Quantitative Finance, Vol. 5, No. 4, August 2005, 357–364 Order book approach to price impact P. WEBER and B. ROSENOW* Institut fu¨ r Theoretische Physik, Universita¨ t zu Ko¨ ln, D-50923 Germany (Received 16 January 2004; in final form 23 June 2005) Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information about potential supply and demand for a stock. The virtual price impact calculated from this information is four times stronger than the actual one and explains it only partially. However, we find a strong anticorrelation between price changes and order flow, which strongly reduces the virtual price impact and provides for an explanation of the empirical price impact function. Keywords: Order book; Price impact; Resiliency; Liquidity In a perfectly efficient market, stock prices change due to to be a concave function of volume imbalance, which the arrival of new information about the underlying com- increases sublinearly for above average volume imbal- pany. From a mechanistic point of view, stock prices ance. However, there is evidence that this concave shape change if there is an imbalance between buy and sell cannot be a property of the true price impact a trader in an orders for a stock. These ideas can be linked by assuming actual market would observe. Firstly, such a concave that someone who trades a large number of stocks might price impact would be an incentive to do large trades have private information about the underlying company, in one step instead of breaking them up into many smaller and that an imbalance between supply and demand trans- ones as is done in practice. Secondly, in the presence mits this information to the market. In this sense, volume of bluffers in the market, the enforcement of a strictly imbalance and stock price changes should be connected linear price impact is the only way in which a market causally, i.e. prices go up if demand exceeds supply and maker or liquidity trader can protect herself against go down if supply exceeds demand. The analysis of huge suffering losses. financial data sets (Takayasu 2002) allows a detailed One possible way to achieve a better understanding of study of the price impact function (Hasbrouck 1991, the average price impact is the analysis of information Hausman et al. 1992, Kempf and Korn 1999, Evans about potential supply and demand stored in the limit and Lyons 2002, Hopman 2002, Plerou et al. 2002, order book. Using this information, one can calculate a Rosenow 2002, Bouchaud et al. 2003, Gabaix et al. virtual or instantaneous price impact, which would be 2003, Lillo et al. 2003, Potters and Bouchaud 2003), caused by a market order matched with limit orders which quantifies the relation between volume imbalance from the order book. This virtual price impact can be and price changes. used as a reference point for an understanding of the In a series of previous studies (Hasbrouck 1991, average price impact of market orders. An analysis of Hausman et al. 1992, Kempf and Korn 1999, Evans the limit order book of the Stockholm Stock Exchange and Lyons 2002, Plerou et al. 2002, Rosenow 2002, (Sandas 2001) suggests that the virtual price impact cal- Bouchaud et al. 2003, Gabaix et al. 2003, Lillo et al. culated from the order book is significantly larger than 2003, Potters and Bouchaud 2003), the average price what is expected from a regression model. Similarly, impact of an imbalance between buy and sell market a difference between hypothetical and actual price impact orders or of individual market orders was studied. was found in Coppejans et al. (2001) and considered as Generally, this average price impact function was found evidence for discretionary trading, e.g. large trades are more likely to be executed when the order book has sufficient depth. In this paper, we calculate both the average price *Corresponding author. Email: [email protected] impact of market orders and the virtual price impact Quantitative Finance ISSN 1469–7688 print/ISSN 1469–7696 online # 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/14697680500244411 358 P. Weber and B. Rosenow Table 1. Summary statistics for the ten stocks studied. All values are calculated for five minute intervals. Numbers in brackets are in units of the respective standard deviation. AMAT BRCD BRCM CSCO INTC KLAC MSFT ORCL QLGC SEBL Returns G 0.004 0.0053 0.0049 0.0034 0.0034 0.0036 0.0025 0.0039 0.0041 0.005 Gmax 0.026 0.057 0.039 0.037 0.023 0.026 0.021 0.049 0.033 0.066 j j (6.46) (10.77) (8.1) (11.05) (6.86) (7.17) (8.3) (12.74) (8.02) (13.23) Median of |G| 0.0022 0.0028 0.0025 0.0018 0.0018 0.002 0.0013 0.002 0.0022 0.0026 (0.55) (0.53) (0.52) (0.52) (0.55) (0.55) (0.53) (0.51) (0.55) (0.52) Volume imbalance Q 9551.78 9700.37 6196.3 22652.52 16660.35 5862.25 11029.98 16010.11 6513.98 7152.31 Qmax 344657 193633 127274 424923 323016 116790 376168 396978 82540 189966 j j (36.08) (19.96) (20.54) (18.76) (19.39) (19.92) (34.1) (24.8) (12.67) (26.56) Median of |Q| 5958 6069 4086.5 14902.5 11208 3648 7307.5 10100 4078.5 4429 (0.62) (0.63) (0.66) (0.66) (0.67) (0.62) (0.66) (0.63) (0.63) (0.62) Market orders N 52.38 45.31 44.97 58.34 72.62 58.89 83.59 47.41 56.82 35.02 h marketi Nmarket 33.89 36.4 36.83 39.3 49.14 39.92 53.31 37.43 37.72 30.92 Limit orders N 321.27 247.06 233.54 302.6 391.91 344.59 429.8 227.17 303.68 199.99 h addedi Nadded 183.49 156.22 160.86 213.87 232.65 169.97 244.83 165 162.02 156.01 N 286.91 220.13 206.39 256.38 343.71 305.64 376.4 191.54 268.41 177.09 h cancelledi Ncancelled 173.15 144.14 144.22 199.23 220.71 154.95 229.11 152.41 146.79 141.82 from information contained in the Island ECN order and cancellation of limit orders. If a trader is willing to book. By comparing the two, we find that the virtual sell a certain volume (number of shares) of a stock at price impact is more than four times stronger than the a given or higher price, she places a limit sell order. actual one. In order to explain this surprising discrepancy, For buying at a given or lower price, a limit buy order we study time-dependent correlations between order flow is placed. Limit orders are stored in the order book at and returns and find strong evidence for resiliency: the their respective price with the respective volume. The market recovers from random uninformative price shocks sell limit order with the lowest price defines the ask as the flow of limit orders is anticorrelated with returns price Sask for that stock. Similarly, the buy limit order in contrast to the positive correlations between returns with the highest price defines the bid price Sbid. If a buy and market orders. Thus, limit orders placed in response limit order with a price higher than the current ask price is to returns strongly reduce the virtual price impact placed, it is executed immediately against the sell limit and provide for a link between virtual and actual price orders at the ask price, vice versa for sell limit orders at impact. or below the bid price. Such marketable limit orders We include the possible influence of discretionary will be called market orders in the following. Market trading in our analysis by studying the average virtual orders are placed by impatient traders who want to trade price impact, the typical virtual price impact and the vir- immediately. tual price impact calculated from the average order book. The time period we study is the entire year 2002. Each The average virtual price impact is strongly influenced day, we disregard the first five minutes due to the build by low liquidity periods and hence not representative up of the order book. We checked that our results are for the actual impact of market orders. In order to include robust with respect to this choice by removing e.g. the the influence of discretionary trading in a semiquantita- first fifteen minutes and the last five minutes per day. tive way, we base our analysis on the virtual price impact We consider 250 trading days and divide each trading as calculated from the average order book, which is day into 77 intervals of five minute length. weaker than the average and the typical price impact. We chose the 10 most frequently traded stocks for Including the effect of resilience as apparent from the the year 2002, ticker symbols and descriptive statistics above-mentioned anticorrelations, the actual price can be found in table 1. The volume of market buy orders impact can be explained quantitatively. is counted as positive and the volume of market sell We analysed limit order data from the Island ECN, orders as negative, and the volume imbalance Q(t) is NASDAQ’s largest electronic communication network, defined as the sum of all signed market orders placed which comprises about 20% of all trades.