Their analysis examined two significant types of product recalls: those in which a product could cause serious harm or death and those in which exposure to a product might cause temporary or medically reversible health consequences.

The study examined the pay packages of 386 chief executives. One curious finding emerged: Product recalls were less common among companies whose chief executives founded the companies or had long tenures there. Such executives may be more risk-averse because they are generally large shareholders and may also feel that their personal reputations are intertwined with their companies’ actions.

“It was interesting for us to see that options don’t affect everybody the same way,” Mr. Wowak said in the interview. “When boards design pay packages, it would be beneficial for them to think about how their C.E.O. might respond and tailor the package around that.”

Mr. Wowak acknowledged that among publicly traded corporations over all, stock option grants as a percentage of total pay had declined recently. Many companies are dispensing restricted stock instead, making sure that executives feel the pain of a falling share price alongside their stockholders. With options, a falling stock price represents a lost opportunity for a future gain, not an actual hit to executives’ wallets.

But stock options remain popular. Data compiled by Equilar, an executive compensation analytics firm in Redwood City, Calif., shows that among the companies in the Standard & Poor’s 500-stock index, option grants totaled 16.1 percent of direct pay for chief executives in 2014. In 2010, that figure was 20.1 percent.

“Of course, not every product recall that happens is caused by stock options,” Mr. Wowak said. “And it’s possible to pay a lot in options and not have a product recall. But boards are wise to have a balanced view of the potential downside to building in heavy option components to executive pay.”

The researchers’ focus on health care companies was appropriate: These companies are the biggest users of stock options, Equilar found. Last year, 84.4 percent of chief executives at these companies received options, while 67.3 percent of top managers at consumer goods manufacturers were recipients, according to Equilar. At utility companies, by contrast, only 27.6 percent of chief executives were granted options.