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What are some analytical methods to find contributions of sectors/industries to the market index?

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I want to know analytical methods (the more innovative, the better!) to calculate contributions of sectors (ex. financials, consumer staples, industirals indices) to the market (ex. s&p index).

In other words, I want to answer this question: which sector had the biggest return and risk contribution to the market from t = t1 to t= t2? What percentage of total return and risk is coming from the TMT sector from t = t1 to t = t2?


Performing simple multiple regression is one way, but what are other advanced/innovative ways?
 
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I think factor analysis and PCA are the standard tools. Look at the MSCI website.

Thank you very much. By factor analysis, you mean something like multi regression? So the dependent variable is the MSCI world index and independent variables are the indices for technology, financials, etc. sectors?
 
Thank you very much. By factor analysis, you mean something like multi regression? So the dependent variable is the MSCI world index and independent variables are the indices for technology, financials, etc. sectors?
Grinold and Kahn - http://a.co/eTdGzcv

If you want a step by step approach, read this:

Multiple Factor Model Summary

BTW, BARRA commercialized all these for years (monthly updates) and a lot of people made a lot of money with it. It just became popular recently with the arrival of ETFs (sector ETFs, etc) and Robo Advisors. Read Fama as well to understand the theory.
 
Grinold and Kahn - http://a.co/eTdGzcv

If you want a step by step approach, read this:

Multiple Factor Model Summary

BTW, BARRA commercialized all these for years (monthly updates) and a lot of people made a lot of money with it. It just became popular recently with the arrival of ETFs (sector ETFs, etc) and Robo Advisors. Read Fama as well to understand the theory.

So I can use the multiple factor model to describe which sectors' indices had the biggest impact on the overall market?
 
So I can use the multiple factor model to describe which sectors' indices had the biggest impact on the overall market?
Yes, based on your Model. Read the book or the paper in the Systematic Investor article.

You will need to create your own model based on your own data. The link uses the Sector ETFs as proxies. There is a lot of work to do but the theory is not complex. The old bible used to be Grinold and Kahn but there is a plethora of resources.
 
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