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I'm studying the BARRA Predicted Beta model, and the common factor covariance between portfolio $p$ and the return on the market $m$ is defined as the product of the transposed vector of the factor exposures for the portfolio, the factor covariance matrix, and the vector of the factor exposures for the market:

$COV(r_p, r_m) = X_p^TFX_m$

and the specific covariance is:

$COV(r_p, r_m) = \sum_{i=1}^{N}{h_{pi}h_{mi}\sigma_i^2}$

where:

$F_{jk}$ is the covariance between factors $k$ and $j$

$\sigma_i^2$ is the specific variance of asset $i$

$X_{mj}$ is the market's exposure to factor $j$

$h_{pi}$ is the holding of the portfolio in asset $i$

$h_{mi}$ is the holding of the market in asset $i$

I find those three definitions a little ambiguous. What is exactly meant by "holding"? Should it mean weights or weighted returns? What is the market's exposure to an asset?

Thank you.

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    $\begingroup$ Hi: holding, $h_{pi}$ just means weight of asset in the portfolio which is total cap of asset in portfolio divided by total cap of portfoio. $h_{mi}$ is weight of asset in whatever index ( market portfolio ) one is referring to. ( so total cap of asset divided by total cap of index ). $\endgroup$ – mark leeds Feb 11 at 4:39

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