Looking at the stock market these days, you can scare yourself right out of your aggressive growth mutual funds.

Everybody from Federal Reserve Chairman Alan Greenspan on down worries that Internet-related stocks are at the center of a speculative bubble that could burst at any time.

In one fit of nerves in mid-March, the composite index of the Nasdaq market, where many computer and telecommunications stocks trade, plunged 11.7 percent in three and a half days.

At that rate, you could have a full-blown bear market in two weeks.

This tests the resolve of people who call themselves long-term investors. After an exhilarating ride up in a stock fund loaded with Internet and biotechnology stocks, the temptation gets very strong to try to jump off before all the gains vanish, and park the money someplace less adventurous.

The trouble is, even if that turns out to be a timely decision, what do you do next? One good market-timing move demands another, and once you start trading on emotion it’s no easy trick to stop. The more you trade, the more mistakes you’re going to make.

To earn your spurs as a long-term investor, you sometimes have to stick with your positions even when their short-term prospects look shaky. That means staying diversified, keeping some money in a safe haven such as a money-market fund, and making sure your stock funds own a broad range of stocks.

It also requires remembering why you’ve invested in stocks at all. For a pep talk on that subject, listen to Edward Kerschner, chief investment strategist at PaineWebber Inc., whose “highlighted list” of 30 stocks makes up the portfolio of the $2.1 billion PaineWebber Strategy Fund.

“The benefits of the Internet are for real,” Kerschner writes in a current bulletin to investors. “A sharp correction in the prices of some egregiously overvalued Nasdaq stocks were it to occur would likely not indicate the end of the bull market. The U.S. economy would continue to reap the benefits, namely a muted business cycle, productivity gains and low inflation.”

Kerschner’s picks at last report include no upstart little Internet or biotech companies, but several big computer and telecom stocks, among them Cisco Systems Inc. and Lucent Technologies Inc.

PaineWebber Strategy Fund’s shareholders are all new to the fund, having come aboard at its initial offering last fall. So it’s way too early for them to agonize over whether to stay in or cash out.

But in many other funds, investors are sitting on gains built up over a period of years. Take the hypothetical case of a $10,000 investment made several years ago in a fast mover like the $18 billion Janus Mercury Fund, which would have since grown to more than $60,000. The example sprang to mind because I own a few shares of Janus Mercury myself.

Under the management of 38-year-old Warren Lammert, a soft-spoken Clark Kent type who has been getting Superman-style results, the fund has returned an average of 36 percent a year since it opened for business in 1993. Assuming your wish to pursue long-term growth of your money hasn’t changed, a strong argument can be made for staying with a fund like this rather than cashing out now.

Could Lammert hit a cold streak? Sure, any manager can. In 1997, Janus Mercury rose just 12 percent, trailing the Standard & Poor’s 500 Index by 21 percentage points.

For the last five years, though, Janus Mercury’s average return beats the S & P; by 16 percentage points.

One of the services you pay for when you invest in a fund like Janus Mercury is management. If you don’t think Lammert can do well consistently in the future, maybe your money belongs in an index fund.

But if you’re impressed with what Lammert has achieved in the past, it’s illogical to fire him now because you think conditions might change.

Any time you invest in an aggressive fund like Janus Mercury, it makes sense to keep a close eye on it. It also makes sense to give the fund every chance to do its stuff.

Chet Currier is a columnist for Bloomberg News.