After recording their worst day since October, stocks rebounded nicely today with the S&P 500 (SNPINDEX:^GSPC) and the narrower, price-weighted Dow Jones Industrial Average (DJINDICES:^DJI) gaining 1% and 0.7%, respectively. The VIX Index (VOLATILITYINDICES:^VIX), Wall Street's fear gauge, dropped 6.5%, to close below 14 (the VIX is calculated from S&P 500 option prices and reflects investor expectations for stock market volatility over the coming 30 days.)

Headline vs. reality
Under the headline "HP board is studying whether to break up the company," business website Quartz is, in my opinion, overselling what sound like relatively routine board-level discussions at Dow component Hewlett-Packard (NYSE:HPQ)That hasn’t stopped some investors from jumping on the "news" and pushing the shares up 2.6% at 6:52 p.m. ET in the after-hours session, on top of a 2.7% gain during the regular session.

According to the report, "The Hewlett-Packard board is studying a breakup of the U.S. tech company among several options the directors are considering to obtain maximum value for shareholders... The HP directors have discussed the details of a possible breakup scenario, but also the merits of the company staying whole..."

But read beyond the first two paragraphs and you soon learn that the same anonymous sources say the board has formed no special committee to evaluate a potential breakup, nor does it have any plans to do so. That suggests that any discussions of a breakup have remained at a high level -- no details, please. Given the enormous challenges and uncertainty HP faces, it would be surprising if the board weren't keeping all its options on the table.

There is no clear impetus for a breakup of HP at this stage -- in fact, Dell's (UNKNOWN:DELL.DL) announcement today that it is going private suggests some savvy investors see value in a combination of hardware and services activities. Furthermore, HP CEO Meg Whitman would be hard-pressed to sell a breakup after reversing course on the plan to sell the PC division in October 2011 shortly after taking the helm.

HP shareholders are martyrs -- the company has not missed an opportunity to wrong-foot them in the past several years --- so it's natural for them to allow hope to triumph over reason. Unfortunately, it will take more than a juicy headline to save them.

Fool contributor Alex Dumortier, CFA has no position in any stocks mentioned; you can follow him on Twitter @longrunreturns. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.