# What is the logic of the eigenvectors of the Johanson cointegration test determining hedge ratios?

Reading Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan and there is a short section about the Johanson test for cointegration where it is mentioned that

the eigenvectors resulting from this test can be used as a vector of hedge ratios for the instruments in question to form a stationary portfolio.

My question is: what is the logic in doing this / how does this make sense (Ie. what is the logic in taking the resulting eigenvector values and using them as the hedge ratios for the portfolio)? What property about using these values then makes the portfolio stationary?

• Of course it comes into play, it is a basic property of co-integration... A vector of prices $p_t$ is said to be cointegrated if there is a vector of weights w (called the eigenvector) such that $wp_t$ is stationary. – noob2 Dec 11 '18 at 1:23
• @noob2 I think there is misunderstanding, updated the question to try to be clearer (and commenting here partly so original comment still makes sense in context). – lampShadesDrifter Dec 11 '18 at 2:26
• Question is still not so clear as the existence of the eigenvalues is the fact that they make the portfolio stationary? The fact that the eigenvalues are good candidates for the hedge ratio is proven here. – Trevor Hansen Dec 12 '18 at 14:29