Rank

I suggest that you look at Johansen's book on cointegration

http://www.amazon.com/Likelihood-Based-Inference-Cointegrated-Autoregressive-Econometrics/dp/0198774508/ref=sr_1_1?ie=UTF8&s=books&qid=1246640896&sr=8-1

His treatment is the most complete and will answer all of your questions. 
A nice empirical/practical follow up to this book is the recent one by K. Jusalius (his wife)

http://www.amazon.com/Cointegrated-VAR-Model-Applications-Econometrics/dp/0199285675/ref=pd_sim_b_2

The issue here is because the Pi matrix has rank 2 there are only two cointegrating relationships among the Y's of the form beta1'(Y1, Y2, X1, X2, X3) and beta2'(Y1, Y2, X1, X2, X3) where the coefficients on the X's are not all zero.

The X variables are unmodeled - which in the cointegration literature means that they are weakly exogenous wrt to the cointegration parameters in the VECM. If there is now feedback from the Ys to the Xs then the reduced form relationship for DX(t) does not involve Y and the Xs are then strongly exogenous. In particular, the error correction coefficients on these variables (alphas) are zero so that the system has the form like

DY1(t) = a1*beta1'(Y1, Y2, X1, X2, X3) + lags of DY(t) and DX(t) + e1(t)
DY2(t) = a2*beta2'(Y1, Y2, X1, X2, X3) + lags of DY(t) and DX(t) + e1(t)
DX(t) = lags of DX(t) + e3(t)

Notice in this type of representation there is no cointegration among the Xs because the reduced form for the Xs is not a VECM. 
Now because the X's are unmodeled, there is the possibility that there are cointegration relationships among the X's that do not involve the Ys. I think this is causing the confusion. In general, it is assumed that such relationships do not exist when the VECM is specified with unmodeled variables.

None of this discussion has to do with finance

Rank

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