Large company CEOs make more money than most people can comprehend, but their jobs are also more demanding than most people can comprehend. If a CEO makes a bunch of money for his employer (that is, the company's shareholders,) he should be well compensated.

A recent study finds the exact opposite relationship. That is, the CEOs who receive the highest pay tend to have produced the lowest long-term stock returns for their shareholders.

Consultant MSCI looked at the cash and stock compensation of 429 large-cap companies (and their 800 CEOs) from 2006 to 2015 and compared chief executive pay to stock performance. The total stock return of companies whose CEO pay was below their respective industry median was 39 percent higher than the returns of companies whose CEO pay was in the top half of their industry.

The highest 10-year stock returns were earned by companies in the lowest quintile of CEO pay. And the lowest stock returns were produced by the 20 percent of the companies with the highest CEO pay.

A $100 investment in the 20 percent of the companies with the highest paid CEOs would have grown to be worth $265 over the 10-year period. An investment in the companies run by the lowest paid CEOs would have grown to $367.

Honest people can disagree whether or not the CEO of a national coffee shop (Starbucks) "deserves" to be paid $20 million a year, but there is something massively perverted about a system that pays the Derek Dooleys of the corporate world more than the Nick Sabans.

A 2014 study by Michael Cooper at the University of Utah looked at the relationship between CEO pay and future stock performance. The results were similar: the more a CEO is paid, the worse the company's stock is likely to perform over the next three years.

The negative relationship was more pronounced as CEO pay and tenure increased, even within the same quintile.

A 2015 CEO pay and corporate performance study by The Wall Street Journal and the Hay Group reached the same conclusion: whether measured coincidentally or prospectively, the more a CEO is paid, the more likely it is that his company's stock will (or has already) underperform its peers.

Boards of directors are responsible for stewardship of a company's assets, including executive compensation. Board members, however, are apparently blind to problems in compensation practices. A February study by researchers at Stanford found that a majority of public corporate directors think CEOs are underpaid.

In 2015, the average pay of the S&P 500 CEOs was $12.4 million.

If directors don't address this problem, politicians might. A Rasmussen poll found that government control of all executive pay is favored by 20 percent of Americans — about the same percentage of presidential primary voters who preferred Bernie Sanders.