I did some cointegration tests on a 50 stocks sample, whith which I created pairs. I used the Engle-Granger approach and the Johansen approach, both of them gave me a high percentage of cointegrated pairs(45% and 96%). I'm fairly sure about the way I did the Engle-Granger test (OLS->get residual and test for stationnarity with ADF test), but a bit less for the Johansen test, which I modeled after an example in Jansen's book about machine learning. In the same book Jansen found less than 5 % of pairs were cointegrated.
Does anyone know how rare is cointegration ?