To understand why executives of American Security Bank are closely following the confrontation between Great Britain and Argentina, you need only to open the bank's annual report.

There in tropical blue living color is the world's first floating polyethylene plant, anchored at a petrochemical complex in Bahia Blanca, Argentina.

"American Security Bank International (Nassau) participated in the financing of this plant," says the report, proclaiming the Washington banking company's expanding international operations.

The Argentine loan is not endangered by the dispute over the Falkland Islands, insists American Security Chairman W. Jarvis Moody, nor is the bank's risk any greater as a result of the economic sanctions imposed against Argentina on Friday by the United States.

The United States cut off future loan guarantees, but that action did not effect guarantees on existing loans, such as the plastics plant deal in which American Security has a stake.

The loan "is not non-performing and we do not expect it to become non-performing," stresses Moody.

American Security officials won't discuss details of the polyethylene financing, but they tacitly confirm banking industry reports that the bank has loaned about $17 million to various Argentine projects. Argentine deposits--if any--and accounts with the Argentine embassy here would add to the Argentine exposure.

With no annual report picture to reveal his hand, Riggs National Bank Executive Committee Chairman Vincent C. Burke Jr. has refused to say whether Riggs has any loans to Argentina.

Despite Burke's reticence at Riggs's recent annual meeting, it is known that Riggs, too, is exposed in Argentina. Riggs' loans there are not as big as American Security's, banking industry sources say.

The observable Argentine connection at Riggs is Jorge Carnicero, who was the largest stockholder of Riggs and chairman of the board before Texan Joe L. Allbritton took over the bank. Carnicero, the chairman of Dynalectron Corp. of McLean, is a native of Argentina and has world-wide business connections, both on his own and through Dynalectron. Carnicero's daughter, Jacqueline Duchange, is still on the Riggs board.

Although Argentine banking officials flew to New York two weeks ago to assure U.S. lenders that they will continue to make payments on their $30 billion in foreign debts, the conflict nonetheless raises the risk to lenders. As of January, the Federal Reserve Board reports, Argentina owed $8.6 billion to U.S. banks, including American Security and Riggs.

The risk is not so much that actual combat could spread from the Falklands to the Argentine mainland, but that a costly war will further damage the Argentine economy, already struggling with the world's highest inflation rate. Military or diplomatic disaster could also be fatal to the nation's ruling military dictatorship, adding political instability to the risks. iggs and American Security find themselves worried about war in the frigid South Atlantic, a hemisphere away, because both banks have aggressively built up their overseas business.

International expansion is one of the routes both institutions are taking to transform themselves from local to regional banks; both have off-shore subsidiaries to facilitate foreign transactions. Financial General Bankshares is expected to bolster its international operations now that Middle Eastern investors have taken it over.

Riggs's foreign lending has nearly doubled in the last three years, from $212 million in 1979 to $305 million in 1980 and to $402 million in 1981. American Security had $162 million in foreign loans at the beginning of 1981 and $217 million in foreign loans by year's end.

Neither bank has yet needed to take any remedial action because of the Argentine situation, but the war isn't over yet.

Financial problems apparently are more pressing for William Graf, publisher of the Business Review of Washington.

Employes complained that their paychecks bounced last week and Graf told them that a bank and the Internal Revenue Service had obtained new liens against him. Getting slapped with a lien is just one of the things that happen when you're in business, Graff told Washington Post researcher Anne Behrens.

There's no sign of a new bank lien in Fairfax County records, which show three old liens totaling about $7,000. The IRS and federal court officials in Richmond say a $13,346 tax lien was filed earlier this year, on top of a $27,440 tax lien last October.

The recession is hurting many publications, but Graf's Business Review faces increased competition on May 17 when Cordovan Publications of Houston begins publishing the weekly Washington Business Journal, link number 11 in a chain owned by the E. W. Scripps subsidiary.

A preview issue is out now, demonstrating Cordovan's product to prospective subscribers and touting the Washington market to prospective advertisers.

The preview promises to explode the myths of Washington, among them the "myth the District of Columbia is becoming a city of the very poor and the very rich."

That's no myth, according to the U.S. Census. "The city seems to be increasingly made up of persons at the opposite ends of the income scale," says Larry Long, acting chief of the Center for Demographic Studies of the Census Bureau. Census figures show the D.C. middle class plunged 27 percent in the last decade, while the poor population grew by 6 percent and the rich gained 4.1 percent, even though the definition of rich was doubled from $25,000 a year to $50,000. So much for myth shattering.