Why Value at Risk Remains in Use Despite Non-Subadditivity

Summary

The document raises a conceptual question about Value at Risk (VaR). It notes that VaR is not subadditive in general: the risk measure for a combined portfolio can exceed the sum of the measures for its parts. This property can make diversification or dividing a portfolio into subportfolios appear counterintuitive. The text contrasts VaR with Conditional Value at Risk (CVaR), which was introduced as a subadditive alternative.

The author asks why VaR remains in practical use and when its failure of subadditivity can be ignored. However, the supplied document contains no answer, examples, or evidence explaining VaR’s continued use or identifying circumstances where the limitation matters less. It therefore serves as a prompt to examine trade-offs among risk measures rather than guidance for choosing one. Readers should not infer from this text alone that VaR is suitable or unsuitable for a particular portfolio; its limitations and potential advantages remain unresolved here.

Key ideas

• VaR can fail subadditivity, so combined portfolio risk may exceed the sum of component VaRs.
• The document identifies CVaR as a subadditive alternative to VaR.
• The text asks why VaR remains in use and when its non-subadditivity matters.
• No answer, examples, or evidence are provided to resolve those questions.

Tags

# Why is VaR metric still used?


# Why is VaR metric still used?












It is well know that VaR is not subaddtive measure which means that condition

$$ \text{VaR}(X+Y) \leq \text{VaR}(X) + \text{VaR}(Y), $$

where $X$ and $Y$ are portfolios, is not satisfied. As a result, in some cases a simple division of portfolio to its subportfolios can lead to lower risk. Especially for this feature, VaR was criticised and subadditive measures like CVaR were introduced.

My question are:

- If VaR has so conterintuitive and unrealistic feature like not being subadditive, why is it still used?

- In which cases can we neglect that VaR is not subadditive?

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