Using Principal Component Analysis to Separate Sector Returns

Summary

The document asks how to find sector data that are uncorrelated or isolate the component of one sector’s return stream that is independent of others. It reports variance inflation factor values for a set of stock-market sectors and notes that several exceed a commonly used level of concern. The response explains that sectors are not made independent simply by seeking different data: observed relationships are properties of the return series under study.

Principal component analysis is offered as a standard way to form uncorrelated combinations of the input series. Its eigenvectors define components that are uncorrelated by construction, providing transformed return streams rather than a guarantee of economically distinct sectors or stable future relationships. The exchange provides no implementation details, validation, or evidence that PCA components improve a portfolio. It also does not explain how to map a component back to a “pure” sector return. The suggestion is therefore a starting point for dimensionality reduction, with interpretation and time stability left open.

Key ideas

• The document uses variance inflation factors to describe overlap among sector return series.
• Sectors cannot be assumed to be independent simply by selecting different sector data.
• PCA forms linear combinations of input series that are uncorrelated by construction.
• PCA components are transformed portfolios and do not guarantee economically independent or stable exposures.
• The response proposes PCA but gives no implementation or portfolio-performance evidence.

Tags

# Correlation among different sectors of the market


# Correlation among different sectors of the market












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.

## Answer by LazyCat (score 3, accepted)

https://quant.stackexchange.com/a/41122

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.