CEO Pay-Rise: A Silly Math Mistake

ceo_options_payAn economics paper published last month in the National Bureau of Economic Research really fascinates me. Maybe that’s because I’m a fundamentally boring person? No, that’s not the main point.

Economists Kelly Shue and Richard Townsend set out to explain the sharp rise of executive pay in the ten-year period 1992 to 2001.

Think of super-manager CEOs like Robert Iger, Chairman and CEO of Walt Disney & Co., who received $76.8 million in total compensation last year, according to data compiled by Bloomberg. Or Marissa Mayer of Yahoo, who received $59.1 million in 2015.

The first thing to know is that this level of ‘super-manager’ pay – a term I’m borrowing from Thomas Piketty – is a relatively new phenomenon. Before thirty years ago, managers who didn’t found their companies didn’t get paid like that. Between 1992 and 2001 for example, median CEO pay in the US rose more than three times (inflation-adjusted!) from $2.9 million to $9.3 million. And super-managers still don’t get paid like that outside of the US and the UK.

So what explains the relatively recent rise, as well as geographic anomaly of ‘super manager’ pay?

The punch line explanation from the Shue and Townsend paper on the rise in CEO pay: corporate boards are bad at math.

If you’ve been thinking about the sharp rise of CEO pay recently – as I have – you might have the impression that efficient markets, or the increasingly global scale of companies, or lower marginal tax rates, or even crony-insider-oriented capitalism explain it. Each of these may also be true, and I want to explore them later. Maybe next week.

But Shue and Townsend present the case that half the reason for the rise in pay is just weak math skills on the part of corporate boards. Which I have to admit, as an explanation, I kind of love.

Fixed numerical options awards

So what did they study?

Shue and Townsend noticed that CEOs usually got awarded a fixed number of company options as part of their pay packages each year. Options give executives the chance to earn part of their pay as a result of increased share prices in their companies. The point of the options awards is to align pay with share price performance. This idea has some theoretical merit.

But they also noticed that as the value of company stocks rose, compensation committees didn’t reset the number of new options awarded the next year. Rather, committees typically just awarded the same number of options as the prior year.

So why is this bad math? The same number of options awarded on a higher price stock are worth far more. It’s an unintentional pay raise, due to the way options work.

Maybe a specific example helps explain why. If the CEO gets 100 options on a company’s stock, and the price goes up 50% in the year, from $10 to $15, the executive reaps $500 as a result. A repeated 100 options award in the next year, if the price goes up another 50%, from $15 to $22.50, will be worth $750. Which is in effect a 50% pay raise for the executives. I’ve used small numbers in this example to keep the math simple, but the effect on CEO pay in that period was anything but small.[1]

Awarding the same number of options led to dramatic raises for CEOs, even though it appears the compensation committees did not intend to give raises, as salaries and bonuses did not increase much during the 1992 to 2001 period.

How else do we know that corporate board compensation committees didn’t intend to give these pay raises? Regulatory changes in the early 2000s required firms to calculate the value of options awards, and to disclose them publically. Once they did that, Shue and Townsend noticed that firms awarded options less often or became more likely to change the option awards from year to year.

The economists also argue, persuasively, that their data show that a lack of sophistication about the value of options grants among board compensation committees partly explains the rise in CEO pay.

Forced to do a little bit of math and disclose it, fixed-number of options awards went away.

If this all seems a bit confusing and obscure, here’s a pro tip: The next time you negotiate your CEO comp package, try to insist on a pre-set number of options grants. Just trust me on this.

Also, if you’re looking for a non-partisan solution to the rise of inequality in America? Try teaching more math.


A version of this post ran in the San Antonio Express News.

Please see related posts:

Yahoo Executive Compensation – It’s all about the stock awards

Executive Pay with Equity Awards – It takes a Buffett to push this agenda



[1] For economists who study this type of thing, the fixed-number of options award fall under the category of irrational human behavior known as ‘number rigidity.’ ‘Number rigidity’ is a little bit like that annoying Facebook video in which the guy predicts you will say ‘7’ when asked to think of any number between 5 and 12. And he’s right every time, darnit! It doesn’t make rational sense, except if you know that our brains are wired for inertia, consistency, and pattern recognition.


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