Trading characteristics of member firms on the Korea Exchange
TT RADING CHARACTERISTICS OF MEMBER FIRMS ON THE K OREA E XCHANGE
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Min-Young Lee
Department of PhysicsPohang University of Science and TechnologyPohang 37673, Republic of Korea [email protected]
Woo-Sung Jung
Department of PhysicsDepartment of Industrial and Management EngineeringPohang University of Science and TechnologyAsia Pacific Center for Theoretical PhysicsPohang 37673, Republic of Korea [email protected]
Gabjin Oh
College of BusinessChosun UniversityGwangju 61452, Republic of Korea [email protected]
April 24, 2020 A BSTRACT
In this paper, we study the characteristics of the member firms on the Korea Exchange. The memberfirms intermediate between the market participants and the exchange, and all the participants shouldtrade stocks through members. To identify the characteristics of member firms, all member firmsare categorized into three groups, such as the domestic members similar to individuals (DIMs), thedomestic members similar to institutions (DSMs), and the foreign members (FRMs), in terms ofthe type of investor. We examine the dynamics of the member firms. The trading characteristics ofmembers are revealed through the directionality and trend. While FRMs tend to trade one-way andmove with the price change, DIMs are the opposite. In the market, DIMs and DSMs do herd and theherding moves in the opposite direction of the price change. One the other hand, FRMs do herd inthe direction of the price change. The network analysis supports that the members are clustered intothree groups similar to DIMs, DSMs, and FRMs. Finally, random matrix theory and a cross-sectionalregression show that the inventory variation of members possesses significant information about stockprices and that member herding helps to price the stocks. K eywords Econophysics · Herding · Network Analysis · Random Matrix Theory · Cross-Sectional Regression
The stock market is a complex system in which a large number of investors with heterogeneous strategies participate.The trading activities of many investors make stock prices fluctuate. Analyzing the trading strategies of participants helpsus to understand the movement of stock prices. The Korea Exchange (KRX) has the 14th largest market capitalizationin the world, and the market is a representative emerging market with different characteristics from a developed market.Individual investors actively participate in the market. The smaller the market capitalization is, the greater the proportionof individuals. In the US market, which is a developed market, the individual investor owned approximately 90% of thestock in 1950. The individual investor owned approximately 30% of the stock in 2009, and only approximately 2%of the trading volume in the NYSE is traded by individual investors[1]. On the other hand, 60.3% of the transactionamount in the KRX from 2007 to 2017 was traded by individual investors. Even individuals account for more than a r X i v : . [ q -f i n . GN ] A p r PREPRINT - A
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24, 202090% of the trading of stocks with small market capitalizations. We analyze the characteristics of the member firmsin the KRX. Member firms are the companies that trade on behalf of their clients or trade their accounts. The clientsare categorized as individuals, institutions, and foreigners. Member firms are only entitled to trade on the exchange;therefore, all investors have to go through their member firms when trading stocks. Because heterogeneous investorstrade through member companies, identifying the characteristics of member companies is a difficult problem. Inaddition, the KRX rarely discloses information about member companies. Through the daily transaction of memberfirms, however, it is possible to get a lot of information about the member firms indirectly. The characteristics ofmember firms are determined by the type of clients, such as individuals, institutions, and foreigners, that trade throughtheir member firm. Few studies have dealt with the characteristics of the identified member firms. To the best of ourknowledge, this study is the first one analyzing the trading behavior of the identified member firms on the Korean stockmarket. The characteristics of individuals, institutions, and foreigners is a subject that many researchers have studied.Gabaix et al.[2] showed the excess volatility from large institutions in illiquid markets. Bohl et al.[3] found no evidencethat institutions destabilize the market. Barber et al.[4, 5, 6] investigated the investment performance of individuals.Foucault et al.[7] showed the effect of individual trading on volatility. Adaoglu et al.[8] showed the cause-and-effectbetween stock returns and foreign investor flows. Bae et al.[9] showed the superior performance of foreign investors.Much research has been conducted on the KRX, which has different characteristics from a developed market. Park andKim studied the performance of individual traders [10] on the KRX. In addition to studies about individuals, studieshave also been conducted on institutions and foreigners. There have been studies focused on the trading of foreigninvestors on the KRX based on herding and positive feedback [11, 12]. However, as far as we know, there have been nostudies of member firms on the KRX. The ambiguity about member transactions is resolved indirectly. Thus, we haveidentified the member’s trading characteristics using the type of clients. We analyzed the transaction characteristics ofmember firms. First, we show the similarity between member firms and investor types such as individuals, institutions,and foreigners. All member firms are categorized into three groups, such as domestic members similar to individuals(DIMs), domestic members similar to institutions (DSMs), and foreign members (FRMs) in terms of the type of investor.We introduce the measures of the directionality and trend to characterize the trading behavior of members. From themeasures, it can be seen that the FRMs trade in the same direction as the changes in stock prices and conduct theirintraday trading in one direction. Herding is investment that mimics other investors and can result from rational orirrational transactions. Herding does not necessarily reverse an unusual return. One of the interesting characteristicsof member firms on the KRX is herding in the opposite direction. In general, investor herding makes a price changein the same direction. The buy herding of investors, for example, makes a return turn positive. In the KRX, however,the herding of member firms makes a price change in the opposite direction. While the herding of FRMs moves inthe direction of the price change. We also construct the network based on the correlation of the inventory variation ofmembers. The community detection algorithm shows that the network is divided into groups that are almost similar tothe previous ones regarding the characteristics of members: DIMs, DSMs, and FRMs. The final step is to find a linkbetween the trading of members and stock prices. Random matrix theory shows that the inventory variation possessesinformation about stock prices. Cross-sectional regression demonstrates that the herding of members complementsthe market factor to explain stock prices. The inventory variation of members possesses significant information onstock prices. Our research contributes four points to this research field. First, we find that member firms do herd in theopposite direction on the KRX. Second, there have been few studies on the characteristics of member firms on the KoreaExchange. We have identified the characteristics of member firms compared with the investor types and used measuressuch as the directionality and trend. Third, from the community structure of the member network, we show how herdingtakes place at the level of each member. Finally, random matrix theory and a cross-sectional regression show that theinventory variation and herding possess a lot of information about the price dynamics and help price stocks.The remainder of this paper is organized as follows. In section 2, we explain the KRX dataset. In section 3, we dissectthe inventory variation of member firms at the level of investor types and analyze the characteristics of the transactionsof each member. In section 4, the herding of members on the KRX is introduced. In section 5, the community structureof the member network is investigated. In section 6, we study the relationship and correlation between the inventoryand stock returns using random matrix theory and a cross-sectional regression.
The dataset we use consists of the daily prices and inventory variations on the Korea Exchange (KRX). The inventoryvariation is the buy and sell transaction amount, and is the product of the transaction volume and price. The period ofthe dataset is from 1 January 2007 to 31 December 2017 (11 years, 2722 trading days) and the time resolution is oneday. The 1210 firms that are continuously traded from 2007 to 2017 are included. The firms are categorized into tendeciles according to their market capitalization. Unlike developed markets, individuals are very active on the KRX.Table 1 shows the transaction amounts and the ratios of the investors by market capitalization. The transaction amount2
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24, 2020Table 1: Total transaction amount ( KRW) of each investor type from Jan. 2007 to Dec. 2017. The numbers inparentheses indicate the proportion of the transaction amount of each investor. The 1210 stocks are divided into decilegroups based on market capitalization. The first decile is the firms with the 121 largest market capitalizations.
Investor type Market capitalization decile1 2 3 4 5 6 7 8 9 10 TotalIndividual 81.17 21.1 15.07 12.43 13.03 10 9.64 8.07 7.19 5.45 183.15(%) (43.11) (77.15) (85.9) (88.98) (91.17) (92.59) (94.85) (96.44) (96.33) (96.54) (60.27)Foreigner 55.98 2.66 1.15 0.73 0.64 0.46 0.31 0.21 0.18 0.13 62.45(%) (29.73) (9.72) (6.58) (5.21) (4.48) (4.22) (3.04) (2.46) (2.44) (2.34) (20.55)Institution 51.12 3.59 1.32 0.81 0.62 0.34 0.22 0.09 0.09 0.06 58.26(%) (27.15) (13.14) (7.52) (5.81) (4.35) (3.18) (2.12) (1.1) (1.23) (1.13) (19.17)Total 188.27 27.35 17.54 13.97 14.29 10.8 10.17 8.37 7.46 5.64 303.86 represents the number of traded shares multiplied by the price. Approximately 43.11% of the transaction amount istraded by individual investors in the first decile of market capitalization. The lower the market cap is, the greater theratio of individual trading. In the tenth decile group, the ratio increases to 96.54%. We use the inventory variation of62 member firms and the inventory variation of 3 investor types (individuals, institutions, and foreigners). The list ofmembers firms is shown in Table 2. Nos. 1 - 41 are the domestic members and Nos. 42 - 62 are the foreign members.KRX categorizes investors into individuals, institutions, and foreigners and provides daily trading information. Becauseonly the member firms are entitled to trade on the exchange, all investors have to make transactions through memberfirms. There are 41 domestic members and 21 foreign members on the KRX. The members are categorized intodomestic members and foreign members according to whether the headquarters of each member is in Korea or anothercountry. Since many investors make transactions through member firms, it is hard to consider them as independentinvestors. However, by analyzing the investor types that trade through the member firms, the characteristics of themember firms can be known. Domestic member firms can be explained as having a combination of individuals andinstitutions. Foreign member firms can be described as foreign investors. In 2003, 99.8% of the foreign investors wereforeign institutional investors[12].
A description of the types of investors that make up the Korean stock market will help to understand the member firms.The market has three major investor categories: individuals, institutions and foreigners. In this context, the institutionsrepresent the domestic institutions. To understand the characteristics of member firms, it is necessary to know the threeinvestor categories. The relation between the three investor types is analyzed using the Pearson correlation coefficientand the partial correlation coefficient as follows. Since the three investors influence each other, the partial correlationcoefficient was introduced to determine the correlation between two variables and to control the other variable. Whencomparing individuals and foreigners, for example, institutional transactions affect the transaction of individuals andforeigners. For that reason, the partial correlation is used to exclude the effects of the institutional transactions. ρ XY = N Σ Ni =1 X i Y i − Σ Ni =1 X i Σ Ni =1 Y i (cid:113) N Σ Ni =1 X i − (cid:0) Σ Ni =1 X i (cid:1) (cid:113) N Σ Ni =1 Y i − (cid:0) Σ Ni =1 Y i (cid:1) (1) w ∗ X = argmin w (cid:40) N (cid:88) i =1 ( x i − (cid:104) w , z i (cid:105) ) (cid:41) (2) w ∗ Y = argmin w (cid:40) N (cid:88) i =1 ( y i − (cid:104) w , z i (cid:105) ) (cid:41) e X,i = x i − (cid:104) w ∗ X , z i (cid:105) (3) e Y,i = y i − (cid:104) w ∗ Y , z i (cid:105) ρ XY · Z = ρ e X ,e Y = N Σ Ni =1 e X,i e Y,i (cid:113) N Σ Ni =1 e X,i (cid:113) N Σ Ni =1 e Y,i (4)3
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24, 2020 T a b l e : S t a ti s ti c s f o r m e m b e r fi r m s on t h e K R X . T h e p e r i od i s t h e ti m e i n w h i c h t h e m e m b e r t r a d e d , a nd N d i s t h e nu m b e r o f t r a d i ngd a y s . N s i s t h e nu m b e r o f s t o c k s t h a t a m e m b e r t r a d e s i n t h e t o t a l p e r i od . V o li s t h e t o t a lt r a n s ac ti on a m oun t fr o m J a nu a r y2007 t o D ece m b e r a nd t h e un iti s . N o N a m e P e r i od ( N d ) N s V o l V o l/ N d s N o N a m e P e r i od ( N d ) N s V o l V o l/ N d s K yobo0701 - ( ) . C A P E - ( ) . S h i nh a n I nv e s t - ( ) . B NK - ( ) . K o r ea I nv e s t - ( ) . I M - ( ) . D a i s h i n0701 - ( ) . NH ( N onghyup ) - ( ) . M i r ae D ae w oo0701 - ( ) . K B I nv e s t - ( ) . S h i nyoung0701 - ( ) . M i r ae A ss e t - ( ) . E ug e n e - ( ) . H a n w h a I nv e s t - ( ) . H a ny a ng0701 - ( ) . B NG - ( ) . M e r it z - ( ) . A pp l e - ( ) . NH I nv e s t - ( ) . H a n m a g0902 - ( ) . B ookook0701 - ( ) . J P M o r g a n*0701 - ( ) . K B - ( ) . M ac qu a r i e *0701 - ( ) . H a n w h a - ( ) . M o r g a n S t a n l e y*0701 - ( ) . H yund a i M o t o r - ( ) . C iti g r oup*0701 - ( ) . Y uh w a - ( ) . H S BC *0701 - ( ) . Y u a n t a - ( ) . C L S A *0701 - ( ) . S K - ( ) . C r e d it S u i ss e *0701 - ( ) . G o l d e n B r i dg e - ( ) . U B S *0701 - ( ) . S a m s ung0701 - ( ) . M e rr ill L yn c h*0701 - ( ) . D B F i n a n c i a l - ( ) . G o l d m a n S ac h s *0701 - ( ) . H II nv e s t - ( ) . S o c i e t e G e n e r a l e *0701 - ( ) . K i w oo m - ( ) . N o m u r a *0701 - ( ) . L ea d i ng I nv e s t - ( ) . D e u t s c h e *0701 - ( ) . H a n a F i n a n c i a l - ( ) . D a i w a *0701 - ( ) . e B E S T - ( ) . B N PP a r i b a s *0701 - ( ) . K o r ea A ss e t - ( ) . S t a nd a r d C h a r t e r e d*0808 - ( ) H e ungkuk0701 - ( ) . C I M B *1302 - ( ) . I B K - ( ) . RB S *0701 - ( ) . B a r o I nv e s t - ( ) . N e w e dg e *0701 - ( ) . T a u r u s I nv e s t - ( ) . B a r c l a y s *1108 - ( ) . K T B - ( ) . I NG *0906 - ( ) . PREPRINT - A
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24, 2020 ρ XY is the Pearson correlation between variables X and Y and ρ XY · Z is the partial correlation between X and Y controlling the other variable Z . N is the number of observations and w ∗ is the regression coefficient vectors. (cid:104) w ∗ X , z i (cid:105) is the scalar product between a and b . e X,i and e Y,i are the residuals.The Pearson correlation coefficient shows that the individuals have a negative correlation with institutions and foreigners;however, there is an insignificant correlation between the institutions and foreigners. The partial correlation coefficientthat controls the variable of individuals reveals that institutions and foreigners also have a negative correlation. Fig. 1(a)-(c) shows the scatter plot of Samsung Electronics (005930) as an example. Fig. 1 (d)-(f) show the correlation andpartial correlation coefficients for the inventory variations of the three investor types for all 1210 stocks.Next, we investigate the relationship between inventory variations and price returns. For the large market caps, theinventory variations of the institutions and foreigners have a positive correlation with the price return. The inventoryvariation of individuals, however, has a negative correlation with the price return. For the stocks with small market caps,the correlation between the price return and inventory variation converges to zero. Fig. 2 shows the correlation betweenthe inventory variations of the three types and the price returns by market capitalization decile.Figure 1: (a)-(c) Scatter plot for the inventory variations of two variables for Samsung Electronics (005930). (a)Individuals(ID) and Foreigners(FR), (b) Individuals(ID) and Institutions(IS), (c) Foreigners(FR) and Institutions(IS).(d)-(f) Distributions of the Pearson correlation and partial correlation coefficients for the inventory variations of 1210stocks. (d) ID and FR. (Control: IS) (e) ID and IS. (Control: FR) (f) IS and FR. (Control: ID)The classification of a member firm is determined by the ratio of the investor types. Individuals and institutions tradethrough the same domestic member firms. On the other hand, foreigners usually trade through foreign member firms.Unfortunately, the KRX provides no information about the portion of individuals, foreigners, and institutions thattrade through each member firm. We indirectly identify the portion of the trader types in Fig. 3 using the correlationbetween the inventory variation of members and the inventory variations of individuals, foreigners, and institutions. Asshown in Fig. 2, the trading behaviors of the three investor types are clearly distinguished for the first decile of marketcapitalization; thus, we use the first decile to investigate the member firms. For example, in Fig. 3 (a), Kiwoom andhave very high proportions of individual investors, whereas KTB and HI Invest have small portions of individual tradersand relatively high portions of institutions. In general, the members with higher proportions of individuals are the largerfirms.Based on the relative proportion of individuals and institutions, we classify the domestic member firms into threecategories. Domestic members with individuals dominant (DIMs) are on the right bottom in Fig. 3 (a): Shinhan Invest,Korea Invest, Daishin, Mirae Daewoo, NH Invest, KB, Yuanta, Samsung, Kiwoom, eBEST, Mirae Asset, and Hanwha5
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24, 2020Figure 2: Correlation between the inventory variations and price returns for 1210 stocks. The shaded area represents thestandard deviation of the decile.Invest. Domestic members with institutions dominant (DSMs) are on the left top in Fig. 3 (a): Shinyoung, Hanyang,Meritz, Bookook, Yuhwa, Golden Bridge, HI Invest, Baro Invest, Taurus Invest, KTB, CAPE, BNK, IM, and KBInvest. The Foreign member firms (FRMs) are in Fig. 3 (b): JP Morgan, Macquarie, Morgan Stanley, Citigroup, HSBC,CLSA, Credit Suisse, UBS, Merrill Lynch, Goldman Sachs, Societe Generale, Nomura, Deutsche, Daiwa, BNP Paribas,Standard Chartered, CIMB, RBS, Newedge, Barclays, and ING.To understand the characteristics of member firms, we analyze the directionality and the trading trend of each member.We also investigate the directionality and the trading trend of the individuals, institutions, and foreigners that tradethrough member firms and compare them with member firms. We define the directionality and trend to measure thecharacteristics of the trading behavior as follows. Tumminello et al. categorized the states into the primarily buying,primarily selling and buying and selling [13]. Similarly, we define the directionality ( D ), which indicates how much adaily transaction consistently appears. A large directionality means that most of the daily transaction amount has thesame direction. The trend ( T ) represents the relative change in the inventory versus the price movement. D j = 1 N N (cid:88) i P ( | B j,i − S j,i B j,i + S j,i | ≥ θ ) (5) T j = 1 N N (cid:88) i E [( x j,i − µ x j,i )( r i − µ r i )] σ x j,i σ r i . (6) where x j,i = B j,i − S j,i , θ = 0 . , and N = 121 , which is the number of stocks in one decile. B j,i ( S j,i ) is thetime series of the transaction amount of a member firm or investor j to buy(sell) stock i . r i is the return of stock i and µ y is the mean of the variable y . The average length of time series B j,i ( S j,i ) is 247 for each year. j is one of themember firms or one of the individuals, foreigners or institutions. T j > means that member firm or investor j tradesstock in the trending way. Tumminello et al. used the states of a primarily buying state, a primarily selling state and abuying and selling state according to the relationship between B − SB + S and θ [13]. Similarly, we define the directionalityaccording to the relationship between B − SB + S and θ .Fig. 4 (a) shows that the directionalities ( D ) and trends ( T ) of individuals, foreigners, and institutions have differentcharacteristics. For the stocks with large market capitalizations, institutions and foreigners trade in the trending wayin which an inventory change moves in the same direction as a price change. Meanwhile, individuals trade in thereverse way in which an inventory change moves in the opposite direction of the price change. However, the differencein the trend gets smaller for stocks with small market capitalizations. When the market capitalization changes, thedirectionality and trend move in opposite directions. The directionality of individuals, foreigners, and institutions isaround . for larger market capitalizations. However, the directionality of foreigners and institutions increases for those6 PREPRINT - A
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ID,IV -0.3-0.25-0.2-0.15-0.1-0.0500.050.10.150.2 I S ,I V Domestic members
Shinhan InvestKorea Invest DaishinMirae DaewooNH Invest KB YuantaSamsungHI Invest KiwoomeBESTKorea AssetKTB Mirae AssetHanwha Invest (a) -0.08 -0.06 -0.04 -0.02 0 0.02
ID,IV I S ,I V ShinyoungHanyang MeritzBookook HanwhaYuhwaGolden Bridge Baro InvestTaurus InvestCAPEBNKIM KB Invest
ID,IV I S ,I V Kyobo EugeneHyundai Motor SKDB FinancialLeading InvestHana FinancialHeungkukIBKNH (Nonghyup) BNGAppleHanmag
FR,IV -0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.0100.01 I S ,I V Foreign members
JP MorganMacquarie Morgan StanleyCitigroupHSBCCLSA Credit SuisseUBS Merrill LynchGoldman SachsSociete GeneraleNomura DeutscheDaiwaBNP ParibasStandard CharteredCIMBRBSNewedgeBarclaysING (b) -0.4 -0.2 0 0.2
FR,IV -0.3-0.2-0.100.10.2 I S ,I V Figure 3: (a) Mean of the correlation between the inventory variation of domestic members (green circle) and theinventory variation of individuals and institutions. The inset figures (right upper and left lower) show the enlarged views.(a) DIMs are on the right bottom, and DSMs are on the left top. (b) Mean of the correlation between the inventoryvariation of foreign members (purple circle) and the inventory variation of individuals and foreigners. The inset on (b)shows the domestic members (green circle) and foreign members (purple circle) at once. The correlations are averagedover the largest market capitalization decile. The radius is proportional to the square root of the transaction amount.with small market capitalizations. Conversely, Fig. 4 (b) shows the directionality and trading trend of each member forthe first decile’s 121 stocks. The members which trade less than a tenth of the average are excluded. Each point in Fig.4 (b) can be roughly classified into three types. The red circles are the DIMs, as shown in Fig. 3 (a). The green circlesare the DSMs. The purple circles are the FRMs. The DIMs tend to trade against the stock price movement and do nottrade in one direction. On the other hand, the FRMs tend to trade in the same direction as the price movement and tradein one direction. Fig. 4 (c) shows the results of the tenth decile. Unlike the first decile, there is almost no differencebetween the members.
Investors who practice herding mimic the investment decisions of others or exploit similar information as others. Thebehavior of herding comes from a rational or an irrational decision. In financial markets, herding can impact stockprices [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Nofsinger et al. [14] showed the impacts of herding and thepositive feedback of institutional investors. Sias [16] verified that institutional investors follow each other and followtheir past trading. Kremer et al. [23] verified the existence of herding on a daily time scale. The strength of herdingdepends on the volatility. Choe [11] et al. analyzed the Korean stock market and found herding and the positivefeedback trading of foreigners.When investors do buy(sell) during herding, in general, the price goes up(down). The herding of member firms on theKRX, however, shows the opposite phenomena. To analyze the herding of member firms, we introduce the herdingindicator h , the herding indicator with sign H and the direction of herding DH as follows, which are modified from thedefinitions of Zhou et al.[26] from which it is possible to consider the direction of herding:7 PREPRINT - A
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Figure 4: (a) Directionalities ( D ) and trends ( T ) of individual (red), foreigner (purple), and institution (green) investors. θ = 0 . . The darker color refers to the larger market capitalization decile. (b) Directionalities ( D ) and trends ( T ) of themembers for the first decile stocks. Red points represent DIMs, the green points represent DSMs and the purple pointsrepresent FRMs. (c) Directionalities ( D ) and trends ( T ) of the members for the tenth decile stocks. h i,d = P (cid:32) f ( k, n, p ) ≤ . (cid:33) (7) f ( k, n, p ) = (cid:18) nk (cid:19) p k (1 − p ) n − k (8) H i,d = h i,d × sign ( N B,i,d − N S,i,d ) (9) DH i = E [( H i − µ H i )( r i − µ r i )] σ H i σ r i (10)where f ( k, n, p ) is a probability mass function for a binomial distribution f ( k, n, p ) = (cid:0) nk (cid:1) p k (1 − p ) n − k and k = N B,i,d , n = N B,i,d + N S,i,d , p = 1 / . N B,i,d ( N S,i,d ) is the number of member firms that buy(sell) stock i on day d . r i is theprice return for stock i . h i,d is the herding indicator compared to the binomial null hypothesis. h i,d = 1 means themember firms herd the i th stock on day d . H i,d is the herding indicator with the sign. If the number of members buyingthe i th stock is equal to the numbers selling the stock on day d , H i,d = 0 . H i is the time series of H i,d . Because wedivide the whole time series into 11 years sub time series, the average length of each H i is 247. H i,d = 1 refers to buyherding and H i,d = − refers to sell herding. µ H i ( σ H i ) is the mean (standard deviation) of H i . µ r i ( σ r i ) is the mean(standard deviation) of r i , where r i is the price return of stock i . We define DH ( i ) > as herding and DH ( i ) < asherding in the opposite direction. Fig. 5 (a) shows that all member firms herd. FRMs also have weak herding, whereasthe herding of DIM is relatively stronger than that of the others. Fig. 5 (b) shows that the buy(sell) herding of allmember firms makes the price goes down(up). FRMs herd in the direction of the price change; otherwise, domesticmembers herd in the opposite direction. The main reason for the herding in the opposite direction is due to the domesticmembers. There have been several studies about the clustering of investors [27, 28, 13, 29, 30]. Musciotto et al. showed thehierarchical structure and cluster of investors in the Finnish market [29]. Schweitzer et al. analyzed the financialnetwork of financial institutions. We construct a network based on the inventory variation correlation. Apple, Hanmag,Standard Chartered, CIMB, RBS, Newedge, Barclays, and ING are excluded from the network because these membershave been on the Korean market for a short time and their transaction volumes are small, which distort the network. Thecorrelation matrix is made using the daily inventory variation of member firms. The nodes of the network correspond toeach member. The strength of an edge is the mean of the correlation coefficient of the inventory variation. Domesticmembers are represented by circles and foreign members are represented by squares, as shown in Fig. 6. The sizeof a node is proportional to the square root of the trading volume of each member. When the members are separated8
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Market capitalization decile < H > (a) AllDSMDIMFRM
Market capitalization decile -0.5-0.4-0.3-0.2-0.100.10.2 < DH > (b) AllDSMDIMFRM
Figure 5: (a) Probability of herding compared to the binomial null hypothesis. (b) Direction of herding of memberfirms. (a)-(b) All member firms (dotted black line), DIMs (red line), DSMs (green line), FRMs (purple line). All valuesare averaged over 121 stocks in the market capitalization decile and 11 years.and integrated, these are regarded as other member firms. Members who do not exist at the same time may appearon the network but are not connected. We construct the network with a threshold of 0.015. The reason for the lowerthreshold is that the correlation matrix is averaged across multiple stocks and periods. The community structure isdetected using the Information-theoretic method (Infomap) on the first decile network. The modularity is 0.312 forthis network. Depending on the community structure, the network nodes are colored. The red nodes correspond to theDIMs and the green nodes correspond to the DSMs and some FRMs. The blue nodes are mainly FRMs. The DIMswith large transaction sizes form a red cluster, and the remaining small DSMs are strongly forming other green clusters.Through the community structure of the network, we confirm the herding of member firms at the level of each member.
Prior to the previous section, we only dealt with the relationship between the inventories of members. Thus, we willanalyze the connection between the stock prices and the inventory variations in this section. The use of random matrixtheory and a cross-sectional regression will reveal the connection between inventories and stock prices. Many researchershave studied a correlation matrix of stock returns using random Matrix Theory (RMT)[31, 32, 33, 26, 34, 35, 36]. Theyhave found that the largest eigenvalue has some information that cannot be explained by the hypothesis of a randommatrix. The eigenvectors of the largest eigenvalues contain some information about the market trend or industrialsectors. There also have been attempts to apply RMT to the inventory variation of investors. W.X. Zhou et al.[26]studied the dynamics of the inventory variation of traders and found that the largest eigenvector is linearly related toreturns on the Shenzhen Stock Exchange. F. Lillo et al.[31] analyzed the dynamics of the inventory variation of themember firms on the Madrid Stock Exchange. They showed that the factor, which is the projection of the inventoryvariation on the eigenvector of the largest eigenvalue, is linearly related to the price return. Like previous studies, wealso analyze the correlation matrix of the inventory variation using RMT. To reduce the noise and to get meaningfulinformation in the correlation matrix, we employ RMT [37] as follows: ρ c ( λ ) = 1 N dn ( λ ) dλ (11) ρ c ( λ ) = Q πσ (cid:112) ( λ max − λ )( λ − λ min ) λ (12) λ maxmin = σ (1 + 1 /Q ± (cid:112) /Q ) (13)where n ( λ ) is the number of eigenvalues smaller than λ . N is the total number of eigenvalues, which, in this case, isthe number of member firms. Eq. 5 is the density of the eigenvalue and Eq. 6 is the density of the eigenvalue from the9 PREPRINT - A
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24, 2020Figure 6: Network and community structure of members for the first decile group. The domestic members arerepresented by circles and the foreign members are represented by squares. The size of a node is proportional to thesquare root of the transaction amount. The color of a node refers the community groups using the Infomap communitydetection method.hypothesis of a random matrix, where Q = T /N (cid:39) / (cid:39) . . The average length of time series is 247 becausewe analyze the data yearly. Time series x of the inventory variation has a dimension of N × T , and so the correlationmatrix of the inventory variation has a dimension of N × N . In this study, N is approximately 62, which is the numberof member firms. F actor ( t ) = (cid:88) i x i ( t ) u i ( λ )( t ) (14) x i is the inventory variation of stock i , λ is the largest eigenvalue, and u i ( λ ) is the eigenvector of the largesteigenvalue.We find the extent to which a factor describes the price return, depending on the size of the market capitalization ofthe stock. We verify that the factor is linearly related to the price return. Fig. 7 (a) shows the eigenvalue spectrumcompared to the random matrix hypothesis. We confirm that there is the largest eigenvalue that is not described by arandom matrix. In Fig. 7 (b), we find that the 1st decile that represents the largest market capitalization group (darker)10 PREPRINT - A
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24, 2020has a larger correlation and eigenvalue than the smallest group (lighter). Fig. 7 (b) is the average values over the tenrespective deciles. The larger the market capitalization is, the more the factor explains the return. This is because theabsolute value of the trend ( T ) is large, as shown in Fig. 4 (b). Because of the large difference between the trendsof each investor type, the differences in the characteristics between member companies become clear and eventuallyexplain the return as a correlation matrix of the inventory variation. largest eigenvalue( )0 1 2 3 4 500.10.20.30.40.50.60.70.80.9 () (a) datasetrandom matrix Corr. factor and return La r ge s t e i gen v a l ue ( ) y=2.28+2.64x, R =0.90 Figure 7: Random matrix theory. (a) Distribution of the eigenvalues of the correlation matrix of inventory varia-tion(histogram) and the distribution of the eigenvalues of the random matrix(dotted line). (b) Largest eigenvalue. andcorrelation between the factor & return. The 1st-10th decile groups. The larger market capitalization group is, thedarker the color is.Furthermore, we quantitatively analyze how the herding of members affects the stock price using a cross-sectionalregression as follows: R it − R ft = α + β ( R Mt − R ft ) + β H DSM (15) + β H DIM + β H F RM + Y ear (16)where R it is the return of stock i at time t and R ft is the return of a risk free asset at time t . We use the Korea 10-yearsbond yield rate as the risk-free asset. H DIM means the herding of DSMs. H DIM andH
F RM mean those of DIMs andFRMs, respectively.
Y ear is the dummy variable representing the yearly effects. As shown in Table 3, in addition tomarket factor, herding also has a significant relationship with the stock price. The DIMs have negative coefficients. Onthe other hand, the herding of DSMs and FRMs has positive coefficients. In the cross-sectional regression, we find thatthe R-squared value increases when considering the herding of members rather than just the market factor. We confirmthat the inventory variation possesses information about the stock price and how much the herding of members affectsthe price through this section.
We analyze the trading characteristics of the member firms on the Korea Exchange. We deal with the difficulty ofidentifying the members by comparing the inventory variations of three types of investors. The properties of membersare determined by their correlations with individuals, institutions, and foreigners. We also measure the directionalityand trend to understand the dynamics of the member firms. The foreign members tend to trade in a one-way directionand trade in the same direction as a price movement. DIMs have a weak trading direction and trade in the oppositedirection of a price movement. The herding of members moves in the opposite direction of a price change, unlikethe common herding of investors. While FRMs do weak herding and move in the direction of a price movements.We construct a network of member firms from which we identify the connections between the members with similar11
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24, 2020Table 3: Table of the cross-sectional regression results. The independent variables are the market factor, the herding ofdomestic members, and the herding of foreign members. The dependent variable is the price return of each stock.
Dep. Variable: returns
R-squared:
Model:
OLS
Adj. R-squared:
Method:
Least Squares
F-statistic:
Log-Likelihood:
Df Model: No. Observations:
AIC: -1.565e+06
Df Residuals:
BIC: -1.564e+06 coef std err t P > | t | [0.025 0.975] α C(year)[T.2008]
C(year)[T.2009] -0.0007 0.000 -3.761 0.000 -0.001 -0.000
C(year)[T.2010] -0.0005 0.000 -2.812 0.005 -0.001 -0.000
C(year)[T.2011] -0.0001 0.000 -0.588 0.556 -0.000 0.000
C(year)[T.2012] -0.0007 0.000 -3.773 0.000 -0.001 -0.000
C(year)[T.2013] -7.659e-05 0.000 -0.415 0.678 -0.000 0.000
C(year)[T.2014]
C(year)[T.2015]
C(year)[T.2016] -0.0007 0.000 -3.936 0.000 -0.001 -0.000
C(year)[T.2017] -0.0003 0.000 -1.711 0.087 -0.001 4.62e-05
Market H DSM H DIM -0.0285 0.000 -225.522 0.000 -0.029 -0.028 H F RM
Acknowledgments
This study was supported by research fund from Chosun University (K206026014-1, 2017)
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