Stocks soared on Tuesday, after an inflation reading raised hopes that the Federal Reserve’s campaign to slow inflation may have reached its limits.

The S&P 500 rose 1.9 percent on Tuesday, while the Russell 2000 index of smaller companies’ stocks, which are more exposed to the ups and downs of the economy, climbed roughly 5 percent.

The stock gains reflected expectations that the Fed may not need to raise interest rates again, after new data showed consumer price inflation slowed in October. The central bank has been increasing borrowing costs since March of last year in an attempt to rein in economic activity and slow the pace of price increases.

The numbers came amid some debate in markets over whether the Fed will have to continue with that campaign — in particular amid signs of a still healthy labor market and other factors that could inhibit policymakers’ efforts to temper inflation. But Tuesday’s report helped cement a view in financial markets that the Fed’s efforts are working.

The government reported that the overall Consumer Price Index slowed to 3.2 percent last month on a year-over-year basis, lower than the 3.7 percent reading in September and the coolest since July.

In the bond market, the two-year Treasury yield, which is sensitive to changes in investors’ interest rate expectations, slumped nearly 0.2 percentage points on Tuesday to around 4.85 percent — a huge move for an asset that typically rises and falls by hundredths of a percentage point.

Alongside dialing down any likelihood that the Fed will surprise markets and still raise rates at its next meeting, in December, investors have also begun to bet on when the Fed will begin to lower interest rates. Jerome H. Powell, chair of the Federal Reserve, recently said that decision was not even being considered by the central bank’s officials as they looked to keep the brakes on the economy until inflation fell further toward their target of just 2 percent.

“This takes a rate hike off the table in December and reinforces our call that July was the last hike of the cycle, and the process will now shift to the Fed attempting to delay cuts as long as possible,” analysts at BMO Capital Markets noted.