Ranking of equity mutual funds: The bias in using survivorship bias-free datasets

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1 Rankng of equty mutual funds: The bas n usng survvorshp bas-free datasets Hendrk Scholz + Olver Schnusenberg ++ Workng Paper Catholc Unversty of Echstaett-Ingolstadt and Unversty of North Florda Frst Verson: Ths Verson: Hendrk Scholz, Ingolstadt School of Management, Catholc Unversty of Echstaett-Ingolstadt, Auf der Schanz 49, Ingolstadt, Germany, phone: , fax: , emal: hendrk.scholz@ku-echstaett.de. ++ Olver Schnusenberg, Coggn College of Busness, Unversty of North Florda, 1 UNF Drve, Jacksonvlle, FL 32224, USA, phone: , fax: , emal: oschnuse@unf.edu. We are grateful for comments and suggestons of John Stowe and Wenjuan Xe. We are also thankful for comments and suggestons of the partcpants of the 2008 SWFA Meetng n Houston and the 2008 EFA Meetng n St. Pete Beach. We are responsble for any remanng errors.

2 Rankng of equty mutual funds: The bas n usng survvorshp bas-free datasets Abstract Usng survvorshp bas-free datasets to rank fund performance ntroduces a market clmate bas that depends on the lengths of the funds return hstores. Based on Carhart s (1997) four-factor model, we analytcally show how the market clmate affects commonly used performance measures. Our emprcal results confrm that ths market clmate bas creates dfferent rankngs dependng on the measure used for US equty funds. Moreover, the data avalablty wthn the fund sample mpacts correlatons between rankngs based on dfferent measures. Adjustng measures for the dfferent fund return hstores corrects for the market clmate bas and produces more consstent rankngs across dfferent measures. JEL: G 11 Keywords: Portfolo performance evaluaton; mutual funds; survvorshp bas; data avalablty; market condtons

3 1 Introducton Several papers nvestgate the mpact of survvorshp bas on mutual fund performance and reach the general concluson that the average performance s based upwards f the fund samples only nclude survvng funds. Papers by Grnblatt and Ttman (1989), Brown and Goetzman (1995), Malkel (1995), Elton et al. (1996) and Carhart et al. (2002) fnd that survvorshp bas n US equty funds ncreases average annual returns by approxmately 10 to 150 bass ponts. Internatonally, Blake and Tmmermann (1998), Otten and Bams (2002) and Deaves (2004) obtan smlar results. Recent studes adjust for survvorshp bas ether by utlzng a survvorshp bas-free dataset such as CRSP or by adjustng for non-survvng funds n other databases lke Mornngstar. Consequently, these datasets nclude both survvng and non-survvng funds wth return hstores of dfferent lengths. The man objectve of ths paper s to nvestgate the mpact of usng survvorshp bas-free datasets to rank the performance of funds that have exsted durng dfferent tme perods. Specfcally, we study the mpact of data avalablty on rankngs based on sx commonly used measures: average excess return, Sharpe rato, Treynor rato, one-, three- and fourfactor alpha. We llustrate the mathematcal relatonshp between these measures and fundspecfc characterstcs as well as market factors based on Carhart s (1997) four-factor model, whch shows how the measures are affected by market clmate. Our secondary objectve s to analyze the mpact of data avalablty and market clmate on correlatons between dfferent measures. Many studes nvestgate whether the use of varous performance measures leads to smlar fund rankngs, but they frequently do not dscuss the mpact of dfferent lengths of fund return hstores or the mpact of the fund sample used. For example, studes such as Wermers (2000) and Stotz (2007) show correlatons between performance measures, but the samples nclude both survvng and non-survvng equty mutual funds, whch may nfluence the rankng due to the prevalng 1

4 market clmate. In contrast, studes lke Bal and Leger (1996), Ferruz et al. (2006), Hübner (2007) and Bessler et al. (2007) report correlatons between performance measures but employ only funds whch have exsted over the full evaluaton perod (so-called full-data funds). Whle these funds exhbt return hstores of the same length, these samples regularly contan only a fracton of all possble funds whch could also mpact the results. Elng and Schuhmacher (2007) compare the rankng of hedge funds based on Sharpe ratos wth rankngs accordng to alternatve measures. They show rank correlatons for a survvorshp bas-free dataset and for subsamples of (end-of-sample) survvors and nonsurvvors. Recently, Elng (2008) extends the latter study by analyzng funds nvestng n seven dfferent asset classes. The present study adds to ths lterature by not only drectly comparng the correlatons of fund rankngs based on dfferent measures, but by nvestgatng how these correlatons are affected by the prevalng market clmate durng the funds lfetmes and by dfferent fund samples employed. Furthermore, we nvestgate how the correlatons change once the prevalng market clmate s controlled for. Our emprcal fndngs confrm the relatonshp between performance measures and market clmate. Includng non-survvors n a fund sample ntroduces a survvorshp basfree bas! Evaluatng non-survvors and survvng funds n a jont sample mpacts resultng rankngs severely. Moreover, rankngs dffer accordng to the measure used and the perod durng whch funds wth dfferent return hstores exsted. Thus the market clmate durng a fund s lfetme clearly affects ts performance and the resultng rankng n the fund unverse. Furthermore, rank correlatons between dfferent measures vary wth the return data avalablty wthn the fund sample used. Whle the dsclosure of the market clmate bas on performance measures and fund rankngs s mportant to researchers and practtoners n tself, we also analyze an approach suggested by Pastor and Stambaugh (2002) that adjusts performance measures for the bas 2

5 due to dfferent return hstores. Applyng ths tme perod adjustment, the market clmate bas n measures dsappears n our sample and fund rankngs become more consstent across varous measures. The nnovatve fndngs reported here are not only useful for researchers nvestgatng fund performance, rankngs and persstence, but are also mportant for ndvdual and nsttutonal nvestors who rank funds based on ther past performance to make nvestment decsons. Emprcal research shows substantal evdence that nvestors ncrease the flow nto funds based on the funds past performance. 1 Many studes confrm a convex flowsperformance relatonshp for mutual funds, wth the funds that show hgher performance especally n terms of unadjusted raw returns recevng hgher nflows. In contrast, Del Guerco and Tkac (2002) fnd a more lnear flow-performance relatonshp related to rsk-adjusted measures lke Jensen s alpha for the penson fund segment. Snce mutual fund managers are rewarded prmarly based on assets under management (Khorana, 1996), and snce assets under management ncrease based on past performance, the results of our study are also useful for nvestment company boards tasked wth rewardng managers for ther funds performance relatve to other funds n the fund unverse. The remander of ths artcle s organzed as follows. The next secton presents the performance measures appled and llustrates how they are mpacted by market clmate. Secton 3 presents the data and analyzes rankngs of funds based on dfferent measures, showng the mpact of data avalablty and market clmate. Subsequently, we determne tme perod-adjusted measures and resultng fund rankngs and compare these results wth rankngs based on orgnal return hstores. Rank correlatons between measures for fund samples exhbtng dfferences n return hstores are also analyzed. Secton 4 concludes. 1 For examples, see Ippolto (1992), Gruber (1996), Chevaler and Ellson (1997), Srr and Tufano (1998), Edelen (1999), Bergstresser and Poterba (2002) and Kempf and Ruenz (2008). 3

6 2 Performance measures and the mpact of market clmate 2.1 Performance measures In order to analyze fund rankngs, we utlze the raw unadjusted average excess returns (henceforth called average ER) and fve commonly used rsk-adjusted performance measures. 2 Our frst measure s the average of the fund s excess returns, whch s computed as the dfference between the total return of a fund (r ) and a rsk-free shortterm nterest rate r f. The second measure used s the Sharpe rato (henceforth SR). The expost Sharpe rato (SR ) of a fund s usually calculated employng the average (er = r r f) and the standard devaton (σ ) of the fund excess returns (Sharpe, 1966 and 1994). SR = er σ (1) The thrd measure s the Treynor rato (henceforth TR), whch utlzes the fund s systematc rsk as the rsk measure (Treynor, 1965). Typcally, systematc rsk s measured by beta and s estmated utlzng a lnear regresson accordng to (3). TR = er M-1F β (2) Our fourth measure s Jensen s one-factor alpha. In the model, the excess return of fund for perod t (er t) s determned n accordance wth a one-factor model utlzng the market excess return ERM t = r M t r f t for the same perod (Jensen, 1968). er t = α 1F + β M-1F ERM t + ε t (3) Jensen s alpha s the constant term α 1F n (3). The coeffcent beta β M-1F denotes the fund s systematc rsk. Postve (negatve) selecton actvtes of the fund yeld a postve (negatve) Jensen alpha. 2 Goetzmann et al. (2007) show that t s possble to manpulate (game) tradtonal performance measures to obtan more favorable rankngs. 4

7 The alpha from Fama and French s (1993) model s the ffth measure used. In ths model, alpha (α 3F ) s calculated by determnng the fund s excess return n accordance wth a three-factor model ncludng the market excess return and addtonal sze and book-tomarket factors SMB and HML. 3F M-3F S-3F H-3F er t = α + β ERM t + β SMB t + β HML t + η t (4) 4F The sxth measure s the alpha (α ) accordng to Carhart s (1997) four-factor model, whch ncludes an addtonal momentum factor MOM. 4F M-4F S-4F H-4F MO-4F er t = α + β ERM t + β SMB t + β HML t + β MOM t + υ t (5) 2.2 Market clmates and ther mpact on performance measures The performance measures llustrated n Secton 2.1 are commonly computed based on fund excess returns whch reflect both the fund-specfc characterstcs manly determned by the fund management as well as market factors (as ERM, SMB, HML and MOM) reflectng the prevalng market clmate. Assumng Carhart s four-factor model as the return-generatng process of funds, the realzatons of these factors over tme, ncludng ther dependences, determne the market clmate. In turn, ths market clmate mpacts the excess returns of funds accordng to (5) dependng on the fund-specfc loadngs aganst M-4F S-4F H-4F MO-4F the four (market) factors (β, β, β and β ). To dsplay the market clmate mpact on performance measures, we now apply an approach by Pastor and Stambaugh (2002) and express all sx measures used n terms of fund-specfc characterstcs and market parameters for the evaluaton perod consdered. Frst, average and standard devaton of fund excess returns for a respectve perod are: er = α 4F + β M-4F ERM + β S-4F SMB + β H-4F HML + β MO-4F MOM (6) σ = β T V β + σ 2 υ, (7) 5

8 where ERM, SMB, HML and MOM denote the means and V the covarance matrx of the four factors for a respectve perod. β s the vector of the fund s factor loadngs wth β = M-4F S-4F H-4F MO-4F {β, β, β, β } and σ 2 υ the fund s specfc rsk accordng to the four-factor model. Based on ths, the Sharpe rato n (1) can be rewrtten as: SR = α 4F + β M-4F ERM + β S-4F SMB + β H-4F HML + β MO-4F MOM β T V f β + σ (8) 2 υ Moreover, based on the fund-specfc characterstcs, alternatvely to (3), the Jensen alpha can be computed as: α 1F = α 4F + β S-4F α 1F SMB + β H-4F α 1F HML + β MO-4F 1F α MOM (9) 1F 1F 1F where α SMB, α HML and α MOM are the one-factor alphas accordng to (3) of the factors SMB, HML and MOM. Ths equaton shows that a fund s Jensen alpha depends on ts fundspecfc characterstcs and the one-factor alphas of the three factors not ncluded n the one-factor model. Moreover, alternatvely to (4), the three-factor alpha can be wrtten as: α 3F = α 4F + β MO-4F 3F α MOM (10) 3F where α MOM s the three-factor alpha accordng to (4) of the MOM factor whch s not ncluded n the three-factor model. Smlar to (9), the fund s one-factor beta β M-1F n (3) can be separated nto ts components: M-1F M-4F S-4F 1F H-4F 1F MO-4F 1F β = β + β β SMB + β β HML + β β MOM (11) 1F 1F 1F where β SMB, β HML and β MOM are the one-factor betas accordng to (3) of the factors SMB, HML and MOM. Based on ths, resortng to (6) and (11), we can alternatvely determne the Treynor rato n (2) as: TR = α 4F + β M-4F ERM + β S-4F SMB + β H-4F HML + β MO-4F MOM (12) β M-4F S-4F + β β 1F H-4F SMB + β β 1F MO-4F 1F HML + β β MOM 6

9 The equatons above effectvely express the performance measures used here n terms of the fund-specfc characterstcs accordng to Carhart s model combned wth the respectve realzatons of the market parameters. When funds exhbt dfferent return hstores, these equatons show all measures except for the four-factor alpha to be nfluenced dfferently by the respectve market clmate durng the funds lfetmes. Consequently, the mpact of market clmate on the performance measures may result n dfferent rankngs dependng on the measure used and dependng on the employed return hstores of funds. 3 Emprcal analyss 3.1 Data In the emprcal analyss, the Center for Research n Securtes Prces (CRSP) mutual fund database for 2006 s utlzed. We focus on equty funds classfed solely as ether Aggressve Growth (AG), Growth & Income (GI) or Long-term Growth (LG), as they are the most wdely used categores n fund research. 3 To examne a relatvely homogeneous sample, we have chosen all funds whch at no tme showed an ICDI objectve dfferent than the three mentoned above. Snce ICDI objectves were avalable for the frst tme n 1993, our evaluaton perod starts n January 1993 and ends n December Ths perod contans both bull and bear market perods and s approprate for nvestgatng the mpact of market clmate on performance measures. Of the funds classfed as ether AG, GI or LG, we requre the funds ncluded to show at least 36 months of contnuous monthly returns to ensure a suffcent number of observatons when estmatng mean returns, rsk and alphas. We use total returns, ncludng renvestments of all dstrbutons (e.g., dvdends), but dsregardng load 3 See, for example, Carhart (1997). 7

10 charges. To avod data-errors and outlers, we elmnate funds wth mplausble monthly returns greater than 50 percent or less than 50 percent. Lastly, funds wth dentcal returns (dfferent batches of the same fund) were elmnated, resultng n a fnal total sample of 6,148 funds. To analyze fund performance, we use the value-weghted CRSP market ndex that contans all NYSE, AMEX and Nasdaq stocks and the factors SMB, HML and MOM. 4 Summary statstcs of the market returns and the SMB, HML and MOM factors are presented n Table 1 and Fgure 1. Table 1 shows the average monthly returns, standard devatons,and p-values for the market excess return and the three factors. Insert Table 1 about here Also presented n Table 1 are the varance covarance matrx and the correlaton matrx for these four factors. Notce that the market excess return s negatvely correlated wth both the book-to-market factor HML and the momentum factor MOM, whle t s postvely correlated wth the sze factor SMB. These statstcs are n lne wth prevous research fndngs. However, for each of the four factors the Varance Inflaton Factor (VIF) s clearly below the crtcal value of ten, ndcatng that the results should not be based due to multcollnearty. Regressng the factors SMB, HML and MOM on the market returns accordng to (3) yelds ther one-factor alphas and betas whch are also presented n Table 1. Moreover, a 3F regresson of the MOM factor on the other three factors accordng to (4) yelds α MOM = 1.04 percent. Snce these values are non-zero, dfferences between fund alphas and betas usng the one-, three- and four-factor approach are explaned by equatons (9) to (11). 4 Monthly ndex, factor and T-bll returns are downloadable from Kenneth French s Webste ( whch also contans a detaled descrpton of the calculaton of the factors SMB, HML and MOM. 8

11 Insert Fgure 1 about here Panel A to D n Fgure 1 present rollng 36-month averages of the market excess return ERM and of the factors SMB, HML and MOM. Obvously, there are dstnct changes n these averages over tme. Rollng 36-month correlatons between the four factors also show varatons over tme. 5 However, the maxmum of the respectve VIFs are well below the crtcal value of ten for all perods. Moreover, 36-month rollng wndows of the market 1F 1F 1F 3F parameters α SMB, α HML, α MOM and α MOM n Panel E to H show that these alphas change over tme as well. That means, for nstance, that accordng to (9) a fund s postve loadng on the SMB factor wll bas ts Jensen alpha downward n the 1990s but wll bas t upward at the begnnng of the 21 st century. To nvestgate whether a bull or bear market clmate mpacts the performance and rankng of funds wth dfferent data hstores, three subsamples are created. The frst subsample A s formed to contan non-bear funds. It contans all funds that ether had no returns n August 2001 or later or that were ncluded n the database n March 2001 or later. 6 These months were chosen so that the market ndex shows postve average excess returns for the last three years or for the frst three years of the data hstores of these non-bear funds, respectvely. Ths nsures that these funds prmarly exsted durng a bull market, snce the subsample contans non-survvors that exsted untl August 2001 and relatvely new funds that entered the database n March 2001 or later. 1,413 funds belong to subsample A. The second subsample B s formed analogously to A so as to contan bear funds; all funds wth return data startng between October 1998 and February 2001 are dentfed. 5 6 The correspondng fgure s omtted for reasons of brevty and s avalable upon request. When utlzng samples based on two months pror to or followng these months, only a small number of funds changed the respectve subsamples. Thus, apart from small alteratons n the numercal results the man economc nterpretatons reman unchanged. 9

12 We agan chose these two months so that the market ndex had negatve average excess returns durng the frst three years of these funds lfetmes. The average lfespan of these funds s rather short, as they only appear late n the dataset. Thus, these funds have a relatvely hgh proporton of monthly declnng perods relatve to ther total lfetmes. 1,649 funds are n subsample B. The remanng 3,086 funds n our sample that are not n ether A or B are classfed as a thrd subsample C. We expect subsample A to have relatvely low alphas, snce t contans a large proporton of non-survvors. However, snce these funds do not lve n long declnng perods, we also expect them to have relatvely hgh average ERs whch should mpact ther SRs and TRs. For subsample B, we expect opposte results of relatvely low average ERs and relatvely low SRs and TRs. Subsample C does not contan many non-survvors and thus should exhbt about average performance. Specfcally, funds n subsample C should have average alphas and average SRs and TRs. 3.2 Performance and rankng of funds based on orgnal return data hstores Table 2 reports fund-specfc characterstcs of the survvorshp bas-free total fund sample and for the three subsamples. For each sample, means and standard devatons of the ndvdual funds alphas and betas, as well as error term standard devatons and R 2 based on the four-factor model accordng to (5) are presented. Insert Table 2 about here Our total fund sample exhbts a mean four-factor alpha of 0.16 percent and a market beta of The mean R 2 of 0.88 s rather hgh. The non-bear fund subsample A, as expected, shows a mean four-factor alpha of 0.22 percent per month that s lower than for the total fund sample, due to the fact that ths subsample contans a large proporton of non- 10

13 survvng funds. 7 Interestngly, the R 2 -value for subsample A of 0.90 s hgher. The bear fund subsample B exhbts only a slghtly lower mean four-factor alpha ( 0.17 percent) than the total sample. The average R 2 of subsample B s almost dentcal to that of the total fund sample. Overall, the results confrm prevous fndngs that equty funds on average exhbt slght underperformance relatve to the market. Table 3 presents the means and medans of the sx measures descrbed n Secton 2.1 as well as the average rank of funds wthn the total sample for each fund subsample. 8 Insert Table 3 about here The second column of Table 3 shows that, on average, funds n the total sample have contnuous monthly returns for 98.1 months, wth a relatvely large standard devaton of 38.9 months. The cross-sectonal mean of the funds average ERs s 0.40 percent (wth a standard devaton of 0.54 percent). As expected, the non-bear fund subsample A has a shorter average lfe, wth only 58.6 contnuously monthly returns and a standard devaton of 13 months. For subsample A, the mean average ER of 0.65 percent (0.46 percent standard devaton) s hgher than that for the total sample, whch s attrbutable to the bull market durng whch funds n subsample A exsted. For the bear fund subsample B, the average lfe s a lttle longer, wth contnuous returns averagng 76.0 months. However, the mean average ER of 0.04 percent s lower than the correspondng fgures for all other 7 The non-survvors n subsample A showng no return n 2001:08 or later have a mean fourfactor alpha of 0.31 percent whle funds born n 2001:03 or later show a respectve alpha of 0.19 percent. 8 Rankng based on alpha s typcal n the lterature and s also utlzed here. However, due to the so-called leverage effect, such rankngs have to be nterpreted wth cauton. Ths bas can be avoded usng the generalzed Treynor Rato ntroduced by Hübner (2005). 11

14 samples, supportng the bear market clmate. Subsample C s smlar to our total sample, although the average lfetme of ts funds s hgher, as s the mean average ER. The fndngs n Table 3 show that the mean alphas for subsample A are clearly lower than the alphas of the total sample and of subsamples B and C for the one-, three- and fourfactor models, as expected. For example, the average one-factor alpha for subsample A s 0.19 percent, whle t s 0.06 percent for the total fund sample. Ths s because subsample A contans a relatvely hgh proporton of non-survvors. As a result, the average rank based on alpha of funds n subsample A wthn the total sample s relatvely poor. For nstance, the average rank accordng to four-factor alpha s 3,410, and thus substantally worse than the average rank for the total fund sample (whch s 3,074.5). Lkewse, all other alpha-based rankngs are below average for subsample A. Unlke the alpha measures, average ER, SR and TR for subsample A are clearly hgher than for the total fund sample. For example, subsample A has a medan average ER of 0.65 percent, compared to a medan value of 0.47 percent for the total sample. As a result, the average rank poston accordng to the average ER, and thus based on SR and TR, s not only substantally better than the average rank of all funds n the total sample, but also more than 1,000 rank postons more favorable than t s accordng to the alpha measures. These hgh average ERs, SRs and TRs and resultng better ranks are undoubtedly attrbutable to the bull market n the perod durng whch these funds exsted. For subsample B, the expected fndngs are also largely confrmed. Alphas are about average, whle average ER, SR and TR are clearly lower than for the total sample. Ths s also due to the bear clmate durng whch these funds predomnantly exsted. As a result, funds n subsample B are ranked about 1,000 postons lower based on average ER, SR and TR than they would be based on the alphas. 12

15 In order to check for the robustness of our results, we also test whether the medans of the cross-sectonal dstrbutons of the sx measures are equal across the fund subsamples nvestgated. Snce these dstrbutons are non-normal (see, e.g., Kosowsk et al., 2006), 9 we apply a varant of the non-parametrc medan test based upon Pearson s χ² test of ndependence to evaluate the sgnfcance of these results. For the SR, the χ² test statstc of and a correspondng p-value of clearly refute the null hypothess of equal medans of SRs across the subsamples A, B, and C. Smlarly, the equalty of medans s rejected for all other measures across the subsamples. Ths further confrms the expected fndng (and the results reported n Table 3) that fund rankngs are nfluenced by the market clmate durng whch the funds exsted. Overall, the results presented here confrm our expectaton that there s a bas n usng a survvorshp bas-free dataset. Market clmate sgnfcantly affects the measures of funds that exst prmarly n bull or bear market perods, resultng n dfferent rankngs dependng on the measure used. 3.3 Performance and rankng of funds based on tme perod-adjusted measures In order to elmnate the market clmate bas n rankngs due to dfferent return hstores of funds, an approach by Pastor and Stambaugh (2002) s appled, usng the longer-hstory estmates of the market parameters to obtan better estmates of fund performance. 10 In 9 Applyng the Jacque-Bera test, the null hypothess of normally dstrbuted measures s refuted at the 1% level for all measures based on the total fund sample. Note that all cross-sectonal dstrbutons show a postve kurtoss. 10 For a comparable approach to account for dfferent return hstores see Stambaugh (1997). Muraldhar (2004) suggests a model for standardzng mutual fund manager evaluaton that focuses on manager skll and confdence for managers wth dfferent tenures. However, he does 13

16 dong so, we standardze the evaluaton perod for all funds by determnng the measures the funds would have shown had they exsted durng the full evaluaton from 1993 to We here assume Carhart s model to be an approprate return-generatng process for the equty funds n our sample. 11 Thus the four-factor characterstcs are utlzed for each fund based on ts respectve return hstory. 12 We combne these characterstcs wth the market parameters determned for the full evaluaton perod utlzng (6), (8), (9), (10) and (12) to compute tme perod-adjusted average ERs, SRs, TRs and one- and three-factor alphas. For the prevously-defned subsamples, Table 4 s smlar n format to Table 3, but the results are adjusted for tme perods. Next to the average rank poston of the fund subsamples wthn the total sample, the average change n rank for the subsamples resultng from the use of tme perod-adjusted measures compared to these measures based on the orgnal fund return hstores s dsplayed. Insert Table 4 about here not consder the mpact of return data avalablty on the magntude of performance measures and gnores ths potental mpact of market clmate on rankngs. 11 The four rsk factors of the Carhart (1997) model capture most of the systematc rsk of the equty funds examned n our study. The mean R 2 of the ndvdual funds s 0.88, the R 2 of an equally-weghted portfolo of these funds Thus the four-factor model s well suted for explanng systematc varatons n equty fund returns. For other fund groups, e.g., hybrd funds, a dfferent set of factors would be more approprate (Comer et al., 2007). 12 One assumpton underlyng ths procedure are the constant fund-specfc characterstcs of ndvdual funds durng the entre perod. However, our man goal s not to generate correct returns but to acheve an approprate average fund rankng for fund subsamples based on tme perod-adjusted measures. Therefore, that assumpton s not crtcal for our purposes. 14

17 For subsample A, Table 4 reports that the average rankngs accordng to the average ER, the SR and the TR change consderably due to the tme perod adjustment. For the average ER, the average rank ncreases by 1,289; for SR and TR, ths ncrease s 1,407 and 1,147, respectvely. The average ranks based on the one- and three-factor alphas change less severely. Usng tme perod-adjusted measures clearly corrects the favorable rankng of non-bear funds accordng to average ER, SR and TR that result from the bull market n whch many non-survvors have exsted. Based on the rsk-adjusted measures, Table 4 shows that the average rank of funds n subsample A s now between 3,375 and 3,450. For subsample B, the correctons of average ER, SR and TR are n the opposte drecton. Usng the respectve tme perod-adjusted measures corrects the unfavorable rankng of these bear funds. The average rank based on all measures s now between 3,038 and 3,089. Thus usng adjusted measures for funds wth non-full data corrects the average rankng for the mpact of the bear market durng whch subsample B funds prmarly exsted. In summary, the results presented n Table 4 show that usng tme perod-adjusted measures standardzes the evaluaton perod and results n a more consstent rankng across the measures employed here to rank funds. Consequently, the market clmate bas reported n Table 3 was corrected for. As a robustness check, the non-parametrc χ² test agan clearly refutes the equalty of the medans of the performance measures across the three subsamples. As expected, more funds from subsample A are below the medan value for each of the sx measures when focusng on the tme perod-adjusted measures. Conversely, more funds from subsample B are above the medan for each of these measures than was the case applyng measures based on orgnal return hstores. Thus, average ER, SR and TR are no longer based upward (downward) for subsample A (B). 15

18 Whle the fndngs n Table 4 llustrate the average changes n the rank postons of the fund samples, they do not speak to the dstrbuton of rank changes of ndvdual funds. Insert Fgure 2 about here Fgure 2 presents hstograms of the changes n ranks of ndvdual funds to llustrate the mpact of the market clmate adjustment across the dfferent measures. Panels A, B and C of Fgure 2 show that the hghest rank changes are for the average ER, the SR and the TR correspondng to the hgh average rank changes reported for fund subsamples A and B. Addtonally, Panels D and E reveal that there are also consderable but less pronounced rank changes of funds based on one- und three factor alphas. 13 Focusng on absolute rank changes, the tme perod adjustment leads to changes based on average ER of at least 1,000 rank poston for 2,283 ndvdual funds (37.13 percent of all funds), for 2,471 funds based on the SR (40.19 percent), for 2,091 funds based on the TR (34.01 percent), for 616 funds based on the one-factor alpha (10.02 percent) and for 582 funds (9.47 percent) based on the three-factor alpha. These results for the alphas show that the tme perod adjustment also corrects for a market clmate mpact on one- and threefactor alphas of ndvdual funds, whch was not apparent when focusng on the average rank postons of the fund subsamples. 3.4 Correlatons between rankng of funds based on dfferent measures Whle the results llustrate that usng tme perod-adjusted measures corrects for the market clmate bas that funds wth non-full return data hstores are subject to, t s also nterestng to analyze how usng tme perod-adjusted measures mpacts the rank 13 The Spearman rank correlatons between the dfferent measures before and after tme perod adjustment reflects these rank changes. For average ER, SR and TR these correlatons are 0.67, 0.65 and 0.72, respectvely. For the one- and three-factor alphas they are 0.92 and

19 correlatons across dfferent measures. Table 5 presents Spearman rank correlatons for three funds samples. 14 Our total fund sample s presented n Panel A and B. Panel A presents the rank correlatons based on tme perod-adjusted measures. Not surprsngly, the Spearman correlaton between SR and TR s rather hgh wth Smlarly, the correlatons between the SR or the TR and the one-factor alpha are also hgh wth 0.97 and 0.98, respectvely. However, the hghest correlaton between the three- and four-factor alphas and ether the SR or the TR s Ths agan confrms that SR and TR may rank funds dfferently than these alphas. Panel B of Table 5 also presents the Spearman correlatons between these measures for the total sample but based on the orgnal return hstores (.e., wthout correctng for dfferences n return hstores). The rght sde of Panel B shows dfferences n correlatons relatve to Panel A where the tme perod-adjusted measures are used. Notce n Panel B that correlatons between SR and TR and all three alphas are clearly lower n all cases compared to Panel A. The largest negatve dfference of 0.35 occurs between the SR and the one-factor alpha. Ths confrms our prevous fndng that usng tme perod-adjusted measures ncreases the consstency of rankngs between dfferent measures. Insert Table 5 about here Panels C of Table 5 presents the correlatons for a subsample of 4,210 (end-of-sample) funds exstng at the end of the evaluaton perod n December 2006, and Panel D for a sample of 600 (full-data) funds wth return data over the entre evaluaton perod. One mght expect to get smlarly hgh correlatons based on these fund samples as n Panel A, snce the dfference n the data avalablty n these samples s clearly smaller than n the total sample. Ths argument apples to the end-of-sample funds and especally 14 Kendall s tau between measures was also computed. Whle Kendall s tau tends to be somewhat smaller, the overall nterpretaton of our results remans the same. 17

20 to the full-data funds where all funds by defnton exhbt the same length of return hstory. However, Panels C and D of Table 5 show these correlatons to be smaller than expected. One reason s that these subsamples are not representatve of all funds n the survvorshp bas-free total fund sample. For nstance, full-data funds are subject to an attrton effect, snce these funds survved the entre 14-year evaluaton perod (Carpenter and Lynch, 1999), so dfferences between the best and the worst funds n ths sample are understated. For example, the average four-factor alpha of the full-data funds s 0.09 percent, compared to 0.16 percent for the total fund sample. Moreover, the standard devaton of the cross-sectonal dstrbuton of the four-factor alpha for these funds s only 0.20 percent, whch s clearly lower than for the total fund sample and for the subsamples reported n Table 2. Therefore, snce four-factor alphas of the full-data funds are qute smlar, dfferent measures wll more easly result n dfferent rankngs, whch explans the lower correlatons between the measures n Panels C and D compared to Panel A Concluson The theoretcal analyss presented here shows that usng survvorshp bas-free datasets to rank fund performance durng dfferent market phases may ntroduce a market clmate bas that depends on the perod durng whch a non-full-data fund exsted. Ths bas tends to create dfferent rankngs dependng on the measure used to evaluate fund performance. Applyng a survvorshp bas-free equty mutual fund sample from 1993 to 2006, we fnd that funds exstng prmarly durng a bull market exhbt above-average average ERs, SRs and TRs, but below-average one-, three- and four-factor alphas due to a relatve hgh proporton of poorly performng non-survvors. Conversely, funds exstng durng a 15 Elng and Schuhmacher (2007) and Elng (2008) also compare rank correlatons based on a survvorshp bas-free dataset wth correlatons based on a sample of end-of-sample survvors. However, they fnd qute small changes n the rank correlatons between the measures appled. 18

21 relatvely long bear market perod exhbt below-average average ERs, SRs and TRs. The market clmate also affects one- and three-factor alphas, whch agan may mpact rank postons of ndvdual funds. Consequently, the market phase durng whch a fund exsts mpacts ts performance dependng on the measure used and the respectve market clmate. Therefore, fund rankngs can be clearly nconsstent across dfferent measures. Once tme perod-adjusted measures are used to correct for the market clmate and to evaluate nonfull-data funds,.e. non-survvng funds and relatve new funds, rankngs become more consstent across varous rsk-adjusted measures. The fndngs reported here are not only mportant to researcher concerned wth fund performance, rankng and persstence, but also to nvestors or analysts comparng the performance of ndvdual funds. Whle future research may reveal addtonal methods and measures to rank funds more consstently, the approach appled here overcomes a market clmate bas n fund rankngs based on the most commonly used performance measures. Several possble future research drectons emerge from these results. Especally n the context of transferrng the use of tme perod-adjusted measures to funds nvestng n dfferent asset classes, the choce of a sutable set of market factors s a challengng emprcal queston. Moreover, whle we have assumed that the equty funds analyzed show constant fund-specfc characterstcs accordng to Carhart s four-factor model over the entre evaluaton perod, prevous research followng the semnal paper by Ferson and Schadt (1996) on condtonal fund performance llustrates that the market rsk of funds may change over tme condtoned on publc nformaton. Thus another possble extenson to the research reported here s to ncorporate condtonal models nto our approach and nvestgate how fund rankngs and ther correlatons change once fund-specfc characterstcs are allowed to vary over tme. We leave the answer to ths queston to future research. 19

22 References Bal, Y., Leger, L.A., The performance of UK nvestment trusts. Servces Industres Journal 16, Bergstresser, D., Poterba, J., Do after-tax returns affect mutual fund nflows? Journal of Fnancal Economcs 63, Bessler, W., Drobetz, W., Zmmermann, H., Condtonal Performance Evaluaton for German Mutual Equty Funds. European Journal of Fnance (forthcomng). Blake, D., Tmmermann, A., Mutual Fund Performance: Evdence from the UK. European Fnance Revew 2, Brown, S.J., Goetzmann, W.N., Performance Persstence. Journal of Fnance 50, Carhart, M.M., On Persstence n Mutual Fund Performance. Journal of Fnance 52, Carhart, M.M., Carpenter, J.N., Lynch, A.W., Musto, D.K., Mutual Fund Survvorshp. Revew of Fnancal Studes 15, Carpenter, J.N., Lynch, A.W., Survvorshp bas and attrton effects n measures of performance persstence. Journal of Fnancal Economcs 54, Chevaler, J., Ellson, G., Rsk Takng by Mutual Funds as a Response to Incentves. Journal of Poltcal Economy 105, Comer, G., Larrymore, N., Rodrguez, J, Controllng for Fxed-Income Exposures n Portfolo Evaluaton: Evdence from Hybrd Mutual Funds. Revew of Fnancal Studes (forthcomng). Deaves, R., Data-condtonng bases, performance, persstence and flows: The case of Canadan equty funds. Journal of Bankng and Fnance 28, Del Guerco, D., Tkac, P.A., The Determnants of the Flow of Funds of Managed Portfolos: Mutual Funds vs. Penson Funds. Journal of Fnancal and Quanttatve Analyss 37, Edelen, R.M., Investor flows and the assessed performance of open-end mutual funds. Journal of Fnancal Economcs 53,

23 Elng, M., Does the Measure Matter n the Mutual Fund Industry? Fnancal Analysts Journal 64 (3), Elng, M., Schuhmacher, F., Does the choce of performance measure nfluence the evaluaton of hedge funds. Journal of Bankng and Fnance 31, Elton, E.J., Gruber, M.J., Blake, C.R., Survvorshp Bas and Mutual Fund Performance. Revew of Fnancal Studes 9, Fama, E.F., French, K.F., Common rsk factors n the returns on stocks and bonds. Journal of Fnancal Economcs 33, Ferruz, L., Pedersen, C., Sarto, J.L., Performance metrcs for Spansh nvestment funds. Dervatves Use, Tradng & Regulaton 12, Ferson, W.E., Schadt, R.W., Measurng Fund Strategy and Performance n Changng Economc Condtons. Journal of Fnance 51, Goetzmann, W., Ingersoll, J., Spegel, M., Welch, I., Portfolo Performance Manpulaton and Manpulaton-proof Performance Measures. Revew of Fnancal Studes 20, Grnblatt, M., Ttman, S., Portfolo Performance Evaluaton. Revew of Fnancal Studes 2, Gruber, M.J., Another Puzzle: The Growth n Actvely Managed Mutual Funds. Journal of Fnance, 51, Hübner, G., The Generalzed Treynor Rato. Revew of Fnance 9, Hübner, G., How do performance measures perform? Journal of Portfolo Management (Summer), Ippolto, R.A., Consumer reacton to measures of poor qualty: Evdence from the mutual fund ndustry. Journal of Law and Economcs 35, Jensen, M.C., Problems n Selecton of Securty Portfolos. Journal of Fnance 23, Kempf, A., Ruenz, S., Famly matters: rankngs wthn fund famles and fund nflows. Journal of Busness Fnance & Accountng 35,

24 Khorana, A., Top management turnover: An emprcal nvestgaton of mutual fund managers. Journal of Fnancal Economcs 40, Kosowsk, R., Tmmermann, A., Wermers, R., Whte, H., Can Mutual Fund Stars Really Pck Stocks? New Evdence from a Bootstrap Analyss. Journal of Fnance 61, Malkel, B.G., Returns from Investng n Equty Mutual Funds 1971 to Journal of Fnance 50, Muraldhar, A.S., Hstory matters. Dervatves Use, Tradng & Regulaton 10, Otten, R., Bams, D., European Mutual Fund Performance. European Fnancal Management 8, Pastor, L., Stambaugh, R.F., Mutual fund performance and seemngly unrelated assets. Journal of Fnancal Economcs 63, Sharpe, W.F., Mutual Fund Performance. Journal of Busness 39, Sharpe, W.F., The Sharpe Rato. Journal of Portfolo Management (Fall), Srr, E.R., Tufano, P., Costly Search and Mutual Fund Flows. Journal of Fnance 53, Stambaugh, R.F., Analyzng nvestments whose hstores dffer n length. Journal of Fnancal Economcs 45, Stotz, O., Selecton, Market Tmng and Style Tmng of Equty Mutual Funds Evdence from Germany. Zetschrft für Betrebswrtschaft 77, Treynor, J.L., How to Rate Management of Investment Funds. Harvard Busness Revew 43, Wermers, R., Mutual Fund Performance: An Emprcal Decomposton nto Stock- Pckng Talent, Style, Transactons Costs, and Expenses. Journal of Fnance 55,

25 Fgure 1: Rollng 36-month averages and alphas of the factors of Carhart s model, January 1993 to December % (A) 2% (B) 1% 1% 0% 0% -1% ERM -2% Dec-95 Dec-98 Dec-01 Dec-04-1% SMB -2% Dec-95 Dec-98 Dec-01 Dec-04 2% (C) 2% (D) 1% 1% 0% 0% -1% HML -2% Dec-95 Dec-98 Dec-01 Dec-04-1% MOM -2% Dec-95 Dec-98 Dec-01 Dec-04 2% (E) 2% (F) 1% 1% 0% 0% -1% 1F-Alpha SMB -2% Dec-95 Dec-98 Dec-01 Dec-04-1% 1F-Alpha HML -2% Dec-95 Dec-98 Dec-01 Dec-04 2% (G) 2% (H) 1% 1% 0% 0% -1% 1F-Alpha MOM -2% Dec-95 Dec-98 Dec-01 Dec-04-1% 3F-Alpha MOM -2% Dec-95 Dec-98 Dec-01 Dec-04 Notes: Panels A to D show the rollng 36-month averages of the four factors ERM, SMB, HML and MOM for the Carhart (1997) model. Panels E to G present the rollng 36-month one-factor alphas from regressng the factors SMB, HML and MOM on the market excess return ERM accordng to (3). Moreover, Panel H shows the rollng 36-month three-factor alpha from regressng the MOM factor on the frst three factors accordng to (4). In every panel, the frst wndow ranges from 1993:01 to 1995:12, the last one from 2004:01 to 2006:12, and wndows are sequentally advanced by one month (a total of 133 observatons). Each observaton represents the average or alpha of the respectve factor over the prevous 36 months. For example, the observaton for December 2001 represents the partcular value from 1999:01 to 2001:12. 23

26 Fgure 2: Rank changes of ndvdual funds resultng from applyng the tme perod adjustment for dfferent performance measures 3,500 Average AVG_ER_RANK_DIFF excess return (A) 3,000 2,500 Frequency 2,000 1,500 1, ,000-4,000-2, ,000 4,000 6,000 3,500 SR_RANK_DIFF Sharpe rato (B) 3,500 TR RANK_DIFF Treynor rato (C) 3,000 3,000 2,500 2,500 Frequency 2,000 1,500 Frequency 2,000 1,500 1,000 1, ,000-4,000-2, ,000 4,000 6, ,000-4,000-2, ,000 4,000 6,000 3,500 _1FA_RANK_DIFF One-factor alpha (D) 3,500 Three-factor _3FA_RANK_DIFF alpha (E) 3,000 3,000 2,500 2,500 Frequency 2,000 1,500 Frequency 2,000 1,500 1,000 1, ,000-4,000-2, ,000 4,000 6, ,000-4,000-2, ,000 4,000 6,000 Notes: Ths fgure shows the frequences of changes n the rankngs of ndvdual funds whch result from usng tme perod-adjusted performance measures compared to the commonly used measures based on the fund s return hstory. Panel (A) contans the results for the average excess return, Panel (B) for the Sharpe rato, Panel (C) for the Treynor rato, Panel (D) for Jensen s (1968) one-factor alpha, and Panel (E) for Fama and French s (1993) three-factor alpha. The fgure shows these rank changes for all 6,148 equty mutual funds n the survvorshp bas-free total fund sample used here. 24

27 Table 1: Model summary statstcs, January 1993 to December 2006 Factor Mean Monthly Return (p-value) Std Dev Varance Covarance Matrx V (Correlaton Matrx) ERM SMB HML MOM VIF 1F α (p-value) 1F β (p-value) ERM 0.64% (0.046) 4.12% 0.17% (1) 0.03% (0.21) -0.08% (-0.52) -0.04% (-0.19) 1.47 SMB 0.20% (0.496) 3.83% 0.03% (0.21) 0.15% (1) -0.07% (-0.49) 0.03% (0.18) % (0.761) 0.20 (0.001) HML 0.50% (0.068) 3.53% -0.08% (-0.52) -0.07% (-0.49) 0.12% (1) -0.01% (-0.04) % (0.007) (0.000) MOM 0.81% (0.038) 5.00% -0.04% (-0.19) 0.03% (0.18) -0.01% (-0.04) 0.25% (1) % (0.003) (0.158) Notes: Ths table presents mean and standard devatons of monthly returns of the four factors from Carhart s (1997) model for the sample perod from 1993:01 to 2006:12. Moreover, the table shows the varance covarance and the correlaton matrx for these factors. The Varance Inflaton Factor (VIF) for a gven factor s calculated as 1/(1 R 2 ) where the R 2 results from a regresson of ths factor on the other respectve three factors. A VIF of 1 sgnalzes lnear ndependency whle a VIF of ten ndcates that problems n nterpretng 1F 1F results caused by multcollnearty are lkely. The one-factor alphas α and betas β of the factors SMB, HML and MOM were calculated usng one-factor regressons accordng to (3). 25

28 Table 2: Fund-specfc characterstcs accordng to Carhart s (1997) four-factor model 4F α M-4F β S-4F β H-4F MO-4F β β σ υ R 2 Total fund sample Mean -0.16% % 0.88 Std Dev 0.30% % 0.08 Subsample A Mean -0.22% % 0.90 Std Dev 0.29% % 0.08 Subsample B Mean -0.17% % 0.89 Std Dev 0.33% % 0.09 Subsample C Mean -0.13% % 0.87 Std Dev 0.29% % 0.08 Notes: Ths table shows descrptve statstcs for monthly excess returns of several fund samples. The table shows the fund-specfc characterstc of funds based on Carhart s (1997) four-factor model accordng to (5). The total fund sample contans all 6,148 funds n the survvorshp bas-free total fund sample used here. Subsample A contans 1,413 non-bear funds showng no returns n 2001:08 or later (473 funds) or startng n 2001:03 or later (940 funds). 1,649 bear funds wth returns startng from 1998:10 untl 2001:02 belong to subsample B, whle all remanng 3,086 funds n the total sample (not ncluded n the subsamples A and B) make up subsample C. 26

29 Table 3: Monthly excess returns and rsk-adjusted performance of funds Performance 1F M Avg. ER SR TR α 3F α 4F α Total fund sample Mean 98.1 Mean 0.40% 9.09% 0.42% -0.06% -0.15% -0.16% Std Dev 38.9 Medan 0.47% 9.28% 0.46% -0.07% -0.14% -0.15% Subsample A Mean 58.6 Mean 0.65% 17.03% 0.65% -0.19% -0.23% -0.22% Std Dev 13.0 Medan 0.65% 15.80% 0.66% -0.16% -0.19% -0.18% Avg. rank 2,247 1,968 2,302 3,554 3,507 3,410 Subsample B Mean 76.0 Mean 0.04% 1.73% 0.07% 0.00% -0.16% -0.17% Std Dev 16.4 Medan 0.05% 1.07% 0.05% -0.07% -0.15% -0.15% Avg. rank 4,134 4,157 4,090 2,896 3,123 3,089 Subsample C Mean Mean 0.47% 9.40% 0.50% -0.04% -0.11% -0.13% Std Dev 30.4 Medan 0.50% 9.61% 0.49% -0.05% -0.12% -0.13% Avg. rank 2,887 3,003 2,885 2,950 2,851 2,913 Notes: Ths table gves descrptve statstcs for average monthly excess returns and rsk-adjusted performance measures for several fund samples. The total fund sample contans all 6,148 funds n the survvorshp bas-free total fund sample used here. Subsample A contans 1,413 non-bear funds showng no returns n 2001:08 or later (473 funds) or startng n 2001:03 or later (940 funds). 1,649 bear funds wth returns startng from 1998:10 untl 2001:02 belong to subsample B, whle all remanng 3,086 funds n our full sample (not ncluded n the subsamples A and B) make up subsample C. M represents the number of contnuous monthly excess returns of funds n the respectve samples. The table also shows the mean and medan of performance measures for these fund samples as well as the respectve average rank postons of the subsamples n the total fund sample. 27

30 Table 4: Average excess returns and rsk-adjusted performance of funds corrected for dfferences n evaluaton perods 1F Avg. ER SR TR α 3F α 4F α Total fund sample Mean 0.56% 12.01% 0.59% -0.09% -0.14% -0.16% Medan 0.55% 12.09% 0.56% -0.07% -0.14% -0.15% Subsample A Mean 0.48% 10.87% 0.51% -0.16% -0.21% -0.22% Medan 0.49% 10.96% 0.50% -0.13% -0.17% -0.18% Avg. rank 3,536 3,375 3,450 3,427 3,444 3,410 Avg. rank change 1,289 1,407 1, Subsample B Mean 0.57% 12.28% 0.60% -0.08% -0.13% -0.17% Medan 0.54% 11.83% 0.55% -0.08% -0.13% -0.15% Avg. rank 3,071 3,055 3,075 3,060 3,038 3,089 Avg. rank change -1,063-1,101-1, Subsample C Mean 0.59% 12.38% 0.63% -0.05% -0.11% -0.13% Medan 0.58% 12.59% 0.59% -0.04% -0.12% -0.13% Avg. rank 2,865 2,947 2,902 2,921 2,925 2,913 Avg. rank change Notes: Ths table gves descrptve statstcs for tme perod-adjusted average monthly excess returns and rsk-adjusted performance measures for several fund samples. The total fund sample contans all 6,148 funds n the survvorshp bas-free total fund sample used here. Subsample A contans 1,413 non-bear funds showng no returns n 2001:08 or later (473 funds) or startng n 2001:03 or later (940 funds). 1,649 bear funds wth returns startng from 1998:10 untl 2001:02 belong to subsample B, whle all remanng 3,086 funds n our full sample (not ncluded n the subsamples A and B) make up subsample C. The table shows the mean and medan of tme perod-adjusted average monthly excess returns and performance measures for these fund subsamples as well as ther respectve average rank poston n the total fund sample. Furthermore, t reports the average rank changes for these subsamples resultng from correctng these measures for dfferences n evaluaton perods. For funds wth non-full data,.e. less than 168 monthly returns, we assume Carhart s (1997) four-factor model as return generatng process and use longer-hstory estmates of the parameter of the factors to obtan better estmates of fund performance. The characterstcs for each fund based on ts own return hstory are combned wth the factor parameters for the full evaluaton perod accordng to (6), (8), (9), (10) and (12) to calculate tme perod-adjusted measures for the average excess return, the Sharpe rato, Treynor rato, and one- and three-factor alphas. 28