Is this assumption true?
For the price of a highly liquid underlying instrument to have increased, there must have been more bought than sold in the period of time measured, not considering Corporate actions that affect number of tradable stocks etc.
Is the same true for the opposite, price decrease = more sold than bought.
If not, is it likely to be true, or completely unconnected?
No. There are two sides on every transaction: A buyer and a seller. Hence, the number of assets bought must equal the number of assets sold (naked shorts and derivatives aside).
ok understood, so can we reweight the metric used to accommodate this? Prices go up because more shares were bought than were sold at the current/previous market price? Is this fair to say?
I know what you're getting at and that seems correct ... except previous makes more sense than current, since every buy/sell is always at the market price.
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