One day in December 1981, a computerized notice from Government Employees Insurance Co. arrived at the home of John J. Byrne, informing him that his three sons would no longer be carried on his automobile insurance policy. The letter was signed by Geico Chairman John J. Byrne.

Policyholder Byrne reacted like many a parent of college students in a similar situation. "I told them they had to go find their own insurance; they had a tough time."

But chairman Byrne did something else; he decided to establish a new insurance company just for high-risk, young, male drivers who have difficulty getting coverage in the voluntary market. Now, after 18 months gestation, Criterion Casualty has just taken on its first policy holder.

Writing substandard insurance is just one of the new business ventures Geico has undertaken in recent years under the stewardship of 51-year-old "Jack" Byrne who took the helm in the stormy days of 1976, when the company's very survival was threatened. Byrne has since guided Geico back to calm waters.

The parent company, Geico Corp., now enjoys a surplus in excess of $300 million. Since its main insurance business--auto coverage for good drivers--does not need extra capital now, the challenge to Geico management is how to utilize it. "That's the one thing I'm responsible for," said Byrne in an interview last week.

"They don't give me much to do any more," he added with self-deprecating humor. "Bill Snyder president and chief executive officer of Government Employees Insurance Co. runs the best insurance company in America; he doesn't need me. And Lou [Louis A.] Simpson senior vice president and chief investment officer , who invests the money, he doesn't pay any attention to me.

"So I just sit up here and try to figure out what we do with the capital that we're not using. It's an extraordinarily complicated question."

With the same dry wit, Byrne said he thought William Agee, chairman of Bendix Corp., had found a smart solution last spring when he advocated leaving the funds in a passive investment portfolio. He was so impressed he distributed Agee's ideas to all his officers. "Three months later, he did just the opposite and went out and shot himself in the foot," Byrne added, referring to the unsuccessful bid for Martin Marietta that led to Agee's ouster.

Will Jack Byrne also shoot himself in the foot? Ask financier Warren Buffet, whose holding company Berkshire Hathaway owns one-third of Geico's stock. Buffet, according to Byrne, was asked at a board of directors meeting if he had any anxieties about the company. He responded by quoting the 17th century French philosopher Blaise Pascal , who wrote, "I have discovered that all human evil comes from this: man's being unable to sit still in a room." Then Buffet added jokingly, "Jack Byrne is unable to sit in a room by himself and someday he's going to shoot himself in the foot."

Byrne may be unable to sit still, but Geico stockholders and Wall Street analysts don't seem to be holding their fingers in their ears waiting for the bang.

Since the expansion activities began, the company has enjoyed good earnings. During the first half of this year, profits climbed to $74 million ($3.47 per share), double what they were last year in the same period. For Byrne, who left Travelers Insurance Co. to join Geico in a year when the company lost $26 million, the company's new profitability also means a share of the earnings. In 1981, he was the highest paid executive in Washington, earning $2.3 million in salary, stock options and bonuses.

Analysts remain bullish on Geico stock and expect the company's surplus to rise to $500 million to $600 million within two years. Geico could return some of the excess to shareholders in the form of increased dividends or by creating a leveraged, closed-end investment trust. Byrne, who abides by the motto "raise the dividend rate only when all else fails," elected instead to anounce a tender offer last week to buy in up to 1,050,000 shares of Geico, thus raising the company's return on equity.

Preference for capital normally would go to the preferred risk automobile business, which accounts for 90 percent of the parent company's business. But at this stage, Geico's main business doesn't need more capital to make it better. It is now growing at a rate of 7 percent to 8 percent a year and the rate is not expected to increase much, according to Byrne.

Back in 1973, Geico got into trouble by writing too mny risky insurance policies and letting costs soar. After Byrne took over, he cut personnel and the number of policyholders and set down a guideline calling for a 5 percent pretax profit on every premium dollar. The company dropped from the nation's seventh largest auto insurer to tenth as a result of this strategy.

Recently, the company decided to modify its profits-over-premium growth approach, which Byrne admitted had not worked as well as anticipated. Geico is prepared to accept a slightly lower profit on its older policies, resulting in lower prices, to attract more customers.

Rather than lower its underwriting standards--the morass into which the previous management fell--Geico is now expanding into insurance markets other than the preferred risk category. In the past year, Geico General (previously named Equitable General) has begun to write personal auto insurance that doesn't meet its tougher standards. And Criterion Casualty--the brainchild of the frustrated father--has begun serving the substandard market. Byrne said he believes there is money to be made in high-risk insurance so long as the company is careful to segregate the drivers by category and build the same percentage of profit into each operation.

Geico also seeks geographical expansion. "We are highly conscious of the fact that our core business is concentrated in the Northeast corridor, and that's dangerous," said Byrne. About 70 percent of its business is in the District of Columbia, Maryland and Virginia. In an attempt to achieve this expansion, Geico tried recently to get the American Association of Retired Persons contract to expand its coverage but lost out to the Hartford Group.

Byrne's strategy for utilizing extra capital involves an A list and a B list. The former identifies all enterprises directly related to Geico's core business of providing low-cost, direct-sale automobile insurance to consumers. The latter includes everything else.

High on the A list is life insurance. For a number of years, Geico had increased its interest in Government Employes Life Insurance Co. (Gelico), but was unable to buy the remaining 35 percent of the company. After two years of futile negotiation, Geico lost out to a British company that purchased Gelico in December 1981. Sad as he was to lose Gelico, Byrne acknowledged that it was perhaps a blessing in disguise, for it enabled Geico to set up what he called the insurance company of tomorrow, unencumbered by yesterday's business.

The parent company is putting $25 million of capital into a new entity, Geico Annuity and Insurance Co. It will sell no whole or ordinary life insurance, the mainstay of the industry for many years. Instead, President Herbert L. DePrenger and Vice President Richard A. Ollen began last spring to test market the direct sale of variable low-cost annual renewable term insurance in the greater Washington area to professional persons earning $35,000 or more.

Minimum coverage is $100,000, but most people buy more. The first-year premium for a $250,000 policy for a 40-year-old, non-smoking woman amounts to $280.

A year ago, Geico acquired and moved to Washington an old-line insurance company, Garden State Life of New Jersey, for its existing licenses and ratings.

Also on the A list is Geivest, an investment management company headed by Ollen. It provides administrative services for Government Securities Cash Fund, a no-load money market mutual fund. It has grown in its first year of its existence to $100 million in assets. Two municipal bond funds are now in registration.

At the top of the B list is Government Employees Financial Corp. (Gefco). The parent company acquired the remaining third of the Denver-based company last April for about $8 million. Gefco owns the largest industrial bank in Colorado and also provides consumer finance services. Through a subsidiary, it offers time-sharing contracts on condominiums in the West. The Florida time-sharing operation is being shut down due to excess competition, Byrne said.

Like most consumer loan companies, Gefco has been through some hard times. Because Byrne believes the unsecured loan business will be mediocre over the next decade, he has turned to lending money on secured, second-mortgage loans. Gefco now has $130 million of receivables in secured loans. The potential for consumer-oriented products using the industrial bank's deposit facilities appeals to Byrne, but the idea has not yet germinated.

Byrne admits he was anxious to complete the Gefco acquisition "to bring the family together." When he took over in 1976, Geico, Gelico, Gefco and Criterion were owned by four sets of stockholders, although they shared common officers. Byrne declined to work for more than one set of stockholders. "The family" is now united under his parental hand.

The aviation insurer Avemco, on the other hand, represents just an investment for Geico. The cash-short insurer this summer asked Geico to increase its stake in Avemco from 22.5 percent to 33.3 percent at a cost of $8.4 million. Byrne said he fully expects Geico will continue to be a passive investor for the next 50 years.

Resolute, Shippan and Polaris may sound like the name of a rock group, Byrne said, but they are actually names of companies though which Geico has a $25 million stake in the reinsurance market.

The Resolute Group, located in New York, writes treaty and facultative reinsurance in domestic and international markets. Geico recently bought a 22.5 percent interest in Polaris Syndicate Corp., a member of the New York Insurance Exchange, and a 9.9 percent interest in Shippan International Insurance Co. Ltd. of Bermuda, which reinsures coal miners. Geico also formed a Netherlands Antilles Co. earlier this year when it was toying with the idea of launching a Eurodollar debt offering.

Unlike the giants Sears, Roebuck and Prudential-Bache, which are rapidly expanding into many types of financial services, Byrne said Geico prefers to find its own niches. For that reason, he recently turned down a proposal from an investment banking firm that Geico take over a broker. "I don't know anything about brokerage," Byrne objected. "It's a step too far afield." Nevertheless, he did not rule out the possibility at some undetermined time.

On his future plans, Byrne seems like a juggler, keeping many balls in the air without giving an observer a clue as to which one he will catch. Last March, the juggler gave a clue to the future in a Wall Street Journal article in which he at least identified the balls: possible purchase of a life insurance company, amalgamation with a large property-casualty insurance company, and establishment of a mutual fund. For this, Byrne noted, his staff permanently retired the Geico "Foot in Mouth" trophy in the chairman's office.

Asked how he envisaged Geico's structure five years hence, Byrne paused and said he would be "awfully surprised if the allied services on the B list amounted to more than 10 percent of the company." He added, "Our investment bankers bring us two or three development ideas a week. But it may be that the lesson we find in exploring them is that it is far better for us to invest our capital and our energy in businesses very close to our core business."