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If a stock shows great performance on the income statement, will the prices rise gradually or immediately after the release of information to the public?

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The time for the price to rise to the level reflecting the new information is the time over which the information becomes known to the dominant traders in the market (i.e., nearly instantaneous). Even if the stock doesn't trade much, the bid and ask will move immediately. It doesn't require the asks to be "hit" by buyers; rather, traders (including market makers) will simply raise the price of (or cancel) their sell orders as soon as they realize the price is going higher. Any who are too slow in doing so will be picked off.

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    Correct, but only if the information is actually new. If the performance is great, but was expected to be that way, then the stock wouldn't move at all. – mastov Jul 3 '18 at 16:55
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    @mastov Indeed. I assumed OP meant "unexpectedly great" leading to a price rise and was asking about the mechanics of that rise. – nanoman Jul 3 '18 at 17:03
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If there is more net buying than selling (volume not people) then share price rises and conversely, if there is more net selling than buying then share price falls.

The size of the excess buying (or selling) pressure determines how fast the stock rises.

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