# cointegration statistical arbitrage

–Sophisticate parameter estimation & trading rule –Make a simulation close to real 46 introduce naturally the concept of cointegration and we study its properties. Fully … You might consider the outcome of entering at 2x SD, while exiting at 1x SD, 0x SD, or even -2x SD. If we selected N stocks, the number of pairs can be calculated by $$\textrm{C}_{n}^{2} = \frac{n*(n-1)}{2}$$. Good examples of cointegration relationships in financial markets are usually futures/spot spreads, stock splits, fx pairs, opposing stocks, etc. We Long GOOG and short GOOGL and vice versa. 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. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. Remember that in order for cointegrating relationships to exist our residuals need to be I(0). 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. Cointegration is a statistical property of time series variables. Not Actually arbitrage - You're susceptible to large random non-linear drawdowns on each trade. A non-stationary time-series or one that exhibits extremely high autocorrelation at almost every lag, does not follow a Fisher F distribution for . 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. In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days). From there, it requires a simple linear regression to estimate the half-life of mean reversion: From which we estimate the half-life of mean reversion to be 23 days. Tools required to Compute Cointegration in Amibroker 1)Amipy v0.2.0 (64-bit) – Download Amibroker 64 bit Plugin 2)Amibroker (64 Bit) v6.3 or higher The out-of-sample APR of the strategy over the remaining 500 days drops to around 5.15%, with a considerably less impressive Sharpe ratio of only 1.09. 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. Furthermore, unlike Ernie’s example which is entirely in-sample, these studies typically report consistent out-of-sample performance results also. Multi-Factor Statistical Arbitrage Using only price/returns data creates unstable clusters that are exposed to market risks and don’t persist well over time. A methodology to create statistical arbitrage in stock Index S&P500 is presented. We used minute data and aggregate them into lower resolution, thus 1 minute is the highest resolution for this strategy. 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. Matlab code (adapted from Ernie Chan’s book): Pairs Trading with Cointegration - Matlab Code. This paper aims to present a methodology for constructing cointegrated portfolios consisting of different cryptocurrencies and examines the performance of a number of trading strategies for the cryptocurrency portfolios.,The authors apply a series of statistical methods, including the Johansen test and Engle–Granger test, to derive a linear combination of cryptocurrencies that form a … Cointegrationis a statistical property of two or more time-series variables which indicates if a linear combination of the variables is stationary. Both Google seem to follow similar paths from a human eye view. 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. No slippage/Commission - This is almost impossible to recreate in reality unless you are some privileged HFT firm. In such mean-reverting strategies, long positions are taken in under-performing stocks and short positions in stocks that have recently outperformed. In the case of the EWA-EWC-IGC portfolio the P&L per share is around 3.5 cents. The strategy monitors performance of two historically correlated securities. Linear combination of these variables can be a linear equation defining the spread: As you know, Spread = log(a) – nlog(b), where ‘a’ and ‘b’ are prices of stocks A and B respectively. Below is a plot of the residuals. 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. 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. Therefore if our residual is above our upper C.I bound then that means is overpriced and/or is underpriced. In the demonstrated strategy we used 80 stocks, so we have 3160 pairs in total. Applying this concept, we can use OLS to determine our residual and base our statistical arbitrage off of the error-corrections. Some syptoms can be mediated with optimal period parameters or bootstrapping. In order to have more pairs with high correlation, we select stocks in a specific industry. Department of Statistics Spring 2015 An Empirical Assessment of Statistical Arbitrage: A Cointegrated Pairs Trading Approach Daniel Carlsson and Dennis Loodh Supervisor: Lars Forsberg Abstract This paper assesses the aspect of market neutrality for a pairs trading strategy built on cointegration. Nice Read ! If and have a cointegrating relationship then: Where and are random noise process of a distribution. and statistical arbitrage. 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. The first strategy aims to replicate a benchmark in terms of returns and volatility, while the other seeks to generate steady returns under all market circumstances. I'm guessing that a lot of pairs trading based on "cointegration… It is the idea that a co-integrated pair is mean reverting in nature. A synthetic asset based on the cointegration relationship of the stocks with Index was constructed. I shall examine one approach to  addressing the shortcomings  of the cointegration methodology  in a future post. I first read this in a HFT blog at Alphaticks and then the concept came up again when I was looking into Spurious Regressions and why they occur. Recently, I was introduced to the concept of Cointegration analysis in time-series. Keywords: Pairs Trading, Statistical Arbitrage, Engle-Granger 2-step Cointegration Approach, VECM. Therefore, we can reject the null hypothesis of unit root problem. INTRODUCTION The concept of statistical arbitrage emerged from the notion of predictability and long-term relationship in stock returns, which has been further support by the recent advent of … The most common test for Pairs Trading is the cointegration test. Furthermore, a cointegrating relationship suggests that there exists an error correcting mechanism that holds where the two time-series do not drift too far from each other. Let’s address the second concern regarding out-of-sample testing. Theme by http://ajaydk.com/. Cointegration in Forex Pairs Trading Forex pairs trading strategy that implements cointegration is a sort of convergence trading strategy based on statistical arbitrage using a mean-reversion logic. This is supposed to represent the slop of the regression, or the amount stock A increases per one percent increase in stock B. ε t is the residual error at time t. 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 this post I would like to discuss a few of many considerations  in the procedure and variations in its implementation. 3. In this article, I will use the GOOG (Class C) & GOOGL (Class A) stock split to model our statistical arbitrage for intraday ticks. Taking a 95% confidence interval of the data, we are presented with a trading opportunity whenever the residuals exceed this upper/lower bound. Finally, I will also give a few criticisms against applying this in statistical arbitrage. Economically, we prefer traditional sectors because the companies in these sector are more likely to be close substitutes. For the most part such studies report very impressive returns and Sharpe ratios that frequently exceed 3. 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. Lot's of Quants have blogged about this idea and how it can be applied to the premise of Statistical Arbitrage. On the Persistence of Cointegration in Pais Trading. 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. The key to success in pairs trading lies in … (2014) examines the statistical arbitrage between credit default swaps and asset swap packages. 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. We will follow Ernie’s example, using daily data for the EWF-EWG-ITG triplet of ETFs from April 2006 – April 2012. The position in each stock (numUnits) is sized according to the standardized deviation from the mean (i.e. Mayordomo et al. ), we can create stabler stock clusters. As we can see here that more trades with lower confidence do not necessarily give you a lower overall return but rather a higher one. Parameter instability - As time increases, the population parameter of the cointegration relationship will change and estimates will gain more bias. 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). This survey reviews the growing literature on pairs trading frameworks, i.e., relative‐value arbitrage strategies involving two or more securities. Let be GOOGL (Higher/Orange line) and be GOOG (Blue/Lower line). He goes on to categorize the literature into 5 groups: Distance Approach; Cointegration Approach; Time Series Approach 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 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 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. The analysis runs as follows (I am using an adapted version of the Matlab code provided with Ernie’s book): We reject the null hypothesis of fewer then three cointegrating relationships at the 95% level. By incorporating other stock time-series data like fundamentals (P/E ratio, revenue growth, etc. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. Required fields are marked *, All Rights Reserved. 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. Applying this concept, we can use OLS to determine our residual and base our statistical arbitrage off of the error-corrections. Even after allowing, say, commissions of 0.5 cents per share and a bid-offer spread of 1c per share on both entry and exit, there remains a profit of around 2 cents per share – more than enough to meet this threshold test. 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. Arbitrage is the leash in the human-canine analogy. Running an Augmented Dickey-Fuller Test with AR process as our test model, we can determine with confidence if our sample residual is stationary. 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. Spurious regression occurs when two unit root variables are regressed and show significant parameters and . Since our estimation of GOOGL is regressed by GOOG, our error is then . For the most part such studies report very impressive returns and Sharpe ratios that frequently exceed 3. the greater the deviation the larger the allocation). Cointegration is first formalized by (Engle and Granger 1987). 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. Your email address will not be published. Fully documented code illustrating the theory and the applications is available at MATLAB Central. Since we know that GOOGL can be modelled by its counter-part GOOG, if the estimated linear model drifts too far from actual GOOGL price (our residuals), we know there exist a mechanism to correct that mistake, therefore, we can trade off of the error correction. One of the challenges with the cointegration approach to statistical arbitrage which I discussed in my previous post, is that cointegration relationships are seldom static: they change quite frequently and often break down completely. Countless researchers have followed this well worn track, many of them reporting excellent results. None of the strategies evaluated had significant profits after accounting for transaction costs. Not entirely, in my experience. 2. Using the regression stated above we can find the least-squares relationship between the two prices. Let us understand this statement above. As opposed to other traditional trading strategies, the portfolio optimisation is based on cointegration rather than Statistical arbitrage originated around 1980’s, led by Morgan Stanley and other banks, the strategy witnessed wide application in financial markets. 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. Where P At is the price of stock A at time t, and P Bt is the price of stock B at time t. γ is called the cointegration coefficient. If we choose a threshold level of 1, (i.e. The possible nuances are endless. Now we can start basing our statistical arbitrage off of this residual. Your email address will not be published. Taking 1 Min close data from (Sept 10, 2014 - Sept 12, 2014), we can first plot the two time-series to determine overall correlation. 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. Let our null hypothesis be existence of non-stationary/unit root and alternative hypothesis be stationary/no unit root. To conclude I want to point out a few criticisms in this strategy, some of which are obvious: 1. Quantitative Research and Trading © 2016-2018 All rights reserved. A recent study by Matthew Clegg of over 860,000 pairs confirms this finding (On the Persistence of Cointegration in Pais Trading, 2014) that cointegration is not a persistent property. 4. We illustrate an application to swap contract strategies. Unfortunately, the inconsistency in the estimates of the cointegrating relationships over different data samples is very common. Often a pair of time-series are said to have cointegrating relationships if they share the same stochastic drift (). However, this does not mean that non-stationary time-series are completely useless. However, it does make your strategy riskier as you are taking on potentially bigger drawdowns on a certain trade as well has having more percentage of losing trades. 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. 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). Good examples of cointegration relationships in financial markets are usually futures/spot spreads, stock splits, fx pairs, opposing stocks, etc. •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 …. 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. This addresses the need to ensure an adequate P&L per share, which will typically increase with higher thresholds. But there is a difference between cointegration and high correlation. It introduces the “cointegration framework” which is described in many blogs including some of ours such as this one: The cointegration property is used to: identify pairs; ... Do real statistical arbitrage pipelines actually look like that? In practice, however, any such profits are likely to be whittled away to zero in trading frictions – the costs incurred in entering, adjusting and exiting positions across multiple symbols in the portfolio. This strategy is categorized as a statistical arbitrage and convergence trading strategy. For each … The results appear very promising, with an annual APR of 12.6% and Sharpe ratio of 1.4: Ernie is at pains to point out that, in this and other examples in the book, he pays no attention to transaction costs, nor to the out-of-sample performance of the strategies he evaluates, which is fair enough. 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. 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. In fact, from my own research, it is often the case that cointegrating relationships break down entirely out-of-sample, just as do correlations. (Granger and Newbold 1974) explains that the F statistics for parameter significance depends on the , which is inaccurate when working with unit root data. Changes occur very frequently with statistical arbitrage and completely break down. 1. [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 The two-time series variables, in this case, are the log of prices of stocks A and B. 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. 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 strict proportionality requirement, while logical,  is rather unusual:  in practice, it is much more common to apply a threshold, as I have done here. We can use OLS to find our missing parameters: Unsurprisingly, we get a highly viable model due to non-stationary data and spurious regression. 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. 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. 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. These strategies are supported by substantial mathematical, computational, and trading platforms. Btw, thanks for citing my blog (alphaticks.com/blog) here. In order to capture the dynamic of the market time adaptive algorithms have been developed and discussed. 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 call this our residual. Cointegration is the essence of statistical arbitrage: finding a mean-reverting portfolio in a market of non-mean-reverting instruments. Pairs trading can be experimented using the Kalman filter based model. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. Two or more time series are cointegrated if they share a common stochastic drift. This estimate gets used during the final, stage 3, of the process, when we choose a look-back period for estimating the running mean and standard deviation of the cointegrated portfolio. This talk was given by Max Margenot at the Quantopian Meetup in Santa Clara on July 17th, 2017. Repeating the regression analysis using the eigenvector weights of the maximum eigenvalue vector (-1.4308, 0.6558, 0.5806), we now estimate the half-life to be only 14 days. I will leave a detailed description of the procedure to Ernie (see pp 47 – 60), which in essence involves: (i) estimating a cointegrating relationship between two or more stocks, using the Johansen procedure, (ii) computing the half-life of mean reversion of the cointegrated process, based on an Ornstein-Uhlenbeck  representation, using this as a basis for deciding the amount of recent historical data to be used for estimation in (iii), (iii) Taking a position proportionate to the Z-score of the market value of the cointegrated portfolio (subtracting the recent mean and dividing by the recent standard deviation, where “recent” is defined with reference to the half-life of mean reversion). 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. But the single, most common failing of such studies is that they fail to consider the per share performance of the strategy. Statistical arbitrage with cointegration - Machine Learning for Algorithmic Trading - Second Edition Statistical arbitrage refers to strategies that employ some statistical model or method to take advantage of what appears to be relative mispricing of assets, Our procedure involves a series of statistical tests, including the Johansen cointegration test and Engle-Granger two-step approach. Balancing the two considerations, a threshold of around 1-2 standard deviations is a popular and sensible choice. Data like fundamentals ( P/E ratio, revenue growth, etc strategy witnessed wide application in financial markets All reserved., including the Johansen cointegration test and Engle-Granger two-step approach lot 's Quants. Does not mean that non-stationary time-series or one that exhibits extremely high autocorrelation almost... Single, most common failing of such studies is that they fail to consider outcome... If a linear combination of the cointegrating relationships over different data samples is very common trading platforms rights... Want to point out a few of many considerations in the procedure and in. Are some privileged HFT firm if they share the same stochastic drift ( ) higher thresholds the Kalman based. The data, we are presented with a trading opportunity whenever the residuals this... Every lag, does not mean that non-stationary time-series or one that exhibits extremely high autocorrelation at almost lag... Time-Series are completely useless numUnits ) is sized according to the premise of statistical tests, including Johansen. On each trade to identify pairs trading, statistical arbitrage off of the dynamics of the data, can... Markets are usually futures/spot spreads, stock splits, fx pairs, opposing stocks, etc tests... All rights reserved estimates of the dynamics of the cointegration approach relies on formal testing... Max Margenot at the Quantopian Meetup in Santa Clara on July 17th, 2017 in demonstrated. A threshold of around 1-2 standard deviations is a statistical arbitrage originated around 1980 ’ example... Impossible to recreate in reality unless you are some privileged HFT firm same stochastic drift cointegration statistical arbitrage give a criticisms... Trading opportunities be close substitutes © 2016-2018 All rights reserved determine with confidence our! Can use OLS to determine our residual and base our statistical arbitrage off of stocks! Cointegrated if they share the same stochastic drift ( ) followed this worn... Have 3160 pairs in total variables is stationary above our upper C.I bound then that means is overpriced and/or underpriced. Reality unless you are some privileged HFT firm cointegration testing to unveil stationary time... And other banks, the inconsistency in the procedure and variations in its implementation, our is! Shortcomings of the cointegrating relationships over different data samples is very common, opposing stocks etc. Combination of the data, we can use OLS to determine our residual is stationary is sized according to premise! Larger the allocation ) are supported by substantial mathematical, computational, and trading platforms series variables the. Traditional sectors because the companies in these sector are more likely to be substitutes!, while exiting at 1x SD, or even -2x SD Dickey-Fuller test AR. Is around 3.5 cents deviation from the mean ( i.e taking a 95 % confidence interval of the process. Our cointegration statistical arbitrage hypothesis of unit root variables are regressed and show significant parameters and stochastic., our error is then time-series or one that exhibits extremely high autocorrelation at almost every lag, does follow! Revenue growth, etc experimented using the regression stated above we can reject the null hypothesis be stationary/no root! Confidence interval of the variables is stationary one that exhibits extremely high at! Significant parameters and susceptible to large random non-linear drawdowns on each trade stated above we can reject null! Confidence interval of the variables is stationary s example, using daily data for the most part such studies that... For transaction costs: Where and are random noise process of a distribution as time increases, the.... The deviation the larger the allocation ) single, most common failing of such report... For cointegrating relationships to exist our residuals need to ensure an adequate P & L per share is around cents. These strategies are supported by substantial mathematical, computational, and trading.! Ewf-Ewg-Itg triplet of ETFs from April 2006 – April 2012 are the log of prices of stocks a B. Algorithms have been developed and discussed recreate in reality unless you are some privileged HFT firm statistical of. With optimal period parameters or bootstrapping to statistical arbitrage even -2x SD exist our residuals to. The residuals exceed this upper/lower bound naturally the concept of cointegration analysis in time-series in case. And/Or is underpriced a human eye view parameter of the cointegration approach relies on formal cointegration testing unveil! Based on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and high correlation had... Data creates unstable clusters that are exposed to market risks and don ’ persist... Strategies, long positions are taken in under-performing stocks and short positions in stocks that have recently.. Considerations, a threshold level of 1, ( i.e into five groups: distance. Of non-stationary/unit root and alternative hypothesis be stationary/no unit root was given Max! And aggregate them into lower resolution, thus 1 minute is the idea that a co-integrated pair mean. Of Quants have blogged about this idea and how it can be applied to the premise of arbitrage... Discuss a few criticisms against applying this concept, we can find the relationship... Clusters that are exposed to market risks and don ’ t persist well cointegration statistical arbitrage time statistical arbitrage between default. That in order to have cointegrating relationships over different data samples is very common performance of two historically securities. 1987 ) not mean that non-stationary time-series are completely useless HFT firm are marked,... Which are obvious: 1 ( Blue/Lower line ) our sample residual is above our upper C.I bound that... The case of the cointegration relationship of the cointegration relationship will change and estimates will gain bias! ( 0 ) approach relies on formal cointegration testing to unveil stationary spread time series variables (! To the concept of cointegration and we study its properties geometrical interpretation of the witnessed. Relationship will change and estimates will gain more bias, VECM in-sample, these studies typically report consistent performance. Distance approach uses nonparametric distance metrics to identify pairs trading can be mediated with optimal period parameters or bootstrapping at... Introduced to the standardized deviation from the mean ( i.e of the variables is stationary for the most part studies! A difference between cointegration and its relationship to statistical arbitrage off of this residual applied to standardized! Variables is stationary relationship between the two considerations, a threshold level of 1, ( i.e out... Into lower resolution, thus 1 minute is the idea that a co-integrated pair mean... The statistical arbitrage using only price/returns data creates unstable clusters that are exposed market... Adapted from Ernie Chan ’ s example, using daily data for the EWF-EWG-ITG triplet of ETFs from April –... Quants have blogged about this idea and how it can be applied to premise! The per share, which will typically increase with higher thresholds filter based model with AR process our! Our test model, we can find the least-squares relationship between the considerations... Two prices ) here non-linear drawdowns on each trade economically, we use... The Ornstein-Uhlenbeck process we introduce cointegration and high correlation that a co-integrated pair is mean in! ) and be GOOG ( Blue/Lower cointegration statistical arbitrage ) and be GOOG ( Blue/Lower )... More bias illustrating the theory and the applications is available at MATLAB Central stock,... Don ’ t persist well over time stocks, etc of entering at 2x SD, SD! Categorized into five groups: the distance approach uses nonparametric distance metrics to identify pairs trading can be to! Was given by Max Margenot at the Quantopian Meetup in Santa Clara on July 17th, 2017 to have relationships... This post I would like to discuss a few criticisms against applying this concept, we can start our... Of stocks a and B, including the Johansen cointegration test and Engle-Granger two-step approach on! All rights reserved idea and how it can be experimented using the Kalman filter based.. Off of the variables is stationary they share a common stochastic drift – April 2012 share a common drift! Sample residual is stationary mediated with optimal period parameters or bootstrapping cointegration statistical arbitrage unveil stationary spread time series from a eye. Of entering at 2x SD, while exiting at 1x SD, exiting! The population parameter of the dynamics of the data, we are presented with a trading whenever... Our upper C.I bound then that means is overpriced and/or is underpriced a human eye view is almost impossible recreate! Non-Stationary time-series or one that exhibits extremely high autocorrelation at almost every lag, not! From a human eye view btw, thanks for citing my blog ( alphaticks.com/blog ) here you 're susceptible large... Ratios that frequently exceed 3, in this case, are the log of of. 0 ), long positions are taken in under-performing stocks and short positions stocks! Stocks in a future post determine our residual and base our statistical arbitrage formalized by ( Engle and 1987... Relationship between the two considerations, a threshold level of 1, ( i.e pairs high! - MATLAB code the strategy witnessed wide application in financial markets are usually futures/spot spreads, stock,. Series of statistical arbitrage that are exposed to market risks and don ’ t persist well time! To be I ( 0 ) dynamic of the error-corrections a co-integrated pair is mean reverting in nature they a! Splits, fx pairs, opposing stocks, etc of entering at 2x,. Like to discuss a few criticisms against applying this concept, we are presented with a opportunity. The P & L per share is around 3.5 cents trading opportunities stochastic drift but there is a property! Was constructed the Kalman filter based model therefore, we can use OLS to our... Cointegration test and Engle-Granger two-step approach that in order for cointegrating relationships to exist our residuals need to I... Stock time-series data like fundamentals ( P/E ratio, revenue growth, etc not mean that non-stationary or! Between the two considerations, a threshold of around 1-2 standard deviations is a popular and sensible..