Progressive Corp., the fourth-largest U.S. auto insurer, is expanding in home coverage to challenge rivals including Allstate Corp. that are better known for bundling different types of policies.

Progressive agreed to pay $875 million for a majority stake in ARX Holding Corp., bringing its ownership of the firm to 67 percent from 5 percent, the Mayfield Village, Ohio-based company said today in a statement. ARX was the No. 18 U.S. seller of homeowners’ coverage last year.

The buyer, known for spunky spokeswoman Flo, is seeking to compete with rivals that sell auto and home policies together. Allstate, which sells policies through agents, purchased online car-insuranceseller Esurance in 2011 in a challenge to Progressive’s business, and said it would offer home policies as well.

“Progressive is committed to becoming the insurance destination brand for consumers,” Chief Executive Officer Glenn Renwick said in the statement. “As such, we need the reliable availability of many more products than we intend to manufacture.”

Renwick’s company slipped 2.2 percent to $25.67 at 9:47 a.m., erasing most of shareholders’ returns for the year. That compares with gains of more than 20 percent at Northbrook, Illinois-based Allstate and at Berkshire Hathaway Inc., parent of online car insurance seller Geico.

XL Group Plc is selling its 40 percent stake in ARX as part of the transaction, the Dublin-based insurer said today in a regulatory filing. XL will receive gross proceeds of about $500 million, the company said.

Expansion Plans

ARX’s American Strategic Insurance offers coverage in 26 states and Washington D.C., and plans to add locations next year. Progressive said the deal announced today is expected to be completed by April 1, and that it intends to purchase the rest of ARX over the next six years.

Progressive said American Strategic will operate as a separate company with its current management team. American Strategic also offers commercial property insurance, personal umbrella policies, and flood coverage.

“Our intention has long been to become the Progressive of home insurance,” American Strategic CEO John Auer said in the statement. The deal “creates a predictable and stable long-term outlook.”