Need some expert advice and suggestions:

I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–Uhlenbeck tests etc) and correlated, I see that the normalized prices of a pair always end up diverging in the end and never converging again even though they will move in a pretty similar fashion. Example: DAX (German index) and CAC40 (French index) are both co-integrated and well correlated.

In particular, I noticed two things that depend on the starting point of the normalized price series-

  1. Either the two normalized prices will first show mean reverting nature but then they diverge away even though they move in a similar fashion never to converge again.

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  1. Or the two normalized prices would diverge from the very beginning even though they move in a similar fashion.

enter image description here

It always depend on the starting point. Any experts here would kindly tell me what is the reason or if I am doing something wrong here? Would really appreciate your comments. Thanks in advance

  • $\begingroup$ You have circled the period of late November 2016 onward, but I would argue that the divergence actually started in August or September of 2016. If only we could think of an event in late 2016 (!) which changed international relations or trade, then maybe that would suggest a structural break. :-) $\endgroup$
    – kurtosis
    Aug 13, 2020 at 22:51
  • 1
    $\begingroup$ Very general comment, but it seems you're kind of chasing your tail here...I'd take your question all the way back to its origin and ask why, a priori, you think the CAC and DAX have any reason to be cointegrated as opposed to simply correlated, as most equity indices are likely to be. Beyond that, even insofar as you evaluated cointegration over a period that evidenced it for the CAC and DAX, I would assert your real issue is bias present in your original assessment. $\endgroup$
    – Chris
    Aug 14, 2020 at 4:18
  • $\begingroup$ @Chris interesting observation. I will look into this. This was helpful. Is there any book or any material that I can read and follow to do pairs trading the proper way? Sorry but I am just starting out. So not very experienced in this. I have only done true arbitrage which is easy. So would definitely appreciate your suggestions. Thanks in advance. $\endgroup$
    – rockav
    Aug 14, 2020 at 6:45
  • $\begingroup$ @rockav, I've read Viyamurthy's 'Pairs Trading' years back and liked it. $\endgroup$
    – Chris
    Aug 14, 2020 at 16:51

1 Answer 1


You circled the plot of both the DAX and CAC 40 from late November 2016 onward. Now... I would say that maybe the divergence between these indices started not reverting sometime in August or September of 2016. Before then, we see return series are very related. After maybe February or March of 2017, the returns again look related but with a new differential that is typical.

When cointegrated processes stop reverting according to past dynamics or change the level of their mean return difference, we suspect there has been a structural break: a change in underlying dynamics, risk, fundamentals, etc.

In late 2016, the US election included lots of rhetoric about changing international relations, renegotiating trade pacts, and the US turning inward. That alone could lead to a difference opening up between the indices. Then, in November, the election outcome was a bit of a surprise and the indices continued their divergence -- and did so sharply. That would suggest that the outcome of the 2016 US election created a structural break between these indices.

  • $\begingroup$ Hi @Kurtosis thanks a lot for commenting. Really helpful insights. But this divergence is always observed depending on the starting points. I see this even on a 5 minute chart- same phenomenon. So there is probably something wrong that I am doing here that I do not know. Hartelijk bedankt!! $\endgroup$
    – rockav
    Aug 14, 2020 at 6:34
  • $\begingroup$ @rockav Well, you make the indices be equal at your starting point, so divergence is very likely to occur. However, persistent or increasing divergence would suggest there are factors still driving a wedge between these economies. The key to finding a good starting point (assuming no structural breaks) is it should yield a long period of divergences that revert and often cross. So I would not just pick any random starting point. Hope that helps! Graag gedaan! $\endgroup$
    – kurtosis
    Aug 14, 2020 at 7:02
  • $\begingroup$ @rockav: kurtosis and chris both make great points but also note that even if you did pick a "good pair", there's nothing written anywhere ( or if there is, it's not true ), that says that cointegrated-ness in the past will guarantee cointegrated-ness in the future. So, you're always going to be dealing with the stability issue when using the cointegration methodology on pairs. $\endgroup$
    – mark leeds
    Jan 11, 2021 at 16:57

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