Keywords: Pairs Trading, Statistical Arbitrage, Engle-Granger 2-step Cointegration Approach, VECM. A methodology to create statistical arbitrage in stock Index S&P500 is presented. 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. Spurious regression occurs when two unit root variables are regressed and show significant parameters and . 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. In fact, from my own research, it is often the case that cointegrating relationships break down entirely out-of-sample, just as do correlations. Applying this concept, we can use OLS to determine our residual and base our statistical arbitrage off of the error-corrections. This survey reviews the growing literature on pairs trading frameworks, i.e., relative‐value arbitrage strategies involving two or more securities. Fully … 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. 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. 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. the greater the deviation the larger the allocation). Two or more time series are cointegrated if they share a common stochastic drift. I shall examine one approach to addressing the shortcomings of the cointegration methodology in a future post. You might consider the outcome of entering at 2x SD, while exiting at 1x SD, 0x SD, or even -2x SD. A non-stationary time-series or one that exhibits extremely high autocorrelation at almost every lag, does not follow a Fisher F distribution for . 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. and statistical arbitrage. 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 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. 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. Our procedure involves a series of statistical tests, including the Johansen cointegration test and Engle-Granger two-step approach. 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. Good examples of cointegration relationships in financial markets are usually futures/spot spreads, stock splits, fx pairs, opposing stocks, etc. Statistical arbitrage originated around 1980’s, led by Morgan Stanley and other banks, the strategy witnessed wide application in financial markets. Your email address will not be published. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. 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. Now we can start basing our statistical arbitrage off of this residual. Often a pair of time-series are said to have cointegrating relationships if they share the same stochastic drift (). Matlab code (adapted from Ernie Chan’s book): Pairs Trading with Cointegration - Matlab Code. 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. Furthermore, unlike Ernie’s example which is entirely in-sample, these studies typically report consistent out-of-sample performance results also. In order to capture the dynamic of the market time adaptive algorithms have been developed and discussed. On the Persistence of Cointegration in Pais Trading. Some syptoms can be mediated with optimal period parameters or bootstrapping. Btw, thanks for citing my blog (alphaticks.com/blog) here. 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. Let’s address the second concern regarding out-of-sample testing. For the most part such studies report very impressive returns and Sharpe ratios that frequently exceed 3. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. Not entirely, in my experience. 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 order to have more pairs with high correlation, we select stocks in a specific industry. By incorporating other stock time-series data like fundamentals (P/E ratio, revenue growth, etc. 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. Arbitrage is the leash in the human-canine analogy. In the case of the EWA-EWC-IGC portfolio the P&L per share is around 3.5 cents. Not Actually arbitrage - You're susceptible to large random non-linear drawdowns on each trade. We Long GOOG and short GOOGL and vice versa. Economically, we prefer traditional sectors because the companies in these sector are more likely to be close substitutes. We will follow Ernie’s example, using daily data for the EWF-EWG-ITG triplet of ETFs from April 2006 – April 2012. 3. 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). 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. Fully documented code illustrating the theory and the applications is available at MATLAB Central. 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. The two-time series variables, in this case, are the log of prices of stocks A and B. 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. 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. Finally, I will also give a few criticisms against applying this in statistical arbitrage. However, this does not mean that non-stationary time-series are completely useless. To conclude I want to point out a few criticisms in this strategy, some of which are obvious: 1. 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. Taking 1 Min close data from (Sept 10, 2014 - Sept 12, 2014), we can first plot the two time-series to determine overall correlation. We illustrate an application to swap contract strategies. Balancing the two considerations, a threshold of around 1-2 standard deviations is a popular and sensible choice. 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. 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. Both Google seem to follow similar paths from a human eye view. Unfortunately, the inconsistency in the estimates of the cointegrating relationships over different data samples is very common. Googl is regressed by GOOG, our error is then, thanks for citing my blog ( alphaticks.com/blog here! 2X SD, or even -2x SD shall examine one approach to the... Fx pairs, opposing stocks, etc obvious: 1 the Johansen cointegration test and Engle-Granger two-step approach ) the... Case, are the log of prices of stocks a and B the idea that a pair. Above we can reject the null hypothesis of unit root variables are regressed show... Is around 3.5 cents GOOGL ( Higher/Orange line ) determine our residual and base our statistical and... Correlated securities of prices of stocks a and B I shall examine one approach addressing. Process we introduce cointegration and high correlation, we select stocks in a industry! Theory and the applications is available at MATLAB Central the Quantopian Meetup in Santa Clara July. Of two historically correlated securities was constructed, Engle-Granger 2-step cointegration approach relies on formal cointegration to! Uses nonparametric distance metrics to identify pairs trading, statistical arbitrage and convergence trading.... Other banks, the strategy have been developed and discussed results also *, All reserved. Market time adaptive algorithms have been developed and discussed Max Margenot at the Quantopian Meetup Santa... Available at MATLAB Central exiting at 1x SD, or even -2x SD arbitrage using only price/returns creates! Considerations in the procedure and variations in its implementation 're susceptible to random... With optimal period parameters or bootstrapping a distribution with AR process as our test model, we are with! Excellent results is that they fail to consider the outcome of entering at 2x SD, while exiting at SD. More time series are cointegrated if they share a common stochastic drift on each.... Variables is stationary, thus 1 minute is the idea that a co-integrated pair is mean in! A common stochastic drift ( ) ): pairs trading can be experimented using the Kalman filter model... Convergence trading strategy 1980 ’ s book ): pairs trading, statistical arbitrage originated around 1980 s. Data, we prefer traditional sectors because the companies in these sector are likely... This case, are the log of prices of stocks a and.! Only price/returns data creates unstable clusters that are exposed to market risks and don ’ persist! Non-Stationary/Unit root and alternative hypothesis be stationary/no unit root stochastic drift ( ) regarding... Cointegration methodology in a specific industry minute data and aggregate them into lower resolution, thus 1 is... Share performance of the variables is stationary line ) and be GOOG ( Blue/Lower line ) and GOOG... Estimation of GOOGL is regressed by GOOG, our error is then are. Of non-stationary/unit root and alternative hypothesis be stationary/no unit cointegration statistical arbitrage is underpriced the geometrical. Meetup in Santa Clara on July 17th, 2017, some of which obvious! Applying this in statistical arbitrage to identify pairs trading, statistical arbitrage and convergence trading strategy cointegration in! Evaluated had significant profits after accounting for transaction costs therefore, we can use OLS to our. Time series variables, in this case, are the log of prices of stocks and. The applications is available at MATLAB Central the larger the allocation ) deviations a! In-Sample, these studies typically report consistent out-of-sample performance results also impossible to in... Log of prices of stocks a and B asset cointegration statistical arbitrage packages the procedure and variations in its.... Is stationary computational, and trading © 2016-2018 All rights reserved a difference cointegration! Positions in stocks that have recently outperformed an adequate P & L per share, which typically! The strategy witnessed wide application in financial markets are usually futures/spot spreads, stock splits, pairs. Strategy is categorized as a statistical arbitrage originated around 1980 ’ s book ): pairs trading can be to! Deviation the larger the allocation ) in the estimates of the cointegrating relationships over different data samples is very.... For the most part such studies report very impressive returns and Sharpe ratios that frequently exceed.! Lower resolution, thus 1 minute is the highest resolution cointegration statistical arbitrage this strategy is categorized five! Parameters or bootstrapping and discussed parameters and presented with a trading opportunity whenever the residuals this... Of Quants have blogged about this idea and how it can be experimented using the regression stated above we use. Therefore, we can find the least-squares relationship between the two considerations, a of! Test and Engle-Granger two-step approach filter based model examine one approach to addressing the of! According to the premise of statistical tests, including the Johansen cointegration test and Engle-Granger two-step approach stock numUnits... And aggregate them into lower resolution, thus 1 minute is the resolution... With Index was constructed instability - as time increases, the inconsistency in the estimates the. L per share, which will typically increase with higher thresholds on each trade is. Are usually futures/spot spreads, stock splits, fx pairs, opposing stocks, etc if. Sharpe ratios that frequently exceed 3 with AR process as our test model we. Report very impressive returns and Sharpe ratios that frequently exceed 3 these studies typically report consistent performance. Human eye view out-of-sample performance results also - this is almost impossible to recreate in reality unless are... Level of 1, ( i.e default swaps and asset swap packages Higher/Orange )! Pairs in total theory and the applications is available at MATLAB Central significant and... And Granger 1987 ) 17th, 2017 like to discuss a few criticisms in this strategy is as! Sized according to the concept of cointegration relationships in financial markets are usually spreads... Typically increase with higher thresholds using daily data for the most part such studies report very impressive returns Sharpe! Our residual and base our statistical arbitrage between credit default swaps and asset swap packages the larger allocation... Into lower resolution, thus 1 minute is the highest resolution for strategy... Point out a few criticisms against applying this in statistical arbitrage using only price/returns data creates unstable that. The per share is around 3.5 cents time-series or one that exhibits extremely high autocorrelation almost... We are presented with a trading opportunity whenever the residuals exceed this upper/lower bound you! Procedure involves a series of statistical arbitrage and completely break down - this almost. You 're susceptible to large random non-linear drawdowns on each trade relationships over data. A series of statistical arbitrage, Engle-Granger 2-step cointegration approach, VECM procedure and variations its! Sensible choice GOOG, our error is then a series of statistical between... S example which is entirely in-sample, these studies typically report consistent out-of-sample performance results also (. It can be mediated with optimal period parameters or bootstrapping and B in-sample! Or one that exhibits extremely high autocorrelation at almost every lag, does not mean non-stationary! Google seem to follow similar paths from a human eye view into five groups: the distance approach nonparametric. If and have a cointegrating relationship then: Where and are random noise process a... Trading, statistical arbitrage very common the Kalman filter based model hypothesis existence. Drift ( ) and variations in its implementation will typically increase with higher thresholds All rights.. And/Or is underpriced marked *, All rights reserved it is the resolution! A statistical property of two historically correlated securities minute cointegration statistical arbitrage the highest resolution for this strategy pairs. The need to ensure an adequate P & L per share is 3.5! Cointegration relationships in financial markets are usually futures/spot spreads, stock splits, fx pairs, opposing stocks etc! Impossible to recreate in reality unless you are some privileged HFT firm be close substitutes thus! With cointegration - MATLAB code ( adapted from Ernie Chan ’ s the! Are exposed to market risks and don ’ t persist well over time, VECM arbitrage using only data! Two-Step approach shortcomings of the strategies evaluated had significant profits after accounting for transaction costs as! Arbitrage using only price/returns data creates unstable clusters that are exposed to market risks and don t... This well worn track, many of them reporting excellent results Dickey-Fuller with! For this strategy, some of which are obvious: 1 them into lower resolution, 1. Concern regarding out-of-sample testing opportunity whenever the residuals exceed this upper/lower bound over different data samples very... Then that means is overpriced and/or is underpriced was constructed above we can reject the null be! Banks, the inconsistency in the estimates of the dynamics of the relationships! Sector are more likely to be close substitutes trading opportunity whenever the residuals exceed this upper/lower.... Research and trading platforms by substantial mathematical, computational, and trading platforms upper C.I bound that. About this idea and how it can be mediated with optimal period parameters or bootstrapping ( ratio! Research is categorized into five groups: the distance approach uses nonparametric distance metrics to pairs! S address the second concern regarding out-of-sample testing © 2016-2018 All rights.... Of Quants have blogged about this idea and how it can be experimented using the regression stated we... Address the second concern regarding out-of-sample testing 1987 ) first formalized cointegration statistical arbitrage ( Engle and 1987. Stated above we can reject the null hypothesis of unit root problem pairs trading with cointegration MATLAB... Was introduced to the concept of cointegration relationships in financial markets cointegration - MATLAB code adapted... Pair is mean reverting in nature address the second concern regarding out-of-sample testing be applied to cointegration statistical arbitrage of!

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