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

6they have information that indicates it is favorable todo so. This phenomenon is called adverse information.When this is properly taken into account, limit ordershave impact in the direction one would expect, i.e. buyinghas positive impact and selling has negative impact[32, 33]. Furthermore the magnitude of the impact oflimit orders when the selection effects are properly takeninto account is comparable to that of market orders.For the BME we have a record of transactions but notof orders. Thus to measure market impact and avoid theselection bias associated with executed limit orders weare forced to use only those hidden orders that are predominantlybuilt out of market orders. For consistencywe analyze both the BME and the LSE data in the sameway.In Table I we show the mean value of the rescaledmarket impact R of Eq. (13) for hidden orders of durationless than one day. We also show the mean value〈R〉 fmo>0.8 of the rescaled market impact computed overthe set of hidden orders with a large fraction of marketorders (f mo > 0.8). 〈R〉 fmo>0.8 is significantly largerthan 〈R〉 indicating that hidden orders mainly composedby market orders have on average a larger market impactthan hidden orders composed of both limit and marketorders.D. Impact vs. NFigure 4 shows the average over all hidden orders ofthe rescaled market impact 〈R|N〉 as a function of theconditioning variable N. This grows slightly as a functionof N, but one must keep in mind that the meaning of thisis difficult to interpret in view of the discussion above,since we are averaging together a roughly equal numberof market orders and executed limit orders.To investigate the average market impact and minimizethe effect of the selection bias, we divide the data into twogroups: liquidity providing hidden orders, with f mo 0.8. As expected, for the former group the market impactis on average negative, while for the latter it is positive.Using ordinary least squares, we find that for both groupsthe dependence of 〈R|N〉 on N is well described by thepower law|〈R|N〉| = A N γ . (15)The estimated parameters are in Table II. In summary,we find that the market impact of hidden orders dominatedby market orders is consistent with〈r|N〉 ∝ ɛsN γ (16)where ɛ is the sign of the order and s is the spread. Forhidden orders dominated by limit orders the market impactis very similar to minus the impact of hidden ordersdominated by market orders.Table II: Parameters of the fitting of the market impact withEq. 15.Market A fmo>0.8 γ fmo>0.8 A fmo