Zooming In on Equity Factor Crowding
Valerio Volpati, Michael Benzaquen, Zoltan Eisler, Iacopo Mastromatteo, Bence Toth, Jean-Philippe Bouchaud
ZZooming In on Equity Factor Crowding
Valerio Volpati,
1, 2
Michael Benzaquen,
1, 2, 3
Zoltán Eisler,
1, 4
IacopoMastromatteo,
1, 2
Bence Tóth, and Jean-Philippe Bouchaud
1, 2, 4, 5 Capital Fund Management, 23-25, Rue de l’Université 75007 Paris, France Chair of Econophysics and Complex Systems, École polytechnique, 91128 Palaiseau Cedex, France Ladhyx UMR CNRS 7646 and Department of Economics,École polytechnique, 91128 Palaiseau Cedex, France CFM-Imperial Institute of Quantitative Finance, Department of Mathematics,Imperial College, 180 Queen’s Gate, London SW7 2RH Académie des Sciences, Quai de Conti, 75006 Paris, France (Dated: January 14, 2020)Crowding is most likely an important factor in the deterioration of strategy performance, theincrease of trading costs and the development of systemic risk. We study the imprints of crowding on both anonymous market data and a large database of metaorders from institutional investorsin the U.S. equity market. We propose direct metrics of crowding that capture the presence ofinvestors contemporaneously trading the same stock in the same direction by looking at fluctuationsof the imbalances of trades executed on the market. We identify significant signs of crowding inwell known equity signals, such as Fama-French factors and especially Momentum. We show thatthe rebalancing of a Momentum portfolio can explain between 1–2% of order flow, and that thispercentage has been significantly increasing in recent years.
Keywords: crowding, equity factors, momentum, market microstructure
I. INTRODUCTION “Crowded trades” or “crowded strategies” are oftenheard explanations for the sub-par performance of aninvestment or, in more extreme cases, for the occurenceof deleveraging spirals. Although seemingly intuitive,the concept of crowding has remained elusive and is,in fact, somewhat paradoxical as every buy trade isexecuted against a sell trade of the same magnitude.Some clarification is therefore needed, and the subjecthas recently garnered substantial interest in academic[2, 6, 10, 11, 20] and applied research [13].Investors in a purportedly crowded strategy may facethree related predicaments. One is that of increasedcompetition for the same excess returns, leading to anerosion of the performance of the strategy. Second isincreased transaction costs: maintaining similar port-folios leads to similar trade flows. This amplifies theeffective market impact suffered by all investors follow-ing the same strategy – an effect called co-impact in [7].This in turn leads to a deterioration of performance evenunder normal conditions, see e.g. [12]. Finally, if theportfolios of different competitors largely overlap, sys-temic risk may arise as the liquidation of one of theseportfolios can trigger further liquidations and even se-vere cascading losses for all investors who shared similarpositions [2, 6, 11]. This phenomenon is well exempli-fied by the Quant Crunch of 2007 [20], which chieflyaffected a certain style of relative value investing, whileit left the market index itself, and therefore long-onlyinvestors, largely unscathed.Crowding has recently been invoked in the context of Equity Factor strategies, which have witnessed sub-stantial inflows in the past decade, and are currently(as of end 2019) in a relatively severe drawdown. Thesestrategies are based on persistent anomalies which arewell known to investors, such as Momentum, Value, orSmall Cap strategies [15]. This makes them potentiallycrowded and thus interesting to investigate.The aim of the present study is to investigate the pos-sible crowdedness of Equity Factor strategies by mea-suring the correlation of market order flow with thestrength of the trading signal that factor investors hy-pothetically follow. We use both (i) the total order flowmeasured using anonymized microstructure data per-taining to stocks of the Russell 3000 index and (ii) theinstitutional order flow identified thanks to a propri-etary database. Although these correlations are small, ∼ , they are strongly significant and are seen to haveincreased over the recent years. The estimated impactcosts suggest that simple Fama-French factor investingis close to saturation. II. DATA AND METRICS
This paper relies on three different datasets: one us-ing equity prices to construct Equity Factor trading sig-nals, and two allowing us to quantify trading activity. a r X i v : . [ q -f i n . T R ] J a n A. Equity Factor Data
We use standard Fama-French (FF) factors [1, 15],extended to Momentum [14, 19], defined on the com-ponents of the Russell 3000 index in a period spanningfrom January 1995 to December 2018. Since rebalanc-ing these FF portfolios is costly, we expect investors toslow down the bare signal to trade less aggressively. Aconceptually sound [17] model that assumes quadratictrading costs leads to an exponential slowing down ofthe signal. More formally, let us denote by s i,t the “sig-nal” followed by an investor, giving the ideal holding ofstock i on the close of day t . For example, s i,t wouldbe the ranking of stocks according to their past returnsin the case of the Momentum factor. The actual hold-ings π i,t of the investor is then given by an ExponentialMoving Average (EMA): π i,t = A (cid:88) t (cid:48) ≤ t s i,t (cid:48) exp (cid:18) − t − t (cid:48) D (cid:19) . (1)The factor A sets the overall risk of the portfolio,whereas the slowing down time scale D is chosen as toprovide a good compromise between performance andtrading costs. The theoretically expected order flowfrom the strategy on day t is thus given by ∆ π i,t = π i,t − π i,t − . (2)This framework is summarized in Figure 1. B. Market Microstructure Data
We also use anonymous market data collected byCapital Fund Management (CFM) covering about , US stocks between January 2011 to May 2018.We process a large majority of trades executed through-out different market venues. For each stock i and eachday t , we define the trade imbalance as I trade i,t = (cid:80) n ∈ t (cid:15) i,n (cid:80) n ∈ t | (cid:15) i,n | , (3)where (cid:15) i,n is the sign of the n ’th trade on stock i , and thesum extends to all trades taking place during the con-tinuous trading session of day t . The sign is consideredpositive if the trade was executed above the prevailingmid price, and negative otherwise. Midprice trades areexcluded. Trades are generated by aggressive orders; I trade i,t hence captures the pressure that they imply.Similarly, we define the volume imbalance as I volume i,t = (cid:80) n ∈ t (cid:15) i,n v i,n (cid:80) n ∈ t v i,n , (4) S i g n a l s i , t P o s i t i o n π i , t Jan2017 Apr Jul Oct Jan2018 Apr Jul Oct Jan2019 T r a d e ∆ π i , t Figure 1.
The slowing down procedure implementedin this paper . (Top panel) The original signal s i,t , cor-responding to ideal position before trading costs are con-sidered. (Middle panel) The slowed down signal π i,t withslowing down timescale D = 3 months, corresponding tothe desired position when transaction costs are taken intoaccount. (Bottom panel) The expected order flow ∆ π i,t ,submitted by the investor who is targeting the position π i,t . where v i,n is the volume executed on stock i at trade n . We do not expect, and in fact do not find, majordifferences between the behavior of I trade and I volume ,because volumes are constrained by liquidity availableat the best quotes, and do not fluctuate wildly.To capture the liquidity in the order book, we averagethe volume available on the bid side V bid i,s and the oneavailable on the ask side V ask i,s over N snapshots s takenevery seconds during the continuous trading sessionof day t , to calculate, for a given day and stock V bid i,t = 1 N (cid:88) s ∈ t V bid i,s , (5)and V ask i,t = 1 N (cid:88) s ∈ t V ask i,s . (6)These allow us to define the daily average order bookimbalance as I book i,t = V bid i,t − V ask i,t V bid i,t + V ask i,t . (7)All imbalances above are, by definition, bounded be-tween -1 and 1. C. Metaorder Data
Finally, we also use the Ancerno dataset, a propri-etary database containing trades of institutional in-vestors, covering about , execution tickets perday, which corresponds to approximately of thedaily volume traded on the market from January 1999to December 2014. This data set has been used in sev-eral academic studies in the past, see e.g. [7–9, 18, 21],and we refer to those papers for more information on thedata set, as well as descriptive statistics. Using labelspresent in the data, we are able to group together dif-ferent trades that belong to the same metaorder, i.e.an ensemble of trades with the same client number,start date, end date, stock symbol, and sign. This al-lows us to gain more information about the decision-making process underpinning the order flow. Further-more, Ancerno trades are representative of institutionalinvestors, for whom we expect a larger propensity to fol-low classical equity factors.Similarly to the above measures of imbalance, wecan define a metaorder trade imbalance I meta i,t and a metaorder volume imbalance I metavolume i,t by restrictingthe sums over all market trades to metaorders executedon stock i on day t . For example: I meta i,t = (cid:80) m ∈ t (cid:15) meta i,m (cid:80) m ∈ t | (cid:15) meta i,m | (8)where (cid:15) meta i,m is the sign of metaorder m on stock i ,and where m runs on the total number of identifiedmetaorders on stock i and day t . III. RETURN-IMBALANCE CORRELATIONS
Before diving into the original part of our study,namely the correlation between imbalances and trad-ing signal, we re-establish some well known factsabout imbalance-return and imbalance-imbalance cor-relations.Figure 2, top panel, shows the lagged correlation be-tween different imbalance measures and returns, aver-aged over all the stocks in our dataset. For zero lag,we recover the usual positive correlations between tradeimbalance and returns, here found to be ≈ . . For pos-itive lags, i.e. when returns are posterior to imbalances,correlation is close to zero, indicating that past imbal-ances have on average no linear predictability on futurereturns. On the other hand, past returns are found to bepositively correlated with future trade imbalance, bothfor the market-wide I trade and for the metaorder imbal-ance I meta . This is compatible with the strong tempo-ral autocorrelation of trade imbalance, documented in[3, 4], and again shown in Figure 2, bottom panel. − − − − . . . C o rr e l a t i o n Correlations with price returns I trade I volume I book I meta I metavolume Lag [days]10 − − C o rr e l a t i o n Autocorrelations
Figure 2.
Correlation of imbalances with price re-turns and autocorrelations . (Top panel) Lagged corre-lations of all imbalances at day t , with price returns at day t + Lag. For Lag > imbalances built with public informa-tion have no correlation with future returns as expected. ForLag = 0 we recover the well known “mechanical” correlationbetween contemporaneous trade imbalance and returns. ForLag < we observe how today’s imbalances are correlatedto past returns. (Bottom panel) We show the time auto-correlation of all imbalances introduced in the text. Whileprice returns are only weakly autocorrelated, the submissionof orders, and in particular metaorders, are strongly auto-correlated, with a power-law decay Lag − γ of the autocorre-lation function (see [3, 4]). We find γ ≈ . for market-widetrades and γ ≈ . for metaorders. We also mention that we find a clear positive correla-tion between metaorder imbalances I meta and market-wide imbalances I trade (not shown). This has to bethe case since metaorders themselves contribute to theanonymous market flow. We also find a negative corre-lation of a few percent between metaorder imbalancesand book imbalances. This can be understood by ar-guing that metaorders are more likely to be executedwhen there is enough available liquidity, and vice-versa:the execution of large metaorders induces more liquidityto be revealed in the order book (a phenomenon calledliquidity refill in [4]). IV. DYNAMICAL CORRELATIONSA. Momentum
Let us now turn to the study of correlations betweendifferent kinds of imbalances and factor trading, start-ing with the standard Momentum Factor [14, 19] forwhich we see the most significant results. As explainedabove, we first slow down the signal using an EMA,and then take the derivative to calculate the trades thatwould follow from rebalancing.In the top panel of Figure 3 we show the correla-tion of anonymous market imbalances with the expectedMomentum order flow for different values of the slow-ing down parameter D , averaged over all stocks in thedataset. The grey stripe denotes the significance bandof the correlations, obtained by reshuffling the time se-ries (in blocks of 6 months in order to preserve the auto-correlation structure) and calculating the standard de-viation of the obtained correlations over 200 reshuffledsamples. We find a significant correlation between tradeand book imbalances and the expected order flow. Thiscorrelation is negative for trade imbalance and positive for order book imbalance, with absolute maxima (cid:38) for D around 3–4 months. This timescale is of the sameorder of magnitude as the autocorrelation time of themomentum signal, and thus quite reasonable.Although the results in the top panel of Figure 3 arehighly significant, the sign of the correlations is some-what confusing. Naively, one would be tempted to arguethat Momentum investors execute their trades with ag-gressive market orders. This should lead to a positivecorrelation between the trading signal and trade imbal-ance, whereas we observe this correlation to be nega-tive. At this stage, one can come up with two oppositeinterpretations: • What we see are in fact aggressive orders by mean-reversion traders. However, this is quite unlikelysince mean-reversion is not a profitable strategyon the time scale of months, but rather on thetime scale of a few days only. • Momentum trades are predominantly executedusing limit orders, thus contributing to a posi-tive correlation with the order book imbalance,as observed in the top panel of Figure 3. Thisis compatible with the behavior of popular bro-ker execution algorithms that chiefly use passiveorders. It also resonates with [16], which statesthat 80 % of the volume executed by a major fundmanager in the factor trading industry is throughlimit orders.The analysis of metaorders helps bolster our interpre-tation. In the middle panel of Figure 3 we see thatboth metaorder and metaorder volume imbalance show − . . . C o rr e l a t i o n Anonymous market data imbalances - Momentum I trade I volume I book . . . . C o rr e l a t i o n Metaorder imbalances - Momentum I meta I metavolume . . . C o rr e l a t i o n Price returns - Momentum returns
Figure 3.
Conditional correlations of all imbalanceswith slowed down momentum. (Top panel) Average cor-relation of market-wide trade imbalances and of book imbal-ance, with the Momentum trading signal slowed down withdifferent timescales D , on the x axis. (Middle panel) Averagecorrelation between metaorder imbalances and the Momen-tum trading signal, slowed down with different timescales D (Bottom panel) Average correlations between the dailyclose to close price returns and the Momentum trading sig-nal, slowed down with different timescales D . The lattercorrelation displays a qualitatively similar behaviour, but itis 10 times smaller ( ∼ . ) than the correlation betweenimbalances and trading signal. a clear positive correlation with the Momentum tradingsignal, with a similar time scale D around 4–6 months.Note that the sign of metaorders (to buy or to sell) re-ported by the data provider is not sensitive to whetherthey are executed actively or passively. Since mostmetaorders in the database correspond to order flowof institutionals who most likely engage in Momentumstrategies, we can safely conclude that the inverted cor-relation observed in the top panel of Figure 3 corre-sponds to Momentum trading using passive orders.We have performed a series of tests for the robust-ness of the observed correlations. These are quite stableacross stocks, regardless of liquidity and tick size. Thesame analysis with different slowing down mechanisms,or using the long (or short) only component of Momen-tum yields qualitatively similar results in all cases.We also show the correlations between the daily close-to-close price returns and the Momentum trading sig-nal, which we can compute on the Russell 3000 from1996 to 2019, i.e. with much more data than for im-balance correlations. This correlation is considerablysmaller: its maximum is around . , to be comparedwith . for the imbalance correlation. Althoughquite small, this correlation is important as it can beused to estimate the impact cost incurred by Momen-tum traders. It should be compared with the correlationbetween the slowed down position π t and the returns,which by definition gives the average profit of the strat-egy, and is found to be ≈ . . Assuming a quadraticcost model gives a trading cost equal to one half of theinstantaneous impact. These numbers therefore suggestthat Momentum has become only marginally profitable:this is a crowded trade, for which co-impact has drivenprofits to zero. Let us stress that this is not the case forother implementations of Momentum that are, accord-ing to the same measure, distinctively less crowded andtherefore still profitable (at least at the time of writing).We can in fact prove directly that Momentum crowd-ing has increased in the recent years, by computing themaximal imbalance/signal correlation computed everyyear, found for D ∈ (2 , months for market-wide dataand D ∈ (3 , months for metaorder data. The re-sults are shown in Figure 4 and are quite consistentover the whole period. Whereas the maximum correla-tion is noisy but quite stable for metaorders from 1999to 2014, market-wide data that we collect up to 2018reveals a clear upward drift since 2012, possibly relatedto the increase of the popularity of factor strategies. B. Other Factors: HML & SMB
So far we discussed results for Momentum only. Wealso explored Fama-French factors, such as “HML” (alsocalled “Value”), comparing the price of a stock to itsbook value, and “SMB”, i.e. buying small cap stocks and A simple, back-of-the-envelope estimation based on a linearimpact model allows one to explain the observed factor be-tween return/signal and imbalance/signal correlations, takinginto account the fact that the unconditional standard devia-tion of I volume is ∼ . . However, one would rather expect asquare-root impact and not a linear impact [7], so it is at thisstage not clear how to reconcile these observations. selling large cap stocks [1]. Our methodology closelyfollows that of the previous section. In Figure 5 weshow our results for HML and SMB. Our results formarket-wide imbalances for these two factors are sim-ilar to those obtained for momentum – although lesssignificant for SMB. This is expected, given that thelonger holding period of these strategies induces a muchsmaller rebalancing activity [5]. For metaorder imbal-ance, on the other hand, correlations are barely signifi-cant.On the other hand, the time evolution of the market-wide imbalances with the HML or SMB signals is toonoisy to confirm that crowdedness in these factors hasalso increased in the recent years. V. CONCLUSIONS
In this empirical study we have shown that crowdingof equity factors can be quantitatively elicited throughcorrelations between real supply/demand imbalances(proxies of market participants trading in the same di-rection) and the rebalancing order flow that would re-sult from tracking slowed-down equity factors. Our re-sults, particularly significant for Momentum, show thatsuch a strategy is indeed crowded, resulting in ratherpoor profitability. Further, our method allows one toconfirm that crowding on equity factors (at least onMomentum) has, as claimed and feared by many, sig-nificantly increased over the past few years.
VI. ACKNOWLEDGMENTS
The authors thank Charles-Albert Lehalle for his ini-tial suggestion to study order flow in relation to An-cerno metaorders. We would also like to thank Ste-fano Ciliberti, Philip Seager and Juha Suorsa for inter-esting discussions on the subject. We would also liketo acknowledge the valuable help and suggestions ofMatthieu Cristelli. This research was conducted withinthe
Econophysics & Complex Systems
Research Chair,under the aegis of the Fondation du Risque, the Fonda-tion de l’Ecole polytechnique, the Ecole polytechniqueand Capital Fund Management.
DATA AVAILABILITY STATEMENT
The data were purchased by Imperial College fromANcerno Ltd (formerly the Abel Noser Corporation)which is a widely recognised consulting firm that workswith institutional investors to monitor their equity trad-ing costs. Its clients include many pension funds andasset managers. The authors do not have permission − . . . C o rr e l a t i o n Anonymous market data imbalances - Momentum I trade I volume I book . . . . C o rr e l a t i o n Metaorder imbalances - Momentum I meta I metavolume Figure 4.
Time evolution of the correlation between imbalances and Momentum signal. (Left panel) Maximum(in absolute value) of the trade imbalance and book imbalance correlation with the Momentum trade signal versus time,since 2011. One observes a clear upward trend, suggesting that Momentum trading has become more and more crowded.(Right panel) Maximum (in absolute value) of the metaorder imbalance correlation with the Momentum trade signal versustime, from 2000 to 2014. The sign and absolute values of these correlations, albeit noisy, are quite stable in time.
200 400 600 800 1000Slowing down [days] − . . . C o rr e l a t i o n I trade - HML I trade - SMB I volume - HML I volume - SMB I book - HML I book - SMB
200 400 600 800 1000Slowing down [days] − . . . C o rr e l a t i o n I meta - HML I meta - SMB I metavolume - HML I metavolume - SMB Figure 5.
Conditional correlations of imbalanceswith slowed-down HML and SMB . We again show, asa function of D , the correlation between different types ofimbalances and the trading signal originating from the HMLand SMB factors. Because these factors have a significantlylonger intrinsic time scale, the signal is weaker and shifted tolarger values of D . Note that the correlation of the tradingsignals to metaorder imbalances is barely significant, andpoints in the opposite direction. [1] A. Ang. Asset Management: A Systematic Approachto Factor Investing (Financial Management AssociationSurvey and Synthesis) . Oxford University Press, 2014. [2] P. Barroso, R. M. Edelen, and P. Karehnke. Institu-tional crowding and momentum tail risk.
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