Economist Burton Malkiel says the downgrade is no reason to panic about the stock market. “Is it time to sell all your stocks, which are still well above their lows of 2009?” Malkiel writes in The Wall Street Journal. “I think not."

"Stocks may continue their decline, but I believe it would be a serious mistake for investors to panic and sell out," says Malkiel. "There are several reasons for optimism that in the long run we will see higher, not lower, market valuations."

“My advice for investors is to stay the course. No one has ever become rich by being a long-term bear on the fortunes of the United States, and I doubt that anyone will do so in the future.”

Malkiel says there is abundant evidence that the average investor tends to put money into the market at or near the top and tends to sell out during periods of extreme decline and volatility.

“Over long periods of time, the U.S. equity market has provided generous average annual returns,” Malkiel notes. But the average investor has earned substantially less than the market return, in part from bad timing decisions.

This is still the most flexible and innovative economy in the world, Malkiel says, and in times like this investors should consider rebalancing their portfolios.

“If increases in bond prices and declines in equities have produced an asset allocation that is heavier in fixed income than is appropriate, given your time horizon and tolerance for risk, then sell some bonds and buy stocks,” he advises.

“Years from now you will be glad you did.”

But not all agree.

Economist Nouriel Roubini says Standard & Poor's decision to downgrade the U.S. at a time of such severe market turmoil and economic weakness only increases the chances of a double-dip recession and even larger fiscal deficits.

"Paradoxically, however, U.S. Treasuries will probably remain the world’s least ugly safe asset: risk aversion, equity declines and a looming slump could even see treasury yields fall rather than rise," Roubini writes in the Financial Times.

However, avoiding another recession “might simply be mission impossible,” says Roubini.