The Standard & Poor’s 500 index sailed up nearly 6 percent, and the Nasdaq composite gained about 6.2 percent. The advances came after the Federal Reserve and the U.S. government rolled out plans to blunt the spread of the disease and its effect on American lives, from a reported $1 trillion stimulus to a $10 billion credit infusion to a pledge to help beleaguered Boeing.

“The volatility shows the desperation on Wall Street to find fair value,” said Michael Farr, president of Farr, Miller & Washington, an investment management firm. “Each news release and statistic is greeted with 1,000-point swings.”

One big fix came Tuesday morning, when the Fed announced plans to launch a special fund to keep credit flowing during

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