Hedge fund crowds and mispricing

August 13, 2013

Blerina Reca, Richard Sias, and H. J. Turtle

ABSTRACT

Recent models and the popular press propose that hedge funds follow similar strategies resulting in crowded trades that destabilize prices. Inconsistent with conventional wisdom, we find that hedge fund equity portfolios are remarkably independent. Moreover, when hedge funds do buy and sell the same stocks, their demand shocks drive prices toward, rather than away from, fundamental values. Even in periods of extreme market stress, we find little evidence that hedge funds exert negative externalities on each other or security prices due to crowded trades.

JEL classification: G01; G12; G14; G23 Keywords: Hedge funds; Crowds; Financial crises

                                                             Reca is from the Department of Finance, College of Business Administration, University of Toledo, Toledo, Ohio, 43606; (419) 530-4056, Blerina.Reca@utoledo.edu. Sias (corresponding author) is from the Department of Finance, Eller College of Management, University of Arizona, Tucson, Arizona, 85721; (520) 621-3462, sias@eller.arizona.edu. Turtle is from the Department of Finance, College of Business and Economics, West Virginia University, Morgantown, West Virginia, 26506-6025; Harry.Turtle@mail.wvu.edu. Copyright © 2013 by the authors. We thank Vikas Agarwal, Nicole Boyson, Gjergji Cici, Darrell Duffie, John Griffin, Andrew Karolyi, Eric Kelley, Alexander Kurov, Jeff Nickel, Blake Phillips, Laura Starks, Sterling Yan, and seminar participants at Texas Tech University, the University of Arizona, the University of Cincinnati, the 2013 Asian FMA meetings, and the 2013 Western Finance Association meetings for their helpful comments. We thank Andrew Ang, Ken French, David Hsieh, Russ Wermers, and Thomson Reuters for providing data.

  

  

Hedge fund crowds and mispricing

“… Hedge funds are crowding into more of the same trades these days, amplifying market swings during crises and unnerving investors. Such trading has stoked market jitters in recent months and helped to diminish the impact of corporate fundamentals on stock-market movements. Droves of small investors have reacted by pulling money from the market, questioning its stability and whether fast-moving traders are distorting prices.” (Wall Street Journal, January 14, 2011)

1. Introduction

Hedge fund assets under management grew more than 1,420% between the end of 1997 ($118

billion) and 2012 ($1.8 trillion, figures from Barclay Hedge). In his AFA presidential address, Stein

(2009) points out, that in contrast to the traditional view of rational speculators moving against

mispricing (e.g., Friedman (1953)), the dramatic growth in these “prototypical sophisticated

investors” could result in larger gaps between prices and fundamental values if hedge funds crowd

into the same stocks.

Stein (2009) theoretically considers two important implications of hedge funds crowding into the

same securities. First, his “crowded trade” model demonstrates that even in the absence of leverage

or market stress, fully rational (but uninformed) hedge funds crowding into the same stocks can

drive prices from fundamentals.1 Second, his “arbitrageur leverage” model points out that hedge

fund leverage exacerbates the negative externalities of hedge fund crowds due to contagion effects

during a funding crisis. That is, if a hedge fund is forced to delever as a result of a negative return

shock in one security, it may liquidate positions in securities held by other hedge funds, driving

prices of these securities lower and thus generating a negative return shock to other hedge funds. As

a result, other hedge funds will be forced to delever, driving even further negative return shocks and

deleveraging, i.e., a “fire sale spillover” (Stein, p. 1542).

                                                            1 In Stein’s (2009) crowded trade model, sophisticated investors employ trading strategies not anchored to fundamental value. They are rational, but uninformed, and recognize the possibility that the security they just purchased may be overvalued as a result of demand shocks from other sophisticated traders following the same signal.

  

 

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Previous research also asserts that hedge fund crowds play a meaningful role in setting asset

prices. Studies claim that hedge fund crowding was a key contributor to the 1998 financial crisis

(e.g., Kyle and Xiong (2001), Gromb and Vayanos (2002)), the 2007 “quant crisis” (e.g., Khandani

and Lo (2011), Brunnermeier (2009)), and the 2008-2009 financial crisis (e.g., Acharya, Philippon,

Richardson, and Roubini (2009)). Pedersen (2009, p. 184) notes, for example, “Despite their

differences in investment philosophies and analysis, one manager’s long position was another

manager’s long more often than it was a short … it is natural to expect that at least the most

sophisticated traders in a specific market have some overlap in their portfolios since they are striving

toward the same goal.”

The popular press and industry research also appear to hold the view that hedge funds crowd

into the same trades and destabilize prices. An International Financial Services London research

report (Maslakovic (2009)) claims, “Hedge funds faced unprecedented pressure for redemptions in

the latter part of 2008, with investors withdrawing funds due to dissatisfaction with the performance

or to cover for even greater losses or cash calls elsewhere. This in turn led to forced selling and

closures of positions by hedge funds causing a cycle of further losses and redemptions.”

Moreover, the European Central Bank (2006) claims, “In addition to potentially high leverage,

the increasingly similar positioning of individual hedge funds within broad hedge fund investment

strategies is another major risk for financial stability which warrants close monitoring despite the

essential lack of any possible remedies.” Lo (see Strasburg and Pulliam (2011)) notes that pairwise

correlations between randomly selected hedge funds increased from 67% in the 2001-2005 period to

79% in the 2006-2010 period and claims, “The whole hedge fund industry is a series of crowded

trades.” Lo (2008) expressed a similar view in his testimony to the U.S. House of Representatives,

“The dynamic and highly competitive nature of hedge funds also implies that such investors will

shift their assets tactically and quickly, moving into markets when profit opportunities arise, and

  

 

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moving out when those opportunities have been depleted. Although such tactics benefit hedge-fund

investors, they can also cause market dislocations in crowded markets with participants that are not

fully aware of or prepared for the crowdedness of their investments.” Similarly, in a 2004 speech to

the Economic Club of New York, Timothy Geithner (later to become U.S. Treasury Secretary)

warned, “While there may be more diversity in the types of strategies hedge funds follow, there is

also considerable clustering, which raises the prospect of larger moves in some markets if conditions

lead to a general withdrawal from these ‘crowded’ trades.”

At least some hedge fund managers also believe hedge fund equity crowding is problematic. For

instance, Daniel Loeb (Third Point, LLC founder) writes in his June 2010 investor letter, “Please

note that we will no longer discuss investments made prior to our public 13F filings. We have found

that discussing our ideas may result in ‘piling on’ by other hedge funds who may subsequently sell at

inopportune times resulting in greater hedge fund concentration and volatility, which is not in the

interest of our investors.”

Despite common perceptions and the potential importance of hedge fund crowds, there is, as far

as we are aware, no direct empirical examination of hedge fund crowding in U.S. equity markets and

the negative externalities associated with such crowding. Therefore, this study has three primary

goals. First, we investigate the basic premise that hedge funds crowd into the same U.S. equity

securities. Second, we examine the characteristics of hedge fund crowds over time. Third, we

examine the associated evidence of negative externalities due to hedge fund crowds with tests of

whether (i) hedge fund crowds’ demand shocks drive prices from value as in Stein’s (2009) crowded

trade model, and (ii) hedge fund crowds exert negative externalities on each other and asset prices

during crisis periods, as predicted in Stein’s arbitrageur leverage and related models.

Our primary conclusion is that, contrary to common opinion, hedge fund equity portfolios are

remarkably independent. On average, 350 hedge fund companies file 13(f) reports each quarter

  

 

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during our sample period (1998-2011). Although these are very large hedge funds holding at least

$100 million in 13(f) securities at some point during the year (thus requiring a 13(f) filing), the typical

(i.e., median) pair of hedge funds holds approximately one stock in common. This amounts to

portfolio overlap of less than one-third of one percent (based on the Cremers and Petajisto (2009) active

share metric). Even at the extreme, hedge fund stock portfolios are surprisingly independent—the

95th percentile of hedge fund pairs with greatest overlap average less than 10% overlap in their

holdings. These findings counter the contention that hedge funds follow similar strategies that result

in greatly overlapping equity portfolios.

To objectively benchmark the size of hedge fund crowds, we compare the portfolio overlap of

hedge funds with the portfolio overlap of non-hedge fund institutional investors. According to the

views implicit in the literature and earlier quotes, non-hedge fund institutions are presumably more

diverse and independent than hedge funds, and should therefore exhibit less crowding. Surprisingly,

we find that non-hedge fund institutions average much greater portfolio overlap than hedge funds.

Based on a matched sample of non-hedge fund institutions holding similar size portfolios, the

median non-hedge fund institution pair overlaps by nine securities. This amounts to portfolio

overlap of more than 5%. For the 95th percentile of non-hedge fund portfolios with greatest overlap,

we find 35% overlap in their long equity holdings, on average.

We next examine the characteristics of hedge fund portfolio overlap (i.e., crowding) over time.

We show that hedge fund crowding did not increase during our sample period. In fact, the time

trend in the propensity for hedge funds to hold the same stocks is meaningfully negative. However,

we do confirm, as is well known, that the number of hedge funds has grown dramatically over time.

As a result, the size of hedge fund crowds in individual stocks has also grown. Although hedge

funds exhibit relatively little propensity to crowd into the same stocks compared to non-hedge fund

institutions, we find that “crowded stocks” do exist and the size of crowds increases over time.

  

 

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We recognize that even relatively “small” hedge fund crowds might have large potential price

effects because hedge fund positions can be large and equilibrium may be fragile (e.g., Brunnermeier

and Pedersen (2009)). Thus, we search for evidence of negative externalities associated with hedge

fund crowds in a number of ways. First, we focus on the key implications of Stein’s (2009) crowded

trade model that predicts large hedge fund demand shocks will drive prices from value. Inconsistent

with the premise that hedge fund crowds destabilize equity prices, we find no evidence that hedge

fund demand shocks systematically drive prices from value. Rather, we find the opposite—large

hedge fund demand shocks appear to drive prices toward fundamental values, i.e., stocks that hedge

funds heavily purchase subsequently outperform those they heavily sell.

The second set of negative externality tests we conduct relate to Stein’s (2009) arbitrageur

leverage model. We examine the association between hedge fund crowds and funding crises. We

find little evidence that hedge funds exert negative externalities on each other or security prices

during periods of market stress. Specifically, we find: (i) hedge funds that have greater overlap with

the aggregate hedge fund portfolio do not liquidate more of their portfolio during stress events, (ii)

the long equity portfolios of hedge funds with greater overlap do not suffer worse returns during

stress events than those with low portfolio overlap, (iii) the relation between hedge fund demand

shocks and contemporaneous returns does not increase during stress events, and (iv) the relation

between hedge fund demand shocks and subsequent returns remains positive during stress events.

These results are inconsistent with the hypothesis that, in general, hedge fund crowds exert negative

externalities on equity markets due to their forced deleveraging during crisis periods.

In addition, our study contributes to the ongoing policy debate regarding hedge fund regulation

and the impact such regulations carry. For instance, the European Union’s Directive on Alternative

Investment Fund Managers (scheduled to be applied by Member States in 2013) is reportedly

causing a number of hedge funds to consider changing their domicile (ClearPath Analysis (2012)).

  

 

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Arguably, appropriate policy responses (such as the European Union’s Alternative Investment Fund

Managers Directive, the U.S. Dodd-Frank Act including form PF, and the JOBS act provision

regarding hedge fund advertising) should consider a holistic approach that admits comparisons

between hedge funds and other institutions when attempting to measure the social costs and

benefits of potential regulatory changes. Adrian and Brunnermeier (2011) and Stein (2009), for

instance, both assert that appropriate regulations depend on the extent to which hedge funds crowd

into the same securities.

In summary, our results are inconsistent with conventional views regarding hedge fund crowds.

First, hedge funds’ long U.S. equity portfolios exhibit relatively little overlap—certainly much less

than non-hedge fund institutional investors. Second, hedge fund “crowds” increase over time

because there are more hedge funds—not because hedge funds exhibit increasing portfolio overlap.

Third, in general, subsequent returns are positively related to large hedge fund demand shocks

consistent with the hypothesis that hedge fund demand pushes prices towards fundamental values.

Fourth, even during stressful quarters, hedge fund demand shocks remain positively related to

subsequent returns and hedge funds that have greater portfolio overlap with the aggregate hedge

fund portfolio do not sell more or suffer worse returns than hedge funds with lower levels of

portfolio overlap. Whether we examine normal or stressful periods, there is little evidence of

widespread systematic negative externalities associated with hedge fund crowds.

Findings from this study do not imply that hedge funds either crowd, or do not crowd, in other

areas such as international equities, currencies, fixed income securities, or even across asset classes,

styles, or industries. Nor does our work suggest whether or not hedge funds exert negative

externalities on each other, or asset prices, in non U.S. equity markets. We also do not claim that

crowding by hedge funds into the same stocks never causes negative externalities.

  

 

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The balance of this paper is organized as follows: Section 2 provides background and details

regarding our hypotheses. We discuss the data in Section 3. We examine the extent of hedge fund

crowding in Section 4, and whether hedge fund crowding increases over time in Section 5. In

Section 6, we test the implications of the crowded trade model by examining the relation between

hedge fund demand shocks and contemporaneous and subsequent stock returns. We examine the

impact of hedge fund crowds during periods of market stress in Section 7. We provide conclusions

in Section 8.

2. Background

Hedge funds may crowd into the same stocks for a number of reasons. Stein (2009) models the

most common rationale—hedge funds following correlated signals. Other models suggest that

sophisticated investors may crowd into overvalued securities and exacerbate mispricing even when

they recognize the mispricing. DeLong, Shleifer, Summers, and Waldmann (1990) propose that

rational speculators may contribute to mispricing in an attempt to exploit later momentum traders.

Abreu and Brunnermeier (2003) build a model where rational arbitrageurs attempt to “ride the

bubble” rather than attack the mispricing. Note that in this model sophisticated investors do not

exacerbate the mispricing, they simply fail to immediately correct it because they are unsure of how

many other sophisticated investors have learned of the mispricing. Hedge funds may also voluntarily

share ideas with other managers to garner feedback or attract additional capital to the stock

following the establishment of a position (Stein (2008)).

Stein (2009) formally considers two separate mechanisms by which hedge fund crowds exert

negative externalities on each other, and as a result, destabilize prices. The first mechanism, the

crowded trade model, does not require any external shock (e.g., a funding crisis) or leverage to have

hedge fund crowds drive mispricing. Specifically, in the crowded trade model, hedge funds profit by

  

 

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exploiting other slower reacting investors. However, when many hedge funds unexpectedly attempt

to exploit the same mispricing (i.e., crowd into the same stock), they mistakenly interpret the price

impact from hedge fund demand as a shock to fundamental value. The crowded trade model has

two direct empirical implications. First, hedge fund demand pushes prices. Thus, stocks heavily

purchased by hedge funds should outperform stocks heavily sold by hedge funds over the period

hedge funds are buying and selling. Second, because an unexpectedly large number of hedge funds

buying or selling a stock within the same period pushes prices beyond fundamental values,

subsequent returns should be inversely related to hedge fund demand when the hedge fund demand

shock is unusually large.

Stein’s (2009) second model (the “arbitrageur leverage” model) evaluates the impact of a funding

crisis when levered hedge funds hold common securities. Stein demonstrates that a shock to a stock

held by one hedge fund may cause the hedge fund to reduce leverage and sell other, commonly held

stocks. This action results in decreased prices for the commonly held stocks, deleveraging by other

hedge funds holding the commonly held stocks, and further associated price declines, i.e., in the

words of Stein (p. 1531), “… correlated selling pressure and a contagious downward spiral in

prices.” As Stein (2009) points out, a number of previous studies (e.g., Brunnermeier and Pedersen

(2009)) also examine the impact of hedge fund leverage during funding shocks.

The arbitrageur leverage model has empirical implications for both hedge fund behavior and

stock returns. First, managers who have greater overlap with the aggregate hedge fund portfolio will

be forced to liquidate more of their portfolio during a funding crisis due to spillover effects. Second,

the long equity portfolios of stocks held by these managers should suffer inferior returns relative to

the portfolios of more independent managers because contagion-induced fire sales drive prices

below fundamental values. Third, the relation between hedge fund demand shocks and

contemporaneous returns should be especially strong during stress quarters as hedge funds trample

  

 

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each other rushing for the exits. Fourth, the relation between hedge fund demand shocks and

subsequent returns should turn negative during high stress quarters because hedge funds’ stress

quarter demand shocks drive prices from value.2

2.1. Empirical evidence

Despite the potential importance and perceived ubiquity of hedge fund crowds, we are not

aware of any direct tests of the extent to which hedge funds crowd into the same stocks. There is,

however, some indirect evidence. Gray, Crawford, and Kern (2012) examine the behavior of

“predominately small hedge fund managers” on a private internet site geared toward fundamental

analysis. The authors find some evidence that these managers voluntarily share ideas to receive

feedback and attract additional arbitrageurs to stocks they already hold.

Ben-David, Franzoni, and Moussawi (2012) show that hedge funds, in aggregate, exited the U.S.

equity market during crisis periods associated with the “quant meltdown” (last two quarters of 2007)

and the Lehman Brother’s bankruptcy (last two quarters of 2008). They suggest this behavior was

primarily driven by funding shocks consistent with the modeled behavior of hedge funds in a

funding crisis.

Boyson, Stahel, and Stulz (2010) present evidence of hedge fund contagion associated with

funding shocks—extreme losses by one type of hedge fund (e.g., convertible arbitrage funds) are

more likely to occur when there are extreme losses to other types of hedge funds (e.g., relative value

funds). In contrast, they find negative codependence in right tail (i.e., good) returns. The

codependence asymmetry suggests that hedge funds suffer from liquidity shock induced contagion.

                                                            2 Note that the source of non-fundamental volatility in both of Stein’s (2009) models is hedge funds driving prices from value. If hedge fund demand shocks do not drive prices from value, then, at least in the context of these models, hedge funds do not increase non-fundamental volatility.

  

 

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Lou and Polk (2012) argue that momentum profits are low when arbitrageurs are crowded into

momentum strategies. Empirically, they find that their measure of crowdedness (excess

comovement between winners or losers) is higher when long-short hedge fund assets under

management is high. Hanson and Sunderam (2013) argue that short interest primarily captures hedge

fund demand and find that value and momentum strategies perform poorly when hedge funds

crowd into such strategies (as measured by aggregate short interest).

Billio, Getmansky, Lo, and Pelizzon (2012) report evidence that hedge fund returns have

become more interconnected over time, potentially increasing systemic risks. The results are

consistent with the hypothesis that hedge fund crowding has increased over time. Brunnermeier and

Nagel (2004) and Griffin, Harris, Shu, and Topaloglu (2011) also report results consistent with

hedge fund crowding. They find that hedge fund portfolios tilted toward overpriced technology

stocks, consistent with hedge fund crowding during the technology “bubble.”

3. Data and the importance of hedge funds in the market

Because hedge funds are typically exempt from the Investment Company Act of 1940, they are

not required to disclose their holdings (or net asset values) in the same manner as other investment

companies.3 Following several recent studies (e.g., Brunnermeir and Nagel (2004), Griffin and Xu

(2009), Blume and Keim (2011), Boyson, Helwege, and Jindra (2011), Ben-David, Franzoni, and

Moussawi (2012), Agarwal, Jiang, Tang, and Yang (2013)), we overcome this limitation by examining

hedge funds’ quarterly 13(f) filings. All institutional investors (including hedge funds) that manage at

least $100 million at year end, are required to file quarterly 13(f) reports of long equity positions

                                                            3 Most hedge funds apply for exemption from the Investment Company Act of 1940 under Section 3(c)(1) or Section 3(c)(7). See www.hedgefundlawblog.com for a detailed discussion. Hedge funds do not typically provide detailed holdings data required for direct tests of portfolio overlap to database vendors (e.g., TASS, Hedge Fund Research). In addition, none of the traditional hedge fund databases are very comprehensive—Fung and Hsieh (2006) report, for instance, that only 3% of hedge funds report to all five major hedge fund databases. There is also a large self-reporting bias in these databases (e.g., Aiken, Clifford, and Ellis (2011)).

  

 

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greater than 10,000 shares or $200,000. These 13(f) reports are usually filed at the manager level. For

example, Tudor Investment Corporation files a single 13(f) report that provides aggregate holdings

of all Tudor funds. From the perspective of examining crowded portfolios, this is a positive

attribute—we are interested in whether different managers make the same decisions, rather than

whether a given manager makes the same decision for multiple funds they control (e.g., an offshore

fund and its “twin” onshore fund).4

We combine the quarterly 13(f) institutional ownership filings with proprietary institutional type

classifications provided by Thomson Reuters. These data identify all hedge fund managers providing

13(f) reports each quarter between 1998 and 2011. Thomson Reuters began providing the data to us

in 2001 for a sample period beginning in 1998. Between 2001 and 2005, Thomson Reuters provided

five classification updates. From September 2006 through December 2011, Thomson Reuters

provided us with investor type updates every quarter. Because Thomson Reuters only keeps current

classification data, we believe our dataset to be the only independent historical record of 13(f)

investor classifications in the post 1998 period.5,6

Our final sample consists of 4,873 unique 13(f) managers including 1,006 hedge funds and 4,021

non-hedge fund institutions.7 Because our time-series of Thomson Reuters’ manager types allows

                                                            4 In linking a sample of 13(f) managers to hedge funds in the TASS database, Ben-David, Franzoni, Landier, and Moussawi (2012) find that for 50% of the hedge fund companies with two funds under management, the return correlation between the two funds is at least 96%. Moreover, in nearly one-quarter of the cases, the fund names (under the same 13(f) manager) differ only in the “offshore” label.  5 The investor classification data are more fully described in Appendix A. Beginning in June 1997, a Thomson Reuters team has met to categorize investment firms that file 13(f) forms into one of 57 organizational types. The Thomson Reuters research group reviews the classifications for large institutions (based on assets under management) every quarter. Institutional investors can be reclassified over time, as they change their investment objectives and strategies or additional information becomes available. As noted by Ben-David, Franzoni, and Moussawi (2012), Thomson Reuters has a long-lasting relation with the SEC with respect to institutional filings (dating back to pre-Internet times) and extensive information about these institutions and their staff. 6 To the best of our knowledge, Thomson Reuters has not provided this dataset to other academics. Several recent studies use other interesting Thomson Reuters’ lists or data. Discussions with these authors reveal that each of these datasets or lists is unique (cf., Ben-David, Franzoni, and Moussawi (2012), Cici, Kempf, and Puetz (2011)). 7 As a robustness test, we also use the Brunnermeier and Nagel (2004) algorithm (that exploits information in ADV filings) and additional hand collected data to classify the Thomson Reuters “hedge funds” (and other, potentially

  

 

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managers to change classifications as their business changes, the sum of the number of unique hedge

funds and non-hedge fund institutions is greater than the number of unique managers.

To be included in the sample, a security must have returns for each month in quarter t=0,

Center for Research in Security Prices (CRSP) share code of 10 or 11, capitalization data at the

beginning and end of the quarter, non-missing shares outstanding at the beginning and end of the

quarter, and non-missing price at the beginning of the quarter. Managers (both hedge funds and

non-hedge fund institutions) must have non-zero portfolio holdings at both the beginning and end of

the quarter to be included in the sample. We are careful to adjust holdings for stocks splits and

dividends and adjust for delays in reporting stocks splits. We also correct the data for known errors.8

3.1. The role of hedge funds over time

We begin by examining the role of hedge funds over time in the 13(f) data. Panel A in Table 1

reports that, on average, there are 350 hedge funds (ranging from 114 to 610) and 1,854 non-hedge

fund institutions (ranging from 1,353 to 2,413) each quarter in our sample between June 1998 and

December 2011. Fig. 1 plots the fraction (left hand scale) and number (right hand scale) of 13(f)

institutions classified as hedge funds over time. The results reveal a dramatic five-fold increase in the

number of hedge funds filing 13(f) reports between June 1998 and March 2008 (from 114 to 610).9

Moreover, because the number of hedge funds filing 13(f) reports grows at a much faster rate than

                                                                                                                                                                                                ambiguous classifications) into hedge funds and non-hedge fund institutions. We then repeated our primary empirical tests on this “hand-collected” sample. Our results remain nearly identical. 8 See Blume and Keim (2011) and Gutierrez and Kelley (2009) for discussion of issues associated with the Thomson Reuters/WRDS 13(f) data. In addition, we find that the change in holdings files downloaded from WRDS are corrupt from June 2006-March 2007. Specifically, in more than 90% of the observations, changes in holdings are the negative of the end of quarter holdings for these four quarters. Following Yan and Zhang (2009) we exclude observations where reported institutional ownership exceeds 100% of shares outstanding. 9 Given the -32% total return for the S&P 500 in the last nine months of 2008, however, the subsequent decline in the number of hedge funds filing 13(f) reports results, at least in part, from a number of hedge funds moving back below the $100M 13(f) hurdle. We also compute the fraction of market capitalization accounted for by hedge funds. Consistent with Ben-David, Franzoni, and Moussawi (2012, Fig. 1) we find that hedge fund ownership of market capitalization grows from about 0.7% in 1998 to 3.5% in 2007 before falling to 2.6% by the end of 2011.

  

 

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the number of non-hedge fund institutions filing 13(f) reports, the fraction of 13(f) filers classified as

hedge funds also experiences dramatic growth—rising from 7% in 1998 to more than 21% in March

2008 before dropping back to 16% in 2011.

[Insert Table 1 and Fig. 1 about here]

Panel B in Table 1 reports the time-series average of the cross-sectional mean and median

portfolio characteristics (number of securities held and portfolio size) for hedge funds and non-

hedge fund institutions. Portfolio size is the total dollar value of their 13(f) holdings. Because

portfolio overlap is related to size (i.e., large managers are more likely to have overlapping portfolios

than small managers), we form a matched sample of similar size non-hedge fund institutions.

Specifically, for each hedge fund-quarter we select (without replacement) the non-hedge fund

institution closest in total portfolio size (based on the dollar value of their beginning of quarter 13(f)

holdings). The mean and median values for the sample of size matched non-hedge fund institutions

are also reported in Panel B. In addition, we report the time-series average of the mean (fourth

column) and median (last column) difference between hedge funds and the matched sample of non-

hedge fund institutions.

The results in Panel B reveal that the average hedge fund manager in our sample holds 84 stocks

worth $681 million versus 230 stocks worth $4.3 billion for the average non-hedge fund institution.

Institutional portfolio size, however, is highly skewed. The medians, therefore, more closely reflect

the “typical” hedge fund and non-hedge fund institution. The median hedge fund holds 37 stocks

worth $202 million versus 88 stocks worth $321 million for the median non-hedge fund institution.

The results in Panel B also reveal that our matching algorithm works well—the average hedge

fund portfolio size does not differ meaningfully from the average matched non-hedge fund

institution. The median hedge fund is about 0.05% smaller than the median matched non-hedge

fund institution. Holding equity portfolio value approximately constant, hedge fund portfolios are

  

 

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much more concentrated—the median hedge fund hold 37 stocks versus 71 stocks held by the

median size matched non-hedge fund institution.10

3.2. Limitations of the 13(f) data for measuring crowded portfolios

The 13(f) data have two primary limitations when measuring crowded portfolios. First, the data

do not capture all hedge funds nor all hedge fund positions. Only institutions (including hedge

funds) with more than $100 million in U.S. equities are required to file 13(f) reports, and filing

institutions are not required to report positions less than 10,000 shares and $200,000. In addition,

the SEC sometimes allows managers to have confidential filings that generally do not show up in the

WRDS 13(f) data. We do not view this limitation as severe for two reasons. First, recent work

suggests that more than 96% of hedge fund stock positions are reported in their public 13(f)

filings.11 Second, our sample includes over 1,000 hedge fund companies and over 1.6 million hedge

fund-quarter positions—presumably adequate to detect evidence of hedge fund crowds.

The second limitation is that the data only capture hedge funds’ long positions in U.S. equities.

We cannot view hedge funds’ equity derivatives or short positions. We believe, however, that these

limitations do not invalidate our conclusions. Recent work suggests U.S. equity derivatives make up

a very small portion of the typical hedge fund’s portfolio. Specifically, based on a sample of 250

hedge fund companies over the 1999-2006 period, Aragon and Martin (2012) report that the dollar

value of assets underlying all option positions (i.e., the holdings if the options were exercised)

averages approximately 4.5% of the value of direct common stock holdings.12 In addition, as we

                                                            10 We also find, consistent with Griffin and Xu (2009), that hedge funds have greater turnover than non-hedge fund institutions. Hedge fund turnover is investigated in Section 5. 11 Figures are inferred from Table I in Agarwal, Jiang, Tang, and Yang (2013). 12 There are, no doubt, a significant number of hedge funds that extensively employ derivatives. Nonetheless, to the extent that derivative contracts are adequately priced relative to equity markets, and hedge funds use all available instruments in their trading strategies, we expect long-only equity positions to provide a good environment to examine the implications of crowded trades. Assume, for example, that hedge funds “like” Apple and half the funds take a long position in Apple stock while the other half buy Apple call options (or some other “long” Apple strategy). As long as a

  

 

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discuss later (and provide details in an appendix), our results remain robust when we incorporate

short interest data into our analysis.13 ,14 Conceptually, we also expect that changes in long-only

positions will capture economically meaningful portfolio decisions in many situations. For instance,

if a hedge fund reduces short exposures during a funding crisis, we expect similar reductions in long

positions (e.g., covering shorts without reducing long positions would increase overall risk exposure

for a market neutral or net long hedge fund).

4. Hedge fund crowds

We measure the extent to which hedge funds crowd into the same stocks by examining overlap

in their long equity portfolios. The advantages of this approach are: (i) we are not required to

identify or hypothesize a specific strategy that hedge funds follow (e.g., to test if they crowd into

value stocks), and (ii) we allow the realistic possibility that “common” strategies may change over

time.

As detailed in Section 6, the 13(f) data do not allow us to examine intraquarter trades. It is

important to recognize, however, that this limitation does not impact our analysis of crowded hedge

fund ownership levels (i.e., overlap in hedge fund portfolios at a point in time) unless, for some

unknown reason, the propensity of hedge funds to crowd is systematically different at the end of the

                                                                                                                                                                                                meaningful number of funds purchase Apple shares directly, our method should: (i) identify a crowded trade situation, and (ii) be able to test if hedge funds’ crowded trades cause negative externalities. For instance, if a funding crisis forces hedge funds to sell Apple shares and Apple call options, both actions should drive Apple’s price lower. The key is simply that hedge funds’ long equity positions are an important part of hedge funds’ portfolios for the sample of hedge funds we examine—our sample averages more than $246 billion of hedge fund direct equity investments each quarter and grows to more than half a trillion dollars in 2007. 13 We also examine the “importance” of U.S. equity markets in the typical hedge fund portfolio by computing the time-series correlation between the aggregate and average hedge fund equity portfolio return (computed from the 13(f) data) and the returns for eight HFRI hedge fund indices. Our results suggest that U.S. equities play an important role in most hedge fund’s portfolios with correlation ranging from 0.35 to 0.95. 14 Griffin and Xu (2009) find that 92.5% of their hedge fund sample report total returns that are positively correlated with their computed long-only equity return, suggesting that most funds are “net long.”

  

 

16  

quarter than at other times during the quarter.15 The 13(f) data provides 55 quarters that allow for

direct measurement of overlap in hedge funds’ equity holdings.16

We use three different measures of portfolio overlap for every pair of hedge funds—the number

of securities held by both funds, the Cremers and Petajisto (2009) portfolio overlap measure (active

share), and cosine similarity. For comparison, we also compute these measures for the size matched

sample of non-hedge fund institutions. If hedge funds are more susceptible to crowding than other

institutional investors, then hedge funds’ portfolios will exhibit greater overlap than other

institutions’ portfolios.

Because we compute each measure for every pair of hedge funds and every pair of similar size

non-hedge fund institutions each quarter, the number of observations for each measure ranges from

6,441 (when there are 114 hedge funds, i.e., Ht*(Ht-1)/2) to 185,745 (when there are 610 hedge

funds) for a total of just under four million hedge fund pair quarter observations and four million

matched non-hedge fund pair quarter observations.

4.1. Number of securities in common

We begin with the simplest measure of commonality—the number of securities that each pair of

hedge funds hold in common. This measure provides an intuitive, albeit crude, measure of portfolio

overlap. The first row of Panel A in Table 2 reports the time-series average of the cross-sectional

95th percentile, median, fifth percentile, and mean number of securities held in common by all hedge

                                                            15 Ben-David, Franzoni, Landier, and Moussawi (2012) find some evidence of portfolio pumping by hedge funds—purchasing additional shares of securities they already hold at the end of the quarter to push those prices higher. Moreover they find this pattern is limited to stocks with high hedge fund ownership (based on fraction of shares held). If anything, this pattern will lead to greater hedge fund crowding at the end of the quarter. 16 Our primary point is straightforward—if hedge funds crowd into the same stocks for any reason, then their portfolios, measured at any point in time, will overlap. For instance, if a large group of hedge funds follow a very short term reversal strategy where they purchase stocks that have declined in the last week (and sell stocks that have increased), then their end of quarter holdings this quarter will reflect overlap in stocks that have declined in the last week and their end of quarter holdings next quarter will reflect overlap in stocks that decline in value the last week of next quarter. The only limitation, per se, is that we can only observe the overlap 55 times (i.e., the end of each quarter in our sample).

  

 

17  

fund pairs. To provide scale, we also report (parenthetically) the time-series mean number of

securities held by funds that make up the 95th, median, and fifth percentiles. The results reveal little

evidence of excessive “crowding” for the typical hedge fund pair—the median fund pair holds less

than one security in common (0.8 securities).17 In contrast, the median size-matched non-hedge fund

institutional pair holds nine securities in common.

[Insert Table 2 about here]

The fourth column reports the time-series average of the quarterly cross-sectional mean number

of securities in common for hedge fund companies and the size-matched sample of non-hedge fund

institutions. The third row reports their difference. The last two columns report the number of

quarters where the difference in means (hedge funds less non-hedge fund institutions) is positive or

negative, respectively. We also report, in brackets, the number of quarters where the difference is

statistically significant at the 5% level (based on a t-test for difference in means). In every quarter, we

find that the average similar size non-hedge fund institution pair exhibits meaningfully greater

overlap than the average hedge fund pair (as measured by number of securities held in common).

Although we find little evidence that the typical hedge fund pair exhibits high levels of portfolio

overlap, it is possible that there are large subsets of hedge funds that have meaningful overlap. To

evaluate this possibility, we examine the 95th overlap percentiles. Even at this extreme, there is

relatively little overlap in long equity holdings—hedge fund companies in the 95th overlap percentile

only hold 16 stocks in common even though individual hedge fund companies in this group average

a total of 278 securities in their portfolio (reported parenthetically). By comparison, the 95th

percentile of similar sized non-hedge fund institution pairs hold 75 stocks in common out of an

average portfolio of 319 securities.18

                                                            17 Because we report the time-series mean of the cross-sectional median, the reported median is not a whole number. 18 In untabulated analysis, we also compare hedge funds with a sample of non-hedge fund institutions matched by the number of securities held in their portfolio (rather than total portfolio value). In all 55 quarters, the number-of-

  

 

18  

4.2. The Cremers and Petajisto (2009) portfolio overlap measure

Cremers and Petajisto (2009) measure a mutual fund’s overlap with the S&P 500 as one half the

sum (across stocks) of the absolute differences in a manager’s portfolio weights and the S&P 500

index weights. They denote this measure as “active share,” with a possible range from zero to one. A

high active share means independence from the comparison portfolio and a low active share means

greater overlap with the comparison portfolio. One minus active share essentially captures the extent

of overlap between the manager’s portfolio and the comparison portfolio. If a manager has perfect

overlap with the S&P 500 (i.e., an indexer), the active share is zero. If a manager holds only half the

stocks in the S&P 500 (that account for half the S&P 500 total capitalization), but at double their

market weights, then the active share is 50%. And if a manager holds none of the stocks in the S&P

500, the active share is one.

We use active share to generate a more refined estimate of portfolio independence. Specifically,

we compute one-half the sum of the absolute difference in portfolio weights between every pair of

hedge funds:

.2

1,

1,,,,

K

ktkjtkhtt wwjhAS (1)

where K is the total number of securities in the market in quarter t, wh,k,t is hedge fund h’s quarter t

portfolio weight in security k, and wj,k,t is hedge fund j’s quarter t portfolio weight in security k. We

continue to denote the measure active share—although we measure hedge funds’ independence

from one another rather than their independence from an index. We analogously compute active

share for every pair of the size-matched non-hedge fund institutions.

                                                                                                                                                                                                securities-matched non-hedge fund institutions exhibit meaningfully greater portfolio overlap than hedge fund institutions. Note that when matching by number of securities, the matched non-hedge fund institutions tend to be smaller than their hedge fund counterparts.

  

 

19  

Panel B in Table 2 reports the time-series average of the cross-sectional descriptive statistics for

the active share portfolio independence measure for hedge fund pairs and the size matched sample of

non-hedge fund institution pairs. Consistent with Panel A, hedge fund portfolios exhibit greater

independence (i.e., higher active share) from one another than do similar size non-hedge fund

institutions’ portfolios. In fact, the median hedge fund pair exhibits almost complete independence

from one another—their portfolios overlap by less than one-third of one percent (i.e., 1-0.997). The

difference in mean values for hedge funds and non-hedge fund institutions is positive and

statistically significant at the 5% level in all 55 quarters. Even at the extremes, there is relatively little

overlap in hedge fund portfolios compared to overlap in non-hedge fund portfolios. The 95th

percentile of hedge fund pairs with the greatest overlap (i.e., the fifth active share percentile) average

less than 10% (i.e., 1-0.904) overlap versus 35% (i.e., 1-0.645) overlap for similar size non-hedge

fund institutions.

4.3. Cosine similarity

One limitation of the active share measure in our context is that the overlap contribution from

any stock is the minimum of the smaller portfolio weight. If, for example, managers A and B each

hold 10% in Apple and the rest of their portfolios do not overlap, then their active share is 90% (i.e.

overlap is 10%).  If investor B moves 100% of his portfolio to Apple, the overlap, as measured by

active share, does not change (i.e., they still overlap by 10%). Yet, intuitively, Apple is more crowded

when B has an Apple portfolio weight of 100% than when it is 10%. Thus, as an alternative to active

share we also consider cosine similarity. 19 Cosine similarity focuses on the product of the

                                                            19 The measure is denoted cosine similarity because it is equivalent to the cosine of the angle between the K-dimensional vectors of portfolio weights for managers h and j. The metric is widely used to measure the similarity between two vectors (in our case, portfolio weight vectors). For instance, the measure is used to examine similarity in music or text documents (e.g., Foote (1999), Cooper and Foote (2003), Hasegawa, Sekine, and Grishman (2004)), to facilitate web searches (e.g., Strehl, Ghosh, and Mooney (2000)), and in facial recognition programing (e.g., Nguyen and Bai (2011)).

  

 

20  

overlapping portfolio weights rather than the minimum of the overlapping portfolio weights.

Specifically, the cosine similarity between hedge fund h’s portfolio weights and hedge fund j’s

portfolio weights is given by:

.,

1

2,,

1

2,,

1,,,,

K

ktkj

K

ktkh

K

ktkjtkh

tt

ww

ww

jhs (2)

Eq. (2) is bound between zero and one. If two hedge funds hold the same portfolio, the cosine

similarity will equal one; whereas, if two hedge funds hold none of the same securities, cosine

similarity will equal zero. In contrast to active share, a higher value for cosine similarity means

greater portfolio overlap.

Panel C in Table 2 reports the cosine similarity analysis. Once again, we continue to find strong

evidence that hedge fund companies exhibit greater independence than non-hedge fund institutions.

For instance, the average cosine similarity for similar size non-hedge fund institutions is over four

times that for hedge funds. Even at the extremes, hedge fund pairs continue to display substantially

lower portfolio overlap than non-hedge fund institutions. The last two columns reveal that hedge

funds exhibit meaningfully less portfolio overlap than non-hedge fund institutions in all 55 quarters.

4.4. Overweight overlap

One potential explanation for the greater portfolio overlap in non-hedge fund institutions is that

they hold portfolios that more closely mimic the market portfolio. To examine this possibility, we

compare the similarity in deviations from market weights for stocks overweighted by hedge funds

versus stocks overweighted by non-hedge fund institutions. We focus on overweighted securities,

                                                                                                                                                                                                Blocher (2012) uses cosine similarity to measure overlap in mutual fund portfolios. Hoberg and Philips (2011) and Hanley and Hoberg (2012) use cosine similarity to measure the degree of similarity in company documents (e.g., IPO prospectuses).

  

 

21  

rather than over- and under-weighted securities, because overlap in under-weighted securities

primarily focuses on commonality in what investors are not holding. Clearly, if no hedge funds hold

Apple, then Apple is not crowded with long hedge fund trades.

Because positive active weights do not sum to one, we focus on cosine similarity rather than

active share to measure overlap in overweighted stocks.20 Specifically, the cosine similarity between

hedge fund h’s positive active weight and hedge fund j’s positive active weight is given by:

,,

1,,,,

2,,,,

1,,,,

2,,,,

1,,,,,,,,,,,,,,,,

K

ktkmkttkjtkmkttkj

K

ktkmkttkhtkmkttkh

K

ktkmkttkjtkmkttkjtkmkttkhtkmkttkh

tt

wwwwwwww

wwwwwwww

jhs (3)

where ,0

,,,,,,,,,,,,,,,,

otherwise

ww if wwwwww tkmkttkhtkmkttkh

tkmkttkhtkmkttkh  and tkmkttkh ww ,,,, denotes

that fund manager h’s weight in stock k is greater than stock k’s market weight for quarter t.

Overweighted cosine similarities vary from zero when a pair overweights none of the same stocks to

one when a pair has identical overweighting.

Panel D in Table 2 reports the analysis of overweighted cosine similarities. The results reveal

that hedge funds exhibit less overlap in their overweighted positions than do similar size non-hedge

fund institutions—the difference is statistically significant at the 5% level in all 55 quarters. The

results also reveal a substantial decline in the overlap for non-hedge fund institutions when moving

from portfolio weights (Panel C) to deviations from market weights (Panel D) for overweighted

stocks. This finding indicates that much of the overlap in non-hedge fund institutions’ portfolios

arises because their portfolios overlap with the market portfolio.

                                                            20 Because positive active weights do not sum to one, it is straightforward to generate examples where active share based on positive active weights is less than one even when managers overweight none of the same stocks.

  

 

22  

4.5. Do large subsets of hedge funds exhibit crowding?

As noted above, it is possible that large subsets of hedge funds follow similar strategies. One

might expect, for example, that large groups of “quantitative directional” funds hold the same stocks

while large groups of “event driven” funds hold a different set of stocks in common. The fifth active

share and 95th cosine similarity percentile figures reported in Table 2 suggest, however, that relative

to non-hedge fund institutions, this is not the case. To more fully explore this possibility, we graph

the entire distribution of portfolio overlap for hedge fund pairs and similar size non-hedge fund

institution pairs. Specifically, we pool the four million hedge fund pairs’ cosine similarities over time

and plot the cumulative fraction of observations over the range of possible cosine similarity values

(zero to one). For comparison, we plot the analogous distribution for the sample of four million size

matched non-hedge fund institutions’ cosine similarities. Fig. 2A presents the results.

[Insert Fig. 2 about here]

Drawing a vertical line from any point on the horizontal axis in Fig. 2A reveals the fraction of

hedge fund pairs (broken line) or non-hedge fund institution pairs (solid line) with a cosine similarity

less than that value. For instance, at the left most side of the figure where cosine similarity equals

zero, we find that 48% of hedge fund pairs (broken line) have no overlap in their portfolios. In

contrast, only 21% of the size-matched non-hedge fund institution pairs (solid line) have no

portfolio overlap.

If large groups of hedge funds crowd into the same stocks (more so than the matched sample of

non-hedge fund institutions), then at some point the broken line should intersect and drop below

the solid line. Clearly that is not the case. For example, a vertical line at cosine similarity equal to

0.25 reveals that approximately 1% of hedge fund pairs (i.e., 1-0.99 on vertical axis) have cosine

similarity greater than 0.25 versus 22% of non-hedge fund institutions (i.e., 1-0.78 on vertical axis).

  

 

23  

Fig. 2B reports the analogous graph for active share. Because a larger active share implies greater

independence, we report a horizontal scale that decreases from one to zero. The left-hand side of

the figure reveals that 48% of hedge fund pairs have an active share of one versus 21% of similar

size non-hedge fund institution pairs (this matches Fig. 2A, in that if two hedge funds have no

overlap, then active share is one and cosine similarity is zero). Moving to the right, 96% of hedge

fund pairs have active share greater than 0.90 (where the hedge fund “arrow” hits the curve) versus

only 62% of matched non-hedge fund institution pairs (where the non-hedge fund “arrow” hits the

curve). Fig. 2 reveals no evidence that large subsets of hedge funds crowd into the same securities.

4.6. Crowds by strategy

One possibility for low levels of hedge fund crowding is that the hedge funds identified in 13(f)

data have very disparate strategies. For instance, and related to the above analysis, one might expect

little long equity portfolio overlap between relative value funds and event driven funds while overlap

between different relative value funds will be high. To examine this possibility, we match hedge fund

manager names from the 13(f) data with hedge fund firm names in the Hedge Fund Research (HFR)

live and dead database. Because our interest is in whether funds with similar strategies have greatly

overlapping portfolios, we restrict the sample to companies that report a single hedge fund style

strategy (180 single-strategy hedge fund managers identified in both the 13(f) data and the Hedge

Fund Research database).21 Specifically, our sample contains four strategies: Equity Hedge (n=85

managers), Event-Driven (n=31 managers), Macro (n=36 managers) and Relative Value (n=28

                                                            21 In untabulated analysis, we limit the sample to 153 hedge fund companies that only report a single substrategy. Our results are nearly identical to those reported in Table 3. For instance, the median (5th percentile) active share for managers with the same substrategy is 0.986 (0.841) versus the 0.989 (0.853) figures reported in Table 3 (Panel B) for managers with the same strategy.

  

 

24  

managers).22 The total number of observations (i.e., paired comparisons) is 46,198 for managers with

the same strategy and 113,424 for managers with different strategies.

We repeat the portfolio overlap tests for hedge fund managers following the same strategies

(e.g., two event-driven managers) versus hedge funds following different strategies (e.g., a macro

manager and an event-driven manager). The results, reported in Table 3, reveal that same strategy

manager pairs tend to exhibit greater overlap in their long equity portfolios. For instance, examining

active share (Panel B), the average same strategy hedge fund pair overlaps by 3.4% of their portfolio

(i.e., 1-0.966) versus 2.2% (i.e., 1-0.978) for managers following different strategies. The difference is

statistically significant in 50 of the 55 quarters.

[Insert Table 3 about here]

The results in Table 3, however, yield little evidence that managers with the same strategy

classification have greatly overlapping portfolios. For instance, again focusing on active share, the

average same strategy hedge fund pair overlaps by 3.4% of their portfolios (1-0.966, Panel B in

Table 3) versus the average non-hedge fund institution pair overlap of 10.5% of their portfolios (i.e.,

1-0.895, Panel B in Table 2). Although we do not report specific results (to conserve space) mean

active share differences between same strategy hedge funds (reported in Table 3) and non-hedge

fund institutions (reported in Table 2) are statistically significant at the 5% level in all 55 quarters.

Results across the other overlap metrics are similar—even when limiting the sample to hedge funds

with the same strategy, hedge fund portfolio overlap is much smaller than the overlap in random

non-hedge fund institutions’ portfolios.

In sum, results in this section reveal little evidence that hedge funds take similar positions in long

equity holdings. Rather, we find that hedge funds exhibit much greater independence in equity

selection decisions than other professional investors. We do not claim that hedge funds never follow                                                             22 It is possible that some managers do not report all their funds to HFR. As a result, the manager’s 13(f) data may reflect holdings of different strategies than those reflected in the HFR data.

  

 

25  

similar strategies, nor that their portfolios are fully independent (e.g., as shown in Fig. 2A, 9% of

hedge fund pairs have cosine similarity greater than 0.10). Nonetheless, the results are inconsistent

with the commonly held view that hedge funds, in general, are more susceptible to crowding than

other institutional investors.23

5. Crowded stocks and hedge fund crowding over time

Many authors and regulatory authorities have expressed concern that hedge funds’ crowding

propensity has increased. To examine this issue we plot the mean cosine similarity for hedge fund

pairs over time in Fig. 3. The results reveal no evidence that overlap in the average hedge fund pair

has systematically increased over time. In fact, the time-trend is negative and statistically significant

at the 5% level (untabulated) as the average overlap level declines steadily throughout much of the

period. There is, however, a spike up between the second and third quarter of 2009. Further

investigation reveals that this is largely driven by many hedge funds purchasing a few financial stocks

in the second quarter of 2009. For instance, the number of hedge funds holding a position in Bank

of America more than doubled in the second quarter of 2009 from 73 at the beginning of the

quarter to 154 at the end of the quarter. (Bank of America was the number one hedge fund stock at

the end of the second quarter of 2009.)

[Insert Fig. 3 about here]

Although the results in Fig. 3 reveal no evidence that hedge funds’ propensity to hold the same

securities has systematically increased over time, the results in Fig. 1 reveal that the number of hedge

funds has increased dramatically over time. In addition, although hedge fund portfolios exhibit

relatively little overlap, individual securities may still become “crowded” with hedge fund positions if

                                                            23 We repeat the analysis in this section using all non-hedge fund institutions rather than the matched sample of similar size institutions. Overlap differences between hedge funds and the complete sample of non-hedge fund institutions are even greater (untabulated).

  

 

26  

the few securities that are common to hedge fund pairs are often the same securities. That is, little

overlap in hedge fund portfolios does not necessarily imply all stocks have little crowding. For instance,

Apple was held by nearly one-third of hedge funds at the end of 2011 even though the mean

number of total securities held in common across all hedge fund pairs was only 3.80.

Thus, we next examine the extent of hedge fund crowding in individual stocks by calculating the

number of hedge funds holding the “most crowded” stocks. Each quarter, we identify the 1, 10, 50,

and 100 stocks with the greatest number of hedge fund shareholders. Fig. 4A plots the fraction of

hedge funds holding these stocks over time. For instance, the far right-hand side of the top line in

Fig. 4A reveals that nearly 32% of hedge funds held a position in Apple (the most crowded stock at

that point) at the end of our sample period.

[Insert Fig. 4 about here]

Fig. 4A reveals two interesting patterns. First, consistent with Fig. 3, there is no evidence that

the propensity of hedge funds to hold the same stocks has increased over time. In fact, the three

bottom lines (the 10, 50, and 100 most crowded stocks) exhibit a statistically significant negative

time trend (at the 5% level; untabulated). Second, concentration drops off relatively quickly. For

example, although 32% of hedge funds held Apple, the top stock, at the end of 2011, the top 100

“most crowded” stocks (at the same point in time) averaged ownership by only 11% of hedge fund

companies (bottom line in Fig. 4A, extreme right-hand observation).

Although hedge funds’ portfolio overlap does not increase over time (see Figs. 3 and 4A), the

growth in the number of hedge funds (see Fig. 1) means that hedge fund crowds have likely grown

over time. To investigate this possibility, Fig. 4B reports the number of 13(f) hedge funds holding

the top 1, 10, 50, and 100 stocks with the greatest number of hedge fund owners. For instance, in

the fourth quarter of 2011, 147 hedge funds held a position in Apple (Fig. 4B top line, extreme right

hand observation). Fig. 4B clearly demonstrates that “hedge fund crowds” have increased over time.

  

 

27  

Consider the 100 “most crowded” stocks with the greatest hedge fund ownership. These stocks

averaged 13 hedge fund shareholders in 1998 versus 52 hedge fund shareholders in 2011. We find

(untabulated) that the time-trend for each line in Fig. 4B is meaningfully positive. In sum, hedge

fund crowds have grown over time as a result of the large growth in the number of hedge funds and

not because hedge funds have increasingly focused on the same securities.

6. Does hedge fund demand drive prices from fundamentals?

We recognize that some stocks are “crowded” with hedge fund positions, and that small hedge

fund crowds might cause large price effects because equilibrium can be fragile (e.g., Brunnermeier

and Pedersen (2009)). In this section, we examine Stein’s (2009) crowded trade model, and examine

the impact of hedge fund demand shocks on contemporaneous and future returns. In the following

section, we extend this analysis to address Stein’s (2009) arbitrageur leverage model with an

examination of hedge fund crowds and related (contemporaneous and subsequent) returns during

stress periods.

6.1. Quarterly 13(f) data and hedge fund trades

We use changes in reported 13(f) holdings to infer each hedge fund’s transactions over each

calendar quarter. Specifically, we define a hedge fund as a buyer of a security if they hold more split-

adjusted shares at the end of the quarter than the beginning of the quarter, and a seller if they hold

fewer.24 The obvious limitation of 13(f) data is that we cannot view intraquarter hedge fund trades

(i.e., stock entered and exited within the same quarter). This may be problematic if many hedge

funds follow short-term strategies that play out within the quarter.

                                                            24 We do not count a manager as “buying” the first quarter that a manager files a 13(f) report.

  

 

28  

To examine this issue, we begin by measuring how often hedge funds tend to exit and enter

securities relative to making adjustments to, or not trading, securities in their portfolio (based on

observable interquarter entries and exits). Our intuition is straightforward—if hedge funds typically

follow short-term strategies that play out within a quarter, then most of the securities they hold at

the end of the quarter will differ from the ones they hold at the beginning. Specifically, we partition

the securities held by each hedge fund-quarter into three groups—the fraction that are observable

entries and exits over the quarter, the fraction that are adjustments to existing positions, and the

fraction that are stocks held but not traded over the quarter:

,2/

#

2/

#

2/

2/##

,1,

,

,1,

,

,1,

,,

thth

th

thth

th

thth

thth

NN

trade not do but Hold

NN

sAdjustment

NN

exits Observedentries Observed1

(4)

where Nh,t-1 and Nh,t are the number of securities hedge fund h holds in its long equity portfolio at the

beginning and end of quarter t, respectively. #Observed entriesh,t is the observable number of securities

the manager enters during the quarter (i.e., holds at the end of quarter t but not at the beginning of

quarter t). Analogously, #Obervable exitsh,t is the observable number of securities the manager exits

during the quarter, and #Adjustmentsh,t is the number of securities that a manager holds at both the

beginning and end of quarter t, but either buys additional shares or liquidates a portion of the

position during quarter t. #Hold but do not tradeh,t is the number of securities that a manager holds

with the same number of (non-zero) shares at both the beginning and end of quarter t.

Panel A in Table 4 reports the time-series average of the cross-sectional descriptive statistics of

each term in Eq. (4) based on the ratio of entries and exits to holdings (i.e., the first term on the

right-hand side of Eq. (4)). As a result, each column in Panel A sums to one. The results suggest that

the typical (median) hedge fund does not appear to primarily engage in short-term intraquarter

trades—approximately two-thirds of the stocks in the manager’s portfolio at the end of the quarter

were there at the beginning of the quarter (i.e., the sum of the second and third rows). However,

  

 

29  

some hedge funds exhibit much higher turnover rates. For instance, nearly 74% of the stocks held at

the end of the quarter differ from the stocks held at the beginning of the quarter for a hedge fund in

the 95th percentile of observable entries and exits.

[Insert Table 4 about here]

Although Panel A demonstrates that most hedge funds exhibit relatively few observable entries

and exits relative to adjustments and no changes, this observable activity is only a portion of all

entries and exits as we cannot view positions both established and liquidated within the same

quarter. However, if we make a few simplifying assumptions, we can estimate the unobservable

fraction of positions established and liquidated within the same quarter using the observable fraction

of positions established (i.e., held at the end of the quarter but not the beginning of the quarter) and

liquidated (i.e., held at the beginning of the quarter but not the end of the quarter). Specifically, we

assume the manager (i) holds a constant number of securities within a quarter (i.e., every exit is

followed by an entry), (ii) does not re-enter a stock liquidated in a quarter within the same quarter,

and (iii) is as likely to liquidate a stock purchased within the quarter as a stock held at the beginning

of the quarter. Assuming continuous trading within the quarter, the ratio of unobservable

intraquarter entries and exits to all (i.e., observable and unobservable) entries and exits is given by

(see Appendix C for proof):25

.

##1ln

##1

##

##

,1,

,,

,1,,,

,,

,,

thth

thth

thththth

thth

thth

NN

exits Observedentries Observed

NNexits Observedentries Observed

ExitsEntries

exits bservedUnoentries observedUn (5)

The double bars indicate the left hand side of Eq. (5) is an estimate of unobservable values

computed from the observed values on the right-hand side of the equation, given the assumptions

                                                            25 The first assumption is unlikely to bias the estimate. To the extent that a manager does exit and enter the same stock multiple times within the same quarter, our estimate will be negatively biased. If a manager is less likely to liquidate a position that was recently entered, then the last assumption will cause a positive bias in our estimate. Alternative models may be considered to describe unobservable intraquarter behavior. What is important is that the richness of discrete data not be mitigated solely due to observed data periodicity, especially in the context of other important benefits.

  

 

30  

outlined above. Eq. (5) provides an estimate of the fraction of total entries and exits (both

observable interquarter and unobservable intraquarter) that are missed by using 13(f) data for a given

hedge fund.

Given this estimate of the ratio of unobservable entries and exits to all entries and exits, as well

as the observable number of entries and exits and adjustments to current positions, we can “back

out” the estimated number of unobservable entries and exits (see Appendix C for additional detail).

The estimated fraction of trades we miss for each manager quarter is given by:26

..#.#.###

##

.#.#

##

,,

,,

,,

,,

sadjustmentObsexitsObsentriesObsexits bs.Unoentries obs.Un

exits bs.Unoentries obs.Un

TradesObsTradesUnobs

exits bs.Unoentries obs.Un

thth

thth

thth

thth

(6)

Panel B in Table 4 reports the time-series mean of the cross-sectional summary statistics of the

fraction of hedge fund entries and exit trades missed (i.e., Eq. (5)) and the fraction of all hedge fund

trades missed by only observing beginning and end of quarter positions (i.e., Eq. (6)). The results

suggest that, in general, the 13(f) data do a good job capturing most hedge funds’ entries and exits.

Specifically, we estimate that the 13(f) data captures 82% of the typical hedge fund’s entries and exits

(i.e., 1-0.18, using the initial row reported median) and 89% of the typical hedge fund’s trades (cf.,

bottom row median). Even at the extremes, our estimates suggest the 13(f) data captures most

entries and exits. For example, we estimate that the 13(f) data captures 55% (i.e., 1-0.45) of the

entries and exits and 58% of trades for hedge funds in the 95th entry/exit turnover percentile.

The results in Table 4 are inconsistent with the notion that hedge funds primarily engage in high

frequency trading. Our results, however, are consistent with Jame (2012), who estimates (based on

ANcerno transaction data) that unobservable intraquarter hedge fund trading accounts for only 3% of

                                                            26 We assume that all adjustments are observable, i.e., we assume a manager does not purchase and liquidate X additional shares of a stock held at the beginning of the quarter.

  

 

31  

the typical (median) hedge funds’ trades.27 Further, and consistent with our estimates, Jame finds

that even at the 95th percentile of intraquarter trading, the 13(f) data still capture 63% of hedge

funds’ trades.

In short, the results in Table 4 reveal that most of the securities held by a typical hedge fund at

the beginning of the quarter remain in the portfolio at the end of the quarter. Moreover, given the

assumptions outlined above, we estimate that the 13(f) data captures most hedge fund trades even

for funds at the 95th percentile of entries and exits.

6.2. The crowded trade model: Hedge fund demand shocks and returns

If unexpected hedge fund demand shocks destabilize asset prices as in Stein’s (2009) crowded

trade model, then extreme hedge fund demand will be positively related to contemporaneous returns

and inversely related to future returns. Alternatively, if hedge funds are better informed than other

investors and their demand drives prices toward equilibrium, then their demand will be positively

related to contemporaneous returns and independent of, or positively related to, subsequent returns.

We reiterate that Stein’s (2009) crowded trade model does not require a funding shock to

generate mispricing. The mispricing occurs simply because each individual hedge fund misinterprets

the fact that contemporaneous price changes are driven, at least in part, by aggregate hedge fund

demand rather than a shock to fundamental value. Thus, in this section, we focus on the more

general question as to whether extreme hedge fund demand shocks are destabilizing as Stein’s model

predicts and the popular press often claims.

The implicit assumption we make in these tests is that hedge funds cannot, in general, predict

other hedge funds’ demand shocks. As a result, the expected end of quarter holdings of any hedge

fund-stock-quarter is their beginning of quarter holdings of the stock. It is possible, of course, that                                                             27 ANcerno no longer reports manager identifications in their data. As a result, we cannot use ANcerno data to examine intraquarter hedge fund trades.

  

 

32  

some hedge funds learn of other hedge funds’ trades through indirect methods or that some hedge

funds recognize that other “similar” funds are likely to trade on the same signal. Nonetheless, we

believe our method is reasonable for four reasons. First, stocks with extreme unexpected hedge fund

demand shocks should end up in the extreme demand shock portfolios. Second, in Stein’s (2009)

model, hedge funds profit when they trade as long as the trade is not crowded with other hedge

funds following the same strategy. Hence, the model predicts that small hedge fund demand shocks

should perform better than large hedge fund demand shocks if hedge fund crowds drive mispricing.

Third, results in the previous section provide little evidence that hedge funds tend to follow the

same strategies. Fourth, a number of robustness tests (discussed below) continue to support the

hypothesis that large hedge fund demand shocks drive prices toward fundamental values.

Because large stocks produce greater absolute changes in the number of hedge funds buying or

selling the stock (e.g., if a small stock is only held by two hedge funds, the maximum number of

hedge fund sellers is two), we begin by sorting all stocks in our sample into capitalization quintiles at

the beginning of each quarter. We then sort stocks, within each capitalization quintile, into five

groups each quarter based on “hedge fund demand” defined as the difference between the number

of hedge funds buying the stock and the number selling the stock. Stocks that experience negative

hedge fund demand (i.e., stocks hedge funds are “selling”) are split into two equal-size groups

(within each capitalization quintile) based on hedge fund demand (heavy selling and light selling).

Analogously, stocks that experience more hedge funds buying than selling (i.e., positive net hedge

fund demand) are also partitioned into two groups by hedge fund demand. The final group consists

of stocks that have an equal number of hedge funds buying and selling (most of these stocks have

no hedge fund ownership). We then re-aggregate the stocks across capitalization quintiles to form

five capitalization-stratified hedge fund demand portfolios.

  

 

33  

Note that for the smallest of stocks, we cannot always form hedge fund demand quintiles

because few small stocks, especially in the early part of our sample, have any hedge fund ownership.

For example, in the first quarter of our sample (June 1998), 88% of stocks in the smallest

capitalization quintile had zero hedge fund ownership. Moreover, the maximum number of hedge

fund sellers was one. As a result, we cannot split small stocks into those heavily sold by hedge fund

and those lightly sold by hedge funds in June 1998. Thus, to be included in the analysis, we require

each hedge fund demand group within a quarter-capitalization quintile to contain at least ten stocks.

For each portfolio, we compute the equal-weighted return for three periods—the same quarter

as we measure hedge fund demand shocks, the following quarter, and the average quarterly return

for the following year. We use Jegadeesh and Titman’s (1993) calendar aggregation method to

calculate returns for the following year. We also compute benchmark adjusted returns as the

intercept from a time-series regression of quarterly excess portfolio returns on quarterly excess

market returns, size, value, and momentum factors (data from Ken French’s website).28

The first two columns in Table 5 report the time-series mean number of securities in each

portfolio and the time-series mean of the cross-sectional average hedge fund demand shock

(number of hedge funds buying less the number selling) for stocks within each of the size-stratified

hedge fund demand shock portfolios. The next three columns report mean quarterly raw returns and

the last three columns report mean benchmark adjusted returns (in percent). The first row reveals

that, on average, there were 638 stocks in the size-stratified portfolio of stocks heavily sold by hedge

funds. These stocks experienced 5.16 more hedge funds selling than buying and earned 1.87% in the

quarter hedge funds sold the stock, 1.67% the following quarter, and averaged 2.47% per quarter

over the following year. Corresponding quarterly benchmark adjusted returns were 0.04%, -0.46%,

and 0.40%. The last row in Table 5 reports the difference between stocks heavily purchased by                                                             28 Because our focus is on understanding equity prices and not hedge fund performance we adopt the risk factors available on Ken French’s website, rather than, for example, the Fung and Hsieh (2001) hedge fund risk factors.

  

 

34  

hedge funds and those heavily sold, along with the associated t-statistic (computed from the time-

series average of the difference and Newey-West (1987) standard errors).

[Insert Table 5 about here]

The results in Table 5 are consistent with the hypothesis that hedge fund demand shocks impact

prices. Stocks heavily purchased by hedge funds outperform those heavily sold by hedge funds by

6.25% in the contemporaneous quarter (5.59% benchmark adjusted return difference). 29 The

coarseness of the quarterly data, however, limits our ability to infer whether hedge fund demand

shocks actually “drive” prices. That is, a positive relation between hedge fund demand and same

quarter returns could reflect intraquarter hedge fund momentum trading, hedge fund demand

shocks driving prices, or hedge fund demand shocks forecasting intraquarter price changes.

Within the context of Stein’s (2009) crowded trade model, if hedge fund demand shocks drive

prices from value, corrections should occur as soon as hedge funds learn of other hedge funds’

trades. Therefore, prices should revert to fundamental values the following quarter when 13(f)

reports are filed and all participants can view hedge fund demand shocks.30 We find no evidence,

however, that hedge fund demand shocks drive prices from value. Stocks heavily purchased by

hedge funds outperform those heavily sold by hedge funds by 2.84% (2.62% benchmark adjusted

return) during the following quarter (statistically significant at the 1% level). We also find a

monotonic relation between hedge fund demand shocks and subsequent returns. The results are                                                             29 A large literature examines whether hedge funds garner abnormal returns (see Stulz (2007) for a review). Although our tests are motivated by examining Stein’s (2009) crowded trade model, these tests are clearly related to hedge fund performance. It is important to recognize, however, that we are not examining the returns earned by hedge funds, but rather the returns garnered by a portfolio long in the stocks hedge funds crowd into and short in the portfolio they crowd out of. As Chen, Jegadeesh, and Wermers (2000) point out, examination of trades may be a more powerful test of informed trading than examination of ownership levels. As far as we know, Griffin and Xu (2009) is the only other study that examines the relation between aggregate hedge fund trades and subsequent stock returns. The authors report evidence of a positive relation between hedge fund demand and returns over the following year (see their Table 3), but find the relation is no longer meaningfully different from zero once accounting for lag returns. A number of substantial differences between our studies may account for the different results including different measures of demand, different sample periods, and perhaps most important, our results are based on a much larger sample of hedge funds—this primarily results from the large increase in the number of hedge funds filing 13(f) reports over time. 30 As Stein (2009, Section C.2) points out, if the newswatcher bias is fixed, arbitragers can “back out” fundamental value once they know other arbitrageurs’ positions.

  

 

35  

inconsistent with the hypothesis that non-crowded hedge fund trades (i.e., small demand shocks) are

profitable while crowded hedge fund trades are not.

Although these results are inconsistent with the mechanism in Stein’s (2009) crowded trade

model in that the mispricing would be corrected as soon as hedge funds learned of the crowd, it is

possible that either: (i) hedge funds cannot back out fundamental value once they observe demand

shocks, or (ii) smart hedge funds attempt to “ride bubbles.” In the latter case, they may knowingly

purchase overvalued stocks in an attempt to exploit later traders that drive prices even further from

value (see, for example, DeLong, Shleifer, Summers, and Waldman (1990)). In either case, we should

see an eventual return reversal. The results in Table 5, however, reveal no evidence of such a

reversal—stocks heavily purchased by hedge funds outperform those heavily sold by hedge funds by

0.66% (0.55% for benchmark adjusted returns) per quarter over the following year (both statistically

significant at the 1% level).

Table 6 reports the analysis by capitalization quintile. To conserve space we only report

benchmark adjusted quarterly returns (although we find the same pattern in raw returns). As noted

above, small stocks sometimes have too few securities with adequate hedge fund ownership to form

demand shock portfolios. Sample sizes (number of quarters where all five institutional demand

groups have at least ten stocks) are given in the heading for each panel. In addition, we report the

fraction of all hedge fund trades accounted for by stocks within each size quintile in the headings.31

[Insert Table 6 about here]

For the three smallest capitalization quintiles, stocks purchased by many hedge funds

meaningfully outperform those sold by many hedge funds in the contemporaneous quarter,

consistent with the possibility that hedge fund demand shocks drive prices. Although the point

estimate is positive, there is no evidence that the difference in contemporaneous returns is                                                             31 The fraction of hedge fund trades reported in the panel headers are based on all observations, i.e., including small capitalization stocks even in quarters where there are few hedge funds trading small stocks.

  

 

36  

statistically significant for stocks in the fourth size quintile. For large stocks, we find an inverse

relation between the net change in size of the “crowd” and contemporaneous returns. The result is

inconsistent with the hypothesis that hedge fund demand shocks, in general, drive prices from value

in large stocks (that account for 58% of hedge fund trades), but is consistent with the hypothesis

that hedge funds often provide liquidity to other traders demanding immediacy.

The analysis by capitalization also reveals no evidence of return reversals the following quarter.

Mean adjusted return differences are positive for every size quintile and statistically significant at the

1% level for the four largest capitalization quintiles that account for 98% of hedge fund trades. The

results are inconsistent with the hypothesis that hedge fund demand shocks drive prices from value

and that mispricings are corrected when hedge funds learn of other hedge funds’ positions. The

results are consistent, however, with the interpretation that hedge fund crowds are better informed

than other traders and therefore push prices toward fundamentals. As with the aggregate results in

Table 5, we continue to find no evidence that the subsequent returns are reversed in the following

year. Our findings also suggest that information captured by hedge funds’ crowded trades is

relatively short-lived. For stocks in the largest capitalization quintile, the annualized mean quarterly

return is just slightly larger than the subsequent quarterly return.

A number of factors could impact the relation between aggregate hedge fund demand and stock

returns. First, it is possible that a few large hedge funds purchasing or selling the same stock results

in much greater mispricing than many small hedge funds simultaneously buying or selling the same

stock. To examine this possibility, we repeat the analysis in Tables 5 and 6 sorting stocks within each

capitalization quintile by the change in the fraction of outstanding shares purchased (or sold) by

hedge funds. Our results (reported in Appendix B) remain qualitatively similar—stocks that

experience a large increase in the fraction of shares held by hedge funds subsequently outperform

those that experience a large decrease (statistically significant at the 1% level).

  

 

37  

Second, some securities may routinely have larger changes in hedge fund ownership than other

securities and, as a result, many of the large changes in hedge fund ownership in these securities may

not be “unexpected.” To examine this possibility, we rerun our results using standardized

unexpected hedge fund demand defined analogous to standardized unexpected earnings. Specifically,

the standardized unexpected demand shock for each security-quarter is estimated as the raw change

in the number of hedge funds holding the stock normalized by the standard deviation of changes in

the number of hedge funds holding the stock over the previous four quarters. The patterns

documented in Tables 5 and 6 continue to hold when sorting on standardized unexpected hedge

fund demand shocks (untabulated).

Third, hedge funds profit in Stein’s (2009) crowded trade model when they exploit other

investors’ underreactions as long as not too many hedge funds jump on the same signal. Thus,

perhaps our classifications in Tables 5 and 6 are too broad, especially for large stocks that experience

many hedge fund trades. For instance, column 2 of Panel E in Table 6 shows that, on average, nine

hedge funds purchase the stocks in the heavily purchased category. Thus, perhaps six or seven hedge

funds purchasing the stock pushes prices toward fundamental values, while 11 or 12 hedge funds

purchasing the stock drives prices beyond fundamentals. To examine this possibility, we rerun the

large capitalization analysis in Table 6 partitioning large stocks purchased by hedge funds into four

groups and large stocks sold by hedge funds into four groups (thus, a total of nine groups after

adding large stocks not traded by hedge funds). We then compare the contemporaneous and

subsequent return patterns for the revised heavy buy and heavy sell categories. The results

(untabulated) reveal no evidence of subsequent reversals. In fact, subsequent return differences are

even greater when using the more extreme definitions of hedge fund demand shocks.

Fourth, it is possible that we fail to capture hedge funds’ extreme demand shocks because we

only examine the long side of their equity portfolio. To examine this possibility, following previous

  

 

38  

work (e.g., Hanson and Sunderam (2013)), we assume all short interest represents hedge fund

positions and compute short-interest adjusted hedge fund demand from the combination of changes

in the fraction of shares held by hedge funds and changes in short interest. Once again, our results

remain intact (details provided in Appendix B).

7. Hedge fund crowds and funding crises

Although the results in the previous section provide little evidence that hedge funds crowd, in

general, or drive prices from value, it is possible that the negative externalities of hedge fund crowds

are limited to periods of extreme market stress. Thus, in this section, we focus on the implications of

Stein’s (2009) arbitrageur leverage and related models. As detailed in Section 2, theory predicts that

during a funding crisis (i.e., forced sales due to lender demands and/or investor withdrawals) four

things should occur (holding everything else equal): (i) hedge funds holding “more crowded”

portfolios will be forced to liquidate more of their portfolio due to spillover effects, (ii) portfolios of

hedge funds with more crowded positions will suffer inferior returns due to spillover effects, (iii) the

positive relation between hedge fund demand shocks and same quarter returns should be especially

strong as hedge funds trample each other while rushing for the exits, and (iv) the relation between

hedge fund demand shocks in stressful quarters and subsequent returns should be negative (even

though, as shown in the previous section, it is positive on average) as prices eventually rebound

toward fundamental values.

7.1. Identifying funding crises

A funding crisis should: (i) force hedge funds, in aggregate, to liquidate positions, (ii) be

widespread (i.e., impact most hedge funds), and (iii) result in poor hedge fund returns due to forced

liquidations and contagious fire sales. Ben-David, Franzoni, and Moussawi (2012) present evidence

  

 

39  

of the first two points during the last two quarters of 2007 (the quant crisis) and the last two quarters

of 2008 (the Lehman Brothers bankruptcy). In these four quarters, the authors find that hedge funds

as a group sold off approximately 11% of their equity portfolios each quarter. They also find (p. 21)

“… nearly a quarter of hedge funds sold more than 40% of their equity holdings” in the last two

quarters of 2008. Boyson, Stahel, and Stulz (2010) focus on points (ii) and (iii) above. Consistent

with a contagion effect, the authors find that extreme losses in one type of hedge fund (e.g.,

convertible arbitrage funds) are much more likely to occur when other types of hedge funds (e.g.,

macro funds) also experience poor performance.

We attempt to objectively identify funding crises by examining five measures of hedge fund

stress: (i) the percent change in the dollar value of aggregate hedge fund equity positions over the

quarter, (ii) the fraction of hedge funds reducing their equity portfolio during the quarter, (iii) the

fraction of hedge funds reducing their equity portfolio by more than 20% during the quarter, (iv) the

quarterly return on the Hedge Fund Research Fund-Weighted Composite Index (an equal-weighted

hedge fund return index, net of fees, comprised of over 2,000 hedge funds), and (v) the lowest

monthly average percentile rank within each quarter for eight HFRI index returns.32

The first three measures are motivated by Ben-David, Franzoni, and Moussawi (2012) and

attempt to capture whether there is evidence hedge funds are being forced to liquidate positions, as

well as the breadth of the hedge fund exodus. To ensure our results are driven by hedge fund trades

rather than stock returns, the first three measures use both beginning and end of quarter values

based on beginning of quarter prices (following Ben-David, Franzoni, and Moussawi).

The final two measures, motivated by Boyson, Stahel, and Stulz (2010), attempt to capture

whether hedge funds suffer large losses, and the breadth of such losses across different types of

                                                            32 We use eight monthly HFRI indices (from Hedge Fund Research) that we examine in a related paper (Reca, Sias, and Turtle (2013)). Specifically, the eight indices are Equity Market Neutral, Quantitative Directional, Technology/Healthcare, Distressed, Merger Arbitrage, Macro, Convertible Arbitrage, and Fixed Income Corporate.

  

 

40  

hedge funds. Note that the last measure—the lowest monthly average performance percentile rank

for eight HFRI indices—is a refined analog to Boyson, Stahel, and Stulz’s (2010) “COUNT8”

variable, defined as the number of HFRI indices with a bottom decile return that month. For

instance, if in June of 1998, four of the HFRI indices experienced a 20th percentile return and the

other four indices experienced a 10th percentile return, then our variable would take a value of 0.15

for the second quarter of 1998 (assuming April and May returns were higher). We focus on the

“worst” month in a quarter for consistency with Boyson, Stahel, and Stulz.

We also compute a composite ranking of hedge fund stress based on the average percentile rank

across the five stress measures. We do not claim these variables are independent (clearly they are

not). We simply compute this composite to allow us to objectively rank quarters on hedge fund

stress levels. Table 7 reports the values for the five stress measures and the composite rank. For

instance, the top row indicates that in the second quarter of 1998 hedge funds increased their

aggregate equity holdings by 3.2%, 32.5% of hedge funds were net sellers, 14% of hedge funds sold

at least 20% of their long equity portfolio, the eight HFRI indexes averaged performance in the 30th

percentile in the “worst” month of that quarter, the HFRI quarterly aggregate hedge fund index lost

1.3% and overall, the quarter was the 33rd most stressful quarter for hedge funds (out of the 55

quarters in our sample). We also report, for the March 2005-September 2009 subperiod, the

percentage change in gross hedge fund leverage from Ang, Gorovyy, and van Inwegen (2011).33

Highlighted cells in Table 7 indicate the decile of most stressful quarters based on that measure, e.g.,

the six (of 55) quarters that experienced the greatest percentage decline in hedge fund equity

holdings are highlighted in column one. Given the hedge fund leverage data is for 19 quarters, we

highlight only the two extreme leverage change observations.

[Insert Table 7 about here]                                                             33 We thank the authors for sharing this data. See Ang, Gorovyy, and van Inwegen (2011) for details regarding this measure.

  

 

41  

The results in Table 7 are largely consistent with those reported by previous studies. For

instance, Ben-David, Franzoni, and Moussawi (2012) comment that hedge funds, in aggregate,

strongly exit equity markets in the last two quarters of 2007 and 2008, consistent with the first

column in Table 7. Boyson, Stahel, and Stulz (2010) point out that most hedge fund indexes had

poor performance during the 2007-2008 period, the third quarter of 1998 (the Long Term Capital

Management crisis), and the second quarter of 2005 (when Ford and GM lost their investment grade

ratings), consistent with the fourth column in Table 7.34

7.2. Arbitrageur leverage model: Overlap, hedge fund exits, and hedge fund returns during stressful periods

Due to the negative externalities hedge funds exert on each other when funding decreases, hedge

funds holding more crowded portfolios during a funding crisis should: (i) be forced to liquidate

more of their positions, and (ii) suffer inferior portfolio returns relative to more independent hedge

funds. To examine these hypotheses, each quarter we compute the overlap (cosine similarity)

between each hedge fund’s portfolio and the aggregate hedge fund portfolio (excluding that fund).

We also compute the percentage change in the hedge fund’s equity holdings due to trading over the

quarter as the dollar value of the manager’s trades over the quarter divided by the average of the

manager’s beginning and end of quarter portfolio value. As before, we use beginning of quarter

prices to ensure we capture changes due to trading and not returns. In addition, following previous

work (e.g., Gaspar, Massa, and Matos (2005), Yan and Zhang (2009), and Cella, Ellul, and Giannetti

(2013)), we scale by the average of beginning and end of quarter portfolio values to ensure that

outliers do not drive the results:

                                                            34 The second quarter of 2005 is not in the bottom decile (of the eight HFRI average return percentile variable) for our sample because our period includes data after October 2008 and excludes data prior to March 1998. Nonetheless, it is this metric’s ninth worst quarter.

  

 

42  

,

2

1%

,,1

1,1,,1

1,

1,,,,1

1,

,

tkh

K

ktktkh

K

ktk

tkhtkh

K

ktk

th

HPHP

HHP

Porttt

t

(7)

where Pk,t-1 is security k’s price at the beginning of quarter t (i.e., the end of quarter t-1), and Hh,k,t is

the number of shares of security k held by hedge fund h at the end of quarter t.

We compute the return on the hedge fund’s beginning of quarter long equity portfolio over the

quarter using:

,,1

1,,, tk

N

itkhth RwRet

t

(8)

where wh,k,t-1 is hedge fund manager h’s weight in stock k at the beginning of quarter t and Rk,t is the

stock’s return over quarter t. In addition, we compute the Daniels, Grinblatt, Titman, and Wermers

(DGTW 1997) characteristic based benchmark adjusted returns for hedge fund’s beginning of

quarter portfolio as the weighted average DGTW return of the securities in their beginning of

quarter portfolio.35 By construction, Eq. (8) measures the return on the long equity portfolio held by

the fund at the beginning of the quarter and not the return earned by the fund (unless the fund does

not trade and only holds 13(f) securities), as we are attempting to determine if hedge funds’ crowded

positions lead to losses in those securities that, at least theoretically, lead to further deleveraging,

further losses, and so on, i.e., those securities subject to a contagious downward price spiral.

We then limit the sample to 13(f) hedge fund companies that we can match with firms in the

HFR live and dead database. Using the HFR data, we compute each hedge fund company’s net flow

(change in assets adjusted for returns) and collect data regarding their use of leverage (from the HFR

                                                            35 We thank Russ Wermers for making this data available on his website: http://www.smith.umd.edu/faculty/rwermers/ftpsite/Dgtw/coverpage.htm. See Daniel, Grinblatt, Titman, and Wermers (1997) and Wermers (2004) for additional detail. Approximately 11% of our hedge-fund-stock-quarter observations lack sufficient data (e.g., lag book value) to compute DGTW adjusted returns.

  

 

43  

administrative file). We then regress, each quarter, the percentage change in the hedge fund’s equity

holdings on the overlap between that hedge fund’s portfolio and the aggregate hedge fund equity

portfolio, portfolio size (the natural logarithm of total equity holdings), net fund flows for the hedge

fund company (because flows can impact the extent to which a fund enters or leaves the market),

and a leverage dummy variable (because levered funds may be more susceptible to liquidity events)

that takes on a value of one if the company uses leverage and zero otherwise.36 In total, our sample

consists of 7,127 hedge fund company-quarter observations (ranging from 48 to 223 hedge funds

per quarter).37

To allow comparison over time, we standardize cosine similarity each quarter (i.e., rescale to

mean zero, unit standard deviation). As a result, the coefficient associated with standardized cosine

similarity can be interpreted as the relation between a one standard deviation increase in cosine

similarity with the aggregate hedge fund portfolio and the percent change in the manager’s portfolio

due to trading:

...% ,,,4,,2,,2,,1, ththtthtthtthttth DumLevlowsFValuePortfoliolnySimilaritCosinePort (9)

If hedge fund crowds exert negative externalities on each other during funding crises, then the

coefficient associated with cosine similarity will be negative during stressful quarters. Fig. 5 plots the

coefficient associated with cosine similarity each quarter where the quarters are ordered by our

composite measure of hedge fund stress. The third quarter of 2008, for instance, is the extreme left-

hand observation in Fig. 5 because it is the “most stressful” quarter for hedge funds (Table 7, sixth

column). Analogously, the first quarter of 2006 (the “least” stressful quarter identified in Table 7) is

                                                            36 On average (across the 55 quarters), 42% of the hedge fund companies in our merged sample do not use leverage according to HFR. 37 We repeat the tests in this section using all 13(f) hedge funds, but excluding fund flows and the leverage dummy from the regressions (i.e., the data garnered from the HFR database). The results remain similar and are detailed in Appendix B.

  

 

44  

the extreme right hand observation in Fig. 5. Solid bars indicate that the coefficient associated with

cosine similarity differs significantly from zero at the 5% level.

[Insert Fig. 5 about here]

Fig. 5 reveals little evidence that hedge funds that hold more crowded portfolios are forced to

liquidate more of their portfolio during a funding crisis. For instance, in the third quarter of 2008

(the “most” stressful quarter), a one standard deviation larger cosine similarity is associated with

selling approximately 8% more of the hedge fund’s portfolio (the coefficient has a p-value of 0.088).

The point estimates for the next three most stressful quarters have the “wrong” sign (although none

are statistically different from zero). Very few of the coefficients associated with the extent the fund

holds a crowded portfolio are statistically significant and there appears to be no relation to stress.

Next we repeat the regression in Eq. (9), but replace the dependent variable with the raw or

DGTW (1997) adjusted return on the manager’s beginning of quarter portfolio:

... ,,,4,,3,,2,,1, ththtthtthtthttth DumLevlowsFValuePortfoliolnySimilaritCosineRet (10)

Figs. 6A and 6B report the coefficients associated with standardized cosine similarity for raw and

DGTW-adjusted returns, respectively. As before, the graphs are ordered from left to right by

aggregate hedge fund stress ranking (see Table 7) and solid bars indicate statistical significance at the

5% level. If hedge funds exert negative externalities on each other, we expect the coefficient

associated with cosine similarity to be negative during high stress quarters.

[Insert Fig. 6 about here]

The results in Fig. 6A reveal, consistent with the negative externality hypothesis, that hedge

funds with greater similarity to the aggregate hedge fund portfolio suffered worse returns in the third

quarter of 2008, although the coefficient is not materially different from zero (p-value=0.065). A one

standard deviation larger cosine similarity with the aggregate hedge fund portfolio is associated with

a 2% smaller portfolio return in the third quarter of 2008. Inconsistent with the negative externality

  

 

45  

hypothesis, however, the portfolios of managers with greater aggregate hedge fund portfolio overlap

perform meaningfully (statistically significant at the 5% level) better in the next three most stressful

quarters—the fourth quarter of 2008, the third quarter of 1998 (the “LTCM” quarter), and the third

quarter of 2011. Most important, the results in Fig. 6A reveal no evidence that the relation between

beginning of quarter hedge fund crowding and returns is related to market stress.

Fig. 6B suggests that many of the meaningful differences reported in Fig. 6A are due to

characteristic differences. Regardless, neither figure suggests that equity portfolios held by hedge

funds with more crowded positions suffer worse returns relative to hedge funds with less crowded

positions during stress events.

7.3. Stress, hedge fund demand shocks, and stock returns

We next examine the relation between hedge fund demand shocks and individual stock returns

during high versus low stress quarters. We follow the general method of Dennis and Strickland

(2002) and estimate a cross-sectional regression, each quarter, of market-adjusted stock returns on

firm size, turnover, idiosyncratic variance, beta, and net demand (number of buyers less number of

sellers) by non-hedge fund institutions and hedge funds:38

tkttkttkttkttjk,t BetaarV Idio.Turn.ln(Cap)Ret ,,4,,3,,2,,1,0 .

.,,,6,,5 tktkttkt demandnetHFdemandnetNHF (11)

We measure capitalization at the beginning of the quarter and turnover as the mean monthly

turnover in a quarter (number of shares traded/shares outstanding). Following Dennis and

Strickland (2002), we compute idiosyncratic variance and beta from a market model estimated over

200 days beginning 50 days prior to the quarter (i.e., days -50 to -250). Retk,t+j is the market-adjusted

                                                            38 We differ from Dennis and Strickland (2002) in that we focus on hedge fund net demand while the authors focus on institutional ownership levels. In addition, we examine both “contemporaneous” (i.e., k=0) and subsequent (i.e., k=1) returns.

  

 

46  

return for stock k in quarter t+j. HF net demandk,t is the number of hedge funds buying security k in

quarter t less the number selling and NHF net demandk,t is analogously defined for non-hedge fund

institutions.

Because larger stocks tend to have greater variation in net hedge fund demand (see Table 6),

each quarter we standardize (rescale to unit standard deviation and zero mean) net hedge fund

demand within each size quintile. The resulting coefficient can be interpreted as the return

associated with a one standard deviation increase in the net number of hedge fund buyers within

each size quintile. In addition, because hedge fund demand is standardized, we can compare

coefficients over time. To ensure our results are not driven by outliers, we Winsorize market-

adjusted returns at the 99% level (our results remain similar, however, when we do not Winsorize).

We estimate two cross-sectional regressions each quarter—where the dependent variable is

either the market-adjusted return in quarter t, or quarter t+1.39 Given the results in Tables 5 and 6,

we expect that hedge fund demand will, on average, be positively related to same quarter returns. If

hedge fund selling causes negative externalities during stress events (e.g., fire sale spillovers) that

drives prices below fundamental values, we expect the positive relation between hedge fund demand

shocks and contemporaneous returns should be much stronger during stressful quarters than non-

stressful quarters.

Given the results in Tables 5 and 6, we also expect a positive relation between hedge fund

demand shocks and subsequent returns, on average. If, however, hedge funds’ forced sales drive

prices from fundamentals during stress events, then the coefficient associated with hedge fund

                                                            39 We also estimate the model with the market-adjusted return over quarter t+1 through t+4 (i.e., the following year) as the dependent variable. These results are qualitatively similar to the next quarter results, and are omitted for brevity. In particular, consistent with Table 5, hedge fund quarter t trading tends to be positively related to subsequent annual returns. And, once again, we find no evidence that hedge funds’ quarter t trades are inversely related to subsequent annual returns for high stress quarters.

  

 

47  

demand shocks should be negative for high-stress quarters (when the dependent variable is

subsequent returns).

Fig. 7A plots the coefficient associated with standardized hedge fund demand from quarterly

cross-sectional regressions of market adjusted returns on the control variables and hedge fund

demand the same quarter (i.e., j=0 in Eq. (11)). As before, quarters are sorted from high-to-low

stress and solid bars indicate statistical significance at the 5% level. Consistent with Table 5, most of

the coefficients are positive and statistically significant. Inconsistent with negative hedge fund

externalities during a crisis period, there is no evidence the relation between hedge fund demand and

returns the same quarter is stronger in high stress periods. Of the six most stressful periods, the

relation between hedge fund demand and same quarter returns is meaningfully larger than zero only

once. At the right of the figure, we also find four of the six least stressful quarters produce a

meaningful positive relation between hedge fund demand and same quarter returns.

[Insert Fig. 7 about here]

Fig. 7B repeats the analysis, but replaces the dependent variable with the return in quarter t+1

(i.e., j=1 in Eq. (11)). Consistent with Table 5, hedge fund demand in quarter t is generally positively

related to quarter t+1 returns. More important, we find no evidence that hedge fund demand in

stress quarters is inversely related to subsequent returns. In fact, the coefficient associated with

hedge fund demand is meaningfully larger than zero (statistically significant at the 5% level) in three

of the five most stressful quarters. The results are inconsistent with the hypothesis that these events

result in hedge fund contagion and spillover effects that drive prices from value.

We consider several further robustness tests. First, we repeat the analysis, but do not standardize

hedge fund demand within each size quintile. To allow comparison over time, we do standardize

hedge fund demand (across all stocks) each quarter. Untabulated results are nearly identical to those

reported in Fig. 7. We also repeat the analysis limiting the sample to stocks within each size quintile.

  

 

48  

For the contemporaneous quarter, the results are consistent with those reported in Table 6—hedge

fund demand is generally positively related to contemporaneous returns for the three smallest

quintiles, becomes weaker for the fourth quintile, and reverses for the largest stocks. Consistent with

Fig. 7A, however, none of these patterns appear to be related to stress. Further consistent with

Table 6, hedge fund demand, in general, is positively related to subsequent quarterly or annual

returns and the relation is weakest for the smallest stocks. Once again, however, we find no evidence

of subsequent reversals following high stress quarters. For instance, in no size quintile do we

document a negative relation between hedge fund demand shocks and subsequent returns for the

decile of most stressful quarters.

As in the previous section, we also consider two alternative measures of hedge fund demand—

the change in the fraction of shares held by hedge fund and the short-interest adjusted change in the

fraction of shares held by hedge funds. Our results remain intact (details provided in Appendix B).

Our results may appear surprising to some readers in light of recent evidence that hedge funds

strongly exited equity markets in the second halves of 2007 and 2008 (Ben-David, Franzoni, and

Moussawi (2012)) and that hedge fund style returns appear to suffer from contagion during crisis

periods (Boyson, Stahel, and Stulz’s (2010)). Appendix B provides a complete reconciliation with

these studies.

7.4 The August 2007 quant crisis

One possible interpretation of our results is that hedge fund demand shocks only have very

short lived effects during crisis periods.40 For instance, Pedersen (2009) shows that during the 2007

“quant crisis,” a large capitalization market-neutral strategy exploiting value and momentum effects

                                                            40 This interpretation would require that the impact of all stress events be unwound within the same quarter. In addition, this interpretation would appear inconsistent with the evidence in Ben-David, Franzoni, and Moussawi (2012) and Boyson, Stahel, and Stulz (2011).

  

 

49  

(scaled to 6% annual volatility) suffers a cumulative return of -25% over August 6-9 and then

recovers approximately two-thirds of those losses over the next two trading days. Also, as discussed

earlier, Hanson and Sunderam (2013) argue that value and momentum strategies perform poorly

when hedge funds crowd into such strategies. In this section we examine hedge funds’ ownership

levels and trading of the value/momentum portfolio around the quant crisis to better understand the

role of hedge funds’ crowded trades in the quant crisis. Our goals in this section are to: (i) test if

hedge funds were crowded into the value/momentum strategy prior to the crisis, and (ii) examine

whether hedge funds strongly exited the strategy in the third quarter of 2007.

We begin by examining the returns for a momentum/value strategy from Friday August 3, 2007

through Monday August 14, 2007 (matching Pedersen’s (2009) Fig. 1A). We follow the methodology

in Asness, Moskowitz, and Pedersen (2013) to form the value/momentum strategy portfolio.

Specifically, value is measured as the book-to-market ratio at the end of June 2007 and momentum

is measured as cumulative raw returns from June 2006 through May 2007 (i.e., includes a “skip”

month for the end of June 2007 formation date). Following Asness, Moskowitz, and Pedersen, we

limit the sample to stocks that cumulatively account for 90% of the market capitalization (Appendix

B provides complete details of the portfolio formation process). We also require the stock be

included in our institutional ownership data. Our final sample consists of 594 stocks (by comparison

Asness, Moskowitz, and Pedersen’s sample ranges from 354 stocks to 676 stocks over the 1972-

2011 period). Each stock is then ranked on value and momentum independently. The stock’s weight

in the value portfolio is given by its value rank less the mean rank times a constant, such that the

portfolio is scaled to have $1 long and $1 short. The stock’s weight in the momentum portfolio is

analogously defined. The stock’s weight in the combination portfolio (that accounts for both its

value and momentum characteristics) is the average of its weight in the value portfolio and its weight

in the momentum portfolio.

  

 

50  

Because our focus is on understanding whether hedge funds crowded into this strategy, we limit

the analysis to the 100 most extreme stocks (i.e., the 50 with the largest value/high momentum

characteristics and the 50 with the largest growth/low momentum characteristics) and scale the 100

stock portfolio to 100% long 50 value/high momentum stocks financed by 100% short growth/low

momentum stocks. Fig. 8 reports the cumulative return to this zero cost portfolio over the eight

trading days in Pedersen’s (2009) Figure 1A.41 The return pattern is essentially identical to that

reported by Pedersen and demonstrates that investors engaging in a long-short value/momentum

strategy suffered large losses between August 3-9, but those losses were mostly recovered over the

next few days.42

[Insert Fig. 8 about here]

If hedge fund crowding into the value/momentum strategy drives the quant crisis return pattern,

we expect that hedge fund ownership of stocks in the value/high momentum portfolio should be

much greater than their ownership of stocks in the growth/low momentum portfolio prior to the

crisis. Panel A in Table 8 reports the mean and median number of hedge funds holding (at the end

of June 2007) the 50 value/high momentum stocks and the 50 growth/low momentum stocks.

Inconsistent with the hypothesis that hedge funds, in aggregate, crowded into this strategy prior to

the crisis, we find no evidence of a meaningful difference in the number of hedge funds holding

value/high momentum stocks versus the number holding growth/low momentum stocks. Point

estimates are actually higher for growth/low momentum stocks. Panel B reports the fraction of each

stock’s outstanding shares held by hedge funds. Once again, we find no meaningful evidence that

hedge funds, as a group, crowd into the same (value/momentum) strategy. The typical (median)

                                                            41 In untabulated analysis, we find the equal-weighted zero-cost portfolio of these 100 stocks produces a nearly identical return pattern over the quant crisis period. 42 Although the return patterns are nearly identical, there is a large difference in scale between our Fig. 8 and Pedersen’s (2009) Figure 1A. This occurs because we set the position to 100% long financed by 100% short (matching Asness, Moskowitz, and Pedersen (2013)). In contrast, Pedersen scales his strategy to have annual volatility of 6%.

  

 

51  

value/high momentum stock has 4.3% of its shares held by hedge funds versus 4.5% for the typical

growth/low momentum stock.43

[Insert Table 8 about here]

If the quant crisis return pattern is driven by hedge funds exerting negative externalities on each

other, we expect that hedge funds will liquidate the value/high momentum stocks to a much greater

extent than the growth/low momentum stocks. That is, if the return patterns revealed in Fig. 8 are

driven by hedge funds trampling each other running for the exits from value/high momentum

stocks (but not growth/low momentum stocks) over August 6-9, then hedge fund ownership of

value/high momentum stocks should sharply decline over the quarter. (Alternatively, if hedge funds

fled both value/high momentum and growth/low momentum stocks over this week, then the

performance of the long-short portfolio (i.e., Fig. 8) should be flat over August 6-9.) Panel C reports

the mean and median net number of hedge funds buying (i.e., number of hedge funds buying the

stock less the number selling) for stocks in each portfolio over the third quarter of 2007. Panel D

reports analogous statistics where hedge fund “demand” is measured as the change in the fraction of

outstanding shares held by hedge funds (in aggregate). The quarterly 13(f) data, of course, do not

allow us to examine the exact timing of these trades (because Panels A and B focus on levels, not

changes, this limitation does not apply to Panels A and B). It is possible that some hedge funds, for

instance, sold value/high momentum stocks on August 8th or 9th only to buy them back a few days

later. 44 Nonetheless, based on the available data, we find little evidence that hedge funds, in

aggregate, exited value/high momentum stocks to a greater extent than growth/low momentum

                                                            43 We form portfolios at the end of June so we can measure hedge fund ownership at the time of portfolio formation. Clearly (see Fig. 8), these portfolios are impacted by the quant crisis. Nonetheless, readers may be concerned that a stock defined as value/high momentum (or growth/low momentum) at the end of June may not be defined as such at the beginning of August. As a robustness check we also examined these same 100 stocks based on a beginning of August formation period, and find 79 of the 100 stocks remain in the portfolio, i.e., the value/momentum strategy Asness, Moskowitz, and Pedersen (2013) examine is a relatively low turnover strategy. 44 This interpretation, however, is inconsistent with a funding shock explanation unless the shock was extremely short-lived.

  

 

52  

stocks. More hedge funds were selling than buying both value/high momentum and growth/low

momentum stocks (consistent with Table 7). For the typical (median) stock, hedge funds net sold

0.6% of the outstanding shares over the quarter for both value/high momentum and growth/low

momentum stocks (Panel D).

Note also that during the crisis period a hedge fund with a larger (long) position in the

growth/low momentum portfolio than the value/high momentum portfolio should benefit (at least

on the long side of their portfolio) from the crisis. Thus, we also compute the fraction of hedge

funds (that hold at least one position in the long or short portfolio at the beginning of July 2007)

with a greater weight in the growth/low momentum portfolio than the value/high momentum

portfolio. Of the 482 hedge funds, 62% have greater exposure to the growth/low momentum

portfolio than the value/high momentum portfolio at the beginning of July 2007.45

If hedge funds, in aggregate, were not crowding into value/high momentum stocks and

subsequently running for the exit from these stocks during the quant crisis, who was? To examine

this question, we compute each institution’s total dollar value position in both the value/high

momentum portfolio and the growth/low momentum portfolio. Because we are interested in the

aggregate impacts that create the observed patterns in Fig. 8, we focus on total dollar value positions

rather than percentage exposures. Panel A in Table 9 reports the ten managers with the largest dollar

value difference between their investment in the value/high momentum portfolio and the

growth/low momentum portfolio. For comparison, the last two rows report the comparable totals

for all hedge funds in aggregate, and for the subsample we obtain when limiting our analysis solely

to hedge funds with a greater position in the value/high momentum portfolio (relative to the

growth/low momentum portfolio). We view hedge funds with a greater position in the value/high

                                                            45 The value/high momentum portfolio has a total capitalization of $971 billion versus $927 billion for the growth/low momentum portfolio. Mean differences in market capitalizations across the two portfolios are not statistically meaningful (untabulated).

  

 

53  

momentum portfolio as our subsample of hedge funds with a “net long exposure to the quant

crisis.”

[Insert Table 9 about here]

The top row in Panel A reveals that Barclays Bank had approximately $16 billion more invested

in the value/high momentum portfolio than the growth/low momentum portfolio at the beginning

of July 2007. In total, the top ten largest relative value/high momentum institutions had

approximately $72 billion more in the value/high momentum portfolio than the growth/low

momentum portfolio. In contrast, all hedge funds had $7 billion more invested in the growth/low

momentum portfolio than the value/high momentum portfolio (second to last row in Panel A).

Even if we limit our sample to solely consider the hedge funds with a greater exposure to the

value/high momentum portfolio (than the growth/low momentum portfolio), in aggregate, these

hedge funds still had less dollar “imbalance” than Barclays Bank alone (last row of Panel A).

Panel B in Table 9 reports the ten managers that moved the greatest total dollar value from the

value/high momentum portfolio to the growth/low momentum portfolio over the third quarter of

2007 (i.e., based on the difference in their net purchases of each portfolio over the quarter).

Specifically, the first two columns report the total dollar value of their net purchases of stocks in the

value/high momentum portfolio and stocks in the growth/low momentum portfolio, respectively.

The third column reports the difference between the first two columns. To ensure values are driven

by trades and not returns, we compute the change in dollar value as the beginning of quarter price

times the difference between end of quarter shares held and beginning of quarter shares held. The

second to last row reveals that hedge funds (in aggregate) exited markets in the third quarter of 2007

(consistent with Table 7). Hedge funds, as a group, however, sold more of the growth/low

momentum portfolio than the value/high momentum portfolio. The last row reveals that, even if we

limit the sample to hedge fund managers with a net long exposure to the quant crisis, sales by these

  

 

54  

“exposed” managers accounted for a relatively small fraction of the imbalance. For example,

Barclays Bank’s sales of value/high momentum stocks alone total nearly twice the total sales from

these exposed hedge funds, in aggregate (first column, first and last rows in Panel B).

We do not claim that some hedge funds did not contribute to the quant crisis. Rather, our point

is that while a zero cost value/high momentum strategy suffered greatly during the quant crisis,

hedge funds were as likely to be long growth/low momentum stocks as value/high momentum

stocks. Thus, these hedge funds would have (relatively) benefited from the crisis. Moreover,

although our examination of changes in positions is limited to quarterly data, we find no evidence

that hedge funds’ sales of value/high momentum stocks were greater than their sales of growth/low

momentum stocks in the third quarter of 2007.

8. Conclusions

The role of hedge funds in U.S. equity markets has dramatically increased over the past 15 years.

Contrary to the classical view that rational speculators move to correct mispricing, the popular press,

regulators, theoretical models, and recent empirical studies suggest that hedge fund crowds can

systematically drive equity prices from value. Stein (2009) models two specific negative externalities

that hedge funds exert on each other and asset prices as a result of their crowded trades. First, if

hedge funds follow similar strategies without a fundamental anchor, then hedge funds crowding into

and out of the same stocks will drive prices from value as hedge funds mistakenly interpret price

shocks resulting from aggregate hedge fund demand as a fundamental shock. Second, hedge funds

exert negative externalities on each other during a funding crisis as their deleveraging drives prices of

commonly held stocks away from fundamentals inducing further deleveraging, and so on—a loss

spiral.

  

 

55  

We contribute to this debate by providing the first direct examination of hedge fund crowds.

Contrary to apparently common beliefs, hedge funds hold long equity portfolios that are largely

independent of one another, relative to other types of institutional investors. A typical pair of hedge

funds holds less than one security in common, accounting for less than one-third of one percent of

their portfolios. As a benchmark, the typical similar size non-hedge fund institution pair holds nine

securities in common, accounting for more than 5% of their portfolios.

Although hedge funds exhibit relatively little portfolio overlap, each quarter a number of

securities experience substantial hedge fund demand shocks. Inconsistent with the hypothesis that

large hedge fund crowds drive prices from fundamental values, we find no evidence that these hedge

fund demand shocks drive mispricing. In fact, we find the opposite—securities heavily purchased by

hedge funds subsequently outperform those heavily sold by hedge funds.

We also find little evidence that hedge funds exert negative externalities on each other or stock

prices during stress events. Specifically, we find: (i) hedge funds that have greater overlap with the

aggregate hedge fund portfolio do not liquidate more of their portfolio during stress events, (ii) the

long equity portfolios of hedge funds with greater overlap do not suffer worse returns during stress

events than those with low portfolio overlap, (iii) the relation between hedge fund demand shocks

and contemporaneous returns does not increase during stress events, and (iv) the relation between

hedge fund demand shocks and subsequent returns remains positive during stress events.

As noted in the introduction, we do not claim that hedge funds never crowd into the same

stocks nor that such crowding does not sometimes exert negative externalities on other hedge funds

or stock prices. Nonetheless, our study—based on the first broad long-term examination of hedge

funds’ crowded trades—is inconsistent with the hypotheses that most hedge funds exhibit strong

crowding propensities (as one should expect if they follow the same strategies), and that hedge fund

crowds systematically exert negative externalities on each other and make equity markets less

  

 

56  

efficient. Rather, our results suggest that hedge funds, in aggregate, improve market efficacy and

contribute to the efficient allocation of resources in the real economy.

  

 

  

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Table 1 Descriptive statistics for hedge funds and non-hedge fund institutions (June 1998 through December 2011).

Panel A reports the time-series descriptive statistics for the number of hedge funds and non-hedge fund institutions filing 13(f) reports between June 1998 and December 2011 (n=55 quarters). Panel B reports the time series average of the cross-sectional mean and median portfolio characteristics of hedge funds, non-hedge fund institutions, and a size-matched sample of non-hedge fund institutions. The t-statistics (reported in parentheses) are based on the time-series of the 55 means or medians and Newey-West (1987) standard errors. The size-matched non-hedge fund sample is selected (without replacement) for each hedge-fund quarter observation as the non-hedge fund closest in total beginning of quarter long equity portfolio value.

Panel A: Time-series descriptive statistics of 13(f) institutional investors

Mean Median Minimum Maximum

Number of hedge funds 350 400 114 610

Number of non-hedge funds 1,854 1,794 1,353 2,413

Number of institutions 2,203 2,194 1,479 2,893

%hedge funds 15.11% 16.46% 7.40% 21.43%

Panel B: Time-series average of cross-sectional means and medians

Mean Median

Hedge funds

Non-hedge funds

Matched non-hedge funds

Difference (hedge fund-

matched) Hedge funds

Non-hedge funds

Matched non-hedge funds

Difference (hedge fund-

matched) No. securities 84 230 129 -45

(-22.88)*** 37 88 71 -34

(-35.77)*** Portfolio size $681M $4,259M $681M -$0.098M

(-1.03) $202M $321M $202M -$0.110M

(-2.59)**

  

 

  

Table 2 Overlap in hedge fund portfolios and similar size non-hedge fund institution portfolios.

Each quarter between June 1998 and December 2011 (n=55 quarters), we compute the number of securities held in common for every pair of hedge funds and every pair of a size-matched sample of non-hedge fund institutions. The first two rows of Panel A report the time-series average of the cross-sectional descriptive statistics for the number of securities in common. The mean number of securities held by each pair is given in parentheses. The third row reports the difference in their mean values. The last two columns report the number of quarters the difference is positive (i.e., hedge fund pairs average more securities in common than non-hedge fund institutions) and the number of quarters the difference is negative, respectively, over the 55 quarters. The number of quarters the difference is statistically significant at the 5% level is reported in brackets (based on a t-test for difference in means). Panel B reports the Cremers and Petajisto (2009) “active share” portfolio independence measure (the sum of the absolute value of the differences in portfolio weights divided by two, see Eq. (1)) across every hedge fund pair and every matched-sample non-hedge fund institution pair. Panel C reports the cosine similarity (see Eq. (2)) of overlap in portfolio weights for every hedge fund pair and every pair of matched sample non-hedge fund institutions. Panel D reports the cosine similarity for hedge funds versus the matched sample of non-hedge fund institutions when examining positive active weights (wk,h,t > wk,mkt,t, see Eq. (3)).

95th

percentile Median 5th

percentile Average

Number positive

[significant]

Number negative

[significant] Panel A: Number of common securities

(Number of securities held) Hedge funds

(No. securities held) 16.000 (278)

0.800 (51)

0.000 (36)

4.131

Non-hedge funds (No. securities held)

74.982 (319)

9.000 (103)

0.000 (54)

20.865

Difference

-16.734 0 [0]

55 [55]

Panel B: Active share

Hedge funds 1.000 0.997 0.904 0.978 Non-hedge funds 1.000 0.946 0.645 0.895 Difference

0.084 55

[55] 0

[0]

Panel C: Cosine similarity in portfolio weights

Hedge funds 0.153 0.002 0.000 0.031 Non-hedge funds 0.509 0.061 0.000 0.139 Difference

-0.108 0

[0] 55

[55]

Panel D: Cosine similarity in active weights|Manager’s weight>market weight

Hedge funds 0.123 0.001 0.000 0.024 Non-hedge funds 0.271 0.022 0.000 0.066 Difference

-0.042 0

[0] 55

[55]

  

 

  

Table 3 Overlap in same and different strategy hedge fund portfolios.

Based on a sample of 180 hedge funds companies (as identified by Thomson Financial) that file 13(f) reports and are included in the Hedge Fund Research database, we compare portfolio overlap for managers following the same strategies (as defined by Hedge Fund Research: Equity Hedge, Event-Driven, Macro, and Relative Value) and managers following different strategies. Specifically, each quarter between June 1998 and December 2011 (n=55 quarters), we compute the number of securities held in common for every pair of same strategy hedge funds and every pair of different strategy hedge funds. The first two rows of Panel A report the time-series average of the cross-sectional descriptive statistics for the number of securities in common. The mean number of securities held by each pair is given in parentheses. The third row reports the difference in their mean values. The last two columns report the number of quarters the difference is positive (i.e., same strategy hedge fund pairs average more securities in common than different strategy hedge fund pairs) and the number of quarters the difference is negative, respectively, over the 55 quarters. The number of quarters the difference is statistically significant at the 5% level is reported in brackets (based on a t-test for difference in means). Panel B reports the Cremers and Petajisto (2009) “active share” portfolio independence measure (the sum of the absolute value of the differences in portfolio weights divided by two, see Eq. (1)) across every same strategy hedge fund pair and every different strategy hedge fund institution pair. Panel C reports the cosine similarity (see Eq. (2)) of overlap in portfolio weights for every same strategy hedge fund pair and every different strategy hedge fund pair. Panel D reports the cosine similarity for same strategy hedge funds versus different strategy hedge fund pairs when examining positive active weights (wk,h,t > wk,mkt,t, see Eq. (3)).

  

 

  

Table 3 (continued) Overlap in same and different strategy hedge fund portfolios.

95th

percentile Median 5th

percentile Average

Number positive

[significant]

Number negative

[significant] Panel A: Number of common securities

(Number of securities held) Same strategy

(No. securities held) 28.109 (273)

1.855 (82)

0.000 (42)

6.949

Different strategies (No. securities held)

28.264 (319)

0.945 (65)

0.000 (43)

6.405

Difference

0.544 42 [10]

13 [0]

Panel B: Active share Same strategy 1.000 0.989 0.853 0.966 Different strategies 1.000 0.996 0.900 0.978 Difference

-0.012 1

[0] 54

[50]

Panel C: Cosine similarity in portfolio weights

Same strategy 0.227 0.010 0.000 0.048 Different strategies 0.155 0.003 0.000 0.032 Difference

0.016 54

[50] 1

[0]

Panel D: Cosine similarity in active weights|Manager’s weight>market weight

Same strategy 0.189 0.006 0.000 0.039 Different strategies 0.116 0.001 0.000 0.023 Difference

0.015 54

[50] 1

[0]

  

 

  

Table 4 Estimating intraquarter trading by hedge funds.

For each hedge fund quarter we partition holdings into observable entries and exits, adjustments to existing positions, and stocks held but not traded (summing to 100% of the portfolio, see Eq. (4)). Panel A reports the time-series mean of the cross-sectional descriptive statistics for these measures. Using Eqs. (5) and (6) (see Appendix C for details), we estimate, for each hedge fund quarter, (i) the fraction of unobservable (intraquarter) entry/exit trades to all entry/exit trades from observable entry/exit trades, and (ii) the fraction of unobservable (intraquarter) entry/exit trades to all trades. Panel B reports the time-series mean of the cross-sectional descriptive statistics for these estimates.

Panel A: The distribution of hedge fund positions

Mean 95th percentile Median 5th percentile Observed entries and exits/holdings 0.356 0.739 0.336 0.041 Observed adjustments/holdings 0.472 0.233 0.500 0.566 No trade/holdings 0.172 0.027 0.163 0.393

Panel B: Estimated fraction of unobservable intraquarter trades to all entries and exits or all trades

Mean 95th percentile Median 5th percentile Estimated unobservable entries and exits as % of all entries and exits

0.205 0.452 0.180 0.021

Estimated unobservable entries and exits as % of all trades

0.139 0.416 0.115 0.005

  

 

  

Table 5 Hedge fund demand, contemporaneous returns, and subsequent returns.

Each stock-quarter we compute “hedge fund demand” as the number of hedge funds buying the stock less the number selling the stock. We then sort stocks, at the beginning of each quarter, into capitalization quintiles, and form five portfolios—stocks with more hedge fund buyers than sellers are partitioned into two groups by hedge fund demand, stocks with more sellers than buyers are partitioned into two groups by hedge fund demand, and the final group consists of stocks with an equal number of hedge fund buyers and sellers (usually zero of both). We then re-aggregate over capitalization quintiles to form capitalization-stratified portfolios of hedge fund demand. We then compute the cross-sectional average return for securities within each portfolio and the intercept from a time-series regression of the portfolio return on market, size, value, and momentum factors. We use Jegadeesh and Titman’s (1993) calendar aggregation method to compute quarterly returns from overlapping observations in the four quarter holding period. The first and second columns report the time-series mean (n=55 quarters) of the number of stocks within each portfolio and time-series mean of the cross-sectional average hedge fund demand for stocks within that portfolio. The remaining columns report mean raw or benchmark adjusted quarterly returns the same quarter as institutional demand shock (q=0), the following quarter (q=1), and the following year (q=1 to 4). The last row reports the difference in mean returns (or benchmark adjusted returns) for stocks heavily purchased by hedge funds and those heavily sold by hedge funds with associated t-statistics in parentheses (computed with Newey-West (1987) standard errors). Statistical significance at the 1%, 5%, and 10% level are indicated by ***, **, and *, respectively.

Mean quarterly return Benchmark adjusted returns

Hedge fund demand:

No. of stocks

Hedge fund demandq=0

Returnq=0 Returnq=1 Returnq=1 to 4 Adjusted returnq=0

Adjusted returnq=1

Adjusted returnq=1 to 4

Heavy sell 638 -5.158 1.873 1.671 2.472 0.039 -0.463 0.397Sell 767 -1.500 1.118 2.093 2.612 -0.881 -0.342 0.405No change 1,404 0.000 1.040 2.672 2.625 -0.805 0.351 0.453Buy 819 1.510 3.347 3.442 3.060 1.163 1.019 0.767Heavy buy 713 5.372 8.125 4.510 3.133 5.628 2.157 0.947

Heavy buy-Heavy sell

6.252 (3.15)***

2.839 (5.14)***

0.661 (2.80)***

5.588 (3.22)***

2.620 (5.28)***

0.550 (3.13)***

  

 

  

Table 6 Hedge fund demand, contemporaneous returns, and subsequent returns (by capitalization).

Each stock-quarter we compute “hedge fund demand” as the number of hedge funds buying the stock less the number selling the stock. We then sort stocks, at the beginning of each quarter, into capitalization quintiles, and form five portfolios—stocks with more hedge fund buyers than sellers are partitioned into two groups by hedge fund demand, stocks with more sellers than buyers are partitioned into two groups by hedge fund demand, and the final group consists of stocks with an equal number of hedge fund buyers and sellers (usually zero of both). The first and second columns report the time-series mean (n=55 quarters) of the number of stocks within each portfolio and time-series mean of the cross-sectional average hedge fund demand (number buyers-number sellers) for stocks within that portfolio. We then compute the intercept from a time-series regression of the equal-weighted portfolio return on market, size, value, and momentum factors. We use Jegadeesh and Titman’s (1993) calendar aggregation method to compute quarterly returns from overlapping observations in the four quarter holding period. The last three columns report the four factor intercepts for securities within each capitalization-hedge fund demand portfolio. The last row in each panel reports the difference in four factor intercepts for stocks heavily purchased by hedge funds and those heavily sold by hedge funds and associated t-statistics (computed with Newey-West (1987) standard errors). Statistical significance at the 1%, 5%, and 10% level are indicated by ***, **, and *, respectively.

  

 

  

Table 6 (continued) Hedge fund demand, contemporaneous returns, and subsequent returns (by capitalization).

Hedge fund demand: No. of stocks Hedge fund demandq=0

Adjusted returnq=0

Adjusted returnq=1

Adjusted returnq=1 to 4

Panel A: Small stocks (n=35 quarters; 1.70% of hedge fund trades)

Heavy sell 53 -2.578 -1.213 0.009 0.877Sell 117 -1.000 -0.868 -0.297 0.251No change 469 0.000 -0.302 0.471 0.596Buy 126 1.000 5.753 0.836 0.597Heavy buy 60 2.543 18.372 1.761 0.744Heavy buy-Heavy sell

19.585(10.81)***

1.752 (0.93)

-0.134(-0.14)

Panel B: Capitalization quintile 2 (n=54 quarters; 5.38% of hedge fund trades) Heavy sell 89 -2.808 -2.168 -0.918 0.871Sell 122 -1.014 -2.249 0.074 0.913No change 501 0.000 -1.343 0.403 0.441Buy 133 1.021 4.959 1.742 1.339Heavy buy 110 2.974 22.255 3.751 1.219Heavy buy-Heavy sell

24.423(3.53)***

4.669 (3.46)***

0.349(0.48)

Panel C: Capitalization quintile 3 (n=55 quarters; 12.18% of hedge fund trades) Heavy sell 125 -3.798 -2.064 -0.777 -0.113Sell 175 -1.247 -2.177 -0.852 0.329No change 329 0.000 -1.753 -0.348 0.049Buy 182 1.242 1.377 1.506 0.860Heavy buy 149 3.990 10.650 2.971 1.110Heavy buy-Heavy sell

12.714(3.10)***

3.747 (4.69)***

1.223 (2.53)**

Panel D: Capitalization quintile 4 (n=55 quarters; 23.03% of hedge fund trades) Heavy sell 183 -4.979 -0.028 -0.658 0.381Sell 186 -1.533 -1.357 -0.452 0.162No change 191 0.000 -0.765 -0.149 -0.144Buy 201 1.515 -0.269 0.574 0.433Heavy buy 198 5.209 3.186 2.233 1.183Heavy buy-Heavy sell

3.214(1.48)

2.891 (4.18)***

0.802(2.31)**

Panel E: Large capitalization stocks (n=55 quarters; 57.71% of hedge fund trades) Heavy sell 207 -8.097 2.200 -0.499 0.472Sell 213 -2.236 0.885 -0.350 0.255No change 94 0.000 -0.319 -0.121 0.218Buy 226 2.308 -1.045 0.675 0.588Heavy buy 220 8.749 -0.601 1.530 0.945Heavy buy-Heavy sell

-2.801

(-2.12)** 2.030

(4.33)*** 0.473(1.67)

  

 

  

Table 7 Identifying hedge fund stress periods.

Each quarter between June 1998 and December 2011 we compute five measures of hedge fund stress: (i) the percent change in the dollar value of aggregate hedge fund equity positions over the quarter, (ii) the fraction of hedge funds reducing their equity portfolio during the quarter, (iii) the fraction of hedge funds reducing their equity portfolio by more than 20% during the quarter, (iv) the quarterly return on the Hedge Fund Research Fund-Weighted Composite Index (an equal-weighted hedge fund return index, net of fees, comprised of over 2,000 hedge funds), and (v) the lowest monthly average performance percentile rank for eight HFRI indices. The second to last column reports a composite ranking of hedge fund stress based on the average percentile rank across the five measures. The last column reports, for the March 2005-September 2009 subperiod, the percentage change in gross hedge fund leverage from Ang, Gorovyy, and van Inwegen (2011). Highlighted cells indicate the top tenth percentile of stress based on that measure (i.e., the six most extreme observations for the first five measures, and the two most extreme observations for the leverage measure).

  

 

  

Table 7 (continued) Identifying hedge fund stress periods.

Quarter

%Chg. in agg. HF equity

%HF selling equities

%HF selling >20%

8 HFRI ave. return p-tile

Agg. HF return index

Aggregate HF stress ranking

%Chg. gross HF leverage

Jun-98 0.032 0.325 0.140 0.303 -0.013 33 Sep-98 -0.043 0.474 0.233 0.013 -0.088 3.5 Dec-98 0.057 0.435 0.183 0.414 0.079 38 Mar-99 0.091 0.317 0.135 0.210 0.041 43.5 Jun-99 0.050 0.439 0.136 0.530 0.091 47.5 Sep-99 0.020 0.432 0.151 0.444 0.007 32 Dec-99 0.050 0.432 0.130 0.463 0.149 50 Mar-00 -0.002 0.417 0.166 0.419 0.078 35.5 Jun-00 -0.112 0.456 0.207 0.317 -0.012 11 Sep-00 0.092 0.359 0.100 0.376 0.019 47.5 Dec-00 0.002 0.485 0.302 0.218 -0.033 7 Mar-01 0.154 0.359 0.160 0.375 -0.005 37 Jun-01 0.062 0.409 0.144 0.406 0.035 40.5 Sep-01 0.030 0.456 0.235 0.278 -0.040 10 Dec-01 -0.017 0.472 0.181 0.529 0.059 26.5 Mar-02 -0.030 0.371 0.127 0.215 0.016 24 Jun-02 0.110 0.430 0.175 0.285 -0.016 26.5 Sep-02 0.100 0.432 0.189 0.128 -0.039 16 Dec-02 0.008 0.466 0.216 0.401 0.025 18 Mar-03 0.117 0.321 0.118 0.388 0.008 49 Jun-03 -0.028 0.441 0.134 0.595 0.077 39 Sep-03 0.025 0.436 0.160 0.517 0.044 35.5 Dec-03 -0.035 0.461 0.178 0.536 0.055 29 Mar-04 0.134 0.365 0.090 0.430 0.037 52 Jun-04 0.054 0.412 0.135 0.211 -0.010 28 Sep-04 0.038 0.431 0.131 0.273 0.008 30 Dec-04 0.045 0.441 0.145 0.540 0.054 42 Mar-05 0.128 0.350 0.109 0.245 0.007 40.5 0.017 Jun-05 0.069 0.460 0.176 0.145 0.011 19 0.032 Sep-05 0.093 0.369 0.094 0.499 0.051 53.5 -0.017 Dec-05 -0.010 0.548 0.183 0.195 0.021 12 0.015 Mar-06 0.081 0.344 0.110 0.498 0.060 55 0.057 Jun-06 0.020 0.477 0.209 0.294 0.000 14 -0.083 Sep-06 0.034 0.472 0.160 0.386 0.010 22 0.008 Dec-06 0.039 0.502 0.150 0.665 0.054 34 -0.004 Mar-07 0.107 0.344 0.100 0.514 0.028 53.5 0.080 Jun-07 0.116 0.394 0.111 0.439 0.046 51 0.058 Sep-07 -0.096 0.487 0.207 0.176 0.012 9 -0.137 Dec-07 -0.016 0.489 0.224 0.123 0.011 8 -0.060 Mar-08 0.054 0.454 0.223 0.135 -0.034 13 -0.050 Jun-08 0.052 0.475 0.188 0.311 0.022 21 0.096 Sep-08 -0.146 0.616 0.370 0.039 -0.096 1 -0.188 Dec-08 -0.108 0.633 0.440 0.127 -0.092 2 -0.217 Mar-09 0.145 0.462 0.226 0.286 0.003 20 -0.004 Jun-09 0.075 0.437 0.198 0.615 0.092 46 0.058 Sep-09 0.079 0.461 0.175 0.695 0.067 43.5 0.010 Dec-09 0.030 0.470 0.159 0.442 0.026 31 Mar-10 0.087 0.409 0.119 0.380 0.024 45 Jun-10 -0.038 0.505 0.227 0.109 -0.027 5 Sep-10 0.012 0.488 0.172 0.414 0.050 23 Dec-10 -0.016 0.551 0.212 0.299 0.053 15 Mar-11 0.011 0.443 0.147 0.397 0.017 25 Jun-11 0.025 0.435 0.154 0.206 -0.009 17 Sep-11 -0.013 0.516 0.260 0.080 -0.068 3.5 Dec-11 -0.080 0.680 0.311 0.229 0.009 6

  

 

  

Table 8 Hedge fund ownership and trading of value/momentum portfolio in the quant crisis.

The value/high momentum (growth/low momentum) stocks consist of the 50 largest capitalization stocks with the highest (lowest) average book-to-market ratio ranking and lag 12 month return ranking as of the end June 2007. Panel A reports the mean and median number of hedge funds holding each stock, on average, in the portfolio. Panel B reports analogous statistics for the mean fraction of outstanding shares held by hedge funds. Panel C reports statistics for the net number of hedge fund buyers (i.e., buyers-sellers) for each stock and Panel D reports the analogous statistics for the net fraction of shares purchased by hedge funds in the third quarter of 2007. The third row in each panel reports the difference and associated t-statistics (from a difference in means test) and z-statistics (from a difference in medians test) of the null hypothesis that the values in the first two rows do not differ.

Mean (t-statistic)

Median (z-statistic)

Panel A: Number of hedge fund positions Value/high momentum stocks 36.82 34.50 Growth/low momentum stocks 41.28 39.50 Value/high mom. – Growth/low mom.

-4.46 (-1.19)

-5.00 (-1.04)

Panel B: Fraction of shares held by hedge funds Value/high momentum stocks 0.060 0.043 Growth/low momentum stocks 0.056 0.045 Value/high mom. – Growth/low mom.

0.004 (0.36)

-0.002 (0.00)

Panel C: Net number of hedge fund buyers over quarter (July-September 2007) Value/high momentum stocks -5.90 -4.50 Growth/low momentum stocks -7.90 -7.00 Value/high mom. – Growth/low mom.

2.00 (1.06)

2.50 (1.19)

Panel D: Fraction of shares purchased by hedge funds over quarter (July-September 2007) Value/high momentum stocks -0.007 -0.006 Growth/low momentum stocks -0.008 -0.006 Value/high mom. – Growth/low mom.

0.001 (0.14)

-0.001 (-0.40)

  

 

  

Table 9 Managers with largest value/high momentum bias and trading around the quant crisis.

The value/high momentum (growth/low momentum) stocks consist of the 50 largest capitalization stocks with the highest (lowest) average of book-to-market ratio ranking and lag 12 month return ranking as of the end June 2007. Panel A reports the ten managers with the largest dollar value difference in the value/high momentum portfolio and the growth/low momentum portfolio. The last two rows report the analogous figures for all hedge funds in aggregate and just those hedge funds with a positive value/high momentum bias (i.e., dollar value of value/high momentum holdings greater than dollar value of growth/low momentum holdings). Panel B reports the ten managers that had the largest difference in the dollar value of their trading out of the value/high momentum portfolio and the dollar value of their trading into the growth/low momentum portfolio. All values are in millions of dollars. The dollar value of trading in a stock is computed as the change in shares held times beginning of quarter prices such that the values are not impacted by returns. The number of “all” hedge funds in Panels A and B differs because Panel A includes all hedge funds with a position in either portfolio at the beginning of July 2007, while Panel B includes all hedge funds with a position in either portfolio at either the beginning of July 2007 or the end of September 2007.

  

 

  

Table 9 (continued) Managers with largest value/high momentum bias and trading around the quant crisis.

Panel A: Managers with largest ($ value) value/high momentum difference Value/high

momentum ($mil)Growth/low

momentum ($mil) Difference

(V/HM – G/LM) Barclays Bank PLC 44,090 27,632 16,458 AXA Financial 24,461 10,360 14,101 Dodge & Cox 11,739 4,656 7,083 State Street Corp. 30,958 25,075 5,884 NWQ Investment Mgmt. 5,682 10 5,672 Goldman Sachs & Company 14,935 9,489 5,446 Barrow Hanley, Mewhinney & Straus 7,217 2,082 5,135 MSDW & Company 9,218 5,142 4,076 Franklin Resources 9,454 5,444 4,011 Dimensional Fund Advisors, LP 4,518 518 3,999 All hedge funds (n=482) 34,624 41,542 -6,919 Value/momentum hedge funds (n=185) 22,754 8,906 13,848

Panel B: Managers with largest ($ value) shifts from value/high momentum to growth/low momentum Net value/high

momentum purchases ($mil)

Net growth/low momentum

purchases ($mil)

Difference (V/HM-G/LM)

Barclays Bank PLC -4,540 1,096 -5,636 Capital Research & Mgmt. -1,703 3,052 -4,755 T. Rowe Price Associates -570 1,372 -1,943 Barrow Hanley, Mewhinney & Straus -1,345 105 -1,450 Goldman Sachs & Company -582 850 -1,432 Legg Mason -572 243 -816 Calamos Advisors -64 522 -586 Grantham Mayo Van Otterlo & Cc. -265 284 -549 Harris Associates -15 532 -547 State Street Corp. 822 1,350 -528 All hedge funds (n=508) -2,875 -6,256 3,381 Value/momentum hedge funds (n=185) -2,345 283 -2,628

  

 

  

 

Fig. 1. Hedge funds in 13(f) data over time (1998-2011). The solid line depicts the fraction of 13(f) institutions identified as hedge fund companies (left hand scale). The broken line depicts the number of 13(f) institutions identified as hedge fund companies (right hand scale).

  

 

  

       

Fig. 2. Cumulative distribution of cosine similarity and active share for hedge funds and size-matched non-hedge fund institutions. Each quarter we compute the cosine similarity (see Eq. (2)) and active share (see Eq. (1)) of portfolio weights between every pair of hedge funds and every pair of size-matched non-hedge fund institutions. In total, we compute just over four million observations for both hedge fund pairs and the matched non-hedge fund pairs. The graph on the left (2A) depicts the cumulative fraction of hedge fund pairs (broken line) and non-hedge fund pairs (solid line) with cosine similarity less than a given level. The “intercepts” on the left-hand side of the graphs indicate that 21% of non-hedge fund pairs have zero cosine similarity (i.e., no overlap in their portfolios) versus 48% of hedge fund pairs. Analogously, drawing a vertical line up from the 10% cosine similarity point on the horizontal axis, reveals that 59% of non-hedge fund pairs and 91% of hedge fund pairs have cosine similarity less than 10%. The graph on the right (2B) depicts the cumulative fraction of hedge fund pairs (broken line) and non-hedge fund pairs (solid line) with active share greater than a given level. The “intercepts” on the left-hand side of the graphs indicate that 21% of non-hedge fund institution pairs have active share of one (i.e., no overlap in their portfolios) versus 48% of hedge fund pairs. Drawing a vertical line from the 90% active share point on the horizontal axis, reveals that 62% of non-hedge fund pairs and 96% of hedge fund pairs have active share greater than 90%.

  

 

  

Fig. 3. Average cosine similarity for hedge fund pairs over time. Each quarter we compute the cosine similarity (see Eq. (2)) of portfolio weights between every pair of hedge funds. The graph depicts the evolution of average cosine similarity for hedge fund pairs over time.

  

 

  

Fig. 4. Number and fraction of hedge funds invested in the “most crowded” stocks. Each quarter, we use 13(f) reports to compute the average number and the fraction of hedge funds holding the most crowded stocks for the 1, 10, 50, and 100 stocks with the greatest number of hedge fund shareholders. For instance, at the end of 2011, the 100 most crowded hedge fund stocks were held by 11.5% of hedge funds filing 13(f) reports (bottom line, extreme right-hand observation in Fig. 4A) and averaged 52 hedge fund shareholders (bottom line, extreme right-hand observation in Fig. 4B).

0%

5%

10%

15%

20%

25%

30%

35%

Jun-98 Jun-99 Jun-00 Jun-01 Jun-02 Jun-03 Jun-04 Jun-05 Jun-06 Jun-07 Jun-08 Jun-09 Jun-10 Jun-11

(4A

) F

ract

ion

of

Hed

ge F

und

s H

oldi

ng

Time

Top stock

Top 100 stocks

Top 50 stocks

Top 10 stocks

0

20

40

60

80

100

120

140

160

Jun-98 Jun-99 Jun-00 Jun-01 Jun-02 Jun-03 Jun-04 Jun-05 Jun-06 Jun-07 Jun-08 Jun-09 Jun-10 Jun-11

(4B

) N

um

ber

of

Hed

ge F

un

ds

Hol

din

g

Time

Top stock

Top 100 stocks

Top 50 stocks

Top 10 stocks

  

 

  

Fig. 5. How portfolio overlap explains hedge fund trading in high and low stress periods. Each quarter we cross-sectionally regress the percentage change in hedge fund managers’ equity holdings (net trades/portfolio value) on portfolio size (natural logarithm of equity portfolio value), the hedge fund’s net flows, a dummy variable indicating the use of leverage, and standardized cosine similarity (as a measure of portfolio overlap) with the aggregate hedge fund portfolio (excluding the manager under evaluation). We then sort the 55 quarters (June 1998-December 2011) by “aggregate hedge fund stress” (see Table 7). The bars represent the impact of a one standard deviation increase in cosine similarity on a manager’s trading. Solid bars indicate statistical significance at the 5% level.

-15%

-10%

-5%

0%

5%

10%

15%

20%

2008

0920

0812

1998

0920

1109

2010

0620

1112

2000

1220

0712

2007

0920

0109

2000

0620

0512

2008

0320

0606

2010

1220

0209

2011

0620

0212

2005

0620

0903

2008

0620

0609

2010

0920

0203

2011

0320

0112

2002

0620

0406

2003

1220

0409

2009

1219

9909

1998

0620

0612

2000

0320

0309

2001

0319

9812

2003

0620

0106

2005

0320

0412

1999

0320

0909

2010

0320

0906

1999

0620

0009

2003

0319

9912

2007

0620

0403

2005

0920

0703

2006

03

%C

han

ge M

anag

er's

Eq

uit

y H

oldi

ngs

←High stress quarters Low stress quarters→

  

 

  

Fig. 6. How portfolio overlap explains hedge fund raw and DGTW-adjusted returns in high and low stress periods. Each quarter we cross-sectionally regress hedge fund managers’ long equity portfolio returns (6A) and DGTW-adjusted portfolio returns (6B) on portfolio size (natural logarithm of equity portfolio value), the hedge fund’s net flows, a dummy variable indicating the use of leverage, and standardized cosine similarity (as a measure of portfolio overlap) with the aggregate hedge fund portfolio (excluding the manager under evaluation). Returns are based on their beginning of quarter portfolio. We then sort the 55 quarters (June 1998-December 2011) by “aggregate hedge fund stress” (see Table 7). The bars represent the impact of a one standard deviation increase in cosine similarity on a manager’s beginning of quarter portfolio return. Solid bars indicate statistical significance at the 5% level.

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

2008

0920

0812

1998

0920

1109

2010

0620

1112

2000

1220

0712

2007

0920

0109

2000

0620

0512

2008

0320

0606

2010

1220

0209

2011

0620

0212

2005

0620

0903

2008

0620

0609

2010

0920

0203

2011

0320

0112

2002

0620

0406

2003

1220

0409

2009

1219

9909

1998

0620

0612

2000

0320

0309

2001

0319

9812

2003

0620

0106

2005

0320

0412

1999

0320

0909

2010

0320

0906

1999

0620

0009

2003

0319

9912

2007

0620

0403

2005

0920

0703

2006

03

(6A

) P

ortf

olio

Ret

urn

←High stress quarters Low stress quarters→

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

2008

0920

0812

1998

0920

1109

2010

0620

1112

2000

1220

0712

2007

0920

0109

2000

0620

0512

2008

0320

0606

2010

1220

0209

2011

0620

0212

2005

0620

0903

2008

0620

0609

2010

0920

0203

2011

0320

0112

2002

0620

0406

2003

1220

0409

2009

1219

9909

1998

0620

0612

2000

0320

0309

2001

0319

9812

2003

0620

0106

2005

0320

0412

1999

0320

0909

2010

0320

0906

1999

0620

0009

2003

0319

9912

2007

0620

0403

2005

0920

0703

2006

03

(6B

) D

GT

W-a

djus

ted

Por

tfol

io R

etur

n

←High stress quarters Low stress quarters→

  

 

  

Fig. 7. Coefficients from cross-sectional regressions of contemporaneous and subsequent quarter returns on standardized hedge fund demand shocks and control variables. Each quarter we cross-sectionally regress (see Eq. (11)) current quarter (q=0, Fig. 7A) and subsequent quarter (q+1, Fig. 7B) market adjusted stock returns on the natural logarithm of beginning of quarter capitalization, average monthly turnover during the quarter, idiosyncratic volatility, beta, quarter q=0 standardized net demand by non-hedge fund institutions (number buying the stock less the number selling), and quarter q=0 standardized net hedge fund demand. We then sort the 55 quarters (June 1998-December 2011) by “aggregate hedge fund stress” (see Table 7). The bars represent the relation between a one standard deviation increase in standardized hedge fund demand and returns. Solid bars indicate statistical significance at the 5% level.

-4%

-2%

0%

2%

4%

6%

8%

10%

2008

0920

0812

1998

0920

1109

2010

0620

1112

2000

1220

0712

2007

0920

0109

2000

0620

0512

2008

0320

0606

2010

1220

0209

2011

0620

0212

2005

0620

0903

2008

0620

0609

2010

0920

0203

2011

0320

0112

2002

0620

0406

2003

1220

0409

2009

1219

9909

1998

0620

0612

2000

0320

0309

2001

0319

9812

2003

0620

0106

2005

0320

0412

1999

0320

0909

2010

0320

0906

1999

0620

0009

2003

0319

9912

2007

0620

0403

2005

0920

0703

2006

03

(7A

) D

epen

den

t V

aria

ble:

Sam

e Q

uar

ter

Ret

urn

s

←High stress quarters Low stress quarters→

-1%

0%

1%

1%

2%

2%

3%

2008

0920

0812

1998

0920

1109

2010

0620

1112

2000

1220

0712

2007

0920

0109

2000

0620

0512

2008

0320

0606

2010

1220

0209

2011

0620

0212

2005

0620

0903

2008

0620

0609

2010

0920

0203

2011

0320

0112

2002

0620

0406

2003

1220

0409

2009

1219

9909

1998

0620

0612

2000

0320

0309

2001

0319

9812

2003

0620

0106

2005

0320

0412

1999

0320

0909

2010

0320

0906

1999

0620

0009

2003

0319

9912

2007

0620

0403

2005

0920

0703

2006

03

(7B

) D

epen

den

t V

aria

ble

: Su

bse

qu

ent

Qu

arte

r R

etu

rns

←High stress quarters Low stress quarters→

  

 

  

Fig. 8. Cumulative return to value/momentum strategy during the quant crisis. This figure shows the cumulative return to a market neutral strategy over eight trading days from August 3-14, 2007. The portfolio is a zero cost portfolio—long in the 50 stocks with the highest book-to-market and lag return characteristics, and short in the 50 stocks with the lowest book-to-market and lag return characteristics. The stocks are selected from securities that comprise the top 90% of the total market capitalization.

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

Aug-3 Aug-6 Aug-7 Aug-8 Aug-9 Aug-10 Aug-13 Aug-14

Cum

ulat

ive

Ret

urns