Pairs Trading, Normalized Prices, and Structural Breaks
Summary
The document asks why normalized prices for a pair can keep separating despite correlated returns and tests suggesting cointegration. The response distinguishes similar short-term return behavior from a stable long-term relationship: two series can move in broadly similar directions while their relative level shifts. A plotted comparison can also look different depending on the normalization starting point, so normalized price levels alone may obscure the behavior of the spread being tested.
The proposed explanation is a structural break, where the relationship's dynamics or average return difference changes because of new risks, fundamentals, or events. The example links a divergence between the DAX and CAC 40 around the 2016 US election to possible changes in international trade expectations. It is an interpretation of one historical episode, not proof that the event caused the shift; a pair strategy must account for changing relationships and cannot assume past mean reversion will persist.
Key ideas
- Correlated returns do not guarantee that normalized price levels will converge.
- A persistent shift in the relative mean can indicate a structural break in a pair relationship.
- The chosen starting point affects normalized price comparisons, so spread analysis should guide interpretation.
- The historical index example offers a possible event-related explanation rather than establishing causality.
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# Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging # Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging 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- - 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. - Or the two normalized prices would diverge from the very beginning even though they move in a similar fashion. 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 ## Answer by kurtosis (score 1) https://quant.stackexchange.com/a/57326 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.
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