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I think you're doing some self study and it looks like you're on a good path. You have this right. It's the square root of time. I would just note as far as your example goes that there are not 30 days in the month of a 252 (trading day approximation) day year. It's closer to 20. And vanguard2k points out in a comment that you need to consider implied vol ...


1

Yes, the answer is correct. Volatility scales with the square root of time, so always take square root. A simple trick to remember this, is to calculate the scaling factor as if volatility were linear (30/252) and then take the square root.



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