Freddie Mac’s $500 million of risk-sharing debt sold yesterday may not give the firm as much protection against homeowner defaults as policymakers seek, according to Amherst Securities Group LP and Deutsche Bank AG.

The structure means that the company would be better off without the securities if refinancing and property sales are initially fast, and then defaults jump amid a real-estate slump, Amherst analysts led by Laurie Goodman wrote today in a report. In addition it transfers less risk than needed to leave Freddie Mac exposed to only catastrophic levels of losses among mortgages, according to Deutsche Bank’s Christopher Helwig.

The type of transaction is “an integral part of introducing more private capital to the mortgage market,” the New York-based analyst wrote today in a report. “However, some serious questions still remain.”

The notes reflect an effort by the Federal Housing Finance Agency to reduce the role of Freddie Mac and Fannie Mae in the residential-mortgage market, where government-backed loans now account for more than 85 percent of lending. The transaction is also similar to the new system of mortgage finance in the U.S. envisioned under bipartisan legislation introduced this year by Republican Senator Bob Corker of Tennessee and Democratic Senator Mark Warner of Virginia.

“We are comfortable with the STACR structure and the credit protection provided,” Kevin Palmer, vice president of costing and portfolio management at Freddie Mac, wrote in an e- mail, referring to the Structured Agency Credit Risk transaction. “We are still reviewing Amherst’s report.”

Denise Dunckel, an FHFA spokeswoman, referred questions to the company.