Wall Street ended a frenetic January with a huge advance Thursday after investors set aside worries about bond insurers and grew more optimistic...

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NEW YORK — Wall Street ended a frenetic January with a huge advance Thursday after investors set aside worries about bond insurers and grew more optimistic that the Federal Reserve’s interest-rate cuts will indeed help lift the economy.

The Dow Jones industrials rose 207.53 to 12,650.36.

Microsoft, one of the 30 Dow stocks, rose 40 cents to close at $32.60 a share. Boeing, also a Dow stock, gained 31 cents to $83.18.

For the month, the Dow lost 4.63 percent — its worst January since losing 4.84 percent at the start of 2000. Overall, January’s pullback was the steepest seen in any month since December 2002.

Broader stock indicators also jumped today. The Standard & Poor’s 500 index rose 22.74 to 1,378.55, and the Nasdaq composite index rose 40.86 to 2,389.86.

The day’s trading emerged as a microcosm of the entire month, with the Dow first falling more than 190 points, and then by late afternoon, soaring more than 250.

Still, the major indexes ended the month with heavy losses, evidence of how dejected investors have become. The Fed’s 1.25 percentage points in interest rate cuts, designed to stave off a recession, ultimately gave Wall Street some reassurance that the economy might soon show signs of recovery — although the market still gyrated after the latest 0.50 percentage point cut on Wednesday.

Bond insurer MBIA also mollified Wall Street on Thursday when its chief executive, Gary Dunton, told investors he is confident the company can retain its crucial AAA credit rating and that MBIA will still be able to raise fresh capital.

The notion that bond insurers could perhaps avoid being felled by a rush of claims over swaths of bad debt offered solace for investors.