generalized pairs trading ... how does the math work? In pairs trading, you long $N and short $N at the same time to make it dollar neutral, how do you do that in the case of generalized pairs trading with more than 2 assets, and you want to formulate an optimization framework that allows some flexibility in weighting?
In a different thread, I demonstrated from actual trading data, that dollar neutral is not optimal. http://www.elitetrader.com/vb/showthread.php?s=&postid=3057864&highlight=pair#post3057864
How could 2 securities with significantly different volatilities... Be consider a "pair" by a competent trader? And pairs trading really ends up as "basket trading"... Which 20 or 50 or 100 pairs split up in long/short baskets. Diversifying with large baskets... Is the only way you can run a stable business.
Yeah, my original question was: if you throw 10 pairs into a basket, each pair with fixed trading ratio, shouldn't that be sub-optimal to consider all those assets in the basket as a generalized pairs trading setup, so you can "optimally" decide the best long short sizes/weights among the constituents of the basket?
I have many times seen people throw to symbols on the screen with different price scale that happen to cross over or touch. There needs to be a real economic relationship for there to be a reason to bet on convergence or divergence. For example, the US treasuries are all highly correlated and cointegrated. They can thus be traded like a pair-trade. The other way, that I see to use correlated baskets is leaders and followers. Just by being in an index, stocks become more highly correlated. For industries and indices, can can trade either overvalued vs group or followers vs group.