The days of relatively cheap money for home mortgages are gone forever, says the new president of the Federal Home Loan Mortgage Corp., Kenneth J. Thygerson.

In a breakfast meeting yesterday with reporters, Thygerson indicated that a three-year transition to higher mortgage financing costs is over, and consumers will have to get used to the idea of paying interest rates that are profitable for investors.

With the deregulation of the thrift industry, there will be no return to mortgage rates below what investors demand in the marketplace, he said. Mortgage instruments will have to be developed to lure pension funds, foreign investors and other untraditional sources of money into the mortgage market, he added.

Thygerson also predicted that mortgage rates are now about as low as they will go anytime soon. It will take two or three years of low inflation and smaller federal deficits to get back to single-digit mortgage rates, he predicted.

Up until deregulation started in the late 1970s, the treatment of housing was too preferential, he contended. "Housing was getting not only its fair share but a preferred position, and it was coming out of the hides of savers," he said. "It was not a fair game being played."

Thygerson also said:

* Freddie Mac has "shelved" its legislative attempt to become a private organization and will stay under the federal government's wing.

* The mortgage market in the future will be divided into three categories of short-term, medium-term and long-term financing. More consumers in the future will be willing to take the higher risks of short-term financing, such as adjustable-rate loans, in exchange for lower rates, he contended.

* With rates having dropped, a record volume of refinancing is occurring. Freddie Mac bought $200 million in mortgages in a single week this month, the highest level for any week in its 11-year history, and most of this probably was refinanced mortgages, he said.

* The number of mortgage instruments should be standardized to five or six rather than the hundreds of variations now springing up.

* He has "real reservations" about graduated-equity mortgages (GEMs) because people can accomplish the same purpose of reducing outstanding principal by making early payments on ordinary mortgages.