[Siegmund]

No, not an upper bound; a best guess at it. (See defition of Maximum Likelihood Estimate for what exactly is meant by "best guess" here.) But the more information you have, the more precisely you can estimate something. If you keep track of your fluctuations hour by hour you know more about your SD than if you only keep track of the end-of-session total. (At one extreme, if you only knew your starting and ending bankroll, you'd know nothing at all about your SD; at the other, if you kept track of the result of every hand you'd know it very well.)

You don't see people talk about the precision of their variance estimates much - the formulas to calculate the uncertainty in your estimated variance are not pretty, and the uncertainty is often high - but there are better and worse ways of doing it.