Traders on the floor of the New York Stock Exchange.

Source: NYSE

Stock futures are slightly lower in overnight trading after major indices rose in May.

Futures on the Dow Jones Industrial Average fell 35 points, or 0.10%. S&P 500 futures lost 0.09% and Nasdaq 100 futures were 0.03% lower.

The moves in overnight trading come after the blue chip Dow and S&P 500 rose 1.93% and 0.55% respectively in May, marking their fourth consecutive positive month. The S&P 500 closed just 0.8% below its record high on Friday.

The Russell 2000 small cap rose 0.11% in May, recording its eighth consecutive positive month – its longest monthly winning streak since 1995.

The Nasdaq was up 2.06% last week, its best weekly performance since April. However, the tech-heavy composite lost 1.53% in May, breaking a six-month winning streak.

A key inflation indicator – the core consumer spending index – rose 3.1% yoy in April, faster than the forecast increase of 2.9%. Government bond yields fell on Friday despite the unexpectedly high inflation data.

“Overall, given the market reaction to [Friday]In the PCE release, investors’ concerns about inflation may be exaggerated – or perhaps already priced in, “said Chris Hussey, managing director at Goldman Sachs, in a press release.

“There could be a consensus that the inflation we see today is ‘good’ inflation – the kind of price spike that comes with accelerated growth, not a monetary policy mistake,” Hussey said.

The investors are waiting for the 15.-16. June scheduled meeting of the Federal Reserve. What matters to the markets is whether the Fed starts to believe that inflation is higher than expected or that the economy will be strengthened enough to move forward without so much monetary support.

The May labor market report, due to be released on Friday, will provide an important overview of the economy. According to the Dow Jones, economists expect around 674,000 new jobs to be created in May after significantly fewer than expected 266,000 jobs were added in April.

Zoom Video Communications and Hewlett Packard Enterprise will release quarterly results on Tuesday after the bell.

– CNBC’s Patti Domm contributed to the coverage.