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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?

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    $\begingroup$ Please read Avellanada & Lee (2008). The idea is that if the 2 stocks are cointegrated, then you can try to model their spread $S_t^1-\beta S_t^2$ as a mean reverting process (since it is stationary). Once done, you can start trading accordingly to where the current observed spread lies wrt to the equilibrium mean reversion value your model predicts. $\endgroup$ – Quantuple May 20 '16 at 7:34
  • $\begingroup$ Thanks for the reference. In the above strategy, could one say that the two stocks are offsetting each other so that the value of the portfolio should stay on some level (long term mean) and one can capitalize on the short term deviations (assuming the correlation will hold long term but there will be short term deviations). I mean, in the simplistic way, the portfolio should stay on some level, if it goes up then short it, if it goes down then buy it. Would that be a correct reasoning? $\endgroup$ – Michal May 21 '16 at 1:03
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    $\begingroup$ Assuming the cointegration relationship holds, you should see the spread (ie $S_1-\beta S_2$) as a new 'asset' which indeed wiggles around a constant value. If you judge the asset value is low wrt to equilibrium, you buy the asset (hence buy the PF) and hold it until it reaches a high at which point you sell (short the PF) to lock a profit and vice versa. $\endgroup$ – Quantuple May 21 '16 at 8:11

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