This study compares historical returns of an underlying to a one standard deviation expected move generated from historic volatility. I am a math novice, which means that all the math I used comes from my best attempts to figure it out and so I am asking for some help to see if I actually did it right. On my first attempts I had thought that I had done it right because in generating a 50 day expected move and comparing it to data from 2002 to present I was getting 68.34% of data staying within one sigma. Pretty good. I was using 50 days because I am usually selling options with about 50 days to expiration. However, when I changed the days the results were changing with it, and very linearly, which is not what I was expecting. I think I have reached my limit with my math professor Mr Google and would love to know what I'm missing here.
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