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Question regarding the article Asset Allocation vs. Factor Allocation—Can We Build a Unified Method? by Jennifer Bender, Jerry Le Sun and Ric Thomas, The Journal of Portfolio Management Multi-Asset Special Issue 2019, 45 (2) 9-22;

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This is a paper about factor allocation and I have some questions about the formula there. So if we go to page 16 we can find the formula R = FB + e. R is a vector of asset returns. B is the exposure matrix of the assets in Exhibit 1(I think it's a typo here it meant Exhibit 4). F is the return vector of the factor-mimicking portfolio.

My first question is What does the Σ mean here? And also what's the intuition of calculating F using the attached formula there?

My second question is given that R is a vector of asset returns with dimension N*1 and F is a dimension of N*1; F*B is never gonna give us R's N*1 as B is in a dimension of N * M.

Sorry maybe I got the entire thing messed up but hopefully, someone can point out my mistakes and errors! Thanks! Please let me know if you want the full version of the paper. Happy to share.

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