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!

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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.

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  • $\begingroup$ Ah yes - the attribute a for a given portfolio is found using the equation $a = V h_a / \sigma_a^2$, whence you need the holdings of each risky asset for the MMI portfolio and the variance of the portfolio $\endgroup$ – Ronnie268 May 14 '19 at 12:14

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