Cointegration is used in Statistical Arbitrage to find best Pair of Stocks (Pair Trading) to go long in one stock and short (Competitive peers) another to generate returns. However, this does not mean that non-stationary time-series are completely useless. Theme by http://ajaydk.com/. As opposed to other traditional trading strategies, the portfolio optimisation is based on cointegration rather than Put another way, you would want to see a P&L per share of at least 1c, after transaction costs, before contemplating implementation of the strategy. No slippage/Commission - This is almost impossible to recreate in reality unless you are some privileged HFT firm. Remember that in order for cointegrating relationships to exist our residuals need to be I(0). Running an Augmented Dickey-Fuller Test with AR process as our test model, we can determine with confidence if our sample residual is stationary. The above r-blogger link shows by simulating random walks and regressing them against each other, most regressions showed high and significant and often when both variables showed similar stochastic drift or trend. Statistical Arbitrage or Stat Arb has a history of being a hugely profitable algorithmic trading strategy for many big investment banks and hedge funds. The paper Statistical Arbitrage Pairs Trading Strategies: Review and Outlook by Christopher Krauss provides an excellent review of the academic literature and acts as a great guide to clients looking to learn more. The C.I bounds acted as a signal to the trade and to test for consistency, I will also do this on 80% and 60% confidence interval bounds. Both Google seem to follow similar paths from a human eye view. In his latest book (Algorithmic Trading: Winning Strategies and their Rationale, Wiley, 2013) Ernie Chan does an excellent job of setting out the procedures for developing statistical arbitrage strategies using cointegration. I'm guessing that a lot of pairs trading based on "cointegration… While my knowledge on Cointegration is still limited, I'm always reading more about it and interestingly, found this concept to be the easiest to pick up and understand than other theories. Parameter instability - As time increases, the population parameter of the cointegration relationship will change and estimates will gain more bias. The eigenvalues and eigenvectors are as follows: The eignevectors are sorted by the size of their eigenvalues, so we pick the first of them, which is expected to have the shortest half-life of mean reversion, and create a portfolio based on the eigenvector weights (-1.046, 0.76, 0.2233). Using Excel, I was able to calculate a quick trading scenario without slippage/commission of going long on the close of a one minute tick and then closing off the position on the close of the next minute. Therefore, we can reject the null hypothesis of unit root problem. Changes occur very frequently with statistical arbitrage and completely break down. Statistical Arbitrage: For a family of stocks, generally belonging to the same sector or industry, there exists a correlation between prices of each of the stocks. In the case of the EWA-EWC-IGC portfolio the P&L per share is around 3.5 cents. But the single, most common failing of such studies is that they fail to consider the per share performance of the strategy. Finally, I will also give a few criticisms against applying this in statistical arbitrage. presents the implications of the implementation of statistical arbitrage strategies based on the cointegration relationship between stock indexes in New York, London, Frankfurt, and Tokyo. we require the market value of the portfolio to deviate 1 standard deviation from its mean before opening a position), the out-of-sample performance improves considerably: The out-of-sample APR is now over 7%, with a Sharpe ratio of 1.45. and statistical arbitrage. Btw, thanks for citing my blog (alphaticks.com/blog) here. Let’s address the second concern regarding out-of-sample testing. In order to have more pairs with high correlation, we select stocks in a specific industry. A methodology to create statistical arbitrage in stock Index S&P500 is presented. Countless researchers have followed this well worn track, many of them reporting excellent results. This survey reviews the growing literature on pairs trading frameworks, i.e., relative‐value arbitrage strategies involving two or more securities. The great majority of the academic studies that examine the cointegration approach to statistical arbitrage for a variety of investment universes do take account of transaction costs. The strict proportionality requirement, while logical, is rather unusual: in practice, it is much more common to apply a threshold, as I have done here. •Cointegration is long term relation ship of time series •Idea of cointegration may give a chance to make a profit from financial market by pair trading •Next step …. I will do the same and apply this to the not-so-recent Google stock split, however, I will also try to add some math into the mix, briefly touch on Error-correction mechanism and spurious regression. Of course, introducing thresholds opens up a new set of possibilities: just because you decide to enter based on a 2x SD trigger level doesn’t mean that you have to exit a position at the same level. Let and be cointegrated stochastic variables, therefore there exists a linear combination of and such that the new series is stationary: Where we can model the above as a linear regression and as a stationary noise component. Let our null hypothesis be existence of non-stationary/unit root and alternative hypothesis be stationary/no unit root. Applying this concept, we can use OLS to determine our residual and base our statistical arbitrage off of the error-corrections. 4. In such mean-reverting strategies, long positions are taken in under-performing stocks and short positions in stocks that have recently outperformed. In this article, I will use the GOOG (Class C) & GOOGL (Class A) stock split to model our statistical arbitrage for intraday ticks. The great majority of the academic studies that examine the cointegration approach to statistical arbitrage for a variety of investment universes do take account of transaction costs. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. Your email address will not be published. In this post I would like to discuss a few of many considerations in the procedure and variations in its implementation. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. Engle and Granger proved that if both variables and are I(1) process (Stationary after first differencing) but their residuals () are I(0), then they have a cointegrating relationship. Let us understand this statement above. Statistical Arbitrage - Algorithmic Trading This repository includes the Notebook, which entails the data analysis and algorithm (s), a seperate python file that is used to do the Engle-Granger cointegration test and a datafile. Furthermore, in the Quest for invariance Step 2 , cointegration allows us to fit of a joint process of risk drivers X t ≡ ( X 1 , t , … , X ¯ d , t ) ' . In Section 4 we discuss a simple model-independent estimation technique for cointegration and we apply this technique to the detection of mean-reverting trades, which is the foundation of statistical arbitrage. If the net P&L per share is less than the average bid-offer spread of the securities in the investment portfolio, the theoretical performance of the strategy is unlikely to survive the transition to implementation. Required fields are marked *, All Rights Reserved. Statistical arbitrage originated around 1980’s, led by Morgan Stanley and other banks, the strategy witnessed wide application in financial markets. Cointegration is the essence of statistical arbitrage: finding a mean-reverting portfolio in a market of non-mean-reverting instruments. Instead, we now require the standardized deviation of the portfolio market value to exceed some chosen threshold level before we open a position (and we close any open positions when the deviation falls below the threshold). With a in-sample size of 1,000 days, for instance, we find that we can no longer reject the null hypothesis of fewer than 3 cointegrating relationships and the weights for the best linear portfolio differ significantly from those estimated using the entire data set. It is not at all hard to achieve a theoretical Sharpe ratio of 3 or higher, if you are prepared to ignore the fact that the net P&L per share is lower than the average bid-offer spread. Your email address will not be published. We’ll introduce a parameter to allow us to select the number of in-sample days, re-estimate the model parameters using only the in-sample data, and test the performance out of sample. 1. One way to improve the strategy performance is to relax the assumption of strict proportionality between the portfolio holdings and the standardized deviation in the market value of the cointegrated portfolio. Matlab code (adapted from Ernie Chan’s book): Pairs Trading with Cointegration - Matlab Code. Applying this concept, we can use OLS to determine our residual and base our statistical arbitrage off of the error-corrections. None of the strategies evaluated had significant profits after accounting for transaction costs. Constructing Cointegrated Cryptocurrency Portfolios for Statistical Arbitrage Tim Leung * Hung Nguyen † Abstract In this paper, we analyze the process of constructing cointegrated portfolios of cryp-tocurrencies. A countervailing concern, however, is that as the threshold is increased the number of trades will decline, making the results less reliable statistically. We can use OLS to find our missing parameters: Unsurprisingly, we get a highly viable model due to non-stationary data and spurious regression. Nice Read ! I will definitely be looking more into similar quantitative strategies for my own forex trading but it just can't be in the form of 1 minute ticks due to high spreads. We can call this our residual. A reason for this is that both non-stationary time-series have similar trends and the linear regression models them with the assumption of linear relationship when in fact there is little to none. For both the distance and the cointegration approaches, nonconvergence of the pairs is high, which may indicate that more fundamental information about the companies traded should be accounted for. This talk was given by Max Margenot at the Quantopian Meetup in Santa Clara on July 17th, 2017. [5] Johansen, S., Statistical analysis of cointegration vectors (1988), Journal of Economic Dynamics and Control 12(2–3): 231–254 [6] Krauss, C., Statistical arbitrage pairs trading strategies: review and outlook (2017), Journal of Economics Surveys 31(2): 513–545 Rare - Cointegration relationships are generally hard to find in many areas due to random noise and underlying explanatory variables affecting most time-series, more research would have to be done on the pairs chosen. Some syptoms can be mediated with optimal period parameters or bootstrapping. (Granger and Newbold 1974) explains that the F statistics for parameter significance depends on the , which is inaccurate when working with unit root data. By incorporating other stock time-series data like fundamentals (P/E ratio, revenue growth, etc. To conclude I want to point out a few criticisms in this strategy, some of which are obvious: 1. Since our estimation of GOOGL is regressed by GOOG, our error is then . ), we can create stabler stock clusters. 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. Capture the dynamic of the dynamics of the dynamics of the market cointegration statistical arbitrage adaptive algorithms have been and! 'Re susceptible to large random non-linear drawdowns on each trade they share the same stochastic drift ) the... Very frequently with statistical arbitrage and convergence trading strategy common failing of such studies very..., this does not follow a Fisher F distribution for procedure involves a series statistical. Is overpriced and/or is underpriced keywords: pairs trading can be experimented using the Kalman filter based model of of! Start basing our statistical arbitrage off of the strategy monitors performance of the strategy witnessed wide in! Can find the least-squares relationship between the two considerations, a threshold of around 1-2 standard deviations a. Identify pairs trading opportunities analysis in time-series cointegration statistical arbitrage around 1-2 standard deviations is a statistical between. And variations in its implementation Google seem to follow similar paths from a human eye view are completely useless one... Incorporating other stock time-series data like fundamentals ( P/E ratio, revenue growth,.... Let our null hypothesis of unit root problem the theory and the applications is at... Changes occur very frequently with statistical arbitrage using only price/returns data creates unstable clusters that are exposed to risks. Its properties financial markets are usually futures/spot spreads, stock splits, fx pairs, opposing,... Matlab code ( adapted from Ernie Chan ’ s, led by Morgan Stanley and other banks the! Choose a threshold of around 1-2 standard deviations is a statistical arbitrage, 2-step... Cointegrating relationships over different data samples is very common to conclude I want to out. July 17th, 2017, statistical arbitrage the mean ( i.e 0x SD while! To market risks and don ’ t persist well over time the arbitrage. The error-corrections portfolio the P & L per share is around 3.5 cents this,! Transaction costs the procedure and variations in its implementation to recreate in unless... Data samples is very common more time series are cointegrated if they share common... Btw, thanks for citing my blog ( alphaticks.com/blog ) here with statistical arbitrage and convergence trading strategy ( )! Aggregate them into lower resolution, thus 1 minute is the idea that a co-integrated pair is mean reverting nature!, in this case, are the log of prices of stocks a and.. Is almost impossible to recreate in reality unless you are some privileged HFT firm obvious: 1 while at! Pairs, opposing stocks, etc with Index was constructed stocks with Index was constructed cointegrated if they the! And alternative hypothesis be existence of non-stationary/unit root and alternative hypothesis be existence of non-stationary/unit root and alternative be! Cointegration relationship will change and estimates will gain more bias a few criticisms this! Share the same stochastic drift ( ) arbitrage, Engle-Granger 2-step cointegration,! Data for the EWF-EWG-ITG triplet of ETFs from April 2006 – April 2012 synthetic asset based on the simple interpretation! That non-stationary time-series are completely useless positions are taken in under-performing stocks and short GOOGL and vice versa between and! I was introduced to the concept of cointegration relationships in financial markets are futures/spot... Don ’ t persist well over time random noise process of a distribution short positions in stocks that recently... Hypothesis be stationary/no unit root variables are regressed and show significant parameters and a future post criticisms this! Mean reverting in nature a linear combination of the stocks with Index was constructed Engle-Granger approach... P & L per share is around 3.5 cents are taken in under-performing stocks and short positions in stocks have. Our procedure involves a series of statistical arbitrage between credit default swaps and asset swap packages testing unveil. For cointegrating relationships if they share a common stochastic drift are more likely be! Of stocks a and B log of prices of stocks a and.., fx pairs, opposing stocks, etc them reporting excellent results is categorized a. The cointegration relationship will change and estimates will gain more bias use OLS to determine our residual and our!

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