“Existing home sales is one of the most important indicators for the housing market,” said Dan Greenhaus, chief global strategist at the brokerage BTIG. “The improvement in today’s data, while not spectacular, is nonetheless encouraging.”

Sales rose 3.4 percent last month to an annual rate of 4.62 million, more than economists had predicted. The median price rose to $177,400, a jump of 10 percent over the past year.

Homebuilders including PulteGroup and Lennar shot up after the report.

In other trading, the Standard & Poor’s 500 index rose 7 points to 1,323. Bank stocks led the S&P 500′s industry groups. The Nasdaq composite index, which had its biggest gain of the year on Monday, rose 18 points Tuesday to 2,855.

Facebook stock kept sliding, dropping 4 percent to $32.68. The social networking company’s stock has fizzled since its long-awaited initial public offering last week at $38. Facebook sank 11 percent on Monday, even as the rest of the stock market rallied.

Among stocks making big moves:

— Urban Outfitters jumped 6 percent, the biggest gain in the S&P 500. The retailer posted earnings late Monday that surpassed Wall Street analysts’ expectations on record sales.

— Benihana soared 21 percent after the restaurant company agreed to be taken private.

— Ralph Lauren rose 2 percent. The clothing company’s quarterly earnings soared 29 percent, helped by strong sales and a lower tax rate. The company doubled its dividend to 40 cents per share.

In a separate report, the Commerce Department said construction spending ticked up in March, following two months of declines.

Sam Stovall, chief equity strategist at S&P Capital IQ, said the two reports looked like evidence that the U.S. economic recovery is on solid footing despite turmoil in Europe and a weak jobs report last month.

“I think investors are encouraged there’s at least one place in the world where it’s still worth investing,” Stovall said. “They’re not ready to give up on this bull market yet.”

Other indexes pushed higher. The Standard & Poor’s 500 index rose 14 points to 1,412, seven points shy of its closing high for the year, set on April 2. The Nasdaq composite climbed 24 points to 3,070.

All 10 industry groups within the S&P 500 were higher, led by energy companies. Chesapeake Energy Corp. jumped 7 percent on reports that the company will replace its chairman, Aubrey McClendon.

McClendon, Chesapeake’s founder, was under fire for taking out more than $1 billion in loans using the company’s wells as collateral. Chesapeake recently agreed to end the program that allowed McClendon to take personal stakes in the wells. McClendon will stay on as CEO.

Major car companies are reporting monthly auto sales on Tuesday. Industry watchers expect overall sales to rise 2 percent for April compared with a year earlier.

The S&P finished April in the red, its first losing month since November. The Dow managed a tiny gain.

Judging by its track record, May isn’t a promising month for stocks. Since World War II, the S&P 500 index has gained an average of 0.31 percent in May. For all months, the average gain is 0.67 percent.

“It’s a very undistinguished month,” Stovall said.

Among stocks making big moves:

— Sears Holdings Corp. soared 17 percent, the biggest gain in the S&P 500. The operator of Kmart and Sears stores expects to post a first-quarter profit thanks to a gain from the sale of some U.S. and Canadian stores. The company’s stock has jumped 99 percent so far this year.

— Archer Daniels Midland Co. gained 6 percent after the food conglomerate reported profits that beat analysts’ expectations. Profits dropped by nearly a third over the past year, pulled down by one-time charges and lower weaker results from its ethanol and oilseeds businesses.

— Avon Products Inc. fell 8 percent, the largest drop in the S&P 500. The company said earnings plunged 82 percent, hurt by a bigger restructuring charge, commodity costs and rising labor costs. The results were worse than analysts had expected.

Figures reported by the European Union’s statistics office confirmed the effects of budget-cutting programs on countries that use the euro currency. Even with widespread spending cuts, overall debt rose to 87.2 percent, the highest level since the euro was created.

Separately, a survey of the euro zone’s manufacturing and services sectors unexpectedly fell in April.

Results of the first round of presidential elections in France was also a cause for concern. The incumbent Nicolas Sarkozy came in second behind Francois Hollande, a critic of austerity as a way out of the debt crisis. The partnership between Sarkozy and Germany’s Angela Merkel has been crucial to negotiations over Europe’s debt crisis.

“To the extent that Europe has any leaders, it’s very much Merkel and Sarkozy,” Greenhaus said. “If Sarkozy were to lose, you’d change the leadership of Europe at arguably the worst possible time.”

Europe’s major indexes fell hard. France’s CAC-40 index dropped 2.9 percent. Germany’s main index fell even more, 3.6 percent. The euro fell against the dollar.

In the U.S., the Standard & Poor’s 500 index fell 16 points to 1,362. The Nasdaq composite fell 48 points to 2,952.

Treasury prices rose as traders shifted money into assets considered safe. The price of the 10-year Treasury note rose 50 cents for every $100 invested. That pushed its yield down to 1.91 percent from 1.96 percent late Friday.

Trouble in Europe is hurting Kellogg, which slashed its full-year forecast, blaming weak sales. Hasbro posted a first-quarter loss on falling sales and costs related to cutting jobs. Kellogg dropped 5 percent and Hasbro 4 percent.

Wal-Mart Stores sank 4 percent following a report in The New York Times about an alleged bribery campaign involving top executives at a Mexican subsidiary. The retailer said it was investigating for any breach of the U.S Foreign Corrupt Practices Act.

“If the trend continues we’ll blow that number away,” says Jeff Tjornehoj, head of Americas Research at Lipper, the company that tracks mutual funds and compiled the numbers.

Buying a junk bond makes you a lender to companies with heavy debts and low credit ratings. That’s why investors demand higher returns in exchange for handing over their money.

Junk bonds still carry a lingering black mark from Milken, who pioneered the market in the 1980s while at Drexel Burnham Lambert. Milken was convicted of insider trading and violating other federal securities laws and has since remade himself as a philanthropist.

And then there’s that unpleasant name.

“A lot of people look at high-yield with a jaded viewpoint,” says Jason Pride, director of investment strategy at Glenmede, an investment management company. “They think, ‘Why would you own anything other than stocks?’”

Stocks have been on a roll. The Standard & Poor’s 500 index is up 11 percent this year and has doubled since it hit its low point during the Great Recession in March 2009.

Professional money managers usually predict disaster when the public flocks to an investment outside of the stock market. To them, it’s often a reliable “sell” signal. If the average Joe shows up, the pros think it’s time to go.

Yet Pride is one of many money managers steering his customers to junk bonds. One reason is the lower risk: When a reckless company goes bankrupt, bondholders and other creditors still get paid.

And most people piling into junk bonds have no need to worry about the bankruptcy of any particular company. Buying into mutual funds that invest in more than 100 companies dilutes the danger of one going under.

The bigger draw is the yield. The typical high-yield bond pays 7.2 percent. With interest rates at record lows, the benchmark U.S. Treasury security, the 10-year note, pays 2.2 percent. It paid as little as 1.76 percent last October.

“Think of high-yield as the middle ground between bonds and stocks,” Tjornehoj says.

Still scarred by the 2008 meltdown, Americans seem comfortable in that middle ground. They’ve bought junk bonds in such great numbers that prices have risen from as low as 91 cents on the dollar last October to a recent $1.01. That’s pushed borrowing costs down from above 10 percent.

The main drawback is that junk bonds are among the more hazardous bond investments around. Rating agencies, using another delicate term, label the bonds “speculative grade.” They’re the candidates considered most likely to miss an interest payment and go bankrupt.

The price of a company’s high-yield bond often shadows its stock. But bondholders are better off when a company runs into trouble. In a bankruptcy, owners of high-yield bonds count as creditors, like banks, and can expect to get back around 40 cents on the dollar. Owners of stock can expect nothing.

Just two years ago, Moody’s warned that companies and the federal government faced a tidal wave of debts coming due, what’s known as a maturity wall. Forced to compete with the U.S. government for new loans, companies could wind up paying crushing interest rates and be pushed into bankruptcy. News reports imagined doomsday scenarios coming from the junk bond market and referred to the Mayan calendar and the world ending in late 2012.

What happened? “Companies kicked out the wall,” says Kevin Cassidy, senior credit officer at Moody’s.

With interest rates at all-time lows, companies managed to borrow cheaply and used the money from investors to refinance their debts. They pushed their due dates years into the future and also have smaller interest payments.

“If the Federal Reserve hadn’t kept rates as low as they kept them, and if the economy hadn’t picked up, you would have had a scarier situation,” Cassidy says.

Despite the predictions of doom, defaults remain rare. Just 2.2 percent of companies that issue low-rated bonds defaulted in the last year, according to Moody’s. That rate will probably inch toward the 5 percent historical average as interest rates rise.

Jack Ablin, chief investment officer at Harris Private Bank, says he understands why many of his clients are drawn to high-yield bonds. They saw stocks plunge for no apparent reason in the Flash Crash of 2010 and watched the Dow take wild swings last August. Now they’re encouraged by the slowly improving economy and willing to take a step out of cash. Buying junk is a way to stay in bonds while creeping closer to the stock market, Ablin says.

“People are skeptical of the stock market for very good reasons.”

But the profit explosion is over, and the Wall Street pros who trade stocks mostly for big institutions and the rich are getting antsy. They’ve been doing the buying. And if Main Street doesn’t join them, the historic rally could slow or even end.

Everyday investors “are more aware of the risk of the market,” says Howard Silverblatt, senior index analyst at Standard & Poor’s. “They’re nervous. They’re scared.”

The Dow closed above 13,000 last week for the first time since May 2008, four months before the financial crisis. In a sense, the milestone was disappointing: Profits are at an all-time high, yet the Dow is well below its record of 14,164, set in October 2007.

Even though profits are growing, individual investors aren’t buying. That shows up in something called the multiple — the ratio of what investors are willing to pay for a company’s stock, compared with its annual profits.

If a stock trades for $100 and the company has made $5 in profit per share, its multiple is a fairly high 20. A higher multiple means more confidence that profits will grow. Maybe investors believe the company will turn a bigger profit next year of $7 or $8.

These days the multiples don’t show much confidence.

Investors are paying a multiple of 13.5 times the past year’s earnings for stocks. The typical multiple over the past 75 years is 16. If that were the multiple today, the Dow would be sitting above 15,000.

“We’ve built profits in the past three years,” says Jim Paulsen, chief investment strategist at Wells Capital Management. “Now we need to value them differently.”

The chatter on Wall Street about multiples comes as stock analysts worry that the double-digit profit growth is largely over.

For the first three months this year, profits of companies in the widely followed S&P 500 index are expected to grow just 0.4 percent over the same period last year, according to FactSet, a provider of financial data.

For all of 2012, they are expected to climb 9 percent. That assumes they will pick up toward the end of the year. That would be a healthy gain but will leave the index short of its record high unless investors get more excited.

If the earnings predictions for this year come true and the multiple stays in its rut, the S&P 500 will reach 1,421, well shy of its own record of 1,565. And the earnings projections may prove optimistic. Analysts have been slashing them lately.

The modest profit picture doesn’t necessary doom the rally. There have been periods when earnings barely budged and stocks soared. In the five years through 1986, stocks in the S&P 500 nearly doubled while earnings slipped 2 percent.

The explanation is the magic of rising multiples. The average zoomed from nine times earnings to nearly 17 times. Could we be entering a similar period of growing confidence?

Paulsen thinks so. He says that investors have shaken off fears of another recession and that debt-ridden Europe appears on the mend. He expects investors will value profits at closer to the average 16 times by the end of year, pushing the Dow and S&P near or past their records.

But Jeffrey Kleintop, chief market strategist at LPL Financial, one of the nation’s largest brokerages, thinks the market won’t reach a record anytime soon. First, “people need to embrace stocks,” he says. “Maybe next year.”

One measure to watch is the flow of money in or out of U.S. stock mutual funds. From June through January, investors pulled $137 billion more from these funds than they put in, according to Strategic Insight, an industry consulting group.

Their apparent skittishness has led to less trading. About 3.9 billion shares of stock have traded on an average day this year at the New York Stock Exchange, down a third from three years ago.

The refusal by ordinary investors to buy stocks is even more surprising when you consider how little they’re making from the alternatives. Their favorite assets of refuge— CDs, money market funds and U.S. government debt — don’t even throw off enough interest income to compensate for inflation.

If stocks do return to a more normal 16 times profits, they’re not likely to hover there for long. They tend to trade at widely varying multiples. Since World War II, stocks have traded as low as six times earnings and as high as 47.

What’s more, stocks can stay at seemingly cheap or expensive multiples for long stretches. For the three years during the boom in dot-com stocks in the late 1990s, stocks in the S&P 500 traded at an average 37 times their previous year’s profits. In the 10 years through 1951, they rarely broke 10.

At today’s earnings, a 37 multiple would put the Dow at more than 36,000, according to FactSet. A multiple of 10 would sink the average to about 9,800.

All these hypotheticals can mislead, of course. To judge whether stocks are cheap or expensive, experts say you need to look at many figures, not just last year’s earnings.

Some also like to look at an average of earnings over the past 10 years to iron out the peaks and valleys in business cycles. By this measure, stocks are trading at 22 times earnings compared with a historical average of 16. In other words, stocks may be too expensive.

One school of thought holds that multiples of all kinds should be lower now because the U.S. has entered a period of slow economic growth and lower profits as governments and households pay off their enormous debts. Bill Gross, co-founder of the giant investment company Pimco, calls this a “new normal.”

Even if you don’t believe Gross is correct, perception could become reality. If enough people refuse to buy stocks because they don’t think prices will rise much, they won’t rise much.

Harvey Rowen, the chief investment officer for Starmont Asset Management, says he’s seen this self-fulfilling attitude among his clients. He says the clients who are calling want him to move more of their holdings into cash, or maybe gold.

“Nobody calls up to say, “Buy equities,” he says.