PMI Group, a mortgage insurer, will be sold to the public by parent Allstate Corp. through a stock offering that could raise as much as $735 million.

If the offering comes off, PMI will become the fourth publicly traded mortgage insurer, joining Mortgage Guaranty Insurance Corp., Commonwealth Mortgage Assurance Corp., and Triad Guaranty Corp.

Allstate's decision to sell PMI stems from its desire to concentrate on its core insurance business, according to the company.

"We are selling PMI in order to realize the return on our long-term investment in the company and focus our resources on core areas of Allstate's business," said Jerry Choate, Allstate's chairman.

Allstate is being spun off from its parent, Sears, Roebuck and Co., a process that is expected to be completed in 1995.

Allstate will offer for sale 21.5 million shares at a maximum price of $30 per share, with an overallotment option of three million shares. Proceeds will be used for general corporate purposes.

After the offering, Allstate will still have a 30% to 38% stake in PMI. That equity will be divested as well, through a sale of three-year notes that will be exchanged for PMI Group stock. Proceeds will also be used by Allstate for general corporate purposes.

The offering is being underwritten by Goldman, Sachs & Co., Dean Witter Reynolds Inc., Morgan Stanley & Co., and Salomon Brothers Inc.

PMI Group is the parent of PMI Mortgage Insurance Co., San Francisco, the third-largest private mortgage insurer in the country, according to Inside Mortgage Finance, an industry publication. Private mortgage insurance is used by lenders to reduce their credit risk on low-down- payment loans.

In the first three quarters of 1994, PMI turned a profit of $79.7 million on net premiums earned of $223 million.

In 1993, the company earned $59.8 million. Earnings that year were reduced by a $28.8 million loss from discontinued operations.

In that year, PMI got out of the pool insurance business, citing losses. Pool insurance is used to protect against loss of principal and interest on groups of loans, which are usually put into securities. In 1992, PMI earned $112.3 million.

The company has assets of more than $1 billion. It has almost 600,000 mortgage insurance policies in force. Those policies have a default rate of 1.84%. PMI's risk-to-capital ratio is 19.5:1. At Sept. 30, the company employed 602 people.

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