Statistical Arbitrage: Profits through Pairs Trading

Abstract

Statistical arbitrage is a popular device among hedge fund managers and assets management professionals. It refers to simultaneous buying and selling two different capital assets to earn super-normal profit. By identifying persistent anomalies that violate the efficient market hypothesis, statistical methods can be used to create a trading strategy to generate profit with high probability. A pair trading is one such trading strategy which is based on statistical arbitrage process. Pairs trading can be simple in concept, but can be one of the most complex types of trading in practice. The starting point of this strategy is that stocks that have historically had the same trading patters will have so in future as well. If there is a deviation from the historical mean this creates a trading opportunity, which can be exploited. Gains are earned when the price relationship is resorted. The basic premise of this strategy is that stock prices follow a mean reverting process. The objective of this paper is to identify arbitrage opportunities and calculating profits earned through these opportunities by using statistical tools.

Many questions need to be answered before one can implement such strategy viz. which pair of stocks should be traded, how much do we buy/sell of each stock, how to catch the signal of an opportunity (i.e opening a position) and when to close the position so that profit could be earned. In this paper we have taken daily closing prices from 1/1/2010 to 1/1/2011 of thirty scrips of BSE-Sensex to form pairs. Pairs are formed on the basis of minimum distances between two stocks. We have decided not to invest anything. That is, purchase the same rupee amount of the long stock as we sell of the short stock so that strategy is self-financing. We open a position when the absolute value of the difference gets larger than two of its historical standardization.  To unwind the position, we wait until the first time it crosses zero. To calculate the profit/loss of this strategy, we have used “R-Software”. It is observed that profit could be earned through pairs trading if it is applied without losing patience. By identifying persistent anomalies that violate the efficient market hypothesis, statistical methods can be used to create a trading strategy to generate profit with high probability.