By Scott Cendrowski
July 16, 2012

FORTUNE — It has happened repeatedly: The housing market shows hints of revving up only to sputter and stall. In fact, by Deutsche Bank’s count, there have been seven false recoveries during the six-year national housing downturn. Now there are signs that a true residential property recovery is under way. Exhibit A: Stocks of homebuilding companies have soared, with many doubling over the past nine months. The good news for investors, according to analysts who track fundamental data, is that even after their gains, these stocks offer rich potential.

The reason is straightforward. There’s a looming shortage of new homes in the U.S., and construction will have to ramp up. Homebuilders slashed production in recent years as demand withered. Now, says Ivy Zelman, CEO of Zelman & Associates, “new-home inventory is at record lows any way you look at it.” Over the years, new properties have represented 0.3% of total U.S. households, she says; today that figure is 0.1%. Census figures show that just 475,000 new homes were completed annually over the past three years, down from a long-term yearly average of 1.1 million.

Zelman was one of the only Wall Street analysts to predict a housing downturn in 2006, and she remained mostly bearish until early this year. Several factors have changed her mind: the paltry inventory of new properties; a national bottoming of prices, which nudges indecisive potential buyers to pull the trigger; and the increased cost of renting in cities across the country.

Consider a new housing community in Delray Beach, Fla., described by Zelman: Potential buyers started lining up at 6 a.m. and snapped up 44 homes over the weekend. Such scenes, though almost disturbingly reminiscent of the late bubble, have given Zelman hope. She recommends shares of Pulte (PHM). Investors fear that Pulte’s mortgage unit may face further losses. But Zelman disagrees with the gloomy outlook and thinks improving profit margins will lift the share price 78% over the next two to three years.

Where home prices are rising for the wrong reasons

Places like Houston, Dallas, and Indianapolis, and even central Florida, have new-home supplies of less than three months, says Mike Castleman, CEO of research firm Metrostudy, which sends field researchers to new-home sites across some two-thirds of the country every three months. Annual housing starts in Metrostudy’s markets are just 20% of their peak in 2006. When demand picks up from those depths, Castleman says, “builders will be starting more homes, pouring more slabs, and buying more lots.”

That’s the case for optimism. But given the gains in homebuilder stocks, have they become overpriced? No, argues Nishu Sood, an analyst at Deutsche Bank. Sood calculates the so-called normalized earnings of homebuilders — what the companies can earn once demand returns to its long-term average. He ignores short-term earnings fluctuations, as they have little bearing on the homebuilders’ future prospects. According to Sood, residential-construction stocks trade for a normalized price/earnings ratio of 5. He recommends companies — such as D.R. Horton (DHI), M.D.C. Holdings (MDC), Meritage (MTH), Ryland (RYL), and Toll Brothers (TOL) — with lower debt levels, which means they can borrow when they need to. They “can stretch their balance sheets and ultimately earn more in a recovery,” Sood wrote in a recent report.

The second concern is foreclosures. Skeptics warn that a wave of foreclosures will flood the market and pummel prices again. Some 3 million to 5 million houses either are burdened by a delinquent mortgage or are foreclosed properties that haven’t yet reentered the sales market, according to economist A. Gary Shilling, who runs a firm of the same name. Once those houses go back on the block, he says, they’re typically sold for 19% less than a comparable non-foreclosed residence. The wide availability of discount properties, Shilling argues, will depress prices and cripple the fragile housing recovery. “If you get a number of [foreclosed] houses being sold, then that really becomes the market,” he says. “At that point I don’t think homebuilders can compete.”

McMansions for half off!

However, Zelman and others counter that it takes a long time for repossessed properties to creep back onto the market. Foreclosure cases are often mired in court for years, and more than 65% of ongoing U.S. foreclosures are in states where a judge needs to approve the process. Repossessed houses will reenter the market for years to come, the housing bulls argue, but it will be a steady trickle rather than a flood.

Take Orange County, Calif. Prices skyrocketed during the boom, only to collapse 36% from 2006 through today. But foreclosed properties, once the hottest thing since cathedral ceilings, are now in short supply. Repossessed homes remain on the market just 20 days on average before being scooped up by buyers (which increasingly include institutional investors). Today homebuilders are pulling out their hammers and their nail guns again and preparing to meet demand. It marks the beginning of a new upward cycle — and one that should soon be repeated across the rest of the country.

This story is from the July 23, 2012 issue of Fortune.

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