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For context, I am building an eigenportfolio following the conventions of Avellaneda and Lee Statistical Arbitrage in the U.S. Equities Market (2008), and I get negative weights for eigenportfolios 2,3,.., and so on.

I wanted to know if the correct way to normalize is to divide each element by the sum of elements, as you would do when you have positive weights? I was thinking of taking the sum of the absolute value and then dividing each element by that.

I was having some difficult time visualizing implications under both cases, and so was unsure which method is more appropriate...

I would be grateful if you could provide some kind guidance on this matter.

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The whole point of the normalization is for the weights to sum to 1. If you wanna take the absolute value, when calculating the portfolio weights (as a ratio of portfolio value to the sum of portfolio values), the value of an eigenportoflio should be in absolute value, and the sum of portfolio values should all be in absolute values.

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  • $\begingroup$ PS. I did not read the paper but just your explanation. $\endgroup$
    – KaiSqDist
    Nov 21, 2023 at 17:28

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