Fund performance persistence and competition keswani
The Journal of Financial Research • Vol. XXIX, No. 3 • Pages 349–366 • Fall 2006MUTUAL FUND PERFORMANCE PERSISTENCE AND COMPETITION: A CROSS-SECTOR ANALYSIS Aneel Keswani Cass Business School David Stolin Toulouse Business School Abstract Existing work on mutual fund performance persistence obtains diverse results, depending on the group of funds studied. We examine whether performance per- sistence within a peer group of competing mutual funds depends on the group’s composition. The U.K. mutual fund industry is ideal for such an examination be- cause funds compete within strictly defined sectors. We consider several attributes related to the intensity of competition within a sector and use them to explain sector-level persistence. We find robust evidence that persistence is higher in sectors where concentration of assets under management is higher. JEL Classification: G23 I. IntroductionIt is well established in the industrial organization literature that the structure ofa sector affects its competitiveness. In more competitive sectors we expect to seefew firms doing persistently well and those performing poorly being forced to exitthe sector. This reasoning is tested by Waring (1996), who finds a strong negativerelation between competitiveness within an industrial sector and the persistence ofprofitability for firms in that sector. We translate this logic to the mutual fund context. To use the terminology ofindustrial organization, mutual funds compete with each other using a combinationof price and nonprice competition strategies. Price competition involves funds We thank Vladimir Atanasov, Andrew Clare, Zsuzsanna Fluck, Gordon Gemmill, Brian Kluger,Tobias Kretschmer, Gordon Midgley, Kenneth Moon, Dennis Stanton, Dylan Thomas, Giovanni Urga, andespecially William T. Moore (former editor) and Jonathan Fletcher (the referee) for insightful comments.We also acknowledge comments received from participants at the 2003 Financial Management Associationmeeting in Denver, and seminars at Cass Business School and the universities of Porto, Reading, Warwick,and Oxford. We thank Benjamin Kogan, Jan Steinberg, James Sullivan, the Allenbridge Group, and theInvestment Management Association for help with data. Part of the research reported here was conductedwhile Stolin was visiting at the Stockholm Institute for Financial Research. All errors and omissions areours. 349
350 The Journal of Financial Researchvarying the fees they charge to obtain a competitive advantage. Nonprice com-petition involves (among other things) funds competing to produce superior invest-ment performance. Numerous studies show that higher investment returns have animportant influence on fund market share (e.g., Siggelkow 2003). We expect funds from more competitive sectors to compete more aggres-sively for abnormal returns. This should result in the exit of funds that underperformand a low probability of remaining funds doing repeatedly well. Competing fundsshould be able to close the performance gap on “star” funds by devoting moreresources to researching investment opportunities, by learning to imitate the bestperformers, or even by poaching their managers. Thus, in more competitive sectorswe expect to see less persistence in funds’ performance relative to their rivals (i.e.,less relative persistence). To examine the influence of competition on investment performance per-sistence, we focus on the U.K. unit trust (open-ended mutual fund) industry. Thisenvironment is ideal for our purpose because U.K. mutual funds compete in alarge number of unambiguously defined peer groups (sectors), whose membershipis monitored and enforced by the industry trade body. This is unlike the UnitedStates, where multiple sector definitions coexist and managers are free to gametheir sector affiliations (Cooper, Gulen, and Rau 2005). Although research into fund performance persistence has a long history,Brown et al. (1992) show that early studies exaggerate the extent of persistence by re-lying on survivorship-biased data sets. Carhart (1997) finds that in his survivorship-free sample of U.S. equity funds, persistence largely disappears after accountingfor momentum in stock returns. However, recent studies argue that after properlyconsidering fund styles, there is persistence in U.S. equity mutual funds (Ibbotsonand Patel 2002; Teo and Woo 2001; Wermers 2003). Outside the United States, there has been debate as well. In the UnitedKingdom, it has involved academics (Blake and Timmermann 1998; Allen and Tan1999; Fletcher and Forbes 2002), practitioners (Quigley and Sinquefield 2000),the trade association (Giles, Wilsdon, and Worboys 2002), and the regulatory body(Rhodes 2000; Blake and Timmermann 2003). This literature agrees that perfor-mance persistence is an important issue but disagrees on whether and to what extentpersistence is present. The preceding studies all focus on funds investing in domestic equity secu-rities. The availability of well-accepted benchmarks for risk adjustment is a majorreason for this focus. Several studies examine persistence for funds investing inother asset classes (e.g., see Blake, Elton, and Gruber 1993 for bond mutual funds)and obtain diverse results, depending on the period used and the fund sector stud-ied. This raises the possibility that levels of persistence may vary depending on theeconomic circumstances. In particular, the market structure of a mutual fund sectormay influence funds’ ability to perform consistently. Our research examines how mutual fund performance persistence at thefund sector level is influenced by competition within the sector. A few studies
Mutual Fund Performance Persistence 351consider determinants of persistent performance at the individual fund level (e.g.,Volkman and Wohar 1995). Several other studies note persistence differences acrosssectors or fund objectives (Blake and Timmermann 1998; Kosowski et al. 2003;Wermers 2003). No study, however, conducts a sector-level statistical analysis ofpersistence, and none investigates the effect of competition on persistence. Massa’s(2003) empirical demonstration that sector-level variables related to competition ex-plain sector-level performance suggests that such an analysis is potentially fruitful. We construct several variables to capture the intensity of competition ina sector. These include the number of funds in a sector, the proportion of maturefunds, and the Herfindahl index of asset concentration. We find robust evidence thatpersistence is higher in sectors where concentration of assets under managementis higher. Our results suggest that the degree of persistence exhibited by a sector’sinvestment managers depends on how competitive that sector is. II. Data and MethodThe U.K. Mutual Fund IndustryUnlike in the United States, a survivorship-bias-free electronic database of mutualfunds does not exist in the United Kingdom. To conduct our study, we thereforemanually collected data from 11 consecutive editions of the annual Unit TrustYearbook.1 Our data span from 1991 to 2001 and include names of funds and theirmanagement groups, annual returns (including reinvested income and excludingfees), fund assets under management, launch dates, and of course the name of thesector to which each fund belongs. We use fund names and an index of name changesto link fund data across years. We consider mergers between funds as creating anew fund. As our primary focus is at the sector level (rather than at the individualfund level), we track the evolution and membership of official fund sectors asdefined by the Association of Unit Trust and Investment Funds (AUTIF) and by itssuccessor, the Investment Management Association (IMA).2 To do this, we use dataon fund movement across sectors, as well as historical announcements by AUTIFand IMA. Appendix A summarizes the history of U.K. mutual fund sectors. We use 1 In the editions corresponding to 2000 and 2001 year-ends, the yearbook had a new publisher, andseveral smaller fund families did not supply information on their funds. However, there is no survivorship biasdue to selective reporting of funds. Post-2001 data are unavailable as the yearbook has been discontinued. 2 In the United Kingdom, all information providers use the official classification system. The IMAenforces its sector definitions, and if the asset allocation of a fund contravenes the allocation rules of itscurrent sector, the IMA will warn the fund to change its allocation if it does not wish to change sectors. Ifthe fund does not comply, the IMA will move the fund to a new sector reflecting its new asset allocation.By contrast, in the United States there is a proliferation of methods for assigning funds to a peer group.This ambiguity allows fund managers to “game” their objectives (Cooper, Gulen, and Rau 2005) and makesobjective-level measures of competition less meaningful.
352 The Journal of Financial Researchofficial sector descriptions to group sectors into four broad categories: domesticequity, global equity, domestic nonequity, and global nonequity. The appendix paintsa picture of substantial innovation at the sector level—with numerous instancesof sectors being opened, discontinued, redefined, or merged—consistent with anindustry seeking to respond to changing conditions. Additionally, there is muchvariability in the number of funds within a sector. Our sample period thus capturesan industry in transition, which is helpful for our analysis of the role of marketstructure characteristics.Measurement of PersistenceMeasures of performance persistence quantify to what extent performance in oneperiod (the “ranking” period) continues into the subsequent period (the “evaluation”period). In this study, we focus on persistence at the one-year frequency (i.e., ourranking and evaluation periods each equals one year). There are several reasonsfor this choice. First, researchers who find evidence of persistence generally findit for one-year horizons. Second, investors and fund managers tend to evaluateperformance over annual periods. Third, tests of performance persistence requirereturn availability for both ranking and evaluation periods. This leads to a look-ahead bias, which can influence how much persistence is detected (Brown et al.1992; Ter Horst, Nijman, and Verbeek 2001). Lengthening the horizon over whichpersistence is measured makes this bias more severe. Over one-year periods, TerHorst, Nijman, and Verbeek (2001) find the look-ahead bias to be negligible. Performance persistence can be measured using both absolute and relativeperformance. We measure persistence using relative performance for two reasons.First, existing research highlights that in determining mutual fund money flows,relative performance matters beyond absolute performance. Second, measures ofabsolute performance persistence depend on the volatility of securities investedin by a given sector, making comparisons of absolute persistence across sectorsmisleading. To measure relative performance persistence, we use raw and not risk-adjusted returns. In our context, examining persistence on a risk-adjusted basis isproblematic for two reasons. First, we do not have access to monthly returns forexisting and extinct U.K. mutual funds. Second, and more important, the quality ofany risk adjustment would inevitably vary across sectors. For example, domesticequity returns can be analyzed with well-researched multifactor models, whereasthis is less likely for global or nonequity funds. This means that sector characteristicsrelated to our ability to risk-adjust would have a spurious effect on a cross-sectionalanalysis of persistence in risk-adjusted returns. Persistence measured on the basis ofraw returns, on the other hand, is important in its own right. Numerous informationproviders such as Money Management, Unit Trust Yearbook, Standard & Poor’s Website, and others rank funds based on raw returns within a sector. Indeed, evidence
Mutual Fund Performance Persistence 353on the return-flow relation indicates that investors react to raw returns. Moreover,implicit in looking at within-sector persistence, as we do, is a peer-group adjustmentof fund returns. Commonly used statistics for studying relative persistence within a peergroup include the Spearman rank-correlation coefficient, and quantities based on2 × 2 winner/loser contingency tables. The latter include the log-odds ratio andthe chi-squared statistic. The chi-squared statistic is disqualified for our purpose(which is to explain the extent of persistence) because high values correspondto either persistence or reversal of performance. The advantage of the Spearmancorrelation over the log-odds ratio is that the latter uses the performance rankof each fund rather than just its winner/loser status. This generally means morepowerful tests for persistence (Carpenter and Lynch 1999). The advantage of thelog-odds ratio is that it has a more straightforward economic interpretation, aswe show shortly. We use both the log-odds ratio and the Spearman correlation asour measures of persistence (equations are given in Appendix B). To avoid ourresults being influenced by the small-sample properties of these statistics, we useonly sector-years with at least 20 funds in existence over both years for whichperformance is measured. Table 1 shows the extent of relative performance persistence across U.K.mutual fund sectors based on raw returns over consecutive years. In Panel A,we present the distribution of the Spearman correlation coefficient and of thelog-odds ratio by type of sector. The first group of eight rows pertains to thelog-odds ratio. In column 1, for all sector-years combined (162), the average log-odds ratio is 0.357. The null hypothesis that the mean log-odds ratio is zero canbe rejected ( p-value < .001) based on applying Student’s t-test to our set of 162sector-years. The median sector-year has a log-odds ratio of 0.405, and the dis-tribution ranges from −2.837 to 4.317. The log-odds ratio is positive for 62% ofthe sector-years. Furthermore, the table reports the proportion of sector-years forwhich the hypothesis of no persistence is rejected in favor of the one-sided alter-native of positive persistence. For the log-odds ratio, this is the case for 29% of thesector-years at the .05 confidence level, and for 17% of the sector-years at the .01confidence level. The next eight rows characterize the distribution of the Spearman corre-lation across sector-years. For all sector-years combined, the average Spearmancorrelation is 0.143 and is significantly different from zero. We note that even atthe .01 confidence level, the hypothesis of no persistence is rejected in favor ofthe hypothesis of positive persistence for 29% of sector-years. This suggests theSpearman-based test is more powerful than the log-odds ratio. To ensure that performance persistence in our sample is not driven by aparticular subperiod, we separately consider sector-years for which the evaluationyears are 1992 through 1996, and those for which the evaluation years are 1997through 2001 (results not reported in a table). The average log-odds ratio for the
354 The Journal of Financial ResearchTABLE 1. Relative Performance Persistence Across Sectors. All Sectors Domestic Other Than Global Domestic Global All Equity Domestic Equity Nonequity Nonequity Sectors Sectors Equity Sectors Sectors SectorsVariable (1) (2) (3) (4) (5) (6)Panel A. Sector-Year StatisticsNumber of sector-years 162 36 126 63 30 33Log-odds ratio by sector-year Average 0.357 0.448 0.331 0.173 0.565 0.421 p-value for H0 : mean = 0 0.000 0.006 0.002 0.192 0.019 0.057 Median 0.405 0.382 0.405 0.365 0.555 0.525 Minimum −2.837 −1.168 −2.837 −2.837 −1.455 −2.485 Maximum 4.317 2.711 4.317 2.398 3.008 4.317 Proportion positive 0.623 0.639 0.619 0.571 0.667 0.667 Proportion positive and 0.290 0.306 0.286 0.270 0.367 0.242 significant at .05 level Proportion positive and 0.167 0.306 0.127 0.143 0.133 0.091 significant at .01 levelSpearman correlation by sector-year Average 0.143 0.147 0.142 0.097 0.180 0.191 p-value for H0 : mean = 0 0.000 0.004 0.000 0.017 0.005 0.001 Median 0.162 0.135 0.166 0.133 0.257 0.176 Minimum −0.642 −0.477 −0.642 −0.642 −0.544 −0.476 Maximum 0.817 0.804 0.817 0.672 0.656 0.817 Proportion positive 0.691 0.583 0.722 0.698 0.733 0.758 Proportion positive and 0.426 0.472 0.413 0.429 0.433 0.364 significant at .05 level Proportion positive and 0.290 0.333 0.278 0.254 0.267 0.333 significant at .01 levelPanel B. Aggregate StatisticsFund-years in winner-winner 2,724 900 1,824 1,240 286 298 categoryFund-years in loser-loser 2,672 895 1,777 1,219 273 285 categoryFund-years in winner-loser 2,276 728 1,548 1,090 225 233 categoryFund-years in loser-winner 2,296 740 1,556 1,096 229 231 categoryAggregate log-odds ratio 0.331 0.402 0.297 0.235 0.416 0.456p-value for aggregate log-odds 0.000 0.000 0.000 0.000 0.001 0.000 ratioFrequency of repeat performance 0.541 0.550 0.537 0.529 0.552 0.557Note: This table reports descriptive statistics for measures of relative performance persistence across U.K.mutual fund sectors, 1991–2001. Sector-years are included if at least 20 funds had returns available in theranking and evaluation years. Panel A reports the distribution of the Spearman correlation coefficient andthe log-odds ratio across sector-years. Both the Spearman correlation coefficient and the log-odds ratio arebased on raw annual returns in consecutive calendar years (formulae are given in Appendix B). In Panel B,sector-years are pooled into an aggregate contingency table.
Mutual Fund Performance Persistence 355earlier (later) period is 0.358 (0.357), and the average Spearman correlation coef-ficient is 0.134 (0.152). All of these averages are statistically significant at the .01level. Moreover, the average log-odds ratio and the average Spearman correlationcoefficient are not significantly different between the two periods ( p-values = .99and .70, respectively). Because research on mutual fund performance persistence tends to focuson domestic equity funds, we separately report results for these sectors in the secondcolumn. The persistence measures are positive and, despite a sample size of only 36sector-years, highly statistically significant. The average log-odds ratio, at 0.448, isslightly lower than the 0.516 average log-odds ratio in Fletcher and Forbes (2002),which is based on raw annual returns for U.K. equity mutual funds from 1982 to1996. The average Spearman correlation, at 0.147, is slightly lower than the 0.188reported by Allen and Tan (1999) for raw annual returns of U.K. equity mutualfunds from 1989 to 1995. Column 3 presents results for sectors other than domestic equity. The levelof persistence is comparable to that in the preceding column. In fact, unreportedtests show that differences between the two columns are never significant. Thelast three columns further disaggregate sectors other than domestic equity intoglobal equity, domestic nonequity, and global nonequity. In each category, perfor-mance persistence is positive and significant, at least for the Spearman correlationcoefficient. As further evidence on the level of performance persistence in our sample,in Panel B we pool data from different sector-years to present an aggregate con-tingency table. In 2,724 (2,672) instances, funds are two-period winners (losers)in their respective sectors, and in 2,276 (2,296) instances, funds win in the rank-ing (evaluation) period and lose in the evaluation (ranking) period. The resultingaggregate log-odds ratio equals ln((2724 × 2672)/(2276 × 2296)) = 0.331 and ishighly significant. The aggregate log-odds ratios for the different sector groups incolumns 2 through 6 are all significant at the .01 level. The economic significance of performance persistence in our sample isperhaps best addressed through the probability that a fund’s winner/loser statuscarries over from the ranking period to the evaluation period. This probability ofrepeat performance can be estimated as the number of fund-years correspondingto two-period winners or two-period losers divided by the total number of fund-years. For all sectors together, this quantity (reported in the last row of the table)equals (2,724 + 2,672)/(2,724 + 2,672 + 2,276 + 2,296) = 54.1%, as comparedto the 50.0% that one would expect in the absence of performance persistence orperformance reversal.3 3 Because we define a winner (loser) as a fund that places in the top (bottom) half in its sector in agiven year, the cell counts in the contingency table are not independent. In fact, if there were no ties andif the number of funds in a sector were always divisible by four, the winner-winner fund count would be
356 The Journal of Financial Research Overall, there is strong evidence that the U.K. mutual fund industry exhibitspersistence in relative investment performance. If at least some of this persistence isdue to sector-level attributes, in particular to those related to sector competitiveness,a cross-sector analysis may reveal this. Such analysis is conducted in the nextsection. III. Determinants of Sector-Level PersistenceSector AttributesBroadly speaking, systematic differences in persistence between sectors can be dueto differences in the composition of sector membership, or to differences in thetypes of assets sector members invest in. We construct several variables designed toquantify how competitive a sector is, and the distribution of these variables is givenin Panel A of Table 2. N is simply the number of funds in a sector at the end of theranking year. The largest number of funds in a sector is 302, corresponding to theUK All Companies sector in 1999 (after sectors dedicated to domestic “growth” and“growth and income” stocks were merged). Because we drop sectors comprisingfewer than 20 funds with recorded returns, the minimum number of funds in a sectoris 24, the median is 79, and the average is 87.4 It is reasonable to conjecture thatconsistent performance is harder to attain in a more crowded sector. For example, instudying fund performance Siggelkow (2003) regards the number of mutual fundsin a category as “a measure of general competition, for instance, for mis-pricedsecurities” (p. 133). We recognize, however, that in such competition, small funds may have rel-atively little effect. We therefore also use the Herfindahl index, which is commonlyconsidered as a measure of intra-industry rivalry. Specifically, HERFINDAHL isthe concentration index of assets under management. Because several funds froma single family of funds can coexist within a sector, we aggregate assets by fam-ily to calculate this measure. Thus, the value of HERFINDAHL for each sector isthe sum across families of the square of each family’s assets as a proportion ofa sector’s total assets. Although we use only sectors with at least 20 funds, thereis substantial variation in the value of the Herfindahl index, ranging from 0.027to 0.629 (by construction, the smallest possible value of the Herfindal index is 0exactly equal to the loser-loser count, and the winner-loser count would be exactly equal to the loser-winnercount. Using this insight, it is straightforward to show that the probability of repeat performance can beobtained directly from the log-odds ratio (L) as 1/(1 + e−L/2 ). For example, using the aggregate log-oddsratio of 0.331, the probability of repeat performance is 1/(1 + e−0.331/2 ) = 0.541. We subsequently use thisconversion to assess the economic significance of our regression results. 4 For comparison, Massa (2003) uses several data providers’ fund descriptions to assign U.S. mutualfunds to 1 of 23 categories. The numbers of funds in his categories range from 14 to 1,149, the median is343, and the average is 411.
Mutual Fund Performance Persistence 357TABLE 2. Descriptive Statistics for Sector-Level Variables.Panel A. MomentsVariable Mean Standard Deviation Median Minimum MaximumN 87 50 79 24 302MATURITY 0.552 0.188 0.626 0.000 0.846HERFINDAHL 0.088 0.070 0.068 0.027 0.629Panel B. CorrelationsVariable N MATURITY HERFINDAHL LATERDOMESTIC EQUITY 0.420 0.420 −0.247 −0.007N 0.476 −0.464 −0.163MATURITY −0.586 −0.040HERFINDAHL −0.078Note: This table contains descriptive statistics for the set of sector-year explanatory variables. Sector-yearsare included if at least 20 funds had returns available in the ranking and evaluation years: 162 sector-yearsmeet this requirement. The variables are as follows. N is the number of funds within the sector. MATURITYis the proportion of sector funds that are at least five years old. HERFINDAHL is the Herfindahl indexmeasuring the concentration of fund assets within the sector, where funds from the same family areaggregated. DOMESTIC EQUITY is a dummy variable equal to 1 if sector funds are primarily invested inU.K. equities, and 0 otherwise.and the largest possible value is 1). We hypothesize that less concentrated (morecompetitive) sectors exhibit lower persistence. Finally, MATURITY is the proportion of funds that are at least five yearsold. In the average sector, most funds are “seasoned,” but the minimum value of 0for the maturity variable indicates that for some sector-years, all of the funds arerelatively recent entrants. Berk and Green (2004) give a powerful reason why mutualfund performance persistence should decrease with fund vintage. If investmentmanagement returns to scale are decreasing, managers have differential ability, andinvestors channel money to best performers, then superior funds grow to the pointwhere outperformance is no longer possible. Empirically, Waring (1996) finds thatearnings persistence in an industrial sector tends to decay over time, as competitiveforces have acted over a longer period. Panel B of Table 2 shows a correlation matrix for the preceding sectorattributes and for a dummy variable indicating sector membership in the U.K.equity category (DOMESTIC EQUITY ), as well as a dummy variable that equals1 for the second half of our sample period (evaluation years from 1997 to 2001),and 0 otherwise (LATER). DOMESTIC EQUITY is included because most studiesof performance persistence focus on domestic equity sectors. LATER controls forthe possibility that the level of persistence may have changed in more recent years.We note that pairwise correlations between N, MATURITY, and HERFINDAHL arehigh in magnitude: sectors with more funds in them tend to be more mature, and
358 The Journal of Financial Researchassets invested in these sectors are more dispersed across fund families. Therefore,in the regressions to follow, we enter these three variables one at a time.Regression ResultsTable 3 presents the results of a pooled regression of sector-level measures of relativepersistence on our set of sector-level explanatory variables. Persistence is measuredover years T (the ranking year) and T+1 (the evaluation year). Explanatory variablesare measured as of the end of year T (with one exception explained below). Thus,we examine whether sector characteristics observed at the end of year T tell us towhat extent year T performance of the sector’s funds persist into year T+1. Wedo not require that funds remain in the same sector until the end of year T+1 (or,indeed, that the sector itself continue to exist until the end of year T+1) becausedoing so would constitute a look-ahead bias. In regressions (1) through (3) we use the log-odds ratio as the measure ofpersistence and proxy for sector competitiveness with N, MATURITY, orHERFINDAHL, respectively. Although the number of funds in a sector is not signif-icantly related to persistence, maturity of funds is significant (t-statistic = −2.71),as is the concentration of assets under management (t-statistic = 3.01). In otherwords, sectors that are less mature and have more concentrated assets—that is,sectors that may be described as less competitive—are characterized by greaterpersistence. The other variables are not statistically significant. Regressions (4) through (6) parallel regressions (1) through (3) but includean additional control variable. CROSSRET is defined as the product of averagesector returns in years T and T+1. Although we do not adjust for differences infund exposure to different risk factors, these differences can generate persistence inraw returns when there is persistence in factor realizations. CROSSRET is intendedto capture spurious persistence due to ex post momentum for the sector as a whole.The regression results confirm this intuition in that CROSSRET is positive andhighly significant ( p-value < .001). Its only other influence is to enhance slightlythe significance of MATURITY and HERFINDAHL (t-statistics = −2.80 and 3.24,respectively). In regressions (7) through (12), the Spearman correlation coefficient is thedependent variable. The results are similar to those based on the log-odds ratio.Once again, MATURITY and HERFINDAHL are statistically significant at the .01level, and CROSSRET continues to capture persistence due to momentum in allspecifications.Robustness ChecksThe preceding subsection presents evidence that HERFINDAHL and MATURITYare sector attributes that are systematically related to the persistence exhibited bythe sector. We now report on the robustness of our results to alternative sample-selection criteria, econometric methods, and other variations.
TABLE 3. Explaining Sector-Level Persistence. Dependent Variable: Log-Odds Ratio Dependent Variable: Spearman Correlation CoefficientExplanatory Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)Intercept 0.586 1.097 0.020 0.568 1.040 −0.070 0.214 0.348 0.048 0.208 0.328 0.016 (2.93)∗∗∗ (3.90)∗∗∗ (0.12) (2.90)∗∗ (3.76)∗∗∗ (−0.40) (3.82)∗∗∗ (4.41)∗∗∗ (0.98) (3.84)∗∗∗ (4.29)∗∗∗ (0.34)DOMESTIC EQUITY 0.224 0.302 0.270 0.257 0.306 0.279 0.038 0.057 0.051 0.050 0.058 0.054 (0.98) (1.40) (1.29) (1.14) (1.45) (1.36) (0.59) (0.93) (0.87) (0.80) (0.99) (0.96)N −0.003 −0.004 −0.001 −0.001 (−1.13) (−1.48) (−1.21) (−1.66)MATURITY −1.297 −1.315 −0.353 −0.359 (−2.71)∗∗∗ (−2.80)∗∗∗ (−2.63)∗∗∗ (−2.76)∗∗∗HERFINDAHL 3.780 3.975 1.104 1.172 (3.01)∗∗∗ (3.24)∗∗∗ (3.15)∗∗∗ (3.47)∗∗∗LATER −0.225 −0.226 −0.139 −0.175 −0.168 −0.075 −0.060 −0.058 −0.033 −0.041 −0.037 −0.011 (−1.25) (−1.30) (−0.80) (−0.99) (−0.98) (−0.44) (−1.16) (−1.18) (−0.68) (−0.84) (−0.78) (−0.22)CROSSRET 4.271 4.062 4.272 1.489 1.422 1.485 (2.80) (2.73)∗∗∗ (2.89)∗∗∗ (3.53)∗∗∗ (3.45)∗∗∗ (3.64)∗∗∗R2 0.017 0.053 0.063 0.063 0.090 0.110 0.015 0.047 0.064 0.087 0.114 0.137Note: This table contains the results of regressing measures of persistence in relative investment performance on sector-level variables. Sector-years are included if at least20 funds have returns available in the ranking and evaluation years: 162 sector-years meet this requirement. The explanatory variables are as follows. N is the number of fundswithin a sector. MATURITY is the proportion of sector funds that are at least five years old. HERFINDAHL is the Herfindahl index measuring the concentration of fund assets Mutual Fund Performance Persistencewithin a sector, where funds from the same family are aggregated. DOMESTIC EQUITY is a dummy variable equal to 1 if sector funds are primarily invested in U.K. equities,and 0 otherwise. LATER is a dummy variable equal to 1 when the evaluation year is 1997 or later, and 0 otherwise. CROSSRET is the product of average sector returns in theranking and evaluation years. The t-statistics are shown in parentheses.∗∗∗ Significant at the 1% level.∗∗ Significant at the 5% level. 359
360 The Journal of Financial Research Because both the log-odds ratio and the Spearman correlation are estimatedwith differing degrees of precision across sectors, the resulting heteroskedasticity inour regression may lead to inefficient estimation. We therefore use the inverse of thestandard error of the log-odds ratio and of the Spearman correlation coefficient asweights in a generalized least squares regression using these measures as dependentvariables. The results are not significantly different from those reported earlier. We also investigate whether time-series correlation affects our results. First,we test for serial correlation in a panel but fail to find evidence of this. Second, weinclude lagged persistence measures in our regressions. This reduces the number ofobservations from 162 to 136. HERFINDAHL and MATURITY remain significant atthe .05 level or better, and N remains insignificant. The lagged persistence measureitself is never statistically significant. To check that our results using Spearman correlation are not influencedby having a dependent variable limited to the [+1,−1] range, we estimate ourmodel using the Papke and Wooldridge (1996) generalized linear approach, whichis designed for estimating models with a fractional dependent variable. Our resultsare broadly unchanged. All coefficient estimates that are significant using ordinaryleast squares at the .05 level and above are also significant using the new approach,and the signs of all significant coefficient estimates remain the same as before. To address the possibility that our results may be influenced by the small-sample properties of our persistence measures, we exclude sector-years with fewerthan 30 funds. This reduces the number of sector-years to 124. When we do this,MATURITY becomes insignificant regardless of the econometric method used.The statistical significance of HERFINDAHL, however, is .05 or better in allspecifications. As the coverage of the last two editions of the Unit Trust Yearbook (corre-sponding to calendar years 2000 and 2001) is reduced because of nonreporting byseveral fund families, we repeat our regressions after omitting these years. We alsoconduct Fama-MacBeth regressions, drop outlier observations, and use differentranges to winsorize our persistence measures. Our results remain basically un-changed: HERFINDAHL is always significant at least at the .10 level and generallyat the .05 level. None of our other variables is consistently significant.Economic SignificanceOur results indicate that the concentration of funds’ assets is statistically signifi-cantly related to the persistence level in that sector. We now assess the economicsignificance of this relation. Consider a fund sector not restricted to U.K. equities(DOMESTIC EQUITY = 0) in the second half of our sample period (LATER =1). When HERFINDAHL is set to its full-sample 10th percentile value of 0.038,using the estimated coefficients in regression (3) of Table 3, the fitted value ofthe log-odds ratio equals 0.025. Using the conversion formula in footnote 3, this
Mutual Fund Performance Persistence 361translates into a 50.3% probability that a fund’s winner or loser status is retainedfrom the ranking period to the evaluation period. This probability exceeds by only0.3% the corresponding probability that one would expect by mere chance in theabsence of any persistence. We now reset HERFINDAHL to its 90th percentile value of 0.162. Thecorresponding fitted value of the log-odds ratio is 0.493, which translates into a56.1% probability of repeat performance, or 6.1% higher than would be expected inthe absence of persistence. In other words, if a sector goes from the 10th to the 90thpercentile of concentration of assets, the excess (relative to the no-persistence case)probability of remaining in the same half of performance rankings increases from0.3% to 6.1%. These numbers indicate that the effect of sector-level concentrationon performance persistence is substantial in economic terms. IV. Longer Term PersistenceBecause we find a link between sector characteristics and persistence, we checkwhether the results hold when persistence is measured over a longer period. To dothis, rather than examining adjacent ranking and evaluation periods as we did inthe preceding section, we use a lagged ranking period (as in Teo and Woo 2001).In other words, one year is allowed to pass between the end of the ranking periodand the start of the evaluation period. Recall that when the ranking period is not lagged, the average (acrosssector-years) log-odds ratio is 0.357 and highly statistically significant. When welag the ranking period by one year, the average log-odds ratio becomes −0.013 andis not significant. Likewise, the average Spearman coefficient drops from 0.143 to−0.012 and is no longer significant. Even though the average level of longer term persistence across sector-years is close to zero, it is still possible that variation in longer term persistence isrelated to sector competitiveness. We therefore repeat our regression analysis whenthe dependent variable is the longer term measure of persistence.5 Consistent withthe notion that our sample exhibits little or no persistence at the longer horizons,HERFINDAHL does not have a significant effect on longer term persistence, andneither do the other sector-level variables.6 5 These results are available from the authors on request. 6 Although we find it important to document that our significant results are limited to the one-yearhorizon, we note that tests for the existence of persistence, and by extension tests for the associationof our sector-level variables with persistence, are weaker when the horizon is longer. First, survivorshipconditioning becomes more serious when the horizon is longer, and depending on the characteristics of thefund attrition process, this can either strengthen or weaken persistence. Second, measurement of persistenceis noisier when the horizon is longer (e.g., because fund characteristics change over time). Indeed, few studiesdetect persistence beyond the one-year horizon.
362 The Journal of Financial Research V. ConclusionPerformance persistence is important to all parties connected with fund manage-ment. Its existence has been the subject of an intense and ongoing debate. Wecontribute to this debate by studying variation in performance persistence acrosspeer groups. The focus of our study is the U.K. mutual fund industry, where officialsectors unambiguously define such peer groups. We study the effect of several sector-level variables on sector-level persis-tence. Our choice of variables is based on the notion that the more competitive asector is, the less likely it is to be characterized by persistence in its funds’ perfor-mance. The variables used to capture intra-sector rivalry are: the number of fundsin the sector, the concentration of fund family assets under management in thesector, and the proportion of mature funds in the sector. We additionally control forthe types of assets in which the sector’s funds are invested. Only the concentrationindex of fund family assets is consistently significant: the less dispersed the sector’sassets are, the more persistence is observed. In all, our results indicate that the com-petitiveness of a fund sector influences the persistence in the relative performanceof its members. The exact channels through which the competitive environmentaffects investment managers’ performance are a subject for future research. APPENDIX A Evolution of U.K. Unit Trust Sectors, 1991–2001
364 The Journal of Financial Research APPENDIX B Calculation of Performance Persistence StatisticsSpearman Rank-Correlation CoefficientFirst, funds that existed in years T (the ranking year) and T+1 (the evaluation year)are identified. Define N to be the size of this sample. For each fund in the sample,the difference d i in the rank of fund i between years T and T+1 is calculated. TheSpearman rank-correlation statistic is defined as N rs = 1 − 6 di (N 3 − N ) i=1and lies between −1 and +1. For sufficiently large N, it is appropriate to test forthe statistical significance of rs using a t-test where the critical t-statistic is givenby
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