This report is from today's CNBC Daily Open, our international markets newsletter. CNBC Daily Open brings investors up to speed on everything they need to know, no matter where they are. Like what you see? You can subscribe here.

What you need to know today

Inflation fears drag down U.S. markets
U.S. stocks fell and Treasury yields rose on Tuesday as the ISM services index shows a big jump in prices for December. Europe's regional Stoxx 600 index added 0.32%. Shares of Volvo Car closed more than 9% higher after the Swedish carmaker reported a new global sales record for 2024.

Meta ends fact-checking program
Meta on Tuesday announced it will eliminate its third-party fact-checking program to "restore free expression" and move to a "Community Notes" model, similar to the system on Elon Musk's platform X. Employees took to their internal forum and criticized the company's decision, made two weeks before U.S. President-elect Donald Trump's inauguration.

UK's long-term borrowing costs surge
Yields on long-dated U.K. government bonds or gilts surged to their highest levels since the late 1990s after a tepid debt auction fueled worries over demand. Susannah Streeter, head of money and markets at Hargreaves Lansdown, said concerns are growing that the U.K. may encounter stagflation — a scenario where inflation stays high or rises while economic growth slows.

Anthropic's potential $60 billion valuation
Anthropic, the artificial intelligence startup founded by former OpenAI research executives, is in late-stage talks to raise as much as $2 billion at a $60 billion valuation, CNBC has confirmed. The funding round is being led by Lightspeed Venture Partners, according to a person familiar with the matter. Anthropic, which has been backed heavily by Amazon, is the creator of the AI chatbot Claude.

[PRO] Cautionary signs in stock market
Howard Marks, the co-founder and co-chairman of Oaktree Capital Management who famously foresaw the dot-com bubble, is seeing five cautionary signs in the stock market. While Marks isn't calling it a bubble, he's concerned over signs of froth in equities. Here's what investors should pay attention to, according to Marks.

The bottom line

In a sign of how much investors are currently worried about inflation returning, the Institute for Supply Management's services index, an inflation reading typically secondary to more significant data points like the consumer price index, is sending shockwaves through the market.

The price index for December's ISM report jumped to 64.4% from 58.2% in November, representing a rise of more than 10%. It's the first time since January 2024 the reading has come in above 60%, noted Steve Miller, chair of ISM's Business Survey Committee.

That might only be the start of an unwelcome upward trend. Miller attributes some of the expansion in service activity to "risk management for impacts from ports strikes and potential tariffs" — both of which generate inflationary pressures.

In response, investors pushed up the 10-year Treasury yield to 4.699% during the U.S. trading day, the highest level since April 26. They also dialed down their expectations for a 25 basis points rate cut at the U.S. Federal Reserve's January meeting, pricing in a 4.8% chance of that happening, down from an 8.6% probability just a day ago, according to CME Group's FedWatch tool.

Stocks suffered. The S&P 500 dropped 1.11%, the Dow Jones Industrial Average declined 0.42% and the Nasdaq Composite slid 1.89%, dragged down by a fall in tech stocks. Nvidia slumped 6.2%, breaking its three-day winning streak.

"You're getting a recalibration of inflation expectations and Fed rate expectations. That's triggered this small sell-off in the equity markets after the earlier enthusiasm," said Tom Hainlin, senior investment strategist at U.S. Bank Asset Management Group.

But the strong ISM report also suggests the U.S. economy's still doing well, which provides fertile ground for profit growth, said Hainlin. And as David Lefkowitz, CIO head of US equities for UBS, wrote in a Monday note, "profit growth matters more" than valuation for returns over the next 12 months.

One data point from one measure of inflation doesn't chart out the path of inflation or corporate health for the year ahead. But it pays to tread carefully for now.

— CNBC's Jeff Cox, Sean Conlon, Pia Singh and Lisa Kailai Han contributed to this report.