By E.S. Browning 

The stock market soared this week, reclaiming ground lost earlier in the month. But many investors worried that, with stock prices high and the world economy unsettled, this year's succession of sudden dips and sharp recoveries may not be over.

Major indexes shook off the fears of global deflation that have gripped U.S. and European markets. A surge of economic optimism and strong corporate earnings pushed the Dow Jones Industrial Average up 425.00 points, or 2.6%, this week, its biggest weekly gain since December. The more volatile Nasdaq Composite Index rose 5.3% for the week, its best weekly percentage gain since 2011. Both indexes, and the broad S&P 500, are less than 3% from returning to their September highs.

Better economic news from Europe and solid U.S. earnings reports came on top of renewed hopes that European central bankers will take fresh steps to support Continental economies, perhaps stepping in to buy corporate bonds. International investors continued to shift money to the U.S., where the economy has been one of the world's steadiest and the Federal Reserve remains committed to only a very gradual tightening of monetary policy.

David Kotok took a deep breath when stocks were collapsing Oct. 15 and jumped back into the market. Mr. Kotok, chairman of money-management firm Cumberland Advisors, oversees $2.25 billion in Sarasota, Fla., and he had cut his stockholdings during the summer.

"We bought them in the middle of the bloodbath," he said, and he has kept buying since, notably transportation, health-care and utilities funds. Many others also have jumped in, fueling the recovery. But in coming weeks, "the Dow could explode up 200 points on some days and could fall 200 points on others. That will upset some investors," Mr. Kotok said. His clients hate these churning ups and downs, and he is spending more time than usual trying to reassure them.

The Dow, at 16805.41 Friday, is up only 1.4% for the year, but it has climbed 157% since bottoming out in 2009. The S&P 500 is up 190% since the 2009 low, and the Nasdaq is up 253%.

But other kinds of investments haven't moved as much as stocks, showing that concerns for the global economy haven't gone away.

Treasury-bond prices have pulled back during the recent rebound, but only mildly, as traders have shifted to riskier investments. Slow world growth and low inflation have kept yields far lower than many thought possible a year ago, meaning Treasury prices, which rise when yields fall, have remained high. Soft foreign growth has held down prices of oil and industrial commodities. With the U.S. one of the few places showing reliable growth, the dollar has remained strong.

Money managers offer several reasons for the stock volatility.

First, even after the recent pullbacks, stocks are no longer cheap. The big advances since 2009 mean many people have significant gains in their portfolios. They are quicker to cash out when stocks fall, and they are having trouble finding bargain-priced investments. The S&P 500 traded Friday at 18.4 times its companies' net earnings for the previous 12 months, according to Birinyi Associates. That was down from about 19 at its September high but is still well above its long-term average of 15.5.

Central banks, meanwhile, have stopped following the same safe, reassuring policies. The U.S. Federal Reserve is getting ready to start slowly raising interest rates next year, for the first time since 2006. But Europe's central bank is still desperately trying to loosen its policy. Shifting policies can make investors nervous.

"If you look at what happens when the Federal Reserve takes stimulus away, before it starts really strong tightening, the markets have experienced about 50% more volatility than in the period prior to that," noted Jason Pride, director of investment strategy at Glenmede Trust Co., which oversees $28 billion in Philadelphia.

On top of that, the world is still a scary place. Although economic news from the countries that use the euro has improved, eurozone economic growth still is running below 1% annually. Chinese growth, while far from slipping into recession, also is slowing. The nation's demand for industrial commodities has slowed, hurting developing countries that provide them.

"Investors are a little bit on guard. They are a little bit nervous about stocks right here," despite the gains, said David Joy, chief market strategist at Ameriprise Financial Inc., which oversees $810 billion. "I don't expect it, but it wouldn't take much for volatility to come roaring back."

Mr. Joy is urging clients to keep a little extra money in cash. A portfolio that typically would hold 60% stocks and 40% bonds, he said, might today contain 55% stocks, 35% bonds and 10% split between cash and hedge funds whose performance isn't linked to the stock market's direction.

As long as the U.S. avoids recession, however, a little anxiety actually can be good for stocks. Nervous investors are less likely to go overboard and push shares to unsustainable levels. And when people keep cash on the sidelines, it creates a pool of available money that they may, if they become less nervous, shift to stocks.

As the news has gotten better, that is what has happened.

Almost 70% of U.S. companies that have reported third-quarter profits have beaten expectations, according to Thomson Reuters I/B/E/S. That has included blue chips such as Microsoft, Caterpillar and 3M, despite the struggles of some other big firms. While the earnings gains have been unspectacular and typically below 10%, they have been enough to reassure SHYinvestors.

Manufacturing reports from Europe also have improved, relieving some fears, as have hiring, consumer-confidence and home-sales data in the U.S.

Lower oil prices, meanwhile, give consumers more to spend on other things than gasoline.

To the amazement of many bond experts, interest rates and bond yields also have remained exceptionally low around the world. Low rates are powerful economic stimulus, because they hold down mortgage rates and the cost of business investment.

Among the reasons rates and yields are subdued: When inflation and global growth are low, there is little to push yields higher.

The 10-year U.S. Treasury note yielded 2.273% Friday, up only slightly from its lows earlier this month and far from the 3% at which it began the year.

And yet, U.S. Treasury notes yield more than government bonds in Germany, Japan and even Spain. That, together with a strong dollar, pulls money to U.S. Treasurys, supporting their prices and holding down yields.

And as long as the U.S. economy can keep growing without recession, many investors consider a severe stock decline unlikely.

"We think we are in the middle of a longer-term global economic expansion, mainly because we don't yet have the excesses that build up in the system late in an economic cycle. We aren't seeing corporate or individual debt buildup, excesses in manufacturing capacity or overspending by consumers," said Mr. Pride of Glenmede.

Write to E.S. Browning at jim.browning@wsj.com