Interpreting Negative Residual Volatility After Index Adjustment

Summary

The document asks how to interpret negative values produced when comparing a single stock’s volatility with index volatility. The motivating research question is whether events such as dividends, earnings announcements, or mergers are associated with higher stock volatility than ordinary trading days, while controlling for broader market movements.

The described procedure fits an ordinary least squares model of stock volatility against index volatility, then subtracts the fitted values from observed stock volatility. The author refers to this residual as excess volatility and wonders whether negative values indicate an error. The document supplies a code example and notes that OLS results were added, but it gives no actual estimates or answer. Its framing leaves important modeling details unresolved, including the specification and interpretation of the regression and how event-day residuals would be tested for statistical significance. The post is therefore a question about a measurement approach, not evidence that events increase volatility or a validated method for isolating their effects.

Key ideas

• The research question concerns event-related changes in single-stock volatility relative to ordinary days.
• The proposed adjustment regresses stock volatility on index volatility and subtracts fitted values.
• Negative residuals indicate observations below the model’s fitted value, not negative raw volatility.
• The document provides no conclusion about whether the adjustment is appropriate or whether event effects are significant.

Tags

# How to interpret the negative volatility of the single stock, after neutralizing against the index?


# How to interpret the negative volatility of the single stock, after neutralizing against the index?












I am trying to find the statistical significance of the certain events on volatility, such as divided/earningsdate/M&A, etc on single stock wise compared to no events. Commonsensewise, these events would bump the volatiliy of the stocks. So actually the volatiliy of these stocks in those particular dates actually has the statistically significant difference from normal trading days.

However, when I try to neutralize those volatility against the index volatility, so that I can rule out some noises that are not related to single stock wise, I am getting the negative volatility results as the residuals. I am using Python for neutralization, and the code is similar to this:

```
Y = df['singlestockvol'].values 
X  = df['indexvol'].values
model = sm.OLS(Y,X)
results = model.fit()
print(results.summary())
df['predictedvol'] = results.fittedvalues
df['adjvol'] = df['singlestockvol'] - df['predictedvol']
```

Here are some samples that I have got:

So according to CAPM model, the adjvol would be the excess volatility that I want to extract. However, considering there are many data that has negative volatility, is there something wrong from this approach?

Edit: adding the OLS results for better reference.

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