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How Negative VaR-Equivalent Volatility Can Arise

Article Quant Q&A · Author: SinusK
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Summary

The document asks whether the VaR-equivalent volatility measure used in PRIIPs key information documents can be negative and what such a value means. The answer says it can occur when the loss at the measure’s 2.5th-percentile threshold is actually a gain. In that case, the risk measure’s percentile input reflects an outcome above the initial capital rather than a loss.

A hypothetical product illustrates the point: most proceeds are used to fund a coupon, while a low-probability outcome wipes out the investor’s capital. The answer says this construction can nevertheless receive the lowest market-risk category under the described measure. This brief example highlights a limitation in interpreting the metric: a favorable percentile does not rule out severe tail loss elsewhere in the distribution. No derivation, broader regulatory context, or additional examples are provided.

Key ideas

  • A negative VaR-equivalent volatility can arise when the measured loss percentile represents a gain.
  • The answer illustrates this with a product that has a rare total-capital-loss outcome and a coupon funded by the proceeds.
  • A favorable percentile-based VEV can coexist with a severe loss in another part of the distribution.
  • The document provides a short explanation and example but no derivation or broader assessment of the measure.

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Risk managementStatisticsOptions
Full text
# Negative VaR equivalent Volatility (VEV) and its meaning?


# Negative VaR equivalent Volatility (VEV) and its meaning?












Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?

## Answer by James Spencer-Lavan (score 1)

https://quant.stackexchange.com/a/40377

You can attain negative VEV if the "loss" measured at the 2.5% percentile is actually a gain.

I build you a product where you lose all capital with 1% measured probability and pay you a coupon with the proceeds.

Under VEV, it will attain a MRM of 1 (I.e. cash-like)

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.