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 David Larcker, James Irvin Miller Professor of Accounting, Director of Stanford Graduate School of Business Corporate Governance Research Program

 And Brian Tayan

 STANFORD GRADUATE SCHOOL OF BUSINESS — In recent years, much attention has been paid to the suitability of CEO compensation among U.S. firms. Of particular concern are whether total compensation packages are too large, whether they encourage “excessive” risk taking, and whether they are merited given the performance of the company. This last issue is known as “pay for performance” and gets at the question of how closely compensation is correlated with the results the executive generates.

There is considerable debate as to whether pay is actually correlated with performance in U.S. companies, with evidence to support both sides. On the one hand, many elements of the compensation package are explicitly linked to performance targets. For example, the annual bonus is awarded based on an executive’s ability to achieve objectives set at the beginning of the year.1 The size of the bonus directly scales in proportion to the executive’s success in these areas. Also, CEOs receive a significant portion of their compensation in the form of equity awards (stock options and restricted stock). The value of this compensation is directly tied to share price and, in the case of stock options, has zero value if the stock price is below what it was on the grant date. The structure of these payments indicates that there must be at least some pay for performance.2

On the other hand, there have been a considerable number of large payments made to executives whose companies have not performed particularly well. For example, in 2007, Robert Nardelli (CEO of the Home Depot) received a severance package of $210 million, even though he resigned under pressure from shareholders who were frustrated with the company’s performance during his six-year tenure.3 Richard Fuld (CEO of Lehman Brothers) sold stock awards worth almost $200 million and Angelo Mozilo (CEO of Countrywide) almost $500 million, none of which they were required to repay through “clawbacks” when their companies collapsed in the financial crisis of 2008.4


In discussing pay for performance, the business media often highlights payments made to an executive in a given year. This measurement, however, is misleading for two reasons: 1) it involves compensation payouts that accrued over a number of years, and 2) it is not framed in terms of the shareholder value created during the executive’s tenure.5

For this reason, it is more instructive to examine the relation between CEO “wealth” (measured in terms of equity ownership through stock and options) and stock price returns. One way to make this assessment (and a method favored by academics) is to measure the dollar change in CEO wealth over small percentage changes in the stock price. Based on a sample of 4,000 publicly traded U.S. companies, the average (median) CEO stands to gain roughly $58,000 in wealth for every 1 percent increase in stock price. Among the largest 100 companies, this figure approaches $640,000.6

 A potentially more informative method is to consider the change in executive wealth over larger changes in stock price (after all the CEO is hired to do more than increase the stock price by 1%). An easy way to do so is to plot the percentage change in the expected value of the

CEO’s equity portfolio against percentage changes in stock price ranging from -100% to 100%. The 0 percentage point on the x-axis is based on CEO wealth at prevailing market prices and the -100 percentage point is where the value of equity goes to zero. By graphing this data and comparing these results to direct competitors or peer firms, observers can better understand the relative risk and reward being offered. Of particular note is the “convexity” of the payout curve. For example, a manager who is rewarded predominantly in restricted stock or only holds stock will see a change in wealth that is essentially linear (low convexity) and coincides one-for-one with the change in wealth of the average shareholder. By contrast, a manager who is rewarded predominantly in stock options (especially those with tranches of stock options with different exercise prices) will see a change in wealth that has a much steeper payout curve (high convexity) and promises significant wealth for superior performance.7 Payout curves with high convexity may encourage more risk taking, while payout curves with low convexity may encourage less risk taking. This can be good or bad, depending on the strategy of the organization.8

 As an example, we can consider the relation between pay and potential performance for a series of direct competitors:

  •  Regulated utilities: If the stock price of Southern Company increases by 100 percent, the CEO of the company’s Georgia Power division will realize a 235% increase in “wealth” (a ratio of 2.35). By comparison, the ratio at Exelon’s ComEd division is 1.23.Compensation at Southern Company therefore seems to encourage more risk taking. Under what circumstances is it appropriate for a public utility to engage in risky activities (see Exhibit 2)?
  •  Food companies: The CEO of General Mills has convexity in his compensation of 2.98, while the CEO of Kraft has convexity of 1.18. The CEO of General Mills, however, was appointed to the position during the year. While it can be appropriate to use options to help a CEO build wealth in the company at a faster rate, will a more aggressive compensation structure impact company strategy and risk (see Exhibit 3)?
  •  Pharmaceutical companies: The CEOs of Johnson & Johnson and Abbott Laboratories have higher convexity in their compensation (2.26 and 2.13, respectively) than the CEOs of Pfizer and Merck (1.78 and 1.67). Does a diversified healthcare model require more risk taking than a pure-play pharmaceutical model (see Exhibit 4)?

 While it is difficult for outside observers to determine whether these payout functions are appropriate, this is the type of analysis that the compensation committee can review to make a reasoned assessment of whether compensation contracts are providing appropriate incentives for performance, and gauge their potential to encourage “excessive” risk taking.9 These are also key inputs for analysts attempting to make a judgment about future cash flows and risks associated with a company.


 1. The current debate on pay for performance is characterized by heated rhetoric with little concrete analysis to inform conclusions. Measuring the relation between change in CEO wealth and shareholder returns is one method shareholders and stakeholders can use to determine whether compensation contracts are appropriate.

 2. While it is reasonable for a CEO to increase wealth at a faster rate than shareholders (because executives are asked to make strategic decisions), it is not clear what the ratio of this relationship should be. Should it be 1.5 times, 2.0 times, 2.5 times, etc? In all likelihood, the ratio should be determined in the context of the company’s industry, competitive positioning, and risk appetite, as well as the size of the executive’s equity holdings and tenure.

1 According to a confidential survey conducted in 2005 by a major HR consulting firm, the top measures used to determine the annual bonus include profit measures (earnings per share, EBITA, net income, operating income, and pretax profit), return measures (return on capital, return on assets, and return on equity), cash flow measures (cash flow, economic value added, and working capital), and other measures (sales growth, customer satisfaction, product/service quality, safety, and employee satisfaction). Typically, there is also a subjective component for “individual performance.””

2 This assumes that shareholders measure performance in terms of value creation and that executive decisions impact stock prices.

3 Julie Creswell and Michael Barbaro, “Home Depot Board Ousts Chief, Saying Goodbye with Big Check,” The New York Times, Jan. 4, 2007.

4 Stock sales occurred between 2003 and 2007. Mark Maremont, John Hechinger and Maurice Tamman, “Before the Bust, These CEOs Took Money off the Table,” The Wall Street Journal, Nov. 20, 2008.

5 For example, James Kilts, CEO of Gillette, came under fire for receiving a severance package worth $185 million following the sale of Gillette to Procter & Gamble in 2005. Less noted was the fact that Kilts increased the value of Gillette by over $20 billion during his four-year tenure, delivering annual returns of 14 percent compared with negative 0.6% for the S&P 500. Sources: Graef Crystal, “Kilts is the Real Winner in P&G Buying Gillette,” Bloomberg, Feb. 23, 2005; and calculations by the authors.

6 Includes the fair value of beneficially held stock and options (both vested and unvested). In calculating stock option fair value, remaining terms are reduced by 30% to adjust for potential early exercise or termination.

Source: Equilar compensation and equity ownership data for fiscal years from June 2008 to May 2009.

7 For simplicity, we use the term “convexity” to mean the percentage return on the CEO’s equity portfolio for a 100%  change in the stock price. This is taking a bit of liberty with the pure mathematical definition of convexity.

8 Since 2006, companies have had to provide detailed information on each tranche of options held by named executive officers. Previously, options outstanding were pooled together. Disaggregation in the disclosure allows us to precisely plot out the changes in value of each, based on prevailing market prices.

9 Obviously, risk taking can be either good or bad for shareholders. Firms are in business to take appropriate risk and generate the required returns for shareholders. Risk taking is negative when the risk assumed by investment, financing, and operating decisions is excessive in relation to the potential return.

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Also on Stanford Knowledgebase:

  1. Executive Stock Options Boost Company Performance but Options to Rank-and-file Workers Show Minimal Effect
  2. CEO Skill and Excessive Pay: A Breakdown in Corporate Governance?
  3. Excessive Executive Pay Makes Headlines, But So What?

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