Using Downside Deviation in Value at Risk Estimates

Summary

The document asks whether downside deviation, also called semi-deviation, can replace standard deviation in a value-at-risk estimate that accounts for expected return. Its motivating case is a portfolio short an asset whose price is falling: the short position may gain even as the asset’s volatility rises, potentially increasing a volatility-based risk estimate despite favorable portfolio performance.

The author suggests downside deviation might avoid this perceived overstatement by focusing on adverse returns. However, the text presents a question and rationale rather than a resolved method. It provides no formula, distributional assumptions, confidence level, backtest, or comparison with conventional VaR. Whether downside deviation is appropriate depends on the chosen loss measure and portfolio-return distribution; the document does not establish that the proposed substitution produces a calibrated VaR.

Key ideas

• The document considers substituting downside deviation for standard deviation in VaR.
• Its motivating example is a profitable short position during a decline accompanied by rising volatility.
• The author expects a downside-focused measure might reduce risk estimates driven by volatility in that scenario.
• No mathematical derivation or empirical validation is provided to establish the substitution’s validity.

Tags

# Can value at risk be computed using downside deviation?


# Can value at risk be computed using downside deviation?












Value at risk is usually computed with a regular standard deviation. But can it be computed using downside deviation (semi-deviation) instead? Particularly if I want to consider a Var that includes the drift of the future returns of the portfolio?

The reason I wonder is because volatility (standard deviation) tends to rise when prices are falling. If a portfolio contains a short position on an asset whose price is falling, the portfolio will gain. But the increase in volatility will push up the VaR estimate, making it seem like the risk has gone up. Over longer time horizons, a negative drift in that case could counterbalance the volatility, but if the volatility is high, it'll dominate the drift and keep the VaR elevated.

Computed with a downside deviation, the VaR wouldn't necessarily go up in such a scenario, and the risk wouldn't be "over-estimated".

Thanks for any insights as to whether this is possible and if this makes sense mathematically or otherwise.

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.