Estimating Portfolio Idiosyncratic Variance from Daily Factor Residuals

Summary

The document asks how to examine historical idiosyncratic volatility for individual stocks at daily frequency, without converting residuals to monthly observations or forecasting. The suggested approach is to estimate factor-model residual variance for each stock and day, then combine those variances for a portfolio using the holdings-weighted expression h′Dh, where D contains the stocks’ residual variances. This gives portfolio idiosyncratic variance while retaining daily inputs.

The exchange provides a concise formula rather than a worked example or empirical comparison. It does not specify how to estimate each day’s residual variance, how much historical data to use, or whether the resulting measure should be annualized. The questioner mentions beginning with a market model and possibly trying a three- or five-factor model, but the answer does not compare factor specifications. The method is framed for a portfolio; it does not fully resolve how to define a single stock’s daily idiosyncratic volatility or establish that the measure is reliable for any particular use.

Key ideas

• Estimate stock residual variances from a factor model at daily frequency.
• Combine residual variances across portfolio holdings using a holdings-weighted quadratic form.
• The proposed formula yields portfolio idiosyncratic variance, not a detailed single-stock estimation procedure.
• The answer does not specify a residual window, annualization convention, or factor-model choice.

Tags

# Daily idiosyncratic volatility?


# Daily idiosyncratic volatility?












I have a long daily times series of individual stocks and would like to obtain daily idiosyncratic volatility (keeping the same frequency). Apparently, the widely used methodology of Ang 2006 would not work in my case as I will have convert the residuals from daily to monthly. I am not interested in forecasting. I just need to examine the historical IVOL for specific days.

I am planning on using a market factor model, CAMP, just to see if there is any potential results and upon the results I might do a three or five factor model. Any suggestions on how to calculate daily idiosyncratic volatility from daily observations and not from intraday data.

Thank you

## Answer by numerairX (score 1, accepted)

https://quant.stackexchange.com/a/42006

Since you mentioned stocks I assume you are looking to calculate in a portfolio sense, one practice is calculating idiosyncratic variance by ${h}'Dh$, where $h$ is your holdings of each stock and $D$ is $\sigma_{i} ^{2}$ of residues you estimated using factor models (at each day and for each stock $i$).

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