund manager? A new measure that predicts performance, Review of Financial Studies 22, 3329-3365. Cuthbertson, Keith, Dirk Nitzsche, and Niall O’Sullivan, 2010, Mutual fund performance: Measurement and evidence, Financial Markets, Institutions & Instruments 19, 95-187.

Daniel, Kent, Mark Grinblatt, Sheridan Titman, and Russ Wermers, 1997, Measuring mutual fund performance with characteristic-based benchmarks, Journal of Finance 52, 1035-1058.

Drew, Michael E., Madhu Veeraraghavan, and Vanessa Wilson, 2005, Market timing, selectivity and alpha generation: Evidence from Australian equity superannuation funds, Investment Management and Financial Innovations 2, 111-127.

Fama, Eugene F., 1972, Components of investment performance, Journal of Finance 27, 551-567.

Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56.

Grinblatt, Mark, and Sheridan Titman, 1989, Mutual fund performance: An analysis of quarterly portfolio holdings, Journal of Business 62, 393-416.

Gruber, Martin J., 1996, Another puzzle: The growth in actively managed mutual funds, Journal of Finance 51, 783-810.

Jensen, Michael C., 1968, The performance of mutual funds in the period 1945-1964, Journal of Finance 23, 389-416.

Kacperczyk, Marcin, Clemens Sialm, and Lu Zheng, 2005, On the industry concentration of actively managed equity mutual funds, Journal of Finance 60, 1983-2011.

Kosowski, Robert, Allan Timmermann, Russ Wermers, and Hal White, 2006, Can mutual fund “stars” really pick stocks? New evidence from a bootstrap analysis, Journal of Finance 61, 2551-2595.

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Matallín-Sáez, Juan C., 2006, Seasonality, market timing and performance amongst benchmarks and mutual fund evaluation, Journal of Business Finance & Accounting 33, 1484-1507.

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Appendix A: Correlation tables

Table A1: Correlation table Asset Manager A

Correlation coefficients larger than 0.5 or -0.5 are marked in red

Manager A Ri-Rf AS Rm-Rf HML SMB MOM TE* TE Stocks Ri-Rm (t-1) σcs

Ri-Rf 1.00 AS -0.09 1.00 Rm-Rf 0.96 -0.13 1.00 HML -0.07 0.28 -0.07 1.00 SMB 0.08 0.06 0.09 -0.40 1.00 MOM -0.55 0.15 -0.52 -0.11 0.11 1.00 TE -0.09 0.51 -0.18 0.22 0.07 0.04 1.00 TE* -0.10 0.51 -0.18 0.22 0.08 0.04 1.00 1.00 Stocks -0.19 0.12 -0.20 0.08 -0.10 0.02 0.18 0.18 1.00 Ri-Rm (t-1) -0.09 0.12 -0.09 0.13 0.06 0.04 0.23 0.23 0.08 1.00 σcs 0.07 0.04 0.00 0.01 0.10 -0.40 0.54 0.54 0.09 0.23 1.00

Table A2: Correlation table Asset Manager B

Manager B Ri-Rf AS Rm-Rf HML SMB MOM TE* TE Stocks Ri-Rm (t-1) σcs

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Table A3: Correlation table Asset Manager C

Manager C Ri-Rf AS Rm-Rf HML SMB MOM TE* TE Stocks Ri-Rm (t-1) σcs

Ri-Rf 1.00 AS 0.22 1.00 Rm-Rf 0.99 0.22 1.00 HML -0.08 -0.10 -0.08 1.00 SMB 0.13 -0.04 0.10 -0.43 1.00 MOM -0.46 0.00 -0.52 -0.10 0.12 1.00 TE 0.13 0.05 0.10 0.04 0.09 -0.10 1.00 TE* 0.11 0.06 0.08 0.06 0.10 -0.07 0.97 1.00 Stocks -0.24 -0.71 -0.23 0.05 0.01 -0.04 -0.26 -0.27 1.00 Ri-Rm (t-1) -0.06 0.00 -0.05 -0.09 -0.08 0.05 0.12 0.13 -0.09 1.00 σcs -0.02 -0.70 0.01 0.00 0.09 -0.40 -0.05 -0.08 0.61 -0.05 1.00

Table A4: Correlation table Asset Manager D

Manager D Ri-Rf AS Rm-Rf HML SMB MOM TE* TE Stocks Ri-Rm (t-1) σcs

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Appendix B: Robustness checks

Table B1: Effects of active share on fund return

t i t i t i AS RMRF HML SMB MOM R, 1 , 2 3 4 5 ,

where Ri,t is gross fund return at the end of month t; α is a constant; ASi,t is active share; RMRF, HML, SMB and MOM are zero investment, factor mimicking portfolios for market exposure, size, book-to-market equity and momentum. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

Constant -0.685 -2.154* AS 0.018 3.135** RMRF 0.988 39.724** HML 0.033 1.167 SMB 0.041 1.570 MOM 0.008 0.332 R-squared 0.931 Adjusted R-squared 0.930 N 454

Table B2: Effects of active share on benchmark adjusted return

t i t i t m t i R AS RMRF HML SMB MOM R,  , 1 , 2 3 4 5 ,

where Ri,t is gross fund return at the end of month t; Rm,t is the benchmark return at the end of month t; α is a constant;

ASi,t is active share; RMRF, HML, SMB and MOM are zero investment, factor mimicking portfolios for market exposure, size, book-to-market equity and momentum. T-statistics are cross-section White consistent, * and ** denote 5% and 1% significance levels respectively.

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Appendix C: Residual plots

Graph C1: Residual plot from results in table IV

Graph C2: Residual plot from results in table V

Residuals Asset Manager A Residuals Asset Manager B

Residuals Asset Manager C Residuals Asset Manager D

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Graph C3: Residual plot from results in table VI 0 2 4 6 8 10 12 14 -6 -4 -2 0 2 4 6 F re q u e n c y RESID_MC 0 4 8 12 16 -8 -4 0 4 8 F re q u e n c y RESID_VIC 0 5 10 15 20 25 -15 -10 -5 0 5 10 F re q u e n c y RESID_GS 0 2 4 6 8 10 12 -30 -20 -10 0 10 20 F re q u e n c y RESID_LA

Graph C4: Residual plot from results in table VII

0 4 8 12 16 -6 -4 -2 0 2 4 F re q u e n c y RESID_MC 0 4 8 12 16 -8 -4 0 4 8 F re q u e n c y RESID_VIC 0 4 8 12 16 -15 -10 -5 0 5 10 15 F re q u e n c y RESID_GS 0 2 4 6 8 10 12 -20 -15 -10 -5 0 5 10 F re q u e n c y RESID_LA

Residuals Asset Manager C Residuals Asset Manager D

Measuring True Active Management Author