The key to understanding this is that everybody’s got their own price. One stockholder might be willing to sell at $5, another one at $4, and a third at $3. Same for buying: various people hoping to buy the stock might offer $1, $2, and $3 for it. In this scenario, the $3 bid would “clear”, since buyers and sellers can agree on a price. The new lowest price to buy is $4 — that’s the “ask price” of the stock.
Now suppose somebody with high hopes and deep pockets comes along and offers $4. The $4 seller’s offer clears, and now the new lowest price is $5. The price of the stock has gone up.
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