Nicholas F. Brady, selected by President Reagan to head an investigation into the causes of last week's stock market collapse, is a veteran investment banker who has been a firm opponent of the debt-driven corporate takeovers that many say contributed to the plunge.

Brady has been outspoken in criticizing the use of risky, high-yielding "junk bonds" to finance corporate takeovers, arguing that excessive debt has added too much risk to corporate balance sheets and to the nation's financial system.

The wave of corporate takeovers, restructurings and stock buybacks financed with borrowed money has been a contributing factor to the dramatic rise in stock prices in recent years; Brady said in an interview that as part of his stock market study he intends to examine why "there was a worldwide overvaluation of equities {stocks}."

In testimony about takeovers before the Senate Banking Committee last January, Brady said, "many have also sensed there was something tilted about a game in which the same group of raiders, arbitrageurs and bankers attack one company after another, reaping profits without ever seeming to take risks or losses. Something was just not right."

At the hearing, Brady made specific recommendations for changes in securities laws, such as a definition of illegal, insider stock trading, but concluded that as far as landmark legislation was concerned, "I truly believe it ain't broke so don't fix it."

As an investment banker, Brady has been on the side of blue-chip corporations, helping them arrange financings and defending them against hostile takeover attempts. While many of Wall Street's investment banks have pursued takeovers and other transactions at the expense of such relationships, Brady has relied more heavily on ties with corporate leaders built over many years.

He handled the takeover defense for Unocal Corp., for example, after that company became the target of a debt-financed hostile takeover bid from T. Boone Pickens Jr. in 1985.

Brady fought hard against Pickens, saying, "Let's not have drunk driving and speeding on our financial highways. We are, by saying there is no limit to what the shareholder can do to maximize wealth, ignoring every other part of the system."

As it happened, Brady was flying back from the Far East on Black Monday, Oct. 19, as stock markets around the world were tumbling like dominoes, and he watched from a London hotel room as the shock wave hit Wall Street.

"One of the things that astounded me about the 500-point drop was the fact that, being in London as I was, you could go back to your hotel room and pick up CNN {Cable News Network} and sit there and watch the world markets buzz around you," Brady said.

"I had been in China and arrived in London on Monday morning. It took me about an hour after arriving to see that London was in a tailspin and then New York opened in a tailspin. That is all very new."

And then, turning to two of the critical issues he will study for the president, Brady asked: "When New York gets a headache, does Tokyo get a stomach ache? Why so much compressed into so short a time?"

In selecting the 57-year-old Brady to oversee the study of the stock market collapse, Reagan picked a Republican who could help to bridge the gulf between Wall Street and Washington. Brady has spent almost his entire career on Wall Street, joining Dillon Read after receiving his M.B.A. from Harvard Business School in 1954.

In 1982, Brady, a close friend and confidante of Vice President George Bush, developed many new and important political ties in Washington when he filled the unexpired term of New Jersey Sen. Harrison Williams, who resigned after he was convicted in the Abscam scandal.

Brady said he intends to complete his study of the stock market within 60 days. While the investigation into the stock market collapse is the first study Brady has directed for the Reagan White House, he has participated in others, including a 1983 Central America study headed by former secretary of State Henry Kissinger.

Two other members of the Brady commission are expected to be named by the end of the week. Brady said that because of the enormous role that computers appear to have played in stock market volatility recently, he wants one of the members to have special expertise in computer technology. He said he wants the other member to be someone who can represent the interest of small investors.

The executive director of the staff of the commission is likely to be the head of the finance department at one of the leading business schools, Brady said, adding that there is a tremendous amount of data to be gathered and examined in a short period of time and he wants it analyzed using a business school case study approach.

Brady said he also wants the executive director to be someone who understands the financial theories that underly the existence of some of the new financial instruments that may have played a role in the stock market collapse.

The Brady commission will operate out of New York, he said, drawing its staff from the financial and academic communities, as well as from consulting firms and other fields where there are experts at data collection and analysis.

Brady, who is the chairman and cochief executive officer of Dillon Read, said his final product should include recommendations for reforms, if he develops any.

"The root cause was that equities {stocks} got too high," Brady said. "It is the fact that the fall was in such big dollar magnitude with such rapidity and with such volatility that is different. Maybe the answer is that that is the way the world is now."

Politicians from both major parties and other Wall Street executives have praised Reagan's selection of Brady, although some reservations have been expressed privately about his views on takeovers and other activities that have relied heavily on borrowing.

Brady is not heading the only panel analyzing stock market volatility and the recent collapse. The financial markets and regulatory agencies are working on studies of their own.

Securities and Exchange Commission Chairman David Ruder said yesterday a study by the SEC should be completed within 60 days, about the same time that Brady finishes his work.

The Commodity Futures Trading Commission, which regulates trading in stock index futures, also has launched a study. Former IBM general counsel Nicholas deB. Katzenbach is heading an NYSE study about stock market volatility and the collapse that he hopes to complete before the end of November.

The Chicago Mercantile Exchange announced yesterday that it has appointed a panel of four experts to assist CME officials in examining the Oct. 19 collapse. The members of the panel are Yale economics professor Burton Malkiel, University of Chicago banking professor Merton Miller, Stanford University professor Myron Scholes and John O. Hawke Jr., an attorney with the Washington law firm of Arnold & Porter.

Meanwhile, Brady said he has had an enormous number of volunteers to assist him in his study of the stock market for the president.

"There is a curiosity as to what happened," Brady said. "This is a new frontier."