Relax, Citigroup (NYSE: C) shareholders. You didn't strike it rich.

Seeing the meandering banking giant's stock trade in the $40s yesterday -- after years of languishing in the single digits -- may have delighted passive investors. Reality is far more sobering.

It's true that Citi's stock opened at $44.89 yesterday after closing out last week at a mere $4.52. It's quite the pop! Technically speaking, though, the stock opened lower. Citi executed the 1-for-10 reverse split that it had announced two months ago. In other words, $44.89 is less than $45.20.

There's no free lunch here. The 1,000 shares your Aunt Milly had at $4.52 last week were turned into 100 shares at $45.20. Mr. Market took it from there.

In defense of reverse splits
I know most people hate reverse splits. Fellow Fool Cindy Johnson even argues that Citi's resorting to a reverse is a signal to dump the financial giant.

I disagree. Are there boatloads of companies that declared reverse splits, only to continue their painful descents? You bet. Orchestrating a reverse to prop up a share price -- while a zero-sum game -- is usually the byproduct of a public company that has fallen out of favor with investors. A turnaround isn't a birthright. Show me a study that shows that most reversers fail to beat the market after the stunt. I won't dispute it.

However, quality companies that declare reverse splits do in fact bounce back.

Shares of Coeur d'Alene Mines (NYSE: CDE) have nearly doubled since the silver miner executed a 1-for-10 reverse split at $1.40 two years ago. Laboratory Corp. of America (NYSE: LH) turned to a 1-for-10 split in 2000. Things have gone so well that it went on to declare a pair of forward splits after that. (Nasdaq: PCLN) figured the best way out of the penny stock muck in 2003 would be a 1-for-6 reverse split. If you haven't checked priceline these days, the stock is trading comfortably in the triple digits.

If you want a more recent case with a financial services bent, consider E*TRADE (Nasdaq: ETFC). The discount broker is trading slightly above its 1-for-10 reverse this past June.

A cynic will argue that Coeur d'Alene spiked when silver stormed back into favor or that priceline marched back into Wall Street fancy as online travel portals bounced back. Of course! That only proves my point. This is a zero-sum game. Fundamentals will ultimately separate the success stories from the inevitable failures.

In offense of reverse splits
Dare I push my luck? Dare I argue that Citi will be better off after this split?

There is a scenario where exactly that may happen, nullifying my "zero-sum" argument.

Has Citi lost business because of its previously low share price? Has someone -- or perhaps even some company -- gone with another banker after seeing Citi's single-digit share price relative to its "too big to fail" peers? It has probably happened. Consumer-facing companies resort to reverse splits in an effort not just to shake off speculators and woo institutional investors, but also to appear successful.

In time, few will remember the Citi reverse. I doubt that anyone buying priceline today at $528 is even thinking about the 2003 split.

Citi did the right thing with yesterday's reverse split. Now comes the hard part: earning it.

Are reverse splits good or bad? Share your thoughts in the comment box below.