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The calculation of historical volatility only takes into account the closing stock prices. Is it a better measure of really how volatile the stock is as compared to a measure like average true range? Is it fair to hypothesize that ATR is a better measure because it calculates the fluctuation between high and low.

If we only consider closing prices as in HV, then basically a stock can jump aorund wildly during the day but so long as the closing prices are not that much different, it will be considered a low volatility stock. Is this the right way to look at volatility, just considering closing prices?

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ATR really looks at the volatility within the day -- So you would be able to see if the stock is becoming more or less volatile in daily trading. This is often useful for charting and finding entry and exit locations.

Traditional historic volatility (as you cited) will give you a look at the long term volatility of the security. The example of this is that there could be trends up or down but the same daily volatility (same ATR)

There are methods that try to incorporate both intraday information along with historic volatility. As for which is a better measure of volatility-- it depends on what you are using the measure for.

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