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I have been doing some reading on factor models. In the literature it mentions that when creating a portfolio that maximises particular attributes it may lead to unwanted bias to other factors. I understand this part.

So they create 'true' factor scores which clean a factor of the influences of all the other factors. It mentions the use of cross-sectional regressions to simultaneously remove these side effects. It is this part I am unsure of. I do not know how they are 'cleaning' their factors and if this is a standard practise?

further information

A variable is decomposed into the true variable and the parts that are shared with other common variables. This is done using the residual variable methodology.

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Which literature are you referring to? Can you give any references? –  Bob Jansen Aug 18 at 9:00
    
its a presentation I have been forwarded by a client. I would normally ask them however the author is away on holiday for the next two weeks. Sadly I cannot give any references. I have edited my post and added some further information although there isn't a huge amount to add. –  mHelpMe Aug 18 at 9:17
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Speaking from equity quant factor building experience, it is a common practice to build multi-factor models by regressing one component against other(s) and using the residual scores. This is done to avoid bias as you mentioned - these biases could be from the factor itself (in different regimes, Quality / Momentum influencing each other - or earnings, value bringing opposite extremes to the portfolio ranking etc.). Robeco have done a few papers on regressed residual factors (mostly momentum ). one of the papers can be found here. papers.ssrn.com/sol3/papers.cfm?abstract_id=1911449 –  Viquar Aug 18 at 11:39
    
@Viquar thanks for the comment. Have just downloaded the paper which I am about to go over. So if there was a momentum factor they would regress this on the other factors. The residual from this regression is that the 'true' part of the momentum factor? –  mHelpMe Aug 18 at 12:20
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Indeed. let's say you have a pool of factors which you believe may have crossover information. the goal is to strip the factors of this linked information and therefore using regressed residuals as clean factor scores. –  Viquar Aug 18 at 12:24

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Speaking from equity quant factor building experience, it is a common practice to build multi-factor models by regressing one component against other(s) and using the residual scores. This is done to avoid bias as you mentioned - these biases could be from the factor itself (in different regimes, Quality / Momentum influencing each other - or earnings, value bringing opposite extremes to the portfolio ranking etc.).

Robeco have done a few papers on regressed residual factors (mostly momentum), such as "Short-Term Residual Reversal".

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