Today, Socially Responsible financial investment has taken on particular importance. Investors normally select their most profitable investments, but over the years they have appreciated that companies develop Socially Responsible policies. Financial indices have also created Socially Responsible versions. In this paper, we run a statistical arbitrage technique known as Pairs Trading using stocks of the FTSE4GOOD Socially Responsible Index. Different strategies will be tested to demonstrate that there are no significant differences between the performance of the portfolio composed by Corporate Social Responsibility (CSR) stocks and those composed by ordinary stocks.