Here is Schwab's early look at the markets for Tuesday, May 12.

If last week was all about jobs, this week puts the focus firmly on prices starting with today's April Consumer Price Index, or CPI.

The report, due at 8:30 a.m. ET, could influence the path of both stocks and Treasury yields, though a sharp headline CPI gain might be dismissed as a short-term move driven mainly by high war-related energy costs.

Today's CPI follows a mixed March report that saw a sharp 0.9% increase in headline CPI as gas prices surged. Core CPI excluding food and energy rose just 0.2% that month.

Analysts expect 0.6% headline CPI growth from March and 0.4% core. If that's the case, it might raise concerns that higher oil is starting to leak into the core price index. A stronger-than-expected core number might get the market's attention and perhaps raise odds of a 2026 rate hike.

On an annual basis, analysts expect core CPI growth of 2.7% and headline growth of 3.7%. The Federal Reserve's goal is 2%, though policymakers there more closely watch the Personal Consumption Expenditures (PCE) price index, which focuses less on housing costs than the CPI does.

The April Producer Price Index, or PPI, is tomorrow, and headline PPI could be up as much as 4.8% year over year, judging from analysts' estimates.

"Inflation reports are likely to be hot," said Cooper Howard, director of fixed income research and strategy at the Schwab Center for Financial Research, or SCFR.

Inflation worries intensified Monday when the U.S. rejected Iran's latest proposal to end the conflict.

In data Monday, existing home sales rose to a seasonally adjusted annual rate of 4.02 million, up marginally from April but below the consensus of 4.05 million. Affordability conditions improved, with mortgage rates down from a year ago and average income gains exceeding the 0.9% year-over-year home price increase, Briefing.com noted. Still, sales were tepid thanks possibly to tight supplies. Also, potential buyers might have been hoping for mortgage rates to fall and delayed stepping in.

Speaking of rates, Monday's $58 billion 3-year Treasury note auction met lackluster demand. Timing wasn't great considering the rally in crude oil after President Trump said the ceasefire is "on life support." The Treasury market remains very sensitive to oil prices and what they may indicate about inflation and Federal Reserve policy.

Trump's comments, reported by the media, appeared to weigh on both stocks and Treasuries late in the session. The weak auction didn't help, either.

Today features a closely watched 10-year note auction, with results expected to be out by early afternoon.

Whatever the results of today's auction, long-term Treasury yields could stay near the high end of recent ranges, boosted by oil and signs of U.S. economic strength. Yields rose across the curve yesterday, with the 30-year again flirting with 5% and the 2-year at 3.93%. The 10-year yield finished the day back above 4.4% and near recent highs.

"Friday's payrolls report surprised to the upside which bolsters the case that the labor market is showing signs of stabilization," Howard said.

Though Kevin Warsh is expected to receive full Senate confirmation this Friday to take over as the next chair of the Fed and has advocated for lower rates in the past, "We don’t believe the Fed will aggressively shift to an easing bias," Howard said. "Although the chair is an influential voice, it is only one vote on the committee. We expect the Fed to be on hold for the time being due to a stable labor market and concerns that inflation could accelerate."

As of late Monday, odds of A Fed rate cut at some point this year were only 5%, according to the CME FedWatch Tool. Odds of a hike rose to nearly 22%, from below 15% last Friday when hopes for a peace agreement pushed oil prices down.

Earnings were sparse Monday. Some worth watching later this week include Alibaba and Cisco tomorrow and Applied Materials on Thursday. Cisco is a good barometer for global tech demand, as it sells its equipment for so many applications.

Beyond data and Treasury auctions, investors this week are likely to focus on the Warsh nomination and President Trump's planned late week visit to China where he'll talk with Chinese President Xi. Topics could include the war and tariffs, while the two also discuss technology and rare earths critical to the data center build-out.

"The meeting is more to 'keep the peace' on the trade war, although there may be some purchase agreements and discussions about access to technology and rare earths," said Michelle Gibley, director of international equity research and strategy at SCFR.

Major indexes managed to post more gains to fresh record highs Monday despite the disappointing oil and Iran news, though none could hold their intraday peaks. Volatility rose, too, with the Cboe Volatility Index, or VIX, up 7%. Typically, rising volatility accompanying rising stocks means something might give.  The relationship is worth monitoring again today.

Another thing to monitor is market breadth, which has been relatively mediocre despite record index highs, a possible sign of concentration in the rampaging tech sector. Outside of that, there's some indication of weakness, with 39 S&P 500 stocks falling to 52-week intraday lows Monday, or nearly 8% of all stocks in the index, Barron's noted.

Also checking below the surface, last week saw call buying in the options market reach sky-high levels for tech companies, possibly a warning sign of "fear of missing out," or FOMO getting the best of many participants. It might be interesting to see if more downside hedges get taken this week, especially in the AI space where overcrowding remains a risk.

Five of 11 S&P 500 sectors managed to finish green on Monday, led by a 2.5% gain in energy as oil prices rose. Materials and industrials held their own, and info tech continued its rapid rally, helped by memory chip stocks and a nearly 2% gain for Nvidia, which reports next week and set all-time intraday highs. Communication services had by far the worst day, dropping more than 2% as Alphabet—one of the biggest names in the sector—cratered 3%.

Alphabet fell after Reuters reported that Alphabet and Amazon could be planning to sell Japanese yen-denominated bonds. This would apparently be to support AI spending. Amazon fell 1.3% Monday. The news appeared to make investors more nervous about rising AI expenditures by mega-caps. Meta Platforms and Microsoft also fell.

Among other individual stock movers Monday, Lumentum added 15.5% after it announced its shares will now be part of the Nasdaq-100. The company is a global leader in optical and photonic technologies behind AI and cloud infrastructure. Shares are up 57% over the last three months.

Circle Internet Group rose nearly 16% despite quarterly revenue slightly missing expectations. Earnings per share topped analysts' consensus. The positive move came after Circle announced it had raised $222 million in an ARC Token presale. This is a method through which early stage blockchain projects can raise money, CNBC noted.

Mining shares rose Monday amid strength in the metals complex. Silver climbed more than 7% and copper rose nearly 3%.

Memory chip names continued their rally, with Micron and Western Digital each up about 7%. Intel climbed another 3.5%, still drawing strength from news last week of Apple's plans to rely on Intel for some of its chips.

Whirlpool fell another 8.5% after last week's sharp losses, hurt by its disappointing earnings and outlook.

Qualcomm rose 8%, helped by underlying momentum in the chip market. Executives from the firm will join President Trump on his China trip, Bloomberg reported, as will executives from Apple, Boeing, Tesla, and several other firms.

Retail stocks lost ground Monday as crude prices and yields rose. Some of the weak performers included Dollar General, Wendy's, Nike, Ralph Lauren, Target, and Macy's. Cruise lines and home builders also got hurt by the fundamental moves in oil and Treasuries.

The Dow Jones Industrial Average® ($DJI) carved out a gain of 95.31 points Monday (+0.19%) to 49,704.47; the S&P 500 Index (SPX) added 13.91 points (+0.19%) to 7,412.84, and the Nasdaq Composite® ($COMP) gained 27.05 points (+0.10%) to 26,274.12.