A key measure of investors’ inflation expectations has slipped in recent days, stirring debate over whether it has finally peaked after this year’s near-relentless climb.

As of Tuesday, the gauge known as the 10-year break-even rate suggested that the consumer-price index will rise by an annual average of 2.48% over the next decade, according to Tradeweb. That was up from 2.01% at the end of last year, but down from its recent high of 2.57% on May 12.

The ups and down of the break-even rate have come under scrutiny in recent months as investors have grown increasingly concerned about inflation. A leveling off of or decline in the rate will cheer those who have worried that accelerating inflation could threaten investors’ portfolios in a way it hasn’t for decades. But it may also reflect expectations for tighter monetary policies from the Fed, which could drag on riskier assets like stocks.

Two assets determine the break-even rate: nominal U.S. Treasurys and Treasury inflation-protected securities, or TIPS, which increase their payouts as the consumer-price index rises. When investors buy TIPS, the yields on the securities are typically lower than nominal Treasurys of the same maturity. That difference is called the break-even rate because holders of TIPS can ultimately earn the same return as holders of nominal Treasurys if average annual CPI inflation matches that gap over the life of the bonds.

As of Tuesday, the yield on the benchmark 10-year U.S. Treasury note was 1.613%, while the yield on the 10-year TIPS was around minus 0.867%.

Several factors have lifted the break-even rate this year to its highest level since 2013. They include a vaccine-fueled economic recovery, massive amounts of government spending and consistent messaging from the Federal Reserve that it will take a patient approach to tightening monetary policy.

In recent weeks, however, some Fed officials have opened the door to talking about scaling back the central bank’s $120 billion a month purchases of U.S. Treasurys and mortgage-backed securities. That is widely seen as the first step in tightening monetary policy, and a precursor to higher short-term interest rates.

Some investors and analysts also said the break-even rate’s decline may reflect investors booking profits after crowding into bets on its rise.

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“The little bit of a pullback may be reflecting a combination of some belief that it maybe has run too far as well as the fact that perhaps the Fed is going to put a little bit of a break on inflation expectations,” said Steven Oh, global head of credit and fixed income at PineBridge Investments.

Any shift in Fed policy would start from a position of unusual lenience. Last year, officials announced a new policy framework, stating explicitly that they would like inflation to spend a period of time above their 2% annual target to make up for the extended period it has spent below that threshold. The Labor Department reported last month that CPI rose 4.2% in April from a year earlier, though that number was inflated by comparisons to deeply depressed prices from the early days of the pandemic.

Even as the economy has picked up momentum, Fed Chairman Jerome Powell has repeatedly emphasized the distance it needs to travel to return to its pre-pandemic levels. After the Fed’s last policy meeting in late April, he insisted it was too soon to discuss tapering the central bank’s asset purchases, given the current state of the economy.

Minutes from the Fed’s April meeting, however, revealed that “a number of participants” had said that “it might be appropriate at some point in upcoming meetings” to begin discussing tapering if the economy continues to improve.

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Reducing bond purchases could cool economic activity by increasing yields on nominal Treasurys—and therefore interest rates across the economy. At the same time, tapering could cause a larger increase in TIPS yields than nominal yields. That is because the Fed has been buying a disproportionately large amount of TIPS as part of its asset purchase program.

Even after a recent adjustment, the Fed is poised to absorb an amount of TIPS equivalent to more than 40% of those issued this year, according to BofA Global Research, compared with about 20% of nominal Treasurys.

Michael Lorizio, a senior trader at Manulife Investment Management, said he “would take the recent peaks [in break-even rates] as pretty firm resistance levels” given how high the rates have already climbed.

Some investors and analysts have noted parallels between the current moment and the so-called taper tantrum of 2013. In that episode, the 10-year break-even rate dropped from around 2.55% to below 2% after then-Fed Chairman Ben Bernanke brought up the possibility of scaling back bond purchases introduced in the wake of the 2008-09 financial crisis.

“It’s May, 10y break-even is at 2.55%: must be time for ill-timed taper talk; first 2013, now 2021,” BofA securitized products strategists Chris Flanagan and Graham Voss wrote in a May report.

The analysts, though, added that they don’t expect a “similar blunder from Powell” and predicted that the 10-year break-even rate will eventually “reach at least 2.75%-3.0%.”

Write to Sam Goldfarb at sam.goldfarb@wsj.com