If it can be proved that two time series
$$S_t^1=\alpha + \beta S_t^2 + \xi_t$$
representing stocks are correlated, with $\beta=-2$ and then are proved to be cointegrated,
how a portfolio should be built to make a profit?
Would be the beta from regression used? or the lambda from AR?
How would this portfolio create a profit assuming $V_t=S_t^1 + 2S_t^2$. wouldn't it be a hedge where those positions offset each other? where the profit should come from?