Millions of Americans are caught in this bear market and terrified. Those nearing retirement, or with children approaching college age, may be especially worried about the dangers of a prolonged downturn. Will there be enough time for your funds to recover, even if and when the market eventually turns?

If you're in this trap, here's one thought: It may not be too late to switch from many higher risk stocks to lower risk, more stable ones.

Oddly enough, this market slump has so far carried them down with the rest. And that means they may offer a far better balance of risk and reward than other investments.

Our ally here is one of the most cautious – and successful – investors around: Fund management legend Jeremy Grantham, chairman of Grantham, Mayo, Van Otterloo & Co. in Boston.

Grantham has been successfully navigating markets for decades. He was among those who predicted the recent crisis before it happened, rather than after the fact.

Right now, he thinks worldwide stock markets have further to fall, and at this point he is so bearish he wants to stick his money in the mattress. "I'm long the mattress," he jokes.

That says, he still likes, at least in relative terms, high-quality U.S. stocks: big, blue-chip companies with solid balance sheets, strong franchises, and fairly stable earnings.

His top 15 picks, as of the end of May, were Wal-Mart, ExxonMobil, Johnson & Johnson , Coca-Cola, Microsoft, Pfizer, Chevron, PepsiCo,  UnitedHealth Group, Merck, Procter & Gamble, Qualcomm, Cisco Systems, Oracle Corp. and 3M.

These were the biggest holdings, in order, in Grantham's U.S. Quality Equity mutual fund. Alas, you need $10 million as a minimum investment to buy into the fund, so you may be better off buying shares in these companies directly. (You will not, of course, benefit from Grantham's active management of the portfolio.)

Grantham says he is surprised that high-quality stocks have not been spared from the recent meltdown. His fund is down about 15% in the past year. That's only slightly better than the 18% fall in the broader Standard & Poor's 500.

In a rational market, these companies would be trading at much bigger premium to everything else. It suggests investors can make an easy switch.

For those who are interested, Grantham also thinks the Japanese stock market is "less expensive than most other countries," – which, for him, is high praise.

Write to Brett Arends at brett.arends@wsj.com

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About R.O.I.

Brett Arends writes R.O.I., or Return On Investment, daily for the Online Journal, dissecting where personal finance meets current affairs, and how the latest news can make you money."

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