President Reagan, displaying his usual unbridled optimism, welcomed his newest Cabinet choice, Nicholas Brady, to "what just might be the most active six months of our administration."

But analysts said they will be very much surprised if the New York investment banker serves as anything but a caretaker treasury secretary in the administration's closing months.They said they expect no new policy initiatives and predicted that Brady's only task will be to make sure nothing derails the economy and jeopardizes George Bush's election chances.

Brady, co-chairman of Dillon, Read & Co., a Wall Street investment house, was nominated by Reagan on Friday to replace Treasury Secretary James A. Baker III, who is stepping down to take command of Bush's presidential campaign.

The president waited until after the financial markets had closed to make the announcement to minimize the impact. But Baker's impending resignation and Brady's selection had been open secrets for weeks and the markets had taken both in stride.

Analysts said Brady's basic goal will be to make sure that the government doesn't do anything inadvertently to unsettle financial markets.

"The main objective is to keep things stable and prevent any mistakes that would look bad for the Bush campaign between now and November," said Michael Penzer, senior economist at Bank of America in San Francisco.

Because he served briefly as a senator from New Jersey, Brady is expected to win easy Senate confirmation, but he will not take office until mid-September at the earliest, after the required background checks and hearings are completed. Until he takes over, the Treasury will be run by M. Peter McPherson, the deputy secretary.

Brady is expected to be in place in time to represent the United States in September at meetings of the World Bank and International Monetary Fund in West Berlin. The finance ministers of the world's seven largest industrial countries will also convene at that time to review developments since the Toronto economic summit.

"The blunt fact is that nobody is particularly concerned about what this administration has to say. The world is waiting to see what the new administration does," said Robert Dederick, chief economist at Northern Trust Co. in Chicago.

There is always the chance that Brady will be called upon to deal with some unforeseen market crisis, similar to last year's October crash.

But analysts say that with his long background on Wall Street, Brady is well equipped to handle such an occurrence. In fact, Brady was the man the administration turned to after the Oct. 19 crash to head up a fact-finding group to recommend reforms.

The Brady commission called for major changes in the financial market regulatory structure, recommendations that were largely ignored by the free-market administration. However, Brady is not expected to try to change the administration's position on this issue.