Geico Corp. yesterday reported improved operating earnings for the latest quarter but posted lower net income because of investment losses.

The big insurance holding company's earnings for the three months ended Sept. 30 climbed to $17.9 million (83 cents a share) from $16.4 million (76 cents) in the same period a year ago. In contrast with a $1.7 million (7 cents) gain on investments last year, Geico Corp. lost $720,000 (4 cents) on its portfolio in the latest quarter. As a result, net income for the quarter fell to $17.2 million (79 cents) from $18.1 million (83 cents) in the third quarter of 1980.

For the year so far, Geico's corporate profits are running about 13 percent ahead of last year, a performance that Chairman John J. Byrne evaluated as "reasonably good."

Operating earnings for the first nine months of the year totaled $49.6 million ($2.27), up from $44.3 million ($1.90). Investment earnings are also up, to $2.2 million (10 cents) from $1.6 million (7 cents). Net income for the three quarters amounted to $51.8 million ($2.37) compared with $45.9 million ($1.97) in the same period a year ago.

Byrne predicted Geico Corp. will show a profit on its insurance underwriting this year "though not to our standards." He said property and casualty underwriting results improved in the third quarter, but he noted "a slowing rate of decline in the number of accidents reported by our customers may be signaling that accident frequency has bottomed."