Stocks started off the second quarter with a soaring rally on Tuesday that sent the Dow Jones industrials up nearly 400 points, its best performance in two weeks. Investors seemed to take heart in a fresh round of mortgage-related write-offs at UBS and Deutsche Bank and a capital infusion at Lehman Brothers, the brokerage firm.

Despite the discouraging numbers — $19 billion in write-downs at UBS and nearly $4 billion at Deutsche in the first quarter alone — investors appeared hopeful that the bad news could signal the last of Wall Street’s subprime woes.

“Nobody’s kidding themselves,” said Ed Yardeni, the investment strategist. “The financial crisis isn’t over. But the Fed and Congress and other financial regulators have made it very clear that they are going to use all the powers available to them to avoid a financial meltdown and end this credit crisis.”

The Standard & Poor’s 500-stock index gained 3.6 percent on the strength of a surge in shares of financial services firms. Lehman Brothers, the bond insurer MBIA and the mortgage giant Fannie Mae — stocks that have suffered painful losses in recent weeks — were among the index’s biggest gainers.

“It’s psychological,” said Richard Sparks, a senior analyst at Schaeffer’s Investment Research. “When a company comes out and writes down more, it leads people to believe that they’re being forthright.”

“We’re hoping that we are closer to the end than the beginning,” he added.

Adding to the good feelings in the financial sector, Lehman said private investors had snapped up a $4 billion offering of preferred stock — more than expected — in a move to dispel a swirl of rumors about its stability. Shares of the brokerage jumped 17 percent. UBS said it would try a similar move with $15 billion in additional funds; its shares closed up 15 percent.

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