Humility is often touted as one of the great qualities any leader should have. Harvard Business School’s Dean, Nitin Nohria, perhaps the person most able to influence leadership thinking in today’s world, certainly thinks so. As he recently told, “moral humility,” or the acknowledgement that your moral compass could fail you, “may be the most important thing we can teach” business leaders.

But according to a new study that’s already getting some attention, that doesn’t mean narcissism doesn’t have a place. The study’s authors—professors at IMD (a top business school in Switzerland), as well as Erlangen-Nuremberg and Pennsylvania State Universities—found that CEOs who “crave acclaim and applause” are more likely to get ahead when it comes to innovation. ”We have uncovered the bright side of narcissism,” IMD professor Albrecht Enders boasts in a release about the paper. “Narcissists might be annoying and even downright selfish, but they may be the best bet when bold and unconventional actions are needed to save an organization.”

The professors, who won the Academy of Management’s 2011 Glueck Best Paper Award for the research, studied how 78 CEOs at 33 U.S. pharma companies responded to biotech’s emergence between 1980 and 2008. How quickly and strategically they created biotech initiatives—whether that meant forming alliances with other companies, making acquisitions, or launching new R&D experiments—were measured for each CEO’s time at the top. In other words, the professors looked at how fast and how intense each CEO was in responding to innovation in their industries.

They found that the CEOs who were deemed “narcissistic” were correlated with those companies at the forefront of biotech innovation. And how did they know if the CEOs thought highly of themselves? Apparently this is an objective factor that can be determined by the number of times their CEOs are mentioned in press releases, the prominence of the CEO’s photo in annual reports, and the difference in cash and non-cash compensation between the CEO and his or her second-in-command. Securities analysts familiar with the CEOs were also consulted .

Like almost every academic leadership study, this finding is rooted in common sense. People who think highly of themselves are more likely to act on that confidence, and ignore the warnings of people who believe they should be more cautious. If they have an outsized fascination with themselves, they are more likely to believe that their ideas are correct.

But measuring narcissism by how many times a CEO is mentioned in the press or the difference between the CEO’s and the No. 2’s pay, even if people who knew them have been consulted, seems like a stretch. As the “Researchers Say” blog over at the Village Voice jokes, “maybe the most narcissistic CEOs didn’t have their photos plastered everywhere because they thought they looked fat or because they insist their image only be portrayed in the form of an oil painting of them crossing the Alps.” Why have 15 stories written about you in a pharmaceutical trade magazine, after all, when you’re holding out for the cover of Time?

Even if a CEO does get a lot of coverage or pay, it may not say much about their narcissism. After all, an over-zealous P.R. director, a board of directors that idolizes its CEO, or the media and shareholder cultures that have fostered a fascination with the supposedly all-powerful chief executive might have something to do with the results. Just maybe.

I don’t doubt that self-confident CEOs, at the very least, are good at betting on their instincts and taking their companies in innovative new directions. And every once in a while, I’m sure hubristic CEOs with an inflated sense of self (a description that would apply, at least a little bit, to almost anyone who reaches this stratospheric stage of a business career) are right about new strategies and bold bets for their companies.

But I’d guess that there are just as many narcissistic CEOs who work at companies that have stronger governance with better compensation standards, or are covered by reporters with more discipline about lauding the CEO. There may be some benefit to narcissism. But given the difficulty of measuring something as subjective as the size of a chief executive’s ego—and how much that has to do with a company’s penchant toward innovation—it’s important to keep in mind that the downsides of narcissism still strongly outweigh any potential upside.

More from On Leadership:

Is it a bad sign if boards are ‘looking for a woman’?

How to be a great boss

Mr. Schmidt goes to Washington

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