RICHARD ROSENBERG, chief executive officer of BankAmerica Corp., knows well that a bank does not print its own money, but has to earn it. At the end of this year, when Mr. Rosenberg leaves his post as CEO - a position he stepped into in May 1990 - he will turn over the helm of a bank that has not only recovered from a string of bad losses in the mid-1980s, but has also gone on to diversify into greater strength than before. Rosenberg joined the San Francisco-based institution as head of retail operations in April 1987. It was the third consecutive year of startling losses for a bank that, until then, largely had had a history of growth since its founding in 1904. He was brought in to turn around the retail area, and he won praise in the bank for his success. ''We are now the 23rd- largest bank in the world in terms of assets, but in terms of profitability, we are third [among the large banks],'' Rosenberg noted in a recent interview in his 40th floor office overlooking the blue-green waters of San Francisco Bay. ''The critical thing in measuring banks is their profitability.'' When the merger of Chemical Banking Corp. and Chase Manhattan Corp. in New York has been completed, BankAmerica will become the US's third-largest bank. It will trail the newly merged Chase bank and Citicorp of New York. Today BankAmerica is the most profitable of these big banks. Bank-stock analyst George Salem agrees that the bank is a big moneymaker. He estimates that its earnings will grow between 10 and 11 percent this year and for each of the next two years as well. Given the bank's diversification and earnings potential, ''we have rated it a buy,'' says Mr. Salem, an analyst with New York-based Gerard Klauer Mattison & Co. The new CEO will be David Coulter, who has been in charge of the bank's large American corporate clients as well as international clients around the world. Mr. Coulter, who joined the bank in 1976, has a background in investment banking. Will Coulter push his bank toward more acquisitions? He says no. But he has a caveat. Any solid chance to expand services will be looked at ''in a hard-headed way.'' He finds the price for merger candidates today is usually too high. But he mentions Texas as an area where the bank might want to pick up a partner. Meshing operations and management is never easy, he adds. BankAmerica, Coulter says, will focus on keeping costs down and growing in its existing markets to increase revenue. ''The key for any company today,'' he says, ''is to ask, 'How can we do it better?''' After buying Security Pacific Bank in 1992, the bank reduced staff by 11,000 over the next year and closed 512 branches. This and other changes cut annual costs by $1.2 billion. Especially after its problems in the 1980s, it has worked to cut its expense/revenue ratio. In the mid-1980s, Rosenberg says, the bank first had to recover its traditional market - consumer or retail banking - which started to slip away through bad loans, loss of market share, old technology, and an unfocused effort. Today, BankAmerica has assets of $226 billion and yearly earnings of more than $2 billion. Its second-quarter earnings of $1.56 a share were 17 percent above the same period a year ago, while net income was up 23 percent. BankAmerica has taken other measures to strengthen the bank, including diversification, Rosenberg notes. His bank garners roughly 50 percent of its earnings from California, and 50 percent from outside the state. Half its earnings come from the consumer (retail) business and half from corporate business. Its retail operations are concentrated in Western states; its corporate lending is national and international. Rosenberg says the US waited too long to allow interstate banking, and the geographic and product diversification it permits can make banks, and hence the nation, much less vulnerable to economic downturns. ''Healthy banks make for healthy economies,'' he says, ''and we now seem to have recessions that roll across the country by region; a diversified bank can stay relatively healthy in a recession and thus help its community come back sooner.'' BankAmerica's profits grew during the last US recession during which California was hard hit. New England in the last recession, he says, is a classic case of banks and regions in deep trouble at the same time, making it harder for an area to recover through strategic loans and other banking services. The bank has invested heavily in electronic banking, a major cost-cutting step. Some 60 percent of its customers never set foot in a bank, Rosenberg says. In California, customers do 36 million transactions a month on automated-teller machines. Like other institutions in the diverse financial industry, BankAmerica must struggle to attract the savings and investment funds of its customers. As do other bank-holding companies, it owns and operates its own mutual funds as a draw for customers - a fast-growing area for the bank. BankAmerica is the only global bank west of New York City. It offers a wide array of services to US international companies, and to foreign corporations and governments. It provides retail banking to citizens in such areas as Taiwan, Hong Kong, Singapore, and the Philippines. It is also very active in Latin America. Rosenberg and Coulter say Asia is a vital and growing market for BankAmerica. It has offices in all the major Asian cities. It set up in mainland China and Vietnam as soon as the US opened the doors in those nations. ''Asia offers better profits than Europe and is much more dynamic,'' Rosenberg says. ''US banks - the top several global players - are in many ways ahead of their competitor banks'' from other nations in offering diversified services, Coulter states. He explains that the bank has ''relationship managers'' who are assigned to large corporations with worldwide activities. These managers do more than just sell products. They assist US and foreign corporations worldwide in solving the many kinds of financial and business problems that come along. ''We build a broad, deep, creative relationship, offering multiple products in multiple locations,'' he says, perhaps recommending selling off parts of a business, or leasing rather than buying property in certain areas. BankAmerica's cash-management services are growing quickly, Rosenberg adds. The bank can collect and disperse cash for an international corporation anywhere in the world, handle exchange-rate needs, and invest and manage money for firms. As the US moves into the international economy, Rosenberg and Coulter stress that a bank such as theirs should be large enough to offer capital and human resources, and telecommunications-based services in a number of offshore locations.