A large Washington compay, Geico Corp., is the midst of an exchange offer to its stockholders that raises a fundamental question about investment strategy that each owner of stock must answer -- and within a week.

Geico, the new parent company of Government Employees Insurance Co., has offered to exchange $50 million or more of debentures for current shares of common and convertible preferred stock.

The offer expires at 5 p.m. one week from today, unless extended.

According to investment firm salesmen and Wall Street analysts, Geico's current investors are faced with a tough decision.

On the one hand, they are being offered debentures with a very high yield of 11 percent. Semiannual interest payments will be made in March and September.

As Geico Corp. Chairman John Byrne told stockholders in a letter enclosed with the exchange offering, owners who decide to pick the debentures are locking in a stable interest income equal to $1.10 a share of common tendered and $2.20 a share on preferred. This contrasts with 32 cents a share on common stock (based on Geico's current quarterly payout rate of 8 cents a share) and 73.6 cents on the preferred stock.

Stockholders who decide to hold on to their common and preferred shares, on the other hand, are looking to the future and betting that longterm appreciation in the value of their shares plus possible dividend increases will add up to more than the debenture yield -- at least at the point they may decide to sell in the future.

According to Paul Schlough, of Legg Mason, Wood Walker Inc., in Baltimore, "One would have to change their mind" about basic reasons for investing if a decision is made to buy the debentures -- which he described basically as an "income vehicle" -- in place of the stock, an equity holding in the company which many brokers recommend as speculative and designed for "aggressive" investors.

"The purpose of their investment would have to change drastically," he added. "You really have to think about it... how do you want to put your money to work?"

Noting tha Geico Corp. investors could have sold their stock and bought steady income-producing investments at any time in recent months, it would be an "odd switch" to change to the debentures now the analyst said.

Donald Franz Jr., of Smith Barney, Harris Upham & Co., said he thinks the offering will be oversubscribed, despit the switch in investment strategy implied.

Older persons seeking the guaranteed, steady income and not anxious to gamble on future stock prices may be among those who want the debentures, several brokers said.

About 41 percent of Geico Corp.'s 13,000 common stockholders, reside in the local area, holding some 23 percent of 18.6 million shares outstanding. In addition, about half of the owners of preferred stock also live in the area, and they control about 10 percent of those shares.

In recent days, many of these stockholders have been deluging stock sales people with letters and telephone calls, all asking what whould be done. What follows, based on interviews and details from the company's published documents, are some questions and answers about the offering.

Question: Why is Geico Corp. making the offer?

Answer: According to Byrne, the firm's board of Directors "believes that a successful exchange offer will improve the financial results of your company as it begins opertations under the new corporate structure."

The offering states that the principal reason is to reduce the number of shares outstanding. If successful, one result would be an increase in reported per-share profits. With fewer shares available for trading, a stock issue generally becomes more volatile -- with greater swings up or down, often attracting investment interest.

Q: What is the offer?

A. Geico Corp. will exchange $10 of its new 11 percent debentures, maturing in 1999, for each outstanding share of common stock and $20 of debentures for each share of convertible preferred stock. Interest on the debentures would begin to accrue on April 1.

Q. Has the company set a limit on how many shares it will exchange for the new debentures. ?

A. Geico Corp. will buy up to 5 million common share equivalents (common shares plus the common shares resulting from conversion of the preferred stock) but may decide to exceed that limitation.

Q: What is the company's advice?

A: Each owner must decide for themselves and they should consult their investment adviser, Byrne says. He cautions that the exchange will be a taxable transaction and that trading for the new debentures is not expected "to be as active as the markets for either our common stock or our convertible preferred stock."