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Recently I've gotten hold of a list or rather a chart of 30-day Implied volatility and historical volatility for the same stock over the course of a year. With these data, I've thought there might be a way to compare these two in order to measure the accuracy of implied volatility and thus the market's accuracy when it comes to individual stocks.

But I've understood that this can be harder than I thought since 30-day Implied volatility refers to calendar days whereas historical volatility is based on business days only, which mixes up the order of every day that otherwise would be equivalent I.e. this day + 30 (for IV 30), would be for HV that day minus everything from around 23 to 19 depending on the presence of non-trading days.

How would you go about if you were tasked to measure the precision of Implied Volatility for a stock? Do you think you could do so efficiently, and if not, how would you make that measurement efficient?

Thank you sooo much to you who took your time to ease my mind! :-)

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    iV is not a predictor of HV. Otherwise there wouldn't be a smile in IV. It's a market price for options.
    – AKdemy
    Nov 3 at 18:11
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    There is no guarantee that the future follows the same pattern as the past, so no, it isn't predictive. Suggestive, maybe.
    – keshlam
    Nov 3 at 18:49
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    For each strike and maturity there is a different implied volatility. If ATM 1M vol on Apple is ~ 26%, that for 80% moneyness could be +71% (as it was back in this example back in may 2021). Looking at 71% in an isolated manner will tell you close to nothing about the standard deviation (SD) of daily returns (in the future). IV is computed from option prices and the only free parameter in Black Scholes. IV is almost always above RV and there exists a smile to compensate for tail risk and a vol risk premium is paid.
    – AKdemy
    Nov 3 at 19:12
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    I do not believe you can gain much from pure numerical analysis. The folks over in the Quant stack might disagree with me, but I would recommend actually looking at the companies instead. Or bypassing the whole question and adopting whole-market strategies, diversifying widely rather than trying to outguess everyone else.
    – keshlam
    Nov 4 at 3:29
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    From where I sit, numerical analysis of stocks is numerology. If it worked we'd have much stronger evidence that it worked, and it would already be priced into the system, rather than being an alchemical theory that ought to turn lead into gold if we can just find the right formula. Your mileage may vary.
    – keshlam
    Nov 4 at 14:11

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