Michael Kassen, the 33-year-old Harvard MBA who manages investments for the Fidelity Freedom Fund, has a wonderful problem: Individual investors are flooding him with $2 million a day to invest in the roaring stock market.

But that isn't entirely good news for Fidelity's Freedom Fund. Kassen's problem is that with so much cash flowing in and the stock market continually hitting new highs, he cannot always find stocks to buy at prices he likes.

"Are there any stocks that still make sense? There are, but it's harder to find them than it was three to six months ago," Kassen said.

Even so, Kassen trades almost every day. "I generally do it by making $6 million in purchases and $4 million in sales," he said. If need be, Kassen can let the cash build up in his fund instead of buying stocks. But that is not what his shareholders expect, he believes.

"If they wanted their money in a money market fund, they could have put their money in a money market fund," Kassen said. "I don't worry about 8 or 10 or 12 percent of the fund in cash. I would worry about 25 percent."

Kassen is not alone. With many individuals aggressively playing the stock market by investing in mutual funds rather than individual stocks, mutual fund managers across the nation are trying to cope with a similar flood of dollars.

"The Legg Mason Value Trust has been averaging $2 million a day of new money," said John Curley, president of the Baltimore-based stock fund. "Our cash balance in the fund is up to about 20 percent. We would be happy to be 100 percent in stocks if we could find investments that meet our criteria. The fact that we are 20 percent in cash means it is difficult in this market environment."

Mutual funds are hot. Americans are pumping more than $500 million a day into 1,531 mutual funds, the greatest torrent of money ever seen by the fund industry. A hefty chunk of these dollars is coming from contributions to Individual Retirement Accounts. Contributions to IRAs must be made by April 15 to qualify for a deduction on last year's taxes. See related story.

The appeal of mutual funds is clear: Rather than picking stocks on their own, individuals buy shares in mutual funds, which purchase diversified stock portfolios. In return for fees, mutual funds offer individuals professional money management. There is a seemingly endless array of stock and bond mutual funds, designed to meet investment needs ranging from current income to long-term growth.

However, even professional management doesn't guarantee red-hot yields for investors. In this year's first quarter, the average stock fund was up 14.2 percent, while the S&P average of 500 stocks was up 14.1 percent, according to Lipper Analytical Services. This was the first time since the second quarter of 1983 that the average stock fund outperformed the S&P. The closely watched Dow Jones average of 30 industrials was up 18.8 percent in the quarter.

The best performing mutual funds in the quarter were international stock funds, up 20.8 percent, and health care funds, up 18.3 percent. The worst performance was turned in by the natural resources funds, which dropped an average of 1.2 percent, as the price of oil plunged.

The recent popularity of mutual funds is due largely to plunging interest rates. Investors, dissatisfied with current rates on bank certificates of deposit and other conservative fixed-income investments, have been moving large sums into mutual funds, especially into bond funds.

For 1985, net mutual fund purchases (purchases less redemptions) increased to $80.6 billion, a quantum leap over the $25.8 billion invested in mutual funds in 1984. The net purchases of stock funds grew to $9.5 billion in 1985, up 21.6 percent over 1984, while net purchases of bond and other fixed-income funds in 1985 increased to $71.1 billion, up 294.2 percent over the year before.

Monte Gordon, senior vice president for research at Dreyfus Corp., estimated that, currently, two-thirds of the money flowing into mutual funds is going to bond or other fixed-income funds while one-third is going to stock funds.

Wall Street experts agree that stock mutual funds are having a positive impact on the overall stock market. However, some believe that mutual fund managers are impatiently and imprudently investing in stocks.

"I think they mutual fund managers have been chasing the market," said Howard Brenner, executive vice president and a director with Drexel Burnham Lambert Inc. "I think people have been in a rush to throw money into the market and that is why the market has moved the way it has. I think they have been impatient to get invested."

But Brenner quickly added that in a market dominated by giant insurance companies, pension funds and Wall Street firms, the trend toward individuals investing in stocks through mutual funds "is very healthy. That is what mutual funds are there for. To give individuals a way of participating in the market."

Alfred P. Johnson, chief economist for the Investment Company Institute, which represents the mutual fund industry, said that despite the huge flow of mutual fund dollars into the stock market, it was difficult to compare their impact on stock prices with the impact created by "a drop in inflation, a drop in energy prices, an influx in dollars from other sectors." The funds, he said, are, "only one player in a much, much larger market." The value of all stocks, he said, was $2.2 trillion at the end of 1984.

Even with the Dow Jones industrial average leaping 400 points in four months, it appears that many individual investors who once bought and sold stocks either have left the market or not returned after unhappy experiences in the late 1970s or early 1980s. Instead of buying several different stocks, brokers said, many individuals eager to profit during this bull market are buying shares in a variety of mutual funds.

Bob Chesek, portfolio manager of the Phoenix Series Funds in Hartford, Conn., thinks he knows why. "The typical broker has forgotten how to sell common stocks," Chesek said. "He recommends mutual funds and if the market goes against him, he can always point a finger at me the fund manager and say, 'Sorry, that guy made a mistake.' "

Chesek, whose relatively small funds draw about $5 million a week, is raising his cash level to about 15 percent. "I'd rather invest with the market going down," he says. "On a valuation basis, I'm uncomfortable with the market but I can't fight the tape."

The mutual fund industry has undergone significant changes during the past 40 years. In the 1950s and 1960s, stock funds predominated. From 1968 to 1974, according to an ICI history, a volatile stock market, rising interest rates and economic problems led investors to leave stock funds and head for the relative safety of CDs and other short-term liquid assets.

The mutual fund industry responded by creating money market funds and new versions of stock and bond funds, which continue to be popular. In 1985, money market funds made up 41.9 percent of the assets of all funds. That was down from 56.6 percent in 1984, as money shifted into higher-yielding investments.

The growth of the mutual fund industry is reflected in the number of new funds. In five years, stock, bond and income funds grew from 486 to 1,071 and money market and short-term municipal bond funds swelled from 179 to 460, according to the ICI. Income funds include government securities funds.

At the end of 1985, the ICI counted almost 35 million shareholders in all funds, of whom 57 percent were in stock and bond and income funds. Some mutual funds are making a major effort to persuade shareholders to open multiple accounts.

"In the financial services business, the customer with multiple accounts is less likely to leave," said one fund official.

In an effort to maximize returns to investors, the mutual funds have developed broad international portfolios and narrow sector funds, which deal with single industries such as health, savings and loans and the brokerage business.

Prudential-Bache, which has its own group of mutual funds, typifies the industry trend to move overseas. In its new First Australia Prime Income Bond Fund, Prudential-Bache seeks to wring high returns from debt securities in Australia and New Zealand where, in a "reverse-yield curve," short-term rates are higher than long-term rates. Australian short-term rates are running at about 16 percent and are higher in New Zealand. However, investments in the closed-end fund run the risk that changes in the value of the Australian and New Zealand dollars, relative to the U.S. dollar, will diminish returns.

Even as some exotic funds appear on the investment scene, James P. Freeman, co-head of stock sales and trading at First Boston Corp., believes the mutual fund boom has been positive for individuals. He hopes the mutual fund industry will not repeat the boom and bust of the late 1960s and early 1970s.

"Mutual funds are an exceedingly efficient way for individuals to invest," Freeman said. "Even among people who know a helluva lot about the stock market, there is a tendency to buy mutual funds and pack 'em away.

" . . . I think this is very different from the middle and late 1960s when there was a great deal of speculation, sort of forcing fund managers to become more and more aggressive. That ended up killing the goose that laid the golden egg. I hope it will not recur. . . . "