Is CEO pay going up or down? Both. Or at least, it depends on how you look at it.

Over the past few days, two widely watched reports examining CEO pay have been released, and the results are stunningly different at first glance. Even though they were prepared by same data source, the executive compensation and governance research firm Equilar, one showed a slight uptick in the paydays of chief executives while the other showed a marked decrease.

The Associated Press's report, released May 25, found that median CEO pay among 341 CEOs in the S&P 500 climbed 4.5 percent from $10.3 million to $10.8 million -- or with a median raise of $468,000, "more than 10 times what the typical U.S. worker makes in a year," the AP reported.

The other, published Friday by the New York Times, looked at 200 CEOs of large companies, and found that their average compensation was $19.3 million, down 15 percent from 2014, when it was $22.6 million. "Even by the topsy-turvy standards of corporate pay, what's remarkable is not how big that number is, but how small," the Times wrote.

Why the difference? It's simple: They didn't look at the same CEOs. The AP report looked at pay trends for chief executives across the S&P 500 index who have served two full consecutive fiscal years at their companies and had filed proxy statements as of April 30 this year. But the Times report first ranked all public companies with at least $1 billion in revenues by their CEOs' pay, and then examined how the average among the top 200 is faring, compared to the year before.

In other words, while there was plenty of crossover -- Expedia CEO Dara Khosrowshahi, who topped both reports with 2015 compensation valued at $94.6 million -- one list represents how pay for big-company CEOs is trending overall, while the other looks at pay for only the most lavishly compensated chief executives.

The results, then, appear to be more logical than they seem at first glance -- and in a way, just what we might expect. One shows the steady escalation in pay at the largest companies -- a long-standing trend that seems unlikely to change as long as boards continue to set pay against CEOs' peers. The other shows some relative restraint at the most stratospheric levels, as investor activism and pressure perhaps start to hold back some of the most jaw-dropping numbers. "We saw fewer large awards," said Dan Marcec, the director of content for Equilar, in an interview explaining the reports' findings. "Last year I think we had at least three to four CEOs paid more than [Expedia's CEO]." 

In either case, whether looking at CEO pay across the largest public companies or just the super-compensated among them, it's worth noting that the reports are based on figures that still don't necessarily represent what ended up in CEOs' wallets in 2015. Studies reporting trends in CEO pay rely on figures pulled from the "summary compensation tables" in company filings. Those numbers are calculated based on how the Securities and Exchange Commission requires companies to value CEO compensation, which is based on the target values of stock grants, as well as valuations for executive pensions, rather than what the CEO actually "took home."

"In most cases, the CEOs are taking more or less than what was disclosed in that summary compensation table -- and sometimes significantly more or less," said John Roe, executive director of ISS Corporate Solutions, a subsidiary of proxy adviser Institutional Shareholder Services that provides research to companies.

For instance, the mega-amount listed for Khosrowshahi is part of a five-year employment agreement that includes stock that will only become available to him over a period of several years, and is based on his continued employment, as well as the stock performance of the company. "Dara Khosrowshahi has been a transformational CEO for Expedia," company spokesman Sarah Gavin said in a statement. "His leadership has elevated the company into a global leader in the online travel market."

Still, even if that payday hasn't yet been fully handed out, it's hard to argue that its potential value, even over a period of several years, is quite a rich reward. And really, that's what these studies remind us of again and again, whether the data is sliced one way that shows CEO pay going up or another way that shows it going down. A simple fact remains: $19.3 million, or even $10.8 million, is a lot of money to earn in one year.

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