On Sunday, Apple filed a preliminary proxy statement revealing some bad news for chief executive Tim Cook: He made $4 million less in 2013 than he might have, had Apple's stock not taken a nosedive. Which isn't to say he didn't do perfectly well; his overall compensation actually increased from $4.18 million in 2012 to $4.25 million in 2013. Considering, though, that he could have doubled his take-home pay had Apple just kept pace with the Standard & Poor's 500-stock index, that's quite a pay cut.

But here's the remarkable thing about the disclosure: The reduction was, to a certain extent, voluntary. According to the board of directors, Cook had asked for a modification to the huge stock award plan he got when he took the CEO job in 2011. Originally, he was going to get an amount of stock that at the time was worth $376 million, one half of it in 2016 and the rest in 2021. Earlier this year, Cook asked to instead get the money spread out over the decade, and to have half of it tied to the company's stock performance as a stick for bad management. He wouldn't get more if Apple outperformed the market, but he'd lose it all if Apple did really badly.

"Because Mr. Cook faces only downside risk from the modification, the Compensation Committee believed that less than 50% of the annual tranches should be placed at risk," the statement reads. "Mr. Cook, however, expressed a strong desire to set a leadership example in the area of CEO compensation and governance and requested a larger at-risk percentage."

The thing is, though, that the new incentive structure isn't exactly cutting edge. Companies have been moving toward pay-for-performance plans -- at least in addition to their traditional awards just for sticking around -- for the past decade. FW Cook reported that the percentage of the top 250 largest U.S. companies granting performance shares reached 75 percent in 2012, and Farient Advisors plotted the long-term trend in the S&P 1500:

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The trend accelerated after the Dodd-Frank Financial Reform law introduced "say on pay" requirements, which allow shareholders to reject executive compensation packages. So Apple is really behind the times, not leading the way. According to Brandon Rees, director of the AFL-CIO's office of investment, companies that are doing well tend to be slow in shaking up their executives' incentive structures.

"It's companies that have stumbled where you see changes adopted," Rees says, offering GE and Disney as companies that performed better after adopting performance-based compensation plans. Nonetheless, it's not clear the board would've done anything if Cook hadn't insisted. "It's a sad day when we have to rely on CEOs to adopt the best practices in compensation, rather than the board. I think Apple shareholders could reasonably ask, 'why not have all the awards based on performance?'" From Rees' perspective as someone who advocates for union pension funds, Apple could do even better by evaluating pay based on specific financial metrics rather than simply the stock price, like return on equity or economic value added.

But why would Cook try to incentivize himself, when he can only lose money on the deal? Two reasons.

One, he wants to send a message to shareholders that he's a good steward of their capital, in the face of strident complaints from people like activist investor Carl Icahn that Apple's mismanaging its gigantic pile of cash. Making a show of the fact that he personally insisted on losing money when they do could inspire confidence.

Or two: He could be setting an example not for the rest of corporate America, but rather members of his own executive team, who will start to get similar compensation plans in the coming years. Most of them have been around for decades, and Cook could be asking them to up their game.