There were some sighs of relief at the Bank of Boston this week. A center-of-the-road government was elected peacefully in Argentina Sunday, enhancing the prospects for steady handling of that nation's severe economic problems and huge international debts.
According to a memo circulating at the bank, the management of its affiliate in Argentina, Banco de Boston, was ''very happy with the results of the election.''
The Argentine development is good news for Richard D. Hill, both as chairman of the Boston-based international bank and as the newly elected chairman of the Institute of International Finance (IIF). This body has launched in the last few months a program for helping its membership of 180 commercial banks from 39 countries deal with the problem of their massive loans to non-OPEC developing countries and East European nations. These nations owe more than $110 billion to American banks.
The Bank of Boston, one of the more conservative of the American international banks, has good reason to be interested in the IIF. It owns the largest foreign bank operating in Argentina, the Banco de Boston, with 21 branches. The US bank's Argentine ''exposure,'' as bankers call their uncovered loans in another country, is about $250 million, equivalent to about 26 percent of the bank's capital. It also has large exposure in Brazil, Mexico, and other Latin nations.
Total exposure of US banks in non-OPEC developing and East European countries has risen from 131.6 percent of capital in 1977 to 155 percent last year. If five OPEC countries not rolling in surplus oil money (Algeria, Ecuador, Indonesia, Nigeria, and Venezuela) are included, the 1982 exposure stands at 182 .8 percent of capital. In other words, should all these nations default completely on their loans - extremely unlikely - many American banks would be in trouble.
The position of major banks in Western Europe and Canada is similar.
Mr. Hill, in an interview, said that the debt situation ''looks a lot better'' than it did a year ago. ''Many things have been accomplished.'' The Mexican situation has ''improved substantially.'' A Brazilian settlement ''seems to be in hand.'' These two nations, plus Argentina, make up the Big Three of Latin debtors.
Default, Mr. Hill reckons, ''is probably less likely now than it was.'' In addition, the banks have now fully launched their ''private-sector initiative'' - the IIF. The general purpose of the institute is to make the banks ''better international lenders.''
It intends to do this, Mr. Hill continued, by gathering ''more information than we have been able to get up to now'' about the international loans and economic position of debtor nations. Further, the institute hopes to get invited by borrowing countries to send a ''visitors group'' to review their economic and loan policies and make suggestions.
He noted that the International Monetary Fund (IMF) sends ''missions'' to countries with extreme imbalances in international payments. ''We hope to do it as a routine measure. We want to help borrowing countries so they don't get into a bind.'' Of course, that means the lending banks also do not get into trouble.
Finally, the institute plans to sponsor seminars on the future of bank lending to the developing world.
The institute has its origins in a small gathering of bankers in May of 1982 at Ditchley Park, just outside London. Now it has a managing director, Andre de Lattre, a former deputy governor of the Bank of France, and a temporary headquarters, and it plans to move to a permanent office at 2000 Pennsylvania Avenue, Washington, down the street from the White House.
So far the membership of the IIF collectively represents banks holding more than three-quarters of the world's total debt of non-industrial countries. Mr. Hill expects further banks to join as the new organization proves its merit, especially smaller banks.
The institute started collecting information in June on 25 to 30 countries. The data will be made available to member banks through data services, and also perhaps in printed form. The institute hopes to have more up-to-date and available data than that compiled by the IMF, the World Bank, or the Bank for International Settlements, in Basel, Switzerland.
The data will include total loan exposure, maturities of debts, balance-of-payments figures, international monetary reserves, percentage of exports needed to cover debt service charges, and so on. This information is expected to be especially helpful to the smaller banks with small or no research departments.
William R. Cline, an economist with the Institute for International Economics , also in Washington, has described the IIF as a ''promising vehicle for improving the organization of bank lending.'' In a major study, he has also concluded that the debt problems of the developing countries ''should be manageable and should show considerable improvement'' if the industrial countries should grow at a 3 percent annual rate in 1984-86, therefore sucking in more imports from the poorer nations. The latest data here in the United States and abroad offer some hope for such growth. Thus Mr. Hill's IIF may face less troublesome times ahead than is generally anticipated.