#Statistical Arbitrage in R [By Jacques Joubert] (https://za.linkedin.com/in/jacquesjoubert)

For those of you who have been following my blog posts for the last 6 months will know that I have taken part in the Executive Program in Algorithmic Trading offered by QuantInsti.

It’s been a journey and this article serves as a report on my final project focusing on statistical arbitrage, coded in R. This article is a combination of my class notes and my source code.

I uploaded everything to GitHub in order to welcome readers to contribute, improve, use, or work on this project. It will also form part of my Open Source Hedge Fund project on my blog QuantsPortal

##History of Statistical Arbitrage:

• First developed and used in the mid 1980s by Nunzio Tartaglia’s quantitative group at Morgan Stanly
• Pair Trading is a “contrarian strategy” designed to harness mean-reverting behavior of the pair ratio
• David Shaw, founder of D.E Shaw & Co, left Morgan Stanley and started his own “Quant” trading firm in the late 1980s dealing mainly in pair trading

##What is Pair Trading: Statistical arbitrage trading or pairs trading as it is commonly known is defined as trading one financial instrument or a basket of financial instruments – in most cases to create a value neutral basket.

It is the idea that a co-integrated pair is mean reverting in nature. There is a spread between the instruments and the further it deviates from its mean, the greater the probability of a reversal.

Note however that statistical arbitrage is not a risk free strategy. Say for example that you have entered positions for a pair and then the spread picks up a trend rather than mean reverting.

##The Concept:

• Step 1: Find 2 related securities Find two securities that are in the same sector / industry, they should have similar market capitalization and average volume traded. An example of this is Anglo Gold and Harmony Gold.

• Step 2: Calculate the spread In the code to follow I used the pair ratio to indicate the spread. It is simply the price of asset A / price asset B.

• Step 3: Calculate the mean, standard deviation, and z-score of the pair ratio / spread.

• Step 4: Test for co-integration In the code to follow I use the Augmented Dicky Fuller Test (ADF Test) to test for co-integration. I set up three tests, each with a different number of observations (120, 90, 60), all three tests have to reject the null hypothesis that the pair is not co-integrated.

• Step 5: Generate trading signals Trading signals are based on the z-score, given they pass the test for co-integration. In my project I used a z-score of 1 as I noticed that other algorithms that I was competing with were using very low parameters. (I would have preferred a z-score of 2, as it better matches the literature, however it is less profitable)

• Step 6: Process transactions based on signals

• Step 7: Reporting