Markets pummeled by the Fed’s rate increases in the first half of the year are racing upward. The S&P 500 is up 17% from its mid-June low. The yield on the 10-year U.S. Treasury note, which is used to help set rates on debt such as mortgages and student loans is down more than half a percentage point from its June peak. Even battered cryptocurrencies have jumped.

For many investors, the rebound reflects a belief that inflation has peaked, and expectation that the Fed will shift from raising rates to lowering them sometime next year.

A parade of Fed officials has tried to push back. “There’s a disconnect between me and the markets,” Minneapolis Fed President

Neel Kashkari

said last week.

An expectation the Fed will start cutting interest rates in the next six to nine months isn’t realistic, Mr. Kashkari said. It is more likely the Fed will “raise rates to some point, and then we will sit there until we get convinced that inflation is well on its way back down to 2%,” he said.

If the Fed follows that path, markets are likely to face a painful reckoning—one that could unwind much of the recent rally and extend what has been a tumultuous stretch for investors from retail traders to hedge funds to pension funds.

“We think the market is getting ahead of itself,” said Wei Li, global chief investment strategist at

BlackRock Inc.

Running Ahead of the Fed

The 10-year U.S. Treasury yield has peaked before the federal-funds rate each time the Federal Reserve has raised interest rates the past few decades. Investors are divided on whether this time will be different.

Interest rates

When the Fed began lowering rates

Lag from peak in bond yields

to when Fed began lowering rates

When the Fed began lowering rates

Lag from peak in

bond yields to when Fed

began lowering rates

When the Fed began lowering rates

Lag from peak in

bond yields to when Fed

began lowering rates

When the Fed began lowering rates

Lag from peak in

bond yields to when

Fed began lowering rates

When the Fed began lowering rates

Lag from peak in

bond yields to when

Fed began lowering rates

Rallying markets also make the Fed’s job tougher. Rising stock and bond prices have loosened financial conditions since the Fed’s June meeting. That works against the central bank’s aim to slow spending and reign in inflation by raising rates enough to tighten the flow of money in the economy.

“You need to keep financial conditions tight. That’s the whole point of this,” said Marc Sumerlin, a senior economic adviser to President

George W. Bush

who is now managing partner at economic consulting firm EvenFlow Macro.

Any acknowledgment by the Fed that inflation is easing risks spurring further market gains. That could lead to even looser financial conditions, slowing the central bank’s efforts to tame inflation, said

Jason Draho,

head of asset allocation for the Americas at UBS Global Wealth Management.

“Now, you’re sort of undoing a lot of the hard work the Fed has been doing this year to slow the economy,” Mr. Draho said.

Fed faith

To understand how the two sides got so far apart, it helps to look back.

For decades, investors have put their faith in the “Fed put,” the belief that when markets fall substantially, the Fed will lower interest rates, purchase bonds or otherwise increase liquidity in the financial system.

The belief dates to the 1980s. Federal Reserve Chairman

Alan Greenspan

was quick to cut interest rates during such upheavals as the Black Monday crash in 1987, the Russian financial crisis and subsequent meltdown of hedge fund Long Term Capital Management in 1998, as well as the dot-com bust in the early 2000s. By the time Mr. Greenspan left the Fed in 2006, investors had come to expect it would always be there to provide cover.

For much of this year, the Fed put was in doubt. The central bank raised interest rates in March and signaled it would continue at a brisk pace to attack inflation, which had reached multidecade highs. U.S. stocks suffered their worst first half of a year since 1970. Investment-grade bonds posted their worst first half in history.

Then came the unexpected. Investors started to believe the Fed would again come to the rescue, despite much evidence to the contrary.

In June, the Fed voted to raise interest rates by 0.75 percentage point, marking its biggest rate increase since 1994—presumably bad news for the markets. But traders clung to Mr. Powell’s words at the postmeeting press conference. The Fed chairman acknowledged the rate increase was “an unusually large one” but not something he expected to be the norm.

Stocks jumped, with the S&P 500 rising 1.5%.

Then at a July 27 news conference, Mr. Powell tried to strike a balance between his earlier public remarks revealing concern about the strength of underlying inflation while also suggesting the Fed was eager for signs of improvement that the central bank won’t have to raise rates much above 4% or 5%. Wall Street interpreted him to mean the Fed was open to slowing down its pace of rate increases.

The S&P 500 ended the day 2.6% higher. The Nasdaq Composite surged 4.1% for its biggest one-day gain in more than two years.

Traders have pulled back from bets on inflation. The five-year break-even rate, a proxy for where traders believe inflation will be over the next five years, has fallen to around 2.6% from as high as 3.6% in April. Labor Department data this month showed inflation eased slightly in July but remained near its highest level since November 1981.

Some of Wall Street’s top analysts have cautioned about reading too much into recent stock gains.

Mike Wilson,

chief U.S. equity strategist and chief investment officer at

Morgan Stanley,

is forecasting the S&P 500 will end the year around 3900, down 8.8% from where the broad index closed Wednesday. At

Bank of America Corp.

, Savita Subramanian, head of U.S. equity and quantitative strategy, is expecting the S&P 500 to finish 2022 even lower—at 3600, a fall of 16% from Wednesday’s close.

Skeptics of the rebound say that even if inflation turns out to be peaking, it likely won’t fall fast enough for the Fed to pivot as quickly as the markets expect.

The Fed’s preferred measure of inflation—the personal-consumption expenditures price index—rose 6.8% in June from the same month a year earlier. That was far above the central bank’s target and the sharpest rise since January 1982. Investors will see the July reading later this month.

“The market is still pricing more aggressive cuts than we think are warranted,” said Ms. Li, of BlackRock. “We see the Fed eventually pivoting on policy, but not as much as the market is expecting.”

A challenge for both sides is that the Fed doesn’t appear to have confidence in its ability to accurately forecast inflation, which makes it difficult to predict when the central bank will stop raising rates.

“We now understand better how little we understand about inflation,” Mr. Powell said at a forum hosted by the European Central Bank in June.

Economists outside the Fed are divided over how aggressively the central bank should attack inflation. One camp says even if it falls over the next 12 months, it is likely to settle at 4% or higher, a level most Fed officials would consider unacceptably high. That would make it difficult for the central bank to lower rates to the levels that fueled markets in recent years.

Some of these economists suspect the Fed isn’t being forthcoming about how high it believes interest rates will need to go for inflation to fall to 2%.

Another camp warns that the Fed, embarrassed about waiting too long to pull back its support of a booming economy last year, will compound the error by tightening too much. These economists believe the current surge in inflation is the result of global shocks rather than an overheated U.S. labor market, which would require a much deeper downturn to bring down inflation.

‘Unpredictable beast’

Investor faith in the Fed put has strengthened in recent years. Markets slumped in 2018 as the central bank raised interest rates four times and investors fretted over the seeming end of easy-money central bank policies. As the central bank paused its rate increases and then switched to cutting rates the following year, stocks went back up.

They tumbled again in March 2020 after the Covid-19 pandemic shut down economies around the world. They bottomed out within the month and surged after the Fed cut interest rates and relaunching its bond-buying program.

“The fact that the Fed is very hawkish today doesn’t mean they can’t go dovish in a few months. That’s happened over and over again,” said

Jim Paulsen,

chief investment strategist of The Leuthold Group in Minneapolis.

Yet in recent instances when the Fed eased rates, the central bank was having difficulty pushing inflation up to its 2% target. Investors and Fed officials were ultimately reacting to the same growth risk. With inflation running high, that is no longer the case.

If the Fed holds tight to its plans, markets could be in for a tough ride. Earlier this year,

Goldman Sachs Group Inc.

research found the stock market had fallen at least 15% on 17 occasions going back to 1950. In 11 of those instances, the market only hit its trough around the time the Fed started easing monetary policy.

Mr. Paulsen believes the case for further interest-rate increases has weakened. But he acknowledged that trying to predict how the Fed will respond to inflation in the months ahead is almost impossible.

“The reality is that right now, the market is enjoying the Fed put,” he said. “We’re all dealing with a very unpredictable beast.”

—Nick Timiraos contributed to this article.

Write to Akane Otani at akane.otani@wsj.com