CEO pay at S&P 500 companies tripled between 1992 and 2001, far outpacing raises paid to other members of the top 1 percent of US households. That marked a dramatic break from the trends established in both preceding and subsequent years, according to research by Chicago Booth’s Kelly Shue and Dartmouth College’s Richard Townsend.

Stock-options grants have been widely mentioned as one possible explanation. Now Shue and Townsend offer evidence that the pay jump can be blamed in large part on one particular way grants were awarded: companies consistently awarded a certain number of options, regardless of how much those options were worth.

Stock options became popular during the 1990s, thanks to regulatory changes that made them attractive, and because they theoretically align a CEO’s incentives with those of shareholders. An options contract gives the holder the right to buy a stock at a defined price, which means that as the stock price rises, so does the value of the option. Corporate boards typically award options that are “at the money” when granted—so if a stock is trading at $20, the recipient has the option to buy the stock for $20. The award has no intrinsic value at that point, but its value can skyrocket if the stock price does too.

“While much of the existing research focuses on the rising grant-date value of these options, we instead start by examining the number of options awarded to executives,” write Shue and Townsend. “We show that there is a high degree of rigidity in the number of options awarded.” They suggest this number rigidity can explain more than half of the off-trend growth in CEO pay in the United States during the tech boom.

The researchers looked at executive compensation data covering firms in the S&P 1500, from 1992 to 2010. Many companies granted executives the exact same number of options year after year, Shue and Townsend find—20 percent of new grants they looked at contained the same number of options as the previous year’s grant.

When companies changed the number of options granted, it was often to a number that is a multiple of what it had been. According to the researchers, “these patterns suggest a tendency to think of options compensation in number rather than dollar terms.” The empirical evidence supports a pattern that the University of Southern California’s Kevin J. Murphy had proposed in earlier research.

Because at-the-money stock-options awards have no intrinsic value when they’re given, “it is not immediately obvious that granting the same number of new options after a stock price increase would coincide with a pay increase,” the researchers write. But in effect, the consistent grants represent a pay raise. If a CEO receives 100,000 options to buy shares of stock trading at $100, and the stock goes up 50 percent to $150, the options would be worth $50,000. The next year, if the stock rises a further 50 percent, 100,000 options contracts granted with a strike price of $150 will be worth $75,000, a form of a pay raise.

Although CEOs’ options grants became worth more and more, boards did not adjust their other forms of compensation to offset the growth in value, the data suggest. It could be that boards didn’t completely understand how to value the options, Shue and Townsend conjecture.

Some companies voluntarily expensed the value of options grants, so presumably they did have someone around who knew how to value them. Those companies were “significantly less likely to use number-rigid option[s] awards,” the researchers find. And when regulators in 2006 began requiring companies to expense the grants, number rigidity declined.

Some CEOs may not have understood the value of the options, either. The researchers find that after a stock split, many CEOs received a split-adjusted number of shares of stock in their pay packages—but continued to receive the same, unadjusted number of options contracts even though those would potentially be worth less than before.

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