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I am looking for a fast to compute, yet plausible risk attribution measure based on the risk measure used to compute overall risk.

To be more specific, assume that my risk measure is the VaR of a portfolio, how could I attribute the total VaR to the portfolio constituents using just the VaR as risk measure?

One approach I have currently found is Shapley Value, but for a portfolio with $d$ assets this would require $2^d$ calculations of the VaR.

The risk measures should fulfill the following properties (as the Shapley Value does):

  1. Efficiency (risk attribution measure sums to total risk)
  2. Symmetry (labeling of constituents does not matter)
  3. Dummy axiom (zero risk constituent has zero risk attribution measure) and
  4. Linearity (risk attribution measure can be computed as linear combination of different risk measures).
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    $\begingroup$ Incremental VaR is a common way to attribute risk to components of a portfolio. It requires one VaR calculation per asset and doesn't satisfy the efficiency property, but that seems like a strange thing to want, since VaR is not coherent. Are you sure you want efficiency? $\endgroup$
    – RossFabricant
    Apr 14, 2016 at 15:51
  • $\begingroup$ Actually I am working in the multivariate Delta-CoVaR context. I will need the efficiency property because my Motivation für a multivariate model is that with a series of bivariate models the sum will not equal the total which is what I want to achieve. $\endgroup$
    – InfiniteVariance
    Apr 14, 2016 at 16:23

2 Answers 2

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Have you considered Marginal Contribution to Total risk (MCTR)? You can decompose your risk across securities/sub-sectors/sectors, such that sum(weight of security * MCTR of security ) = portfolio risk (standard deviation). A good discussion on the topic can be found in Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk

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You can check the Euler-based risk attribution/ risk allocation, for example here: http://arxiv.org/pdf/0708.2542.pdf

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