The Federal Housing Administration caters too much to higher-income home buyers despite the perception that it was designed to help lower-income borrowers, an association of private mortgage insurance companies alleges in a new report.

The study, conducted by a Boston management consulting firm for the Mortgage Insurance Companies of America, said the FHA provides insurance for at least 10 times as many low down payment loans to higher-income borrowers than it does to lower-income borrowers.

The study found that 35 percent of FHA's loan insurance originations between 1982 and 1986 went to borrowers earning more than $40,000 and that 9 percent went to borrowers earning more than $60,000. In 1986, 42 percent of all FHA loans with less than a 10 percent down payment went to borrowers with incomes of $40,000 or more and 4 percent went to borrowers with incomes of $20,000 or less. Between 1982 and 1986, 69 percent of the loans insured by private mortgage insurers were for mortgages of less than $60,000, compared with 57 percent for the FHA.

"The study proves that many of the perceptions of the FHA are just not true," said William E. Lacy, president of the Mortgage Guaranty Insurance Co. and the association's vice president. "I was surprised by the study because I expected the FHA to be doing more on the lower-income end."

FHA officials said they are still reviewing the study and were not prepared to comment on it.

Established in 1934 to insure home loans for moderate-income home buyers, the FHA reimburses the lender for any losses if a homeowner defaults. Last year, the Reagan administration proposed selling the agency on the private market, but it backed off the recommendation after there was strong opposition from some lawmakers and special interest groups.

The mortgage insurers association represents the 13 privately owned companies in the United States that insure lenders against default by home mortgage borrowers, particularly buyers who can afford to make a down payment of less than 20 percent of the value of the house.

The association hired Temple, Barker & Sloane, the Boston consulting firm, to study FHA loan information and mortgages insured by the association's members for the 1982-86 period. By citing housing loan data from 12 major cities (not including Washington), a mail survey and personal interviews, the association hopes that it will influence Congress and FHA officials to redirect the benefits of government-backed mortgage insurance to lower-income home buyers.

William A. Simpson, president of the association who also runs the Republic Mortgage Insurance Co. of Winston-Salem, N.C., said the study "should alert Congress to retarget the FHA to serve those home buyers either with lower incomes or those living in economically distressed markets." Lacy added, "We want the FHA. Our concern is the overlap at the higher {income} end."

But John M. Teutsch Jr., president of the Mortgage Bankers Association of America, said he did not agree with the study's conclusions. Teutsch said the report "ignores the fact that FHA continues to provide homeownership opportunities, as repeatedly mandated by Congress, for moderate-income Americans, especially in rural, economically depressed and innercity areas."

Teutsch said the mortgage insurers' finding that one-third of the FHA loan volume in 1986 went to borrowers refinancing their existing mortgages was not unusual. "Refinancing activity in 1986 represented about 35 to 40 percent of all mortgage lending, not just that of FHA," he said.

But the mortgage insurers association said the wide gap between the perceptions of how the FHA works and how it actually performs should be narrowed.

Another portion of the report noted that borrowers with incomes of $40,000 or more who make less than a 10 percent down payment default on their loans several times as often as those with lower incomes who make similar down payments. "Some lower-income borrowers are, in fact, subsidizing many higher-income borrowers," the study said.

"The FHA should help homeownership among people that the private industry isn't reaching," said Gregory T. Barmore, president of the General Electric Mortgage Capital Corp. "If {the FHA} isn't reaching them, then why have an FHA?"