Stocks surged Tuesday as Wall Street built on a sharp rally seen in the previous session and bond yields continued to fall.

The Dow Jones Industrial Average rose 825.43 points, or 2.8%, to 30,316.32. The S&P 500 added nearly 3.1% to close at 3,790.93, and the Nasdaq Composite was up 3.3% to end at 11,176.41.

Tuesday's gains also put the S&P 500 up 5.7% for the week and marked its biggest two-day rally since March 2020{

S&P 500 heads for biggest 2-day rally since 2020

The S&P 500 is up more than 5% in the first two sessions of October, putting the broader market index on pace for its biggest two-day rally since 2020.

Energy has been the big outperformer during this stretch, rising 9.1%. Marathon Oil, APA and Devon are also among the S&P 500's best performers week to date, gaining more than 13% each.

But it's not just energy. The other 10 S&P 500 sectors are also up sharply during these past two days. What's more, just four stocks in the S&P 500 are lower this week.

— Fred Imbert

Markets have had a strong start to the month, bringing a respite from the swift declines seen September and the prior quarter. On Monday, the Dow jumped about 765 points for its best day since June 24. The S&P 500 advanced about 2.6% in its biggest one-day gain since July 27, and the Nasdaq added 2.3%.

"After falling more than 9% in September and extending its year-to-date decline to nearly 25% as of Friday's close, we think the S&P 500 was looking oversold," said Mark Haefele, chief investment officer at UBS Global Wealth Management. "In addition, some of last week's selling pressure may have been driven by quarter-end rebalancing, which has now ended."

"With sentiment toward equities already very weak, periodic rebounds are to be expected," he added. "But markets are likely to stay volatile in the near term, driven primarily by expectations around inflation and policy rates."

Sentiment has improved these past two sessions as Treasury yields come off more-than 10-year highs. The 10-year Treasury yield traded at about 3.63% on Tuesday, down from more than 4% at one point last week. Earlier in the day, it broke below 3.6%.

Sentiment on Tuesday also got a boost as shares of Credit Suisse ended the day 12% higher. Earlier in the week there were concerns regarding the bank's financial health. The bank told CNBC it would provide updates to its strategy alongside its third-quarter numbers.

In other notable stock moves, Twitter leapt 22% after Elon Musk changed course and agreed to purchase the social media giant for the price of $54.20 a share

Stocks extended their advance following job openings data{

U.S. job openings fall for the month of August

There were about 1.1 million fewer job openings than expected in August, the Bureau of Labor Statistics reported Tuesday, providing a potential early sign that the massive U.S. labor gap is beginning to close.

Available positions totaled 10.1 million for the month, less than the 11.1 million FactSet estimate, according to the Job Openings and Labor Turnover Survey.

Hires edged higher while total separations jumped by 182,000. Quits, or those who left their jobs voluntarily, rose by 100,000 for the month to 4.16 million.

— Tanaya Macheel, Jeff Cox

Still, the current bounce is "nothing different from the rally we had this summer," Holly Newman Kroft, senior wealth advisor at Neuberger Berman, said on CNBC's "Closing Bell" Tuesday.

"People like to hang onto good news but… we're not going to have a recovery in this market until the Fed signals that they're going to stop raising rates, and that's not going to happen until inflation starts coming down," she said.

Lea la cobertura del mercado de hoy en español aquí.

Stocks continue their rally into the close

The major averages posted their second consecutive day of gains, continuing their rise all the way into the close on Tuesday, helped by the spike in Twitter shares.

The Dow Jones Industrial Average ended the day up 825.43 points, or 2.8%, to 30,316.32. The S&P 500 added 3.1% to 3,790.93, and the Nasdaq Composite was up 3.3% to 11,176.41.

— Tanaya Macheel

Twitter resumes trading, jumps above $51 per share

Shares of Twitter extended their gains after a multi-hour pause in trading as Elon Musk has filed his letter to complete the deal at its original price.

The stock was trading near $51.81 per share, up more than 21% for the session and well above the $49.23 where it had been paused for most of the afternoon.

Under the terms of the deal, Elon Musk will have to pay $54.20 per share for the social media company. The market price implies that there is still some skepticism that the buyout will be completed.

— Jesse Pound

Dollar index falls back to 110

One factor helping equity markets on Tuesday could be a slightly weaker dollar, which is falling for the fifth-straight day.

The DXY US Dollar Currency Index was down 1.5% in afternoon trading at 110.06. The index was trading as high as 114.78 last week, when there was concern about a failure of the UK government bond market.

The British pound and the euro were each more than 1% against the dollar on Tuesday. The greenback was also down against the Japanese yen.

—Jesse Pound, Gina Francolla

S&P 500 poised to hit record not seen since at least 2000, Susquehanna says

Ninety-seven percent of S&P 500 stocks are up for the third time in the past five trading days. If that holds through the close, it would be the first time since at least 2000 that the broader market index has seen such strength at the stock level.

Investors typically watch the 97% marker because it can signal a pull back coming, according to Susquehanna. Excluding this past week, this week marked the first time since Aug. 25, 2015 that 97% of S&P 500 components were up in two of the previous five trading days.

— Alex Harring

October a 'make-or-break' month for the bear market, says eToro’s Cox

Callie Cox, eToro U.S. investment analyst, said that while this week's rally feels "a bit like a panic," it could be setting up for another bounce similar to the rally earlier this year off June lows.

"The bulls are back in force after a rough few weeks," Cox said. "However, it's interesting to think that we've only seen this magnitude of a rally in the depths of bears, or shortly after a bottom."

"One has to wonder if we're setting ourselves up for a mirror of July's rally," she added. "Either way, this month feels like a make-or-break for the bear market. We're getting the regular slate of economic data – including updated jobs and inflation data – the start of earnings season, the final stretch before mid-term elections and a Fed meeting," after October.

She also warned that "good volatility is still volatility, and it can trick you into making snap decisions with your portfolio."

— Tanaya Macheel

Stocks making the biggest moves midday: General Motors, Illumina and more

These are some of the stocks making the biggest moves during midday trading on Tuesday.

• Travel stocks — Shares of airline and cruise line stocks surged Tuesday and were among leaders in the S&P 500. Norwegian Cruise Line jumped 13%. Royal Caribbean and Carnival gained 12% and 11%, respectively. Delta Air Lines and American Airlines each advanced more than 8%.
• Illumina — The biotech stock jumped more than 9% after SVB Securities upgraded Illumina to outperform from market perform.
• General Motors — Shares of automaker General Motors gained 7% after the company announced sales rose 24% in the third quarter, rebounding from 2021 when supply chain issues hindered production.

Twitter, Rivian and Poshmark were also among the biggest movers.

Read the full list of stocks moving midday here.

— Tanaya Macheel

Market bounce nearing technical resistance levels, strategist says

The market's two-day rally has brought the S&P 500 back up to a potential area of resistance, according to Janney technical analyst Dan Wantrobski.

The broad market index was trading at 3,771 on Tuesday afternoon after closing below 3,600 on Friday. But that quick bounce could soon hit a technical ceiling.

"For the S&P 500, watch for a potential resistance range of 3800-4000 on further rally efforts," Wantrobski said in a note to clients. :Beyond that, the declining 200-day MA ... currently resides at 4200- and we would note that this offered stiff resistance to the June rally just a few months ago."

If this week's rebound doesn't hold, there is some major downside possible from here, according to Wantrobski.

"Continue to watch for first support within the 3500-3600 zone, followed by 3100-3200 (which we would consider a wash-out range given the extremes in sentiment we have already experienced)," he said.

— Jesse Pound, Michael Bloom

100% of institutional investors polled by Evercore ISI expect a recession

Every institutional investor surveyed by Evercore ISI on Oct. 3 expects the U.S. will fall in to a recession — 89% seeing it in 2023 and 11% in 2022.

(The silver lining for investors is that that expectation means, by definition, that a recessionary outlook is already reflected in current prices.)

Investors' consensus end-of-2022 forecast for the S&P 500 came in at 3490, or 5% below Monday's close of 3678. Consensus fed funds were pegged at 4.00% — below market expectations, according to Evercore ISI founder and head of economic research Ed Hyman.

Core consumer price index inflation, excluding food and energy, was forecast at 4.2% by the end of 2023 by those surveyed, or about a percentage point above the public market consensus.

— Scott Schnipper

Twitter shares pop on report that Elon Musk plans to go through with company buyout deal at $54.20

Twitter shares rallied more than 12% after Bloomberg News reported that Tesla's Elon Musk planned on proceeding with a buyout of the company for $54.20 per share. The stock was then halted for news pending.

Click here to read more.

— Fred Imbert

European stocks rally

U.S. stocks weren't the only ones surging Tuesday.

The Stoxx 600 index, which tracks a broad swath of European stocks, popped 3.1% on the day — marking its biggest one-day gain since March. Travel and leisure names led the gains, rising 6.1%. Tech and industrials also advanced 5% and 4.2%, respectively.

The German Dax surged 3.8%, while France's CAC 40 soared 4.2% — its best day since March.

Read more here.

— Fred Imbert

Tesla is topping, Strategas says

Tesla may be hitting a peak, even as the broader market rallies, according to Strategas Technical and Macro Research.

"We're in the camp TSLA is topping and rallies should be used to reduce exposure," Strategas partner Chris Verrone wrote in a Tuesday note.

Verrone said Tesla's underperformance compared to the S&P 500 is "in step with what the trend has been all year." The stock is down about 27.6% so far in 2022.

Meanwhile, he said it is notable the rates are down around 40 basis points in recent days. At the same time, he doesn't see a relative advantage in Ark.

— Alex Harring

Poshmark deal provides validation for secondhand retail, but be wary of a rally among its rivals

Poshmark's acquisition by Korean internet company Naver has sparked a rally among its rivals that also sell secondhand apparel and other goods. Both RealReal and ThredUp gained more than 19%, luxury-brand focused Farfetch rose nearly 12% — and even eBay and Etsy shares are getting a bump.

Naver is scooping up Poshmark for $1.2 billion, which is less than half its January 2021 IPO price.

Investors who are hoping for more consolidation in the sector should tread carefully. Many of the names are heavily shorted. In a research note, Jefferies analyst Ashley Helgans said the deal backs the notion that resale is a "fast-growing and attractive LT industry." But it also highlights how much pureplay e-commerce companies have sold off, she said.

At the end of the day, Helgans said she expects many acquirers will be looking for companies that have a history of profitability or at least "the clearest path" to it.

—Christina Cheddar Berk

S&P 500 heads for biggest 2-day rally since 2020

The S&P 500 is up more than 5% in the first two sessions of October, putting the broader market index on pace for its biggest two-day rally since 2020.

Energy has been the big outperformer during this stretch, rising 9.1%. Marathon Oil, APA and Devon are also among the S&P 500's best performers week to date, gaining more than 13% each.

But it's not just energy. The other 10 S&P 500 sectors are also up sharply during these past two days. What's more, just four stocks in the S&P 500 are lower this week.

— Fred Imbert

Adam Parker says we're underwriting a recovery that's 'a little too optimistic'

Trivariate Research's Adam Parker says investors may be "a little too optimistic" on a 2023 recovery.

"I've been sort of warming to this idea in the last two to three weeks that the consensus view that we get a bottom and then recovery in 2023 might be wrong," Parker said Tuesday on CNBC's Squawk on the Street.

"We might have just a slower decline from a very strong nominal GDP now, and maybe 2024 numbers are a little bit below '23, and maybe we're underwriting a recovery that's maybe a little too optimistic right now," he added.

The CEO and founder at Trivariate Research advised investors to keep an eye on overstocked inventory levels in apparel, industrials and other sectors as they head into corporate earnings reporting season next week.

Parker also advised investors seek out stocks that have "relative estimate achievability" in order to outperform in a challenging environment.

"My suspicion is that we have kind of a equal 10% down, 10% upside over the next six months. That's not great risk reward," he said.

— Sarah Min

Market's broad rally leaves just three stocks behind

Tuesday's market rally is so broad that just three stocks are in the red in late morning trading, and none of those are down even 1% for the session.

The breadth marks a complete reversal of some of the market's worst days in late November, when nearly every stock was falling and just a few utility and health care stocks were managing to tread water.

The lonely laggards on Tuesday are:

• Teleflex
• Netflix
• Regeneron Pharmaceuticals

— Jesse Pound

The Fed's tightening is the wrong policy, according to Barry Sternlicht

Billionaire investor Barry Sternlicht thinks that the Federal Reserve's aggressive rate hike path is the wrong call and it could further hurt the global economy and markets going forward.

"They are going to cause unbelievable calamites if they keep up their action, and not just here, all over the globe," the chairman and CEO of Starwood Capital Group said on CNBC's "Squawk Box" Tuesday.

As evidence, he pointed to this year's stock market rout as well as the stronger U.S. dollar roiling global currency markets.

Instead, the Fed should move slower and look more closely at economic data, he said.

Read more here.

—Carmen Reinicke

Shares of cruise operators and airlines jump

Cruise operators and airlines helped propel the S&P 500 as the index extended its rally on Tuesday.

Shares of Norwegian Cruise Line Holdings added 8% shortly after 10 a.m. The rally follows news that the cruise operator is ending Covid testing, masking and vaccination requirements, effective Tuesday. Customers will still be subject to local Covid travel requirements.

Carnival gained more than 7%, and Royal Caribbean jumped 6.2%. Both cruise lines still require testing for unvaccinated passengers.

Shares of air lines also rallied. Delta and American each jumped 7%, while United added 6.5%.

—Darla Mercado

U.S. job openings fall for the month of August

There were about 1.1 million fewer job openings than expected in August, the Bureau of Labor Statistics reported Tuesday, providing a potential early sign that the massive U.S. labor gap is beginning to close.

Available positions totaled 10.1 million for the month, less than the 11.1 million FactSet estimate, according to the Job Openings and Labor Turnover Survey.

Hires edged higher while total separations jumped by 182,000. Quits, or those who left their jobs voluntarily, rose by 100,000 for the month to 4.16 million.

— Tanaya Macheel, Jeff Cox

Stocks open higher as investors look to extend Monday's rally

Stocks jumped to start the day Tuesday as Wall Street aimed to build on a sharp rally seen in the previous session.

The Dow Jones Industrial Average rose 405 points, or 1.4%. The S&P 500 increased 1.6%, and the Nasdaq Composite was up 2%.

— Tanaya Macheel

No sign that the bear market bottom is in, DataTrek's Colas says

Investors shouldn't get too excited about the big start to October, as such rallies rarely signal the end of bear markets.

"History strongly suggests that [Monday's] 2.6 pct S&P rally is neither healthy nor a sign that the index has troughed," Data Trek Research co-founder Nicholas Colas wrote in his daily market note Monday.

In fact, Colas pointed out, the index posted average gains of 6.4% the day after the 2002, 2009 and 2020 bear market troughs. That indicates the market will need some stronger rallies before it can climb out of the difficult 2022 environment.

"The low for US equities only happens when geopolitical developments or fiscal/monetary policy reduces investor uncertainty," Colas wrote.

—Jeff Cox

Stocks making the biggest moves premarket

These companies are making headlines before the bell:

• Rivian — Rivian's stock rallied 9.3% after the electric vehicle maker announced that third-quarter production rose 67% from the second quarter.
• Poshmark — Poshmark shares rallied 12.1% following news that South Korean internet giant Naver is purchasing the popular online retail site in an all-cash deal.
• Gilead Sciences — The biopharmaceutical stock added 3.1% in the premarket after JPMorgan Chase upgraded the stock and said shares are currently undervalued.

Check out more premarket movers here.

— Samantha Subin, Tanaya Macheel

Ferguson says there's a 'disconnect' and traders shouldn't expect Fed pivot

Former Federal Reserve Vice Chair Roger Ferguson said on "Squawk Box" that traders appear to be reading too much into whether the Fed could change its hardline stance to fighting inflation.

"I think what's going on in markets is they are building up on an expectations of some sort of pivot, which I personally believe is premature. The job of markets is to anticipate, and I think they're anticipating something that would make their lives better so to speak," he said.

The Bank of England announced a temporary bond buying program last week to calm financial markets in London, but the Federal Reserve has not hinted at any such program in the U.S. That move also appeared to be sparked by a budget proposal from U.K. politicians that unnerved bond traders.

Ferguson, who also worked as CEO of TIAA, said this week's U.S. market rebound and pullback in Treasury yields is probably not what the Fed wants to see as it is evaluation how tight financial conditions are.

"There's bit of a disconnect between the hope in the market versus the reality of the Fed," Ferguson added.

— Jesse Pound

Credit Suisse shares rebound

Shares of Credit Suisse rose 4% in Tuesday premarket trading after falling as much as 10% the prior day.

The stock tumbled on Monday, before rebounding to close down nearly flat, after a Financial Times report said Credit Suisse executives are reassuring major investors on the financial health of the Swiss bank. Shares are down roughly 60% this year.

The bank said it would provide updates on its strategy alongside its third-quarter results, according to a statement to CNBC on Monday. Credit Suisse is reporting results later this month on Oct. 27.

"It would be premature to comment on any potential outcomes before then," the statement read.

— Sarah Min

Rivian surges after hitting new production high

Shares of electric vehicle maker Rivian jumped nearly 9% in premarket trading Tuesday after the company announced on Monday that it had produced more than 7,000 vehicles in the third quarter.

That's the company's highest quarterly production to date. The company also said that it is on track to meet its 2022 production goals after having to cut the target in half earlier in the year due to supply chain issues.

Read more here.

—Carmen Reinicke

'Cash is probably not trash,' says BNY Mellon Investment Management

Conventional wisdom suggests that holding cash in an inflationary environment is not recommended, but "cash is probably not trash anymore," according to Aninda Mitra, head of Asia macro and investment strategy at BNY Mellon Investment Management.

Asked if cash and Treasury bills look attractive given the inverted yield curve, Mitra said he agreed, emphasizing the benefits of holding cash in U.S. dollars.

"I think that's an area which still looks pretty good, it's an extension of the overall long dollar story," he said.

The U.S. dollar index has steadily climbed this year, from below 98 to above 111 as of Tuesday.

— Abigail Ng

CNBC Pro: Here’s what's next for stocks, according to Wall Street pros

September is finally behind us, much to the relief of many equity investors who endured a difficult month, with all major U.S. indexes posted steep losses.

With a historically weak month now firmly in the rearview mirror, what is the outlook for stocks as we enter into the fourth quarter of the year?

CNBC Pro combed through the research to find out what Wall Street thinks.

Pro subscribers can read more here.

— Zavier Ong

Watch fourth quarter earnings guidance more than third quarter actual numbers, S&P Global says

Fourth quarter earnings forecasts companies give when reporting third quarter results will be far more important to the market's future direction than the actual third quarter numbers themselves, S&P Global believes.

"October brings earnings, with Q3 estimates already declining 7%, and the whisper numbers a bit more than that," Howard Silverblatt, senior index analyst wrote over the weekend. "The larger concern (than the actual numbers for Q3, when consumers were still spending) is the guidance for Q4, as consumers have pulled back, inflation continues and the Fed's `adjustments' will have a more substantial impact."

Third quarter earnings for the S&P 500 are projected by analysts to grow 6.1% compared with the same quarter a year ago, and almost 18% over the second quarter of 2022, S&P Global said.

Next year's estimates call for a 14.3% earnings growth over 2022, and a corresponding forward P/E ratio of 15.0.

Silverblatt also looked at typical performance for the S&P 500 in the month of October. "Historically, the index posts gains 57.4% of the time, with an average gain of 4.18% for the up months, a 4.67% average decrease for the down months and an overall average decrease of 0.46%," he wrote.

-- Scott Schnipper

Stocks moving after hours: Rivian, Dynatrace and more

Some stocks were moving after hours on news, including:

• Rivian — The electric vehicle maker went up 2.7% after announcing after the bell that production met expectations in its quarter ending Sept. 30.
• Dynatrace — The software intelligence company increased 4.6% after being upgraded to a buy from JPMorgan. The stock rose 3% during regular trading.

See the full list here.

— Alex Harring

Futures open up slightly

The three major indexes for after-hour trading opened up slightly Monday.

Nasdaq 100 futures saw the biggest gain at open, up 0.26%.

Futures tied to the S&P 500 increased 0.17%. Futures for the Dow Jones Industrial Average were up 31 points, or 0.10%.

— Alex Harring