The issue of CEO pay and how to compensate managers in a way that encourages the “right” amount — and type — of risk to grow a company and protect stakeholder interests has garnered a significant amount of debate. Many executive pay packages include incentives that tie compensation to a firm’s performance, often through the use of stock options. But a number of research studies have found that if a manager’s wealth is tied to share price, he or she may be more likely to misreport financial data.

A recent paper by Wharton accounting professors Christopher Armstrong and Daniel Taylor, however, shows that it is not enough to only consider the relationship between executives’ financial well-being and stock price; it is also important to look at the association between equity portfolios and changes in risk.

According to Armstrong and Taylor, there is no easy way to fine-tune an incentive package to induce a CEO to take only certain kinds of risks — a manager with a strong risk appetite, they note, may be enticed to invest in a cutting-edge new product, but he or she also may be encouraged to engage in financial misreporting. In “The Relation between Equity Incentives and Misreporting: The Role of Risk-Taking Incentives,” Armstrong and Taylor find strong evidence of a positive relationship between misreporting and the sensitivity of a manager’s wealth to changes in risk. The paper, which was co-authored by David Larcker of Stanford University and Gaizka Ormazabal at the University of Navarra in Pamplona, Spain, was published in the Journal of Financial Economics.

“A lot of papers have looked at the relationships between different kinds of compensation, but they focused entirely on the benefit piece,” Armstrong says. “What we’re doing is talking about risk and return, which tend to go hand-in-hand. You can’t really only look at the benefit; you also need to look at the accompanying risk.”

Equity incentives encourage CEOs to take risks that have a high payoff, which is often what shareholders want, he points out. “But when you’re talking about a manager, the scope of projects that he or she can engage in is very broad and may encompass [misreporting], which benefits the manager but not the shareholders.”

In, At or Out?

An unambiguous sign of inclination to take risk lies in the relative “moneyness” of stock options (whether an options contract is set to make or lose money), the researchers note. Risk appetite changes predictably, it turns out, if options are in-the-money, at-the-money or out-of-the-money (that is, set to make money, break even or lose money). “Our results suggest that stock options provide managers with incentives to misreport not only because they tie their wealth to equity values, but also because they tie their wealth to equity risk,” the researchers write.

To understand the link between moneyness and risk appetite, consider a pair of CEOs. The first CEO holds 1,000 in-the-money stock options with a $100 strike price, and the firm’s stock price is $125. The second CEO holds 1,000 at-the-money options, with a $100 strike price, and the firm’s stock price is $100.

The first CEO can cash in right away and pocket $25,000. Alternatively, he or she can accept a risk with potential to move the stock price. If the price moves up by $1, the CEO can pocket $26,000. If it goes down by $1, the proceeds are $24,000. Either way, the value of the options changes in lock-step with stock price — as long as the options remain in the money.

Now consider the CEO with 1,000 options issued at-the-money. Exercising these options will not generate a gain or a loss (excepting transaction costs). But suppose misreporting ultimately causes the stock to lose $25. The stock price slips to $75. No exercise of options means no money made or lost.

“What we’re doing is talking about risk and return, which tend to go hand-in-hand. You can’t really only look at the benefit; you also need to look at the accompanying risk.” –Christopher Armstrong

All else equal, the CEO with at-the-money options has a stronger incentive to take added risk, the researchers say. Why? Because at-the-money options have an intrinsic value that is less sensitive to stock price declines. They limit the downside without capping the upside — a thought worth exploring when boards vote to grant options. “The at-the-money CEO is in a real position to take risk,” Taylor notes. “If it turns out bad, the intrinsic value of the option is unaffected. If it goes well, the intrinsic value increases.”

Countless twists are easy to imagine. If, for instance, the first CEO embarks on a project that adds $50 to the current $125 stock price, or $75 above the strike price, he or she can exercise the option and pocket $75,000. A $50 decrease has an uneven — or convex — effect. It sends the stock to $75. The CEO surrenders $25,000 that he or she could have netted when the stock changed hands for $125. Thus, the most the CEO stands to lose is $25,000. In that case, says Taylor, lose and the downside is capped. Win and the sky is the limit.

The Real Impact of Misreporting

A robust sample of 20,000 companies that filed restatements supports the researchers’ findings. Because benign errors trigger some restatements, the researchers focused their attention on statements found by AuditAnalytics to stem from fraud, misrepresentation or an investigation by the Public Company Accounting Oversight Board (PCAOB). The research examined three common measures of misreporting: discretionary accruals, accounting restatements and SEC Accounting and Auditing Enforcement Releases (AAERs).

“We’re using the manager’s potential payoffs as a measure of who will swing for the fences.” –Daniel Taylor

Two types of investigation — regression analysis and matched pairs — reinforce the unambiguous correlation between equity incentives and the propensity to misreport financial data. In both, moneyness risk trumps the stock price as an indicator of risk appetite. (In the paper’s formal jargon, a proxy for the sensitivity to equity risk, vega, subsumes delta, a proxy for the sensitivity to stock price.) “We’re using the manager’s potential payoffs as a measure of who will swing for the fences,” Taylor notes.

Evidence shows that the effect of risk on misreporting is economically large and greater than many other determinants of misreporting. Firms responsible for the positive correlation between risk-taking incentives and misreporting have much larger discretionary accruals — more instances of restating financial results and a heightened chance of SEC enforcement actions.

The researchers questioned whether the impact of misreporting stems more from the moneyness of the options at the time they were granted to the executive or from subsequent changes in moneyness due to stock price fluctuations. Their data show that the relation between stock price and misreporting is driven by the component of risk-taking incentives attributable to features of the grant itself, rather than changes in risk-taking incentives attributable to company performance after grants are issued.

Taylor and Armstrong both caution against overreaction. Scrapping equity incentives might reduce incentives to misreport, but at a cost, they warn. Many, if not most, shareholders accept certain side effects of equity incentives as a cost of doing business. “At-the-money options incentivize managers to take risks that provide them with a benefit — risks that benefit both shareholders and managers and risks that benefit managers at the expense of shareholders,” Taylor points out.