Geico Corp. reported yesterday it sold off some of its old low-interest bonds at a $17 million loss and sacrificed third-quarter profits to improve its investment portfolio and cut its income tax bill for the year.

As a result, net income for the Bethesda-based insurance holding company plunged to $3.9 million (19 cents a share) from $17.2 million (79 cents) for the quarter ended Sept. 30, and profits for the first nine months of the year slipped to $39.9 million ($1.92) from $51.8 million ($2.37).

Despite the drop in net profits, Geico Chairman John J. Byrne said, "the year continues to develop well for us" because operating income climbed to $21.3 million from $17.9 million for the quarter and is up to $56.2 million for the year so far from $49.6 million in the first three quarters of 1981.

Byrne noted that Geico early in the year said it planned to clear out its low-interest bond holdings at a loss so it could invest in better yielding securities. The losses on the sale of the bonds, he said, will offset the gain Geico made last year on the sale of its Gelico subsidiary and reduce the taxes Geico would otherwise have to pay on that deal.

One of Geico Corp.'s subsidiaries, Government Employees Financial Corp. of Denver, reported a profit of $580,000 (40 cents) for the third quarter, against a loss of $210,000 (25 cents) a year ago. Gefco posted earnings of $1.3 million (78 cents) for the first nine months of the year, compared with a loss of $50,000 (27 cents) in the same period a year ago.