NEW YORK — A wave of optimism swept through U.S. stock markets on Tuesday as most major indexes posted gains, reversing losses from the previous week. The S&P 500 managed a modest increase of 0.2% after a volatile start, reflecting a market still navigating through fluctuations following a significant dip earlier.

The Dow Jones Industrial Average surged by 559 points, or 1.2%, reaching a new record high, surpassing the previous peak set just two weeks ago. In contrast, the Nasdaq composite underperformed, experiencing a slight decline of 0.3% amid continuing concerns over heavily invested technology stocks, particularly Nvidia, which faced scrutiny over inflated valuations tied to the ongoing artificial intelligence boom.

Paramount Skydance emerged as one of the day’s standout performers, with its shares climbing nearly 10% despite a lackluster earnings report. Investors reacted positively to the entertainment company’s revised cost-cutting goals, which were raised from $2 billion to at least $3 billion. This was Skydance’s first earnings report following its acquisition of Paramount in early August, and the stock’s leap signaled confidence in its future.

Another notable gainer was FedEx, whose stock rose 5.4% after the delivery giant raised its profit forecast for the upcoming quarter. This optimistic outlook extended beyond summer, as FedEx anticipated improved performance during the upcoming holiday season compared to last year.

These advancements helped the S&P 500 climb within 0.6% of its all-time high, although the lingering influence of Nvidia’s decline weighed on market sentiment. The company saw its stock drop 3% as a major stakeholder, SoftBank, announced the sale of its entire stake in the AI chipmaker for $5.83 billion last month. Despite this move, SoftBank indicated it remains committed to investing in AI through other ventures like OpenAI.

On the earnings front, CoreWeave faced a stark contrast, with its stock tumbling 16.3% despite reporting better-than-expected revenue and a smaller quarterly loss. Investors appeared more focused on ongoing supply-chain challenges that could push revenue accelerations further into the future.

In a positive turn, BigBear.ai saw its shares increase by 6.1% after outperforming expectations in its quarterly results. The company also announced its acquisition of AskSage, a generative AI platform, signaling growth ambitions in a competitive sector.

Overall, the S&P 500 rose 14.18 points to close at 6,846.61, while the Dow finished at 47,927.96, up 559.33 points. The Nasdaq ended the day lower, down 58.87 points, at 23,468.30.

Internationally, stock indexes rose in Europe following a mixed finish in Asian markets. Japan’s Nikkei 225 saw a minor decline of 0.1%, even as SoftBank celebrated a significant profit that exceeded analysts’ expectations.

In the bond market, trading was limited due to the Veterans Day holiday, with yields trending upwards since Federal Reserve Chair Jerome Powell recently indicated that further interest rate cuts may not be imminent. The Fed has already reduced rates twice this year in response to a sluggish job market, but persistent inflation remains a concern, complicating the decision-making process for monetary policy.

Heightening the Fed’s challenges is the ongoing government shutdown, which has delayed critical economic updates, including labor statistics. The Senate is making efforts to resolve the shutdown, but uncertainty looms. Investors are relying on non-government reports, which have painted a mixed picture of economic health.

Data from Goldman Sachs suggests slowing growth in the job market, with estimates indicating potential job cuts in October, which could influence the Fed’s monetary policy decisions going forward. Market analysts are now forecasting a two-in-three chance of rate cuts at the Fed’s next meeting in December, reflecting traders’ hopes that such actions will stimulate growth and bolster stock prices.