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I have been playing with mean reverting pairs, but seems that most of the low hanging fruit (ie pairs) have been squeezed already. I would like to start with mean reverting baskets (>2 securities) in order to find unexplored, juicier strategies.

Please can you guide me recommending books, articles, etc., on how to build such mean reversing baskets?

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  • $\begingroup$ What you are talking about is known as Cointegration. Just look for it $\endgroup$
    – mepuzza
    Commented May 8, 2012 at 15:50
  • $\begingroup$ Thanks mepuzza. I know about cointegration and how to test for cointegration of pairs using (for example) Augmented Dickey-Fuller test. Do you have any reference I can read about building/testing cointegrated baskets? $\endgroup$
    – Victor
    Commented May 8, 2012 at 16:41
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    $\begingroup$ @VictorP: Your question is very similar to the one asked just yesterday by Quant Guy. The paper I cite in my answer is an attempt to build such portfolios. There is also a post on the tr8dr blog related to that matter. You can find it by searching "cointegration clusters Tr8dr" on google. $\endgroup$
    – Zarbouzou
    Commented May 8, 2012 at 20:07
  • $\begingroup$ @lehalle I've rolled back your edit since the question never mentioned "cointegration". I feel like a broken record here. $\endgroup$
    – chrisaycock
    Commented May 12, 2012 at 7:23

2 Answers 2

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There are multiple approaches that you could consider. The basic idea across all of them is that you want to find a portfolio that is stationary. In the two-asset case, it is well known how to accomplish this. This paper by Marcelo Perlin describes one approach: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=952782 but I am not particularly inclined to use this. Alternately, see Section 4 of this paper by Attilio Meucci: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1404905 which provides a more general framework. One way to think about it is that if you arrange the principal portfolios (through PCA) by variance, then the lowest variance ones would be more stationary than the highest variance ones. However, you have to offset the fact that since they have less variance, there is less opportunity to make profitable trades.

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Pairs trading is just one type of statistical arbitrage (check out references on wikipedia page). It sounds like you are talking about trading "factors" against each other. Factors could be industries, size, fundamentals, or purely statistical.

Start with Ed Thorp's Wilmott articles on statistical arbitrage. Then read Attilio Meucci's Review. An example stat arb strategy is studied by Avellaneda and Lee.

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