I think I can guess your reaction if I told you that, on average, just 2 percent of chief executive officers of Fortune 500 companies are fired annually.

That's not enough! Off with their heads!

And it would be a natural sentiment even if we weren't muddling through our 19th month of economic recovery. We're impatient with anemic job growth and persistent long-term unemployment.

Luke Taylor, an assistant professor of finance at the University of Pennsylvania's Wharton School, had heard the knee-jerk reaction that more CEOs should be fired and decided to study how boards chose whether their No. 1 employee should stay or go. (You can read a synopsis of his research in a posting on Knowledge@Wharton here.)

Taylor's paper, published in the December edition of the Journal of Finance, gives four reasons boards rarely fire CEOs. First, it takes a CEO at least a year to learn his or her job, and boards are slow learners when it comes to figuring out whether a CEO is any good.

Second, there are real costs to firing a CEO. Severance alone can run into the millions of dollars. Plus, there are costs to retain an executive-search firm, hire a new CEO, and even replace other senior managers.

Third, there's a certain inertia at the board level. Good CEOs could simply be unlucky, leading their companies during a recession. A bad CEO could benefit from a robust recovery. With so much out of the CEO's hands, why bother to change?

But the last reason, to me, is the most telling. Taylor said in an interview that firing a CEO can be "personally costly" to board members - often the CEO's friends - and that has nothing to do with maximizing shareholder value.

Though the stress and anxiety caused by firing a peer count as intangible costs, they weigh on board members greatly. Taylor calculated the value for this "entrenchment" cost at $1 billion.

He said the direct costs of firing the CEO of a large firm average $300 million. But their reluctance to fire CEOs shows boards tend to believe that doing so would cost their companies $1.3 billion.

"Boards act like it is really, really painful to fire a CEO," he said. "But it's not that painful."

Still, done badly, a CEO firing may resemble the train wreck that has been Hewlett-Packard Co., where the board removed Mark Hurd for violating business-conduct standards. That led to shareholder lawsuits and ignited criticism by CEOs at other firms. Last week, four of the 13 directors at H-P stepped down, ostensibly to give the computer-maker a fresh start.

Using the model he'd built, Taylor asked what the firing rate would be if there were no entrenchment costs. He calculated that 13 percent of CEOs of Fortune 500 companies, or 65 executives, would be fired annually.

We're a long way from that level. Challenger, Gray & Christmas Inc., the Chicago outplacement firm, said the number of CEO "departures" was up slightly in 2010 at 1,234 from the 1,227 counted in 2009. Not one of them is classified as a firing because the firm tends to pick up the language used in the company news releases, where you'll never see the word fired.

However, Challenger Gray also relies on media reports about CEO changes. That's how it classified 26 departures as "removed" in 2010, nine as "scandal," and four as "pressure from board."

In Taylor's research, shareholder activists may see a billion reasons why the number in that category should be higher next year.