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Portfolio Systematic Risk, Breaking it down into factor % contributions

Paulius

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I have a portfolio (p) of N equities, with lets say weights vector (m) at the start of the calculation period. Each equity has it's own set of factors (like corresponding country, industry index, etc.), some of the equities has the same factors.

I am trying to breakdown the systematic risk into individual factor contributions to portfolio's (p) systematic risk.

What I do is for each component of portfolio (p) I calculate corresponding factors exposures (betas), and say that portfolio's (p) expo to those factors are weighted (based on weights m) sums of betas.

Systematic risk is R2 of portfolio's (p) returns vs sum of factor returns with calculated weights (sums of betas).
Factor k % contribution to portfolio's risk is corr(p,k) * p expo to k * standard deviation of k / standard deviation of the whole portfolio.
Using this methodology I am able to sum up each factors k % contribution to R2 only if portfolio is made of one instrument but if it is of multiple instruments
the sum of factor's % contributions does not exactly equal R2.

Q - How to calculate factors % contribution to portfolio's systematic risk? Or sum of contributions does not need to be equal portfolio vs factors (with calculated weights) R2?


Help would be appreciated a lot,
thank you in advance
 
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