NEW YORK — Hopes that inflation is finally heading back in the right direction swept through Wall Street Wednesday and ignited a record-setting rally for U.S. stocks.

The S&P 500 jumped 1.2% to top its prior high set a month and a half ago. The Nasdaq composite added 1.4% to its own record set a day earlier, and the Dow Jones Industrial Average gained 349 points, or 0.9%, to beat its all-time high set in March.

Relief came from the bond market, where Treasury yields eased to release some of the pressure on the stock market. The moves resulted from strengthening expectations among traders that the Federal Reserve may indeed cut its main interest rate this year.

Stocks that tend to benefit the most from lower interest rates helped lead the market. Homebuilders were strong on hopes that cuts by the Fed could lead to easier mortgage rates, with Lennar, D.R. Horton and PulteGroup all rallying more than 5%. Big Tech and other high-growth stocks also rode the wave of expectations for lower rates, and Nvidia’s gain of 3.6% was the strongest force pushing the S&P 500 upward.

Real-estate stocks in the S&P 500 climbed 1.7%, while stocks of electricity companies and other utilities rose 1.4%. The dividends they pay look better to investors when bonds are paying less in interest.

The optimism came from a report showing U.S. consumers had to pay prices for gasoline, car insurance and everything else in April that were 3.4% higher overall than a year earlier. While that’s painful, it’s not as bad as March’s inflation rate of 3.5%.

Perhaps more importantly, the slowdown was a relief after reports for the consumer price index, or CPI, earlier this year had consistently come in worse than expected. That string of disappointing data had washed out forecasts for the Federal Reserve to lower its main interest rate soon.

The federal funds rate is sitting at its highest level in more than two decades, and a cut would goose investment prices and remove some of the downward pressure on the economy.

“There was a lot lying on today’s CPI print to prove that disinflation was simply delayed these last three months and not derailed,” according to Alexandra Wilson-Elizondo, co-chief investment officer of the multi-asset solutions business in Goldman Sachs Asset Management.

A separate report showed no growth in spending at U.S. retailers in April from March. It was a weaker showing than the 0.4% growth economists expected.

Slowing growth in retail sales could be seen as a positive for markets, because it could reduce the upward pressure on inflation. But a stalling out also raises worries about cracks forming in U.S. consumer spending, which has been one of the main pillars keeping the economy out of a recession.