You know what it takes to succeed in business--you've got to command respect. Ooze leadership. Bleed charisma. Take control from the minute you walk in the room.

At least, that's the stereotypical successful CEO in a nutshell.

We're conditioned from early education to believe that the traits typically associated with extroversion are desirable if we want to be leaders in business: openness, outgoing nature, and oodles and oodles of confidence.

We're taught to speak authoritatively; to be fantastic orators. We're told to project confidence. Own the room.

After all, it takes a great, big personality to dominate a negotiation, inspire an investor, or motivate an entire company of workers.

What if that didn't really matter after all?

Scary thought, right? How would we know what to look for in a company leader?

Well, a recent study by researchers at Harvard, Stanford and the University of Chicago and published by the National Bureau of Economic Research suggests we might have been looking at our leaders all wrong. In their study of 4,591 CEOs, they found that companies run by introverted CEOs outperformed their peers. In fact, publicly traded companies run by extroverts averaged a 2% lower return on assets.

It's crazy, right?

I mean, extroversion is great. We love extroverts--they're entertaining, inspiring and fun to be around.

Even so, it seems that introverts might still have the edge when it comes to business prowess. How can this be?

First of all, the study authors warn, we should be careful not to confuse correlation with causation. More research needs to be done to count out factors that could skew the results, such as the tendency to choose CEOs based on personality traits in the first place. Companies that seek out big personalities to lead during times of turmoil might very well have failed or underperformed anyway.

Yet all the way back in 2004, Rakesh Khurana took a deep dive into the CEO selection process in Searching for a Corporate Savior: The Irrational Quest for Charismatic CEOs (Princeton University Press) and shone a light on the disturbing trend towards hiring based on personality. It was the first time we saw real evidence of this proclivity for choosing CEOs based not on their experience or demonstrated successes, but on their charisma. He concluded that the labor market for CEOs is a lot less rational than many think.

Considering the massive amount of money CEOs are paid, it's definitely worth making sure you have the best candidate lined up--not just the most impressive or likeable in person. Sure, you want a powerful orator and motivator at the helm, but at the end of the day, performance is what really matters.

And that's where introverts can really shine. They're fantastic listeners, great storytellers and often approach problems in creative ways. Introverted bosses give their employees more leeway in developing their own ideas, says researcher Adam Grant, and they tend to be great collaborators.

Because they don't have that great, big extroverted and out-there personality to woo a hiring panel, introverted CEO candidates rely on their experience and past performance to win the position. It sounds like that's what we should be looking for anyway!