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Finding the Characteristic Implied by a Market Index Portfolio

Article Quant Q&A · Author: Ronnie268
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Summary

The note explains how to interpret a question from Grinold and Kahn’s portfolio theory exercises about the characteristic associated with the Major Markets Index portfolio. The proposed interpretation is to identify the attribute for which the MMI portfolio serves as the characteristic portfolio.

The suggested method is to calculate each asset’s beta against the MMI portfolio, using the appendix proposition cited in the answer. The document gives no worked calculation, data, or empirical evidence, so it offers a conceptual pointer rather than a complete solution. Its usefulness depends on the reader having access to the referenced book and understanding the relationship between attributes, characteristic portfolios, and asset betas.

Key ideas

  • The MMI portfolio is interpreted as the characteristic portfolio for a particular attribute.
  • Calculate each asset’s beta against the MMI portfolio to identify that attribute.
  • The answer points to a proposition in the book’s appendix but does not show the calculation.

Tags

Factor investingPortfolio constructionStatistics
Full text
# What is the "characteristic" associated with the MMI portfolio? How would you find it?


# What is the "characteristic" associated with the MMI portfolio? How would you find it?












I found the above question in Grinold and Khan "Active Portfolio Management", p39 Chapter 2 Q3 of the Exercises. I presume the MMI portfolio is the Major Markets Index portfolio, but I'm struggling to work out what is meant by "characteristic", let alone answer the question.

Is it referring to the attribute which that portfolio expresses most effectively (they defined a relationship between attributes and characteristic portfolios at the beginning of the Technical Appendix to chapter 2)? Or is it something else?

Any help on clarifying the above and answering the question is appreciated!

## Answer by Steve Jenkins (score 1, accepted)

https://quant.stackexchange.com/a/44538

I think one is expected (as you say) to find the attribute such that the MMI portfolio works out to being the characteristic portfolio of the attribute. This can be obtained by calculating the beta of all assets against the MMI. (See part (2) of Proposition 1 in the appendix.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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