When you have negative weights in the context of portfolio construction, what is the correct way normalize them?
When you have negative weights in the context of portfolio construction, what is the correct way normalize them?
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Kenfisherman · External communityPost link
External question — Quantitative Finance Stack Exchange
Author: Kenfisherman
Original post: https://quant.stackexchange.com/questions/77432
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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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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Hasselhoff · External communityPost link
External answer — Quantitative Finance Stack Exchange
Author: Hasselhoff
Original post: https://quant.stackexchange.com/a/80333
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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Didn't read the paper, but my intuition says depends if you need to normalize for the purpose of returns or value. if the weight is negative, that just means it's a short position, so for value its a credit to the account when you enter, while the positive weights are a debit, and you want to leave them as is. But the for returns, as long as you have the sign of the return wrt to gains or loss, then you could use absolute value of weights. Either way, you use n = count of weights as your denominator.
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Quoted from Forex.com.bd-Editorial External question — Quantitative Finance Stack Exchange Author: Kenfisherman Source score (net votes, not local likes): 0 Original post: https://quant.stackexchange.com/questions/77432 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. 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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