Suppose you have 3 stocks, say X Y Z. You also know that

X is cointegrated to Y using some test (say ADF)


Y is cointegrated to Z.

However, no transitivity, and no threesome cointegration whatsoever (in other words, neither X is directly cointegration to Z, nor is there a 3 symbols cointegration using Johansen).

Is there a way to generalize pair trading to make a dynamic portfolio of X Y Z?

Intuitively I would say yes, by thinking of two pairs, XY and YZ. But I don't see yet a good strategy managing both efficiently.

  • 1
    $\begingroup$ Are you okay with upper and lower bounds on the other correlations? $\endgroup$
    – will
    Jul 23 '19 at 22:39

Assuming we are talking about Pearson correlation, then we may apply the triangle inequality. Let $\rho(X,Y)$ denote the correlation between $X$ and $Y$. Then,

$(1-\rho(X,Z))^{1/2}\le (1-\rho(X,Y))^{1/2} + (1-\rho(Y,Z))^{1/2}$

  • $\begingroup$ great! Actually in my OP I conflated two questions: one is for CORRELATION, which you have answered, another one is for COINTEGRATION. Any clue how to proceed if X Y Z are not Pearson correlated, but are cointegrated (Y cointegrated to X, Z to Y) ? $\endgroup$ Jul 24 '19 at 14:23
  • $\begingroup$ I edited the question to specify cointegration. However, I still like you answer $\endgroup$ Jul 24 '19 at 14:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.