Stocks closed higher on Tuesday, with the S&P 500 reaching a record-high close for the second straight day.

The broad market index added 0.25% to close at 5,732.93. The Nasdaq Composite advanced 0.56% to 18,074.52, while the Dow Jones Industrial Average gained 0.2%, or more than 83 points, to finish the session at 42,208.22.

— Brian Evans

Liberty Broadband headed for its best day ever after offering a counterproposal to Charter's business combination plan.

Shares of Liberty surged more than 28%, putting the stock on track for its biggest one-day gain ever. Daily trading volume is more than five times higher than the average seen over the past 30 days.

Charter shares, meanwhile, slid more than 2%.

— Alex Harring

Shares of Flowserve rose more than 6% during the session after Bank of America said its nuclear exposure was "underappreciated."

Analyst Andrew Obin believes the company's long-term growth algorithm underpinning its midsingle-digit growth outlook does not account for a "meaningful inflection in nuclear demand." With that, it sees potential upside to its forecasts for 2026 and 2027, saying it could ultimately be a beneficiary of the Three Mile Island nuclear plant's restart in 2028.

"Flowserve is optimistic on chances to expand its market share as companies revive facilities such as Three Mile Island," the analyst said in a Tuesday note. "While more long-term, the company is constructive on the recent COP 28, where 30 countries indicated an intention to triple nuclear generating capacity by 2050."

The firm's price target implies more than 23% upside from Monday's close, and shares have already jumped more than 25% this year.

— Sean Conlon

While Goldman Sachs has taken a positive stance on the wireless market more generally, AT&T is one name in particular that it is upbeat on.

"T is our top pick heading into the quarter as we expect positive wireless results and potentially a capital allocation announcement with the initiation of a buyback," analyst James Schneider wrote in a note to clients. "Management commentary during conference season was broadly bullish for the company, and we sensed no downtick to the company's view on wireless trends."

Along with capital allocation, the firm cited improving clarity on the state of the competitive broadband market and a "normalizing" outlook for the wireless industry as another catalyst for the stock.

Shares have jumped around 28% this year and nearly 8% this month.

— Sean Conlon

Two casino stocks with exposure to the Macao region popped after China's central bank announced economic support measures.

Las Vegas Sands jumped 6%. Wynn Resorts added more than 4%.

The People's Bank of China said it would cut the amount of cash banks need to have available by 50 basis points. This is part of a salvo of new measures aimed at boosting the economy.

Macao, which is part of China, is considered a major gambling destination globally.

— Alex Harring

Hedge fund billionaire John Paulson, who is a prominent donor and campaign advisor to former President Donald Trump, said the stock market would suffer if Vice President Kamala Harris was elected due to her aggressive tax policy.

"If Harris is elected, it increases corporate taxes, increases the marginal tax rate, increases capital gains taxes, and, God forbid, put taxes unrealized gains, I would be very negative on the outlook for equities," Paulson said on CNBC's "Squawk Box" on Tuesday. "If Trump is elected, I think all systems go."

Harris has proposed a 28% tax on long-term capital gains for any household with an annual income of $1 million or more, while endorsing the tax increases proposed by President Joe Biden that include a 25% tax on unrealized gains for households worth at least $100 million. However, people close to the Harris campaign have said she has no interest in taxing unrealized gains and there are doubts if any such plan could make it through Congress.

Paulson shot to fame and made a fortune after taking a massive bet against mortgage bonds using credit default swaps before the financial crisis. The founder and president of family office Paulson & Co. just last week warned of a market "crash" if Harris' proposed tax plans become a reality.

"If something comes to a change — the tax policy or the direction of the economy — I think the markets would be vulnerable," he said.

— Yun Li

Here are some stocks making big moves in midday trading:

• Visa — Shares dropped nearly 4% following a Bloomberg report that the Justice Department is preparing to file an antitrust lawsuit against the credit card network and payments processor.
• Smartsheet — Shares surged more than 6% after Blackstone and Vista Equity Partners agreed to buy the software maker for $56.50 a share in cash, or about $8.4 billion. Unless another offer is made, the deal is expected to close by January 2025, pending shareholder approval.
• China stocks — Shares of Chinese companies soared after China's central bank unveiled a host of stimulus measures. E-commerce giants JD.com, PDD Holdings and Alibaba jumped between 7% and 11%, while automakers Nio and Li Auto each advanced more than 8%

Read here for the full list.

— Sean Conlon

On Tuesday morning, 50 stocks in the S&P 500 were trading at new 52-week highs.

Of these stocks, 22 hit new all-time highs. Tickers that reached this milestone included:

— Lisa Kailai Han, Christopher Hayes

Investors have been disproportionately punishing stocks that have missed their earnings, a team of analysts at Barclays discovered.

"As shown by regression coefficients of stock excess returns of S&P 500 stocks on negative surprises in earnings per share, which were relatively elevated this quarter, the earnings announcement reaction to misses has been stronger than in almost any other quarter since 2000. On the contrary, positive EPS surprises have been met with typical stock price responses," the analysts, led by Renate Marold, wrote in the Tuesday report.

— Lisa Kailai Han

The Conference Board said Tuesday that its consumer confidence index fell sharply in September, putting pressure on equities.

The index came in at 98.7, down from an upwardly revised August reading of 105.6. That is also well below a Dow Jones consensus forecast of 104.

"September's decline was the largest since August 2021 and all five components of the Index deteriorated. Consumers' assessments of current business conditions turned negative while views of the current labor market situation softened further. Consumers were also more pessimistic about future labor market conditions and less positive about future business conditions and future income," Dana Peterson, chief economist at the Conference Board, said in a statement.

— Fred Imbert

Caterpillar shares were up more than 3% on Tuesday after the Chinese central bank unveiled new stimulus measures to support the country's economy. That gain put the industrial giant on track for its best day since Jan. 25.

Year to date, the stock is up 30%, on pace for its biggest one-year advance since 2017, when it rallied 69.9%.

— Fred Imbert

Stocks opened higher on Monday, with the Dow Jones Industrial Average touching a fresh record high.

The 30-stock Dow advanced 42 points, or 0.1%, after briefly notching a new record. The S&P 500 added 0.15%, while the Nasdaq Composite gained 0.42%.

— Brian Evans

— Sarah Min, Tom Rotunno

While stocks still remain at record-high levels, volatility has not fully exited equity markets and could play a larger role as the election looms, according to Piper Sandler.

"Equity markets remain constructive as the quarter-end nears. However, we anticipate some backing and filling in the weeks before the November elections," analyst Craig Johnson wrote Tuesday.

— Brian Evans

Chinese stocks soared after the country's central bank unveiled new stimulus to spur economic growth. Adam Crisafulli of Vital Knowledge called the easing measures the biggest news out of the overnight session.

"The news is undoubtedly bullish for Chinese stocks (and cyclical/industrial sentiment broadly), although many are adopting a dismissive "here we go again" attitude toward the headlines, lamenting the scope and scale of the actions and anticipating a reversal of the present euphoria within a few days or weeks," he wrote. "We're not quite as cynical — the volume and coordinated nature of China's stimulus steps overnight may not qualify as 'bazooka', but it's close.

— Fred Imbert

Small caps are poised to see massive gains over the next few months, according to Richard Bernstein of Richard Bernstein Advisors.

"The reason, I think, that we're such big bulls on mid-caps and small caps is that that's where the earnings growth is forecasted to be," the firm's CEO and chief investment officer told CNBC's "The Exchange" on Monday. "By the end of this year [or] early next year, we're going to find that small caps … are going to grow at a multiple of what, say, the 'Magnificent Seven' are going to grow at."

He added that while this small-cap performance is not particularly unusual in a trough, it is unusual for it to be happening when the Federal Reserve is "actually easing into this accelerating profits environment" rather than tightening.

"As profits rev up, we should see, normally, the economy just gets stronger, naturally," he continued. "Now we've got the Fed easing on top of that. That's like putting fuel on the fire."

When looking at deglobalization as a key investment theme, Bernstein anticipates that midcap industrial stocks that have a focus on the U.S. economy in particular will be the "big growth beneficiaries."

"As globalization contracts, we have to realize that it's not just semiconductors that open up the United States to national security implications," he said. "It's the fact that we don't produce anything here in the United States. That's basically what our trade deficit shows. We think that presents a tremendous opportunity."

— Sean Conlon

Check out the companies making headlines in extended trading:

• Snowflake — Shares of the data cloud company fell 3% after Snowflake announced a proposed private placement of $2 billion of convertible senior notes.
• AAR — The defense stock rose nearly 4%. In the first fiscal quarter, AAR reported adjusted earnings of 85 cents per share, up 9% from the year-ago period. Revenue came in at $661.7 million, up 20% from the prior year.

The full list can be found here.

— Hakyung Kim

U.S. stock futures were flat Monday night.

Dow Jones Industrial Average futures slipped just 23 points, or 0.05%. Futures tied to the S&P 500 and Nasdaq 100 inched down 0.06% and 0.1%, respectively.

— Hakyung Kim