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How two stocks fully correlated over short timescales

How two stocks fully correlated over short timescales?

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Two stocks may be completely correlated over short timescales until now diverge in the long run, with one growing and another decaying. On the other hand, two stocks may follow each other, never being additional than an exact distance apart, but along with any correlation, negative, positive or varying. When we are delta hedging then maybe the short timescale correlation issues but not, if we are holding stocks for a long time in unchanged portfolio. To notice whether two stocks stay close together we require a definition of stationarity.

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