Bank stocks and the broader markets rallied Tuesday on reassurances from Federal Reserve Board Chairman Ben Bernanke that the economy could improve as early as next year if the government can stabilize the financial sector.

The KBW Bank Index soared 13.59% after several days of declines last week and uncertainty over the banking industry's health and the government's ability to help. (The index had been unchanged Monday.)

"We're finally getting a dead cat bounce — let's see how sustainable it is," said Matthew Shields, a trader at FIG Partners LLC.

The Dow Jones industrial average gained 3.32% a day after hitting its lowest level since May 1997. The Standard & Poor's 500 rose 4.01%.

Mr. Bernanke told the Senate Banking Committee on Tuesday that only strong government action could reverse the economic downturn as early as next year. "If actions taken by the administration, the Congress, and the Federal Reserve are successful in restoring some measure of financial stability — and only if that is the case, in my view — there is a reasonable prospect that the current recession will end in 2009 and that 2010 will be a year of recovery," he said.

Cassandra Toroian, the president and chief investment officer of Bell Rock Capital LLC in Rehoboth, Del., said investors were also encouraged that Mr. Bernanke reiterated the government's preference for increasing its stakes in companies that fail stress tests by using mandatory convertible preferred shares that would only be converted into common stock on a case-by-case basis, instead of nationalizing institutions.

"He made it very clear that the amount of ownership in the companies would not a be majority ownership," and investors were particularly relieved to hear that, Ms. Toroian said.

Peter McCorry, a senior trader at KBW Inc.'s Keefe, Bruyette & Woods Inc., said investors were also anticipating President Obama's speech Tuesday night. "Nothing he can say will have enough detail, enough breadth, to cover enough ground to please everybody, so there's bound to be some disappointment," Mr. McCorry said. "But having said that, the market has been sold off so hard that it may not care at that point."

The traders said bank stocks rose across the board, particularly companies that had been hammered especially hard over the past several weeks. Citigroup Inc. rose 46 cents, to $2.60 a share, and Bank of America Corp. rose 82 cents, to $4.73. JPMorgan Chase & Co. rose 7.7%, Wells Fargo & Co. rose 18.3%, and U.S. Bancorp rose 12.7%. Among regionals, Regions Financial Corp. rose 60 cents, to $3.29, and Fifth Third Bancorp rose 21 cents, to $1.45.

The stocks rose despite some bad news for bankers. The fourth-quarter Standard & Poor's/Case-Shiller U.S. National Home Price Index fell 18.2% from a year earlier. The drop was the largest in the index's 21-year history. Also, the Federal Housing Finance Agency said Tuesday that fourth-quarter home prices dropped 8.2% from a year earlier — the largest decline since 1991.

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