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What is factor contribution to risk and how is it computed?
What is factor contribution to risk and how is it computed?
Alexa Catalano avatar
Written by Alexa Catalano
Updated over a week ago

Rev. Date May 29, 2019

Contribution to risk (CRisk) provides the investor with insight into the breakdown of the portfolio risk by its systematic and idiosyncratic components (Grinold and Kahn (1999)). It measures the percentage of the total portfolio volatility due to factor exposure.

The contribution to risk of factor(i) is computed as:

r(p) = investment or portfolio returns
β(i) = investment's or portfolio's exposure to factor(i)
f(i) = returns of factor(i)
i = 1, 2, ..., N

The first term in the numerator is the weighted factor risk. This term is adjusted by the second term, which is the correlation between the weighted factor returns and the investment or portfolio returns. Finally the result is divided by the risk of the total investment or portfolio to arrive at the risk contribution of factor(i).

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