Survivorship Bias and Mutual Fund Performance

Survivorship Bias and Mutual Fund Performance: Relevance, Significance, and Methodical Differences.

Martin Rohleder+ Hendrik Scholz++ Marco Wilkens+++

Working Paper Ingolstadt School of Management Catholic University of Eichstaett-Ingostadt

First version: 2007-08-28 This version: 2007-12-03

+

Martin Rohleder, Ingolstadt School of Management, Catholic University of Eichstaett-Ingolstadt, Auf der

Schanz 49, D-85049 Ingolstadt, Germany, phone: +49 841 937 1991, fax: +49 8421 93 2991, email: [email protected]. ++

Corresponding author: Hendrik Scholz, Ingolstadt School of Management, Catholic University of Eichstaett-

Ingolstadt, Auf der Schanz 49, D-85049 Ingolstadt, Germany, phone: +49 841 937 1878, fax: +49 8421 93 2878, email: [email protected]. +++

Marco Wilkens, Ingolstadt School of Management, Catholic University of Eichstaett-Ingolstadt, Auf der

Schanz 49, D-85049 Ingolstadt, Germany, phone: +49 841 937 1883, fax: +49 8421 93 2883, email: [email protected].

Survivorship Bias and Mutual Fund Performance: Relevance, Significance, and Methodical Differences.

Abstract Since many commercial datasets still include only those funds that are currently in operation, survivorship bias is an important issue in studies of mutual fund performance. This article is the first to systematically examine the existence, significance, and the drivers of survivorship bias by applying the various different methods and definitions used in previous research on a uniform fund dataset (CRSP). We show that there is significant survivorship bias when closed funds are ignored, and that the choice of methods and definitions is crucial for the magnitude of the survivorship bias estimates. Furthermore we examine in detail the performance and fund size of closed funds which drives survivorship bias. Closed funds clearly underperform surviving funds years before they are actually closed. Fund size is a key characteristic for closing decisions. The larger a fund, the lower the likelihood that funds are closed, even if the returns are temporarily relatively low.

Keywords: Mutual Fund Performance, Survivorship Bias

JEL Classification: G 11, G 12

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Introduction Survivorship bias affects almost every study of mutual fund performance as many

commercial datasets include only those funds that are currently in operation and available for investment. Not accounting for closed funds can produce inaccurate results especially in studies analysing the performance of fund portfolios, fund styles, or the entire fund market. In general, survivorship bias overestimates the performance of a fund portfolio as the predominant reason for closing funds lies in inferior performance (e.g., Malkiel, 1995, Brown/Goetzmann, 1995, Elton/Gruber/Blake, 1996). In order to avoid biased results in empirical analyses of fund portfolios, it is therefore important to carefully account for survivorship bias. Consequently a considerable number of articles address this issue either as main subject or as additional information by estimating the amount of (potential) survivorship bias in their particular datasets. Noticeably the results reported by these studies vary from one to 271 basis points per year (e.g., Grinblatt/Titman, 1989, Deaves, 2004). Apart from differences in the datasets most studies also show different approaches and methods which make it difficult to compare the results or decide on the actual size of survivorship bias. The main differences lie in the definition of survivor, in the weighting schemes used for the aggregate portfolio performance, as well as in different aggregation methods. We found two different definitions of survivor in the literature. The first definition is known as end-of-sample conditioning. Here all funds operating at the end of the sample period are defined as survivors (e.g., Carhart et al., 2002). This approach is followed by, e.g., ter Horst/Nijman/Verbeek (2001), Carhart et al. (2002), Otten/Bams (2004), and Deaves (2004). Some studies define only funds that were operational throughout the whole sample period, henceforth full-data, as survivors. These are a subset of the end-of-sample survivors. The full-data definition is used in studies by, e.g., Brown/Goetzmann (1995),

1

Grinblatt/Titman (1989), and Elton/Gruber/Blake (1996). Malkiel (1995) uses both definitions. Another important difference lies in the weighting schemes used for the aggregated portfolio performance. There are two different schemes to be found in the literature, equal weighting and value weighting of individual funds. Despite many studies showing that nonsurviving funds show smaller total net assets than surviving funds (e.g. Zhao, 2005, and Carhart, 1997), most studies only compute equally weighted estimates for survivorship bias. The few studies using value weighted performance are Brown/Goetzmann (1995), Malkiel (1995), and Deaves (2004). As there are no two studies sharing an identical set of definitions and methods to compute survivorship bias there is a certain need to analyse the differences resulting from different approaches. The present analysis fills this gap by systematically computing survivorship bias with different combinations of alternative survivor definitions and alternative weighting schemes on basis of a uniform fund sample. We show that the methodical approach is crucial for the resulting estimates and that the differences are significant. In addition we examine in detail the performance of non-surviving funds and show that inferior performance and loss of total net assets can already be observed years before funds are actually closed. The remainder of this article is organized as follows. Section two presents the methods we use in our analysis and derives hypotheses from methodical differences. Section three describes our fund sample and reports summary statistics. Section four presents empirical results and interpretations. Section five concludes.

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Methodology and hypotheses Considering the variety of approaches followed by previous authors it is important to

explicitly show the definition of survivorship bias we analyse in this study. Survivorship bias is defined as the performance difference of two portfolios, one is unbiased and the other is 2

biased. The unbiased portfolio consists of all relevant funds that were operational at any time during the sample period. The biased portfolio is a subset of the unbiased portfolio and includes only the funds defined as survivors. A portfolio that does not allow for newly opened funds to enter (Grinblatt/Titman, 1989, and Elton/Gruber/Blake, 1996) is not an unbiased portfolio by this definition. Such a portfolio is likely to suffer from a different kind of bias. The performance difference of survivors and non-survivors examined as survivorship bias by Deaves (2004) also does not match our definition, as it does not describe the distortion caused by simply ignoring closed funds. To compute the performance of the above mentioned portfolios there is a wide choice of measures. Following the majority of articles on survivorship bias we will present results for four different measures based on monthly return time series, namely the portfolios (1) mean excess return, (2) its Jensen 1-factor-alpha, (3) its Fama-French 3-factor-alpha, and (4) its Carhart 4-factor-alpha.

(1)

1 T µER i = n ∑ (Rit − Rft) t=1

(2)

Rit − Rft = αi + βi (Rmt − Rft) + εit

(3)

Rit − Rft = αi + β1i (Rmt − Rft) + β2i SMBt + β3i HMLt + εit

(4)

Rit − Rft = αi + β1i (Rmt − Rft) + β2i SMBt + β3i HMLt + β4i MOMt + εit

We estimate performance measures on basis of time series representing the monthly returns of a respective fund portfolio. As mentioned before there are different methods for aggregating fund returns. We construct our aggregate fund return time series by monthly averaging the excess returns of all funds currently present in the portfolio. This method allows us to use data on all relevant funds regardless of the length of their return history.

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A second approach first computes performance measures for individual funds and then averages the results (e.g., Elton/Gruber/Blake, 1996, and Carhart et. al., 2002). This has the disadvantage that funds need to have a return history of a certain length to receive reliable regression estimates. Funds not meeting this criterion, especially funds that survived only for a short period of time, are excluded systematically. This can heavily bias the results. A third aggregation method first computes aggregate time series for the respective portfolios as we do. But in the next step differences of these time series are taken and a single measure is computed on basis of the differences which can already be interpreted as survivorship bias (Bu/Lacey, 2007). The disadvantage of this method is that by subtracting two time series that are affected by market factors in the same way the character of a fund time series might get lost and the application of the model might not be justifiable anymore. In our empirical study we report significance levels for performance measures, for survivorship bias estimates in form of performance differences of unbiased and biased portfolios, and for survivorship bias differences in form of performance differences of different biased portfolios. The majority of the underlying time series are tested negative for normal distribution with the Jarque-Bera test. This means that parametric testing methods cannot be applied. Therefore we have to rely on non-parametric tests, which we apply on the time series of the partial returns not explained by the respective models. The sign test is the least restrictive test and checks if the median of a sample is equal to a hypothesized median (Daniel). Testing differences of two related time series the sign test checks if the median of the time series of differences is equal to zero. The Wilcoxon signed-ranks test has higher statistical power but requires the tested sample to be symmetrically distributed. It also tests if the median of a sample is equal to a hypothesized median. Through the symmetry assumption evidence on the median approximately allows conclusions about the mean of a distribution. The Wilcoxon matched-pairs signed-ranks test checks if the symmetrically distributed time series of differences of two related samples is equal to zero. We assume asymmetry in cases 4

where the skewness component of the Jarque-Bera test statistic alone rejects the normal distribution hypothesis. Recapitulating the various approaches to survivorship bias found in the literature, survivor definitions and weighting schemes form the two main methodical differences. Concerning the former, it can be assumed that there is only a small exclusive number of full-data survivors which could have unique characteristics that make them survive for a longer period of time. Concerning the later different studies show that closed funds have smaller total net assets than surviving funds or, respectively, that the decision to close a fund is made easier if it is small (Zhao 2005). Therefore it is reasonable to assume that different approaches cause different estimations of survivorship bias. Consequently our empirical analysis will concentrate on the following hypotheses. Hypothesis 1: Regardless of the methods applied there exists significant survivorship bias in form of the performance difference of an unbiased and a biased portfolio. Hypothesis 2: The survivorship bias estimated on basis of a full-data survivor portfolio is significantly different to the survivorship bias computed on basis of an end-of-sample survivor portfolio. Hypothesis 3: The survivorship bias estimates based on equally weighted aggregate fund performance are significantly different to the survivorship biases based on value weighted aggregate fund performance.

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3

Data As it is the most complete and accurate commercial dataset on mutual fund data currently

available we rely on the CRSP Survivor-Bias-Free US Mutual Fund Database. Our initial dataset contains monthly returns and total net assets as well as quarterly fund characteristics on 32,420 US based funds from January 1990 through December 2006. From this dataset we extracted our final sample on basis of five selection criteria. First, all funds not continuously classified as US domestic equity funds by Standard & Poors fund objective code were excluded.1 As this classification was first introduced in 1993 we restricted our sample period to January 1993 through December 2006 leaving 11,197 funds in the sample. Second, 140 funds with fragmentary return histories where eliminated. Third, 67 funds without any total net asset data available were excluded. Fourth, funds with identical return histories (different batches of the same fund) were merged leaving 10,951 funds in the sample. Fifth, 21 funds with implausible data (falsely reported or recorded)2 were excluded from the dataset. The final sample contains 10,930 US domestic equity funds. Figure 1 shows the total quantity of funds and the monthly development of the fund sample from January 1993 through December 2006. The figure also shows how the sample divides into the different survivor groups. Full-data survivors and survivors without full-data together are end-of-sample survivors. Of the 10,930 funds in the sample 3,330 (30.5 %) where closed before December 2006. 658 of the funds (6 %) meet the full-data criterion. In total 7,600

1

The Standard & Poors US domestic equity fund objective codes are Equity USA Aggressive Growth (AGG),

Equity USA Midcap (GMC), Equity USA Growth & Income (GRI), Equity USA Growth (GRO), Equity USA Income & Growth (ING), and Equity USA Small Companies (SCG), and Allocation USA Preferred (CPF). 2

Implausible data means monthly returns higher than 50 % or lower than -50 %, respectively. Whenever

possible we checked implausible data through comparison with Morningstar data. Funds were erased if (1) suspicion was confirmed by Morningstar, or (2) the suspicious data did not fit into the overall return history of the fund or the respective month.

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funds (69.5 %) are operating in December 2006. On average, funds survived 71 months, or 5.9 years respectively.

[Insert Figure 1 about here.]

Figure 1 clarifies that the US domestic equity fund market experienced substantial growth in the number of funds throughout our sample period starting with 1,167 funds in January 1993 and ending with 7,600 operational funds in December 2006. It also becomes clear that with 30.5 % of the total quantity of funds closed there is high potential for survivorship bias.

[Insert Figure 2 about here.]

Figure 2 presents the development of the markets total net assets split up into the different survivor groups as of December 2006. It is obvious that although full-data survivors represent only 6 % of the total quantity of funds they hold just above half (52.5 %) of the markets total net assets in December 2006 and an even bigger portion throughout our sample period. Table 1 presents mean total net assets, monthly mean excess returns, and survivor group membership for deciles of funds sorted by their individual mean total net assets. It shows very clearly that there is a strong connection of fund size, performance, and full-data survivorship. Not surprisingly the majority of full-data survivors concentrate in the first decile while it contains only few non-surviving funds. Survivors without full-data are distributed almost evenly across all deciles. Non-survivors, although present in all deciles, have an obvious overbalance in the lower deciles.

7

[Insert Table 1 about here.]

This confirms previous studies and further encourages our assumption that different approaches yield different survivorship bias estimates. An average non-surviving fund holds total net assets of 118 million USD when still alive. An average end-of-sample survivor holds 541 million USD, and full-data survivors hold even more with 1,878 million USD. This clearly shows that there is substantial difference between full-data survivors and survivors without full-data. Table 2 reports annual fund openings and fund closings throughout our sample period. Note that “fund opening” stands for “fund starts reporting to CRSP”, and “fund closing” stands for “fund is no longer reporting to CRSP” (e.g. Amin/Kat, 2003). In absolute terms fund openings and closings are accelerating. Comparing seven year sub periods it becomes clear that fund closings have more or less quadrupled while fund openings increased by about 25 %. In relative terms the picture becomes also clearer as relative fund openings decrease while relative fund closings grow. For the period 1962 through 1995 Carhart (1997) reports an even smaller annual fund closing rate of 3.6 %. This means that for future fund performance studies survivorship bias becomes an increasingly important issue.


A problem we faced with the CRSP database is that data on total net assets is sometimes incomplete. This means that we had to fill the missing values in order to have a complete set of weighting factors. Missing values were estimated with a three step procedure. First we 8

computed monthly value weighted average fund growth rates on basis of the available data. In step two we filled gaps within time series by geometric interpolation, assuming constant relative growth between available values. In step three we extrapolated the values missing in the beginning and at the end of the time series with the average fund growth rates taken from step one. On average we had to estimate less than 5 % of the data points, or less than 1.5 % of total net assets per month, respectively. From this we conclude that the possible impact of estimation is, if at all, very small. As robustness checks we twice replicated our empirical analysis without estimating any missing values, and with estimates computed by simple extrapolation of the first/last known value instead of using average growth rates. Apart from very small alterations in the actual results the economic conclusions and relations were unchanged. The four market factors market excess return (Rmt Rft), small-minus-big (SMBt), highminus-low (HMLt), and momentum (MOMt) for the regression models were provided by Kenneth R. French who regularly publishes a variety of market factors via an online data library.3

4

Empirical Results Table 3 reports monthly performance measures for the different portfolios as well as the

corresponding survivorship biases described in the previous sections. As there are four different methodical combinations per measure the results are presented in form of a 2x2matrix with columns representing survivor definitions and rows (sub panels) representing weighting schemes. A first look at the performance of the unbiased portfolio reveals that all risk adjusted measures are negative, most of them statistically significant. For the biased portfolios this is not always the case. For the Jensen 1-factor-model three of four alphas based

3

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

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on biased portfolios are positive, one even significantly. This emphasizes that ignoring closed funds can cause seriously misleading results.


Looking at the results for survivorship bias, across all performance measure the sixteen estimates are positive and, with just one exception, highly significant. The statistically significant results range from 1.74 to 9.04 basis points per month, or 21 to 109 basis points per year, respectively.4 Estimates based on the Jensen 1-factor-model on average show the highest survivorship bias, estimates from the Fama/French 3-factor-model the lowest. Taking equally weighted results for the end-of-sample portfolio the annual bias is on average 95 basis points across all measures. These numbers confirm Hypothesis 1 made in Section 2. Regardless of the methods applied there is a statistically significant survivorship bias in our sample if closed funds are ignored.


Table 4 analyses the differences from the four method combinations by reporting ratios of full-data and end-of-sample survivor portfolios (Panel I), and ratios of value weighted and equally weighted results (Panel II), respectively. Panel I shows that end-of-sample is larger than full-data for equal weighting with high statistical significance for the Jensen 1-factormodel and low significance for the Carhart 4-factor-model. A possible explanation is that fulldata survivors are too big to be closed even if their performance is temporarily unsatisfying, 4

Annualized by {(1 + monthly survivorship bias)12 − 1}. Cf. Deaves 2004.

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or that small funds with inferior performance are closed while small funds with superior performance drive the performance of the end-of-sample portfolio, respectively. Supporting evidence is given in Table 3 which shows that end-of-sample survivors always outperform full-data survivors in the case of equal weighting. With value weighting full-data results are on average higher than end-of-sample results with high statistical significance for the Fama/French 3-factor-model and low significance for the Carhart 4-factor-model. An explanation might be derived from Table 1 which shows that more than half of the full-data survivors are in the highest decile where funds have on average about 10 times the size than in the second decile. Survivors without full-data are evenly distributed across all deciles. This means that value weighting has much more impact on the full-data portfolio. Table 3 supports this assumption by showing that the difference from equal to value weighting is always bigger when using the full-data definition. Comparing these results Hypothesis 2 from Section 2 can be confirmed with two limitations. There are differences in the survivorship bias estimates depending on the survivorship bias definition, but the differences are quite small, so that only a part of the results show statistical significance. The sign of the differences depends on the weighting scheme used. Not surprisingly Panel II shows more distinct relations, as for both survivor definitions value weighted results are smaller than equally weighted results. Also statistical significance is higher than in Panel I. For end-of-sample there is fair statistical significance for the Fama/French 3-factor-model, and for the Carhart 4-factor-model. Full-data shows high statistical significance for all risk adjusted performance measures.5 In the case of end-ofsample conditioning the equally weighted survivorship bias has four times the size as the

5

In general, it is not surprising that results for risk adjusted performance measures show higher significance than

mean excess returns because the volatility of the unexplained part of the returns is smaller.

11

value weighted. With full-data the equally weighted survivorship bias has still about twice the size. This means that Hypothesis 3 from Section 2 can be confirmed as well. The biases resulting from different weighting schemes differ significantly. Equal weighting always yields higher estimates. The inferior performance of non-surviving funds is the driver of survivorship bias. As the amount of underperformance can not be derived directly from the survivorship bias the first two columns of Table 5 compare the performance of end-of-sample survivors and nonsurvivors. Annualized performance differences range from 241 to 362 basis points, all of which are statistically significant at 1 % level. These results are supported by the numbers for the Canadian market reported by Deaves (2004) which range from 232 to 271 basis points per year in the equally weighted case.


The five remaining columns of Table 5 report the performance of non-survivors in different runtimes before fund closure (Panel I), as well as average total net assets held by non-survivors (Panel II). Starting with the latter it becomes clear that funds already start losing total net assets about four years before they are finally closed. Concerning performance Table 5 shows that non-survivors under perform end-of-sample survivors regardless of their runtime before closure, with very few exceptions. It also becomes clear that non-survivors massively under perform their own average already three years before they are finally closed. Noticeably, after constantly decreasing from year five to two before fund closure the performance of non-survivors slightly increases in their last year.

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5

Conclusion Comparing previous studies on survivorship bias it becomes clear that there is no

consistent set of definitions and methods researchers use. This makes it difficult to compare the results or decide on the actual size of survivorship bias. There are different aggregation methods for aggregate portfolio performance. We chose the method which in our view had advantages towards the known alternatives. As main differences in the methods commonly applied we identified different definitions of survivor, end-of-sample and full-data, and different weighting schemes for aggregate portfolio performance, equal and value weighting. With our analysis of survivorship bias in US equity mutual fund data we illuminate this problem by applying different method combinations on a uniform dataset. This allows us to compare the results of different methods and shows the impact of different method combinations on the magnitude of survivorship bias. Concerning the weighting scheme applied equally weighting yields results twice as high (full-data), or four times as high (end-of-sample) as value weighting. This is no surprise as non-surviving funds hold smaller total net assets than surviving funds. This means that their influence on the unbiased portfolio is bigger when equally weighted and smaller when value weighted. Concerning the different survivor groups, the end-of-sample definition shows higher survivorship bias estimates when equally weighted, and the full-data definition yields higher estimates when value weighted. That is because the influence of the different weighting schemes is much stronger for the full-data survivor portfolio. These results show that the performance measures as well as the following survivorship bias estimates highly depend on the set of methods a researcher chooses to apply. To enable the reader of a study to compare the results to previous research it is therefore very important to predefine the methods used in the respective study.

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References Amin, Gaurav S., Kat, Harry M., Welcome to the Dark Side: Hedge Fund Attrition and Survivorship Bias over the Period 1994-2001, Journal of Alternative Investment, summer 2003, pp. 53-73. Brown, Stephen J., Goetzmann, William N., Performance Persistence, Journal of Finance, June 1995, vol. 50, no. 2, pp. 679-698. Bu, Qiang, Lacey, Nelson, Exposing Survivorship Bias in Mutual Fund Data, Journal of Business and Economics Studies, spring 2007, vol. 13, no. 1, pp. 22-37. Carhart, Mark M., On Persistence in Mutual Fund Performance, Journal of Finance, March 1997, vol. 52, no. 1, pp. 57-82. Carhart, Mark M., Carpenter, Jennifer N., Lynch, Anthony W., Musto, David K. (2002), Mutual Fund Survivorship, Review of Financial Studies, winter 2002, vol. 15, no. 5, pp. 1439-1463.# CRSP Survivor-Bias-Free US Mutual Fund Database Guide, 2007, Version CA295.200701. Daniel, Wayne W., Applied Nonparametric Statistics, 1990, Second edition, PWS-Kent Publishing Company, Boston, Massachussets. Deaves, Richard, Data-conditioning biases, performance, persistence and flows: The case of Canadian equity funds, Journal of Banking and Finance, 2004, vol. 28, pp. 673-694. Elton, Edwin J., Gruber, Martin J., Blake, Christopher R., Survivorship Bias and Mutual Fund Performance, Review of Financial Studies, winter 1996, vol. 9, no. 4, pp. 1097-1120. Fama, Eugene F., French, Kenneth R., Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 1993, vol. 33, pp. 3-56. Grinblatt, Mark, Titman, Sheridan, Mutual Fund Performance: An Analysis of Quarterly Portfolio Holdings, Journal of Business, 1989, vol. 62, no. 3, pp. 393-416. Jensen, Michael C., The Performance of Mutual Funds in the Period 1945-1964, Journal of Finance, May 1968, vol. 23, no. 2, pp. 389-416. Malkiel, Burton G., Returns from Investing in Equity Mutual Funds 1971 to 1991, Journal of Finance, May 1995, vol. 50, no. 2, pp. 549-572. Otten, Rogér, Bams, Dennis, How to measure mutual fund performance: economic versus statistical relevance, Journal of Accounting and Finance, 2004, vol. 44, pp. 203-222. 14

terHorst, Jenke R., Nijman, Theo E., Verbeek, Marno, Eliminating look-ahead bias in evaluating persistence in mutual fund performance, Journal of Empirical Finance, 2001, vol. 8, pp. 345-373. Zhao, Xinge, Exit Decisions in the U.S. Mutual Fund Industry, Journal of Business, 2005, vol. 78, no. 4, pp. 1365-1401.

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Figure 1 Fund sample development The figure shows the sample development in the period from 01/1993 through 12/2006 and how the sample divides into different survivor groups. Of the 10,930 funds 30.6 % where closed before December 2006 (non-survivors), 69.4 % where in operation in that month (endof-sample survivors) and 6 % of the funds survived throughout the whole sample period (full-data survivors).

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Figure 2 Total net asset development for the survivor groups as of 12/2006 The figure shows the development of the markets total net assets split up into different survivor groups as of 12/2006 throughout the period from 01/1993 through 12/2006. In 12/2006 full-data survivors represent 52.5 % of the markets total net assets.

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Table 1 Deciles of funds sorted by individual mean total net assets mean total monthly mean full-data Decile net assets excess returns survivors 1 1,875.40 0.6621 372 2 195.12 0.6414 127 3 83.01 0.6090 76 4 42.00 0.5604 43 5 20.90 0.5089 16 6 10.93 0.4795 14 7 5.26 0.3961 4 8 2.27 0.3413 5 9 0.78 0.2692 1 10 0.12 0.2415 0

survivors without full-data 587 727 739 728 720 697 661 647 683 753

non-survivors 134 240 278 322 357 382 428 441 409 339

The Table shows mean total net assets, monthly mean excess returns (equally weighted), and survivor group membership for deciles of funds sorted by their individual mean total net assets. The first decile represents the largest 10 % of funds, the tenth decile represents the smallest 10 % of funds. Mean total net assets are quoted in million USD. Monthly mean excess returns are quoted in percentage points.

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Table 2 Funds opened and closed. Year ++

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Average 1993-2006 Average 1993-1999 Average 2000-2006

Funds opened absolute relative+ 336 28.79 % 424 29.00 % 435 23.72 % 589 26.92 % 772 28.68 % 823 24.48 % 821 20.28 % 913 19.42 % 939 17.58 % 964 16.15 % 681 10.31 % 676 9.84 % 802 11.12 % 609 8.12 % 698.86 19.60 % 600 25.98 % 797.71 13.22 %

Funds closed absolute 41 52 81 85 102 137 168 272 311 326 422 333 508 513 239.36 95.14 383.57

relative+ 3.51 % 3.56 % 4.42 % 3.88 % 3.79 % 4.07 % 4.15 % 5.79 % 5.82 % 5.46 % 6.39 % 4.85 % 7.05 % 6.84 % 4.97 % 3.91 % 6.03 %

The table shows fund openings and fund closings throughout the sample period from 01/1993 to 12/2006. +Relative numbers refer to the total count of operational funds in December of the prior year. ++Reference for the 1993 numbers is January 1993.

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Table 3 Survivorship bias unbiased fund sample end-of-sample survivors full-data survivors performance ST WT performance ST WT performance ST WT Panel I. monthly mean excess return a. equally weighted measure 0.5556 *** (**) 0.6400 *** (***) 0.6061 *** (**) ( ) survivorship bias 0.0845 *** *** 0.0506 ** *** b. value weighted measure 0.6066 *** (***) 0.6281 *** (***) 0.6227 *** (***) survivorship bias 0.0215 *** *** 0.0162 Panel II. 1-factor-alpha (Jensen) a. equally weighted measure -0.0791 ** * 0.0113 -0.0141 survivorship bias 0.0904 *** (***) 0.0650 *** *** b. value weighted ( measure -0.0189 0.0056 0.0101 * **) ( survivorship bias 0.0245 *** *** 0.0290 *** ***) Panel III. 3-factor-alpha (Fama/French) a. equally weighted measure -0.1420 *** (***) -0.0676 *** (***) -0.1004 *** (***) ( ) survivorship bias 0.0744 *** *** 0.0416 *** *** b. value weighted ( ( ) measure -0.0314 * **) -0.0140 * * -0.0112 * ( survivorship bias 0.0174 *** ***) 0.0202 ** *** Panel IV. 4-factor-alpha (Carhart) a. equally weighted measure -0.1481 *** (***) -0.0803 *** (***) -0.1002 *** (***) ( ) survivorship bias 0.0679 *** *** 0.0480 *** *** b. value weighted -0.0365 ** (**) -0.0288 ** (**) measure -0.0545 ** (***) ( ) survivorship bias 0.0180 *** *** 0.0257 *** *** The table shows performance measures and survivorship bias estimates for the period from 01/1993 through 12/2006. All factor models are based on monthly excess return data. Numbers are quoted in percentage points. Significance levels are presented for sign tests (ST) and Wilcoxon (matched-pairs) signed-ranks tests (WT). Significance levels in brackets indicate that non-symmetry was suggested by examining the skewness component of the Jarque-Bera test statistic. ***, **, * indicates statistical significance on 99%, 95%, 90% level.

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Table 4 Ratios of survivorship bias estimates Panel I. full-data vs. end-of-sample

mean excess returns 1-factor-alpha 3-factor-alpha 4-factor-alpha

ratio 59.85 71.91 55.91 70.68

Average ratio

64.59

equally weighted ST

WT (

***

*

value weighted ST

**

WT ( ) * *** *

113.20

Panel II. value weighted vs. equally weighted end-of-sample ratio ST mean excess returns 25.45 1-factor-alpha 27.13 3-factor-alpha 23.33 ** 4-factor-alpha 26.53 ** Average ratio

***)

ratio 75.27 118.38 116.45 142.70

WT

*** **

25.61

ratio 32.01 44.67 48.59 53.58

full-data ST

WT

** *** ***

*** *** ***

44.71

The table shows ratios between the monthly survivorship bias estimates presented by Table 3. All numbers are quoted in percentage points. Significance levels were computed on basis of monthly performance differences time series’. Most of these time series’ were tested negative for normal distribution with Jarque-Bera implying non-parametric testing methods. Methods used are the sign test for two related samples (ST) and the Wilcoxon matched-pairs signed-ranks test (WT) which assumes symmetry. Significance levels in brackets indicate that nonsymmetry was suggested by examining only the skewness component of the Jarque-Bera test statistic. ***, **, * indicates statistical significance on 99%, 95%, 90% level.

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Table 5 Performance and size of non-surviving funds end-ofsample nonsurvivors+ survivors++ Panel I. Performance a. equally weighted mean excess return 0.5556 0.3630 1-factor-model -0.0791 -0.2828 3-factor-model -0.1420 -0.3047 4-factor-model -0.1481 -0.2978 b. value weighted mean excess return 0.6066 0.3817 1-factor-model -0.0189 -0.2703 3-factor-model -0.0314 -0.2121 4-factor-model -0.0545 -0.2450 Panel II. Fund size total net assets 541.10 118.44

non-survivors in months before fund closure 167- 49

48-37

36-25

24-13

12-1

0.3492 -0.1444 -0.1391 -0.1372

0.4075 -0.1781 -0.1939 -0.2047

0.3154 -0.3195 -0.3459 -0.3535

0.1394 -0.4966 -0.5526 -0.4971

0.2010 -0.4112 -0.5096 -0.4529

0.3056 -0.1942 -0.1362 -0.1852

0.3482 -0.2438 -0.2275 -0.2966

0.2200 -0.4345 -0.3665 -0.3901

0.1829 -0.4619 -0.4742 -0.4424

0.2664 -0.3545 -0.4158 -0.3606

198.57

90.43

77.40

62.05

55.42

Panel I of this table shows monthly performance measures of non-surviving funds in comparison to end-of-sample survivors as well as in different runtimes before fund closure. + Measures for end-of-sample survivors refer to the whole sample period from 01/1993 through 12/2006. ++ For non-survivors (by definition not operational in 12/2006) the numbers refer to the period from 01/1993 through 11/2006. All performance measures are denoted in percentage points. Panel II shows mean total net assets of end-of-sample survivors and non-surviving funds. All total net assets are quoted in million USD.

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