The acquisition of foreclosed homes has slowed in recent years as real estate prices have recovered in many markets that were a focus of big rental-home companies. Lately, there has been a wave of consolidation in the business.

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Two of the bigger institutional owners of single-family rentals in the United States are planning to merge in the latest sign that affordable housing is becoming harder to find as home prices recover in much of the United States.

Invitation Homes and Starwood Waypoint Homes on Thursday announced a $4.3 billion stock deal, which the companies called a merger of equals. The merger would create a landlord with about 82,000 homes in more than a dozen big markets.

In the Seattle area, Invitation owns 3,203 homes and Starwood owns none. That’s enough to make it the combined firm’s 10th largest market, generating 4.6 percent of revenue, according to a presentation for investors.

The deal comes nearly seven months after Invitation Homes, which owns about 50,000 properties, raised $1.5 billion in an initial public offering.

Invitation Homes is majority owned by the Blackstone Group, one of the first private equity firms to begin buying foreclosed homes in the aftermath of the 2008 financial crisis, then fixing them up and renting them out. Blackstone is estimated to have spent $10 billion on its foreclosed-home-to-rental bet.

Since the financial crisis, institutional investors like hedge funds and investment firms, as well as private equity firms, have bought an estimated 200,000 single-family homes to operate as rentals. There are about 17 million single-family rentals in the United States, most of which are owned by mom-and-pop landlords. Before the crisis, there were about 10 million.

Yet the acquisition of foreclosed homes has slowed in recent years as real estate prices have recovered in many markets that were a focus of companies like Invitation Homes and Starwood Waypoint Homes. Lately, there has been a wave of consolidation in the business. This deal would be the biggest of its kind this year.

Invitation Homes’ own buying of homes has dropped precipitously since 2013, when it was buying hundreds of homes each week. Home purchases by Invitation Homes are down more than 90 percent from four years ago and the period of “hyper growth” for the industry had passed, a person close to the company said.

After the deal is completed, John Bartling, chief executive of Invitation Homes, will step down. The new chief executive of the combined company will be Fred Tuomi, the current chief executive of Starwood Waypoint.

Under the terms of the deal, each Starwood Waypoint Homes share will be converted into 1.614 Invitation Homes shares. The total enterprise value of the combined company, including debt, would be $20 billion, the companies said.

Invitation Homes’ shareholders will own roughly 59 percent of the combined company’s stock, while Starwood Waypoint investors will own the rest. Blackstone, which owns 70 percent of Invitation Homes, would own 41 percent of the combined company.

The combined company will operate as Invitation Homes and trade under the Invitation Homes ticker symbol INVH.

Starwood Waypoint shares climbed 5.2 percent Thursday as the broad market fell sharply. Invitation Homes stock rose 3.9 percent.