In-sample volatility measurement

External question — Quantitative Finance Stack Exchange Author: Gianluca Original post: https://quant.stackexchange.com/questions/45682 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) volatility measurement if one is not interested in forecasting future volatility? For context, as mentioned in a comment below, I need a measure of past monthly volatility to study the relationship between (monthly) mutual fund alphas and (monthly) market volatility over a past period of time.

External answer — Quantitative Finance Stack Exchange Author: Dhruv Mahajan Original post: https://quant.stackexchange.com/a/45711 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Why would you need to model volatility to test an hypothesis. Just use the historical realised volatility and if you want to test the hypothesis how funds relate in the near future, then use the VIX index, it's a forward looking measure. Or you use some volatility tracking fund as a proxy, why use some model to estimate relationships when obviously some modelling errors will creep in.