Improved Risk Reporting with Factor-Based Diversification Measures

Improved Risk Reporting with Factor-Based Diversification Measures — February 2014

2. Portfolio Diversification Measures

which leads to the following percentage variance contributions:

,

where

Note that Equation (2.9) and the properties of given above show that vector FF ⊥ simply contains the betas of the linear regression of r P with respect to the orthogonalised four factors. Since the factors are uncorrelated by construction, this leads to:

, for all k = 1, ..., 4,

where denotes the correlation between the portfolio of the k th orthogonalised factor. Then, replacing the values obtained for in the variance contributions leads to the following simplification:

. (2.10)

In the next section, we analyse how these factor-based measures of portfolio concentration can be used within the context of improved reporting techniques that allow for a better measurement of portfolio risk exposures.

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An EDHEC-Risk Institute Publication