Parabolic Impact Law of High Frequency Exchanges on Price Formation in Commodities Market

Transcription

1 Parabolic Impact Law of High Frequency Exchanges on Price Formation in Commodities Market L. Maiza, A. Cantagrel, M. Forestier, G. Laucoin, T. Regali Undergraduate Students, ECE Paris School of Engineering, France. Abstract Evaluation of High Frequency Trading (HFT) impact on financial markets is very important for traders who use market analysis to detect winning transaction opportunity. Analysis of HFT data on tobacco commodity market is discussed here and interesting linear relationship has been shown between trading frequency and difference between averaged trading prices above and below considered trading frequency. This may open new perspectives on markets data understanding and could provide possible interpretation of Adam Smith invisible hand. Keywords: Financial Market, High Frequency Trading, Analysis, Impacts, Adam Smith Invisible Hand 1

2 1. Introduction The High Frequency Trading (HFT) came out in the context of computerization of financial markets, and grew up significantly in the last decade. On Thursday May 6, 2010, the so-called flash crash greatly perturbed all financial markets and the question arose to understand the role of HFT in this event [6]. Since then, many papers have been written on HFT [9,10,12,13,17] with non-definitive assessments on its real impact in usual close-loop market situation, implying that there might exist self-correcting effects guaranteeing price convergence at least within some robustness ball which is still to be defined. It might be said that HFTs engage in successful intra-day market timing, that spreads are wider when HFTs provide liquidity and tighter when HFTs take liquidity[2,8,15] and prices incorporate information from order flow and market-wide returns more efficiently on days when HFT participation is high. On the other side, HFT actors are hiding their strategy by the possibility to slice their orders in seemingly completely random way which gives them advantage for better optimal execution of their orders, making market conditions uneven [5,20] or costly [4,19]. On both sides, long run traditional bid-ask decisions should not be affected by very short time market operations as they are resting on more global economic approach to company stocks and economy background in general [1,3,7]. Nevertheless, ultra-short term strategies can endanger the market by decoupling too much price from share flow and making stocks oscillations more unstable with observed flash crash risk [16,18]. It is thus important to evaluate the influence of HFT on different markets as today one of the most significant market structure developments in recent years is high-frequency trading [14]. HFT activity in the market is estimated to represent over 70% of orders, placed on stock exchange according to Figure 1. Figure 1 : Flash Order Trading HFT is nowadays an important transaction component for price formation in most markets implying direct exchange between the two classes of buyers and sellers which was previously regulated by classical search of an agreement from order book [11,14]. This new much faster possibility of influencing price formation has been raising very important questions concerning the meaning of a price as its speed imposes it to be only managed by machine programs, in the double aspect of market quality parameters, such as liquidity, volatility or 2

3 prices informativeness, and of profitability and fairness (especially fair access) with evident robustness and risk management issues [1,2]. In this context, the goal of present Note is to specifically analyse the impact of HFT on commodities market on the very basic aspect of price variation with trading frequency. Effectively, because HFT is managed by computers with pre-established optimizing program, it is important prior to more detailed analysis to check how much influential is trading frequency on price formation. For instance, if HFT price appears to be only depending on trading frequency without any other market parameter, the representative system model is a decoupled one with two different, regular and high frequency, markets interacting by the only effect of volume exchange. In any case access to the nature of interaction between regular and high frequency markets is fundamental for system model construction. A first step will be started here by extracting from collected data the variation of HFT price with trading frequency, which will be shown to have a canonical parabolic dependence. As the domain is still too much undefined, the analysis will be further concentrated on a single commodity on which there exists enough data. Present choice has been to focus on tobacco markets for which available data are yet unexploited especially concerning the impact of HFT on them. In fact there are many parameters impacting rates like weather, political agreements, wars and other ones much too difficult to predict, making HFT difficult to position on these markets. 2. Data Analysis High Frequency Data have been collected from BATS Chi-X Europe database on quoted indexed funds. To deal with them, a VBA Excel code has been set up for translating rough reference given by the BATS to more understandable references, see Figure 2. Figure 2. Rough vs Processed Usable Data Large data sets can be collected on different ETF Equity stock. Only tobacco data collected under the files BATSl and IMTl will be considered here. They refer to British American Tobacco ( BATSl in BATS data) a large tobacco-producing company in the world (BAT owns Lucky strike, Dunhill ), and to Imperial Tobacco ( IMTl ) the fourth tobacco group producer in the world. Behaviours of their stock are displayed on Figures 3 and 4 3

4 respectively. They show that daily price variation between lowest and highest trade (thin vertical bar) is usually very large, even if final variation of the day (rectangular block) can be relatively small, either in gain (green block) or in loss (red block). At the same time volume variation does not seem to indicate a strong correlation with price evolution. Figure 3: Weekly BATSl Cotation and Volume from 27/04 to 18/05/2012 Sources: Graph: les echos Figure 4: Weekly IMTl Cotation and Volume from 27/04 to 18/05/2012 Sources: Graph: les echos 3. Treament Model However, as high frequency in HFT acronym is up-to-now not clearly determined previous statement is not firmly based. Indeed in finance the high frequency is not associated to a specific reference frequency. In present study, order frequency will be considered as high one when it cannot manifestly be executed by human operator. Minimum frequency cutoff F c,min is here taken as 5/mn and in the sequel different cut-off frequencies F c F c,min will be considered. Order files have then been associated to their specific ID, and one will associate to them from records of order book a frequency of passing order (F p = Number of orders placed / time to place these orders), from which the different identified orders can be separated into two groups depending on whether the average daily order frequency <F p> is 4

5 larger or smaller than a given F c. Data are now treated to obtain representative curves of order frequency impact on price trend. It is possible to observe a gap between average sale prices when the orders are passed with frequency <F p> > F c. Data are thus plotted according to obtained frequencies, see for instance Figure 5 for high segment. Clearly, prices have very small amplitude variations except for very specific frequencies (the high peak on Figure 5). Figure 5: High Frequency Traded Stock Price ( ) vs. Time (ms) To relate transaction price average to placing order frequency, and instead of using classical averaging methods, a specially adapted filtering operator F(.) will be applied to collected data. This smoothing filter is designed for extracting real dependence behind fluctuating spurious observations sometimes related to outer effects. Let I = [F m,f M] the F M m. For a cut-off frequency F c (F m F c F M), define the upper and lower sub- + = F M c = F c m and the upper and lower average transaction prices <P> + and <P> by the expression <P> ±( F c ± P(F)dF (1) ± is the interval over which the integral is performed with F>F c (resp. F<F c) for frequency above and below F c. Finally the difference F(P) = [P] = <P> + between these two averages is performed in order to obtain its variation vs cut-off frequency F c. The curve is plotted on Figure 6. 5

6 Figure 6: Average Price Variation [P] vs. Cut-off Frequency Fc Four remarks are in order concerning this curve. First, the minimum high frequency F c,min taken as the limit above which transactions are considered as HF corresponds in fact to a break point of the curve. Second, the variation of difference [P]( F c) is much lower in HFT domain, which may express the fact that in this domain of frequency automatizing transactions makes them more reactive to any even small variation in stock values. Third, a remarkable observation is the almost perfect linearity of variation law [P]( F c) = AF c + B G(F c) (2) for F c > F c,min = 5orders/mn and which extends over a factor of 33 (from 5 to 165). Fourth, the error of obtained points with respect to the straight line is extremely small, indicating the high efficiency of filter F(.) [21]. To return back to P(F), it can be noted that (2) with (1) can also be written in explicit form with c) = D M(F c M + D m(f c m M m)d m(f c)d M(F c)g(f c) (3), D M(x) = (F M m) m), D m(x) = (F M m) (F M (4) and M = M) m m). It is then possible to reconstitute function P = P(F) from (3,4). With linear form (2) one easily gets P(F) P(F m) = D M(F){2B F M F m)] + AF} (5) which is exactly parabolic in interval I = [F m,f M]. Conversely, it can be checked that if P(F) is parabolic, then [P](F) is just linear, a property which can be verified with greater accuracy than initial parabolic behaviour of P(F), and justifies the use of filter F. Note that when B 6

7 M m) < 0, P (F m) < 0 ie P(F) decreases for F > F m. This means that for A,B > 0, there exists an upper bound F MAX MAX m) = 0. Beyond this value and if linear form (2) is still valid, HFT practice would lead to a loss and does not represent any interest. Present result suggests that price formation is not a completely random phenomenon as commonly assumed for convenience in most models. Clearly access to HFT opens new possible trade-offs compared to classical trading which are apparently not endangering market convergence. The origin of very strong dependence of P vs F could be the tight nature of optimizing program deciding sell-buy orders on HFT market. These points will be verified elsewhere on other commodities and stocks. 4. Conclusion From observed data, HFT operators play a role as "market makers", as they place orders to the best limits of order book, which tends to improve available price for investors. In quantitative terms, it has been shown from analysis of collected data concerning flow and price of tobacco commodity that there exists a linear relation between the gap from equity prices and frequency of orders, expressing through this analysis filter the fact that order price has parabolic dependence with respect to trading frequency. This would mean that price difference increases significantly when the flow increases. As flow and price are not evolving independently, this may question on possible manifestation of an Adam Smith hidden hand driven by HFT acting on the market. References Alridge, I., High Frequency Trading: a Practical Guide to Algorithmic Strategies and Trading Systems, J. Wiley and Sons, New York, Bessembinder, H., Venkataraman, K., Does an Electronic Stock Exchange Need an Upstairs Market? J. Financial Economics, Vol.73, pp.3-36, Brogaard, J., Hendershott. T., Riordan. R., High Frequency Trading and Price Discovery, Working Paper UC Berkeley, Carrion, A., Very Fast Money: High Frequency Trading on the NASDAQ, J. Financial Markets, Vol.16, pp , Cartea, A., Jaimungal, S., Modeling Asset Prices for Algorithmic and High Frequency Trading, Applied Math. Finance, Vol.20(6), pp , Cont, R., Stoikov, S., Talreja, R.,: A Stochastic Model for Order Book Dynamics, Operations Research, Vol.58, pp , Domowitz, I., Yegerman, H.,: The Cost of Algorithmic Trading: A First Look at Comparative Performance, B.R. Bruce, ed.: Algorithmic Trading: Precision, Control, Execution, Institutional Investor, London, Domowitz, I., Yegerman, H.,: the Cost of Algorithmic Trading: a First Look at Comparative Performance, J. Trading, Vol.1 (1), pp.33-42,

8 Durbin. M.: All about High Frequency Trading, McGraw-Hill, Gomber, P., Arndt, B., Lutat, M., Uhle, T.,: High-Frequency Trading, Deutsche Börse AG, Frankfurt, pp.1, Groth, S.,: Does Algorithmic Trading Increase Volatility? Empirical Evidence from the Fully Electronic Trading Platform Xetra, Proc. & Àth Intern. Conf on Wirtschaftsinformatik, Zurich, Gsell, M., Gomber, P.,: Algorithmic Trading Engines vs Human Traders. Do they Behave Different in Securities Markets?, in S. Newell, E.A. Whitley, N. Pouloudi, J. Wareham, L., Mathiassen, eds: Proc. 17th European Conference on Information Systems, pp , Verona, Italy, Hendershott, T., Jones, C.M., and Menkveld, A.J.: Does Algorithmic Trading Improve Liquidity? J. of Finance, Vol.56 (1), pp.1-34, Jarrow, R.A., Protter, P.,: Liquidity Suppliers and High Frequency Trading, to appear in SIAM J on Financial Mathematics, Kearns, M., Kulesza, A., Nevmyvaka, Y.,: Empirical Limitations on High Frequency Trading Profitability, J. of Trading, Vol.5, pp.50 62, Kirilenko, A.A., Kyle, A.S., Samadi, M. Tuzun, T., : The Flash Crash: The Impact of High Frequency Trading on an Electronic Market, Working paper, 2011, Maiza, L.,: A New Filter for Data Analysis, to be published. Maystre, N., Bicchetti, D.,: The Synchronized and Long-Lasting Structural Change on Commodity Markets: Evidence from High Frequency Data, Algorithmic Finance, Vol.2 (3-4), pp , Menkveld, A.J.,: High Frequency Trading and the New-Market Makers, J. Financial Markets, Vol.16(4), pp , Securities and Exchange Commission: Concept Release on Equity Market Structure. Release No , Jan. 13, Wei-Pan, A.S., Pentland : High Frequency trading, a Simulation, Working Paper, 2012, MIT. 8