Literature review – Pairs trading

Several researchers propose methods and techniques for selecting the appropriate pairs of assets, identify the spread magnitude that should trigger a trade, predict the next step of the process so as to proceed or not to opening or

Cointegrated System

integration mehtod Engel and Granger [6] and Engel and Yoo [7] see Figure 1.

Other approaches that can be found in the literature are those of stochastic modeling, copulas and artificial neural networks. Scholars also model the spread process in the context of continuous time – Ornstein-Ulenbeck

processes (Ulenbeck-Ornstein [8])– or discrete time. Several empirical studies have also been conducted to investigate the effectiveness of this trading strategy in different markets under various economical conditions. In this talk a review of the several proposed methodologies will, first, be presented .

Reviewing pairs trading literature it is obvious that most scholars focus on improving the modeling of either spread or prices time series attempting to develop models that better reflect reality. Various models have been developed so far. Some can be found in the studies of Elliot et al. [9] who propose the use of a mean reverting Gaussian Markov chain model for the spread of pairs trading strategies. In another study, Dattasharma [10] introduce a general framework that can be used to predict the dependence between two stocks based on any user-defined criterion by applying the concepts of events and episodes. Triantafyllopoulos and Montana [11] propose a Bayesian state-space model for spread processes with time varying parameters. In this study the researchers also developed an on-line estimation algorithm that could be used to monitor data for mean reversion. Gatarek et al. [12] suggest a

combination of Dirichlet process prior techniques with Bayesian estimation to estimate co-integrated models with non-normal disturbances.

Triantafyllopoulos and Han [13] propose a methodology for detecting mean-reverted segments of data streams in algorithmic pairs trading using a state-space model for the spread and propose two new recursive least squares (RLS) algorithms with adaptive forgetting for predicting mean-reversion in real time.

Tourin and Yan [14] in their study suggest the use of an optimal stochastic control model to address the problem of analyzing dynamic pairs trading strategies. In Fasen [15] the asymptotic properties of the least squares estimator for the model parameter of a multivariate Ornstein-Uhlenbeck model are investigated. Alrasheedi and Al-Ghamedi [16] apply a Vector Auto-Regressive model (VAR) for the simulation of the time series of two stocks and examine the influence of some of the model parameters on the total profits earned.

Improving and developing models is indeed very important since more accurate predictions of assets future prices can then be obtained. Unlike other processes, financial processes are difficult to be predicted because of the nature of financial data and it is generally argued that the best prediction of a

tomorrow's asset price is the price of the asset today. This explains the vast amount of studies published on modeling financial time series considering continuous or discrete time. There are also non-parametric approaches proposed for handling financial data, as well. An example is the study of Bogomolov [17] in which a novel non-parametric approach for pairs trading is proposed in which the only assumption to be made is that the statistical properties of the volatility of the spread process remain reasonably constant.

Gatev et al. [5] proposed the GGR model for applying a pairs trading strategy. The study leads to the conclusion that excessive returns are likely to be generated for market participants that have relatively low transaction costs and the ability to short sell securities. It is also observed that there is a latent risk factor that affects the profitability of pairs trading over time. Papadakis and Wysocki [18] examine whether accounting information events, such as earnings announcements and analysts’ earnings forecasts, have an effect on the profitability of the pairs trading strategy proposed by Gatev et al. [5]

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Broussard and Vaihekoski [19] extended the work of Gatev et al.[5] through an empirical study showing that the aforementioned investment strategy is profitable even in markets with reduced liquidity. In the study of Wang and Mai [20] a comparison of GGR, Herlemont and FTBD pairs trading openning position strategies is conducted. The main conclusion obtained from this study is that after deducting the trading cost, the absolute income of the three strategies considered is significantly bigger than zero.

Portfolio optimization, i.e. the choice of which assets and the number

multivariate version of pairs trading which can be used to create an artificial pair for a specific stock using the information associated to m assets.

Mudchanatongsuk et al. [22] propose a stochastic control approach to address pairs trading portfolio optimization. Chiu and Wong [23] investigate the continuous-time mean-variance portfolio selection problem considering co-integrated assets. Alsayedand and McGroarty [24] introduce a solution to the portfolio optimization problem when risky arbitrage trading is considered through the introduction of a nonlinear generalization of Ornstein-Uhlenbeck model which takes into consideration important risk factors.

Moreover, the trading costs are also taken into consideration in some studies. Transaction costs are those associated to opening or closing a position.

In the study of Lin et al. [25] researchers propose the integration of loss limitation within the statistical modeling of pairs trading strategies. In several empirical studies transaction costs are also considered in order to assess the performance of the different methodologies. Trading costs can be significant and if not taken into consideration the returns of applying a pairs trading strategy could be minimized.

Various trading rules have also been proposed in order to perform successful pairs trading. In the study of Song and Zhang [26] pairs trading is investigated and a pairs trading rule is proposed which takes into account profit maximization or losses minimization. The approach of the researchers to address the problem considered is dynamic programming.

Some recent studies also consider the process's microstructure using intra-day data. Microstructure theory focuses on how specific trading mechanisms affect the price formation process. Zebedee and Kasch-Haroutounian [27] in their study examine the microstructure of the co-movement among the returns of stocks on an intra-day basis applying a combination of a traditional lead-lag model with a pseudo-error correction mechanism. Marshall et al. [28] investigate the microstructure of pairs trading on an intra-day basis. In other words, they examine the intra-day market characteristics that can be observed when arbitrage opportunities appear. Since pairs trading could be applied on an a daily basis and traders exploit daily market disturbances the examination of process' microstructure is indeed very interesting.

A basic step in pairs trading is to be able to identify suitable pairs so that the pairs trading to be profitable. To this end, several researchers try to develop an optimal methodology for choosing the most suitable pairs. Gatev et al. [5] proposes choosing the pairs having the smallest sum of squared

deviations for trading. Ehrman [1] suggests pairs to be chosen using the correlation coe cient. When this coefficient is greater than or equal to 0.7, the ffi pair is tradable. Engle [6] introduce co-integration approach and proposed choosing pairs whose prices are co-integrated. In the study of Huck [29] the sensitivity of pairs trading strategies' returns on the length of the pairs formation period is investigated. Through an example it is shown that the choice of the formation period affects the returns of the strategy employed and after taking into consideration the data snooping bias this result does not change.

Various empirical studies have also been published. In Matteson et al.

[30] researchers introduce a new methodology in identifying local stationarity of non-stationary processes. Through an empirical approach robust estimates of time varying windows of stationarity are “produced”. Moreover, it is proven that using the adaptive window leads to higher returns and, in some cases, holding the positions open for a shorter period of time. Mai and Wang [31]

published a limited study on the impact of the structure of the market on the returns of a pure statistical pairs trading. The researchers suggest that the annual rate of return of pairs trading can be improved by choosing the markets the traders are operating in.

Some different approaches have also been recently developed. Huck [29] proposes a methodology that can be used for pairs selection in a highly non-linear environment. The researcher combines forecasting techniques

(ANN) are presented by Gomide and Milidiu [32] that are used to predict spread time series. Through obtaining spread predictions, times of the day when to perform a particular Pair Trading can be recommended. The use of copulas in development of pairs trading strategies is investigated in Liew and Wu [33] It is suggested that copulas approach is a good alternative to the traditional ones – distance approach and co-integration approach – since it is not necessary to assume the existence of correlation among the values of the assets to be traded and thus, argued to be realistic and robust.