Options trader Chris Dattolo works on the floor of the New York Stock Exchange on Friday. (AP Photo/Richard Drew)

NEW YORK (AP) — More swings hit Wall Street on Friday, except the U.S. stock market finished higher this time.

After bobbing up and down through the morning, the S&P 500 took off and rallied nearly 2% before finishing with a gain of 1%. The Dow Jones Industrial Average climbed 493 points, or 1.1%, and the Nasdaq composite rose 0.9%.

It was a fitting finish for a week that left the S&P 500 just 4.2% below its record but also forced investors to stomach the sharpest hour-to-hour swings since a sell-off in April. The jarring moves are testing investors following a monthslong and remarkably smooth surge for stocks, and they come down to two basic questions, neither of which has been answered yet.

Have prices for Nvidia, bitcoin and other stars of Wall Street shot too high? And is the Federal Reserve done with its cuts to interest rates, which would boost the economy and prices for investments?

On the second question, financial markets found some assurance from a speech by the president of the Federal Reserve Bank of New York. Markets perked up immediately after John Williams told a conference in Chile that he sees “room for a further adjustment” to interest rates.

That could signal he’ll vote for another cut to rates in December. What the Fed does is critical for Wall Street because stock prices ran to records through last month in part because of expectations for a series of reductions.

Other Fed officials, though, have argued against a December cut given how high inflation remains. The uncertainty created by such sharp disagreement has triggered dramatic moves back and forth for markets.

The swings hit a crescendo on Thursday, when U.S. stocks initially surged after Nvidia seemed to tamp down worries about a potential bubble in artificial-intelligence technology. But the market quickly dropped to a sharp loss in its biggest one-day reversal since April, when President Donald Trump shocked markets with his “Liberation Day” tariffs.

Despite the strong profit report from Nvidia, whose chips are powering the move into AI, worries are still hanging around about the longer term. Will all those AI chips that Amazon, Meta Platforms and other companies are gobbling up actually yield profits and productivity as big as proponents are envisioning? If not, some investors fear, all the investment won’t be worth it.

AI-linked stocks continued to swing on Friday, helping to drag the rest of the market behind them. Nvidia went from an initial gain to a drop of 4.3% and then swung back and forth before finishing with a loss of 1%, for example. Amazon went from an early loss to a gain of 1.6%.

Bitcoin, meanwhile, briefly plunged below $81,000 before pulling back toward $85,000. That’s down from nearly $125,000 last month and brought it back to where it was in April, when markets were shaking because of Trump’s tariffs.

All told, the S&P 500 rose 64.23 points to 6,602.99. The Dow Jones Industrial Average gained 493.15 to 46,245.41, and the Nasdaq composite climbed 195.03 to 22,273.08.