Herding at the Security Level

We now turn to the analysis of herding among hedge fund firms at the security level. First, we introduce the measure that statistically identifies if a given stock exhibits correlated trading from several firms. We then use the measure to obtain results for all trades in our

consider herding for different subsets of trading firms or for different subsets of securities to differentiate among alternative underlying reasons for herding and to gain further insights into the trading by our firms.

2.4.1 LSV Measure

Various measures for herding behavior among money managers were proposed in the lit-erature. The diversity is mainly explained by the different datasets used, which reach from daily stock return data (e.g. Christie and Huang (1995)) to annual ownership data (e.g. Nofsinger and Sias (1999)). On the other hand, different herding measures aim at capturing different kinds of herding. For example, Oehler (1998) puts a special focus on herding into a common benchmark and develops an according measure. Even though all measures have been subject to critique, for quarterly holdings data and the herdingwithin one quarter, the LSV measure has become standard in the herding literature and serves as our main measure. Potential drawbacks and some prominent alternatives will be discussed after introducing the LSV measure.

The 13F filings that we use are filed on a quarterly basis. We follow the common terminology and refer to one particular stockiover one quarter fromt−1 tot, as stock− quarteri,t.

For the trading in a givenstock−quarter_i,t we denote, Bi,t = no. of firms buying stock-quarter_i,t Ni,t = no. of firms trading stock-quarter_i,t. The LSV measure is then defined as,

Hi,t =|p_i,t−E[pi,t]| −E|p_i,t−E[pi,t]|

whereItis the number of all stocks traded by at least one of the firms over the quarter t, andp_i,t is the proportion of firms buying stockiover quartert, among all firms trading stocki. The true expectation of this fractionE(p_i,t) is unknown. As a proxy, the average of pi,t over all i at t is used. Hence, the expected proportion of buyers is the same for all stocks at one quarter, and changes only over time. However, it is not the same for different sets of considered firms, as well as for different subsets of included stocks. Note, that this expectation must not be zero because the firms can be net buyers or net sellers over a given quarter.

The first term in Equation2.4.1captures the absolute deviation of the actual fraction of buyers in stockifrom the expected fraction of buyers. It is positive, even if the regarded trades exhibit cross-sectional temporal independence. Therefore, the second term serves as

an adjustment factor, which is deducted to keep the expectation ofH_i,t at zero under the null hypothesis of independent trading. The adjustment factor is positive and approaches zero as the number of tradersN_i,t grows large.

Under the null hypothesis, the number of firms that are buyers inB_i,tfollows a binomial distribution with intensity E[pi,t]. Given the total number of funds tradingNi,t, and the expected fraction of buyers E[p_i,t], the probability of observing exactly b_i,t funds being buyers, and the adjustment factor are given as

Pr(B_i,t=b_i,t) =

The null hypothesis of independent trading is rejected if H is significantly different from zero because the AF translates random fluctuations to fluctuations around zero. To measure the herding for a given set of firms trading a given set of stocks over a given period, the measures Hi,t are averaged across all included stock-quarters to obtain the overall herding measureH. Differences in means (H) can be tested with t-tests and, as in the earlier papers using the LSV measure (e.g. Lakonishok, Shleifer, and Vishny (1992), Wermers (1999)), t-tests will be used to assess if the null holds.

The measure can be interpreted as the tendency of the considered firms to buy or sell securities together more often than expected under random and independent trading.

For example, a H of 2% means that for a stock-quarter that is traded by 100 firms, on average two more firms either buy or sell the stock-quarter than expected under random and independent trading. Note that if the majority of the included stock-quarters exhibit little or no herding (Hi,t close to zero), an average value of 2% could imply much higher levels of herding for some of the included stock-quarters.

Because the LSV measure captures herding on the buy and on the sell side alike, Grinblatt, Titman, and Wermers (1995)introduced two modified measures to distinguish buy side from sell side herding. The buy side herding measureB and the sell side herding measureS are defined as

B_i,t=H_i,t |p_i,t > E[p_i,t],

S_i,t=H_i,t |p_i,t < E[p_i,t]. (2.7) The two measures represent conditional versions of H. This conditioning implies that the adjustment factors must be calculated separately for both measures to assure that under the null hypothesis the measures are zero in expectation. If herding behavior is identified by the unconditional measure, the relative sizes of the two conditional measures to each other give an indication, whether this herding comes from funds jointly trading into or out of securities. The conditional measures are averaged over security-quarters and over time in the same way as the unconditional measureH.

A critique that applies to most herding measures is that they do not take the size of trades into account. But the definition of herding as correlated trading depends only on the direction of the trades. The trade sizes are, however, of particular importance when potential impacts of herding (e.g. on share prices or overall fund firm performance) rather than the potential underlying reasons for such behavior are analyzed. That is why the strand of the literature that focuses on impacts took various approaches to capture the size of the trades. Lakonishok, Shleifer, and Vishny (1992)) for example augment the analysis by additional size measures. An adequate measurement of the size and especially of the significance of one trade for an overall stock portfolio prove difficult, when neither the precise time (price) of the trade within the quarter, nor the benchmark, nor the rebalancing frequency are known. That is why measures that aim at showing the sizes of trades and associated money flows are problematic, and why no convincing herding measure that takes the relative importance of trades into account is available. Bikhchandani and Sharma (2001) provide a detailed discussion of this issue. They also discuss a measure that was proposed by Wermers (1995) in an unpublished earlier version of Wermers (1999), but not included in the final paper. Eventually, even though trade sizes would be captured adequately, the herding literature that focuses on potential price impacts still suffers from a lack of precise knowledge about the price elasticities for the stocks. Hence, we will stick to the LSV measure for our analysis of herding at the security level. However, we need to make sure that herding does not only result from small portfolio adjustments. Otherwise joint reweighting to a common benchmark could explain the correlation in trades, and we address this issue in Section 2.4.2.

Bikhchandani and Sharma (2001) point out that the LSV measure does not reveal intertemporal persistence in the herding at the security and at the firm level. That is, it does not show whether the securities that herds trade in one quarter are more likely to be traded by herds in the following quarter. We consider the issue by augmenting our analysis and measuring the persistence as proposed by Barber, Odean, and Zhu (2003).

Also, we use a firm herding measure and check for intertemporal persistence at the firm level in Section2.5.

A critique that applies to the LSV measure in particular was brought forward byOehler (1998). His point can be illustrated by the following example. Assume all considered firms hold the benchmark portfolio. They trade the benchmark in response to flows of client money over the quarters and do not engage in any other trading. The LSV measure is zero in this case because LSV controls for aggregate money flows by E[pi,t] being equal to the observed fraction of buyers p_i, t in all stock-quarters. If all firms enjoy money inflows, all firms would buy the stocks in the benchmark portfolio, rather than picking stocks individually and independently, or investing in securities other than stocks. Oehler (1998) argues that this scenario represents “bench mark herding” by the firms, which has a potentially large impact on share prices, and that the LSV measure captures only

“excess herding” and is “rather too conservative.” Therefore, it is important to stress that the correlation in trades measured by LSV is the correlation that is not explained by aggregate money flows and benchmark herding. We will address these issues later

and consider if E[p_i,t] takes extreme values, which would be an indication of benchmark herding, in Section2.4.2. Also, we will analyze if aggregate money flows to the industry explain some of the observed herding in Section 2.4.6. Eventually, we will also address individual money flows at the firm level later in Section2.5.4.

A further critique was expressed by Frey, Herbst, and Walter (2006), who show that the LSV measure can be biased downwards. The bias depends on the characteristics of the data and generally decreases when the number of traders increases. They introduce a slightly modified measure. However,Bellando (2010)shows that their measure is unbiased only under special conditions and otherwise can be biased upwards. Since we provide the first evidence that hedge fund firms herd, we prefer to use the more conservative LSV measure, rather than using a measure that is potentially biased upwards.

2.4.2 General Results for Herding at the Security Level

We start the empirical analysis with calculating herding measures including the trades of all hedge fund firms in all stocks in our sample. The average proxy for E[pi,t] over all securities and all quarters is 0.51. It shows that the firms are on average net buyers, which corresponds to growth of the hedge fund industry over this period. The time series of the quarterlyE[pi,t] is given in Figure 2.1. Coming back to the critique by Oehler (1998), we see thatE[p_i,t] does not take extreme values during the sample period. Strong benchmark herding by our firms should, however, result in rather large deviations, and does not seem to play a major role in our sample.

Figure 2.1: Average Fraction of Buys over Time

The figure shows the time series of the average fraction of buys across all traded securities at every quarter by all firms on our sample. The average fraction is used as a proxy for the expected fraction of buyersE[p_i,t].

Table2.2:GeneralHerdingResults min.1tradermin.2tradersmin.5tradersmin.10tradersmin.20tradersmin.50tradersmin.100traders 1995-2009H2.16(0.00)[270’870]2.66(0.00)[222’292]2.71(0.00)[165’239]2.60(0.00)[119’182]2.43(0.00)[66’948]2.27(0.00)[12’673]1.96(0.00)[1’219] B1.95(0.00)[135’779]2.37(0.00)[111’836]2.55(0.00)[85’391]2.40(0.00)[61’491]2.12(0.00)[33’801]1.77(0.00)[5’685]1.83(0.00)[467] S2.11(0.00)[135’091]2.58(0.00)[110’456]2.80(0.00)[79’848]2.77(0.00)[57’691]2.73(0.00)[33’147]2.66(0.00)[6’988]2.03(0.00)[752] 1995-1999H1.83(0.00)[92’809]2.39(0.00)[71’763]2.68(0.00)[44’144]2.69(0.00)[24’050]2.91(0.00)[8’430]4.51(0.00)[677]7.15(2.69)[13] B1.61(0.00)[45’770]2.08(0.00)[35’407]2.44(0.00)[22’649]2.31(0.00)[12’218]2.42(0.00)[4’118]4.84(0.00)[272]18.02(23.51)[3] S1.73(0.00)[47’039]2.23(0.00)[36’356]2.84(0.00)[21’495]3.03(0.00)[11’832]3.35(0.00)[4’312]4.27(0.00)[405]3.84(0.22)[10] 2000-2004H2.57(0.00)[91’967]3.11(0.00)[75’860]2.96(0.00)[58’275]2.76(0.00)[43’230]2.42(0.00)[24’060]2.40(0.00)[4’113]2.28(0.00)[312] B2.27(0.00)[45’430]2.74(0.00)[37’729]2.89(0.00)[30’142]2.70(0.00)[22’321]2.10(0.00)[11’972]1.66(0.00)[1’717]3.20(0.06)[106] S2.52(0.00)[46’537]3.07(0.00)[38’131]2.94(0.00)[28’133]2.76(0.00)[20’909]2.73(0.00)[12’088]2.93(0.00)[2’396]1.81(0.00)[206] 2005-2009H2.09(0.00)[86’094]2.45(0.00)[74’669]2.50(0.00)[62’820]2.43(0.00)[51’902]2.32(0.00)[34’458]2.01(0.00)[7’883]1.77(0.00)[894] B1.97(0.00)[44’579]2.27(0.00)[38’700]2.30(0.00)[32’600]2.18(0.00)[26’952]2.06(0.00)[17’711]1.60(0.00)[3’696]1.29(0.00)[358] S2.08(0.00)[41’515]2.40(0.00)[35’969]2.64(0.00)[30’220]2.65(0.00)[24’950]2.57(0.00)[16’747]2.35(0.00)[4’187]2.08(0.00)[536] Thetablecontainstheherdingmeasuresforallsecurity-quarterstradedoverdifferenttimeperiods.Forasecurity-quartertobeincluded,werequire differentminimumnumbersofhedgefundfirmswhichmusttradethesecurity-quarter.ThemeasuresareexplainedinSection2.4.1.Foreach measure,thetablepresentsthecorrespondingp-valueinpercentinparenthesis,andthenumberofincludedsecurity-quartersinsquaredbrackets.

in all periods. Over the full observation period the mean herding measure for all stocks traded by at least 5 hedge fund firms is 2.71 percent. Corresponding to the large numbers of stock-quarters included for the calculation of the measures, nearly all values are highly significantly different from zero. The values for the direction herding measures indicate that the identified herding seems to result from funds buying stocks together as well as from selling together. The levels of herding do not vary much over different subperiods.

We require a certain minimum number of firms trading a security-quarter to be in-cluded in the calculation, because, arguably, the herding might depend on the number of firms trading. The columns of Table 2.2 correspond to different minimum numbers of required traders. The results reveal that this requirement does not influence the values in a systematic way. We follow the common convention in the literature, and restrict our further analysis to stock-quarters traded by at least 5 of the hedge fund firms under consideration.

Most of the existing research on herding among professional money managers is based on quarterly holding data and the LSV measure what makes our results directly compa-rable in terms of methodology. However, mutual funds file positions on the individual fund’s level rather than at the firm level, which is why most of the paper by Wermers (1999)is for mutualfunds rather than mutual fund firms. But he also provides the herd-ing measures on the mutual fund firm level. He finds an average LSV measure for mutual fund firms over the period 1975-1994 of 2.22%. To compare his sample to earlier research, Sias (2004)also uses the LSV measure for within-quarter herding. For his sample, which comprises all institutional investors, he finds a level of herding of 1.78 percent over the period 1983-1997. Having in mind that the time periods do not overlap, the 2.71 per-cent in our sample suggest that the herding of hedge fund firms is of comparable order of magnitude or even slightly higher than the herding found for mutual fund firms and other institutional investors by earlier research.

Our result is highly statistically different from these values. Also, we usually argue for non-randomness of our herding measure outcomes by them being statistically significantly different from zero, which corresponds to the null hypothesis of no herding. Given the large sample size it is, however, not surprising that most presented measures are statistically different from zero, and from each other. Before we turn to potential explanations for herding, we conduct a robustness check to assure that the identified herding is not a statistical fluke resulting from random correlations among the trades, which are arguably likely to appear in a large sample. FollowingWermers (1999), we obtain the distribution of all H_i,t under the null from a Monte Carlo simulation, and compare it to the actual distribution. We obtain 10 simulated measures H_i,t^∗ for each security-quarter that was traded by at least 5 hedge fund firms over the sample period. Given the actual number of firms that trade a given stock-quarter N_i,t and the proxy for E[p_i,t] in the quarter, the number of buyers is simulated by drawing Ni,t times from a Bernoulli distribution with intensity E[p_i,t]. The sum of the draws gives one simulated number of buyers B^∗ under random trading, and the according simulated fraction of buyers isp^∗_i,t = _N^B∗

i,t. The simulated measureH_i,t^∗ is then calculated using the actual E[pi,t], and the simulatedp^∗_i,t.

Figure2.2 shows the actual and the simulated distributions of the herding measure.

Figure 2.2: Distribution of the Herding Measure

The figure shows on the left the distribution of the herding measureHi,t for all stock-quarters in our sample. On the right is the distribution of the corresponding simulated measureH_i,t^∗ which come from a Monte Carlo simulation as described in Section2.4.2.

Comparing the two distributions, the actual distribution has more probability mass in the right tail, which corresponds to the overall herding measure values resulting from a relatively small number of stock-quarters exhibiting large herding. The mean and median of the simulated measure show that the measure is zero and unbiased under independent trading in our sample. The herding which we identify does, hence, clearly not result from random matching of the firms’ trades.

As a further robustness check, we ensure the herding does not result from small trades only. Wermers (1995)notes that small portfolio adjustments, e.g. a common reweighting to a joint benchmark, would result in positive values for the LSV measure. Recall that due to the minimum filings threshold we do not know the precise size of the trades and use a proxy as described in Appendix2.A.4instead. At every quarter we include only the largest 25% of all trades, where the trade size is measured as relative size of our proxy for trade size to the overall 13F stock portfolio, to ensure that small and large firms are equally contained. The H is slightly larger than the average 2.71 percent in all trades.

Hence, the identified herding is not resulting from unimportant trades only.

2.4.3 Herding among Different Investment Styles

Herding is defined as non-independent and non-random trading, i.e. correlated trading.

The trading of the fund firms results from their investment strategies. Hedge funds are known to follow very different kinds of investment strategies, which are commonly re-ferred to as hedge fund “styles”. Under all theoretical explanations for herding the more homogeneous the investment strategies of a sample of traders are, the stronger are the incentives to herd. Wermers (1999) as well asSias (2004) find that the herding behavior varies across mutual fund styles and different types of institutional investors, respectively.

Hence, the levels and the potential reasons of herding should vary across hedge fund firm styles, too. Therefore, in our first detailed analysis, we measure herding separately for different hedge fund firm styles.¹⁷

Table 2.3: Herding Measures across Investment Styles

All Equity Style Merger Arbitrage Other H 2.71 [165’239] 1.52 [85’283] 7.63 [1’936] 0.76 [25’151]

B 2.55 [85’391] 1.43 [43’647] 5.99 [1’029] 0.51 [12’568]

S 2.80 [79’848] 1.57 [41’636] 8.96 [907] 0.96 [12’583]

The table contains the herding measures for all stock-quarters traded by at least 5 hedge fund firms belonging to different style classes. The measures are explained in Section 2.4.1 and the number of security-quarters considered are given in squared brackets. All p-values are zero.

In Table2.3we see herding among all considered style groups, though, it substantially differs for different styles.¹⁸ The equity style group is a very broad category in terms of the trading objective. For example, firms that focus on stock picking in very special industries and technical traders that trade in all stocks are equally contained in this style group.

The potentially higher heterogeneity serves as an explanation why firms in the style group other exhibit even lower levels of herding.

The merger arbitrage firms show a very high propensity to trade the same securities together and in the same direction. If merger events, which provide the profitable oppor-tunities to these firms, are rather limited relative to the number of firms, this would result in herding in and out of these securities partly together. This corresponds to explanations of herding due to either correlated private information or informational cascades. On top of following a more coherent investment strategy than alternative style groups, the more limited nature of trading opportunities serves as an explanation for fiercer herding by these firms.

17The style classification is as defined in Section2.3.

18The differences are all highly statistically significant.

2.4.4 Herding in Different Stocks

2.4.4.1 Herding Persistence in Stocks

We start our more detailed analysis of herding across various stock characteristics with an assessment of the persistence in the herding at the stock level. The persistence could give some indication what kind of characteristics attract herds. Low persistence would indicate that herds do not tend to form on the same stocks subsequently, and we should direct our further focus more on dynamic characteristics, such as lagged returns. To the contrary, high persistence would imply that herds are attracted by stock characteristics which do not change rapidly over time.

The LSV measure indicates the level of herding in the average stock-quarter. A cri-tique mentioned earlier already is that LSV does not reveal whether the stocks which are traded by herds in one quarter are more likely to be traded by herds in the following quar-ter. Therefore, similar to Barber, Odean, and Zhu (2003), we analyze the intertemporal persistence of herding at the security level by calculating the mean correlations between

The LSV measure indicates the level of herding in the average stock-quarter. A cri-tique mentioned earlier already is that LSV does not reveal whether the stocks which are traded by herds in one quarter are more likely to be traded by herds in the following quar-ter. Therefore, similar to Barber, Odean, and Zhu (2003), we analyze the intertemporal persistence of herding at the security level by calculating the mean correlations between