The number of shares traded in a single day can be greater than the number of a company's outstanding shares, but this is relatively rare. This high trading volume tends to occur during important company events and is more common with companies that have a relatively small float. It is also usually marked by a large price movement. This essentially means that there is so much buying and selling of shares that a lot of the shares are changing hands in a single day. This does not, however, mean that every shareholder is selling his or her shares while new holders are taking that shareholder's place.
Companies receive a large amount of market focus and stock activity during important events such as public offerings or takeover bids, which bring it to the focus of traders—regular traders and day traders—and increases trading volume. The day traders are trying to make a quick buck on the stock's movement by entering and exiting positions with the intention of only holding the shares for a few hours or even minutes. Longer-term traders, on the other hand, are buying or selling off of the news, which also contributes to the increased stock activity. The day traders or short-term investors provide the liquidity required to trade more shares than the actual shares outstanding. In other words, while a lot of investors who held the shares before an event will not trade on this particular day, it is the day traders and short-termers that trade the shares many times during a trading session.
How Trading Volume and Shares Outstanding Interact
For example, assume that the number of shares outstanding in a company is 10 million. Before the market opens, the company announces that its new drug has been approved to be sold on the market—a huge breakthrough. Imagine that half of the shareholders do not sell their positions based on the news and continue to hold them. But 5 million shares are sold on this news throughout the trading session by investors who may feel that the new drug won't bring in much extra business or simply to lock in any gains. And there will be buyers, with different views and aims, for those shares. All this activity boosts trading volume. If, say, each of the 5 million shares are each traded 10 times in a day, this would be recorded as a trading volume of 50 million shares, which is five times more than the number of outstanding shares.
This can happen when a lot of new investors—both long and short term—enter the stock. So, while not all shares are being actively traded, a fair portion are, and it is these that are being bought and sold multiple times, resulting in more shares traded, or changing hands, than there are shares outstanding. (See also: The Basics of Outstanding Shares and the Float.)