It probably comes as no surprise that this year's stagnant home sales have put many real estate brokerages into the red. What may be surprising is that the hardest hit are not Mom and Pop operations, but real estate franchises, and multi-office and corporate firms.

A study by the National Association of Realtors finds the average net firm income, before taxes, fell 22 percent from the average in a survey taken during the 1976-77 housing boom.

"The number of firms reporting losses [30 percent] was nearly twice as large as in the last survey," the association reports. "This is attributable to the adverse market conditions which prevailed during part of the [1979-80] year."

If the fees paid to firm owners, excluding commissions, are added to the net firm income, the profit decline since the 1976-77 study was only 9 1/2 percent, the report notes, and only 16 percent of the firms are losing money.

The portion of the company dollar left as pretax profits (gross income less sales commissions), dropped to 9.6 percent from 13.4 percent, despite a reported 23 percent increase in average gross income.

The expense that increased most was advertising, which represented 18.1 percent of firms' operating costs. That's up from 16.7 percent in the last report. Because broker expenses varied widely between firm type and region, "There is no one 'right' way to operate a brokerage firm and maximize the return to the owners," the Realtors study concludes.

Franchise firms, like Century 21 and Electronic Realty Associates, kept only 5.8 percent of the company dollar, compared with 11.2 percent held by nonaffiliated brokerages. Still, profits are down for both types of firms from the earlier survey, when franchised and nonaffiliated brokerages kept 12 1/2 percent and 13.6 percent, respectively.

While corporate brokerages showed a 5.9 percent profit before taxes, this was down from 11.2 percent in 1976-77. Noncorporate firms showed a 19.3 percent profit, down from 19.7.

Single-office brokerages showed an 11.7 percent profit, down from 14.8 percent in 1976-77. Multi-office firms had a profit of just 6 percent, down from 11 percent.

Realtor economists say they cannot explain why the larger firms have been hurt more than smaller ones during this turndown. They plan further study and will issue another report in several months.