In theory, dividends shouldn't be big market movers. But in reality, when a company announces an unexpected dividend, investors often defy economic theory by bidding its shares through the roof. That could be the next step for the market's most valuable stock.

Apple (Nasdaq: AAPL) has had an impressive cash hoard for some time, and it just keeps getting larger. In its most recent quarter, the company boasted more than $97.6 billion in cash and securities. For years, Apple has resisted pressure to start paying a dividend. But as a MarketWatch report speculated, one answer could be for the company to pay a one-time special dividend -- thereby accomplishing the dual goal of returning capital to shareholders while avoiding any expectations of ongoing regular dividend payments in the future.

Why are special dividends special?
When you think about what a dividend actually does, you wouldn't think a special dividend would have any impact on a stock's price. After all, when a company pays a special dividend, it reduces its cash on hand by exactly the amount it pays out to shareholders. The net impact should be a wash.

In practice, that's often basically what happens. When VirnetX (AMEX: VHC) announced a $0.50 special dividend in June 2010, the stock price jumped $0.41 in the next day's trading. Yet in the ensuing trading sessions, the stock gave back those gains, so that by the time the stock actually paid the dividend, the shares were trading a lot closer to where they had been before the announcement.

But special dividends don't always work out that way. Microsoft (Nasdaq: MSFT) announced a $3 special dividend in July 2004, when shares traded at $28 per share. By the time the company actually paid the dividend in November, the shares had risen to around $30 -- and after the dividend, the shares traded above $27, netting more than $2 in profit for those who bought on news of the payout.

More recently, money manager Diamond Hill (Nasdaq: DHIL) saw even more dramatic moves. After the company announced a $5 special dividend in December, the shares jumped almost $5 on the day; over the ensuing week before the payout, the stock added another $2. Yet on the actual payout day, the stock plunged $7 -- more than the amount of the payout -- but ended up trading very close to the pre-announcement value. That gave long-term shareholders $5 per share in "free" money.

Not all dividends are alike
Of course, it makes a difference why a company is paying a special dividend. In the case of VirnetX, the company had received a piece of a $200 million settlement from Microsoft related to alleged patent infringement. So the real value behind the dividend came from the settlement, and so the time when the shares should have risen was immediately after the settlement announcement.

But in other cases, such as with Microsoft and Diamond Hill, the move was more of a nonevent. It isn't as if those companies created any value with the moves -- rather, they only unlocked value that was already there.

Indeed, in some cases, special dividends are made for entirely different purposes. When Weyerhaeuser (NYSE: WY) paid out a massive $26-per-share dividend in 2010, the reason had to do with its converting to a new status as a real estate investment trust. The dividend was necessary in order for Weyerhaeuser to claim the preferential tax treatment that REITs enjoy. Any intention of returning capital to shareholders was a secondary benefit at best.

What an Apple dividend would mean
If Apple were to pay a special dividend, the impact on the shares would tell a lot about investors' opinion of Apple's cash management. One reason a stock might go up is if investors figured that a company would otherwise waste the money that's going toward the special dividend. On the other hand, if a special dividend forecloses opportunities to spend the money more productively -- say, on a valuable acquisition -- then you can expect shares to fall.

For now, the idea of an Apple dividend is speculative at best. But as long as the company hangs on to its $100 billion, you can expect speculation to swirl.

Meanwhile, if you'd rather own stocks that already pay dividends, let us point the way toward some great ones. Let me invite you to learn about 11 dividend stocks for income-hungry investors. The report is absolutely free -- but don't wait: Click here and read it today.