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It is known that many sectors/industries within the stock market are correlated with each other. For example, using VIF as a measure of correlation, I have the following result:

Sector  ENERGY   CONSUMER STAPLES   CONSUMER DISCR   MATERIALS   INFORMATION TECH   INDUSTIRALS   HEALTH CARE   FINANCIALS   UTILITIES   TELECOM SVC
 VIF    2.937214     4.268179      10.755497        6.150606     5.023864           14.064349       2.795279      6.054236     2.985639     3.360512

As you can see, VIF for most industries are greater than 5. I was just wondering if

1) there exists data for the uncorrelated sectors or

2) there eixsts a way to extract the "pure" part of a given return stream which is uncorrelated with other parts. I am not even sure if it's possible.

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  • $\begingroup$ That's the whole big field. PCA is a part of it, but there are more things to do. Please check out Grinold, R. C., & Kahn, R. N. (1999). Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk (2nd ed). McGraw-Hill.. $\endgroup$ – stans - Reinstate Monica Aug 6 '18 at 18:28
  • $\begingroup$ In particular, PCA is not enough because correlations (factor loadings) are notoriously difficult to estimate. They change from one period to another. They explode upwards or downwards during crises. For that reason, you might need to build a parametric or semi-parametric model for them. $\endgroup$ – stans - Reinstate Monica Aug 6 '18 at 18:32
  • $\begingroup$ @stans thank you so much for your advice. Are you aware of any sources related to the parametric/semi-parametric models you talk about? $\endgroup$ – Jun Jang Aug 6 '18 at 18:39
  • $\begingroup$ Start with reading the book I suggested. People who are serious about factor models, in asset management and hedge funds, turn to the methods of machine learning sooner or later. $\endgroup$ – stans - Reinstate Monica Aug 6 '18 at 18:54
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1) Not sure what you mean by the "data for uncorrelated sectors" - the sectors are what they are, if they are correlated to the market and each other, that's that.

2) The standard way to extract uncorrelated streams is to run PCA analysis - the eigenvectors will be uncorrelated by construction

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  • $\begingroup$ But wouldn't the PCA analysis give you a linear combination of the original variables, which is hard to interpret? right? $\endgroup$ – Jun Jang Aug 6 '18 at 14:02
  • $\begingroup$ It will certainly give you linear combinations, but they will be (a) uncorrelated (b) sorted in the order of importance. Isn't it exactly what "extract the pure part" is? Interpretation may not be hard if it's just 8 or so sectors. $\endgroup$ – LazyCat Aug 6 '18 at 14:23

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