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VaR and Expected Shortfall Allocation: Simplicity Versus Sophistication

Article Quant Q&A · Author: Marco
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Summary

The document discusses whether Euler or Constrained Aumann–Shapley allocation is preferable for attributing portfolio Value at Risk or Expected Shortfall to risk factors. Its central practical point is that capital attribution must be explainable to its audience, especially when the audience includes regulators. Component and marginal VaR or ES are described as familiar approaches with a long history of use in banking regulation.

More sophisticated allocation methods may still help portfolio managers analyze how changes to a book could reduce measured risk. The response offers no mathematical comparison, worked example, or evidence that one allocation method is more accurate or stable than another. Its guidance is therefore about communication and use case: established measures may be easier to explain for regulatory reporting, while advanced methods may support internal analysis. The brief answer does not specify the assumptions, constraints, or conditions under which Euler or CAS allocations are suitable.

Key ideas

  • Regulatory risk attribution often favors familiar component or marginal VaR and ES measures.
  • Euler and Constrained Aumann–Shapley methods raise practical questions about explainability.
  • More advanced allocation tools may help assess portfolio changes intended to lower risk.
  • The response provides no technical comparison or evidence establishing a universally superior method.

Tags

Risk managementPortfolio constructionStatistics
Full text
# Capital Allocation, VaR, Expected Shortfall


# Capital Allocation, VaR, Expected Shortfall












Are there any serious drawbacks / weaknesses in the Euler allocation method, when used to allocate VaR capital (and potentially Expected Shortfall) to risk factors in a portfolio? I notice that recently people have started talking about Constrained Aumann Shapley (CAS) allocation approaches - does this offer advantages? Thanks.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/59668

The biggest problem with Euler or CAS is that an explanation of where VaR/ES came from has to be so simple than even a bank regulator can understand it. :)

So everybody uses component, marginal, etc VaR/ES that have been around since the widespread Basel II VaR adoption in the 1990s. Regulators understand those.

More sophisticated tools may be useful for problems such as figuring out how a book might be tweaked to decrease its VaR; just don't show them to regulators who don't appreciate sophistication for sophistication's sake.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.