A trader walks by the New York Stock Exchange (NYSE) in Manhattan, New York City, U.S., May 19, 2022.
A trader walks by the New York Stock Exchange (NYSE) in Manhattan, New York City, U.S., May 19, 2022. Reuters / ANDREW KELLY

A rebound in U.S. stocks may have another 5% to go but likely remains just a "bear market rally," according to Morgan Stanley's equity strategist, who sees negative trends in corporate earnings and economic indicators.

The S&P 500 as of Friday had bounced back 6.6% from May 19, when it closed down 18.7% from its Jan. 3 record high. The benchmark index was down about 1% in morning trading on Tuesday.

In a note published before the market opened on Tuesday, Morgan Stanley Equity Strategist Michael Wilson said the index could rise another 5% as "it's not surprising we are now seeing some relief given how oversold the market had become."

However, while more people on Wall Street are now concerned about risks from higher inflation and slowing growth, "that doesn't mean it's fully discounted," Wilson said.

"We remain firmly in the bear market camp but relief rallies can happen at any time, and it appears we are now in the midst of one," said Wilson. He projects the S&P 500 will be around 3,400 by mid August, which would be an 18% decline from Friday's close.

The market has already had one rally that faded this year, with the S&P 500 rising some 11% in March before giving up all of those gains.

The latest rally appeared predicated in part on expectations that the Federal Reserve may slow its plans to raise rates later this year. BofA strategists said last week the central bank would likely pause its tightening in September, leaving its benchmark overnight interest rate in a range of 1.75% to 2% if financial conditions worsened.

However, the Fed's tightening path is far from certain.

Fed Governor Christopher Waller said on Monday that the central bank should be prepared to raise interest rates by a half percentage point at every meeting from now on until inflation is decisively curbed. After already raising rates by 75 basis points so far this year, the Fed is widely expected to raise rates by 50 basis points at each of its next two meetings.