<<Suppose you had just one
VWAP value say at 12:30 and you wanted to know its variance. You would compute the difference between that value and all the old prices. Take the square of each difference and sum them up to get the unnormalized variance.>>
right but when historically charting variance/std dev, don't you want the bands to show what the variance was relative to the distribution at the time of the 'price' reading. for example, lets say you wanted to plot the band that occured at 12:28 (1 bar before 12:30 on a 2-min chart)... you would then want the variance calculated through 1 bar ago, not the 'current' (12:30)
VWAP... that is -- you want the distribution up through 12:28 (VWAP_H[1]), not the variance +1 period (the 12:30 VWAP_H) -- right?