Market impact and trading profile of large trading orders in stock ...

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2data sets each transaction is labeled with codes identifyingthe members of the exchange who made the transaction.In most cases the member is acting as a broker,i.e. they are handling a trade for another institutionwho is not a member of the exchange. In other cases themember may trade for their own account. Thus a singlemembership code may lump together trades from manydifferent institutions, originated by many different tradingstrategies. As a consequence several hidden ordersfrom different trading accounts may be active with thesame broker at the same time, making it impossible tobe certain that all orders are correctly identified.The detection problem is aided by the fact that thesize of hidden orders has a heavy-tailed distribution, andlarge hidden orders can cause dramatic changes in therate at which a given membership code participates intrades to either buy or to sell. The method we use wasoriginally developed for detection of local stationary regionsin physiological time series [28]. As we use it here, itlooks for time intervals in the time series of orders comingthrough a given membership code when the firm acts asa net buyer or seller at an approximately constant rate.As in reference [27] we interpret these series of tradesas belonging to hidden orders. This method can neverbe perfectly accurate, but a variety of tests performedin reference [27] suggest that the reconstruction is goodenough to recover the most important statistical propertiesof hidden orders reasonably well. An importantadvantage of this approach is that we are able to studylarge samples of hidden orders coming from the wholemarket rather than only a subset belonging to a specificinstitution.The paper is organized as follows. In Section II wediscuss our data sets, the algorithm for detecting hiddenorders and the investigated variables. In Section IIIwe discuss the statistical properties of the variables characterizingthe hidden orders. In Section IV and V wepresent our empirical results on the impact of hidden ordersand on their trading profile, respectively. Section VIconcludes.II.DATA AND INVESTIGATED VARIABLESOur databases contain the on-book (SETS) markettransactions of the London Stock Exchange (LSE) fromJanuary 2002 to December 2004 and the electronic openbookmarket (SIBE) of the Spanish Stock Exchange(BME, Bolsas y Mercados Españoles) from January 2001to December 2004. Roughly 62% of the transactionsat the LSE are executed in the open book market androughly 90% of the transactions at the BME are executedin the electronic market.We have initially considered a subset consisting of themost heavily traded stocks in the two markets, 74 stockstraded in the LSE and 23 stocks traded in the BME. Forboth markets we have considered exchange members whomade at least one trade per day for at least 200 tradingdays per year and with a minimum of 1000 transactionsper year. This filter yielded approximately 60 exchangemember firms per stock. We then applied the algorithmfor detecting hidden orders described in Ref. [27], whichwe have already discussed, to identify hidden orders thatconsist of at least ten transactions. It is worth notingthat the detected patches are not necessarily composedof the same type of trades (buy or sell) but that at least75% of the transacted volume in the patch must have thesame sign. The algorithm detected 90,393 hidden ordersin the LSE and 55,309 in the BME.This study is based entirely on trades that take placethrough a continuous double auction. “Continuous”refers to the fact that trading takes places continuouslyand asynchronously, and “double” to the fact that bothbuyers and sellers are allowed to place and cancel ordersat any time. There are two fundamentally different waysto execute an order in such a market. One is to use alimit order, in which an order is placed inside the orderbook, which is essentially a list of unexecuted orders atdifferent prices. The other is to place a market order,which we define as any order that results in an immediatetransaction. Every transaction involves a marketorder transacting against a limit order. A given real ordermight act as both, e.g. part of it might result in animmediate transaction and part of it might be left in theorder book. We only consider transactions, so in the exampleabove we would treat the first part as a marketorder and treat the second part as a limit order, but thesecond part will enter our analysis only if it eventuallyresults in a transaction. The LSE database allows us toidentify whether the initiator of the transaction was thebuyer or the seller. For BME this information is not availableand we infer it with the Lee and Ready algorithm[29]A hidden order is characterized by several variables.These are• The execution time T (in seconds) of the hidden order,measured as the trading time interval betweenthe first and the last transaction of the hidden order.• The number N of transactions of the hidden order.We consider hidden orders of length N > 10.• The volume V of the hidden order defined asV =N∑v j , (1)j=1where v j is the signed volume of each transactionof the hidden order. For buy trades v i > 0 and forsell trades v i < 0. We consider the hidden order tobe a buy order if V > 0 and a sell order if V < 0.The buying/selling nature of a hidden order is thusencoded in its sign, ɛ = sign(V ). The volume is theproduct of the number of shares times the price andis measured in Pounds (LSE) or in Euro (BME).
3• The volume fraction of market orders f mo . A hiddenorder can be implemented with very differentliquidity strategies, i.e. with different compositionsof market and limit orders. In order to quantifythis we define the fraction (in volume) of marketorders within a hidden order as∑ Nj=1f mo =|v j,mo|∑ Nj=1 |v , (2)j|where v j,mo is the traded volume at each transactiondone through market orders. Values of f moclose to zero mean that the broker completed thehidden order by using mainly limit orders, whilevalues of f mo close to one imply the broker usedmainly market orders during the execution of thehidden order.• The participation rate α of a hidden order definedas∑ Ni=1α =|v i|, (3)V Mwhere V M is the unsigned volume of the stocktraded in the market concurrently with the hiddenorder. Values of α close to zero imply the hidden orderwas negligible compared to the activity in themarket, while values of α close to one mean thatmost of the activity in the market came from thetransactions of the hidden order.Summarizing, we expect that the market impact of ahidden order is a functionr = f(N, V, T, f mo ), (4)plus possibly other variables specific of the stock, suchas the participation rate, the capitalization, the volatility,or the spread. We will now try to simplify this byunderstanding some of the relationships between the dependentvariables and by conditioning on some of themin our analysis. Note that in all the analyses and figureswe compute error bars as standard errors. It should beborn in mind that this procedure underestimates the errorsdue to the heavy tails of the fluctuations and due topossible long-memory properties of the data.III.STATISTICAL PROPERTIES OF HIDDENORDERSWe investigate the statistical properties of the variablescharacterizing hidden orders. Ref. [27] considered a set of3 most capitalized stocks traded at the BME and studiedthe probability distribution of the variables characterizingthe hidden orders and the scaling relations betweenthese variables. In Ref. [27] no restriction on the lengthor on the fraction of market orders was set on the hiddenorders. The authors of Ref. [27] found that the distributionof hidden order size is fat tailed and consistent witha distribution with infinite variance. They also showedthat this broad distribution is due to an heterogeneity ofscales among different brokerage firms rather than to theheterogeneity of scales within the hidden orders of eachbrokerage firm. By using Principal Component Analysis(PCA) on the logarithm of the variables characterizingthe hidden orders, it was found that N, V and T arerelated through scaling relationshipsN ∼ V g1 , T ∼ V g2 , N ∼ T g3 . (5)where g 1 ≃ 1, g 2 ≃ 2 and g 3 ≃ 0.66 for 3 highly capitalizedstocks in the BME and including all hidden orders.We repeat the two dimensional PCA analysis of [27] onour much larger data set. Figure 1 shows the value ofthe three exponents for all the stocks as a function ofthe number of hidden orders per year. We observe thatfor stocks with a small number of hidden orders the heterogeneityin the value of the exponents is pretty large,while, as the number of hidden orders detected by the algorithmincreases, the exponent estimations become lessnoisy and tend to converge to similar values. Moreoverfor BME stocks there is a clear trend of the exponents asa function of the number of hidden orders. In order tomeasure market impact in a statistically reliable way, wepool together data from different stocks. We need thereforean homogeneous sample of stocks. To this end in thefollowing analysis we restrict our dataset to those stocksfor which our algorithm detects at least 250 orders peryear. These stocks are TEF, SAN, BBVA (as in [27]) butalso REP, ELE, IBE, POP and ALT for the BME marketand AZN, BSY, CCH, DVR, GUS, KEL, PO, PSON,SIG, TATE and TSCO for the LSE market. Moreover, inthis paper we will focus mainly on short hidden orders,considering the set of hidden orders of time duration Tsmaller than one trading day. The reason for this choice,detailed below, is to obtain stable statistical averages forthe market impact. Applying these two restrictions, weobtain a final dataset that contains 14,655 hidden ordersin the BME and 11,165 orders for the LSE (see Table I).We repeat the two-dimensional PCA analysis of [27] onthe pooled set of hidden orders from different stocks. Wefind for the BME market the following exponentsg 1 = 0.81 (0.79; 0.82), (6)g 2 = 1.57 (1.43; 1.72), (7)g 3 = 0.67 (0.65; 0.68), (8)where quantities in parenthesis are 95% confidence intervalsobtained through bootstrapping the data. Theserelations explains 83%, 61% and 80%, respectively, of thevariance observed in the data. For the LSE dataset wegetg 1 = 0.99 (0.98; 1.01), (9)g 2 = 2.41 (2.29; 2.52), (10)g 3 = 0.58 (0.57; 0.59), (11)
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