It’s pretty clear by now that many CEOs of public companies make more money than their performance warrants, and that boards of directors often ignore shareholders who complain about it. But how much does paying the chief executive officer more than he (or, rarely, she) is worth really cost stockholders?

Plenty, says a new study that examined CEO pay, stock price performance, and return on assets in a database of the 1,500 largest U.S. public companies for each year from 1994 to 2013. The 10 highest-paid CEOs in any given year presided over an average $1.4 billion loss in market capitalization, compared to their more modestly compensated peers.

There’s more: Even if a given CEO made the top 10 for only one year, the stock lost value for three years afterward, compared to the shares of other companies in the same industry. And, if a company with a CEO in the top 10 made an acquisition or underwent a merger, “the market reacted more negatively,” pushing the share price down farther than for comparable deals made by lower paid CEOs, says Mike Cooper, a finance professor at the David Eccles School of Business at the University of Utah and a co-author of the study.

“We’re not saying that high CEO pay is necessarily bad,” he adds. “But we did find a clear link between high CEO pay and decreased financial performance.”

The main reason, Cooper says, is that extravagant pay gives rise to what the study calls “overconfidence,” or the belief that “you have better information and know more than everybody else,” which leads to a penchant for risk—making too many acquisitions, over-investing in dicey projects that usually fail, and generally spending too much of the company’s money.

“This is why the highest paid CEOs in any industry tend to do things that destroy shareholder wealth,” Cooper notes. A telltale sign of overconfidence, according to the study: chief executives with costly delusions of grandeur often hold “a larger number of in-the-money stock options that they haven’t exercised than other CEOs,” he says.

They’ve often been in the top job longer than their lower-paid peers, too. Cooper and his colleagues found the highest pay and the most overconfident behavior among chief executives who had been in office for an average of six years. “That’s not surprising,” Cooper notes. “The longer tenure means a CEO has had more of a chance to make friends with the board, or to put friends on it.”

Chief executives in the study who had held the post the longest and made the most money also showed more lackluster financial results than their peers at other companies, at least by one measure: return on assets over the course of their tenure underperformed their industries’ ROA by 12%.

Although Cooper is careful to say that the study isn’t prescriptive, the research does suggest that setting term limits for CEOs would help to curb both out-of-control pay and expensive, overconfident moves. Shareholders might suffer less long-term damage to their investment if no one who’s paid more than 90% of his or her industry peers could hold the top job for longer than, say, three years. Right now, that doesn’t seem to be happening: The average time in office of Fortune 500 CEOs in 2013 climbed to 9.7 years, nonprofit research firm The Conference Board reported in April. That was the longest average tenure reported since 2002.