A recent Gallup poll found that only one in six Americans thinks highly of business executives. Is it any wonder? This past year—in addition to the unceremonious exits of chief executives from such companies as Bristol-Myers Squibb and Viacom, and the convictions of two Enron CEOs—there was the scandal over backdating stock-option grants and the revelations at Hewlett-Packard of prying into telephone records. Meanwhile, the average CEO of a large, publicly traded American company now has annual compensation of $10.5 million—or about 300 times higher than the average U.S. worker. “How do I feel about executive compensation?” said John Bogle, founder of Vanguard mutual funds. “Terrible.” CEO pay packages are “outrageous” and “inexcusable,” he added.

But are they really? In fact, there’s strong evidence that, far from being paid too much, many CEOs are paid too little. Not only do the top managers of multibillion-dollar corporations earn less than basketball players (LeBron James of the Cleveland Cavaliers makes $26 million), they are also outpaced in compensation by financial impresarios at hedge funds, private equity firms, and investment banks. Should we care? Yes. If other positions pay far more, then the best and the brightest minds will be drawn away from running major businesses to pursuits that may not be as socially useful—if not to the basketball court, then to money management.

Still, the legend of the overpaid CEO persists. A widely accepted explanation for excessive CEO pay goes like this: Contrary to the theory that a board of directors sets the boss’s pay in order to maximize profits for shareholders, powerful CEOs actually control boards. Directors owe their well-paying positions to the chief executive, so they give him a pay package far in excess of what it should be. The compensation committee of the board of directors effectively acts as a rubber stamp for the CEO. How else, we are told, can we explain the fantastically high pay packages of the likes of Richard Grasso and Dennis Kozlowski?

Three law school professors—Lucian Bebchuk of Harvard, Jesse Fried of the University of California at Berkeley, and David Walker of Brown—laid out this argument in an influential academic paper titled “Managerial Power and Rent Extraction in the Design of Executive Compensation.” It’s a simple story with obvious media appeal.

While the explanation is undoubtedly true in some cases, it is less than satisfactory as a general proposition, especially at a time when Sarbanes-Oxley legislation has closed the kind of managerial-power loopholes that might have been exploited by some CEOs, and has instead elevated the authority of directors. And, in an age when shareholders judge performance on a quarterly basis, the CEO who fails to produce results is often shown the door by directors rather than dominating them. According to executive recruiter Challenger, Gray & Christmas, in the first half of this year, 728 chief executive officers lost their jobs. That number was 6.9 percent higher than the same period last year, which itself set a record.

If Bebchuk and his colleagues are mistaken, then what is the theoretical model that offers a convincing market-based explanation for the hiring trends in the CEO marketplace? Two professors at the University of Southern California’s Marshall School of Business, Kevin J. Murphy and Jan Zabojnik, may have the answer. They start with the observation that big businesses in recent years have been hiring more outsiders—that is, CEOs who don’t work for the company that is bringing them on, or even in the same industry. In addition, the outsiders make more money than the insiders. (You would expect that, if anything, directors would be more beholden to insiders.)

These two developments, according to Murphy and Zabojnik, reflect a fundamental change in the types of managerial skills required to run large companies. General managerial skills like finance, marketing, and strategy are increasingly more important than firm-specific skills, such as understanding the drug pipeline of a pharmaceutical company or knowing how to negotiate with a steel company’s suppliers, unions, and big customers. In the 1970s, outside hires accounted for 15 percent of all new CEOs; in the 1980s, there was a small increase to 17 percent; and in the 1990s, a larger jump to 27 percent.

In the past, a firm typically promoted from within, preferring to select someone with a proven track record within a certain industry. At times, companies might have hired a former McKinsey consultant with broader experience, or poached a star manager from an unofficial CEO training ground like General Electric. More commonly, an automaker, for example, would hire a CEO from the auto industry, a consumer-electronic manufacturer from consumer electronics.

But that is changing. IBM made one of the best CEO hires in history when it went far afield in 1993 to select Lou Gerstner, who had been chief executive of RJR Nabisco for four years and had spent 11 years at American Express before that. On September 5, 2006, Ford Motor Company hired as its CEO Alan Mulally, who came straight from Boeing, where he had worked since 1969.

Some excessive corporate pay packages are “outrageous,” as critics claim. But even more outrageous is a system where Dr. Phil makes more than twice as much as Jeffrey Immelt, CEO of the world’s most valuable company.

As markets grow increasingly globalized and information—thanks to the Internet—becomes more accessible, it’s not hard to see why boards of directors are going outside their companies and industries to find CEOs. But, if aviation and packaged-goods executives are added to the pool of CEO candidates for an auto company, doesn’t that increase supply and thus drive down price? Shouldn’t compensation fall rather than rise?

Not necessarily. The variety of candidates in the pool may increase, but not the number. In the past, companies were content to promote from within because they did not need someone with, for example, broad strategic and financial experience in the greater world. Now, they do, but such folks aren’t easy to find. In fact, it’s likely that the supply of top-notch CEOs for global companies is leveling off or even falling.

One reason for this is that the smartest potential CEOs are being siphoned off by higher-paid professions where public scrutiny and board control are less pronounced. After all, the same talent pool that produces doctors, lawyers, portfolio managers, and investment bankers also produces a fair share of CEOs. When it comes to compensation, the peer group for a CEO is not just the CEO next door, but also the venture capitalist on the other side of the country, or the investment banker on the other side of the world.

The latest statistics from Holt Private Equity Consultants and Dow Jones Private Equity Analyst show that the average employee at a venture capital firm will receive $770,000 in total compensation this year while the average employee of a private-equity firm earns $1.2 million. That’s the average employee, not the boss. Senior partners at venture firms earn about $1.5 million, general partners $2 million. Even those figures pale in comparison to hedge funds. According to Institutional Investor magazine, average compensation for the top 25 hedge fund managers was $251 million in 2004—that’s more than 20 times as much as the average CEO. Leading the pack was Edward Lampert, who earned just over $1 billion.

Charles Munger, who is Warren Buffett’s close associate at Berkshire Hathaway, Inc., and heads Wesco Financial himself, has eloquently lamented these developments. “I regard the amount of brainpower going into money management as a national scandal,” he said at Wesco’s annual meeting. “I think it’s crazy to have incentives that drive your most intelligent people into a very sophisticated gaming system.” The incentive, of course, is money. There may be not enough of it in running public companies, and too much of it elsewhere.

Private equity, or buyout, firms—which use cash from investors such as pension funds to purchase companies, refurbish, and then sell them—now have $1 trillion in assets. When they enter the market for CEO talent, they aren’t shy about offering high pay and demanding high performance. David Calhoun, a former vice chairman of GE, was recently picked by a group of buyout firms to lead a privately held Dutch company called VNU, which owns Billboard and The Hollywood Reporter, among other properties. Press reports valued his total compensation package at $100 million. Clearly, Calhoun wasn’t extracting excess rents from a captive board. He was paid well because private firms have more room to offer market prices to CEOs than public ones. Wrote Geoffrey Colvin in Fortune: “Any public company that now offered a new CEO $100 million would be scourged without mercy by shareholder activists and TV talking heads nationwide.”

A CEO should be paid according to what he is expected to produce. But how to anticipate his performance? If Alex Rodriguez hit 40 or more homers and drove in 130 or more runs as a Texas Ranger, was it wrong for New York fans to assume that he would do the same as a New York Yankee? Likewise, if a super-star CEO delivered 10 percent year-over-year earnings growth and a 50 percent increase in the share price during a tenure elsewhere, is it wrong to assume that he will do the same at his next destination?

Unfortunately, there is little way of knowing whether the past is prologue—and, as it turns out, little correlation between CEO pay and stock performance—as detractors delight in pointing out. In fact, the market for CEOs is not much different from the market for money managers, most of whom— educated at the best schools in the nation and paid extremely well—fail to beat the Standard & Poor’s 500 Stock Index. And it is extremely difficult to predict whether managers who beat the index this year will do so next year.

Those few portfolio managers who do manage to beat the S&P 500 benchmark fairly consistently (think Buffett) are said to possess “positive alpha”—that is, their actual returns are better than expected returns when you consider the amount of risk they assume. If the primary role of the CEO is to allocate capital efficiently and maximize the profitability (and thus, the stock price) of the firm, then the duty of a board of directors is to identify CEO candidates with positive alpha. Steve Jobs of Apple seems to have it, as did Jack Welch at GE and Lou Gerstner at IBM. In an efficient market, one would expect that only a small percentage of CEOs would be able to beat expectations and turn in superior performance.

One way to match pay with performance is to offer incentive pay, but, even with such a package, a CEO presents a risky bet for a board since, if he underperforms for two years, the savings in pay don’t come close to the loss in expected profits or decline in stock price. And, even with incentives that link pay to stock prices or profits, the mismatch between compensation and performance can be extreme—down as well as up. Some CEOs are clearly underpaid. Forbes recently calculated that, over the past six years, Robert K. Cole, CEO of New Century Financial—a company with a market capitalization of $2.2 billion—received average annual compensation of only $1.6 million while his company’s stock returned 36 percent yearly. Over the same period, Mark Pigott, CEO of Paccar, made just $3.1 million annually while his company’s stock returned 30 percent a year.

'It’s crazy, ' Charles Munger says, 'to have incentives that drive your most intelligent people into a very sophisticated gaming system.' The incentive, of course, is money. There may be not enough of it in running public companies, and too much of it elsewhere.

Let’s go back to Alan Mulally. He is reportedly being paid more than $15 million in annual compensation to turn around the ailing carmaker, and, if he meets his performance targets over the next two years, his compensation could reach as high as $34 million. Is that too low or too high? As a Ford spokesperson explains, the level of compensation is simply the market rate, and that is the only rate that matters: “Mr. Mulally’s compensation was based on the competitive environment for world-class talent, the demands of the position, and the need to recruit Mr. Mulally from a long, established career at Boeing.” Ultimately, the answer to the question of whether Mulally is underpaid or overpaid rests on whether he will find the right deployment of capital to satisfy Wall Street investors, and in doing so, lift the company’s stock price. If he can, then he is worth every penny of that salary—and a lot more.

In early October, Ford’s market capitalization was $15 billion. If Ford can be restored to profitability in the next two or three years, it’s not difficult to imagine a market cap of $25 billion or more. If Mulally is paid $50 million or even $100 million to pull off such a huge gain, would the compensation be worthwhile? Of course. Even at $100 million, the leverage is spectacular.

An able leader has an enormous impact on the success of a business. Certainly, some excessive corporate pay packages are “outrageous,” as Bogle and other critics claim. But even more outrageous is a system where Dr. Phil makes more than twice as much as Jeffrey Immelt, CEO of GE, the world’s most valuable company; where Jessica Simpson makes more than the average earned by the CEOs of America’s 500 largest corporations; and where hedge fund managers who make the right bet on the yen-dollar relationship can take home ten times as much as the head of the nation’s largest exporter.

Because of the growing complexity of the corporate leadership role and the paucity of CEOs with positive alpha, it’s almost certain that pay will rise—at least among companies that are not listed on stock exchanges and subject to the regulatory regime of Sarbanes-Oxley and media scrutiny of compensation. CEO pay at some of the largest and most important publicly traded companies, however, may remain constrained. That’s not a good thing—not for those businesses, their shareholders, or the economy as a whole.

Dominic Basulto is editor of the Fortune Business Innovation Insider.

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