NEW YORK The “fiscal cliff” compromise, even with all its chaos, controversy and unresolved questions, was enough to ignite the stock market on Wednesday, the first trading day of the new year.

The Dow Jones industrial average careened more than 300 points higher, its biggest gain since December 2011. It’s now just 5 percent below its record high close reached in October 2007. The Russell 2000, an index that tracks smaller companies, shot up to the highest close in its history.

The reverie multiplied across the globe, with stock indexes throughout Europe and Asia leaping higher. A leading British index, the FTSE 100, closed above 6,000 for the first time since July 2011.

In the U.S., the rally was extraordinarily broad. For every stock that fell on the New York Stock Exchange, roughly 10 rose.

Technology stocks rose the most. U.S. government bond prices fell sharply as investors pulled money out of safe-harbor investments. And the VIX, an index that measures investors’ expectations of future market volatility, plunged more than 18 percent to 14.68, the lowest close since October.

The very last week of each year and the first two days of the new year usually average out to a gain for U.S. stocks. But this year stood out. From 2008 to 2012, the Dow rose an average of 93 points on the first trading day of the year, less than a third of Wednesday’s gain of 308.41. During that period, the Dow fell on the first trading day of the year only once, in 2008.

Despite the euphoria, many investors remained cautious. The deal that politicians hammered out merely postpones the country’s budget reckoning, they said, rather than averting it.

“Washington negotiations remind me of the Beach Boys song, ‘We’ll have fun, fun, fun ’til her daddy takes the T-Bird away,’ ” Jack Ablin, chief investment officer of BMO Private Bank in Chicago, wrote in a note to clients.

“Nothing got solved,” added T. Doug Dale, chief investment officer for Security Ballew Wealth Management in Jackson, Miss.

According to these and other market watchers, investors were celebrating Wednesday not because they love the budget deal that was cobbled together, but because they were grateful there was any deal at all.

“Most people think that no deal would have been worse than a bad deal,” said Mark Lehmann, president of JMP Securities in San Francisco.

The bill passed Tuesday night ended the stalemate for now, but it leaves many questions unanswered.

The deal doesn’t include any significant deficit-cutting agreement, meaning the country still doesn’t have a long-term plan or even an agreement in principle on how to rein in spending. Big cuts to defense and domestic programs, which were slated to kick in with the new year, weren’t worked out but instead were just delayed for two months. And the U.S. is still bumping up against its borrowing limit, or “debt ceiling.”

The political bickering that’s almost certain to persist could have another unwelcome effect: influencing ratings agencies to cut the U.S. government’s credit score. That happened before, when Standard & Poor’s cut its rating on U.S. government debt in August 2011, and the stock market plunged.

Even so, Wednesday’s performance gave no hint of the dark clouds on the horizon.

The Dow enjoyed big gains throughout the day, up by more than 200 points within minutes of the opening bell. It swelled even bigger in the final half hour of trading, and closed up 2.4 percent to 13,412.55.

The Standard & Poor’s 500 jumped 36.23, or 2.5 percent, to 1,462.42. The Nasdaq rose 92.75, or 3.1 percent, to 3,112.26.