The Federal Housing Administration has a “close to 50” percent chance of requiring a bailout if the housing market deteriorates next year, the agency’s independent auditor said in a report released Tuesday.

The F.H.A., which offers private lenders guarantees against homeowner default, has just $2.6 billion in cash reserves, the report found, down from $4.7 billion last year.

The agency’s woes stem from the national foreclosure crisis. In the last three years, the F.H.A. has paid $37 billion in insurance claims against defaulting homeowners, shrinking its cash cushion.

The auditors determined the agency’s level of supplemental cash reserves by projecting losses on its mortgage portfolio and counting them against expected premium revenue. This year, the audit found that the F.H.A. supplemental reserve was less than one-quarter of a percentage point of its current portfolio: $2.6 billion against a $1.1 trillion mortgage portfolio, as of Sept. 30. Legally, the housing agency is required to keep a 2 percent cash buffer, a target it has not met since 2008.

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