U.S. stocks hit a fresh all-time high on May 15, powered in part by a softer-than-expected April inflation report that has reignited bets on a fall Federal Reserve rate cut and triggered some big changes in Wall Street forecasts.

The S&P 500 has clawed back all of its April decline, while powering to a year-to-date gain of around 12%, despite a host of warnings from Fed officials, including Chairman Jerome Powell, that interest rates are likely to remain elevated until inflation is seen moving definitively toward the central bank's 2% target.

The Commerce Department's April CPI report provided the first real piece of evidence that price pressures in the world's biggest economy could see their final leg of easing into the summer months and beyond.

Headline inflation fell for the first time this year, easing to a year-on-year rate of 3.4%, while so-called core prices slowed to 3.8%, the lowest in nearly three years.

"Looking ahead, the case for expecting a further slowdown in core CPI inflation remains compelling," said Ian Shepherdson of Pantheon Macroeconomics. "Supply chains have normalized, wage growth is weakening, and corporate margins are flat but still hugely elevated, indicating clear scope to fall ahead."

Rate-cut foundations 'are in place'

"The foundations, therefore, are in place for a further deceleration in the core CPI this summer, enabling the Fed to start easing in September," he added.

Following the data report, rate traders immediately repriced bets on a September Fed rate cut, while still expecting no change in the current rate of 5.25% and 5.5% over the next two policy meetings, in June and July.

CME Group's FedWatch now pegs the odds of a quarter point cut in September at 52.1%, with the overall chance of any move now trading at 68.8%.

Related: S&P 500 aims for biggest gain in Fed interest rate pause history

In between, of course, comes the Fed's June policy meeting, which will include fresh growth and inflation projections — and a new set of dot plots, the Fed officials' rate projections — for the back half of the year.

That said, the prospect of lower Fed rates, alongside better-than-expected corporate profits and a resilient domestic economy, has not only lifted stocks to the recent all-time peaks. It has also compelled some Wall Street analysts to overhaul their end-of-year price targets for the broadest benchmark of U.S. stocks.

“It has become clear to us that we underestimated the strength of the market momentum," said BMO Capital Markets' chief investment strategist, Brian Belski, in a note that lifted the bank's S&P 500 price target by 500 points, to 5,600 points, the highest on Wall Street.