Statistical Arbitrage in High-Frequency Trading

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 Previous studies and theoretical framework

Conception of algorithmic trading. Literature, approaches and methods

Substantial development of information technologies (IT) stimulated the beginning of “electronic revolution”, which allowed market participants to use all the accessible market services without the need of physical presence in exchanges centers. For relatively short period of time, IT led to dramatically increased automation of order-execution process.
From the end of 1990s, the electronification of market orders’ execution made it possible to transmit orders electronically, but not by telephone, mail, or in person, as it was before that, and, as a result, the biggest part of trading on modern world financial markets is implement by internet and computer systems (Chlistalla, 2011).
This fact, obviously, made it possible to use different trading algorithms widely in everyday trading practice.
Algorithmic trading is a formalized process of making deals on the financial markets based on a given algorithm and using special computer systems (trading robots) (Lati, 2009).
Algorithmic trading (AT) is a broad term that can describe quite a wide range of methods and different techniques. It is crucial to understand that algorithmic trading should not be necessary associated with the speed of decision making and sending orders. These things characterize a subgroup of algorithmic trading, which is called high-frequency trading (HFT). Originally, AT was mainly used for managing orders, as an attempt to decrease market influence by optimizing trade execution.
Possible definitions of algorithmic and high- frequency trading that are mainly used in academic literature and papers can be found in Table and Table in Appendix 5.
“Programs running on high-speed computers analyze massive amounts of market data, using sophisticated algorithms to exploit trading opportunities that may open up for milliseconds or seconds. Participants are constantly taking advantage of very small price imbalances; by doing that at a high rate of recurrence, they are able to generate sizeable profits. Typically, a high frequency trader would not hold a position open for more than a few seconds. Empirical evidence reveals that the average U.S. stock is held for 22 seconds.” Chlistalla (2009, p. 3).
The algorithmic trading is widely used both by institutional investors, for the efficient execution of large orders, and by proprietary traders and hedge funds for getting speculative profit.
In 2009, the share of high-frequency algorithmic trading accounted for about 73% of the total volume of stocks trading in the U.S. (Lati, 2009).
On the MICEX in 2010, the share of high-frequency systems in the turnover of stock market was about 11-13%, while the number of orders evaluated as 45%. According to RTS, in 2010 the share of trading robots in the turnover of derivatives market on RTS FORTS section accounted for approximately 50% and their share in the total number of orders at certain times reached 90% (Smorodskay 2010).
According to Finansinspektionen report Investigation into high frequency and algorithmic trading (February 2012), approximately 83% of market participants used algorithmic trading in 2011, and approximately 12% of market participants used high-frequency trading on Swedish market.
Detailed information about the share of algorithmic high-frequency trading on world stock exchanges can be found in Appendix 1.
As Aldridge (2009) writes “for a market to be suitable, it must be both liquid and electronic to facilitate the quick turnover of capital. Based on three key elements of each market:

  • Available liquidity
  • Electronic trading capability
  • Regulatory considerations

It is possible to systematize different assets with respect to the optimal frequency of its’ usage for high-frequency trading.” Let’s illustrate it in Figure 3.
Among experts, academics and practitioners there a lot of discussion about the possible influence of high-frequency trading on markets, namely, on market efficiency. Some experts (Hendershott, Riordan, 2009; Jovanovic, Menkveld, 2010) note, that high-frequency trading can provide market with liquidity, decrease spreads and helps align prices across markets, if it is implemented as market-making or arbitrage strategy.
But, according to Chlistalla (2011), though there is no exact evidence in academic literature, that high-frequency trading makes negative influence on market equality, still there some concerns:
As a result, from one point of view, high-frequency traders help to detect and correct anomalies in market prices. From another point of view, high-frequency traders might distort price formation if it creates an incentive for natural liquidity to shift into dark pools as a way of avoiding trans-acting with ever-decreasing order size

The main types of algorithmic strategies

Despite the variety of existing algorithmic strategies, most of them use the general principles of trading signal’s construction or similar algorithms, which allow us to combine them in couple of groups.
From the perspective of the “main goal”, strategies can be divided into two broad categories: execution strategies and speculative strategies (Katz, 2000)

Execution strategies

These strategies solve the problem of buying or selling large orders of financial instruments with a minimum difference of the final weighted average transaction price from the current market price of the instrument. This category of strategies is actively used by investment funds and brokerage firms around the world.
According to Katz (2000), there are three most common algorithms among execution strategies
1.1) Iceberg algorithm – based on the total execution of order by placing bids with a total maximum capacity no more than some predetermined value. Placing of orders should be continued till the total execution of order. This greatly improves the efficiency of the algorithm, since for its realization it is enough to put only one bid, which will be executed much faster than the number of sequentially exposed trading orders.
1.2) Time Weighted Average Price (TWAP) algorithm – implies the unified execution of the total amount of orders for the specified number of iterations during a specified period of time – by placing the market orders at prices better, than demand or supply price, adjusted for a given value of percentage deviation.
1.3) Volume Weighted Average Price (VWAP) algorithm – implies the unified execution of the total amount of orders for the specified number of iterations during a specified period of time – by placing the market orders at prices better, than demand or supply price, adjusted for a given value of percentage deviation, but not exceeding the weighted average market price of the security, designed from the start of the algorithm

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Speculative strategies

The main purpose of the speculative strategies is to get profit in the short term due to the “exploitation” of fluctuations in market prices of financial instruments. In order to classify them, experts distinguish seven main groups of speculative strategies, some of which use the principles and algorithms of other groups (Colby, 2002).
2.1) Market-making strategy – suggests the simultaneous offering and maintenance of buy and sell orders of financial instrument. These strategies use the principle of “random walk” in prices within the current trend, in other words, despite the rise in security price at a certain time interval, some part of transactions will lead to decrease the security/commodity prices, and vice-verse, in the case of a general fall in the price of the instrument, some part of transactions will result to increase its prices comparing with previous values. Thus, in the case of well- chosen buy and sell orders, it’s possible to buy low and sell high, regardless of the current trend direction.
There are various models of determining of optimal price of orders, selection of which is based on the liquidity of instrument, the amount of funds placed in the strategy, the allowable time of holding position and other factors (Edwards, Magee, 2007).
The key factor in the success of this type of strategies is the maximization of compliance of quotations to the current market conditions for chosen instrument, which can be reached by high speed of obtaining the market data and the ability to change quickly the order’s price, otherwise, these strategies become unprofitable.
Market-makers are among the main « suppliers » of instant liquidity, and at the expense of competition they help to improve the “liquidity profile”. That is why stock exchange centers quite often try to attract market-makers in illiquid instruments, providing them with favorable conditions of the commissions, and in some cases, paying fees for the maintenance of prices.
2.2) Trend following strategy – based on the principle of identifying the trend on the time series of price values of financial instrument (using for that purpose a variety of technical indicators), and buying or selling an instrument with the appearance of corresponding signals (Colby, 2002).
A characteristic feature of trend following strategies is that they can be used on almost all time frames – from the tick to monthly, but because of the fact that profitability of these strategies depends on the ratio of correct to incorrect predictions about the future direction of price movements, it might be quite risky to use them on too large time frames, since an error of prediction usually can be detected after relatively long period of time – which can lead to serious losses.
The effectiveness of trend following strategies, especially in intra-day trading, depends mostly on the instantaneous liquidity of financial instrument, because most of transactions take place through the market orders at current prices of supply and demand. Therefore, if the financial instrument has a wide spread and the horizontal curve of instant liquidity, then even in the case of a large number of true predictions strategy can cause damage

1 Introduction
2 Purpose and research question
3 Previous studies and theoretical framework
3.1 Conception of algorithmic trading. Literature, approaches and methods
3.2 Index investment strategies. Literature and review of investing implementation
4 Empirical methodology
4.1 Exponential moving average with a variable factor of smoothing
4.2 Statistical Arbitrage in High-Frequency Trading
4.3 Organization of trading infrastructure. Development of trading robots
5 Empirical results and analysis .
5.1 Data
5.2 Observation, calculations and results of index strategies’ performing
5.3 Observation, calculations and results of algorithmic trading strategies…
5.4 Results discussion
6 Conclusion

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