You probably hugely underestimate how much the average CEO makes a year. (Soe Zeya Tun/Reuters)

Quick: How much does the the typical CEO of one of the largest U.S. companies make each year?

A new study from researchers at Stanford Graduate School of Business finds that the typical American gets the answer wrong -- very wrong. A survey of 1,200 individuals released Thursday shows that the median respondent said they make just $1 million a year.

The right answer? More than 10 times more than the typical guess: $10.3 million.

That underestimation of what the CEOs of America's 500-largest companies make is not reserved for the less well-off, either. While lower income respondents (those making less than $20,000 a year) vastly underestimated how CEOs get paid -- their median response was $500,000 -- even those who make more than $150,000 a year were wrong by half, guessing the corporate brass take home $5 million a year.

"I think it’s really hard for some people to even think about making $10 million a year," said David Larcker, one of the co-authors who studies corporate governance and executive pay at Stanford. "It's hard for them to appreciate. Your reference point is what you or your family or people you know are making."

An average of the guessed amounts in Stanford's survey was more on target, at over $9 million. But Larcker said that number isn't as representative of what the typical American thinks, because it can be skewed when single individuals enter extremely high or low estimates in the survey. "If you add those in, it does pull the mean away from the central number," he said. Executive pay figures are also typically reported as median figures.

This isn't the first time researchers have taken a look at how out-of-touch most Americans are with the high levels of compensation at the top. For instance, Harvard Business School professor Michael Norton has examined the issue, finding that Americans think CEOs are making only roughly 30 times the average worker, when in fact they're off by a factor of 10. Some calculations have put the average CEO to worker pay ratio at 373-to-1, while others say it's more like 300- or 204-to-1.

Norton and others have also looked at Americans' views of income inequality more broadly, finding that Americans vastly underestimate how wealth is distributed in this country and how much of it is held by the most affluent.

The average American will soon get a better idea of what the ratio of CEO-to-worker pay really is when new SEC rules go into effect and companies have to start calculating those figures in 2017. Companies will have to report this simple piece of arithmetic each year, creating a figure that either grabs headlines and shames outliers -- or gets buried in the corporate proxy and does little to change the overall trend of executive pay.

One thing that is clear from Stanford's new survey is that a majority of Americans think there should be a cap on that ratio, regardless of a company's size, how well it performs -- or the political party of the respondent. Nearly two-thirds (62 percent) said there should be a cap, a belief that was held by 66 percent of Democrats and 52 percent of Republicans.

Respondents were also asked how much they think CEOs should get to share the wealth when companies perform well. For instance, they were asked, if a CEO oversees an increase in a company's value by $100 million, how much of that should they receive as compensation? The median respondent said just 0.5 percent, or $500,000.

Their answer provides a reminder to compensation committees everywhere. "The regular person out there thinks that if the value went up, the guy ought to be rewarded," Larcker said. "That's good, but it was relatively muted. That could be a function of fairness — they may be asking how much was due to them and how much was due to everyone else, how much was fortuitous, how much was luck." All good questions, of course, that every board of directors should be asking, too. 

Read also:

Finding out how much the boss earns

This new rule could reveal the huge gap between CEO pay and worker pay

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