Recalling the 2001-2003 hard market, he said that while insurance industry losses from the 9/11 attacks had enormous impact on the market conditions, “even before 9/11 exhaustion had crept into the market. Insurers were at the end of their rope with depressed pricing. The mood was bad [and] at some point people just got tired.”

A typical scenario had underwriting leaders saying, “I’m not lowering prices anymore. Get out of my office. Just fix it.”

Mr. Duperreault said, “You can’t underestimate the impact of the market psyche. I have come to understand that a hard market may be accelerated by a catastrophe or other major event, but it must [start] in a less obvious place—the mindset of the market.”

Supporting his view, he said that if any event should have turned the market, it was the Great Recession of 2008 and global financial meltdown.

It didn’t. “The market just wasn’t ready,” he said.

Is the market psyche reaching a point that could bring about a hardening?

“It may not be [there] today, but we’re all getting tired. So in terms of timing, I’d say it’s sooner rather than later,” Mr. Duperreault predicted.

Imparting some of the lessons he said he taught to underwriters when he worked at insurance companies, the former CEO of ACE Limited said that “the best companies see soft markets as opportunities” to get better and smarter “than the other guys,” and they also recognize “there can be profit in saying no” to underpriced risks.

Speaking directly to the D&O insurance professionals in attendance at the gathering—which included underwriters, brokers and lawyers—Mr. Duperreault suggested that a healthy dose of intuition needs to be used in conjunction with analytical tools to underwrite this particular line profitably.

“Hurricanes are unpredictable, but people are even more so,” he said, noting that D&O insurance underwriting involves trying to “gauge human behavior.”

To sort out the good guys from the bad guys—to determine which risks to write—“you have to ask yourself, ‘Can I trust this broker and this client? When I evaluate risk, am I doing so by combing through paperwork, or am I looking someone in the eye,’” he said, giving the basics of profitable underwriting.

“Intuition and perception” can still play a significant role in determining what business to write, he said, urging underwriters to be realistic about limitations of modeling tools.

“There’s no substitute for this kind of experience,” he said.