Momentum Investment Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior By MARK GRINBLATT, SHERIDAN TITMAN, AND RUSS WERMERS* This study analyzes the extent to which mutual funds purchase stocks based on their past returns as well as their tendency to exhibit "herding" behavior (i.e., buying and selling the same stocks at the same time). We find that 77 percent of the mutual funds were "momentum investors," buying stocks that were past winners; however, most did not systematically sell past losers. On average, funds that invested on momentum realized significantly better performance than other funds. We also find relatively weak evidence that funds tended to buy and sell the same stocks at the same time. (JEL G14, G23) The amount of wealth managed by institu- tional investors has grown considerably over the past 20 years. Due perhaps to decreased trading costs, brought about by the termination of fixed commissions in May 1975, these in- stitutional investors have become much more active traders and, as a result, have become increasingly important in terms of setting mar- ket prices.' The growing influence of institu- tional investors has led to increased scrutiny both by policymakers and by journalists, who tend to believe that these investors trade ex- cessively and move in and out of stocks in a herd-hke manner. This tendency to invest with * Grinblatt: John E. Anderson Graduate School of Management, tJniversity of California, Los Angeles, Box 951481, Los Angeles, CA 90095-1481; Titman: Depart- ment of Finance, Carroll School of Management, Boston College, Chestnut Hill, MA 02167; Wermers: Division of Finance and Economics, Graduate School of Business and Administration, tJniversity of Colorado, Boulder, CO 80309. The authors are grateful to Narasimhan Jegadeesh, as well as to seminar participants at National Taiwan Uni- versity, National Chinese tJniversity, Osaka University, University of California at Berkeley, University of Chi- cago, Stanford University, UCLA, University of Texas, and Yale University for comments on earlier drafts. ' Institutional holdings are now about 50 percent of to- tal equity holdings in the United States, while institutional trading, when added to member trading, accounted for about 70 percent of total NYSE volume in 1989 (Robert Schwartz and James Shapiro, 1992). the herd, in combination with the alleged ten- dency of institutions to follow momentum- based fads by buying past winners and selling past losers is of concern, since this behavior could potentially exacerbate stock- price volatility. Momentum trading strategies and herding behavior are also used by academics to mo- tivate models of seemingly irrational mar- kets. Fischer Black (1986) and Brett Trueman (1988) provide reasons why insti- tutional investors may trade excessively, and a number of recent theory papers provide ra- tionales to explain why institutional inves- tors would analyze the same groups of stocks and trade in the same direction.^ In addition, J. Bradford De Long et al. (1990) describe what they call "positive-feedback traders," who have a tendency to buy stocks after they perform well. Our study provides empirical evidence on the trading patterns of fund managers by ex- amining the quarterly holdings of 155 mutual funds over the 1975-1984 period. We char- ^ These papers include Robert J. Shiller and John Pound (1989), Michael Brennan (1990), David S. Scharf- stein and Jeremy C. Stein (1990), Josef Lakonishok et al. (1991), Abhijit Banerjee (1992), Sushil Bikhchandani et al. (1992), Kenneth A. Froot et al. (1992), and David Hirshleiferetal. (1994). 1088
Transcript
Momentum Investment Strategies,Portfolio Performance, and Herding:
A Study of Mutual Fund Behavior
By MARK GRINBLATT, SHERIDAN TITMAN, AND RUSS W E R M E R S *
This study analyzes the extent to which mutual funds purchase stocks based ontheir past returns as well as their tendency to exhibit "herding" behavior (i.e.,buying and selling the same stocks at the same time). We find that 77 percent ofthe mutual funds were "momentum investors," buying stocks that were pastwinners; however, most did not systematically sell past losers. On average, fundsthat invested on momentum realized significantly better performance than otherfunds. We also find relatively weak evidence that funds tended to buy and sellthe same stocks at the same time. (JEL G14, G23)
The amount of wealth managed by institu-tional investors has grown considerably overthe past 20 years. Due perhaps to decreasedtrading costs, brought about by the terminationof fixed commissions in May 1975, these in-stitutional investors have become much moreactive traders and, as a result, have becomeincreasingly important in terms of setting mar-ket prices.' The growing influence of institu-tional investors has led to increased scrutinyboth by policymakers and by journalists, whotend to believe that these investors trade ex-cessively and move in and out of stocks in aherd-hke manner. This tendency to invest with
* Grinblatt: John E. Anderson Graduate School ofManagement, tJniversity of California, Los Angeles, Box951481, Los Angeles, CA 90095-1481; Titman: Depart-ment of Finance, Carroll School of Management, BostonCollege, Chestnut Hill, MA 02167; Wermers: Division ofFinance and Economics, Graduate School of Business andAdministration, tJniversity of Colorado, Boulder, CO80309. The authors are grateful to Narasimhan Jegadeesh,as well as to seminar participants at National Taiwan Uni-versity, National Chinese tJniversity, Osaka University,University of California at Berkeley, University of Chi-cago, Stanford University, UCLA, University of Texas,and Yale University for comments on earlier drafts.
' Institutional holdings are now about 50 percent of to-tal equity holdings in the United States, while institutionaltrading, when added to member trading, accounted forabout 70 percent of total NYSE volume in 1989 (RobertSchwartz and James Shapiro, 1992).
the herd, in combination with the alleged ten-dency of institutions to follow momentum-based fads by buying past winners andselling past losers is of concern, since thisbehavior could potentially exacerbate stock-price volatility.
Momentum trading strategies and herdingbehavior are also used by academics to mo-tivate models of seemingly irrational mar-kets. Fischer Black (1986) and BrettTrueman (1988) provide reasons why insti-tutional investors may trade excessively, anda number of recent theory papers provide ra-tionales to explain why institutional inves-tors would analyze the same groups of stocksand trade in the same direction.^ In addition,J. Bradford De Long et al. (1990) describewhat they call "positive-feedback traders,"who have a tendency to buy stocks after theyperform well.
Our study provides empirical evidence onthe trading patterns of fund managers by ex-amining the quarterly holdings of 155 mutualfunds over the 1975-1984 period. We char-
^ These papers include Robert J. Shiller and JohnPound (1989), Michael Brennan (1990), David S. Scharf-stein and Jeremy C. Stein (1990), Josef Lakonishok et al.(1991), Abhijit Banerjee (1992), Sushil Bikhchandani etal. (1992), Kenneth A. Froot et al. (1992), and DavidHirshleiferetal. (1994).
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VOL. 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1089
acterize the portfolio choices of these fundsto determine the extent to which they pur-chase stocks based on their past returns andthe extent to which they "herd," that is, theextent to which the group either predomi-nantly buys or predominantly sells the samestock at the same time. We tJien examine theextent to which herding and momentum in-vesting affect the performance of the funds.^If either irrationality or agency problems gen-erate these trading styles (as discussed, forexample, by Scharfstein and Stein [1990]),then mutual funds that exhibit these behaviorswill tend to push the prices of stocks that theypurchase above intrinsic values, thereby re-alizing lower future performance. However,if this type of behavior arises because in-formed portfolio managers tend to pick thesame underpriced stocks, then funds that ex-hibit these styles should realize high futureperformance.
Our analysis of momentum investing andperformance is also motivated by two previousstudies (Gdnblatt and Titman, 1989a, 1993),which indicate that, at least before transactioncosts, a number of mutual funds earned sig-nificant risk-adjusted abnormal returns. Thisobserved performance is not related to knownanomalies that involve cross-sectional differ-ences in expected returns, like the small-firmeffect. However, before we conclude that theseabnormal returns are generated by either su-perior information or analysis, we would alsolike to rule out the possibility that the observedabnormal performance was generated by ex-ploiting time-series anomalies. Specifically,we would like to determine the extent to which
' Irwin Friend et al. (1970) were perhaps the first toexamine the trading patterns of mutual funds. They found,among other things, that there was a tendency of somemutual funds to follow the prior investment choices oftheir more successful counterparts. Alan Kraus and HansR. Stoll (1972) examined the tendency of mutual fundsand bank trusts to buy and sell the same stocks at the sametime but did not find evidence of herding beyond that dueto chance. Lakonishok et al. (1992) examined the amountof herding exhibited by pension fund managers. Theyfound only weak evidence of the funds either buying orselling in herds (above chance occurrences) and a weakrelation between herding in stocks and the past returns ofthe stocks.
the observed performance was generated bythe simple momentum strategy of buying pastwinners and selling past losers, as described inNarasimhan Jegadeesh and Titman (1993).This simple strategy would generate abnormalperformance with either of the Grinblatt andTitman (1989a, 1993) performance measures,as well as with any of the more traditionalmeasures.
The paper is organized as follows. SectionI describes the data, while Section II de-scribes the methodology used to compute thedegree of momentum (or contrarian) invest-ing behavior exhibited by a fund. Section IIIpresents empirical results on momentum in-vestment styles and performance. Section IVinvestigates the tendency of the funds to en-gage in herding behavior and also considersthe relation of herding behavior to momen-tum investing and performance. Finally,Section V summarizes and concludes thepaper.
I. Data
Quarterly portfolio holdings for 274 mutualfunds that existed on December 31,1974, werepurchased from CDA Investment Technolo-gies, Inc. of Silver Springs, Maryland. Thesemutual fund data, used previously by Grinblattand Titman (1989a, 1993) to examine fundperformance, include 155 funds that existedduring the entire 10-year time period of De-cember 31,1974, to December 31,1984.'* Cen-ter for Research in Security Prices (CRSP)monthly returns for each NYSE- and AMEX-listed stock held by the funds were computedby compounding returns in the CRSP daily re-turns file. Over-the-counter (OTC) stocks andfixed-income holdings were treated as missingvalues in a manner that we will describeshortly.
" The analysis in Grinblatt and Titman (1989a) and Ste-phen J. Brown and William N. Goetzmann (1995) indi-cates that this fund-survival requirement has only a smalleffect on inference tests of performance abilities. In ourlater analysis of the herding of funds into individualstocks, we expand our sample to include all 274 funds,which includes nonsurvivors.
1090 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
II. Methodology
A. The Momentum Measures
A momentum investor buys past' 'winners''and sells past "losers." A contrarian investordoes the opposite. Our measure of momentuminvesting is
. T N
•' / = I J = I
where vv,,, is the portfolio weight on security 7at date t, and Rj,-k+\ is the return of securityj {j = 1, . . . , N) from date t - kXo date t -k + 1, the historical benchmark period.
This statistic is designed to measure the de-gree to which a fund manager tilts his portfolioin the direction of stocks that have experiencedhigh returns in some historical benchmark pe-riod, and away from stocks that have experi-enced low returns. Since this measure equalsthe difference between two portfolio returnsduring the benchmark period, a positive mea-sure means that, on average, the fund's currentportfolio had higher returns than the portfoliothat the fund would have held had no portfoliorevisions been made.
Since the mutual fund holdings are onlyavailable quarterly, while stock returns areavailable monthly, further modifications of themeasure given by equation (1) are needed toarrive at the measures of momentum that areimplemented. Given that we have 41 quartersof holdings, with three monthly returns perquarter, equation (1) is modified as follows:'
I 40 3 A/
Since the most recent returns are probably ofthe greatest interest to portfolio managers, k =
^ Using monthly returns rather than quarterly returnsreduces the problem of missing returns. For example, ifreturns for the Boeing Corporation common stock areavailable from the CRSP for January and February, butnot March, then Boeing drops out of our momentum in-vesting measure in only one observation out of 120 (usingmonthly returns), instead of one out of 40 (using quarterlyreturns). See also footnote 6.
1 and /t = 2 are the two measures that we willfocus on, although we will present some re-sults for k> 2. We will refer to equation (2)as "lag-0 momentum" (LOM) when ^ = 1,and as "lag-1 momentum" (LIM) whenk = 2.
B. Statistical Inference
As described by equation (2), the differ-enced portfolio weights were updated everycalendar quarter, while the differenced port-folio return was generated each month.* Thisprocess resulted in a time series of 120monthly return differences for each mutualfund. If the return differences associated withthese measures are serially uncorrelated underthe null hypothesis of no momentum invest-ing, then inference-testing for the significanceof the measures is simple. Testing whether themomentum measure has a mean value of zerois identical to a test of whether two given port-folios (with dynamic weight vectors) have thesame mean return.'
We employ many cross-sectional regres-sions in our analysis, mainly of fund perfor-mance on fund characteristics. Statisticalsignificance cannot be infe r̂red from thecross-sectional t and F statistics typically re-ported in such regressions, since the regressionresiduals are correlated across mutual funds.Thus, we use alternative t and F tests that arederived from a time-series procedure (seeGrinblatt and Titman, 1994).
""The differenced weights are identical for any threemonths in the same calendar quarter, except when returndata are not available for one or more securities in some(but not all) of the three months. For example, if returnsfor the Boeing Corporation are available in January andFebruary, but not in March, then the differenced portfolioweight of Boeing is set to zero only for March, and it isidentical for January and February.
' Since most portfolios of interest, such as value-weighted portfolios, have changing weights, the ordinaryt tests that are usually applied in these tests are technicallyinappropriate. However, if securities returns are seriallyuncorrelated, the central-limit theorem can be applied andasymptotic z tests and chi-square tests are valid for non-normal portfolio returns. Given the length of our time se-ries, these asymptotic test statistics are virtually identicalto the f and F statistics used here and have negligibly dif-ferent significance levels.
VOL. 85 NO. 5 GRINBLATT ET AL.: MOMENTUM INVESTMENT AND HERDING 1091
C. Modifying the Measures to Eliminate' 'Passive Momentum Investing''
The portfolio weights of winning (losing)stocks increase (decrease) even if the numberof shares held stays constant. In this case, thelag-0 momentum measure would indicatemomentum investing for buy-and-hold in-vestment strategies. To correct this, we cal-culate the weights using the average of thebeginning- and end-of-quarter share prices.*For consistency, we make the same modifi-cation for all momentum measures, eventhough passive momentum investing affectsonly the lag-0 momentum measure.'
D. Extensions of the Measure
We will also use decomposed versions of theLOM measure, called "Buy LOM" and "SellLOM." A high Buy (SeU) LOM measure for afiind means that it bought winners (sold losers)strongly, on average. These two measures are thedecomposition of equation (2) into partial sums:
(3a) Buy LOM
r - l , - . | »5,,,
(3b) Sell LOM
/ = l *, . , ,<*;_„-,
* If the beginning-of-quarter price was not available fora given security in a given quarter, the end-of-quarter pricewas used, and vice versa.
' Because each fund's stock holdings are observed onlyquarterly in our data set, it is tempting to think that I^Mmay spuriously be nonzero because of fund performance. Itis true that when the fund manager can achieve superiorreturns, the actual portfolio weights are correlated with fu-ture returns. However, since LOM uses differenced portfolioweights, a bias only arises when the portfolio revisions arepredominantly at the beginning of the quarter (spuriouslyindicating momentum investing) or at the end of the quarter(spuriously indicating contrarian investment behavior).Since there is no a priori reason to believe that portfoliorevisions that occur for the purpose of achieving superiorperformance should occur closer to the beginning of a quar-ter than to its end, we do not believe that a bias exists.
Here, we subtract means from returns in or-der to have measures that asymptotically ap-proach zero under the null hypothesis of nomomentum investing. The monthly returnfrom 12 months ̂ head for security 7 is usedas a proxy for Rj.'° We also use a similardecomposition of LIM into "Buy L I M "and "Sell L IM."
While the LOM and LIM statistics are ap-propriate measures of the extent to whichpast returns affect the total holdings of afund, we also use a turnover-adjusted LOM(TALOM) which measures the extent towhich past returns affect portfolio trades, in-dependent of the number of trades made bya fund during a time period. This measure isgiven by
(4 ) TALOM
T20 ,
The turnover-adjusted measure (TALOM)is the LOM measure, normalized so that thechanges in weights of the stocks purchased(and the changes in weights of the stockssold) sum to 1 during each quarter. The re-sults give a more accurate picture of the av-erage difference in past returns betweenstocks purchased and stocks sold across allquarters by a mutual fund, since a constant$1 is invested and shorted each quarter. Amutual fund that trades very little, but buyspast extreme winners and sells past extremelosers, will have a very high TALOM mea-sure, even though the unmodified LOM mea-sure will be relatively small. Analogous toBuy LOM and Sell LOM, "Buy TALOM"and "Sell TALOM" decompose TALOMinto terms having vvy,,, > Wy,3,_3 and vvy,,, <M>j,3, _ 3, respectively.
'" Admittedly, this is a noisy proxy for the expectedreturn, but since there are large numbers of stocks and timeperiods averaged in the measures we report, the noisinessof the proxy has a negligible effect on our results.
1092 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
TABLE 1—MOMENTUM-INVESTING SUMMARY STATISTICS FOR SAMPLE OF 155 MUTUAL FUNDS (QUARTERLY FUND
PORTFOLIO HOLDINGS ARE FOR THE PERIOD DECEMBER 31,1974, THROUGH DECEMBER 31,1984)
Venture-capital/
Aggressive- Growth- Special- special-Total sample growth Balanced Growth income Income purpose situations
Buy TALOM (percent/quarter){ statisticPercentage positiveWilcoxon probability
2.311.93*51.70.63
3.642.56*56.70.06
1.291.3249.20.81
2.782.18*52.50.47
0.980.8952.50.47
0.930.9646.70.34
0.020.0244.20.10
3.351.95+58.30.02
E\ statistic (Buy TALOM in every category = 0): F = 2.48*Fl statistic (Buy TALOM is equal across categories): F = 0.06
Notes: The LOM statistic is the measure of momentum investing based on stock returns in the same quarter as the portfoliorevisions. The LIM statistic is the measure of momentum investing based on stock returns in the quarter before theportfolio revisions. "TALOM" is the LOM statistic, with portfolio revisions normalized so that $1 of stocks are boughteach quarter and $1 are sold. For each category above, an equally weighted portfolio of all funds in that category isformed. Then, the appropriate momentum-investing statistic is calculated for that mean portfolio for each month. Finally,the time-series mean and t statistic are calculated for that portfolio across all 120 months. Wilcoxon probability is theprobability that the absolute value of the Wilcoxon-Mann-Whitney rank z statistic is greater than the absolute value ofthe observed z statistic, under the null hypothesis.
* Statistically significant at the 10-percent level.* Statistically significant at the 5-percent level.
** Statistically significant at the I-percent level.
in. Results
A. Summary Data on the Degree ofMomentum Investing
Table 1 presents the average LOM measurefor the entire sample, as well as for variousinvestment-objective categories." Accordingto this table, about 77 percent of the mutualfunds, 119 out of 155, buy "winners" and/or
" The mutual funds in this study were subdivided intoseven investment-objective categories, according to theirstated objectives. Aggressive-growth and growth funds in-vest in the common stock of growth companies, with theprimary aim of achieving capital gains instead of dividendincome. Growth-income funds seek to provide both capitalgains and a steady stream of income by buying the sharesof high-yielding conservative stocks. Balanced funds in-vest in both stocks and bonds, intending to provide capitalgains and income while preserving principal. Incomefunds seek to provide high current income by buying gov-ernment and corporate bonds as well as high-yieldingcommon and preferred stock. Finally, special-purpose andventure-capital/special-situations funds, as their namessuggest, have very specialized strategies that vary fromfund to fund. These two categories represent a very smallportion of our sample.
sell "losers," as defined by the LOM measure.The average LOM measure for all 155 fundsover the 10-year period is 0.74 percent perquarter, indicating that, on average, the stocksheld by a fund at the end of a given quarterhad returns 0.74-percent higher, during thatquarter, than the stocks held at the end of theprevious quarter, which was highly statis-tically significant.'^ F tests strongly rejectboth that the average LOM is equal acrossinvestment-objective categories and that it iszero across categories. In unreported results,we also find that funds with the greatest ten-dency to buy winners in the first five years ofthe sample period are more prone to buy win-ners in tiie second five years of the sample pe-riod, indicating that some managers followconsistent "styles."
Table 1 also provides the average BuyLOM and Sell LOM measures for each cate-gory. Note that the results for the Buy LOMmeasure are largely similar to the LOM
" Nonparametric test results, designated by Wilcoxonprobabilities, generally agree with the standard t statistics.
1094 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
results. For example, the aggressive-growth,growth, and growth-income categories havethe highest average LOM measures amongthe five investment-objective categories withnonnegligible numbers of funds, while theaggressive-growth, growth, and income cat-egories have the highest Buy LOM measures.Note, however, that the Sell LOM measuresare insignificant (at the 5-percent level) forevery category, and a joint test of signifi-cance cannot reject that the seven averageSell LOM measures are all equal to zero.Therefore, momentum investing appears tobe almost entirely driven by funds buyingwinners, and not by selling losers.
The results for LIM, Buy LIM, and SellLIM are much the same. The LIM measure issignificantly positive, on average, indicatingthat fund managers had a tendency to selectstocks based on superior returns over the priorquarter. The average one-quarter-lagged mo-mentum measure is about 0.30 percent perquarter, suggesting that, on average, the mostrecent quarter's returns were more importantdeterminants of portfolio choice (as shown byLOM) than the returns realized in the more dis-tant past (as shown by LIM). In unreportedregressions, we found a strongly positivecross-sectional correlation between the LOMand LIM measures of the funds. The regres-sion of LIM on LOM gave a coefficient of0.48, with a time-series t statistic of 5.5; thereverse regression of LOM on LIM gave a co-efficient of 0.88, with a time-series t statisticof 10.0).'^ As with the LOM measure, theaggressive-growth and growth categories had,on average, the highest levels of LIM-measured momentum investing, which isdue, in part, to a larger percentage of thesefunds trading on momentum, relative to otherfunds (about 89 percent and 82 percent ofaggressive-growth and growth funds, respec-tively, followed momentum strategies, accord-ing to their LOM measures).
Despite its statistical significance, the 0.74-percent (0.30-percent) quarterly return for theLOM (LIM) measure seems economically in-
" These two regressions imply a correlation of 0.65between LOM and LIM.
significant. The results for the turnover-adjusted measures, TALOM and Buy TALOM(also shown in Table 1), provide a more dra-matic confirmation of the momentum invest-ing behavior of the funds. For both measures,the average difference between buy and sellportfolios across all 155 funds was about 2percent per quarter, confirming that buyingwinners is the chief method of momentum in-vestment. In unreported results, we found thatthe top 10 funds, ranked by TALOM, boughtportfolios of stocks with returns that weremore than 8 percent (quarterly) greater thanthe portfolios of stocks they sold, on average;the top 25 had a difference of about 6 percent.
The TALOM results in Table 1 also confirmthat the aggressive-growth and growth fundswere much more likely to have traded on mo-mentum than funds in other large categories:their larger LOM measures were not primarilydue to higher turnover than other categories(since TALOM is adjusted for turnover).Again, results from nonparametric tests gen-erally agree with the standard f-statistic results.
In results not reported in Table 1, we alsocomputed Buy LOM measures for partitions ofstocks in the portfolio based on the marketcapitalization of the stocks, in order to mea-sure the relative contribution of buying win-ners in different size deciles to the overallLOM measure. For all objective categories,and for the total sample of ftinds, buying large-capitalization past winners provided almost allof the contribution to the observed momentum-investing behavior. We also found no signifi-cant evidence of selling past losers in any sizedecile.
B. The Relation between MomentumInvesting and Superior Portfolio
Performance
In this subsection, we examine the extent towhich a fund's tendency to hold past winnersrelates to its performance. As mentioned ear-lier, past research (Jegadeesh and Titman,1993) suggests that stocks that perform rela-tively well over a 3-6-month period tend torealize relatively good performance during thenext year. Hence, mutual funds that holdstocks that performed well in the recent past
VOL. 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1095
should realize better performance than thosefunds that hold stocks that did not performwell.
In order to measure mutual fund perfor-mance, we employ the method developed byGrinblatt and Titman (1993), which does notrequire that we select a benchmark portfolio.The performance measure ( a ) developed inthat paper uses a four-quarter change in (un-modified) portfolio weights and multipliesthe differenced weights by a future return;that is.
777
With this measure, the benchmark used toadjust the return of a portfolio for its risk in agiven month is the current month's returnearned by the portfolio holdings four quartersprior to the current quarter's holdings. There-fore, a represents the mean return of a zero-investment portfolio.'" If the systematic risksof the current and benchmark portfolios are thesame from the point of view of an investorwith no selectivity or timing abilities (as de-fined by Grinblatt and Titman [1989b]), theperformance represented by a should be insig-nificant for that investor.'^
We first split our sample of 155 funds intomomentum and contrarian investors, based onthe sign of LOM and LIM, and examined theperformance of these two subgroups. Table 2Acompiles mean LOM measures f̂ or the totalsample and for the five largest investment-objective categories. For the sample of all 155
funds, the 119 funds using momentum invest-ment strategies clearly outperformed the 36funds using contrarian strategies over theten-year period. The performance of the mo-mentum investors averaged about 2.6percent per year, while the contrarians hadan insignificant average performance ofabout 0.1 percent per year. Similar resultsheld for most of the individual investment-objective categories.
Table 2B repeats this analysis with LIM asthe momentum investing measure. The 91LIM momentum investors outperformed the64 LIM contrarians by about 1.8 percent peryear, on average. The LIM momentum inves-tors actually had slightly higher performanceth£tn the LOM momentum investors (althoughthere is a large degree of overlap between thetwo). The LIM contrarians also achieved bet-ter performance than the LOM contrarians, andtheir performance was statistically significant(but relatively small in magnitude).'*
Table 2 also shows that the investment-objective categories having the best perfor-mance are those that most strongly used amomentum strategy in selecting stocks (seethe "total" columns). Of the three categorieswith significant (at the 99-percent confi-dence level) performance (aggressive growth,growth, and income funds), two have signifi-cantly positive LOM and LIM measures. Infact, among the five major categories, theaggressive-growth category ranks first inperformance, LOM, and LIM, while thegrowth category ranks second in each ofthese three measures." Interestingly, these
'* The weights of this zero-investment portfolio repre-sent the difference between the vector of fund portfolioweights in the current period and the vector of fund port-folio weights four quarters earlier. We found that an al-ternative performance measure which uses a one-quarterlag rather than a four-quarter lag revealed relatively littleperformance, on average, which indicates that the stockspicked by these funds performed well in the following fourquarters, and not simply in the first quarter the stocks wereheld. This finding rules out the possibility that funds maybe affecting their measured performance by heavily buy-ing (or selling) the same stock during consecutive quar-ters.
"Grinblatt and Titman (1993) provide evidence thatthe two portfolios have the same market betas.
"•At first glance, it seems surprising that the LIMtrend-following and contrarian portfolios both outperformtheir LOM counterparts. However, this follows from thefact that LIM classifies fewer funds as trend-followers.We expect that the sample of LIM trend-followers willcontain stronger trend-followers than the LOM trend-followers. For this reason, the average returns of the LIMtrend-followers are higher. In addition, since the LIM con-trarians include some of the funds that were classified astrend-followers by the LOM criteria, we also expect theaverage returns of the LIM contrarians to be higher thanthe expected returns of the LOM contrarians.
" Tlie special-purpose (SP) and the venture-capital/special-situations (VS) categories each had only threefunds.
1096
A, Based on LOM statistic:
LOM (percent/quarter)
Performance (percent/year)
Performance of differencedportfolio (percent/year)
B, Based on LIM statistic:
LIM (percent/quarter)
Performance (percent/year)
Performance of differencedportfolio (percent/year)
Total
(N = 155)
0,74(10,96**)
2,04(3,16**)
{N = 155)
0,30(5,46**)
2,04(3,16**)
THE AMERICAN ECONOMIC REVIEW
TABLE; 2—MEAN
All 155 funds
Momentum
(W= 119)
1,06(10,78**)
2,61(3,25**)
2,46(3,32**)
(/V = 91)
0,74(8,81**)
2,79(3,02**)
1,81(2,44**)
Contrarians
(W = 36)
-0,30(-5,20**)
0,15(0,51)
(W = 64)
-0,33(-7,93**)
0,97(2,82**)
PORTFOLIO STATISTICS
1Mean portfolios
Aggressive growth
Total
(N = 45)
1,25(9,80**)
3,40(3,55**)
(/V = 45)
0,53(4,18**)
3,40(3,55**)
Momentum Contrarians
(N = 40) (N = 5)
1,45 -0,31(10,07**) (-2,92**)
3,75 0,63(3,56**) (0,71)
3,12(2,49*)
(A' = 31) (A'= 14)
0,94 -0,38(6,65**) (-2,48*)
3,92 2,26(3,14**) (3,10**)
1,66(1,36)
Total
(N = 10)
0,29(3,83**)
0,01(0,03)
(N = 10)
-0,02(-0,33)
0,01(0,03)
DECEMBER 1995
Balanced
Momentum
(yv = 6)
0,62(5,27**)
0,03(0,05)
0,04(0,06)
(A/= 4)
0,35(2,75**)
0,16(0,19)
0,25(0,27)
Contrarians
(/V = 4)
-0,20(-2,18*)
-0,01(-0,03)
(^ = 6)
-0,27(-4,13**)
-0,09(-0,23)
Notes: For each category, the funds were separated into two sets: those with a positive momentum investing measure ("Momentum"), andthose with a negative measure ("Contrarians"), Equally weighted portfolios were then formed, and time-series mean and t statistics areshown in the table. The "differenced portfolio" is long the momentum-investing portfolio and short the contrarian portfolio. Numbers inparentheses are / statistics,
' Statistically significant at the 10-percent level,* Statistically significant at the 5-percent level,
** Statistically significant at the 1-percent level.
categories also tend to have the highestamount of portfolio turnover and tend to bethe smallest in terms of the size of total as-sets managed. Only the income-fund cate-gory shows significant performance and aninsignificant level of momentum investing.Other categories of funds show some degreeof momentum investing, but their levels arerelatively small.
Regression results, all of which control forinvestment objective,, are found in Table 3.The first two regressions show a strong cor-relation between performance and momentuminvesting, whether measured with LOM orLIM. For the sample of all 155 funds, the es-timated regression coefficient of L27 for thefirst regression indicates that an increase of 1percent in momentum investing, according to
the LOM measure, increases performance byabout L27 percent.'*
Multiple regressions of performance onLOM and LIM and of performance on LOM,LIM, L2M, L3M, and L4M show that LOMprovides the main explanatory power. This isnot surprising, given the high correlation be-tween LOM and the momentum measuresbased on longer lags. The next two regressions
'" Note that the turnover-adjusted LOM (TALOM) wastiot included as one of these momentutn investing mea-sures because it is not a metric of the tendency of a fundto choose a portfolio based on past returns of stocks,TALOM was only used to compare the tendency of fundsto invest on momentum, without regard to differences inthe intensity of trading across funds.
VOL 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1097
TABLE 2—Extended.
Total
(N = 44)
0.89(10.71**)
2.41(2.94**)
(/V = 44)
0.43(6.16**)
2.41(2.94**)
Growth
Momentum
(N = 36)
1.17(10.85**)
2.82(2.94**)
2.26(2.37*)
(N = 33)
0.73(8.08**)
2.69(2.69**)
1.15(1.31)
Contrarians
(N = 8)
-0.39(-4.67**)
0.56(1.00)
( / V = l l )
-0.45(-6.50**)
1.54(3.05**)
Total
(JV = 37)
0.32(6.33**
0.83(1.75')
(/V = 37)
-0.04(-1.01)
0.83
Mean portfolios
Growth—income
Momentum
1 (N = 25)
0.58) (7.44**)
1.19(1.99*)
l.ll(2.16*)
(yv= 13)
0.39(4.99**)
1.34(1.96*)
0.79(1-52)
Contrarians
(N = 12)
-0.23(-2.83**)
0.08(0.22)
(N = 24)
-0.28(-4.96**)
0.55(1.27)
Total
(A/= 13)
0.17(1.63)
1.33(2.64**)
(W = 13)
0.03(0.36)
1.33(2.64**)
Income
Momentum
(/V = 8)
0.48(3.77**)
1.85(2.38*)
1.35(1.26)
{N = (,)
0.37(2.69**)
1.88(2.19*)
1.02(1.00)
Contrarians
(^ = 5)
-0.33(-2.04*)
0.51(0.81)
(N = 7)
-0.26(-2.34*)
0.86(1.52)
show that LOM and Sell LOM do not explainperformance, after controlling for Buy LOM(similar results are shown for Buy LIM andSell LIM). This finding is consistent with ourprior finding that momentum investing wasconcentrated in buying large-capitalizationwinners. The regression in the last row con-firms that Buy LOM explains performance bet-ter than Buy LIM.
In unreported results, we compared thehypothetical gross (not risk-adjusted) port-folio returns of momentum investors andcontrarians with a market benchmark, thevalue-weighted CRSP index (with daily div-idend reinvestment). In calculating grossreturns, we assumed that the portfolio indi-cated by the beginning-of-quarter holdingswas held constant until the end of the quar-ter, when the weights were updated. Wefound that, in general, momentum investorsrealized higher gross returns than contrari-ans, and both realized higher returns than theCRSP index. For example, the mean grossreturn of the 119 LOM momentum investors
was 17.9 percent per year, while that of the36 contrarian investors was 17.2 percent peryear." The mean return of the CRSP indexduring this period was about 14.7 percent peryear. From Table 2A, the average differencebetween the risk-adjusted performance ofmomentum and contrarian investors was 2.5percent (per year) during this period, whichwas higher than the average difference be-tween their gross returns (0.7 percent peryear). Contrarians held more priced risk intheir portfolios by holding smaller stocksthan momentum investors.
rv.. The Herding Behavior of the Mutual Funds
The preceding analysis indicates that mutualfunds show a tendency to buy stocks based on
" The top 20 percent of LOM momentum investors hadan average hypothetical gross return of 19.0 percent peryear, while the bottom 20 percent (the most contrarianinvestors) had an average return of 17.5 percent per year.
1098 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
TABLE 3—CROSS-SECTIONAL REGRESSIONS ACROSS ALL 155 FUNDS,
DEPENDENT VARIABLE = PERFORMANCE (PERCENT PER YEAR)
Independentvariable
LOM
LIM
L2M
L3M
L4M
Buy LOM
Sell LOM
Buy LIM
Sell LIM
R^:
F:
(i)
1.27(2.67**)
0.03
(ii)
1.20(2.02*)
0.29
(iii)
1.15(2.53*)
0.27(0.50)
0.39
3.68(0.03)
Regression
(iv)
1.13(2.33*)
0.32(0.58)
-0.51(-0.81)
0.31(0.46)
0.44(0.70)
0.39
2.49(0.03)
(V)
0.66(1.00)
0.94(1.65t)
0.40
6.03(0.003)
(vi)
1.66(3.26**)
0.63(0.84)
0.40
6.19(0.002)
(vii)
1.42)(2.22*)
0.14(0.22)
0.34
3.66(0.03)
(viii)
1.33(2.48*)
0.44(0.71)
0.39
5.48(0.01)
Notes: In each regression, the time-series average fund performance (in percent/year) is regressed, cross-sectionally, onthe time-series average momentum investing measures (in percent/quarter). For example, in regression (i), the time-seriesmean performance is regressed, across funds, on the time-series mean LOM measure. The method of computing / and Fstatistics is based on a time-series procedure (see Grinblatt and Titman [1994] for details). Separate dummy interceptswere used for funds in different investment objective categories to control for differences in non-momentum-investing-related performance across categories. Therefore, the common intercept was fixed at zero. The t statistics are given inparentheses beneath coefficient estimates; numbers in parentheses beneath F statistics are p values.
* Statistically significant at the 10-percent level.* Statistically significant at the 5-percent level.
** Statistically significant at the 1-percent level.
their past returns. This, by itself, suggests thatmutual funds should show some (possiblyweak) tendency to herd (i.e., buy and sell thesame stocks in the same quarter). For exam-ple, we would expect to observe more mutualfunds buying than selling those stocks thathave recently increased in price. In this sec-tion, we examine this tendency to herd moregenerally.
As a starting point, we replicate the analysisof Lakonishok, Andrei Shleifer, and Robert
W. Vishny (1992) (henceforth, LSV) on oursample of mutual funds. LSV calculated a sta-tistic, described by equation (6), that mea-sures the average tendency, of pension fundseither to buy or to sell particular stocks at thesame time:
(6) UHM,,, = \pi,-p,\ - E\p,,, - p,I
where /?,,, equals the proportion of funds, trad-ing in stock i during quarter t, that are buyers;
VOL. 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1099
Pi, which is the expected value of p,,,, is cal-culated as the mean of p,., over all stocks dur-ing quarter t. Therefore, p, is the proportion offund trades in quarter t that are buys, for theaverage stock. We refer to the statistic givenby equation (6) as the "unsigned herdingmeasure" (UHM) to distinguish it from whatwe later describe as the "signed herding mea-sure" (SHM), which separates buy and sellherding.
Table 4A presents the mean unsigned herd-ing statistics, averaged over all stock-quarters(see the "total" column) and averaged overtwo subgroups of stock-quarters (see the"buy" and "sell" columns). Membership ofa stock-quarter in one of the subgroups wasdetermined by whether the set of all funds wasbuying or selling the stock during the quarterto a greater degree than would be expectedwith random buying and selling (i.e., stock iduring quarter t was considered to be a ' 'buyherding" stock-quarter if p,,, > p,; similarly,stock "sell herding" categorization occurredwhen Pij < PI). This partition allows us todetermine whether herding was stronger onthe buy side than on the sell side of institu-tional trades. Analogous to LSV, the statis-tics given in Table 4 are from the perspectiveof individual stocks (instead of from a fundperspective) and are based on the entire sam-ple of 274 mutual funds (including nonsur-vivors) that existed on December 31, 1974.In addition, we segregated the stock-quartersby whether they had a return among the top50 percent of NYSE and AMEX returns dur-ing the quarter, or among the bottom 50percent.
The herding statistic of 2.5 percent (in Table4A under the "total" column for all 274funds) is the unsigned herding measure,averaged over all NYSE and AMEX stock-quarters (where trades by at least one fund oc-curred in that stock) during the period fromDecember 31, 1974 to December 31, 1984.This overall herding measure can be thoughtof as meaning that, for the average stock-quarter, if 100 funds traded in that stock-quarter, 2.5 more funds traded on the sameside of the market than would be expectedunder the null hypothesis that the stockswere picked independently. This overall
level of herding does not seem economicallysignificant, and it is similar to the mean levelthat LSV found for pension funds, 2.7percent.
Not surprisingly. Table 4A shows that theset of all funds exhibits more herding in buy-ing past winners than in buying past losers.However, herding that occurs on the sell side,although positive, appears to be less related topast returns. These findings are consistent withthe average fund being a momentum investorthat buys past winners but does not systemat-ically sell past losers, which results in severalfunds herding into (but not out of) the samegroups of stocks based on their past-quarterreturns.
The average herding measure for the set ofall funds appears to be small. Two explana-tions for this are examined in Table 4. The firsthas to do with the possibility that we are mea-suring herding over a sample of investors thatis too broad. For example, by definition, allinvestors cannot be buying and selling as aherd, since, in the aggregate, the buys mustequal the sells. As a result, if our sample ofmutual funds is representative of a large frac-tion of trading, then we would not expect tofind much evidence of herding. However,herding may exist among various subsets ofthe mutual funds. For this reason, we also ap-ply the LSV herding measure [equation (6)]to measure imbalances between buys and sellsof the smaller subgroups represented by theinvestment-objective categories. The results inTable 4A indicate that we find even less evi-dence of herding within investment-objectivecategory subgroups.
A second reason why we may not havefound strong evidence of herding is that theherding measure was aggregated across allstock-quarters, including those with very littletrading by the mutual funds. Intuitively, itmakes sense to condition the herding measureon the number of funds trading in the stockduring the particular quarter. It is certainlymuch more meaningful to analyze the ten-dency of funds to be either simultaneouslybuying or selling a particular stock that severalfunds are trading in a particular quarter than astock which only a few funds are trading. Be-cause of this, we present the average herding
1100 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
TABLE 4—MEAN HERDING STATISTICS, SEGREGATED BY PAST-QUARTER-RETURN DECILES ANDBY " B U Y " OR " S E L L " HERDING
Statistic
Total sample of funds (N = 274)
Buy Sell Total
A. Mean Herding Statistic (Percentage) for Volume of Trade ^ 1:
Past losers(Number of stock-quarters)
Past winners(Number of stock-quarters)
All stock-quarters(Number of stock-quarters)
1.11(9,631)
2.51(11,462)
1.87(21,093)
B. Mean Herding Statistic (Percentage) for
Past losers(Number of stock-quarters)
Past winners(Number of stock-quarters
All stock-quarters(Number of stock-quarters)
3.11(3,341)
4.58(4,079)
3.92(7,420)
C. Mean Herding Statistic (Percentage) for
Past losers(Number of stock-quarters)
Past winners(Number of stock-quarters)
All stock-quarters(Number of stock-quarters)
5.26 •(1.350)
5.94(1,687)
5.64(3,037)
3.48(9,527)
2.85(11,285)
3.14(20,812)
2.29(19,158)
2.68(22,747)
2.50(41,905)
Volume of Trade ^ 5;
4.89(3.987)
4.47(4,267)
4.68(8,254)
4.08(7,328)
4.53(8,346)
4.32(15,674)
Volume of Trade ^ 10:
5.42(1,653)
5.35(1,816)
5.38(3,469)
5.35(3,003)
5.63(3,503)
5.50(6,506)
Aggressive-growth funds(N = 73)
Buy
0.02(5,700)
1.03(7,426)
0.59(13,126)
5.18(586)
6.50(823)
5.95(1,409)
7.86(106)
9.06(127)
8.52(233)
Sell
3.57(6,987)
2.66(6,930)
3.12(13,917)
7.53(700)
5.04(760)
6.23(1,460)
9.14(138)
6.77(132)
7.98(270)
Total
1.98(12,687)
1.82(14,356)
1.89(27,043)
6.46(1,286)
5.80(1,583)
6.10(2,869)
8.59(244)
7.89(259)
8.23(503)
Balanced funds (N
Buy
1.63(1,705)
0.95(1,942)
1.26(3,647)
4.92(56)
3.82(62)
4.34(118)
14.55(3)
6.55(9)
8.55(12)
Sell
-2.22(2,003)
-1.91(2,028)
-2.07(4,031)
1.38(59)
-1.26(45)
0.23(104)
0.18(2)
-0.10(8)
-0.04(10)
= 19)
Total
-0.45(3,708)
-0.51(3,970)
-0.48(7,678)
3.10(115)
1.68(107)
2.42(222)
8.80(5)
3.42(17)
4.64(22)
Notes: Past-quarter returns are defined as those returns during the same quarter as the portfolio revisions. Individual herding statistics arecalculated as \p — E(p)\ — E\p — E(p)\, where p = the proportion of funds buying the given stock during the given quarter among allfunds that traded that stock during that quarter. E(p) and E\p — E(p)\ are calculated under the null hypothesis of no intentional herding.The "mean herding statistic" is the average of the individual herding statistics across time and across stocks, for a given category. Thecolumn labeled "total" is the mean herding statistic calculated over all stock-quarters having at least the volume of trade by the fundsindicated in the panel. "Buy" is calculated as the average over only those stock-quarters where p > E(p), that is, the proportion of buyswas greater than the expected proportion of buys. "Sell" is calculated as the average only over those stock-quarters for which p < E{p)."Past losers" are those stocks having past returns in the lower 50 percent among all NYSE and AMEX stocks during the given quarter,while "past winners" are those having past returns in the upper 50 percent.
measures over all stock-quarters with at leastfive active funds in Table 4B, and over allstock-quarters with at least ten active funds inTable 4C.
Panels B and C of Table 4 show that, whenwe limit our analysis to stock-quarters withat least five or ten trades, respectively, evi-dence of herding increases significantly. Forexample, for the entire sample of funds, theaverage herding measure is about 5.5 percentwhen we include only stock-quarters with atleast ten funds active. Note that, when atleast ten funds were active, funds in the ob-
jective categories with the highest averageperformance (aggressive growth, growth,and income [see Table 4A]) showed thegreatest tendency to herd in the averagestock-quarter.
The next step in our analysis is tocharacterize individual funds by the extent towhich they "go with the crowd." In order tomeasure a particular fund's tendency to herd,we first develop what we call a "signed'' stockherding measure (SHM), defined below,which provides an indication of whether afund is "following the crowd" or "going
VOL 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1101
against the crowd'' in a particular stock duringa particular quarter:
(7) SHM,,
= /,,, X UHM,, - X UHM,,,]
where SHM,,, = 0 if fewer than 10 fundstraded stock / during quarter t. Otherwise,
'o if lp , , , -p , | < £ | p , , , - p , | ;
I if/?,./ — P, > £\Pij — Pi\ and the mutual fund is a
buyer of stock i during quarter /. or if — (p,,, — p,) >
E\Pfj - P,\ and the fund is a seller (i,e,, the fund
/,,,= ' "follows the crowd");
- 1 if p,,, - p,> E\pi,, - p,\ and the mutual fund is a
seller of stock i during quarter r, or if - (p,., - p,) >
E\pi., - p,\ and the fund is a buyer (i,e,. the fund
"goes against the crowd"),
Note that SHM,, = 0 if a stock-quarter showsnegative herding or if only a small number offunds have traded it, since there is no mean-ingful way in which the fund can herd (or in-vest against the herd) in these cases. Also,Iij = 1 if the fund trades "with the herd" instock i during quarter t, and /,, = — 1 if thefund trades ' 'against the herd'' in that stock-quarter. The second term in SHM,, is calcu-lated under the null hypothesis of no herdinghy the funds in the stock-quarter (above thatdue to chance).^"
™ Under the null hypothesis of independent trading de-cisions among funds, the number of trading funds that arebuyers is binomially distributed. We can calculate thevalue of £(/ X UHM) for stock i in quarter t starting withthe following known binomial parameters:
1102 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
TABLE 5—MEAN PORTFOLIO STATISTICS
Measure
FHM(percent)
LOM(percent/quarter)
Performance(percent/year)
Totalsample
(N = 155)
0.84(6.73**)
0.74(10.96**)
2.04(3.16**)
Aggressivegrowth
{N = 45)
1.05(6.49**)
1.25(9.80**)
3.40(3.55**)
Balanced{N = 10)
0.66(5.99**)
0.29(3.83**)
0.01(0.03)
Growth(A/= 44)
0.89(6.95**)
0.89(10.71**)
2.41(2.94**)
Growth-income
(N = 37)
0.72(6.84**)
0.32(6.33**)
0.83(1.75+)
Income(N= 13)
0.60(4.46**)
0.17(1.63)
1.33(2.64**)
Special-purpose{N = 3)
0.12(1.920
-0.05(-0.33)
0.21(0.19)
Venture-capital/special-
situations(yv = 3)
0.83(6.73**)
0.95(3.17**)
2.66(1.43)
Notes: For each category above an equally weighted portfolio of all funds in that category is formed. Then, for the "fundherding measure" (FHM), we calculate the portfolio-weighted "signed herding measure" (SHM) of the stocks held bythat equally weighted portfolio at the end of a quarter, less the portfolio-weighted SHM of the stocks held at the beginningof that quarter, based on the herding measure of the stocks during that quarter. Finally, the time-series mean and t statisticare calculated across all 40 quarters. For the LOM measure, the same procedure is followed, but the portfolio-weightedstock returns are used instead of the portfolio-weighted herding measure (giving a time series of 120 months of data).For the performance measure, we calculate for each quarter the portfolio-weighted stock returns (of the next quarter)based on the end-of-quarter portfolio, less the portfolio-weighted returns (of the next quarter) based on the portfolio heldfour quarters previously. This procedure gives a time series of 111 months of data. Time-series t statistics are given inparentheses.
* Statistically significant at the 10-percent level.** Statistically significant at the 1-percent level.
The fund herding measure for an individualfund (FHM) is then calculated by substitutingthe signed herding measure in place of the stockreturn in equation (2) (for k = 1); that is,
(8) FHM=-^i i i(H>,.!, - vv,,,,,-,)SHM;.,,.,,,
n = the number of funds trading stock i in quarter t,p = the proportion of trading funds in the population that
are buyers, estimated as described for equation (6).
Note that in the above expectation UHM = UHM(p),where p = the proportion of funds trading in stock-quarter(i, 0 that are buyers. Then, for stock i in quarter t.
£ [ / X UHM] = (2p - l)UHM(p)Pr(p)
(2p - l)UHM(p)Pr(p)
where, for the n discrete values that p can assume,
Pr(p) = ( " )p"''(l -P)"""-\npl
As the above equation illustrates, a positive(negative) portfolio revision is multiplied bya positive (negative) SHM if the set of allfunds bought (sold) heavily in a given stockduring a given quarter, giving a positive con-tribution to that fund's FHM. Conversely, apositive (negative) portfolio revision is mul-tiplied by a negative (positive) SHM if the setof all funds sold (bought) heavily in a givenstock during a given quarter, giving a negativecontribution to that fund's FHM. Hence, fundsthat tend to buy (sell) when other funds arealso buying (selling) will be characterized asherders by this measure.
Table 5 presents the fund herding results.All categories of funds showed highly signif-icant levels of FHM, and unreported F testsstrongly rejected that the average FHM fundherding measure is equal across categories, orthat it is zero for all categories. We can inter-pret the reported 0.84 value for FHM as mean-ing that, if the average fund traded 10 percentof its portfolio each quarter, it bought stocksthat, on a portfolio-weighted average, had
VOL. 85 NO. 5 GRINBLATT ET AL: MOMENTUM INVESTMENT AND HERDING 1103
TABLE 6—CROSS-SECTIONAL REGRESSIONS OF FUND PERFORMANCE
Independentvariable
Totalsample
(N = 155)
Aggressivegrowth
(N = 45)Balanced(N = 10)
A. Cross-Sectional Regressions of Fund Performance on
Constant
FHM
Adjusted R^)
1.61(2.82**)
0.25
2.99(3.01**)
0.40(0.57)
-0.0001
0.21(0.33)
-0.30(-0.29)
0.02
B. Cross-Sectionat Regressions of Eund Performance on
Constant
LOM
FHM
F:
Adjusted R\
1.24(2.23*)
0.12(0.20)
4.39(0.01)
0.39
2.65(3.02**)
0.87(1.42)
-0.32(-0.39)
1.10(0.34)
0.12
0.20(0.30)
-0.02(-0.02)
-0.28(-0.24)
0.04(0.96)
0.02
GrowthiN = 44)
Growth-income
(N = 37)Income
(N= 13)
Fund Herding Measure (FHM):
-0.25(-0.45)
2.97(3.37**)
0.32
-1.17(-2.16*)
2.78(2.80**)
0.25
LOM and FHM:
0.49(0.67)
1.08(1.54)
1.06(1.12)
6.00(0.003)
0.42
-0.35(-0.53)
1.22(1.91+)
1.10(1.01)
4.47(0.01)
0.35
2.35(2.44*)
-1.69(-1.29)
0.04
2.39(2.30*)
2.86(2.07*)
-0.21(-1.79)
2.66(0.07)
0.39
Special-purpose(Af=3)
1.60(0.60)
-11.67(-.85)
0.73
—"
Venture-capital/special-
situations(AT = 3 )
-2.79(1.26)
9.93(2.38*)
0.56
a
Notes: In panel A, for each category, the benchmark-free fund performance measure (percent/year) is regressed, acrossfunds, on the fund herding measure (FHM, as a percentage). In panel B, for each category the benchmark-free fundperformance measure (percent/year) is regressed, across funds, on the fund momentum-investing measure (LOM, percent/quarter) and on FHM. The method of computing t and F statistics is given in Grinblatt and Titman (1994). For theregressions across all 155 funds, separate dummy intercepts were used for funds in different investment-objective cate-gories to control for differences in non-regressor-related performance across categories. Therefore, the common interceptwas fixed at zero for those regressions. Student / statistics are in parentheses below the coefficient estimates; the numbersin parentheses beneath the F statistics £ire the associated p values.
" Insufficient data.* Statistically significant at the 10-percent level.* Statistically significant at the 5-percent level.
** Statistically significant at the 1-percent level.
about 8.4-percent excessive buying by allfunds, or sold stocks that, on a portfolio-weighted average, had 8.4-percent excessiveselling by all funds (or some combination ofthese two extreme outcomes); while an aver-age aggressive-growth fund trading 10 percenteach quarter bought (sold) stocks with about10.5-percent excessive buying (selling) by theset of all 155 funds.
Note that aggressive-growth funds had thehighest average levels of FHM, LOM, and per-formance, while the growth funds were secondin all three categories (among the five major
fund categories). Funds that invest on mo-mentum are more likely to invest in herds andare more likely to perform.
Table 6A presents results for cross-sectionalregressions of performance on FHM. Theresults show that fund performance is signifi-cantly correlated with the tendency of a fundto herd (FHM). This finding by itself wouldsupport the idea in some theoretical herdingpapers that informed investors have a tendencyto herd (Brennan, 1990; Froot et al., 1992;Hirshleifer et al., 1994). However, this is dueto the high correlation between the tendency
1104 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995
to herd and the tendency to buy past winners,which was confirmed in an unreported regres-sion of FHM on LOM. Table 6B shows that,at the margin, FHM does not significantly ex-plain fund performance, given the explanatorypower already provided by LOM. Therefore,on average, performing funds tend to buy pastwinners, with herding in past winners appar-ently occurring as a result.
V. Conclusion
This paper characterizes some of theinvestment strategies of mutual funds and an-alyzes how these strategies relate to realizedperformance. The evidence indicates that mu-tual funds have a tendency to buy stocks basedon their past returns, and that they tend to buyand sell the same stocks at the same time (i.e.,herd) in excess of what one would expect frompure chance. The average level of herding andmomentum investing was statistically signifi-cant, but not particularly large. However, therewas a significant degree of cross-sectional dis-persion across funds in their tendency to buypast winners and to trade with the herd.
The tendency of individual funds to buy pastwinners as well as to herd was shown to behighly correlated with fund performance overour period of study. The relation between thetendency to buy past winners and performancewas especially strong. On average, those fundsfollowing momentum strategies realized sig-nificant excess performance, while contrarianfunds realized virtually no performance. Therelation between a fund's tendency to go withthe herd and its performance was less con-vincing, and it largely disappeared after con-trolling for the fund's tendency to buy pastwinners.
This research provides some insightsabout the extent to which mutual funds areable to profit from their security-analysis ef-forts. The positive relation between momen-tum trading and performance suggests thatthe positive performance of mutual fundsobserved in Grinblatt and Titman (1989a,1993) may have been at least partially gen-erated by a simple trading rule rather than bysuperior information. This suggests that ifthe momentum profits observed in Jegadeesh
and Titman (1993) disappear in the future,then the performance of these funds is likelyto diminish.
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