# Pairs Trading Research Paper Example

 Paper Type:Â  Research paper Pages:Â  5 Wordcount:Â  1283 Words Date:Â  2022-06-22
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## INTRODUCTION

Pairs trading is a statistical approach (Busjahn, 2009. Pg. 470). created to evaluate deviations (short-term) from an equilibrium pricing relationship involving two stocks Past techniques of pairs trading have identified pairs regarding the correlation as well as non-parametric decision rules (Broussard, 2012.Pg 411).

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Nevertheless, these techniques are inferior to approaches applied in the study that we are carrying out. The methods are inferior since they are unable to guarantee fundamental statistical property (Caldeira, 2013). This property is fundamental to a gainful pair of trading approach, known as mean reversion. The study chooses trading pairs based on the cointegrating relationship between the two stock prices series. The cointegrating relationship enables us to combine the stocks. The stock is combined in a particular linear combination. The resulting portfolio is a stationary process. Combined portfolio is created by increasing the relative overstock and decreasing the relative understock.

To gain from the pricing, it is important to open a long position in the portfolio. The long position is opened when the expected value drops down sufficiently below its equilibrium. The position is closed out when the portfolio value returns to its expected value. Also, the profits might be gained if the portfolio is sufficiently above the value of equilibrium. Trading can be done by shorting the portfolio. Shorting makes the portfolio to return to its expected value. Questions that should be answered when constructing a pair trading strategy include 1. What is the best approach in identifying trading pairs? 2. When is the combined portfolio sufficiently far away from its equilibrium value to open a position and (3) what is the right time to close the position?

It is crucial to specify the optimum allowable time from a risk management perspective. Specification of maximum allowable time enables maintenance of the maximum allowable value, open trading positions and reduction of measures such as loss triggers. The aim of conducting this research is to come up with a technique for implementing pairs trading strategy. The study does not try to evaluate the profitability of the strategy. The first step is to evaluate the approach for the identification of trading pairs. We use the method Johansen test for cointegration. We then approximate the cointegrating relationship occurring between our pairs. The estimate is done by regressing one pair on the other. To specify the order in which the regression occurs, the study uses Granger Casualty, the residual series from the explanation of the mean-reverting portfolio dynamics. The residual series can help us to choose to model the equation as a Vector-Error- Correction model.

The choice is natural. We can identify this by using Granger Representation Theorem (Engle and Granger, 1987). In the cointegrating relationship , the choice is an equivalent relationship. To extract sufficient information, we choose to model the residual series. The information is about co-movement that occurs between trading pairs. This information will be important in creating a trading rule. For instance, estimation of the adjustment coefficients speed in the VECM is necessary. The estimation provides us with the notion of how the system returns to its equilibrium. The system evaluates a short-term deviation and identifies the stock as the cause of error correction function. Finally, the extension of the estimation of the impulse response functions of VECM is conducted. Also, analysis of variance decomposition is carried out. The variance analysis techniques are essential. The methods provide us with the understanding of how every stock price series respond to itself, stocks and stock sequence. The techniques also provide us with the knowledge to the extent on which each stock improve independently. This study continues in the following five sections.

### Purpose of the Study

The aim of this study is to examine whether a trading approach based on cointegration property for Dow Jones Stock prices can be profitable over a period of 20 years. To achieve this objective, the paper has retrieved daily stock prices from DJ30 index for a period of 20 years. The paper will use one optimization and one extension to compare earlier used models.

### Research Objectives

Here are the primary objectives:

• To investigate whether Pairs Trading is a profitable venture
• To provide recommendations, conclusions and need for future studies

### Research Question

Here are the main research questions:

• Can a trading approach use the aforementioned properties based on the stock prices for cointegration provide returns in the excess of the Dow Jones market?
• If the trading approach can yield returns, under what settings?

### Research Hypothesis

The research hypothesis is as follows:

H1: Pairs Trading Approach through Cointegration is profitable

H0: Pairs Trading Approach through Cointegration is not profitable

### Discussion of Key Issues

Long/Short Equity Investing: Profit from both losers and Winners. Investing equity has been all about identifying stocks to purchase and those that provide a chance for appreciation. Investors are not interested in including short selling into their equity methods to make maximum use of over-valued stocks. However, there has been an increased number of institutional investors who have started holding both short and long-term positions within equity portfolios. Short selling includes the concept of selling out the stock at the current price, though delaying the stock delivery to its new owner. The practice involves the seller buying the stock later at a lower price than the price collected for the stock.

The difference between the purchase price and the selling price is the profit that the short seller can earn. The investors are willing and ready to open a short position in any stock if they expect the fall in the price of the stock. Levy and Jacobs (1993) combined short/long equity approaches such as market equitized, neutral and hedge approaches. The neutral approach holds both short and long positions with equal risk exposures of the market at all times. This can be done by equating betas of both the short position and long position in the portfolio.

The strategy eliminates the net equity market exposures so that the realized returns does not correlate with the returns on the market portfolios. This is equal to the portfolio of zero betas. The returns on the zero beta portfolios can be generated by isolating the alpha.

ARIMA models appear to characterize several financials variables, and it follows that stochastic trends can explain the increase in these variables. The fundamental advantage of cointegration analysis, when compared to the classical, is that it allows the use of ever information set consisting of the financial variables levels. Moreover, a cointegrating relationship can describe the behavior of cointegrated series (long run), and correlation, as a co-dependency measure, does not have stability and is a short run measure only.

If the price series stocks are cointegrated, then the combination may be in such a way that the spread is mean reverting or stationery. Pairs trading are after identification of the stocks where some kind pricing measure can be estimated by the equilibrium relationship of a long run. It is vital to note that identifying cointegrated pairs is not a basic requirement for a successful pair trading strategy. Pairs trading technique is based on the cointegration to ensure mean reversion. Mean reversion is one crucial characteristic of a successful pair trading. No other approach guarantees this characteristic.

### Literature Review

In this section, we introduce one study that describes the fundamentals techniques used in the implementation of pair trading that we label as the cointegration technique. The cointegration technique is outlined in Vidyamurthy (2014). The approach represents an effort to parameterize pairs trading through modeling explicitly the mean-reverting feature of the spread.

### Cointegration

Cointegration refers to a statistical that involves two times series that are integrated and are of same order d, that is , I(d), can be combined linearly and results in a single tim...

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