How do we calculate a stocks normal distribution 20 days from now if we only know the intraday volatility? The share is trading at 50. The average intraday volatility (intraday high-low) is 3 % with a 1 % standard deviation (yes, itâs a hypothetical question).

You can't calculate the stock's "normal distribution", you can only calculate a moment of a normal distribution or it's functions. In other words - what are u tryign to calculate...volatility, variance, CDF, PDF? If you need the volatility for 20 days, then: (0.03/(sqrt(1/252)))*sqrt(20/365) Which is about 11% according to google.

You sure about that genius? Even assuming the 3% is an annualized volatility (which it isn't; the poster said it's intraday vol), your equation is pretty wrong. Assuming your date count convention (which is pretty inconvenient, but let's leave that side), 3% = DailyVol * Sqrt(252) DailyVol = 3%/Sqrt(252) 20D Vol = Sqrt(20)*DailyVol Using your formulation (the second part where you try to rescale into 20-day), you get 3%/sqrt(1/252) = DailyVol 3% = DailyVol*Sqrt(1/252) Annual Variance = Daily Variance / 252 Doesn't make a lot of sense does it?

so an idiot like you doesn't have any other job than stalking internet people? Anyway i am busy right now. So 252|| 365 is the right way to calculate it and NOT 252 || 252. http://en.wikipedia.org/wiki/Volatility_(finance) cheers

true, but it seems that he is trying to predict that volatility in a 'technical analysis' fashion based on historical volatility. I am not saying this is the right approach - but it's the best one based on his/her question.

What stalking? I'm correcting your formula mistake. You might actually want to read the link you put there: it confirms your mistake. Note, the numerical example has monthly vol = annual vol MULTIPLIED by sqrt(1/12). The analogous daily vol is then daily vol = annual vol * sqrt(1/252), not annual vol / sqrt(1/252) as you put it. Don't hide behind the date count convention when you completely mis-scaled volatility.

I assume you mean that the average intraday high to low averages 3% of the share price. What do you mean by "1% standard deviation?"