Compensation in all its excesses for top corporate executives is a hardy perennial for astonishment, outrage and fruitless demands for reform. I have said more than once that many, indeed, most, chief executive officers at publicly traded U.S. companies are wildly overpaid. But some recent research adds some nuance that deserves a closer look.

First, a quick reminder: For more than four decades U.S. executives have received much bigger pay increases than their brethren in Europe and Japan. Today, top German executives make about half of what their U.S. counterparts are paid; Japanese CEOs get paid about 10 percent of comparable American CEOs.

In 1965, an American CEO was paid about 20 times -- a ratio of 20-to-1 -- more than the median pay of other workers. Then executive compensation took off, peaking at 383-to-1 in 2000. The ratio checked in at 296-to-1 in 2013, according to Economic Policy Institute, a liberal think tank.

This explosion traces back to an unintended consequence of a change in the tax code while Bill Clinton was president, putting limits on how much executive compensation was deductible against corporate earnings. But the cap only applied to cash pay, not stock grants. This turned into a penalty-free way to give outsized pay packages to executives. Thus, stock compensation has become an ever-larger proportion of executive pay at public companies.

Recent research has looked into several factors on this topic, including short-termism, performance pay and stock-based compensation. Let’s consider all three.

We all assume that executives, like everyone else, respond to incentives. Part of the idea behind stock options was to resolve the so-called principal-agency problem, in this case, when executives can make decisions that affect shareholders. As stock-market index provider MSCI Inc. noted: “In theory, such rewards were intended to convert these corporate agents into corporate principals, and thus ensure the alignment of their personal interests with those of the company’s shareholders.” However, it’s not clear that stock grants reconcile the mismatch between executive actions that yield short-term stock gains versus strategies that raise revenues and profits over the long haul.

It may be comforting to blame short-termism, but validating that hunch is tricky. For example, a 2004 survey of executives found that “a surprising 78% of our sample admits to sacrificing long-term value to smooth earnings.” But that is just a survey, which is a good way to discover what people may believe, but not what they actually do.

Hard data confirming this sort of short-term behavior has been difficult to find. A recent paper in the Review of Financial Studies did identify a strong correlation between “the CEO’s concerns for the current stock price to reductions in real investment.” But as the authors themselves noted,  “It’s extremely hard to document causation rather than simply correlation.” The authors’ solution is that compensation reform should focus not on the level of pay, but instead on the horizon of pay. Big stock-option payouts should be tied to corporate success over longer periods of time -- years instead of quarters -- even after the CEO has retired.

Back to that evaluation of equity incentives for executives performed by MSCI. Using a sample set of 429 large U.S. companies from 2006 to 2015, the study concluded that “Companies that awarded their Chief Executive Officers (CEOs) higher equity incentives had below-median returns.” Even more damning, 10-year cumulative returns found that companies that had below median total executive pay outperformed those above the median by as much as 39 percent. The correlation, according to MSCI, is definitely there. Showing causation is another issue.

Perhaps the biggest concern for shareholders is how we compensate public CEOs in America: They get paid not for how well their companies do, but for how well the stock market does. As we noted in 2016, the factors that go into how well a company’s stock performs are often things beyond the control of even the most talented manager. These include the state of the economy, Federal Reserve policy, industry trends, bull-and-bear stock-market cycles, inflation and the quality of the management team among other things.

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