Stocks rallied Tuesday, building on their strong November gains, as Wall Street cheered new U.S. inflation data that raised hopes of the Federal Reserve wrapping up its rate-hiking campaign.

The Dow Jones Industrial Average jumped 489.83 points, or 1.43%, to end at 34,827.70. The S&P 500 rallied 1.91%, briefly trading above the key 4,500 level, to settle at 4,495.70. It was the best day since April for the broad-market index. The Nasdaq Composite jumped 2.37% to close at 14,094.38.

Tuesday's gains added to an already stellar performance this month for stocks. The S&P 500 and Dow are up 7.2% and 5.4%, respectively, in November. The Nasdaq is up 9.7%, on pace for its biggest monthly gain since January.

CPI was flat last month, while economists polled by Dow Jones expected a gain of 0.1% month over month. So-called core CPI, which strips out food and energy prices, was also lower than expected and rose at the slowest rate in two years. This instilled optimism into the market that the Federal Reserve could finally end its rate-hiking campaign for good.

"There's optimism that inflation is cooling to a level where the Federal Reserve can take its foot off the brake," said Keith Buchanan, portfolio manager at Globalt Investments.

Following the report, fed-funds futures pricing data suggested rates are likely to remain steady at the next Fed policy meeting, according to the CME FedWatch Tool.

The 10-year Treasury yield, which shocked investors by leaping over 5% in October, tumbled below 4.5% following the soft inflation report.

Leading the equity rally Tuesday was the Technology Select Sector SPDR Fund (XLK), which tracks the tech stocks in the S&P 500. The fund closed at a record high, as investors returned to the sector that has been one of the hardest hit by rate hikes. Shares of Tesla gained more than 6%.

Bank stocks such as Bank of America and Wells Fargo jumped on the hope that the economy could skirt a recession.

Shares of Home Depot, which were up 5% on better-than-expected third-quarter earnings, led the gains for the Dow. Enphase Energy, Boston Properties and SolarEdge Technologies — each up more than 10% — led the S&P higher.

Stocks finish Tuesday higher

Stocks ended Tuesday's session in positive territory on a soft inflation report.

The Dow Jones Industrial Average finished nearly 490 points higher, or 1.43%. The S&P 500 added 1.91%, while the Nasdaq Composite gained 2.37%.

— Lisa Kailai Han

Oil settles flat as traders weigh Middle East tensions, stronger demand forecasts

Oil settled flat Tuesday as traders weighed signs that Middle East tensions may be easing against higher crude demand forecasts.

Brent crude contracts for January fell 5 cents to settle at $82.47 a barrel, while U.S. West Texas Intermediate contracts for December held steady at $78.26.

There were some signs that Middle East tensions may ease with President Joe Biden saying he believes a deal can be reached to free hostages taken by Hamas. Fears that the Israel-Hamas war could spread had sent crude prices higher in mid-October.

Crude prices rose earlier in the day after the International Energy Agency boosted its crude demand forecasts and cooling U.S. inflation strengthened the case that the Federal Reserve may be done hiking interest rates.

-- Spencer Kimball

Tuesday's stock move exceptionally broad and deep, finally reaching lagging groups

Tuesday's stock market rally — sparked by lower Treasury yields themselves led lower by weaker-than-forecast October inflation — has been exceptionally broad and deep, touching areas of the market that have lagged all year.

For example, 91% of all the volume on the New York Stock Exchange advanced in price, while just 9% declined. On the Nasdaq, it was 85% up vs 15% down. Similarly, nine out of 10 NYSE stocks rose while advancers outpaced decliners on Nasdaq by 7 to 3. New highs swamped new lows on the NYSE by 6 to 1.

The SPDR S&P Regional Bank ETF that was decimated in the spring after Silicon Valley Bank failed, soared 7.6%. Western Alliance Bancorp jumped 10.5%; PacWest Bancorp by 9.9%

The S&P 500 Real Estate Index, previously hurt by concerns surrounding commercial real estate loans in 2023, bounced back 5.5% — the strongest of the S&P's 11 main sectors on the day. The Russell 2000 index of smallcap stocks climbed 5.2% — more than double the 2.1% advance in the S&P 500.

— Scott Schnipper

Abbott makes the case that patients on Ozempic fare better with continous glucose monitoring

Abbott shares are up in trading Tuesday after it posted the results of study it conducted with patients who have type 2 diabetes and take a GLP-1 drugs like Novo Nordisk's Ozempic. These patients had struggled to lower their HbA1c levels, but after using Abbott's Libre continuous glucose monitor saw improvements in this important metric.

Abbott's data is the latest to be released from manufacturers of CGM devices that make the case that GLP-1 drugs can co-exist with the monitoring devices.

Sentiment does appear to be shifting this week, with medical device stocks clawing back recent losses in trading. Other beaten up names like Insulet and Tandem Diabetes Care were logging even bigger gains of nearly 5% and 16%, respectively.

In a research note about Abbott's study, Bank of America analyst Travis Steed reiterated his buy rating on Abbott shares saying, "estimates for 2024 seem derisked and ABT's gross margin expansion gives room for upside along with its balance sheet."

—Christina Cheddar Berk

Communications services ETF notches new high

Tuesday's stock market rally pushed the Communication Services Select Sector SPDR Fund to its highest level since April 2022.

Shares of the exchange traded fund climbed nearly 2%, pushing the price close to $70.

Shares of Meta and Take-Two Interactive Software at least reached their 52-week highs. Biggest gainers also included Paramount and Warner Brothers, which were both up at least 6% during midday trading.

— Lisa Kailai Han, Gina Francolla

Real estate stocks lead S&P 500 higher

Real estate stocks in the S&P 500 outperformed on Tuesday as the index saw a broad rally.

The sector jumped more than 5%, making it the best performing of the 11 that make up the broad index. Consumer discretionary and utilities saw the next largest gains, with each up more than 3%.

To be sure, it was a broad rally with all 11 sectors trading higher. The S&P 500 as a whole was up 2% on the day.

Real estate led in part from rallies of more than 10% in Alexandria Real Estate Equities and Boston Properties. Every stock in the sector advanced notably in the session.

— Alex Harring

Inflation cooling at near-record pace, says Chicago Fed President Austan Goolsbee

Inflation is dropping this year at a near-record pace, but more progress needs to be made, Chicago Federal Reserve President Austan Goolsbee said Tuesday.

This year may be the quickest cooling, outside of wartime, while there is full employment, he said in remarks prepared for a Detroit Economic Club event Tuesday. Goolsbee is the first Fed official to react to Tuesday's consumer price index report, which was flat month over month in October.

Improvements in supply and accelerating productivity drove the declines, he said.

"Progress continues, though we still have a way to go," Goolsbee said. "In 2023, we may equal or even surpass that one-year mark for a fall in CPI inflation. And we may do that with an unemployment rate that never gets above 4 percent," he added.

Goolsbee said the U.S. can have strong growth without inflation due to the unwinding of supply shocks. The key to further cooling of inflation will be housing, he said.

— Michelle Fox, Jeff Cox, Steve Liesman, Reuters

Software ETF hits highest level since January 2022

The latest rally for software stocks is pushing a major fund to its highest level in nearly two years.

On Tuesday, the iShares Expanded Tech-Software ETF (IGV) hit its highest level since January 2022.

The fund has nearly $7 billion in assets under management. Its top holdings include Microsoft, Adobe and Salesforce.

— Jesse Pound

Michael Burry reveals potential new bet against semiconductor stocks

Michael Burry's Scion Asset Management added a potential new bet against a major chip stock fund during the third quarter, according to a securities filing released Tuesday.

The move comes after Burry made bets against the S&P 500 and Nasdaq 100 earlier this year. He closed those bets during the third quarter.

Read more about Burry's latest move on CNBC Pro.

— Jesse Pound

Stocks making the biggest moves midday

Check out some of the companies making headlines in midday trading.

V.F. Corp – Shares of the apparel company, which owns Timberland and The North Face, gained 12%. The move occurred a day after V.F. Corp disclosed in a regulatory filing that director Matthew Shattock purchased 20,000 shares of the company, valued at more than $291,000 in total.

Amazon, Snap — Stock in the e-commerce giant climbed 2%. The action came a day after The Information reported that Amazon would allow people to buy products advertised on Snapchat. Shares of Snap climbed more than 7%.

C3.ai — Shares added more than 7% in midday trading. C3.ai announced the expansion of a strategic collaboration agreement with Amazon Web Services. The partnership allows the two companies to offer generative AI solutions for businesses.

Read the full list here.

— Brian Evans

Solar stocks surge as U.S. inflation cools

Solar stocks are surging after U.S. inflation cooled in October and Treasury yields dropped.

The Invesco Solar ETF that tracks the industry is up nearly 9%.

The inverter manufacturers Enphase and SolarEdge surged more than 13% and 10% respectively, while the installers SunPower, Sunnova and Sunrun jumped more than 13%, 16% and 18%. Panel manufacturer First Solar jumped more than 10%.

U.S. consumer prices were flat in October compared to the month prior, strengthening the case that the Federal Reserve will is one raising interest rates. The 10-year Treasury yield tumbled below 4.5% on the inflation data.

High interest rates have slammed the residential solar industry this year, dramatically softening consumer demand and leaving companies saddled with inventory.

-- Spencer Kimball

Market is 'celebrating' after latest inflation data, market participants say

The market is in a celebratory mood after the consumer price index reading Tuesday morning and could be readying for an end-of-year climb, said Gina Bolvin, president of Bolvin Wealth Management Group.

"We need to see more months with soft inflation data, but the stock and bond market is celebrating today," Bolvin said. "We're set up nicely for a year-end rally."

Similarly, AXS Investments CEO Greg Bassuk called the data an "early holiday present" for investors unclear about what the Federal Reserve will do with interest rates for the remainder of 2023.

The data "is being cheered by Wall Street and Main Street alike, as a Fed move from hawkish to dovish interest rate policy is just the holiday gift coveted by investors," Bassuk said.

"October's cooler CPI data, combined with a slowing but resilient economy, bodes well for the economy's soft landing, while positioning 2024 for lower interest rates and the prospects for robust stock market growth," he added.

— Alex Harring

A massive market divergence could signal trouble ahead for stocks, BTIG says

A pullback for stocks could be on the horizon after a unique technical signal was flashed, BTIG said.

Last week, the tech-heavy Nasdaq 100 closed less than 5% below a 52-week high, while the small cap Russell 2000 index closed less than 5% above a 52-week low — an occurrence BTIG called "extremely rare." The Russell 2000 ended last week down 3.2%, while the Nasdaq 100 gained 2.9%. Historically, this extreme bifurcation hasn't been good for the market.

"This is often a sign of crowding as the NDX is a cap-weighted index of just 100 large-cap names, while the RTY is more equally weighted of 2k smaller companies," BTIG chief market technician Jonathan Krinsky wrote in a note.

CNBC Pro subscribers can read more here.

— Pia Singh

The Fed looks 'smart' after recent inflation data, portfolio manager says

The Fed appeared justified in its interest rate cycle after the latest consumer price index reading, according to Bryce Doty, senior portfolio manager at Sit Fixed Income Advisors.

"The Fed looks smart for effectively ending its tightening cycle as inflation continues to slow," he said. "Yields are down significantly as the last of investors not convinced the Fed is done are likely throwing in the towel."

— Alex Harring

Technology ETF notches new high

Tuesday's rally propelled the Technology Select Sector SPDR Fund (XLK) to an all-time high.

The ETF, which tracks technology stocks in the S&P 500, climbed more than 1%, pushing the price above $181. That marks its most expensive ever, despite trading close to the level earlier this year and in 2021.

Part of Tuesday's gain is due to an advance among solar stocks. SolarEdge and Enphase led the fund higher with rallies of more than 10% each. With a jump of more than 8%, First Solar was the next best performer.

Outside of solar, ON Semiconductor and EPAM Systems were also among the biggest winners with each stock adding more than 5%.

Motorola Solutions was the only stock in the ETF trading down in Tuesday's session.

— Alex Harring

NYSE advancers lead decliners 15-1

Advancers at the New York Stock Exchange held a wide lead over decliners Tuesday, as traders cheered the latest inflation data. There were 15 advancers for every decliner at the NYSE. In other words, about 2,550 NYSE-listed names were higher, while just 160 fell, FactSet data shows.

— Fred Imbert

Wall Street fear gauge hits lowest level since September

The Cboe Volatility Index (VIX) hit a low of 13.91 on Tuesday, a level not seen since Sept. 20. The move on Wall Street's preferred fear gauge comes after a softer-than-expected U.S. inflation report.

— Fred Imbert

Oil rises as U.S. inflation flat, crude demand outlook improves

Oil price rose more than 1% as inflation cooled in the U.S. month over month and the International Energy Agency raised its crude demand forecast.

Brent crude contracts for January rose $1.06, or 1.28%, to $83.58 a barrel, while West Texas Intermediate contracts for December increased $1.02, or 1.30%, to $79.28 a barrel.

Consumer prices in the U.S. were flat in October from the previous month, strengthening the case that the Federal Reserve is done raising interest rates. Higher rates can slow economic activity and hit crude demand.

The IEA also raised its 2023 crude growth forecast to 2.4 million barrels per day from 2.3 million barrels. The agency increased its 2024 growth forecast to 930,000 barrels per day from 880,000 previously.

-- Spencer Kimball

Markets now think there's almost no chance the Fed will hike again

Markets have almost completely taken off the table any chance that the Federal Reserve will raise interest rates again this cycle.

Following Tuesday morning's inflation report indicating that prices were broadly unchanged in October from the previous month, traders in the futures market were assigning just a 5% probability to a hike at the central bank's December or January meetings, according to the CME Group's FedWatch gauge of futures pricing.

The probability for a December hike was around 14% and 25% for January prior to the consumer price index release.

Instead, futures pricing now points to the Fed's next move as a cut, coming as soon as the May meeting.

—Jeff Cox

Dollar drops after inflation report

The U.S. dollar index fell 1% on Tuesday after the latest consumer price index came in weaker than expected.

The dollar index, which measures the currency against a basket of six others, hit a low of 104.54 in morning trading.

— Michelle Fox

Stocks open higher

Stocks opened higher on Tuesday after October consumer price index came in flat, lower than analysts expected.

The Dow Jones Industrial Average added 357 points, or 1%. The S&P 500 gained 1.3%, while the Nasdaq Composite ticked up 1.9%.

— Lisa Kailai Han

October's CPI was flat

October's consumer price index, a key inflation gauge for the Federal Reserve, came in lower than analysts expected.

Inflation was flat from the previous month, versus the 0.1% increase expected by economics surveyed by Dow Jones. The CPI increased 3.2% from a year ago, lower than the 3.3% consensus.

Stock futures rallied on the news.

— Lisa Kailai Han

VIX back down to historical averages, spelling good news for the market, DataTrek says

The CBOE Volatility Index — or VIX, a popular gauge of market volatility — is back to normal levels after spiking above 20 last month, its long-run average since 1990, according to DataTrek Research.

The VIX tends to have an inverse relationship with the equity market. This proved true last month when the VIX closed at 21.3 on October 27, the same day the S&P 500 posted near-term lows and closed at 4,117.

But with the gauge back down to bull market territory, or trading at a level around 15, DataTrek co-founder Nicholas Colas is optimistic what this means for stocks ahead.

"Markets are confident that rates will stabilize/decline and stocks will continue to rally," he wrote. "We agree."

— Lisa Kailai Han

Oil flat as IEA raises demand forecast

Oil was largely flat on Tuesday after the International Energy Agency forecast higher demand for crude.

The Brent crude contract for January fell 17 cents to $82.35 a barrel, while the West Texas Intermediate contract for December fell 10 cents to $78.16 per barrel.

Oil futures traded largely flat despite the IEA raising its 2023 growth forecast to 2.4 million barrels per day from 2.3 million barrels. The agency also raised its 2024 growth forecast to 930,000 barrels per day from 880,000 previously.

Crude sold off last week on worries that demand will fall in the China and the United States as the global economy is expected to slow. But the Organization of Petroleum Exporting Countries said the market is strong, blaming speculators for the selloff.

-- Spencer Kimball

Home Depot earnings beat expectations, but offers weak outlook

Home Depot reported third-quarter earnings and revenue that beat expectations. However, the home improvement retailer issued tepid guidance, keeping shares in check.

"A customer who might have remodeled their entire home may be opting for a partial remodel," CFO Richard McPhail told CNBC. "Maybe they won't redo their entire kitchen. Maybe they'll just do the countertop and backsplash. And so it's really just the downscaling of projects that we've seen."

— Fred Imbert

A muted open in Europe

European markets were mixed on Tuesday, with investors looking ahead to preliminary third quarter gross domestic product data from the euro zone, along with October's U.S. inflation print.

The pan-European Stoxx 600 index was roughly flat in early trade. Basic resources added 0.9% while financial services stocks dropped 0.5%.

CNBC Pro: Morgan Stanley picks global 'alpha' opportunities for November — and gives one about 60% upside

Asian markets have had a tumultuous year.

The MSCI Asia ex Japan Index plunged from its January high, losing around 12% since then.

Chinese stocks are especially volatile. Hong Kong's Hang Seng index is down around 12% in the year to date, while the Shenzhen Component has fallen over 9%.

Those keen on investing in Asia in the face of such uncertainty can consider Morgan Stanley's selection of Asian stocks it calls "alpha" opportunities for November.

CNBC Pro subscribers can read more here.

— Weizhen Tan

CNBC Pro: Goldman Sachs: These 'conviction list' global stocks will benefit from a circular economy boom

Rising commodity prices, increased regulation and a growing recognition of sustainability benefits are set to be "key catalysts" of the circular economy, Goldman Sachs said, naming its "conviction list" stocks to play the theme.

Quoting estimates from McKinsey, Accenture and the United Nations Environment Program, the bank said that the economic benefits of the circular economy range from $2.9 trillion to $4.5 trillion by 2030.

"While regulators, corporates, and investors have placed much emphasis on achieving Net Zero emissions and Biodiversity goals, we believe the critical role a Circular Economy will play in solving for both has been overlooked, particularly as a lack of available resources threatens the speed, scale, and affordability of a clean energy transition," Goldman's analysts wrote in a Nov. 2 note.

CNBC Pro subscribers can read more here.

— Amala Balakrishner

Australia November consumer confidence slides after rate hike

Australia's consumer confidence slid in November, according to a Westpac-Melbourne Institute survey.

The Westpac-Melbourne Institute index of consumer sentiment fell to 79.9 in November, down from 82 in October. The current reading reflects deeply pessimistic levels, according to the survey.

It notes that the Reserve Bank of Australia's decision to raise interest rates by 25 basis points to 4.35% last week, knocked about 6 points off confidence during the survey week.

"The RBA's November rate hike has put renewed pressure on family finances and reignited concerns about both the rising cost of living and the prospect of further rate rises to come," said Matthew Hassan, senior economist of Westpac Group.

"Responses over the survey week show sentiment was heading for a slight gain prior to the RBA move, responses amongst those surveyed before the decision consistent with an index read of just over 83."

The RBA had held interest rates steady four straight months until its meeting in November.

— Shreyashi Sanyal

Moody’s cuts outlook on banking subsidiaries of JPMorgan, Wells Fargo and more

Moody's Investors Service lowered its outlook late Monday to negative from stable on a slate of banking subsidiaries, including those of JPMorgan and Wells Fargo.

The move comes after the ratings agency cut its outlook on the U.S. government Friday.

In particular, the ratings agency affirmed the Aa1 long-term deposit ratings for certain bank subsidiaries and branches of Bank of America, JPMorgan Chase & Co. and Wells Fargo. However, Moody's updated its outlook on these ratings to negative from stable.

The ratings agency pointed to "the potentially weaker capacity of the Government of the United States of America (Aaa negative) to support the US's systemically important banks, as reflected in the recent change in the outlook on the Government of the United States of America to negative from stable."

-Darla Mercado

Look for a ‘strong’ consumer price index report in October, says Vanguard’s Andrew Patterson

Tuesday's consumer inflation report will likely show some "strong to quite strong" data for October, according to Andrew Patterson, senior economist at Vanguard.

"Near-term risks are skewed to the upside for this month and could come from goods inflation deflating at a slower than expected pace as the fall in used car prices stalls, and from healthcare insurance and [owners' equivalent rent] coming in higher than expected," he said.

Looking at the components of core inflation, Patterson sees shelter inflation slowing below 0.4% month over month for October, but there is an elevated risk of a higher-than-expected print on owners' equivalent rent.

He noted that supply pressures have normalized to pre-pandemic levels, which means there's limited downside to prices on goods. "In our view, slowing consumer demand will be crucial for future deceleration in the component," Patterson said.

The CPI report is due at 8:30 a.m. on Tuesday.

— Darla Mercado

No let up in chocolate prices as price of cocoa hits an all-time high

Don't expect any let up in the price of chocolate at the holidays after the price of December cocoa bean contracts climbed to a record $4,073 per metric tonne (2,205 pounds) on Monday.

As recently as June, cocoa contracts were trading for less than $3,200 per metric tonne.

Cocoa is more than 56% higher in 2023, but that's not necessarily good news for the companies who use it as a raw ingredient in their products. Hershey is lower by 16% in 2023, Nestle's sponsored ADRs are off 5% while Mondelez is higher by just 4%.

— Scott Schnipper, Gina Francolla

Science stocks rise in extended trading

A handful of science-oriented stocks made notable moves in extended trading.

Azenta climbed more than 4% after delivering a strong financial report for the fiscal fourth quarter. The life science stock beat the consensus forecasts of analysts polled by FactSet and offered guidance for the full year that was in line with expectations.

Viking Therapeutics also added more than 4%. Viking shared new data from the second phase of a trial for patients with patients with non-alcoholic steatohepatitis, known in short as NASH.

— Alex Harring

CPI inflation gauge to get market's attention Tuesday morning

Markets will be watching Tuesday for the first of two key inflation reports that the Labor Department will release this week.

The consumer price index for October is expected to show that prices increased just 0.1% for the month, after rising 0.4% in September, according to a Dow Jones consensus estimate. On a year-over-year basis, the CPI is expected to increase 3.3%, after being up 3.7% the previous month.

Excluding food and energy, core CPI is projected to rise 0.3% and 4.1% respectively, after showing the same levels in September.

The release, due at 8:30 a.m. ET, precedes Wednesday's producer price index, which reflects prices at the wholesale level.

—Jeff Cox

Stock futures are flat

Stock futures were little changed shortly after 6 p.m. ET Monday.

Futures tied to the Dow, S&P 500 and Nasdaq 100 all sat near flat. It followed a relatively muted trading day on Monday as investors readied for the inflation report coming Tuesday.

— Alex Harring