A majority of the biggest U.S. commercial auto liability insurers saw direct premiums written rise on a yearly basis in the third quarter, according to an S&P Global Market Intelligence analysis.

Progressive Corp. continues to lead the industry by a significant margin, with $1.44 billion in premiums written. It also recorded the largest year-over-year increase in premiums among the top 20 commercial auto liability insurers, at 30%.

Progressive CEO Tricia Griffith on a third-quarter earnings call said enrollment for the company's Smart Haul product for commercial truck drivers set a record in September, with the monthly take rate climbing to about 24%. She also noted that the commercial side of the direct-to-consumer segment has performed well in recent months, though it is difficult to know if the trend will continue.

"It could be what's happening with the pandemic, it could be what's happening with younger truckers, for example, starting new ventures, and they're more comfortable going direct," Griffith said. "But what I would say is, we're glad that we've invested in the direct side of the business."

By premiums written, Travelers Cos. Inc. is a distant second in the commercial auto liability space. It grew premiums written by 1.6% year over year to $531.4 million for the quarter. Old Republic Insurance, Nationwide and Liberty Mutual rounded out the top five with premiums written of $368.1 million, $333.4 million and $315.3 million, respectively.

Liberty Mutual's commercial auto liability premiums written slid 11.8% compared to a year earlier, pushing the company down two spots in the rankings to fifth.

Keefe Bruyette & Woods analyst Meyer Shields wrote in a research note on motor vehicle insurance pricing that claims frequency will likely normalize over the medium- to long-term. He wrote that this could pressure auto insurers' core underwriting margins, especially with sustained or worsening price competition as several leading insurers pursue market-share growth.